Analysis and Interpretation of Astronomical Spectra 1
Analysis and Interpretation of
Astronomical Spectra
Theoretical Background and
Practical Applications for
Amateur Astronomers
Richard Walker
Version 9.2 12/2013
Analysis and Interpretation of Astronomical Spectra 2
Table of Contents
1 Introduction ............................................................................................................. 7
2 Photons – Messengers from the Universe........................................................... 8
2.1 Photons – Carriers of Information ..................................................................................................8
2.2 The Duality of Waves and Particles ................................................................................................8
2.3 The Quantisation of the Electromagnetic Radiation......................................................................8
2.4 Properties of the Photons ................................................................................................................9
2.5 Photons – Carriers of Energy ..........................................................................................................9
3 The Continuum ......................................................................................................10
3.1 Black Body Radiation and the Course of the Continuum Level ................................................. 10
3.2 Plank's Radiation- and Wien's Displacement Law ...................................................................... 10
3.3 The Pseudo Continuum................................................................................................................. 11
4 Spectroscopic Wavelength Domains ..................................................................13
4.1 The Usable Spectral Range for Amateurs ................................................................................... 13
4.2 The Selection of the Spectral Range ........................................................................................... 13
4.3 Terminology of the Spectroscopic Wavelength Domains .......................................................... 14
5 Typology of the Spectra........................................................................................15
5.1 Continuous Spectrum.................................................................................................................... 15
5.2 Absorption Spectrum .................................................................................................................... 15
5.3 Emission Spectrum........................................................................................................................ 15
5.4 Absorption Band Spectrum........................................................................................................... 16
5.5 Band Spectrum with Inversely Running Intensity Gradient ....................................................... 16
5.6 Mixed Emission- and Absorption Spectrum ................................................................................ 17
5.7 Composite Spectrum..................................................................................................................... 17
5.8 Reflectance Spectrum................................................................................................................... 18
5.9 Cometary Spectrum ...................................................................................................................... 18
6 Form and Intensity of the Spectral Lines............................................................19
6.1 The Form of the Spectral Line ...................................................................................................... 19
6.2 The Information Content of the Line Shape ................................................................................ 19
6.3 Blends............................................................................................................................................. 19
6.4 The Saturation of an Absorption Line in the Spectral Diagram ................................................. 19
6.5 The Oversaturated Emission Line in the Spectral Diagram ....................................................... 20
7 The Measurement of the Spectral Lines.............................................................21
7.1 Methods and Reference Values of the Intensity Measurement ................................................ 21
7.2 Metrological Differences between Absorption and Emission Lines ......................................... 21
7.3 The Peak Intensity P...................................................................................................................... 22
7.4
7.5 Full Width at Half Maximum Height .............................................................................. 22
7.6 , Equivalent Width ................................................................................................................... 23
7.7 Normalised Equivalent Width ................................................................................................ 24
7.8 FWZI Full Width at Zero Intensity ............................................................................................ 24
7.9 Influence of the Spectrograph Resolution on the FWHM- and EW Values .............................. 24
7.10 Practical Consequences for the FWHM and EW Measurements .............................................. 26
7.11 The Measurement of the Wavelength ......................................................................................... 26
Additional Measurement Options ................................................................................................ 26
Analysis and Interpretation of Astronomical Spectra 3
8 Calibration, Normalisation and Radiometric Correction ...................................27
8.1 The Calibration of the Wavelength .............................................................................................. 27
8.2
8.3 The Selective Attenuation of the Continuum Intensity .............................................................. 27
8.4
8.5 Relationship Between Original-Continuum and Pseudo-Continuum ...................... 28
8.6
8.7 Attenuation of Absorption Lines .................................................................................................. 28
8.8
8.9 Attenuation of the Emission Lines ............................................................................................... 29
8.10
8.11 Summary of the consequences: ................................................................................................... 30
8.12
8.13 The Importance of the Pseudo-Continuum ................................................................................. 30
8.14
8.15 Proportional Radiometric Corrections of the Pseudo-Continuum............................................. 30
Rectification of the Continuum Intensity..................................................................................... 31
Relative Radiometric Flux Calibration by a Synthetic Continuum ............................................. 32
Relative Radiometric Profile Correction by Recorded Standard Stars...................................... 35
Absolute Flux Calibration.............................................................................................................. 37
Intensity Comparison between Different Spectral Lines ........................................................... 37
Reconstruction of the Original Emission-Line Intensities.......................................................... 37
Summary – Which Method Fits to Which Task........................................................................... 38
9 Visible Effects of Quantum Mechanics ...............................................................39
9.1 Textbook Example Hydrogen Atom and Balmer Series .............................................................. 39
9.2 The Balmer Series ......................................................................................................................... 40
9.3 Spectral Lines of Other Atoms ..................................................................................................... 41
10 Wavelength and Energy .......................................................................................42
10.1 Planck’s Energy Equation.............................................................................................................. 42
10.2 Units for Energy and Wavelength ................................................................................................ 42
10.3 The Photon Energy of the Balmer Series..................................................................................... 43
10.4 Balmer- Paschen- and Bracket Continuum ................................................................................. 44
11 Ionisation Stage and Degree of Ionisation .........................................................45
11.1 The Lyman Limit of Hydrogen....................................................................................................... 45
11.2 Ionisation Stage versus Degree of Ionisation ............................................................................. 45
11.3 Astrophysical Form of Notation for the Ionisation Stage ........................................................... 45
12 Forbidden Lines or –Transitions..........................................................................46
13 The Spectral Classes ............................................................................................47
13.1 Preliminary Remarks ..................................................................................................................... 47
13.2 The Fraunhofer Lines .................................................................................................................... 47
13.3 Further Development Steps.......................................................................................................... 48
13.4 The Harvard System ...................................................................................................................... 49
13.5 “Early” and “Late” Spectral Types ................................................................................................ 50
13.6 The MK (Morgan Keenan) or Yerkes System .............................................................................. 50
13.7 Further Adaptations up to the Present ........................................................................................ 50
13.8 The Rough Estimation of the Spectral Class ............................................................................... 52
13.9 Diagrams for Estimation of the Spectral Class ........................................................................... 53
13.10 Additional Criteria for Estimation of the Spectral Class............................................................. 54
13.11 Appearance of Elements, Ions and Molecules in the Spectra ................................................... 55
13.12 Effect of the Luminosity Class on the Line Width ....................................................................... 56
13.13 Spectral Class and B-V Colour-Index ........................................................................................... 56
14 The Hertzsprung - Russell Diagram (HRD) .........................................................57
14.1 Introduction to the Basic Version................................................................................................. 57
14.2 The Absolute Magnitude and Photospheric Temperature of the Star ...................................... 58
Analysis and Interpretation of Astronomical Spectra 4
14.3 The Evolution of the Sun in the HRD............................................................................................ 59
14.4 The Evolution of Massive Stars .................................................................................................... 60
14.5 The Relation between Stellar Mass and Life Expectancy .......................................................... 60
14.6 Age Estimation of Star Clusters ................................................................................................... 61
15 The Measurement of the Radial Velocity............................................................62
15.1 The Radial Velocity ........................................................................................................................ 62
15.2 The Classical Doppler Effect......................................................................................................... 62
15.3 The z-Value - A Fundamental Measure of Modern Cosmology.................................................. 63
15.4 The Relativistic Doppler Effect for Electromagnetic Waves ...................................................... 64
15.5 The Measurement of the Doppler Shift ....................................................................................... 64
15.6 Radial Velocities of Nearby Stars ................................................................................................. 65
15.7 Relative Shift within a Spectrum caused by the Doppler Effect................................................ 65
15.8 Radial Velocities of Galaxies ........................................................................................................ 65
15.9 The Apparent Dilemma at ................................................................................................... 66
15.10 Radial Velocity- and Cosmological Spacetime Expansion at Messier-Galaxies....................... 66
15.11 The Redshift of the Quasar 3C273.............................................................................................. 68
15.12 The Gravitational Redshift ............................................................................................................ 69
15.13 Short Excursus on "Hubble time" tH ............................................................................................. 69
16 The Measurement of the Rotation Velocity........................................................70
16.1 Terms and Definitions ................................................................................................................... 70
16.2
16.3 The Rotation Velocity of the Large Planets ................................................................................. 70
16.4
16.5 The Rotation Velocity of the Sun.................................................................................................. 71
16.6
16.7 The Rotation Velocity of Galaxies ................................................................................................ 71
Calculation of the Value with the Velocity Difference ................................................ 71
The Rotation Velocity of the Stars ............................................................................................... 73
The Rotation Velocity of the Circumstellar Disks around Be Stars ........................................... 75
17 The Measurement of the Expansion Velocity.....................................................79
17.1 P Cygni Profiles.............................................................................................................................. 79
17.2 Inverse P Cygni Profiles ................................................................................................................ 79
17.3 Broadening of the Emission Lines................................................................................................ 80
17.4 Splitting of the Emission Lines ..................................................................................................... 80
18 The Measurement of the Stellar Photosphere Temperature............................81
18.1 Introduction.................................................................................................................................... 81
18.2 Temperature Estimation of the Spectral Class ........................................................................... 81
18.3 Temperature Estimation Applying Wien’s Displacement Law................................................... 82
18.4 Temperature Determination Based on Individual Lines ............................................................. 85
18.5 The “Balmer-Thermometer“.......................................................................................................... 85
19 Spectroscopic Binary Stars ..................................................................................87
19.1 Terms and Definitions ................................................................................................................... 87
19.2 Effects of the Binary Orbit on the Spectrum ............................................................................... 88
19.3 The Perspectivic Influence from the Spatial Orientation of the Orbit ....................................... 90
19.4 The Estimation of some Orbital Parameters ............................................................................... 91
20 Balmer–Decrement...............................................................................................93
20.1 Introduction.................................................................................................................................... 93
20.2 Qualitative Analysis ....................................................................................................................... 93
20.3 Quantitative Analysis .................................................................................................................... 94
20.4 Quantitative Definition of the Balmer-Decrement ...................................................................... 95
Analysis and Interpretation of Astronomical Spectra 5
20.5 Experiments with the Balmer-Decrement ................................................................................... 95
21 Spectroscopic Determination of Interstellar Extinction....................................96
21.1 Spectroscopic Definition of the Interstellar Extinction .............................................................. 96
21.2 Extinction Correction with the Measured Balmer-Decrement .................................................. 96
21.3 Balmer-Decrement and Color Excess .......................................................................................... 97
21.4 Balmer-Decrement and Extinction Correction in the Amateur Sector ...................................... 97
22 Plasma Diagnostics for Emission Nebulae .........................................................98
22.1 Preliminary Remarks ..................................................................................................................... 98
22.2 Overview of the Phenomenon “Emission Nebulae”.................................................................... 98
22.3 Common Spectral Characteristics of Emission Nebulae............................................................ 98
22.4 Ionisation Processes in H II Emission Nebulae ........................................................................... 98
22.5 Recombination Process ................................................................................................................ 99
22.6 Line Emission by Electron Transition ........................................................................................... 99
22.7 Line Emission by Collision Excitation.........................................................................................100
22.8 Line Emission by Permitted Transitions (Direct absorption)....................................................100
22.9 Line Emission by Forbidden Transitions ....................................................................................100
22.10 Scheme of the Photon Conversion Process in Emission Nebulae...........................................102
22.11 Practical Aspects of Plasma Diagnostics ..................................................................................103
22.12 Determination of the Excitation Class ....................................................................................104
22.13 The Excitation Class as an Indicator for Plasma Diagnostics ..................................................104
22.14 Estimation of Te and Ne with the O III and N II Method...........................................................105
22.15 Estimation of the Electron Density from the S II and O II Ratio ...............................................106
22.16 Distinguishing Characteristics in the Spectra of Emission Nebulae .......................................106
23 Analysis of the Chemical Composition ............................................................ 108
23.1 Astrophysical Definition of Element Abundance ......................................................................108
23.2 Astrophysical Definition of Metal Abundance Z (Metallicity) ..................................................108
23.3 Quantitative Determination of the Chemical Composition ......................................................108
23.4 Relative Abundance-Comparison at Stars of Similar Spectral Class ......................................109
24 Spectroscopic Parallax ...................................................................................... 110
24.1 Spectroscopic Possibilities of Distance Measurement ............................................................110
24.2 Term and Principle of Spectroscopic Parallax ..........................................................................110
24.3 Spectral Class and Absolute Magnitude ...................................................................................110
24.4 Distance Modulus........................................................................................................................112
24.5 Calculation of the Distance with the Distance Modulus..........................................................112
24.6 Examples for Main Sequence Stars (with Literature Values) ..................................................112
25 Identification of Spectral Lines......................................................................... 113
25.1 Task and Requirements ..............................................................................................................113
25.2 Practical Problems and Solving Strategies ...............................................................................113
25.3 Tools for the Identification of Spectral Lines ............................................................................114
26 Literature and Internet....................................................................................... 115
Analysis and Interpretation of Astronomical Spectra 6
Change log of the Document Versions
Version 8.0:
Sect. 5.9: New: “Cometary Spectra“
Sect. 6.4: Supplement
Sect. 10.4: New: “Balmer- Paschen- and Bracket Continuum”
Sect. 18: New: “The Measurement of the Stellar Photosphere Temperature“
Sect. 23: New: “Chemical Composition Analysis“
Sect. 24: New: “Spectroscopic Parallax”
Versions 8.5 and 8.6:
Sect. 8: General revision “Calibration and Normalisation of Spectra” in consideration of re-
cent test results on "correction curves”.
Version 8.7:
Sect. 15.7: Review and corrections in the table of Messier galaxies and appropriate ad-
justments in the text.
Version 9.0:
Sect. 8: General revision: Consideration of the different attenuation-behavior of absorption-
versus emission lines, in relation to the continuum-intensity.
Sect. 13: New Subtitles, 13.10, 13.11 and 13.13 with new table: Spectral Class and B-V
Colour-Index
Sect. 15: General revision: Derivation of the classical and relativistic, spectroscopic Dop-
pler formula. Several corrections and supplements, particularly in sect. 15.8 Ra-
dial Velocities of Galaxies. New: sect. 15.12: Gravitational Redshift
Sect. 16.3: Supplement of the Sun's rotation with spectral profile and measurement results
by SQUES Echelle Spectrograph.
Sect.. 17.1: Supplement of literature reference
Sect. 18: Content of former sect. 18.6, now integrated in 18.4.
Sect. 20, 21, 22: Various modifications and additions due to the general revision of sect. 8.
Literature and Internet: New entries
Analysis and Interpretation of Astronomical Spectra 7
1 Introduction
Technological advances like CCD cameras, but also affordable spectrographs on the mar-
ket, actually cause a significant upturn of spectroscopy within the community of amateur
astronomers. Further freeware programs and detailed instructions are available to enable
the processing, calibrating and normalising of the spectra. Several publications explain the
function and even the self-construction of spectrographs and further many papers can be
found on specific monitoring projects. The numerous possibilities however for analysis and
interpretation of the spectral profiles, still suffer from a considerable deficit of suitable lit-
erature.
This publication is intended as an introduction to practical applications and the appropriate
astrophysical backgrounds. Further the Spectroscopic Atlas for Amateur Astronomers [33]
is available, which covers all relevant spectral classes by commenting most of the lines,
visible in medium resolved spectral profiles. It is primarily intended to be used as a tool for
the line identification. Each spectral class, relevant for amateurs, is presented with their
main characteristics and typical features.
Further, Practical Aspects of Astro-Spectroscopy – Instructions and Information for Ama-
teur Astronomers [30], is downloadable. It provides detailed instructions for operational
aspects and data reduction of spectral profiles with the Vspec and IRIS software.
Spectroscopy is the real key to astrophysics. Without them, our current picture of the uni-
verse would be unthinkable. The photons, which have been several million years “on the
road” to our CCD cameras, provide an amazing wealth of information about the origin ob-
ject. This may be fascinating, even without the ambition to strive for academic laurels. Fur-
ther there is no need for a degree in physics with, specialisation in mathematics, for a re-
warding deal with this matter. Required is some basic knowledge in physics, the ability to
calculate simple formulas with given numbers on a technical calculator and finally a healthy
dose of enthusiasm.
Even the necessary chemical knowledge remains very limited. In the hot stellar atmos-
pheres and excited nebulae the individual elements can hardly undergo any chemical com-
pounds. Only in the outermost layers of relatively "cool" stars, some very simple molecules
can survive. More complex chemical compounds are found only in really cold dust clouds of
the interstellar space and in planetary atmospheres – a typical domain of radio astronomy.
Moreover in stellar astronomy, all elements, except hydrogen and helium, are simplistically
called as "metals".
The share of hydrogen and helium of the visible matter in the universe is still about 99%.
The most "metals", have been formed long time after the Big Bang within the first genera-
tion of massive stars, which distributed it at the end of their live in to the surrounding space
by Supernova explosions or repelled by Planetary Nebulae.
Much more complex, however, is the quantum-mechanically induced behavior of the ex-
cited atoms in stellar atmospheres. These effects are directly responsible for the formation
and shape of the spectral lines. Anyway for the practical work of the "average amateur"
some basic knowledge is sufficient.
Richard Walker, CH 8911-Rifferswil © [email protected]
Analysis and Interpretation of Astronomical Spectra 8
2 Photons – Messengers from the Universe
2.1 Photons – Carriers of Information
Photons are generated in stars, carrying valuable information over immense periods of time
and unimaginable distances, and finally end in the pixel field of our CCD cameras. By their
“destruction” they deposit the valuable information, contributing electrons to the selective
saturation of individual pixels – in fact trivial, but somehow still fascinating. By switching a
spectrograph between the telescope and camera the photons will provide a wealth of in-
formation which surpasses by far the simple photographic image of the object. It is there-
fore worthwhile to make some considerations about this absolutely most important link in
the chain of transmission.
It was on the threshold of the 20th Century, when it caused tremendous "headaches" to the
entire community of former top physicists. This intellectual "show of strength" finally cul-
minated in the development of quantum mechanics. The list of participants reads substan-
tially like the Who's Who of physics at the beginning of the 20th century: Werner Heisen-
berg, Albert Einstein, Erwin Schrödinger, Max Born, Wolfgang Pauli, Niels Bohr, just to
name a few. Quantum mechanics became, besides the theory of relativity, the second revo-
lutionary theory of the 20th Century. For the rough understanding about the formation of
the photons and finally of the spectra, the necessary knowledge is reduced to some key
points of this theory.
2.2 The Duality of Waves and Particles
Electromagnetic radiation has both wave and particle nature. This principle applies to the
entire spectrum. Starting with the long radio waves, it remains valid on the domains of in-
frared radiation, visible light, up to the extremely short-wave ultraviolet, X-rays and gamma
rays.
Source: Wikipedia
For our present technical applications, both properties are indispensable. For the entire
telecommunications, radio, TV, mobile telephony, as well as the radar and the microwave
grill it's the wave character. The CCD photography, light meter of cameras, gas discharge
lamps (eg energy saving light bulbs and street lighting), and last but not least, the spectros-
copy would not work without the particle nature.
2.3 The Quantisation of the Electromagnetic Radiation
It was one of the pioneering discoveries of quantum mechanics that electromagnetic radia-
tion is not emitted continuously but rather quantised (or quasi "clocked"). Simplified ex-
Analysis and Interpretation of Astronomical Spectra 9
plained a minimum "dose" of electromagnetic radiation is generated, called “photon”, which
belongs to the Bosons within the "zoo" of elementary particles.
2.4 Properties of the Photons
– Without external influence photons have an infinitely long life
– Their production and “destruction” takes place in a variety of physical processes. Rele-
vant for the spectroscopy are electron transitions between different atomic orbital (de-
tails see later).
– A photon always moves with light speed. According to the Special Theory of Relativity
(STR) it can therefore possess no rest mass.
2.5 Photons – Carriers of Energy
Each photon has a specific frequency (or wavelength), which determines its energy – the
higher the frequency, the higher the energy of the photon (details see sect. 10.1).
Analysis and Interpretation of Astronomical Spectra 10
3 The Continuum
3.1 Black Body Radiation and the Course of the Continuum Level
The red curve, hereafter referred to as continuum level corresponds to the course of the
radiation intensity or flux density, plotted over the wavelength, increasing from left to right.
As a fit to the blue continuum it is cleaned by any existing absorption or emission lines
(blue curve). The entire area between the horizontal wavelength axis and the continuum
level is called continuum [5].
Continuum Level Ic
Continuum
Most important physical basis for the origin and course of the continuum is the so-called
black body radiation. The blackbody is a theoretical working model which, in that perfec-
tion, doesn’t exist in nature.
For most amateurs it is sufficient to know, that:
– The blackbody is an ideal absorber which absorbs broadband electromagnetic radiation,
regardless of the wavelength, completely and uniformly.
– The ideal black body represents a thermal radiation source, which emits a broad-band
electromagnetic radiation, according to the Planck's radiation law, with an exclusively
temperature-dependent intensity profile.
– Stars in most cases may simplified be considered as black-body radiators.
3.2 Plank's Radiation- and Wien's Displacement Law
This theory has practical relevance for us because the intensity profile of the spectrum pro-
vides information about the temperature of the radiator! The radiation distribution of differ-
ent stars shows bell-shaped curves, whose peak intensity shifts to shorter wavelength, re-
spectively higher frequency with increasing temperature (Planck Radiation law).
Inten- T=12‘000 K
sity λmax=2415 Å
T=6000 K
λmax=4830 Å
T=3000 K
λmax=9660 Å
0 5000 10‘000 15‘000 20‘000
Wavelength [Å]
Analysis and Interpretation of Astronomical Spectra 11
With Wien's displacement law (German physicist Wilhelm Wien 1864-1928) and the given
wavelength [Å] of the maximum radiation intensity it is theoretically possible to
calculate the atmosphere temperature [K] of a star. This is also called “Effective tempera-
ture” or “Photosphere temperature”.
[Å]: Angström, 1 Å = 10-10m [K]: Kelvin K ≈ °Celsius + 273°
Examples: Alnitak = ca. 25‘000 K = 1‘160 Å (Ultraviolet)
Sun = ca. 5‘800 K = 4‘996 Å (Green)
Betelgeuse = ca. 3‘450 K = 8‘400 Å (Infrared)
3.3 The Pseudo Continuum
By all stellar spectra, the course of the unprocessed continuum differs strongly from the
theoretical shape of reference curves, regardless if recorded with professional or amateur
equipments. The reasons are primarily interstellar, atmospheric and instrument-specific at-
tenuation effects (telescope, spectrograph, camera), which distort the original intensity
course of the spectral profile to a so called pseudo continuum (details see sect.8.2).
Therefore, the Wien’s displacement law, on the basis of the maximum profile intensity, can
qualitatively only be observed. The following chart shows a superimposed montage of spec-
tral profiles (pseudo continua) of all bright Orion stars, obtained with a simple transmission
grating (200L/mm), a Canon compact camera (Powershot S 60) and processed with the
Vspec software. Denoted are here the spectral classes, as well as some identified absorp-
tion lines.
Relative Alnilam B0Ia
Intensity
Alnitak O9.7Ib
Bellatrix B2III
Mintaka O9.5II OII 4638/-49 A Beteigeuze M1-2Ia-Iab
Rigel B8Ia
TiO
TiO
TiO
Saiph B0.5Ia TiO Na I 5890 A
TiO TiO
TiO
Hδ 4102 A
Hγ 4340 A
He I 4471 A
Hβ 4861 A
Wavelength [Angström]
Here it is obvious, that the profile shapes and their maximum intensities of the late O- and
early B-classes (sect. 13) are nearly identical. As expected, the maximum intensity in the
green profile of Rigel, a slightly lesser hot, late-B giant, and in stark extent in the orange
profile of the cool M-giant Betelgeuse, is shifted to the right towards larger wavelengths.
Theoretically and according to sect. 3.2, the maximum intensities of the O and B stars
should be located far left, outside of the diagram in the UV range. On the other hand the
maximum for the cold Betelgeuse should be also moved, but here to the IR range, on the
Analysis and Interpretation of Astronomical Spectra 12
right side, also outside of the diagram. Main causes for this error are the spectral selectivity
of the CCD chip and the IR filter in the compact camera, pretending that all the peaks would
be located within the diagram. Here is also clearly visible, that the absorption lines (sect.
5.2) are quasi "imprinted" on the continuum profile, similar to the modulation on a carrier
wave. These lines carry the information about the object, the course of the continuum re-
veals only the temperature of the radiator. The profile of Betelgeuse shows impressively,
that the spectra of cool stars are dominated by broad molecular titanium oxide (TiO) bands
(sect. 5.4). The example also shows the dramatic influence of the spectral characteristics of
the camera. In the blue wavelength range, the sensitivity of most cameras drops quickly.
Astronomical cameras usually have easy removable/upgradable IR filters, exclusively used
for the astrophotography and without them spectra can be recorded well in to the IR range.
Analysis and Interpretation of Astronomical Spectra 13
4 Spectroscopic Wavelength Domains
4.1 The Usable Spectral Range for Amateurs
The professional astronomers nowadays study the objects in nearly the entire electro-
magnetic spectrum – including also Radio Astronomy. Also space telescopes are used,
which are increasingly optimised for the infrared region in order to record the extremely
red-shifted spectra of objects from the early days of the universe (sect. 15.8–15.11). For
the ground-based amateur, equipped with standard telescopes and spectrographs only a
modest fraction of this domain is available. The usable range for us is, in addition to the
specific design features of the spectrograph, limited mainly by the spectral characteristics
of the camera including any filters. The Meade DSI III or Atik 314L+ e.g. achieves with the
DADOS spectrograph useful results in the range of approximately 3800 – 8000 Å, i.e.
throughout the visible domain and the near infrared part of the spectrum. Here also the
best known and best documented lines are located, such as the hydrogen lines of H-Balmer
series and the Fraunhofer lines (see later).
4.2 The Selection of the Spectral Range
For high-resolution spectra, the choice of the range is normally determined by a specific
monitoring project or the interest in particular lines. Perhaps also the calibration lamp
emission lines have to be considered in the planning of the recorded section.
For low-resolution, broadband spectra mostly the range of the H-Balmer series is preferred
(sect. 9). Hot O- and B- stars can be taken rather in the short-wave part, because their
maximum radiation lies in the UV range. It usually makes little sense to record the area on
the red side of Hα, except the emission lines of P Cygni, Be stars, as well as from emission
line nebulae (sect. 22). Between approximately 6,200 – 7,700Å (see picture below), it lit-
erally swarms of atmospheric related (telluric) H2O and O2 absorption bands.
Hα Fraunhofer H2O Absorption Fraunhofer
B Band O2 A Band O2
Apart from their undeniable aesthetics they are interesting only for atmospheric physicist.
For astronomers, they are usually only a hindrance, unless the fine water vapour lines are
used to calibrate the spectra! They can partly be extracted with the Vspec software or
nearly completely with the freeware program SpectroTools by Peter Schlatter. [413].
By the late spectral types of K, and the entire M-Class (sect. 13), however, it makes sense
to record this range, since the radiation intensity of these stars is very strong in the IR
range and shows here particularly interesting molecular absorption bands. Also, the reflec-
tion spectra (sect. 5.8) of the large gas planets show mainly here the impressive molecular
gaps in the continuum.
Useful guidance for setting the wavelength range of the spectrograph are eg the microme-
ter scale, the calibration lamp spectrum or the daylight (solar) spectrum, respectively. At
night the reflected solar spectrum is available from the moon and the planets. A good
marker on the blue side of the spectrum is the impressive double line of the Fraunhofer H-
and K-Absorption (sect. 13.2.).
Analysis and Interpretation of Astronomical Spectra 14
4.3 Terminology of the Spectroscopic Wavelength Domains
Terminology for wavelength domains is used inconsistently in astrophysics [4] and depends
on the context. Furthermore many fields of astronomy, various satellite projects etc. often
use different definitions.
Here follows a summary according to [4] and Wikipedia (Infrared Astronomy). Given are ei-
ther the center wavelength λ of the corresponding photometric band filters, or their ap-
proximate passband.
Optical range UBVRI λλ 3,300 – 10,000 (Johnson/Bessel/Cousins)
Center wavelength Astrophysical wavelength Required instruments
domain Most optical telescopes
λ [μm] λ [Å]
0.35 3,500 U – Band (UV)
0.44 4,400 B – Band (blue)
0.55 5,500 V – Band (green)
0.65 6,500 R – Band (red)
0.80 8,000 I – Band (infrared)
Further in use is also the Z–Band, some λλ 8,000 – 9,000 and the Y–Band, some
λλ 9,500 – 11,000 (ASAHI Filters).
Infrared range according to Wikipedia (Infrared Astronomy)
Center wavelength Astrophysical wave- Required instruments
length domain
λ [μm] λ [Å] Most optical- and dedicated
infrared telescopes
1.25 10,250 J – Band Some optical- and dedicated
1.65 16,500 H – Band infrared telescopes
2.20 22,000 K – Band
3.45 34,500 L – Band Submilimeter telescopes
4.7 47,000 M – Band
10 100,000 N – Band
20 200,000 Q – Band
200 2,000,000 Submilimeter
For ground based telescopes mostly the following terminology is in use [Å]:
– Far Ultraviolet (FUV): λ <3000
– Near Ultra Violet (NUV): λ 3000 – 3900
– Optical (VIS): λ 3900 – 7000
– Near Infrared (NIR): λ 6563 (Hα) – 10,000
– Infrared or Mid-Infrared: λ 10,000 – 40,000 (J, H, K, L – Band 1 – 4 μm)
– Thermal Infrared: λ 40,000 – 200,000 (M, N, Q – Band 4 - 20μm)
– Submilimeter: λ >200,000 (200 μm)
Analysis and Interpretation of Astronomical Spectra 15
5 Typology of the Spectra
5.1 Continuous Spectrum
Incandescent solid or liquid light sources emit, similar to a black body radiator, a continu-
ous spectrum, eg Bulbs. The maximum intensity and the course of the continuum obey the
Plank's radiation law.
5.2 Absorption Spectrum
An absorption spectrum is produced when radiated broadband light has to pass a low pres-
sure and rather cool gas layer on its way to the observer. Astronomically, the radiation
source is in the majority of cases a star and the comparatively "cooler" gas layer to be trav-
ersed, its own atmosphere. Depending on the chemical composition of the gas it will ab-
sorb photons of specific wavelengths by exciting the atoms, ie single electrons are momen-
tarily lifted to a higher level. The absorbed photons are ultimately lacking at these wave-
lengths, leaving characteristic dark gaps in the spectrum, the so-called absorption lines.
This process is described in more detail in sect. 9.1. The example shows absorption lines in
the green region of the solar spectrum (DADOS 900L/mm).
Hβ Fe Fe Fe Mg Fe
5.3 Emission Spectrum
An emission spectrum is generated when the atoms of a thin gas are heated or excited so
that photons with certain discrete wavelengths are emitted, eg neon glow lamps, energy
saving lamps, sodium vapor lamps of the street lighting, etc. Depending on the chemical
composition of the gas, the electrons are first raised to a higher level by thermal excitation
or photons of exactly matching wavelengths – or even completely released, where the
atom becomes ionised. The emission takes place after the recombination or when the ex-
cited electron falls back from higher to lower levels, while a photon of specific wavelength
is emitted (sect. 9.1). Astronomically, this type of spectral line comes mostly from ionised
nebulae (sect. 22) in the vicinity of very hot stars, planetary nebulae, or extremely hot stars,
pushing off their gaseous envelops (eg, P Cygni). The following picture (DADOS 200L/mm)
shows the emission spectrum (Hα, Hβ, Hγ, He, [O III]), of the Planetary Nebula NGC6210,
which is ionised by the very hot central star (some 58‘000K), [33].
Hγ Hβ [O III] He Hα
Analysis and Interpretation of Astronomical Spectra 16
5.4 Absorption Band Spectrum
Band spectra are generated by highly complex rotational and vibrational processes, caused
by heated molecules. This takes place in the relatively cool atmospheres of red giants. The
following spectrum originates from Betelgeuse (DADOS 200L/mm). At this resolution it
shows only a few discrete lines. The majority is dominated by absorption bands, which are
here mainly caused by titanium oxide (TiO) and to a lesser extent by magnesium hydride
(MgH). In this case, these asymmetric structures reach the greatest intensity on the left,
short-wave band end (called bandhead), and then slowly weaken to the right. The wave-
length of absorption bands always refers to the point of greatest intensity ("most distinct
edge").
But also several of the prominent Fraunhofer lines in the solar spectrum are caused by mo-
lecular absorption. The following picture, taken with the SQUES Echelle spectrograph
[400], shows a high-resolution O2 band spectrum of the Fraunhofer A line (sect. 4.2 and
13.2).
5.5 Band Spectrum with Inversely Running Intensity Gradient
The following picture (DADOS 200L/mm) shows C2 carbon molecular absorption bands in
the blue-green region of the spectrum of the carbon star Z Piscium [33]. Generally at some
carbon molecules (eg CO, C2), the intensity gradient of the absorption bands runs in the op-
posite direction as with titanium oxide (TiO) or O2.
Already in the middle of the 19th Century this effect has been recognised by Father Angelo
Secchi (Sect. 13.3). For such spectra, he introduced the “Spectral type IV”.
Analysis and Interpretation of Astronomical Spectra 17
5.6 Mixed Emission- and Absorption Spectrum
There are many cases where absorption and emission lines appear together in the same
spectrum. The best known example is P Cygni, a textbook object for amateurs. To this un-
stable and variable supergiant of the spectral type B2 Ia numerous publications exist. In the
17th Century, it appeared for 6 years as a star of the third magnitude, and then "disap-
peared" again. In the 18th Century it gained again luminosity until it reached its current,
slightly variable value of approximately +4.7m to +4.9m. The distance of P Cygni is esti-
mated to ca. 5000 – 7000 ly (Karkoschka 5000 ly).
The picture below shows the expanding shell, taken with the Hubble Space Telescope
(HST). The star in the center is fully covered. The diagram right shows the typical formation
of the so-called P Cygni profiles, which are shown here in the violet region of the spectrum
(DADOS 900L/mm).
In the area of the blue arrow a small section of the shell, consisting of thin gas, is moving
exactly toward Earth and generating blue-shifted absorption lines (Doppler Effect). The red
arrows symbolise the light, emitted by sections of the shell, expanding sideward, producing
emission lines. In the combination results a broad emission line and a generally less intense
blue-shifted absorption line. P Cygni profiles are present in almost all spectral types and are
a reliable sign of a massive radial motion of matter ejected from the star.
Direction toward
earth
Based on the wavelength difference between the absorption and emission part of the line,
the expansion velocity of the envelope can be estimated using the Doppler formula (sect.
15). This object is further described in sect. 17, where also the estimation of the expansion
velocity is demonstrated.
5.7 Composite Spectrum
Superimposed spectra of several light sources are also called “composite”- sometimes also
“integrated spectra”. The English term “composite” was coined in 1891 by Pickering for
composite spectra in binary systems. Today it is often used also for integrated spectra of
stellar clusters, galaxies and quasars, which consist from hundreds of thousands up to sev-
eral hundred billions superposed individual spectra.
Analysis and Interpretation of Astronomical Spectra 18
5.8 Reflectance Spectrum
The objects of our solar system are not self-luminous, but only visible thanks to reflected
sunlight. Therefore, these spectra always contain the absorption lines of the solar spec-
trum. The continuum course is however coined, because certain molecules in the atmos-
pheres of the large gas planets, eg CH4 (methane), absorb and/or reflect the light differ-
ently strong at specific wavelengths.
The following chart shows the reflection spectrum of Jupiter (red), recorded with the DA-
DOS spectrograph and the 200L/mm grating. Superimposed (green) is generated by dawn
light, previously captured in the daylight- (solar) spectrum. Before rectifying, both profiles
have been normalised on the same continuum section [30]. In this wavelength range, the
most striking intensity differences are observed between 6100 and 7400 Å.
5.9 Cometary Spectrum
Such can be considered as a special case of the reflectance spectra. Comets, like all other
objects in the solar system, reflect the sunlight. However on its course into the inner solar
system core material increasingly evaporates, flowing out into the coma, and subsequently
into the mostly separated plasma- and dust tails. The increasing solar wind, containing
highly ionised particles (mainly protons and helium cores), excites the molecules of the
comet. Thus the reflected solar spectrum gets more or less strongly overprinted with mo-
lecular emission bands, chiefly due to vaporised carbon compounds of the cometary’s ma-
terial. The most striking features are the C2 Swan bands Further frequently occurring emis-
sions are CN (cyan), NH2 (Amidogen Radicals), and C3. Sometimes also Na I lines can be
detected. Only slightly modified appears the solar spectrum, recorded from sunlight, which
has exclusively been reflected by the dust tail. All these facts and the associated effects,
create complex composite spectra. The influence of the possible components depends pri-
marily on the current intensity of the core eruptions, as well as on our specific perspective,
regarding the coma, as well as the plasma- and dust tail. Further details see [33].
Analysis and Interpretation of Astronomical Spectra 19
6 Form and Intensity of the Spectral Lines
6.1 The Form of the Spectral Line Continuum Level Red Wing
Blue Wing
The chart on the right shows several
absorption lines with the same wavelength, Intensity I Continuum
showing an ideal Gaussian-like intensity dis-
tribution but with different width and inten- saturated Core
sity. According to their degree of saturation,
they penetrate differently deep into the con- λ
tinuum, maximally down to the wavelength Wavelength λ
axis. The red profiles are both unsaturated.
The green one, which just touches the deep-
est point on the wavelength axis, is saturated
and the blue one even oversaturated [5]. The
lower part of the profile is called "Core",
which passes in the upper part over the
"Wings" in to the continuum level. The short-
wavelength wing is called "Blue Wing", the
long-wave- "Red Wing" [5].
Emission line profiles, in contrast to the presented absorption lines, always rise upwards
from the continuum level.
6.2 The Information Content of the Line Shape
There hardly exists any stellar spectral line, which shows this ideal shape. But in the devia-
tion from this form a wealth of information is hidden about the object. Here are some ex-
amples of physical processes which have a characteristic influence on the profile shape
and become therefore measurable:
– The rotational speed of a star, caused by the Doppler Effect, flattens and broadens the
line (rotational broadening), see sect. 16.
– The temperature and density/pressure of the stellar atmosphere broaden the line (tem-
perature/pressure-/collision broadening), see sect. 13.12.
– Macro turbulences in the Stellar Atmosphere, caused by the Doppler Effect, broaden the
line, see sect. 16.6.
– Instrumental responses broaden the line (instrumental broadening)
– In strong magnetic fields (eg sunspots) a splitting and shifting of the spectral line occurs
due to the so-called Zeeman Effect.
– Electric fields produce a similar phenomenon, the so-called Stark Effect.
The combined effects of pressure- and Doppler broadening result in the so-called Voigt pro-
files.
6.3 Blends
Stellar spectral lines are usually more or less strongly deformed by closely neighbouring
lines - causing this way so-called "blends". The lower the resolution of the spectrograph,
the more lines appearing combined into blends.
6.4 The Saturation of an Absorption Line in the Spectral Diagram
The following spectral profile is generated with Vspec, based on the course of an 11-step
gray-scale chart, running parallel to the wavelength axis. The maximum possible range from
Analysis and Interpretation of Astronomical Spectra 20
black to white, covered by Vspec, comprises 256 gray levels [411]. The Profile section in
the black area is here, as expected, saturated to 100% and runs therefore on the lowest
level, ie congruent with the wavelength axis. The saturation of the remaining gray values
decreases staircase-like upward, until on the continuum level, it finally becomes white. If an
underexposed spectral stripe was prepared in advance with IRIS [410] [30], the gray scale
is stretched, so that the highest point on the chart becomes white. Thus, a maximum con-
trast is achieved.
Continuum Level = white
saturated = black
Gray-values
Gray-scale chart
Wavelength axis = black
So far remains the theory, covering the electronic recording and the data reduction level.
According to [11] however, in astronomical spectra, an absorption line reaches already full
saturation before it touches the wavelength axis. In fact the "Wings" in the upper part of an
oversaturated line profile, appear massively broadened, without penetrating much further
into the continuum (sketch according to [11]).
I/Ic
saturated
oversaturated
λ [Å]
6.5 The Oversaturated Emission Line in the Spectral Diagram
No tricks are required for the presentation
of an oversaturated emission line. This
just needs to overexpose the calibration
lamp spectrum. Such oversaturated Neon
lines appear flattened on the top. Such an
unsuccessful neon spectrum must never
be used for calibration purposes!
Analysis and Interpretation of Astronomical Spectra 21
7 The Measurement of the Spectral Lines
7.1 Methods and Reference Values of the Intensity Measurement
Depending on the specific task, the line intensity is determined either by simple relative
measurement, or quite complexly and time consuming, with absolutely calibrated dimen-
sions. Here we focus exclusively on the relative measurement which is sufficient for most
amateur purposes, and is supported by the analysis software (eg Vspec). As a reference or
unit usually serves the local or normalised continuum level (sect. 8) but possibly also val-
ues of a linear, but otherwise arbitrary scaling of the intensity axis.
7.2 Metrological Differences between Absorption and Emission Lines
For measurements of spectral lines the following differences must be noted.
The absorption lines can simplified be considered as the product of I IC λ)
a "filtering process". The photons of a specific wavelength λ, which, in IA λ)
most of the cases are absorbed in a stellar photosphere, cause a gap
in the continuum of defined area, shape and penetration depth. λ
Therefore, the parameters of the absorption remain always propor-
tionally connected to the continuum-intensity . IE λ)
The emission lines are generated independently of the continuum I λ
by recombination and/or electron transitions (sect. 9). Because this
process is mostly also excited by the stellar radiation, it results a cer-
tain strongly object-dependent, time related degree of coupling to the
continuum radiation. For instance at P Cygni these lines are generated
directly in the turbulent expanding gas envelope – at the Be stars
(sect. 16) mostly in the relatively nearby circumstellar gas disk – and
in the cases of the H II regions or Planetary Nebulae PN, even up to
some ly away, where almost regular laboratory conditions exist!
The combination of emission lines and continuum radiation results in I
a superposition of the two intensities: IC λ) + IE λ)
Due to the physically, and often even locally, different generation, IE λ)
as well as may fluctuate independently of each other. The IC λ)
continuum-level is dependent on the specific radiation density, λ
which the star generates at the wavelength . To this level, the emis- IE λ
sion intensity is adding up independently.
The combination of emission lines and absorption lines results also in I
a superposition of the two intensities.
At Be-stars, the slim hydrogen emission line is produced in the cir-
cumstellar disk or -shell, and appears superimposed to the rotation-
and pressure-broadened H-absorption of the stellar photosphere. The
resulting spectral feature is therefore called “Shell Core” [4]. The H- IA λ
absorption of such a spectral feature may also originate from the pho-
λ
tosphere of a hot O-star and the emission line from the surrounding H II region, see eg the
Hβ line of Θ1Ori C / M42 [33].
Analysis and Interpretation of Astronomical Spectra 22
7.3 The Peak Intensity P Ic Ic I
The Line Intensity I
P=I/Ic
The intensity offers the easiest way to measure a spectral
line in a linear but otherwise arbitrarily scaled intensity axis..
However this measure is only significant in a radiometrically
corrected or absolutely calibrated profile as described in
section 8.10 - 8.12.
The Peak intensity
In a pseudo-continuum, but also in a just rectified profile ac-
cording to sect. 8.9, the intensity gets only comparable
with other lines if related to its local continuum level . This
is expressed as the dimensionless Peak intensity .
The Peak intensity at absorption lines
is here also called for “Line Depth”. Related to the continuum level , the peak inten-
sity of the absorption line, corresponds to the maximum intensity or flux density ,
which is removed from the continuum radiation by the absorption process. This further cor-
responds to the photon energy per time, area, the considered wavelength interval and re-
lated on the level (units see sect. 8.12). In addition, it qualitatively shows the degree of
absorption, or the share of photons, which is absorbed in the peak of the absorption line
with the penetration depth .
The Peak intensity at emission lines
If the upwards striving and independently generated emission lines appear superimposed
on a continuum {3}, they are, just as a pure makeshift, sometimes also related to the inde-
pendent continuum-level {4}, eg for investigations of individual lines. Related to the inde-
pendent continuum-level , the peak intensity of the emission line corresponds to the
maximum intensity or flux density . This further corresponds to the photon energy per
time, area, the considered wavelength interval and related on the level .
7.4 Full Width at Half Maximum Height
The FWHM value is the line width in [Å] at half height of I=0 FWHM
the maximum intensity. It can be correctly measured even ½ Imax
in non-normalised spectral profiles. The width of a spec-
tral line is inter alia depending on temperature, pressure,
density, and turbulence effects in stellar atmospheres. It
allows therefore important conclusions and is often used
as a variable in equations, eg to determine the rotational
velocity of stars (sect. 16.6).
This line width is specified in most cases as wavelength-
difference . For the measurement of rotational and ex-
pansion velocities, is also expressed as a velocity Imax
value according to the Doppler principle. For this purpose
[Å] is converted with the Doppler formula {16}
to a speed value [km/s] (sect. 15).
The FWHM value, obtained from the spectrum [30] has now to be corrected from the in-
strumental broadening.
Analysis and Interpretation of Astronomical Spectra 23
corresponds to the theoretical maximum resolution [Å] of the
spectrograph, ie the smallest dimension of a line detail, which can be resolved.
The resolution is limited on one side by the optical design of the spectrograph (dispersion
of the grating, collimator optics, slit width, etc.). It can normally be found in the manual of
the spectrograph as so-called -Value which is valid for a defined wavelength
range ( = considered wavelength) [302].
This value is determined by measurements at thinnest possible spectral lines, eg
atmospheric H2O absorptions or somewhat less accurate, at emission lines of calibration
light sources [11], [123], [302]. In the laboratories for example emissionlines, generated by
microwave excited mercury lamps are used, in order to minimise temperature broadening.
Such profiles are called "instrumental profile" or "δ-function response" [11]. The resolution
may further be limited by the pixel grid of the connected camera [Å/pixel], if this value is
greater than of the spectrograph. For a wavelength-calibrated profile, this value is
shown in the head panel of the Vspec screen. Compared to monochrome-, with color CCD
cameras, a significant loss of resolution must be accepted.
7.5 , Equivalent Width
The EW-value or Equivalent Width is always based on the continuum level and is a
relative measure for the area of a spectral line.
Definition
The profile area between the continuum level and
the profile of the spectral line has the same size as 1 Continuum level Ic = 1
the rectangular area with the fully saturated depth Profile
(here ) and the equivalent width [Å]. area
Intensity I = EW
The -value must therefore be measured in a spec- 0 Wavelength λ
trum, normalised to ([30], sect. 10). This is the
mathematically correct expression for :
In simple terms the red area above the spectral
curve is calculated by summing up an infinite
number of vertical, infinitely narrow rectangular
strips with the width and the variable heights 1 λ1 Ic = 1 λ2
, within the entire range from to . To get Intensity I Ic - Iλ
finally the equivalent width , these values are still
Iλ
to divide by the entire height of the continuum-, Wavelength λ
resp. of the saturated square. Ic
The integral sign ∫ is derived from the letter S, and 0
stands here for "sum". is the continuum intensity,
the variable intensity of the spectral line
depending on (or a function of) the wavelength
.
Analysis and Interpretation of Astronomical Spectra 24
The EW value at absorption lines
As sketched above and related to the continuum-level , corresponds to the measure
of the total radiation flux , which the entire absorption line removes from the
continuum radiation. This further corresponds to the photon energy per time, area and re-
lated on the continuum-level (common units see sect. 8.12). The EW value is for absorp-
tion lines an absolute measure, because they are inseparably and proportionally linked to
the continuum level.
The EW value at emission lines
The value of the just relatively to the independent continuum level related emission
lines, corresponds to the measure of their entire radiation flux . This further corre-
sponds to the photon energy per time, area, and relatively related on the independent
level . In contrast to the absorptions the EW value is for the emission lines not an absolute
measure, because the relation to the independently generated continuum is always relative,
just by makeshift, but never absolute.
Measurement and signs of the EW values
values of absorption lines are by definition always positive (+), those of emission lines
negative ( ).
Since the value is always measured at a continuum level, normalised to , it is
neither influenced by the course of the continuum, nor by the absolute radiation flux.
Should be measured in a non rectified profile, the continuum must be normalised
immediately at the base of the spectral line to !
In scientific publications is also designated with the capital . designates the
equivalent width of the Hα Line.
Somewhat confusing: In some publications I have also found the FWHM value expressed as
. The conclusion: One must always simply check which value is really meant.
7.6 Normalised Equivalent Width is used [128]:
Rather rarely the normalised value
This allows the comparison of -values of different lines at different wavelengths , tak-
ing into consideration the linearly increasing photon energy towards decreasing wave-
length λ, according to formula {8}. Anyway, in astrophysics this is not applied by most of the
mainly empirical formulas and procedures.
7.7 FWZI Full Width at Zero Intensity
Rather rarely the FWZI value of a spectral line is applied. The Full With at Zero Intensity cor-
responds to the integration range of the definite integral according to formula and
chart {6a}:
7.8 Influence of the Spectrograph Resolution on the FWHM- and EW Values
The above outlined theories about FWHM- and must realistically be relativated. This
need is dramatically illustrated by the following spectral profiles of the Sun, taken with
different highly resolving spectrographs (M. Huwiler/R. Walker). The R-values are here
within a range of approximately 800 – 80,000.
Analysis and Interpretation of Astronomical Spectra 25
Sun Spectrum λ 5256 – 5287 Å
Comparison Prototype Echelle- with Cerny Turner Spectrograph
Cerny Turner R ≈ 80‘000
Echelle R ≈ 20‘000
Sun Spectrum λ 5160 – 5270 Å
Comparison Prototyp Echelle- with DADOS Spectrograph 900- and 200 L mm-1
Echelle R ≈ 20‘000
DADOS 900L mm-1 R ≈ 4‘000
DADOS 200L mm-1 R ≈ 800
Magnesium Triplet: λ 5167, 5173, 5183 Å
Richard Walker 2011/03
The comparison of these graphs shows the following:
If the resolution (R) is increased it becomes clearly evident that in stellar spectra practi-
cally no "pure" lines exist. Apparent single lines almost turn out as a "blend" of several
sub lines, if considered at higher resolutions.
Analysis and Interpretation of Astronomical Spectra 26
Striking is also the so-called "Instrumental Broadening" effect. Even relatively well-
insulated seeming lines broaden dramatically with decreasing resolution (R), due to the
instrumental influences. This affects the measured FWHM or the half-width of a line.
The value, related to the profile area, remains theoretically independent of the reso-
lution. At higher resolutions, the area of the slimmer line profile is compensated by a
higher peak-value .
7.9 Practical Consequences for the FWHM and EW Measurements
FWHM values must always be corrected in respect of the "Instrumental Broadening",
applying the formulas {5} to {5b}.
The comparability of the values, obtained with different resolutions, remains purely
theoretical and is limited to discrete and well isolated single lines. Assuming the case of
a blended absorption line, a high-resolution spectrograph measures, in an ideal case, the
value of only one, well-defined single line. However, at low resolution and the same
wavelength, a substantially larger value is measured due to a blend of several insepara-
ble lines. In this case, only -values are seriously comparable, if they have been ob-
tained from profiles with similar resolution. This necessarily requires a declaration of the
R-value.
According to formula {6a}, the -value is clearly defined. However to determine this
value e.g. for strongly deformed, broad emission lines, possibly even with a double peak,
remains a serious problem. With Gaussian fits in such cases reasonably reproducible, al-
beit relatively imprecise results may result. The profile fit with Spline filter, or similar al-
gorithms is perhaps more accurate, but the result is subjectively influenced by the inves-
tigator.
For amateur monitoring projects it is important, that all participants work with similarly
high resolutions and the recording and processing of the spectra is clearly standardised.
A problem with the values poses the standardisation of the integration area
(FWZI) of formula {6a}, since the width of the line base may change significantly with
varying intensity. Further the section of the continuum must be specified, on which the
profile is to normalise. This is unavoidable at least for the later spectral classes, which
exhibit a rather diffuse continuum. When monitoring emission lines one must always
keep in mind that the measured values are related to a possibly independently fluc-
tuating continuum level (sect. 7.2).
7.10 The Measurement of the Wavelength
The wavelength of a spectral line (Nanometer [nm] or Angström [Å]) can be obtained in a
wavelength calibrated spectrum directly via Gaussian fit (Vspec) or by positioning of the
cursor at the peak of the line. Which method is better, depends upon whether a strongly
asymmetric blend or an isolated single-line is present.
7.11 Additional Measurement Options
Depending on the applied analysis software, further information can be obtained from the
calibrated spectral profile. In Vspec these are, among other, e.g. the signal to noise ratio
SNR and the dispersion in Å/pixel, etc. For details see the respective manuals.
Analysis and Interpretation of Astronomical Spectra 27
8 Calibration, Normalisation and Radiometric Correction
8.1 The Calibration of the Wavelength
Usually spectra are plotted as course of the radiation intensity over the wavelength. In prin-
ciple, both dimensions can be calibrated. For most applications, only the calibration of the
wavelength is required. This can be done relatively easy with lines of known wavelength
within the spectrum, or absolutely with appropriate spectral calibration lamps. These pro-
cedures are well documented in literature eg [30], [411].
8.2 The Selective Attenuation of the Continuum Intensity
The intensity profile of the undisturbed stellar original spectrum is determined mainly
by the black body radiation characteristics of the star and its effective temperature
(sect. 3.2). On the long way to the unprocessed raw spectrum the continuum of be-
comes deformed by the following damping influences into a so called pseudo-continuum
(sect. 3.3).
1. The Attenuation by the Interstellar Matter is mainly caused by scattering effects
of dust grains and gas. Thereby the intensity is selectively much stronger dampened in the
blue short wave part of the spectrum. Thus the maximum of the continuum radiation is
shifted in to the red, long-wavelength range, which is called "Interstellar Reddening" (sect.
21). The extent of this effect depends on the object-distance, the direction of the line of
sight and is, as expected, most intensive within the galactic plane. It can roughly be esti-
mated with a corresponding 3D model by F. Arenou et al. [209], [201].
2. The Attenuation in the Earth's Atmosphere acts similarly. Well known effects
are the reddish sunsets. The modelling of the atmospheric transmission is mainly applied in
the professional sector. It is rather complex and depends inter alia on the zenith-distance
(or the complementary elevation angle) of the observed object, the altitude of the observa-
tion site and the meteorological conditions [303].
3. The Attenuation by Instrumental Influences of the system telescope-
spectrograph-camera follows at the very end of the transmission chain. This can be deter-
mined quite precisely, eg by comparison with the exactly known radiation distribution of a
continuum light source (eg special calibration lamps) [11], [300], [313], [315], [316],
[480].
The resulting attenuating effect does:
The empirical function provides to any wavelength the correction factor between
the continuum-intensity of and .
This empirical scaling- or "correction function" can be determined as a rough ap-
proximation only. The intensity profile of the original stellar spectrum can be simulated just
on a theoretical basis and the individual factors can just very roughly be estimated. Similar
approaches with empirical functions can be found in [300] and [303]. The practical calcula-
tion with profiles is normally enabled – including all basic operations – by the software of
the analysis tools. At Vspec this feature is to find under Operations/Divide-, /Multiply,-
/Add-, or /Subtract profiles by a profile.
Analysis and Interpretation of Astronomical Spectra 28
8.3 Relationship Between Original-Continuum and Pseudo-Continuum
The following diagram shows two identical sections of the same spectrum: on the left the
undisturbed original profile and on the right the recorded raw spectrum with the
pseudo-continuum It shows each an absorption and an emission line. Within this fic-
tional spectral section, the course of , and is assumed to run horizon-
tally.
I Original Recorded
Profile Profile
IEO
Or λ ΔIC IE
ICO IAO Ps λ
IC IA
λλ
The following relationships and its consequences can be derived:
Due to the selective attenuation, at a certain wavelength , the continuum-intensity of
the recorded profile appears to be reduced by , compared with the original-
spectrum .
8.4 Attenuation of Absorption Lines , are at-
The continuum intensity and the penetration depth of the absorption line
tenuated equally proportional.
As an example the following graph shows the Sirius spectrum with the virtual original pro-
file and the recorded pseudo-continuum . The absorption lines always remain
proportionally and inseparably connected to the continuum. Therefore the -related
measurement categories – Peak Intensity , and Equivalent width – cannot be
changed by a simple division or multiplication by .
Analysis and Interpretation of Astronomical Spectra 29
Or(λ) IA / IC = IAO / ICO
EWPs(λ) = EWOr(λ)
Hγ
IAO Hβ
Ps(λ)
ICO Hα
IC IA
Anyway the example of the Hγ line also shows that the relative line intensity of , which
is measured independently of the continuum-level, appears strongly attenuated, com-
pared with . At , corresponds to the intensity of the original profile.
Further in the original profile of Sirius, spectral class A2V, it gets clearly evident,
that the absolute energy flux ,(sect. 8.12) which is absorbed by the Hγ – line and is not
related to the continuum-level , is much higher, compared to the Hα – Absorption.
8.5 Attenuation of the Emission Lines
Completely different is the behaviour of the emission lines, which appear superimposed on
the continuum, but are otherwise extensively independent of . Therefore, in contrast to
the absorptions, also the continuum related peak intensities as well as the equivalent
width are affected here by the attenuation process, and both appear selectively damp-
ened, dependent on their specific wavelength. Thus, these values significantly differ from
the undampened so-called Balmer-Decrement according to sect. 20. This becomes clearly
evident in the recorded spectra of objects with intense hydrogen emission (eg P Cygni).
This effect totally excludes an attenuation, which acts proportional to the continuum-level
, and therefore would never change this way the or values. However, as a rough
approximation, even in the professional practice, for emission-lines quite often – and for
accordingly non-critical applications – an attenuation, acting proportional to , is assumed.
Analogously to the absorption , , for emission lines:
Due to the wavelength-dependent- and therefore differently strong attenuation, the in-
tensity ratio of two arbitrary emission - or absorption-lines , measured in the original
profile , appears as changed in the recorded pseudo-continuum :
, therefore it follows .
Analysis and Interpretation of Astronomical Spectra 30
8.6 Summary of the consequences:
For absorption lines, absolutely connected with the continuum, the -related measure-
ments – peak intensity and equivalent width – remain untouched by the attenua-
tion due to . The original ratio of remains the same also in the pseudo-
continuum .
The emission lines, superimposed to the pseudo continuum , stay independent of
the continuum level . In contrast to the absorption lines, their values appear here
to be attenuated, depending on the specific wavelength. This effect excludes an attenua-
tion, acting proportional to the dampened continuum-level , and shows up by the so-
called Balmer-Decrement of the hydrogen emissions according to sect. 20. Nevertheless
as a rough approximation, sometimes an attenuation is assumed, which acts propor-
tional to .
The intensity values and , which are measured in arbitrary measuring units, and in-
dependently from the continuum-level, appear to be attenuated in the pseudo-continuum
,.
The original intensity ratios between two different absorptions , or emissions ,
which are measured within the original profile in arbitrary measuring units, ap-
pears to be modified in the pseudo-continuum , .
8.7 The Importance of the Pseudo-Continuum
If the attenuation-function is approximately known, the pseudo continuum
contains the information, to enable the approximate reconstruction of the original profile
, applying formula . Further, according to sect. 3.2 and 3.3, the wavelength of the
maximum intensity is, even in the strongly dampened pseudo-continuum, a very rough indi-
cator at least for the order of magnitude of the effective temperature .
Apart from these effects the course of the recorded pseudo-continuum , is useless.
Depending on the wavelength, just shows the amount of electrons, which has been
read out of the individual pixels, amplified by the camera electronics and finally averaged by
the spectral processing software over a defined height of the vertical pixel rows. Thus it re-
flects roughly proportional the recorded photon flux which however is loaded with all the
mentioned attenuating influences. As intensity unit for raw profiles therefore often [ADU]
(Analog – Digital Units) is used.
8.8 Proportional Radiometric Corrections of the Pseudo-Continuum
In the following sections 8.9 – 8.12 several proportional-radiometric correction processes
are presented, which transform the recorded pseudo-continuum for different applica-
tions to appropriate forms. All are based on the division of by empirical correction-
functions. Thus , the intensities of the embedded absorption lines and also the su-
perimposed appearing emission lines , are scaled proportionally to a new value.
Important:
The -related measurements – peak intensity and equivalent width – remain un-
touched by the division. Just the intensity values and , which are measured in arbi-
trary measuring units, and independently from the continuum-level, are concerned.
These effects are appropriate only for the absorption lines.
For the emission lines, however, only a rough approximation is achieved this way. Be-
cause, related to , the original equivalent widths can't be reconstructed by a
simple division, and the original -values can just very roughly be approximated. The
original intensity ratios of the emission lines can only be determined by individual, ar-
ithmetical scaling, proportional to the values of the theoretical Balmer-Decrement of the
Analysis and Interpretation of Astronomical Spectra 31
hydrogen lines, according to sect. 20 and 21. Practical example are the strongly attenu-
ated hydrogen lines of P Cygni.
8.9 Rectification of the Continuum Intensity
The most simple correction process is the rectification of the recorded profile by dividing of
the pseudo-continuum by its own “smoothed” or fitted intensity course . Ac-
cording to [11], this method is appropriate even for most professional applications. This
way the continuum-intensity is unified or "normalised" through the entire range, and set
to . The resulting profile is called „Residual Intensity“
Due to this division, the profile runs now horizontally and the intensity of the emissions -
and absorptions is related to the unified continuum intensity . This process
proportionally scales by the intensities of all spectral lines from their individual -
values in the pseudo-continuum, up to the level . This corresponds now to the origi-
nal, not attenuated profile of a virtual star which shows a horizontally running, but physi-
cally impossible radiation characteristic. For the intensity of the emission lines this correc-
tion process is just a rough approximation (see sect. 8.8).
Consequences and benefits of Rectifying the Pseudo-Continuum
Useful for certain applications – the profile normalisation allows the elimination, of
the often irrelevant, or even hindering, wavelength-dependent distribution, of the stellar
radiation intensity. It generates a "quasi neutralisation", but never a real correction of the
attenuating effects.
Between individual absorption lines, enables the direct comparison of the peak in-
tensities between individual absorption lines, according to . The scaling effect of
a rectified profile is impressively demonstrated at the absorptions in the solar spectrum
by the two Fraunhofer H- and K- lines of ionised calcium (Ca II). The blue profile of the
pseudo-continuum shows these lines only stunted at the short wavelength end of the
spectrum (blue arrow). After rectifying of the continuum (red profile), the H- and K- lines
appear now obviously as the strongest absorptions, which the sun generates itself (red
arrow).
The original ratio of the individual emission lines is maintained just as a rough
approximation {7h}.
, with the unified and normalised radiation-intensity , enables for the re-
corded emission lines the intensity comparison with those of the original, unattenuated
Balmer-Decrement (sect. 20).
Analysis and Interpretation of Astronomical Spectra 32
Like in the recorded pseudo-continuum , also in changes the intensity ratio of
any two emissions or absorptions , measured in the original profile {7i}, {7j}.
The rectified profile, normalised to , enables the determination of the -values
and facilitates the measurement of the , the Doppler-shift , as well as the de-
termination of the spectral class.
By the rectification of the profile, by the information gets lost, which allows, by
means of the known attenuation function , to approximately reconstruct the
original profile (according to formula ).
Anyway, even for most professional applications – with just a few exceptions –, the pro-
file normalisation is clearly the best and easiest option [11].
8.10 Relative Radiometric Flux Calibration by a Synthetic Continuum
The goal of this procedure is a rough approximation of the recorded profile with the
pseudo-continuum , to the original- and therefore not reddened continuum . This
procedure is described in the manual of the Vspec software. With dividing by correction
curves, the spectral lines of the pseudo-continuum are directly transferred to the syn-
thetically produced and fitted continuum course of a virtual model star with the
same spectral class and unreddened by any interstellar dust. Similar to sect. 8.9, this proc-
ess proportionally scales the intensities of all spectral lines from their individual -values in
the pseudo-continuum, up to the level of . For specific applications this procedure
is also applied in the professional field [301].
In the following chart the blue spectrum is the recorded profile with the pseudo-continuum
of Sirius. The red profile is the aimed, fitted continuum course of the syn-
thetic model star of the same spectral type, from the Vspec library (CDS Database). It ap-
pears cleaned from all spectral lines and thus roughly corresponds to the black body radia-
tion characteristics of this star:
.
Smoothed reference profile of
the model star
Ms Fit (λ)
Pseudo-continuum Ps(λ)
On the following graph, the green correction curve is generated by division of the fit-
ted blue pseudo-continuum with the red synthetic reference profile . It is
called by Vspec “Instrumental Response” and is denoted hereinafter with correction func-
tion .
Analysis and Interpretation of Astronomical Spectra 33
Correction-function Ir(λ)
Radiometrically corrected
profile
Rc(λ)
Ps(λ)
In a rough approximation corresponds here to the attenuation-function , ac-
cording to .
Finally the division of the blue recorded raw profile , by the green correction-function
, results in the radiometrically corrected profile (black). It shows now the same
continuum course like the red smoothed reference profile , but now overprinted
with the accordingly scaled lines of the recorded profile.
Remarks to the „Instrumental Response“
For a correction function , obtained according to , the term "instrumental re-
sponse" is misleading and possibly just acceptable if the spectrum was recorded with a
space telescope. In professional fields, this term is used as "Instrumental System Re-
sponse", which is clearly restricted to the erroneous recording characteristic of ,
considering just the system telescope – spectrograph – camera [305]. In contrast, the cor-
rection curve , generated according to , is additionally loaded by the wavelength
dependent damping effects of the Interstellar Matter and of the earth's
phere .
Experiments have shown that such correction curves , which are generated just with
an unreddened virtual model spectrum of the same spectral class, are not universally appli-
cable. They can generally not be applied to any other raw profiles of different spectral
classes, which have been recorded at different atmospheric conditions as well as different
zenith distances and observation sites.
Deviation between and
The following figure shows for the spectral classes B, A, F, G, the ranges of the smallest de-
viation between (pink) and (blue), valid for the setup C8/DADOS/Atik 314L+.
This information may be useful to estimate the rough size of error, when intensity ratios, for
applications as described in sect. 20 – 22, are measured approximately, ie without any ra-
diometric corrections. This applies also for the detailed analysis of the Hα line!
Analysis and Interpretation of Astronomical Spectra 34
Hβ
Kr(λI) ε Ori, Alnilam B0 Iab HHαα
Hβ I / Ic = I / Ic
Ps(λ)
α Cma, Sirius A1V
ζ Leo, Adhafera F0 III
Sun G2V
Consequences and benefits of a radiometric profile correction with a synthetic continuum
This procedure provides not a true correction of the attenuation influences
, , . With the direct transformation of the intensity profile from
to , the pseudo continuum is just scaled up to the level of the synthetic and
therefore unreddened model star, and not to the original profile of the observed
ject . Thus, the attenuating effects are simply bypassed here and just a “synthetic”,
rough approximation to the original profile is reached this way. Therefore fluctua-
tions of the continuum radiation cannot be measured in such a profile.
Since complies now very roughly to the original profile , also the relative in-
tensities of the absorption lines correspond approximately with those in the original
profile. For emission lines , generated independently from the continuum, this applies
just as a rough approximation (sect. 8.8).
The original relative relationship between two absorption-intensities and ,
which are measured directly and independently of the continuum level, can be estimated
here {7i}, {7j}. For emission line intensities and this applies just as a rough
approximation.
However it must generally be kept in mind that between different stars, even of the very
same spectral class, considerable differences in the continuum course may occur. This
effect can be significantly enhanced by a strongly different metallicity and/or rotation ve-
locity ( s ). This method does not yet allow any calibration of the intensity axis in
physical units!
Analysis and Interpretation of Astronomical Spectra 35
8.11 Relative Radiometric Profile Correction by Recorded Standard Stars
Correction methods in amateur fields
With this somewhat time consuming procedure the recorded profile is corrected,
similarly to section 8.10, with a correction function . However is obtained here,
analogously to formula , by a recorded and real existing standard star , mostly of
the spectral type A0V. The continuum course of is very well known and corresponds
to the profile, just reddened by interstellar dust, as it would have been recorded outside the
Earth's atmosphere and without any instrument influences [300]. Such flux-calibrated spec-
tra can eg be found in the ISIS software [410], containing profiles from the MILES-, ELODIE,
UVES and Pickles databases [104], [105], [106], [107].
Standard stars must be recorded with a minimum of time difference and as close as possi-
ble to the object under investigation. Subsequently, the obtained raw profile is divided by
the specific reference spectrum of the very same star from the catalogue. Thus, the atmos-
pheric and instrumental influences can be corrected in a good approxima-
tion. Anyway the resulting spectrum remains here – star-dependent differently strong –
reddened by the interstellar matter , however in the "close range" of a few dozen
light years, just very slightly [209] [11]. In contrast to and the correction function
is determined here only by and , which corresponds also
to common practice in professional astronomy.
In contrast to sect. 8.10 such real standard star correction curves, recorded very promptly
and with similar elevation angle to the investigated object, can be applied to any spectral
classes. With the graphic below, Robin Leadbeater [481] shows, that for different spectral
classes, very similar correction curves are obtained this way (many thanks Robin!).
Analysis and Interpretation of Astronomical Spectra 36
Consequences and benefits of the Radiometric Correction with recorded standard stars
The achievable accuracy of this rather delicate method is highly dependent on the quality of
execution. By amateurs it tends to be rather overestimated. Numerous are the potential
sources of errors and in addition, some of the reference profiles of the various databases
show significant differences in their continuum courses.
Anyway, if applied appropriately and accurately, this fairly time consuming method pro-
vides a reasonable approximation to the original theoretical spectral profile , which
still appears individually reddened by the interstellar matter .
This way, at least theoretically, also greater fluctuations in the continuum radiation are
detectable.
The effective temperature according to sect. 18.3 can roughly be estimated.
This time consuming correction procedure is required if spectra must be obtained for
certain scientific databases. For the intensities of emission lines , even this correction
procedure applies just as a rough approximation (see sect. 8.8).
Correction methods in professional fields
Anyway the professional astronomy applies significantly higher sophisticated and more ac-
curate methods. For most of the large professional telescopes is well known.
is usually determined separately by observations of standard stars with different
zenith distances . This way not a correction curve is generated, but instead a model of the
atmospheric extinction becomes parameterised, like MODTRAN [314]. Thus, finally the pro-
file of the examined object will be corrected in function of the zenith distance [305]. Fur-
ther methods are presented in [300] and [303].
The recording of standard stars consumes valuable telescope time. To relieve the main in-
strument of this "annoying" task, the separate determination of with smaller
“Photometric Monitoring Telescopes” was already proposed [314]. Further possibilities are
based on the measurement of atmospheric Cherenkov radiation as well as on LIDAR [314].
In the infrared range the spectral class A0 shows just few and very faint stellar lines. There-
fore, these more or less purely telluric influenced profiles are generally used to extract the
atmospheric H20 and O2 lines in any stellar spectra [300].
Analysis and Interpretation of Astronomical Spectra 37
8.12 Absolute Flux Calibration [erg s-1 cm-2 Å-1] F
As a final step of the radiometric correction, the intensity axis Fλ
could be absolutely calibrated in physical units for the spectral
flux density – normally [erg s-1 cm-2 Å-1]. This calibration is very [erg s-1 cm-2]
challenging, time consuming and just needed by some special
sectors of the professional astronomy. It is relatively common for λ1 λ2 λ
spectra, recorded by space telescopes, which of course at least
remain clean of any atmospheric influences [301].
For amateur applications an acceptable accuracy of the results
is usually prevented already by the inadequate quality of the ob-
servation site. Thus even in the professional sector, such abso-
lutely flux-calibrated spectra can be found rather rarely.
The total flux of an emission line, here in a simplified form di-
rectly drawn on the wavelength axis, corresponds to their area,
[302]. The unit for the total flux of the line is [erg s-1 cm-2].
If the emission line is superimposed on a continuum, the continuum flux must
be subtracted from formula . However, there exists no easy way to determine the real
original undamped flux of an emission line (sect. 8.14).
This process is based on the comparison of the absolute calibrated radiation flux of a stan-
dard star. However, many additional data are required here, such as the exposure time of
the spectral recordings. Further, the recording usually requires a large slit width to measure
really the total flux of the object.
8.13 Intensity Comparison between Different Spectral Lines
The intensities of two different lines can be compared in normalised profiles with
their equivalent widths . However if the widths of the lines are not too different, a rough
comparison is also feasible with the peak intensities .
8.14 Reconstruction of the Original Emission-Line Intensities
Most of the emission nebulae (sect. 22), don’t show any evaluable continuum. But even in
spectra with existing continuum (eg P Cygni), the original values of the emission lines
in , can never be reconstructed with the already presented, proportional-radiometric
procedures according to sect. 8.10 to 8.12. At least for amateurs here just remains the ar-
ithmetical scaling of the individual, attenuated emissions, proportionally up to the known
line ratios of the undampened Balmer-Decrement for the hydrogen emissions (sect. 20 and
21). These corrected intensitiy ratios allow now to perform the appropriate procedures, eg
for plasma diagnostics (sect. 22), with higher accuracy. Anyway with the extinction at
, according to sect. 21.1, formula , the original, absolute values of the -
emissions could roughly be estimated.
Analysis and Interpretation of Astronomical Spectra 38
8.15 Summary – Which Method Fits to Which Task
The following table provides an overview of which calibration-, normalisation- or radiomet-
ric correction methods are appropriate, or even required for the following tasks.
Legend: R = Requirement B = Best option, P = possible option
Methods of Cali- Relative λ-Calibration with
bration, Normali- known Lines
sation or Radio- Absolute λ- Calibration with
metric correction calibration-light-source
Pseudo-continuum of the raw
Task profile
Rectified continuum,
normalised to
Relative Flux calibration with
synthetic model star
Relative Flux calibration with
recorded standard star
Scaling of emission-intensities
to theor. Balmer Decrement
Absolute Flux calibration
Calibration of the profile to the rest R
wavelength λ0
Absolute calibration of the profile to R
the measured wavelength λ
Measurement of the relative RPPBPP P
difference Δλ P
P
Absolute Measurement of the RPBPP
Doppler shift
Measurement of FWHM PPPBPP
Measurement of EW PP R
Determination of the spectral class B P P B B B
Optical intensity comparison of the P P R
absorption lines B P R
Measurement of the reddened P P BP P
Balmer -Decrement
Estimation of the original IE- and IA- P P BP P
values in the unreddened original P P
profile P P R
Comparison of the absorbed fluxes P P
at different absorption lines R R
Evaluation of the emission intensi- R
ties (eg for plasma diagnostics)
R
Estimation of the effective tempera-
ture Teff based on continuum slope
Fluctuations of the continuum
radiation
Profile processing for certain, scien-
tific databases
Flux measurement in physical units P P E
Analysis and Interpretation of Astronomical Spectra 39
9 Visible Effects of Quantum Mechanics
9.1 Textbook Example Hydrogen Atom and Balmer Series
The following energy level diagram shows for the simplest possible example, the hydrogen
atom, the fixed grid of the energy levels (or "terms") , which a single electron can occupy
in its orbit around the atomic nucleus. They are identical with the shells of the famous
Bohr's atomic model and are also called principal quantum numbers. Which level the elec-
tron currently occupies depends on its state of excitation. A stay between the orbits is ex-
tremely unlikely. The lowest level is . It is closest to the nucleus and also called the
ground state.
With increasing number (here from bottom to top):
– increases the distance to the nucleus
– increases the total energy difference, in relation to
– the distances between the levels and thus the required energy values to reach the next
higher level, are getting smaller and smaller, and finally tend to zero on the Level
(or ).
The energy level E on the level is physically defined as [5] and also called
Ionisation Limit. The level number is to consider as "theoretical", as a limited number
of about 200 is expected, which a hydrogen atom in the interstellar space can really occupy
[6]. By definition, with decreasing number the energy becomes increasingly negative.
Above , ie outside of the atom, it becomes positive.
Hydrogene Series General Transitions
E = 0 eV nn == ∞
E5 6
E4 n=5
E3
n=4
E2
n=3
Energy Levels Paschen
Hα (Infrared)
Hβ
Hγ n=2
Hδ
HεBalmer
(visible)
Emission
Absorption
Ionization
Recombination
Excitation Levels
E1 n=1
Lyman
(Ultra violet)
Absorption occurs only when the atom is hit by a photon whose energy matches exactly to
a level difference by which the electron is then briefly raised at the higher level (resonance
absorption).
Emission occurs when the electron falls back to a lower level and though a photon is emit-
ted, which corresponds exactly to the energy level difference.
Analysis and Interpretation of Astronomical Spectra 40
Ionisation of an atom occurs when the excitation energy is high enough so the negative
electron is lifted over the level and leaves the atom. This can be triggered by a
high-energy photon (photo ionisation), by heating (thermal ionisation) or a collision with ex-
ternal electrons or ions (collision ionisation).
Recombination occurs if an ionised atom recaptures a free electron from the surrounding
area and becomes "neutral” again.
9.2 The Balmer Series
A group of electron transitions between a fixed energy level and all
higher levels is called “Transition Series”. For amateurs primarily the
Balmer series (red arrow group) is important, because only their spec-
tral lines are in the visible range of the spectrum. It contains the fa-
mous H-lines and includes all the electron transitions, which start up-
ward from the second-lowest energy level (absorption) or end
here, “falling” down from an upper level (emission). The Balmer series
was discovered and described by the Swiss mathematician and archi-
tect (!) Johann Jakob Balmer (1825-1898). The lines of the adjacent
Paschen series lie in the infrared, those of the Lyman series in the ul-
traviolet range.
This sounds very theoretical, but has high practical relevance and can virtually be made
"visible" using even the simplest slitless spectrograph! For this purpose the easiest way is
to record the classical beginner object, a stellar spectrum of the class A (sect. 13.4). Most
suitable is Sirius (A1) or Vega (A0). These stars have a surface temperature of about
10,000 K, which is best suited to generate impressively strong H-Balmer absorptions. The
reason for this: Due to thermal excitation at this temperature, the portion of electrons
reaches the maximum which occupy already the basic level of the Balmer series.
With further increasing temperature, this portion decreases again, because it is shifted to
even higher levels (Paschen series) and will finally be completely released, which results in
the ionisation of the H atoms.
In the following Sirius spectrum six of the H-Balmer lines appear, labelled with the relevant
electron transitions. These absorption lines are labelled consecutively with lowercase
Greek letters, starting with Hα in the red region of the spectrum, which is generated by the
lowest transition . From Hε upwards often the respective level number is used, eg
Hζ = H8. Here is nice to see how the line spacing in the Blue area gets more and more
closer – a direct reflection of the decreasing amounts of energy, which are required to
reach the next higher level. In my feeling this is the aesthetically most pleasing, which the
spectroscopy has optically to offer!
Triggering electron transitions
n2 – n8
n2 – n7
n2 – n6
n2 – n5
n2 – n4
n2 – n3
Hζ Hε Hδ Hγ Hβ Hα
Denotation of the lines
Analysis and Interpretation of Astronomical Spectra 41
9.3 Spectral Lines of Other Atoms
For all other atoms, i.e. with more than one electron, the description of line formation can
be very complex. All atoms have different energy levels and are therefore distinguished by
different wavelengths of the spectral lines. Another factor is the number of valence elec-
trons on the outer shell, or how many of the inner levels are already fully occupied. Further
the main levels are subdivided in a large number of so-called Sublevels and Sub-Sublevels,
each of them with completely other implications in respect of quantum mechanics. The en-
ergy differences between such sublevels must logically be very low. This explains why
metals often appear in dense groups, a few with distances even <1Å! Typical examples are
the sodium lines at 5896 Å and 5890 Å, and the famous Magnesium Triplet at 5184, 5173,
5169Å in the solar spectrum. By the hydrogen atoms these sublevels play no practical role,
particularly for amateurs, because they are degenerated here [5]. The stay of the electrons
within this complex level system is also subject to a set of rules. The best known is proba-
bly the so called Pauli Exclusion Principle which demands that the various sublevels may be
occupied by only one electron at the same time.
For most spectroscopic amateur activities, detailed knowledge of this complex matter is not
really necessary. For those, deeper interested in quantum mechanics, [5] is recommended
as a “first reading”, which provides a good overview on this matter and is relatively easy
and understandable to read.
Analysis and Interpretation of Astronomical Spectra 42
10 Wavelength and Energy
10.1 Planck’s Energy Equation
In the above wavelength-calibrated Sirius spectrum we want to calculate the
corresponding photon energies of the hydrogen lines. This is possible with
the familiar and simple equation of Max Planck (1858 – 1947):
Radiation Energy in Joule [J]
Planck’s Quantum of Action [6.626 10-34 J s]
(Greek: „nu“) Radiation frequency [s-1] of the spectral line.
The Radiation frequency of the spectral line is simply related to the wave-
length [m] ( = light speed 3 108 m/s):
Insert {9} into {8}:
The most important statement of formulas {8} and {10}: The radiation energy is propor-
tional to the radiation frequency and inversely proportional to the wavelength .
10.2 Units for Energy and Wavelength
To express such extremely low amounts of energy in Joules [J] is very impractical and not
easy to interpret. Joule has been defined to be applied in traditional mechanics. In quantum
mechanics and therefore also in spectroscopy, the units of electron volts [eV] is in use [5].
Further in the optical spectral domain also the wavelengths are extremely small and there-
fore in astronomy usually measured in angstroms [Å] or nanometres [nm]. One should be
aware that 1Å corresponds about to the diameter of an atom, including its electron shells!
In the infrared range also [μm] is in use:
,, ,,
Rather rarely, the frequency is also expressed as “Wavenumber” . This is the reciprocal
value of the wavelength , usually expressed somewhat “special” in number of waves
within
In the optical spectral domain, the wavelength is usually based on the standard atmos-
phere (atmospheric pressure 1013.25 hPa, temperature 15° C). The program SpectroTools
[413] by Peter Schlatter, enables also to convert vacuum wavelengths to this atmospheric
standard (or vice versa) and to demonstrate the temperature dependency of a measure-
ment. So it becomes clear why the calibration spectrum should, as quick as possible, be re-
corded immediately prior to, and/or after the object spectrum!
The following simple formulas, suitable for pocket calculators, allow to convert the wave-
length [Å] into energy [eV] and vice versa,:
Analysis and Interpretation of Astronomical Spectra 43
10.3 The Photon Energy of the Balmer Series the
To the wavelengths of the hydrogen lines we can now calculate with formula
corresponding values of the photon energy .
3647 Å n2 – Balmer- 4861 Å n2 – n4 6563 Å n2 – n3 Electron
Edge transition
Wavelength [Å]
3889 Å n2 – n8
3970 Å n2 – n7
4102 Å n2 – n6
4340 Å n2 – n5
Balmer Hε Hδ Hγ Hβ Hα
Edge Hζ
3.40 eV 2.55 eV 1.89 eV Photon
3.19 eV Energies Ep [eV]
3.12 eV
3.02 eV
2.86 eV
In professional publications, spectra in the UV region are often calibrated in photon energy
[eV], instead of the wavelength .
On the left side, the so-called Balmer Edge or Balmer Jump is marked with a red bar (also
called Balmer Discontinuity). The Balmer series ends here at 3647 Å and the continuum
suffers a dramatic drop in intensity. This takes place due to the huge phalanx of highly con-
centrated and increasingly closer following absorption lines, acting here as a barrier to pho-
tons at corresponding wavelengths (see sect. 10.4).
The Value of a spectral line corresponds to the energy difference between the initial and
final level of the causal electron transition. It fits therefore also to the arrow lengths in the
following energy level diagram. In the spectrum above e.g. 2.55eV corresponds to the tran-
sition or Hβ. This relationship enables now to calculate the energy levels of the
H-Balmer series.
0 nnn === ∞56
-0.54 n=4
-0.85
-1.51 Paschen n=3
(Infrared)
Energy level E [eV]
-3.40 Hα Balmer n=2
Hβ(visible)
Hγ
Hδ
Hε
Excitation level
-13.6 Lyman n=1
(Ultra violet)
Analysis and Interpretation of Astronomical Spectra 44
Since by definition the energy on the level is set to , we shift the value of
the Balmer edge 3.40 eV with negative sign to the initial level of the Balmer Series .
3.40 eV corresponds also to the energy difference between the initial level and the
Balmer edge, as well as to the minimum required energy to ionise a hydrogen atom from
the initial level . For the calculation of the other energy levels the values of the
corresponding level differences must now be subtracted from 3.40 eV. For the energy level,
eg , the subtraction 3.40 eV – 1.89 eV = 1.51 eV is required (1.89 eV = EpHα). Per
definition the values of the energy levels have here negative signs.
10.4 Balmer- Paschen- and Bracket Continuum
Hot stars, with main radiation intensity in the UV region of the spectrum, show a steeply
rising continuum level toward shorter wavelengths. As already shown above, this tendency
is abruptly stopped by the Balmer Jump at 3646 Å. After a dramatic drop in intensity, the
continuum rises again in the UV range, until it reaches the final ionisation limit of hydrogen
(also called the Lyman limit) at 912 Å. The following graph shows the Balmer Jump at a
synthetic A0 I profile from the Vspec database.
A similar process occurs near the border to the infrared region at 8207 Å, the so-called
Paschen Jump. Somewhat confusing is the designation of the intermediate continuum sec-
tions which always bear the name of the preceding jumps or series. The Balmer Series
is therefore located within the so-called Paschen Continuum. On the shortwave
(UV) side of the Balmer Jump, follows the Balmer Continuum with the Lyman Series
. In the infrared region, the Paschen Series is located within the Bracket
Continuum. The dramatic influence of the hydrogen absorption on the continuum can be
explained by the extremely high occurrence of this element in most of stellar photospheres.
I
Paschen Jump
8207 Å
λ [Å]
Analysis and Interpretation of Astronomical Spectra 45
11 Ionisation Stage and Degree of Ionisation
11.1 The Lyman Limit of Hydrogen
In the second diagram of sect. 10.3 the energy for the lowest excitation level of the Lyman
. Converted with formula {10}, this gives the well-
Series results to
known Lyman limit or Lyman edge in the UV range with wavelength λ = 912 Å. It is func-
tionally equivalent to the “Balmer edge” of the Balmer Series (sect. 10.4). This value is very
important for astrophysics, because it defines the minimum required energy to ionise the H-
atom from its ground state . This level is only achievable by very hot stars of the O-
and early B-Class. [3]. The very high UV radiation of such stars ionises first the hydrogen
clouds which are shining due to emitted photons by the subsequent recombination (H II re-
gions, eg M42, Orion Nebula, sect. 22).
11.2 Ionisation Stage versus Degree of Ionisation
The term “Ionisation stage” refers here to the number of electrons, which an ionised atom
has lost to the space (Si IV, Fe II, H II, etc.). This must not be confused with the term “De-
gree of ionisation” in plasma physics. It defines for a gas mixture the ratio of atoms (of a
certain element) that are ionised into charged particles, regarding the temperature, density
and the required ionisation energy of the according element. This “Degree” is determined in
astrophysics with the famous Saha equation.
11.3 Astrophysical Form of Notation for the Ionisation Stage
Unfortunately, in astrophysics the chemical form of notation is not in use but instead of it
another somewhat misleading version. The neutral hydrogen is denoted by chemists with
H, and the ionised with H+, which is clear and unambiguous. On the other hand astrophysi-
cists, denote already the neutral hydrogen with an additional Roman numeral as H I and the
ionised with H II. The doubly ionised calcium is referred by chemists with Ca++, for astro-
physicists this corresponds to Ca III. Si IV is for example triply ionised silicon Si+++. This sys-
tem therefore works according to the “(n–1) principle”, ie in astrophysics the ionisation
stage of an atom is always by 1 lower than the Roman numeral. A high ionisation stage of
atoms always means that very high temperatures must be involved in the process.
Analysis and Interpretation of Astronomical Spectra 46
12 Forbidden Lines or –Transitions
Based on the already presented theories this phenomenon can just roughly be explained.
For a more comprehensive understanding, further quantum mechanical knowledge would
be required. For practical amateur spectroscopy, this is anyway not really necessary.
Most amateurs certainly have an [O III] filter for the contrast enhancement of emission
nebulae. It lets pass the wavelengths of the two green emission lines of the doubly ionised
oxygen [O III] at 4959Å and 5007Å. These lines are generated here by so-called "Forbidden
Transitions" between the energy levels (sect. 22). The initial levels of such transitions are
called “metastable”, because they are highly sensitive to impacts and an electron must re-
main her for a quite long time (several seconds to minutes) until it performs the forbidden
“jump”. These circumstances increase drastically the likelihood that this state is destroyed
before the forbidden transition happens.
"Forbidden" therefore means that in dense gases, such as on the earth's surface or in stel-
lar atmospheres, these transitions are extremely unlikely, because they are prevented by
frequent collisions with other particles. This disturbing effect occurs very rarely within the
extremely thin gases of the interstellar space. Thus such transitions are possible here. Such
forbidden lines are denoted within square brackets eg [O III], [N II], [Fe XIV].
In addition to nitrogen bands, the forbidden airglow line [OI] (5577.35Å) is the main cause
for the formation of the usually greenish polar lights in the extremely thin upper layers of
the atmosphere. For the generation of higher ionisation stages such as [O III] the required
ionisation energy is missing here.
Source: Wikipedia
Analysis and Interpretation of Astronomical Spectra 47
13 The Spectral Classes
13.1 Preliminary Remarks
Basic knowledge of the spectral classes is an indispensable prerequisite for a reasonable
spectroscopic activity. Combined with appropriate skills and tools, this classification sys-
tem contains a considerable qualitative and quantitative information potential about the
classified objects. The average-equipped amateur will hardly ever come into the embar-
rassment, that he really must determine an unknown classification of a star, unless of cer-
tainly recommendable didactic reasons. The spectral classes can nowadays be obtained
from Internet sources [100], planetarium programs, etc. For a deeper understanding of the
classification system, a rough knowledge of the historical development is very useful since
from each development step something important remained until to date!
13.2 The Fraunhofer Lines
At the beginning of the 19th Century, the physicist and Line Element Wavelength Å
optician Joseph von Fraunhofer (1787-1826) investi- A – Band
gated, based on the discovery of Wollaston, the sunlight B – Band O2 7594 – 7621
with his home-built prism spectroscope. He discovered C O2 6867 – 6884
over 500 absorption lines in this very complex spectrum. a – Band H (α) 6563
The more intensive of them he denoted with the letters D 1, 2 O2 6276 – 6287
A – K, at that time still unaware of the physical context. E Na 5896 & 5890
Picture below: Original drawing by Fraunhofer from Inter- b 1, 2 Fe 5270
net sources. This line names can frequently be found even F Mg 5184 & 5173
in recent papers! D H (β) 4861
E Fe 4668
Fraunhofer has been studied the brighter stars with this F Fe 4384
spectroscope, and already recognised that in the spectrum G – Band H (γ) 4340
of Sirius broad strong lines are dominating and Pollux G CH 4300 - 4310
shows a similar pattern as the spectrum of the sun! Further H Ca 4227
he observed the spectrum of Betelgeuse which shows H H (δ) 4102
barely discrete absorption lines but broad absorption K Ca II 3968
bands. Ca II 3934
The table on the right and the graphics below show how
this system was expanded later on. (Source: NASA).
Analysis and Interpretation of Astronomical Spectra 48
Here are some of the identified Fraunhofer lines in the solar spectrum, obtained with the
DADOS Spectrograph in the range of 4200 – 6700 Å (200L/mm).
Below left, the H and K lines of ionised calcium. Ca II are the most intense of the sun-grown
absorption lines (3968/3934 Å). Below right is the beautiful so-called A-band (7594 –
7621 Å), caused by the O2 molecule in the earth’s atmosphere (DADOS and 900L/mm grat-
ing).
13.3 Further Development Steps
In the further course of the 19th to the early 20th Century, the
astronomy, and particularly the spectroscopy benefited from im-
pressive advances in chemistry and physics. So it became in-
creasingly possible to assign the spectral lines to chemical ele-
ments - primarily the merit of Robert Bunsen (1811 - 1899) and
Gustav Kirchhoff (1824 - 1887)
Father Angelo Secchi (1818 - 1878) from the Vatican Observa-
tory decisively influenced the future path of the stellar spectral
classification. He is therefore referred by many sources as the
father of the modern astrophysics. He subdivided the stellar
spectra into five groups according to specific characteristics (I-V “Secchi Classes”).
Type I Bluish-white stars with relatively simple spectra, which are dominated by small but
very bold lines. These are distributed like thick rungs over the spectral stripe and turned out
later as the hydrogen lines of the famous Balmer series. This simple characteristic allows
even beginners, to roughly classify such stars into the currently used A- or late B-Class (Sir-
ius, Vega, Castor).
Type II Yellow shining stars with complex spectra, dominated by numerous metal lines,
like they exhibit the Sun, Capella, Arcturus, Pollux (now Classes ≈ F, G, K).
Analysis and Interpretation of Astronomical Spectra 49
Type III Reddish-orange stars with complex band spectra and a few discrete lines. The ab-
sorption bands get darker (more intense) towards the shortwave (blue) side. Such features
show, e.g. Betelgeuse, Antares, and Mira. Not until 1904, it became clear that these ab-
sorption bands are mainly caused by the titanium oxide molecule TiO (today's Class M).
Type IV Very rare reddish stars with absorptions bands getting darker (more intense) to
the longwave (red) side. Angelo Secchi already recognised that it is generated by carbon
(sect. 5.5)!
Type V Finally, stars with "bright lines" – emission lines as we know today.
13.4 The Harvard System
It soon became clear that the classification system of Secchi was too
rudimentary. Based on a large number of spectra and preliminary work
by Henry Draper, Edward Pickering (1846-1919) refined Secchi’s sys-
tem by capital letters from A – Q. The letter A corresponded to the
Secchi class type I for stars with dominant hydrogen lines. Finally this
classification solely survived up to the present time! As director of the
Harvard Observatory, he employed many women, for its time a truly
avant-garde attitude. Three women of his staff took care of the classi-
fication problem until after many detours and “meanders” the system
of Annie J. Cannon (1863 - 1941) became widely accepted around the
end of the World War I.
Its basic structure has survived until today and is essentially based on
the letters O, B, A, F, G, K, M. The well-known and certainly later cre-
ated mnemonic: Oh Be A Fine Girl Kiss Me. With this system, even
today still over 99% of the stars can be classified. This sequence of
letters follows the decreasing atmospheric temperature of the classi-
fied stars, starting from the very hot O-types with several 10,000 K up
to the cool M-types with about 2,400 –3,500 K. This reflects the abso-
lutely ground-breaking recognition that the spectra depend mainly on
the photospheric temperature of the star and secondarily only on other
parameters such as chemical composition, density, rotation speed etc.
This may not be really surprising from today's perspective, since the shares of hydrogen
and helium with 75% and 24%, even about 13.7 billion years after the “Big Bang” still
comprise about 99% of the elements in the universe. This systematic also forms the hori-
zontal axis of the almost simultaneously developed Hertzsprung Russell Diagram (sect. 14).
It was later complemented by the classes:
– R for Cyan (CN) and Carbon Monoxide (CO)
– N for Carbon
– S for very rare stars, whose absorption bands are generated, instead of TiO, by zirconium
oxide (ZrO), yttrium oxide (YO) or lanthanum oxide (LaO). Moreover, the entire class system
was further subdivided with additional decimal numbers from 0–10. Examples: Sun G2,
Pollux K0, Vega A0, Sirius A2, Procyon F5.
Analysis and Interpretation of Astronomical Spectra 50
13.5 “Early” and “Late” Spectral Types
One of the faulty hypotheses on the long road to this classification system postulated that
the spectral sequence from O to M represents the chronological stages of a star. Unaware
at that time of nuclear fusion as a "sustainable" energy source, even the hypothesis was
discussed, that the stars could generate their energy only by contraction, ie starting very
hot and finally ending cool. This error has subsequently influenced the terminology until to-
day. Thus the O, B, A classes are called "early", the F and G classes "medium" and K and M
as "late" types. This systematic is also applied within a class. So M0 is called an “early” and
M8 a “late” M-type. Logically is for example M1 "earlier" than M7.
13.6 The MK (Morgan Keenan) or Yerkes System
Later on, the progress in nuclear physics and the increasing knowledge of the stellar evolu-
tion required a further adaptation and extension of the system. It was eg recognised, that
within the same spectral class, stars can show totally different absolute luminosities,
mainly caused by different stages of stellar development.1943, as another milestone, the
classification system was extended with an additional Roman numeral by Morgan, Keenan
and Kellmann from the Mt Wilson Observatory. This second dimension of the classification
specifies the so called six luminosity classes.
Luminosity class Star type
I Luminous Super Giants
Ia-0, Ia, Iab, Ib Subdivision of the Super Giants according to decreasing lu-
minosity
II Bright Giants
III Normal Giants
IV Sub Giants
V Dwarfs or Main Sequence Stars
VI Sub Dwarfs (rarely used, as specified by prefix)
VII White Dwarfs (rarely used, as specified by prefix)
This system classifies the Sun as a G2V star, an ordinary Dwarf on the main sequence of
the Hertzsprung Russel Diagram. Sirius, classified as A1Vm, is also a Dwarf on the main se-
quence. Betelgeuse, as a Super Giant and rated with M1–2 Ia–Iab, moves as a variable be-
tween M1 and M2 and fluctuates between the luminosity class Ia and Iab. It has given up
the Dwarf stage on the main sequence long ago and expanded into a Super Giant.
13.7 Further Adaptations up to the Present
Up to the presence, this classification system has been adapted to the constantly growing
knowledge. Thus, new classifications for rare, stellar "exotics" have emerged, which today
even amateurs successfully deal with. Furthermore with additional lower-case letters at-
tached as a prefix or suffix, unusual phenomena, such as a higher than average metal con-
tent or "metallicity" are referred. Some of these supplements are, however, over determin-
ing, eg because White Dwarfs, Sub Dwarfs and Giants are already specified by the luminos-
The words you are searching are inside this book. To get more targeted content, please make full-text search by clicking here.
Discover the best professional documents and content resources in AnyFlip Document Base.
Search