analysis-and-interpretation-of-astronomical-sp

Analysis and Interpretation of Astronomical Spectra 101

In comparison, for the permitted Hα line, at least 12.1 eV would be required from the
ground state (n1 – n3). For this, the electrons in the nebula are by far too slow, i.e. by about
one order of magnitude (see diagram below). This explains the strong intensity of the for-
bidden-as compared to the allowed transitions. These metal ions are also called "cooler"
[237] in the context of model computations. Influenced by the highly effective line emission
they contribute significantly to the cooling of the nebula and therefore to the thermal equi-
librium. The following chart shows just the relevant small excerpts of the highly complex
term diagrams [10], [222]. For the most important metal ions, the required excitation ener-
gies and the wavelengths of the “forbidden” emissions are shown.

[eV]

7

6

5 3344
1815
4 4363 1794
7331
7319.6
7330
7318.6

3 5755
3071
2 10338 3063
10373
10278
10320
4076

4068

1 6731 6583 5007 4014
6717 6548 4959 3967
4932 3869
3729
3726

0 [N II] [O III] [Ne III] [O II]

[S II]

The following chart shows by Gieseking [222], the Maxwellian frequency distribution of
electron velocities for relatively "cool" and "hot" nebulae, calculated for Te 10,000K and
20,000K. Mapped are the two minimum rates for the excitation of the [O III] lines. The up-
per edge of the diagram I have supplemented with the values of the kinetic electron energy.
The maximum values of the two curves correspond to the average kinetic energy according
to formula {54} (0.86eV and 1.72eV).

Kinetic Energy [eV]

0 0.25 0.5 1 2 3 4 5 6 7 8 9 10 11

0.86 eV
Relative Frequency
1.72 eV
2.5 eV
5.3 eVO III 5007/4959/ 4932

O III 4363

0 200 400 600 800 1000 1200 1400 1600 1800

Electron Velocity [km/s]

Analysis and Interpretation of Astronomical Spectra 102

22.10 Scheme of the Photon Conversion Process in Emission Nebulae
This scheme summarises the previously described processes in H II regions and PN and il-
lustrates important relationships. Not shown here are the bremsstrahlung processes, which
become typically relevant just in SNR due to the relativistic electron velocities. Processes
with photons are shown here in blue, those with electrons in red. So-called bound-bound
transitions between the electron shells are marked with black arrows. The broad, gray ar-
rows show the two fundamentally important equilibriums in the nebula:

 The Thermal Equilibrium in the nebulae between the heating process by the kinetic en-
ergy of free electrons and the permanent removal of energy by the escaping photons,
regulates and determines the electron temperature Te.

 The Ionisation Equilibrium between ionisation and recombination, regulates and de-
termines the electron density Ne. If this balance is disturbed, the ionisation zone of the

Ionniesbaultaioenith-,erReexpcaonmdsboirnsahtriinokns-[2a3n9d]. Excitation Processes in Emission Nebulae

Fee Electrons heating Thermal Escaping Photons
the Nebula Equilibrium cooling the Nebula

Te Ne

Electron Ionisation Electron
Equilibrium

Electron

UV Photon Exactly
Fitting
Photon

Ionisation Recombination Collision Direct
Excitation Absorption
Photons

Photons Photons

Teff > 25‘000K Star ©Richard Walker 2011/12

Analysis and Interpretation of Astronomical Spectra 103

22.11 Practical Aspects of Plasma Diagnostics

The main focus for amateurs is here the determination of the excitation class of emission
nebulae. Their diagnostic lines are relatively intense and quite close together. Moreover,
some of them are located in an area, where the difference between the original and
pseudo-continuum is relatively low – see early spectral classes in the last graph of sect.
8.10. This allows for galactic objects, even at the raw profile, ie without any extinction- or

other corrections, a reasonable classification with accuracy of about 1 class. Due to the

slightly greater distance of the He II diagnosis line (λ 4686), at middle and high excitation
classes the classification may result in up to one step to low. For emission lines, the propor-

tional-radiometric correction procedures, presented in sect. 8.8 – 8.11, are ineffective for

the correction of the continuum related measurements ( and ). For more precise

analyses, the intensity of the individual lines to be analysed, should be corrected according
to formula {53}, see comments sect. 21.4.

The measurement of the attenuated emission lines must be performed in an intensity-
normalised profile according to sect. 8.9 (see comments in sect. 20.5). Emission nebulae
usually generate an extremely weak and diffuse continuum. Thus these objects do not allow
any reliable determination of the continuum-based or values. Therefore the direct
measurement of the values in arbitrary units is preferable.

Typical galactic decrement values are in the range of D ≈ 3.0–3.5 [10]. However, there are
stark outliers like NGC 7027 with D ≈ 7.4 [10]! Since the classification lines lie close to-
gether, for a rough determination of the excitation class even this effect can usually be ne-
glected. In such extreme cases, a substantial part of the extinction can also be caused by
massive dust clouds around the star itself. E.g. at the extremely young T-Tauri objects the
measured deviation from the Balmer-Decrement is even used as a classification criterion,
see [33] sect. 13.2!

Special cases are here the faint, not two dimensional, but rather star-like appearing Plane-
tary Nebulae. In contrast to M27 and M57 they generally require relatively short exposure
times. Further they cannot be recorded on a specific area within the nebula but only in the
total light, integrated within the slit of the spectrograph. Since within these tiny discs, lar-
ger intensity differences at individual emissions occur. So even the measured Balmer-
Decrement may be distorted, aggravated by possible shifts in the slit position during re-
cording due to bad seeing and/or poor autoguiding. However, even this influence on the
determination of the excitation class has been found as low.

The determination of additional plasma parameters such as the electron temperature Te
and the electron density Ne specifically requires low-noise spectra with high resolution, re-
garding these faint objects, a real challenge with amateur equipments. In addition, some of
the used diagnostic lines are extremely weak and the error rate is correspondingly high.
Even between values in professional publications, often major deviations are noted!

Analysis and Interpretation of Astronomical Spectra 104

22.12 Determination of the Excitation Class

Since the beginning of the 20th Century numerous methods have been proposed to deter-
mine the excitation classes of emission nebulae. The 12-level “revised” Gurzadyan system
[10], which has been developed also by, Aller, Webster, Acker and others, is one of the cur-
rently best accepted and appropriate also for amateurs. It relies on the simple principle that
with increasing excitation class, the intensity of the forbidden [O III] lines becomes
stronger, compared with the H-Balmer series. Therefore as a classification criterion the in-
tensity sum of the two brightest [O III] lines, relative to the Hβ emission, is used. Within the
range of the low excitation classes E: 1–4, this value increases strikingly. The [O III] lines at
λλ4959 and 5007 are denoted in the formulas as and .

For low excitation classes E1 – E4:

Within the transition class E4 the He II line at λ 4686 appears for the first time [225]. It re-
quires 24.6 eV for the ionisation. That's almost twice the energy as needed for H II with
13.6 eV. From here on, the intensity of He II increases continuously and replaces the now
stagnant Hβ emission as a comparison value in the formula. The ratio is expressed here
logarithmically (base 10) in order to limit the range of values for the classification system:

For middle and high Excitation Classes E4 – E12:

The 12 -Classes are subdivided in to the groups Low ( , Middle and
. In extreme cases 12+ is assigned.
High

Low 0–5 Middle High 1.7
5 – 10 1.5
–Class 10 – 15 – Class – Class 1.2
0.9
E1 >15 E4 2.6 E9
E2 E5 2.5 E10 0.6
E3 E6 2.3 E11
E4 E7 2.1 E12
E8 1.9 E12+

22.13 The Excitation Class as an Indicator for Plasma Diagnostics

Gurzadyan (among others) has shown that the excitation classes are more or less closely
linked to the evolution of the PN [10], [226]. The study with a sample of 142 PN showed
that the E-Class is a rough indicator for the following parameters; however in reality the
values may scatter considerably [8].

1. The age of the PN
Typically PN start on the lowest E- level and subsequently step up the entire scale with
increasing age. The four lowest classes are usually passed very quickly. Later on this
pace decreases dramatically. The entire process takes finally about 10,000 to >20,000
years, an extremely short period, compared with the total lifetime of a star!

2 The Temperature of the central star

The temperature of the central star also rises with the increasing E-Class. By pushing of
the envelope, increasingly deeper and thus hotter layers of the star become "exposed".
At about E7 in most cases an extremely hot White Dwarf remains, generating a WR-like
spectrum. For [K] the following, very rough estimates can be derived [33]:

Analysis and Interpretation of Astronomical Spectra 105

E-Class E1-2 E3 E4 E5 E7 E8-12

35,000 50,000 70,000 80,000 90,000 100,000 – 200,000

3. The Expansion of the Nebula
The visibility limit of expanding PN lies at a maximum radius of about 1.6 ly (0.5parsec).
With increasing E-class, also the radius of the expanding nebula is growing. Gurzadyan
[226] provides mean values for [ly] which however may scatter considerably for the
individual nebulae.

E-Class E1 E3 E5 E7 E9 E11 E12+

0.5 0.65 0.72 1.0 1.2 1.4 1.6

22.14 Estimation of Te and Ne with the O III and N II Method

Due to the very weak diagnostic lines, these methods can be applied only to spectra with
high resolution and quality. Further J. Schmoll outlines in his dissertation [201], what influ-
ence the slit width and the method of background subtraction exert on the analysis of weak
lines! The procedure is based on the fundamental equations by Gurzadyan 1997 [10],
which uses for the O III method the lines at λλ 5007, 4959 and 4363, and for the N II
method at λλ 6548, 6584 and 5755.

For the calculation of the electron temperature, these equations can’t be explicitly con-
verted and solved by and contain additionally the variable . But for , empirical formu-

las exist, which are valid for thin gases (typical for H II regions and SNR).

“ “ is the natural logarithm to base e.

For the explicit calculation of , with known , I have converted the formulas {57} {58}
accordingly:

Analysis and Interpretation of Astronomical Spectra 106

If the recording of a spectral profile can be limited on a defined region within the nebula, in
both equations {61} and {62} the variables become identical. can then be eliminated
by equalisation of {61} and {62}. The implicitly remaining variable anway requires finally
an iteratively solving of the equation. However this requires that the values of all diagnostic
lines, for both methods, are available in good quality.

22.15 Estimation of the Electron Density from the S II and O II Ratio

The electron density can be estimated by Osterbrock from the ratio of the two sulfur
lines [S II] λλ 6716, 6731 or the oxygen lines [O II] λλ 3729, 3726 [201]. The big advan-
tage of this method: These lines are so close together, that the extinction and instrumental
responses can’t exert any significant effect on the ratio. The disadvantage is, that the two
lines, except by SNR, are generally very weak and therefore difficult to measure.

1.6

1.4

1.2

Intensity Ratio 1.0
[S II] 6716 / 6731

0.8

0.6
[O II] 3729 / 3726

0.4

0.2

0.0 102 103 104 105
101 Electron Density [cm-3]

22.16 Distinguishing Characteristics in the Spectra of Emission Nebulae

Due to the synchrotron and bremsstrahlung SNR show, especially in the X-ray part of the
spectrum, a clear continuum see [33], Table 85. This appears especially pronounced in the
X-ray domain, so X-ray telescopes are highly valuable to distinguish SNR from the other
nebula species, particularly at very faint extragalactic objects. For all other types of Emis-
sion Nebulae the detection of a continuum radiation is difficult.

In the optical part of SNR spectra, the [S II] and [O I] lines are, relative to Hα, more intense
than at PN and H II regions. This effect is caused here by shock wave induced collision ioni-
sation, see [33], Table 85. The [S II] and [OI] emissions are very weak at PN and almost to-
tally absent in H II regions [201].

The electron density is very low in SNR, ie somewhat lower than in H II regions. It
amounts in the highly expanded, old Cirrus Nebula to about 300 cm-3:

By the still young and compact Crab Nebula it is about 1000 cm-3 [201]. By PN, gets
highest and is usually in the order of 104 cm-3 [201]. In the H II region of M42, is within
the range of 1000–2000 cm-3 [224].

In H II regions, the excitation by the O- and early B-class stars is relatively low and there-
fore the excitation class in the order of E = 1-2 only modest [33].

Analysis and Interpretation of Astronomical Spectra 107

Planetary nebulae usually pass through all 12 excitation classes, following the evolution of
the central star.

In this regard the SNR are also a highly complex special case. By very young SNR, eg the
Crab Nebula (M1), dominate higher excitation classes whose levels are not homogeneously
distributed within the nebula, according to the complex filament structure [231]. The diag-
nostic line He II at λ 4686 is therefore a striking feature in some spectra of M1, see [33],
Table 85.

Analysis and Interpretation of Astronomical Spectra 108

23 Analysis of the Chemical Composition

23.1 Astrophysical Definition of Element Abundance

In astrophysics, the abundance of an element is expressed as decadic logarithm of the

amount of particles per unit volume , to that of the hydrogen , whose abundance is

defined according to convention to [57], [11]. The mass ratios do not matter here.

By transforming logarithmically we directly obtain the relationship :

23.2 Astrophysical Definition of Metal Abundance Z (Metallicity)

Of great importance is the ratio of iron to hydrogen . This is also computed with the

relative number of atoms per unit volume and not with their individual masses. The metal-
licity in a stellar atmosphere, also called , is expressed as the decadic logarithm

in relation to the sun:

values, smaller than found in the atmosphere of the Sun, are considered to be metal poor
and carry a negative sign (–).The existing range reaches from approximately +0.5 to –5.4
(SuW 7/2010). Fe is used here as a representative of the metals because it appears quite
frequently in the spectral profile and is relatively easy to analyse.

23.3 Quantitative Determination of the Chemical Composition
The identified spectral lines (sect. 25) of the examined object inform directly:

– which elements and molecules are present
– which isotopes of an element are present (restricted to some cases and to high

resolution profiles)
– which stages of ionisation are generated

In this context the quantitative determination of the abundance can be outlined only
roughly. It is very complex and can’t be obtained directly from the spectrum. It requires ad-
ditional information, which can partly be obtained only with simulations of the stellar pho-
tosphere [11]. The intensity of a spectral line is an indicator, which provides information on
the frequency of a particular element. However this value is influenced, inter alia, by the
effective temperature , the pressure, the gravitational acceleration, as well as the

macro-turbulence and the rotational speed of the stellar photosphere. Furthermore

also affects the degree of ionisation of the elements, which must be calculated with the so-
called Saha Equation [11].

These complications are impressively demonstrated in the solar spectrum. Over 90% of the
solar photosphere consists of hydrogen atoms with the defined abundance of .

Nevertheless, as a result of the too low temperature of 5800 K, the intensity of the H
Balmer series remains quite modest. The dominating main features of the solar spectrum,
however, are the two Fraunhofer H and K lines of ionised calcium Ca II, although its abun-
dance is just [Anders & Grevesse 1989]. According to {65}, this corresponds to a

ratio of . From Quantum-mechanical reasons, at the solar photospheric

Analysis and Interpretation of Astronomical Spectra 109

temperature of 5800 K, Ca II is an extremely effective absorber. The optimum conditions
for the hydrogen lines, however, are reached not until nearly 10,000 K (see sect. 9.2). In
the professional area the element abundance is also determined by the iterative compari-
son of the spectrum with simulated synthetic profiles of different chemical composition
[11].

23.4 Relative Abundance-Comparison at Stars of Similar Spectral Class
A simplified special case is formed by stars with similar spectral- and luminosity class and
comparable rotational velocities. Thus the physical parameters of the photospheres are
very similar. Here the equivalent widths EW of certain lines can simply be compared and
thus the relative abundance differences at least qualitatively be seen. In the Spectroscopic
Atlas [33] this is demonstrated at the classical example of the two main-sequence stars Sir-
ius A1Vm and Vega A0V. The basic principle is the so called Curve of Growth. It shows that
within its unsaturated and somewhat linearly running part, the equivalent width EW of a
certain spectral line of an element, behaves roughly proportional to its number of atoms
within a plasma mixture.

Equivalent width EW [Å] Saturated line

Curve of Growth

Linear region
Linie profile deepening

Number of atoms

Analysis and Interpretation of Astronomical Spectra 110

24 Spectroscopic Parallax

24.1 Spectroscopic Possibilities of Distance Measurement

Distances can spectroscopically be determined either with the spectroscopic parallax or in
the extragalactic range, with help of the Doppler-related redshift, combined with the Hub-
ble’s Law (sect. 15.8). These methods are supplemented by radar and laser reflectance
measurements (solar system), the trigonometric parallax (closer solar neighborhood) and
the photometric parallax (Milky Way and extragalactic area). The latter is based on the
brightness, compared with precisely known, so-called "standard candles" as Cepheids and
supernovae of type Ia.

24.2 Term and Principle of Spectroscopic Parallax

The spectroscopic parallax allows the rough distance-estimation to a star, based solely on
the spectroscopically determined spectral class and photometrically measured, apparent
brightness. Therefore the term "parallax" is here a misnomer. However, it is correct for the
trigonometric parallax. This corresponds to the apparent shift of the observed celestial body
relative to the sky background, caused by the Earth's orbit around the sun. The principle of
spectroscopic parallax works similar to the photometric parallax. The absolute magnitude
of an object is generally defined for the distance of 10 parsecs [pc] or 32.6 light years [ly].
This value is first compared with the actually measured, apparent brightness, enabling the
calculation of the distance. Applying the spectroscopic parallax, the absolute brightness of
a star is determined by its spectral class.

24.3 Spectral Class and Absolute Magnitude

The following table shows the values of the absolute magnitudes for the main sequence
stars (V) from a lecture at the University of Northern Iowa http://www.uni.edu/. Their devia-
tion, in comparison with known literature values, remains, for our purpose, within accept-
able limits. For instance, the table value for the spectral class G2V does 5.0M, compared to
the literature value for the sun of 4.83M. For the giants (III) and supergiants (I), I have col-
lected some literature values of known stars from different sources in order to give an im-
pression of the magnitude and the enormous spread. At these luminosity classes no usable
conjunction with the spectral classes can be recognised. Further supergiants of early spec-
tral classes are often spectroscopic binaries. These facts also drastically demonstrate the
limitations of this method. Therefore the determination of the distance, applying the spec-
troscopic parallax is, at least for amateurs, restricted to main-sequence stars. To find In the
annex to Gray/Corballi [4] is a calibration table of the absolute magnitudes for all spectral-
and luminosity classes of the MK System.

Spectral Main Sequence (V) Giants (III) Supergiants (I)
Class

O5 –4.5

O6 –4.0

O7 –3.9

O8 –3.8 Meissa, λ Ori –4.3

O9 –3.6 Iota Ori –5.3 ζ Ori, Alnitak –5.3

B0 –3.3 Alnilam, ε Ori –6.7

B1 –2.3 Alfirk, β Cep –3.5

B2 –1.9 Bellatrix, γ Ori –2.8

Analysis and Interpretation of Astronomical Spectra 111

B3 –1.1

B5 –0.4 δ Per –3.0 Aludra, η Cma –7.5

B6 0

B7 0.3 Alcione, η Tau –2.5

B8 0.7 Atlas, 27 Tau –2.0 Rigel, β Ori –6.7

B9 1.1

A0 1.5

A1 1.7

A2 1.8 Deneb, α Cyg –8.7

A3 2.0

A4 2.1

A5 2.2 α Oph, 1.2

A7 2.4 γ Boo, 1.0

F0 3.0 Adhafera, ζ Leo –1.0

F2 3.3 Caph, β Cas 1.2

F3 3.5

F5 3.7 Mirfak, α Per –4.5

F6 4.0

F7 4.3

F8 4.4 Wezen, δ CMa –6.9

G0 4.7 Sadalsuud, β Aqr –3.3

G1 4.9

G2 5.0 Sadalmelik, α Aqr –3.9

G5 5.2

G7 Kornephoros, β Her –0.5

G8 5.6 Vindemiatrix, ε Vir 0.4

K0 6.0 Dubhe, α Uma –1.1

K1 6.2

K2 6.4 Cebalrai, β Oph 0.8

K3 6.7

K4 7.1

K5 7.4 Aldebaran, α Tau –0.7

K7 8.1 Alsciaukat, α Lyn –1.1

M0 8.7

M1 9.4 Scheat, β Peg –1.5 Antares, α Sco –5.3

M2 10.1 Betelgeuse, α Ori –5.3

M3 10.7

M4 11.2

M5 12.3 Ras Algethi, α Her –2.3

M6 13.4

M7 13.9

M8 14.4

Analysis and Interpretation of Astronomical Spectra 112

24.4 Distance Modulus
The distance modulus is defined by the difference between the apparent- [m] and absolute
magnitude [M], expressed in the generally used, logarithmic system of the photometric
brightness levels [mag].

In contrast to the Apparent Distance Modulus , the so called True Distance

Modulus applies to the simplified calculation, assuming no Interstellar Extinction,

[12].

24.5 Calculation of the Distance with the Distance Modulus

Assuming no Interstellar Extinction, the relationship between the distance and the

True Distance Modulus can be expressed as:

If the interstellar extinction is considered, must still be added:

( average interstellar extinction .

By logarithmic transforming can be expressed explicitly:

According to [12] in worst case, ie within the galactic plane, results . If

dark clouds are located on the line of sight, may rise up to 1 to 2 . Further it

becomes recognisable, that the extinction starts normally to be noticable not until about
100 pc.

Anyway [58] proposes the rule of thumb to take for the solar neighbor-

hood. The problem here is that depends also on the desired distance {69}.

24.6 Examples for Main Sequence Stars (with Literature Values)

Sirius, α Cma A1Vm m=–1.46 M=1.43 r = 2.64 pc = 8.6 Lj

Denebola, β Leo A3V m= 2.14 M=1.93 r = 11.0 pc = 36 Lj

61 Cyg A, K5 m= 5.21 M= 7.5 r = 3.5 pc = 11 Lj

Analysis and Interpretation of Astronomical Spectra 113

25 Identification of Spectral Lines

25.1 Task and Requirements

With the line identification, to an absorption- or emission
line with the wavelength , the responsible element or
ion is assigned. Considered purely theoretical this would
have to be relatively simple, as shown by the adjoining
excerpt of the "lineident" table, provided by the Vspec
software. In practice, however, inter alia the following
should be noted:

– The spectrum must show a high S/N ratio, further be
calibrated very precisely and adjusted by possible
Doppler shifts. Only that way we can exactly deter-
mine the wavelength of each line.

– The higher the resolution of the spectrum, the more
accurate can be determined and the fewer lines are
merging into so-called “Blends”.

25.2 Practical Problems and Solving Strategies

However the table shows, that in certain sections of the spectrum, the distances between
the individual positions are obviously very close. This happens from quantum mechanical
reasons for several of the metal lines, generating corresponding ambiguities, especially in
stellar spectra of the medium and later spectral classes.

Commonly concerned are also noble gases, as well as the so-called rare earth compounds
– eg praseodymium, lanthanum, yttrium etc. Such we find in the spectra of gas-discharge
lamps, acting here as dopants, alloy components and fluorescent agents.

Here, in most of the cases, helps the process of elimination. Most important is the knowl-
edge of the involved process temperature. For stellar spectra it is supplied by the according
spectral class. With this parameter the graphic at the end of sect. 13.11, provides on one
hand possible proposals, but excludes a priori also certain elements or corresponding ioni-
sation stages. As there already discussed, eg for normal photospheric solar spectra, Helium
He I can be excluded.

At certain stages of stellar evolution, detailed knowledge of the involved processes are
necessary. Since e.g. stars, in the final Wolf Rayet stage, first of all repel their entire outer
hydrogen shell, this element can therefore subsequently hardly be detected in such spec-
tra. Critical is here the mostly very significant He II emission at 6560.1 Å, which is often
misinterpreted by amateurs as Hα line at 6562.82 Å, see [33] tables 5 and 6.

Relatively easy is the line identification for calibration lamps with known gas filling. Thus
Vspec allows the superimposing of the corresponding emission lines, with their relative in-
tensities, directly into the calibrated lamp spectrum (see below). For such "laboratory spec-
tra" in Vspec [411] the "element" database has proven (Tools/Elements/element). For stel-
lar profiles, however, the "lineident" database is to prefer (Tools/Elements/lineident).

In cases of unknown gas filling, on a trial basis, the emission lines of the individual noble
gases He, Ne, Ar, Kr and Xe can be superimposed to the calibrated Lamp spectrum. In most
cases already the pattern of these inserted lines instantly shows, if the corresponding ele-
ment is present or not. This was also the most successful tactic for the line identification in
[32] [33] [34] [35]. However some of the noble gas emissions can be located very close to
each other such as Ar 6114.92 Å and Xe 6115.08 Å, see [33] Table 102.