7 Stellar Spectra and Stellar Classification (Contd)

V. B. Bhatia

1. Learning Outcomes

After studying this module, you should be able to

appreciate that there is great diversity in stellar spectra and all stars cannot be accommodated in the eight major classes O, B, A, F, G, K and M
describe the new classes Q, P and W (Wolf-Rayet Stars) introduced before class O
state special features of Wolf-Rayet stars
name the suffixes and prefixes which are used to describe the characteristic features of some stars
explain the insertion of new classes like R, N and S classes after M stars
appreciate that R and N stars have bands of carbon compounds while the S stars have bands of ZrO
understand that the Harvard classification scheme is based on the decreasing surface temperature from class O to M
derive the expression for the fraction of hydrogen atoms in excited states

2. Introduction

In the last module (Module 11) we introduced the spectral classification of stars. We explained the nature of the spectra as that containing mainly absorption lines. We discussed the variety in the spectra of stars. Even within this variety it was possible to discern patterns. There are stars with a very few lines. On the other hand, there are stars with huge number of lines and molecular bands. On the basis of the increasing complexity in the stellar spectra, Annie Cannon was able to devise a simple classification scheme, known as Harvard Stellar Classification System. Seven major classes, O, B, A, F, G, K, and M were identified on the basis of their spectra. Each major class was subdivided into ten sub-classes. For example, class A9 is followed by F0, which, in turn, is followed by F2. It was pointed out that the stars belonging to the first three major classes, that is, classes O, B and A are called the early type stars, while the stars belonging to the last four major classes are referred to as late type stars. Stellar spectra are much more diverse than we have noticed so far. We now dwell upon this complexity. Later, following M. N. Saha, we will attempt to account for the classification scheme in terms of the decreasing stellar surface temperature.

3. Diversity in Stellar Spectra

The stellar spectra show more complexity and diversity than we took notice of in the last module. Therefore, the spectral classification outlined above is not adequate to describe all the observed spectra. Three major classes (to which decimal subdivision is not applicable) before class O, and many prefixes and suffixes are used in conjuction with the spectral classes to describe comprehensively the spectra of many stars.

3.1. Wolf-Rayet Stars

The classes placed before O are Q, P and W, all hot stars showing emission lines. P stands for planetary nebula, believed to be the stage in the evoltion of a star just before it becomes a white dwarf star. W stars are Wolf-Rayet stars, named after two the French astronomers who studied them. The Wolf-Rayet stars show in their spectra broad and intense emission lines of ionized carbon, nitrogen and helium.

Fig. 12.1. Spectra of Wolf Rayet star WR137. Notice the intense emission lines of ionized carbon. (Source: Source: Wikipedia – Spectrum of Wolf-Rayet star WR137 by Gypaete )

Wolf-Rayet stars are very hot stars, Their surface temperatures range from ~ 30000 K to ~ 50000 K. These stars are very luminous; the mean absolute magnitude is ~ -5. They are about 10 times as massive as the Sun. The stars of this mass tend to have very strong stellar winds.

These winds blow away as much matter as 10-4 ?⨀ per year, leaving behind a thin atmosphere, through which we are able to observe the central region of the star. This region is rich in carbon and nitrogen. It appears, therefore, that the Wolf-Rayet stars are helium burning stars (second stage after hydrogen burning), producing carbon and nitrogen whose lines we see in their spectra. The central temperatures may be of the order of 108 K. Clearly, Wolf-Rayet is a stage in the evolution of a star, lasting a few hundred thousand years.

Fig. 12.2. After hydrogen burning in the core of the star is complete, the temperature rises to 108 K. At this temperature helium burning can commence to supply the energy need by the star to radiate from the surface.

3.2. Scheme of Prefixes and Suffixes to Denote Special Characteristics of Spectra

An example of a prefix attached to the spectral class of a star is c which denotes that most of the lines in the star’s spectrum have narrow profiles, such as in the star α – Cygni. Some of the other prefixes and suffixes used are the following:

n – denotes wide and diffuse lines;

s – used in spectral classes B and A to denote lines of narrow profiles (but not as narrow as denoted by the prefix c);

e – denotes the appearance of emmission lines in the classes O to M where they are not normally expected. The prefix appearing in classes O and B means that Blamer lines of hydrogen are in emission;

v – denotes the variable spectrum and ev denotes the variable emission spectrum;

k – denotes the presence of H and K lines of Ca+;

p – denotes that the spectrum contains peculiarities not normally found in the spectral class in which the spectrum is classified. In certain stars of class A, for example, the tines of SiII and SrII are exceptionally strong. These stars are designated as Ap stars.

3.3. Addition of Classes R, N and S to the Major Spectral Types

Recall that the late type stars show characteristic bands of TiO molecules. However, a few late type stars are distinguished by the fact that they show strong bands of C, CH and CN, but not of TiO which are so prominent in class M. These stars are classified as R and N stars and are called carbon stars. On the other hand, there is a class of stars which show bands due to ZrO, LaO and YtO. These are called S stars. The bands of ZrO are the defining feature of these stars. The S stars are variable stars with long periods. They are also quite small in number. With the addition of these classes, the complete classification is sometimes written as

Fig. 12.3. HST image of W Aquilae, a Mira variable star, showing the faint companion. (Source: Wikipedia; Hubble Legacy Archive image constructed from blue (F435W) and green/red (F606W) exposures.)

Fig. 12.4. Spectra of R, N and S stars along with the other major classes. (Source: http://prc.nao.ac.jp/extra/uos/ja/no04/ )

Fig. 12.5. Spectra of two S-Type stars. Notice bands due to ZrO, the distinguishing feature of S stars. (Source: htt ps://ned.ipac.cal tech.edu/level5/Gray/Gray31.html )

4. Surface Temperature and Spectral Classification – Saha’s Theory

We have already noted that spectral sequence from simple to complex spectra is a temperature sequence. At the top of the sequence, the surface temperature of O stars is so high that most atoms are ionized. The exception is HeII, which is difficult to ionize a second time. So, these stars show only lines of HeII and a few other lines. As we progress to lower temperatures, first we encounter lines of hydrogen (class A) which has a high ionization potential, and then ionized metal atoms (classes F, G and K). At still lower surface temperatures, even metal atoms cannot be ionized, so we have neutral metal atoms. In classes K and M, the surface temperatures are so low that even molecules cannot be dissociated. In the spectra of these classes we have molecular lines in addition to a host of neutral atom lines.

M. N. Saha, grasped the true meaning of the spectral sequences. He pointed out that the ionization process is like a chemical reaction and is subject to the same conditions of equilibrium as is a chemical reaction. This notion leads immediately to relative numbers of atoms in various stages of ionization existing in equilibrium at a given temperature. Since the intensity of an absorption line is proportional to the number of atoms which can absorb radiation corresponding to this line, and this number being a function of temperature, the intensity of various lines is obtained as a function of temperature. This, then, allows us to understand the spectral classification as classification based on surface temperature of stars.

4.1. LTE and Boltzmann Law of Population of Excited Atomic States

Consider an assembly of various kinds of non-interacting or weakly interacting particles in statistical equilibrium at a certain temperature �. This implies that the assembly is in thermodynamic equilibrium (TE). TE implies thermal, mechanical and chemical equilibria.

However, as we shall discuss later, these conditions are not generally satisfied in stars. The conditions may be very close to TE, and we may assume that TE exists. Such equilibrium is termed as local thermodynamic equilibrium (LTE), to be discussed later.

The number of particles of a given kind in energy range ?and ?+ �?is given by the usual distribution law:

Here d? is the statistical weight or the number of possible quantum states of a single typical particle of the chosen kind between energies ?and ?+ d?. For a non-interacting system, the kind assumed here, the quantum states of a particle of the chosen kind can be enumerated as if the particles of other kinds were not present. The negative sign in the denominator of Equation

Summary

Because of very high diversity in stellar spectra, all spectra cannot be accommodated in the eight major classes of the Harvard System.
Classes Q, P and W (Wolf-Rayet) are added before class O.
Wolf-Rayet stars are very hot stars and contain broad and intense emission lines.
The mass of these stars is ~ 10 ?⨀. These stars have very strong winds.
It is possible that the Wolf-Rayet stars are helium burning stars and represent a stage in the life of a star.
There are several suffixes and prefixes which are used to denote the spectral characteristics of stars.
A few late type stars are distinguished by strong bands of C, CH and CN, but not of TiO. These stars are classified as R and N stars and are called carbon stars.
There are also stars which show bands of ZrO, LaO and YtO. These are called S stars.
S stars are generally variable stars with long periods.
M. N. Saha pointed out that spectral sequence from simple to complex spectra is a temperature sequence.
Boltzmann law of population of excited atomic states is given by .
The fraction of excited atoms of hydrogen is a function of temperature.
There is a rapid decrease in the fraction of excited hydrogen atoms with decreasing temperature.

The basic material is from Textbook of Astronomy and Astrophysicsby V. B. Bhatia, supplemented by diagrams and graphs from the following sources:

http://www.star.ucl.ac.uk/~pac/spectral_classification.html
https://en.wikipedia.org/wiki/Stellar_classification
http://hyperphysics.phy-astr.gsu.edu/hbase/starlog/staspe.html
http://www.atlasoftheuniverse.com/startype.html
https://www.cfa.harvard.edu/~pberlind/atlas/htmls/note.html
https://en.wikipedia.org/wiki/S-type_starhttp://prc.nao.ac.jp/extra/uos/ja/no04/
https://ned.ipac.caltech.edu/level5/Gray/Gray31.html
https://en.wikipedia.org/wiki/Wolf%E2%80%93Rayet_star
https://en.wikipedia.org/wiki/Atmospheric_refraction
https://en.wikipedia.org/wiki/Astronomical_seeing
http://spiff.rit.edu/classes/phys373/lectures/atmos/atmos.html