Stellar Spectra

Friday, Feb. 7, 2025

astrophysics of stars and planets - spring 2025 - university of arizona, steward observatory

Today’s Agenda

1. Announcements (2m)

2. Reading Overview/Key Points (10m)

3. In-Class Activity 8 (20m)

4. Debrief/Reminders (2m)

Spectral types or classes

See Appendix A of HKT for more details

Henry Draper classification scheme, which is based on the appearance of spectral lines of hydrogen, helium, and various metals.

The current spectral classification scheme was developed at Harvard Observatory in the early 20th century. Work was begun by Henry Draper who photographed the first spectrum of Vega in 1872. After his death, his wife donated the equipment and a sum of money to the Observatory to continue his work. The bulk of the classification work was done by Annie Jump Cannon from 1918 to 1924. The original scheme used capital letters running alphabetically, but subsequent revisions have reduced this as stellar evolution and typing has become better understood. The work was published in the Henry Draper Catalogue (HD) and Henry Draper Extension (HDE) which contained spectra of 225,000 stars down to ninth magnitude.

The International Astronomical Union adopted Cannon’s method as the official spectral classification system. In addition to her scientific work, Cannon also worked for women’s rights. She was dedicated to fighting for women’s suffrage and was a member of the National Women’s Party.

O star - strong HeII (second ionization) lines of helium. Since the ionization potential is high, such stars are the hottest in terms of effective temperature.

B star - Spectral type “B” stars show strong HeI plus some HI lines.

A to F star - The Balmer lines (spectral line emissions of the hydrogen atom) reach their peak in the “A” stars and begin to disappear in “F”.

G star - Calcium H&K lines strengthen.

K star - show other metallic lines

M star - The “M” stars have strong molecular bands (particularly TiO).

L star - Spectra show strong metal-hydride molecular bands (CrH & FeH), and neutral metals, but TiO and VO bands are nearly absent.

T star - Spectra show strong bands of Methane (CH4), like the spectrum of Jupiter.

The effective temperatures decrease in the order O, B, A, F, G, K, M, L, and T

Subdivisions such as G0, G1, G2, etc. are in order of decreasing temperature. The sun is a G2 spectral class star.

Spectra of main sequence (luminosity class V) stars of spectral classes O–M derived from the work of Silva and Cornell (1992).

For reference:

Name	Wavelength intervale unit
Extreme ultraviolet	< 1000 Angstrom
Ultraviolet	1000-3000 Angstrom
Classical	3000-4900 Angstrom
Visual	4900-7000 Angstrom
Near infrared	7000-10\(^5\) Angstrom
Far infrared	1-10\(^3\) \(\mu\)m
Radio	0.1-10\(^4\) cm

Luminosity classes

The Morgan–Keenan (MK) classification uses spectral class and luminosity class as a two- dimensional scheme to phrase the HR diagram another way.

Luminosity class I stars - are the most intrinsically luminous. Because they are usually large (especially the cooler ones) they are also called supergiants.

Luminosity class II (giants) are intrinsically bright, but not as bright as class I.

The numbers increase until luminosity class V is reached. These are the dwarfs and primarily refer to main sequence stars.

The sun is a G2V star. An M3I star is huge, intrinsically very luminous, and very cool.

Line Profiles and the Curve of Growth

We can describe absorption of radiation by a classical oscillator assuming that the atoms are not moving producing a Lorentz profile or Lorentzian or as a Doppler-shifted cross section with the velocity distribution to get an ensemble average for the cross section.

Shown is the behavior of the absorption cross section from pure Lorentzian (\(\delta \nu_{D} = 0, T = 0\)) to lines well-broadened by increasing temperature. The natural width is taken so that \(\gamma/4\pi = 1\).

For the stationary case, \(\nu_{0}\) is the photon frequency necessary to promote an electron to a particular higher state and \(\gamma\) is the sum of the damping constants for the two levels involved.

Doppler width - that measures the half-width at half-maximum of the cross section if Doppler broadening dominates over the natural line width \(\gamma\).

The evolution of a spectral absorption line with increasing number density of absorbers is shown for sample values of \(\beta_{0}\).

The more absorbing atoms in the path, the more the attenuation; that is, the radiation acts as a probe of both the abundance of absorbing atoms and their temperature.

In practice, the equivalent width is often measured instead

Definition 74

\[ W_{\nu} = \int^{\inf}_{0} \left ( 1 - \frac{I_{\nu}}{I_{0}} \right ) d \nu = \int^{\inf}_{0} (1-e^{\beta_{0}}) d \nu \]

The solid curve is the curve of growth corresponding to the line profiles of Fig. 4.10 with \(a = 10^{−3}\). For \(a = 10^{−2}\) (dashed line) the damping portion of the curve begins sooner because \(\delta \nu_{D} \) has been reduced.

For small \(\beta_{0}\) (weak line), \(W_{\nu} \approx \beta_{0}\) so that on a log–log plot we have a straight line. (See Mihalas, 1978, §10–3 for more details.) Hence the “linear region” in the figure. In the saturated section, \(W_{\nu} \sim \sqrt{\rm{ln}\beta_{0}}\), which is a mild dependence on \(\beta_{0}\) and thus the curve rises very slowly. For large \(\beta_{0}\), \(W \sim \beta^{1/2}\) and we have a straight line again, but not as steep as the linear \(\nu_{0}\) region.

In-Class Assignment

In-Class Assignment 8 on the opacities is here.