Lecture 15: Stellar Atmospheres, Variable Stars

Stellar Atmospheres: How the layers above the photosphere affect a star's spectrum

What controls the widths and strengths of spectral lines?

    What is observed:

        The "strength" of a spectral line is the area of the spectral line in a wavelength versus intensity plot -- often expressed as "equivalent width".

To understand what effects the width and strength of a line, remember what causes a spectral line: individual atoms or molecules containing electrons that change orbits.

Some nomenclature:

If an atom has had an electron completely removed, it is said to be ionized. "Neutral" H, meaning that its electron is still preset, is designated as HI while ionized hydrogen is HII. Note that elements with more electrons can have values like FeIX meaning that 8 electrons have been removed.

Strength of a line: Depends on the number of atoms/molecules with electrons in the starting orbit for the spectral line under consideration. For example, the H- line at 656.3 nm involves an electron moving from level 2 to level 3 when it is seen in absorption. For the H atoms to have electrons in level 2, they must already have absorbed a photon which raised them from level 1 to level 2 -- a very cold region won't have any H- absorption because there are no atoms with electrons in level 2. The text in Chapter 4 shows how a branch of physics called "statistical mechanics" can be used to compute the relative numbers of atoms in different states -- the number depends on the total number of atoms present and the temperature.

In figure below, N = total number of H atoms, N₁= number with electrons in ground state, N₂= number with electrons in level 2, N₊= number of ionized atoms.

The number in each state is a function of temperature.

The strength of a spectral line, measured by the equivalent width, depends on the number of atoms along the line of sight that are in the correct state to absorb a photon:

If we measure the equivalent width, we are measuring how many photons have been absorbed and assumming that we can measure the absoprtion coefficient for the atom in question in a laboratory, we can get N and hence the "abundance" of the element in the star. Actual measurement is tricky because we don't know L and have to either give the aubndace relative to hydrogen or have some more complicated scheme for estimating L.

Width of a line: Depends on a number of factors:

• Natural broadening results from the fact that quantum mechanics shows that the energy of an electron cannot be specified (or known) any more accurately than

           

• Thermal Broadening is due to the motions of the atoms due the fact that they are at some temperature T:

               

• Collisional broadening results from collisions between atoms -- depends on the frequency of collisions and hence on the density of the gas
• Any motion of the atoms will result in a Doppler shift. This can either change the observed wavelength of a line or if a collection of randomly moving cloudlets is being observed, the line may also get broader.

Any star whose output varys, regardless of the cause, is called a variable star.

The tradition for naming variable stars is that the first to be found in a constellation is given the name R ConName where ConName = name of the constellation. The second is S ConName and then through Z; the names then go to RR through RZ, SS to SZ, and so on through ZZ. The names then go to AA and so on. If a constellation has many variables, the names will go to the form V335, V336 and so on.

Categories of Variable Stars:

Pulsating variables: change size in a repeatable fashion.

    -- RR Lyraes,  P~1 day

    -- Cepheids, P~1 to 50 days

    -- Pop II Ceps = W Vir stars, P~2-45 days

    -- Long period vars (Miras), P~100-500days

    -- RV Tauri stars, P~20 to 150 days

-- semi-regular vars, P~100 to 200 days

    -- various stars with periods measured in hours

The light output from pulsating variables changes because the star is expanding and contracting (and hence cooling off and heating up).

Notice how the brightness changes are related to the changes in temperature and radius. Phase refers to the fraction of the star's period.

Recall that

If you can measure the temperature at each time, you can compute the ratio of the radii.

You can also understand the P-L relations for such stars: it results from higher mass stars having higher luminosities. The more massive the star, the longer the period.

Think of the outer layers of the star being in a radial orbit with respect to the star's core. The outer layers would have to obey Kepler's 3rd Law:           

The period of a pulsational variable is inversely proportional to the square root of its density -- low density, red giants have long periods while the much higher density Cepheids have short periods.  Recall that the central temperature of a star is proportional to the central pressure/density confirming that longer periods go along with higher central temperatures which produce higher luminosities.

Non-pulsating variables include

    -- T Tauri stars which are pre-main sequence stars that have not yet reached hydrostatic equilibrium. Their variability is likely an extreme form of magnetic storms and flares.

    -- Flare stars are young M dwarfs where an event as energetic as a typical flare on the Sun can increase the brightness of these dim stars by factors of two or even more.

Together, T Tau stars and flare stars suggest that stars have stronger magnetic fields and related activity than older stars. Young stars are also known to rotate much more rapidly than the Sun which may explain the higher activity. Do stars slow down when older because the angular momentum gets transferred to planets?

    -- Magnetic variables have variable spectra and strong magnetic fields. One explanation may be that the magnetic and rotation axes are not aligned.

    -- RS CVn stars are binary stars with rotation rates synchronously locked to their few day orbital periods. The rapid rotation drives magnetic activity and flares.

    -- Cataclysmic and eruptive variables include novae and supernovae.

    -- Eclipsing binaries are binary stars where we see the orbits nearly edge-on. The shape of the light curve gives an indication of the inclination of the system: