1. Chapter 15 – Measuring Pressure (con’t) Temperature spans a factor of 10 or so from M to O stars Pressure/luminosity spans six orders of magnitude from white dwarfs to supergiants Pressure indicators –Continuum (Balmer jump) –Hydrogen lines (Stark broadening) –Other strong lines (van der Waals broadening) –Weak lines –Molecular features

2. Molecules Hydrides, oxides, other diatomic molecules (CN, C 2 ) Molecular equilibrium depends on pressure Different molecules depend on pressure in different ways Molecules are also sensitive to other abundances (C 2, for example – C and O) Molecules in these spectra include –TiO (6200-6300) –CN (4215, 3883) –CH (G-band, 4300) –MgH (5200, near Mgb lines) K4 V K4 III

3. Disentangling Temperature and Pressure Weak lines vary with both pressure and temperature Pressure can be determined independently if lines from two different ionization states are present (Fe I and Fe II, Ti I and Ti II) Generally, fix temperature & abundance from neutral lines, set gravity so ionized lines agree with abundance from neutral lines

4. Getting Temperature and Pressure Simultaneously Select lines sensitive to pressure (preferably weak ones – why?) Assume metallicity and microturbulence Determine log g vs. T eff curve that produces correct equivalent width for each line Intersection of all such curves should be the correct temperature and gravity

5. In reality… Various temperature, pressure methods subject to uncertainties Temperature and gravity often not well constrained Hundt et al. 1972, A&Ap, 21, 413; “Analysis of the Spectrum of the Metal Line Star 63 Tau”

6. The Wilson-Bappu Effect The strength of the emission in the core of the Ca II K line is a function of luminosity Empirical calibration (for giants): M v = alogW 0 + b Uncertainty ~ 0.5 mag (1  ) ditto for Mg II h&k lines Higher luminosity > Bigger radius > Lower gravity > More gradual drop in pressure > More extended chromosphere > More emission Wilson 1976, ApJ, 205, 823

7. Helium Can’t see it in stars cooler than A0… but it’s there! He increases mean molecular weight of gas – larger pressure at a given optical depth because the mass absorption coefficient is less Effects generally modest for small changes in the He abundance But note He rich stars – supergiants, hot subdwarfs, HB stars, post-AGB stars, white dwarfs

8. Surface Gravities from Binaries Visual binaries - well determined orbits + parallax > masses Eclipsing binaries > accurate masses independent of distance Inferring Gravity Spectral type Log g vs. (B-V) Matching stellar evolution models (T eff and M v ) (recall Arcturus…)