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

Molecules• Hydrides, oxides, other

diatomic molecules (CN, C2)

• Molecular equilibrium depends on pressure

• Different molecules depend on pressure in different ways

• Molecules are also sensitive to other abundances (C2, 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

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

Getting Temperature

and Pressure

Simultaneously

• Select lines sensitive to pressure (preferably weak ones – why?)

• Assume metallicity and microturbulence• Determine log g vs. Teff curve that produces correct

equivalent width for each line• Intersection of all such curves should be the

correct temperature and gravity

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”

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):Mv = alogW0 + 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

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

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 (Teff and Mv)

(recall Arcturus…)