Chapter 15 – Measuring Pressure (con’t) Temperature spans a factor of 10 or so from M to O stars...
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Transcript of Chapter 15 – Measuring Pressure (con’t) Temperature spans a factor of 10 or so from M to O stars...
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…)