White Dwarf Atmospheres

Pierre BergeronUniversité de Montréal

Sirius B

What is a stellar atmosphere?

What is a stellar atmosphere?

Atmosphere

Input parameters

• Effective temperature (Teff)

• Surface gravity (log g)

• Atmospheric composition (NHe/NH, Z)

• Rotation

• Magnetic field

• Mass loss

« If the Sun did not have a magnetic field, it would be as boring a star asmost astronomers believe it to be »

(attributed to R.B. Leighton)

center surface

Basic structure

center surface

Basic structure

Gilles

Fontaine

Photosphere

H conv

He conv

P/g 270 km for the Sun

What are white dwarfs showing us ?

80% are DA stars 20% are «non-DA stars»

DB

DA

DB

DA

Gravitational settling

Magnetic White Dwarfs

Basic Atmospheric Equations

H : Radiation (Eddington) Flux

Opacity calculations cross-section + population calculations

bound-bound transition

bound-free transition

free-free transition

scattering

Population calculations

• Local Thermal Equilibrium (LTE) Saha / Boltzmann

• Non-local Thermal Equilibrium (NLTE) Statistical equilibrium equation

• Equation of state (ideal gas, but not always…)

H b-f

H f-f

H–

H+2 f-f

e-scat

+ hydrogen lines

(Stark broadening)

H–

H+2 f-f

H b-f

H2– f-f

H f-f

H– b-f / f-f

H2– f-f

H2 collision

induced opacity

Temperature structure Emergent (Eddington) flux

Boundary conditions for stellar interior models

Measuring atmospheric parameters using model atmospheres :Spectroscopic technique

NLTE

convective

Flux calibration is difficult…

Flux calibration is difficult…

Balmer line profiles are sensitive to both Teff and log g

Balmer line profiles are sensitive to both Teff and log g

Stark broadening

atomic level destruction

i

Hummer-Mihalas occupation probability formalism

j

i

j

i

Hummer-Mihalas occupation probability formalism

j

i

j

photoexcitation(bound-bound opacity)

i

j

i

photoionisation(bound-free opacity)

κ

e−

wj

wj ››

wj ‹‹

occupationprobability

i

Hummer-Mihalas occupation probability formalism

j

i

j

photoexcitation(bound-bound opacity)

i

j

i

photoionisation(bound-free opacity)

κ

e−

wj

wj ››

wj ‹‹

occupationprobability

Spectroscopic technique used for measuring Teff and log gσ(Teff) = 1.2 % Teff σ(log g) = 0.038 dex

log g converted into mass using the mass-radius relation for WDs(mechanical structure provided by degenerate electrons)

log g ~ 8

Smallerradii !

log g converted into mass using the mass-radius relation for WDs

Mass and log g distributions of 770 DA stars

Chandrasekhar mass ~ 1.36 M⊙

Chandrasekhar mass ~ 1.36 M⊙

electronsbecome

relativistic

ZZ Ceti stars + photometrically constant white dwarfs

Mass distribution as a function of Teff

DA stars from the SDSS / DR4

high-log g problem

Mass distribution as a function of Teff

DA stars from the SDSS / DR4

high-log g problem

Application to DB (helium-line) white dwarfs

Application to DQ (carbon-line) white dwarfs

Application to DZ (metal-line) white dwarfs

Application to hot DO (helium-line)

white dwarfs

Application to DC (featureless!) white dwarfs

Stellar flux integrated over filter bandpasses (magnitudes)

http://www.astro.umontreal.ca/~bergeron/CoolingModels/

http://www.astro.umontreal.ca/~bergeron/CoolingModels/

For Dummies

Photometric method

fλ = π (R/D)2 4Hλ

Hλ = Hλ(Teff , log g)

D = 1 / π

g = GM / R2

M-R relation for WDs

Hybrid spectroscopic and photometric approach

Application to «ultracool» white dwarfs

H2 collision-induced absorption (CIA)

DB gap

Cooling time →

G. Fontaine & F. Wesemael (1987, 2nd conf. on Faint Blue Stars)

DB gap

Cooling time →

Evidence for the spectral evolution of white dwarfs

H → HeHe → H

G. Fontaine & F. Wesemael (1987, 2nd conf. on Faint Blue Stars)

He

H

Photosphere

He

H

DO DA

Photosphere

Requires only10-16 M

of

hydrogen

Photosphere

HeII conv

HeI conv

Photosphere

HeII conv

HeI convH

He

Convective dilution DA DB

Photosphere

H conv

Photosphere

H conv

H

He

Convective mixing DA ???

Photosphere

H conv

H

He

Convective mixing DA ???

Photosphere

H conv

H

He

Convective mixing DA ???

Origin of carbon in DQ stars

Helium convection zone

Helium convection zone

Carbon core (diffusion tail)

Helium convection zone

Carbon core (diffusion tail)

Carbon in DQ stars is being dredged up from the core

The Z in DZ stars !