## Detlev Koester's Astrophysics

### Most important links

Universität KielAstrophysik Kiel

ADS Strasbourg

Simbad

other astrophysical links

### DK papers in ADS

### White dwarf atmosphere models

My models for many spectral types of white dwarfs have been used by many groups and large numbers of individual authors.A recent description of input physics and methods can be found here.

### Thermohaline instability in white dwarfs

### White Dwarf

by John Updike*Welcome, welcome little star!*

I'm delighted that you are

Up in heaven's vast extent

No bigger than a continent.

Relatively minuscule

Spinning like a penny spool

Glinting like a polished spoon

A kind of kindled demi-Moon,

You offer cheer to tiny Man

'Mid galaxies Gargantuan -

A little pill in endless night

An antidote to cosmic fright.

I'm delighted that you are

Up in heaven's vast extent

No bigger than a continent.

Relatively minuscule

Spinning like a penny spool

Glinting like a polished spoon

A kind of kindled demi-Moon,

You offer cheer to tiny Man

'Mid galaxies Gargantuan -

A little pill in endless night

An antidote to cosmic fright.

### A cautionary note on diffusion timescales for white dwarfs

Diffusion timescales have recently been calculated in Koester and Wilken (2006, A & A, 453,1051) and Koester (2009, A & A, 498, 517). In the course of changing the equations describing element diffusion from the version in Paquette et al. (1986, ApJS 61, 197, eq. 4) to the one in Pelletier et al. (1986, ApJ 307, 242, eq. 5), which is more accurate in the case of electron degeneracy, we (D.K.) discovered a typographical error in the former paper. A factor of rho^{1/3} is missing in the second alternative of eq. 21, which we had not noticed before. A rederivation of all our equations uncovered another error by us in the implementation of the contribution of thermal diffusion. These errors have only a very small effect in stars with relatively shallow convection zones, like the DAs. However, for cool DBs with very deep convection zones, the diffusion timescales can get larger by factors 2-3, with correspondingly lower diffusion fluxes. Fortunately, the relative timescales for different elements, which are important for the determination of the abundances in the accreted matter, change much less.We also made several numerical experiments with the calculation of the outer envelopes, which determines the masses in the convection zones. In the helium-rich cool objects, the bottom of this zone reaches mass densities between 1 and 1000 g/cm^3. This range includes the regime of pressure ionization in helium. In the equation of state we use (Saumon et al. 1995, ApJS 99, 713) this regime is not treated explicitely but bridged by a smooth interpolation. The quantity most important for the convection zone calculation is the adiabatic gradient, since the structure is almost exactly adiabatic throughout the zone. Numerical experiments show that because of the cumulative effect of the inward integration a very small change in the adiabatic gradient can change the mass in the cvz by one or two orders of magnitude. As is demonstrated by Fig. 23 in Saumon et al. (1995) the adiabatic gradient is significantly different between various EOS calculations. It can also show irregular behaviour, which is probably not realistic but caused by the numerical calculation of the necessary second derivatives, if the EOS is determined by a Free Energy minimization method. As a consequence, absolute values of diffusion timescales and diffusion fluxes in cool DBs depend on the details of the EOS and may be quite uncertain. We are confident, however, that the relative timescales of different elements are probably correct to within a factor of two.

**Updated tables, which use the convection parameters ML2/0.8 in the case of DAs as recommended by the Montreal group, are available with the following links.**

Diffusion timescales for hydrogen-rich white dwarfs (DA, DAZ)

Diffusion timescales for helium-rich white dwarfs (DB, DBZ, DC, DZ)