3D Model Atmospheres of White Dwarfs

Pier-Emmanuel Tremblay, N. Gentile Fusillo, E. Cukanovaite, T. Cunningham,H. Ludwig, B. Freytag, M. Steffen

1D Mixing-Length TheoryPrandtl (1926, Proc. Sec. Conf. App. Mec.)Böhm-Vitense (1958, Z. Astrophys.)

Mean free path vs. First principles(free parameters) (numerical parameters)

3D Radiation HydrodynamicsNordlund (1982, A&A), Pomraning (1973 book)

CO5BOLD, MURaM, and Stagger codes(comparison in Beeck et al. 2012, A&A)and a few other codes.

Models of convection

3D model atmospheresfluid mechanics w/ gravity field and radiation

• Mass conservation

• Momentum conservation

• Energy conservation requires solving radiative transfer at each t

Input parameters

• log g + radiative flux (closed bottom) / entropy of inflow (open bottom)

• EOS / opacities (same as 1D or with additional approximations)

• No free parameter

• Size of the box, time and spatial resolution, boundary conditions, viscosity

• White dwarfs same as the Sun except for EOS / opacities

CO5BOLD simulations (Freytag et al. 2012)

The SunTeff = 5800 Klog(g) = 4.44

White dwarfTeff = 6000 Klog(g) = 8.00

Brown dwarfTeff = 1500 Klog(g) = 5.00

SupergiantTeff = 4500 Klog(g) = -0.40

Sun simulated

Sun observed

1D3D

The Sun

Nordlund et al. 2009, Living Reviews

White dwarf CO5BOLD simulationsPure-hydrogen (Tremblay et al. 2011, 2013a,b,c, 2014a, 2015a,b,c)

Teff = 6000 K Teff = 12 000 K log(g) = 8

120m

log g = 8Te ff = 10,000 Klog g = 6.0

1D

surface

bottom ofatmosphere

Teff = 10 000 K, log g = 8.03D

1D ML2/α=0.8

2nd step: full radiative transfer

3D

1DML2/α=0.8

Teff = 10000 Klog g = 8.0

1D to 3D Teff/log(g) corrections for DA white dwarfs(Tremblay et al. 2015b, ApJ)

1.5D

DA white dwarfs in the SDSS1D models (Tremblay et al. 2011, ApJ)

DA white dwarfs in the SDSS3D models (Tremblay et al. 2013c, ApJ)

Essentially no impact from numerical parameters

White dwarf CO5BOLD simulationsPure-hydrogen (Tremblay et al. 2014a & in prep.)

Teff = 3500 K Teff = 16500 K log(g) = 8

3D convection zones

Unstable: Convection zone in 1D and 3D

1D Stable: Convection zone in 3D (Fconv > 0)

1D Stable: Overshoot zone in 3D (Fconv < 0)

1D Stable: Overshoot zone in 3D (Fconv = 0, v > 0)

Te ff = 10,000 Klog g = 8

Bottom ofatmosphere Surface

Resolved 3D

Tremblay et al. 2015a, ApJ

Tremblay et al. 2015a, ApJ

Calibration of mixing-length for structures

1D definition(entropy)

3D convectiveflux profile

Mixed masses in accreting white dwarfsSee poster by Tim Cunningham

Teff = 12 000 K, log(g) = 8.0Tracers for 155 seconds

0s 10s 20s… 1D convection zone

Cooling rates do not depend (directly)on convection for Teff > 6000 K

radiativeconvective

Tremblay et al. 2015c, ApJ

DB white dwarfsSee poster by Elena Cukanovaite

Teff = 14 000 K Teff = 24 000 K log(g) = 8

1D to 3D Teff/log(g) corrections for DB white dwarfsPlot taken from Elena Cukanovaite’s poster

Magnetic white dwarfsSee poster by Nicola Gentile Fusillo

B = 0 kG B = 5 kG

Teff = 10 000 K, log(g) = 8

HST/COS evidence of radiative atmosphere for WD2105-820See poster by Nicola Gentile Fusillo

Conclusions

• Improved 3D atmospheres.Effectively no free parameters for model spectra, thermal structures.

-> DA, DB, magnetic white dwarfs -> no observable 3D effects under adiabatic conditions

(ultracool WDs, DC, and likely DZ and DQ)

• Challenge to understand overshoot and mixed masses in evolved planetary systems

• Challenge to understand time-domain white dwarf research(magnetic variability, pulsating WDs, outbursts, etc)

• Test of all WD models with Gaia DR2

Postdoc position soon in Warwick!