The problematic modelling of RCrB atmospheres Bengt Gustafsson Department of Astronomy and Space Physics Uppsala University Hydrogen-Deficient Stars Tübingen, September 2007

Standard MARCS models 1D (plane-parallel or spherically symmetric) Detailed blanketing LTE Mixing-Length Convection See Asplund, Gustafsson, Kiselman & Eriksson (1997): A&A 318, 521 Asplund, Gustafsson, Lambert & Rao (2000): A&A 353, 287 as well as Eriksson, Edvardsson, Gustafsson & Plez (2007), in preparation

No HI and H - opacity => Heavy blanketing => Steepened grad T

Increasing T eff => increasing  => decreasing  and P g, unaltered P e.

Model-structure variations with fundamental parameters

/, Density inversion -- Super Eddington?

/, < 0 in ioniz. zone >1 < 0

/, Density inversion -- Super Eddington? < 0 in ioniz. zone >1 < 0 => < 0 Density inversion occurs (first) due to ionization -- not radiative force

Yet,  >1 does not automatically lead to mass flows -- a positive pressure grandient may balance Additional effects due to P dyn Instabilities deserve further studies! Border case at  = 1?

Super-Eddington luminosities cause RCB declines? From Asplund & Gustafsson (1996), ASP Conf. 96, 39 RCB:s evolve from right to left: Expansion => Cooling => Stability LBV:s from left to right: Expansion => Cooling => Instability Yet very uncertain whether effect works, See Asplund (1998), A&A 330, 641 Effects of spheriicity and convection!

Low H increases line blanketing from C I and other atoms => flux pushed redwards. So does also C I continuum

Dominating opacity sources Total He I Mg e-e- C I He - N I See also Pavlenkos talk!

A reasonable fit to observed fluxes

C I lines at Å  ~ 8.5 eV gf values from TOP data base W ~ l /  mainly from C I bf,  ~ 9.2 eV Data also from TOP Incidently, also other opacities (He -, C -, e - ) reflect C abundance since most electrons come from C

C = [C] pred - [C] obs

A real problem! ”The Carbon Problem”

What could be the reason? Errors in FP:s? No! Errors in codes etc? No! W ? No! Extra-photospheric flux? (> 3x photosp., No!) Basic atomic data for C I in error? (~10-30%, much too little!) C I opacity not dominant? (C/He = 1%, must be lowered by more than x 20, inconsistent with hot RCrB stars and EHe stars) NLTE? (~ 2%, Asplund & Ryde 1996, No (?)) Model atmospheres? - incomplete opacities? - sphericity? - dep. from hydrostatic equilibrium? Hardly! - temperature inhomogeneities? Not per se - errors in structures due, e.g. due to dynamical fluxes

, New better opacities  More heavy blanketing  Steeper grad T Sphericity => Steeper grad T Effects on abundances : ~ ± 0.1 dex New MARCS New Marcs models (Eriksson et al. 2007, in prep) Goes the wrong way for C I!

Decrease grad T in C I -line forming layers! This works reasonably well but requires F heat ~ 4  P  (4T 3  T)s ~ 10% F tot Compare to F mech ~  v turb 3   v turb ~ 40 km/s

C problem also for [CI] Pandey et al. (2004), MNRAS 353, 143

… however not for C II (?)

No real progress in 8 years. Errors in abundances at least x2 - x4 in absolute numbers. Time to resolve this now?

No real progress in 8 years. Errors in abundances at least x2 - x4 in absolute numbers. Time to resolve this now? ”Truth is the daughter of time, and I feel no shame of being her midwife” Johannes Kepler