Mass-loss and diffusion in subdwarf B stars and hot white dwarfs: do weak winds exist?

Context. According to previous investigations, the effect of diffusion in the stellar atmospheres and envelopes of hot white dwarfs and subdwarf B (sdB) stars strongly depends on the presence of weak winds with mass-loss rates $\dot M$ < 10-11 $M_{\odot}/\rm yr$. Aims. As in most of these stars with luminosities $L /L_{\odot}$ $\la$ 100, no wind signatures have been detected, the mass-loss rates are unknown. In the present paper mass-loss rates are predicted from the original theory of radiatively driven winds. Methods. The method of solution is modified so that the usual parametrization of the line force multipliers is not necessary. This is important especially for very thin winds. In addition we checked whether a one-component description is justified. As a consequence of various simplifications, the mass-loss rates are expected to be overestimated. Results. Results are presented for effective temperatures in the range 25 000 K ≤ Teff ≤ 50 000 K and for various metallicities between solar and $Z / Z_{\odot}$ = 0.01. For (pre-) white dwarfs and sdB stars a stellar mass of $M_{*}$ = 0.5 $M_{\odot}$ is assumed. For fixed values of Teff, $M_{*}$, and Z, the results predict decreasing mass-loss rates with increasing surface gravity and an increasing dependence of the mass-loss rates on the metallicity. For white dwarfs with log g > 7.0 no wind solution exists even if the metallicity would be solar. Winds with mass-loss rates around 10-11 to 10-10 $M_{\odot} / \rm yr$ are predicted for the most luminous sdB stars with surface gravities of log g $\la$ 5.5, if the metallicity is not significantly lower than solar. For lower values of $\dot M$ metals decouple from hydrogen and helium. Conclusions. If weak winds with $\dot M$ $\la$ 10-12 $M_{\odot} / \rm yr$ exist, the metals cannot be coupled to hydrogen and helium. This should lead to additional changes in the surface composition, which have not yet been taken into account in the diffusion calculations with and without mass-loss. A possible scenario is the existence of pure metallic winds with mass-loss rates of $\dot M$ $\la$ 10-16 $M_{\odot} / \rm yr$ and with hydrostatic hydrogen and helium.