Coupling hydrodynamics with comoving frame radiative transfer

Abstract

Context. For more than two decades, stellar atmosphere codes have been used to derive the stellar and wind parameters of massive stars. Although they have become a powerful tool and sufficiently reproduce the observed spectral appearance, they can hardly be used for more than measuring parameters. One major obstacle is their inconsistency between the calculated radiation field and the wind stratification due to the usage of prescribed mass-loss rates and wind-velocity fields. Aims. We present the concepts for a new generation of hydrodynamically consistent non-local thermodynamical equilibrium (non-LTE) stellar atmosphere models that allow for detailed studies of radiation-driven stellar winds. As a first demonstration, this new kind of model is applied to a massive O star. Methods. Based on earlier works, the PoWR code has been extended with the option to consistently solve the hydrodynamic equation together with the statistical equations and the radiative transfer in order to obtain a hydrodynamically consistent atmosphere stratification. In these models, the whole velocity field is iteratively updated together with an adjustment of the mass-loss rate. Results. The concepts for obtaining hydrodynamically consistent models using a comoving-frame radiative transfer are outlined. To provide a useful benchmark, we present a demonstration model, which was motivated to describe the well-studied O4 supergiant ζ Pup. The obtained stellar and wind parameters are within the current range of literature values. Conclusions. For the first time, the PoWR code has been used to obtain a hydrodynamically consistent model for a massive O star. This has been achieved by a profound revision of earlier concepts used for Wolf-Rayet stars. The velocity field is shaped by various elements contributing to the radiative acceleration, especially in the outer wind. The results further indicate that for more dense winds deviations from a standard β-law occur.

Driving classical Wolf-Rayet winds: A Γ- and Z-dependent mass-loss

“…In fact, we even see this in OB models, such as the HD calculations for ζ Pup (Sander et al 2017) and Vela X-1 (Sander et al 2018). It is also hinted in the slope of Γ rad shown in our demonstration model from Sander et al (2015).…”

“…For our study we use the PoWR model atmopshere code (e.g. Gräfener et al 2002;Hamann & Gräfener 2003;Sander et al 2015) with the option to solve to hydrodynamically consistent stratifications introduced in Sander et al (2017). The models assume a spherically symmetric star with an expanding, but stationary outflow.…”

“…Instead the -empirically highly uncertain -onset of clumping can play an important role. However, since this would add at least one more dimension, we limit this work to models using the depth-dependent descriptions via τ and explained in Sander et al (2017) with τ cl = 10 or cl = 100 km s −1 and point out the need for a future, more in-depth study of the imprint of the clumping stratification on the driving of WR winds. Our choice of D ∞ = 50 affects of course the derived terminal velocities ∞ .…”

“…As introduced in Sander et al (2015) and discussed in Sander et al (2017), we can write the hydrodynamic equation of motion as…”

Coupling hydrodynamics with comoving frame radiative transfer

“…However, as soon as not only the global stellar and wind parameters are of interest, but the particular physical properties throughout the stratification, especially closer to the star, the use of such an approximate treatment can lead to significant errors in the deduced properties. To overcome this problem, we present a hydrodynamically self-consistent atmosphere model for the donor of Vela X-1, using the method recently presented in Sander et al (2017) for a new generation of models developed with the Potsdam Wolf-Rayet (PoWR) code. A comparable approach has been used by Krtička et al (2012), who calculated a set of 1D wind models for different orbit inclination angles.…”