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Table 1

Characteristics of different stellar atmosphere codes concerning their treatment of the (quasi-)hydrostatic regime.

PoWR CMFGEN FASTWIND TLUSTY

Radiative transfer comoving frame comoving frame CMF/Soboleva static (obs. frame)
Blanketing full full approximative full
Temperature stratification obtained by radiative equilibriumb or thermal balance radiative equilibriumb,c thermal balance radiative equilibriumb
Photosphere quasi-hydrostatic quasi-hydrostatic quasi-hydrostatic hydrostatic
(ρ,ν)-update consistent injectionsd start iterationse ν ≡ 0, ρ consistentf
Radiative acceleration used in hydrostatic Eq. full arad full arad acont approximationg full arad
νturb parameter in hydrostatic Eq.? yes yes no yes
Domain connection continuous dν/drh 0.75 νsonic i 0.1 νsonic (adjustable) no wind domain

Notes.

(a)

Comoving frame (CMF) method for main elements, Sobolev approximation for trace elements. Details are given in Puls et al. (2005).

(b)

InPoWR and TLUSTY, the radiative equilibrium is considered in two different flavors, the so-called integral form, and the flux consistency (Hubeny & Lanz 1995a; Hamann & Gräfener 2003). CMFGEN instead only uses the integral form (Hillier 2003).

(c)

In CMFGEN, the thermal balance is called “electron energy balance” (EEB) and used to check convergence and superlevel assignments, but not explicitly for temperature corrections (Hillier & Miller 1998; Hillier 2003).

(d)

After convergence of the statistical equations, the stratification in the quasi-hydrostatic part is adjusted and the model calculation is “restarted” from a gray temperature distribution. The total number of these “restarts”, which are also referred to as “injections”, must be specified beforehand.

(e)

At the start of a model an iteration is done for the quasi-hydrostatic domain, where a Rosseland optical depth based on LTE opacities is calculated along with the calculation of the temperature and density stratification. The details are explained in Santolaya-Rey et al. (1997).

(f)

The hydrostatic equation is part of the set of linearized equations, which are solved consistently in every iteration (Hubeny & Lanz 1995b).

(g)

The continuum acceleration is approximated by a nonintegral term with a parameterized Rosseland opacity (Santolaya-Rey et al. 1997).

(h)

The continuous velocity gradient is the standard option in PoWR to find a connection point. Alternatively, the user can specify that the connection point is forced at ν= f·νsonic.

(i)

Models before ~2013 used ν= 0.5 νsonic for the connection point (Massey et al. 2013).

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