ner_tags: O B-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model I-Model I-Model O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O B-Citation I-Citation O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O
tokens: called NLTE equations) for non-monotonic velocity law. To our knowledge, there is no such code that is able to treat this problem in its full complexity. Therefore, to make the problem tractable, we calculate a mean value of the mass-loss rate in the region close to the star, where the wind blanketing originates, where ρ and v are the wind density and radial velocity in particular time. Most of the flux in the optical domain is emitted from the region below the sonic point, which typically appears at radii 1.01 − 1.02 R * in the numerical simulations. Therefore, we selected r 1 = 1.01 R * and r 2 = 1.02 R * . However, the final light curve does not significantly depend on the choice of r 1 and r 2 . As a result of this choice, in Eq. ( 1 ) we average over 50 grid points of hydrodynamical simulation. A plot of is given in Fig. 1 . Fig. 1. Mass-loss rate from the numerical simulations averaged over r ∈ [1.01 R * , 1.02 R * ] (see Eq. ( 1 )). 2.2. Global wind models The variations of the emergent flux with wind mass-loss rate were derived from spherically symmetric stationary METUJE global wind models ( Krtička Kubát 2017 ). The code calculates the wind model in a global (unified) approach that integrates the description of the hydrostatic photosphere and supersonic wind. The model solves the radiative transfer equation in the co-moving frame (CMF) with opacities and emissivities calculated using occupation numbers derived from the kinetic equilibrium (NLTE) equations. For given stellar parameters, the model enables us to predict the radial dependence of the density, velocity, and temperature from hydrodynamical equations and to derive the wind mass-loss rate and the stellar emergent flux that accounts for the wind blanketing. For our modelling we assumed a typical parameters of O stars corresponding to HD 191612 , T eff = 36 000 K, R * = 14.1 R ⊙ , and M = 29.2 M ⊙ . To model the dependence of the emergent flux on the mass-loss rate with fixed stellar parameters, we artificially scaled the radiative force in the wind. This yields a series of wind models and emergent fluxes parameterized by the wind mass-loss rate. Because the amount of the flux redistributed by the wind depends on the effective temperature, we expect slightly different dependence for stars with different temperature. However, because we are concerned with typical light variations, we limited our study to just one star. On the other hand, such selection affects only the amplitude of the light curve. The preliminary results derived for 300-1 model of Krtička Kubát (2017 , the model has parameters close to that used in hydrodynamical simulations) indicate that the amplitude of the variability due to the wind blanketing does not significantly depend on stellar parameters. The light variability is derived from a relation between the H p magnitudes and mass-loss rate ( Krtička 2016 , Eq. ( 2 )) where Δ F = 1.6 × 10 7 erg s −1 cm −2 , F 0 = 9.0 × 10 8 erg s −1 cm −2 is the emergent