Self-consistent Solutions for Line-driven Winds of Hot Massive Stars: The m-CAK Procedure

Abstract

Massive stars present strong stellar that which are described by the radiation driven wind theory. Accurate mass-loss rates are necessary to properly describe the stellar evolution across the Hertzsprung-Russel Diagram. We present a self-consistent procedure that coupled the hydrodynamics with calculations of the line-force, giving as results the line-force parameters, the velocity field, and the mass-loss rate. Our calculations contemplate the contribution to the line-force multiplier from more than ∼ 900, 000 atomic transitions, an NLTE radiation flux from the photosphere and a quasi-LTE approximation for the occupational numbers. A full set of line-force parameters for T eff ≥ 32, 000 K, surface gravities higher than 3.4 dex for two different metallicities are presented, with their corresponding wind parameters (terminal velocities and mass-loss rates). The already known dependence of line-force parameters on effective temperature is enhanced by the dependence on log g. The terminal velocities present a stepper scaling relation with respect to the escape velocity, this might explain the scatter values observed in the hot side of the bistability jump. Moreover, a comparison of selfconsistent mass-loss rates with empirical values shows a good agreement. Self-consistent wind solutions are used as input in FASTWIND to calculate synthetic spectra. We show, comparing with the observed spectra for three stars, that varying the clumping factor, the synthetic spectra rapidly converge into the neighbourhood region of the solution. It is important to stress that our self-consistent procedure significantly reduces the number of free parameters needed to obtain a synthetic spectrum.

New self-consistent wind parameters fitting optical spectra of O-type stars observed with HERMES spectrograph

“…As a consequence, new theoretical values for the wind parameters (mass-loss rate, terminal velocity) can be determined for any specific set of stellar parameters (effective temperature, surface gravity, stellar radius, abundances). In the particular case of mass-loss rates, self-consistent values have proven to agree with those determined by observations when homogeneous wind is assumed (see figure 13 in Gormaz-Matamala et al 2019); whereas for the case of clumped winds, the clumping factor is a free parameter in the spectral fitting. This is an important result because these spectral fittings were achieved without using the power law that is commonly assumed to describe the velocity profile of stellar winds, namely β-law…”

Analytical solutions for radiation-driven winds in massive stars – II. The δ-slow regime

“…The m-CAK line force parameters should be in principle selfconsistently calculated coupling the hydrodynamics with the contribution to the line-acceleration from hundreds of thousand spectral lines (Lattimer & Cranmer 2021;Gormaz-Matamala et al 2019;Pauldrach 2003, and references therein). This type of calculations has not been performed for the -slow regime, so far.…”

“…In Araya et al (2014) a relationship between the MV08 line-force parameters (ˆ0, 1 ,ˆ0, and ) and the stellar and m-CAK lineforce parameters was given. This relationship is an easy-to-use and versatile method to compute the velocity profile analytically, because both stellar and m-CAK line force parameters are already available for a wide range of spectral types (see, Abbott 1982;Pauldrach et al 1986;Lamers & Cassinelli 1999;Noebauer & Sim 2015;Gormaz-Matamala et al 2019;Lattimer & Cranmer 2021).…”

Analytical Solutions for Radiation-Driven Winds in Massive Stars II: The $δ$-slow Regime

“…The m-CAK line force parameters should be in principle selfconsistently calculated coupling the hydrodynamics with the contribution to the line-acceleration from hundreds of thousand spectral lines (Lattimer & Cranmer 2021;Gormaz-Matamala et al 2019;Pauldrach 2003, and references therein). This type of calculations has not been performed for the 𝛿-slow regime, so far.…”

“…In Araya et al (2014) a relationship between the MV08 line-force parameters ( ĝ0 , 𝛿 1 , r0 , and 𝛾) and the stellar and m-CAK lineforce parameters was given. This relationship is an easy-to-use and versatile method to compute the velocity profile analytically, because both stellar and m-CAK line force parameters are already available for a wide range of spectral types (see, Abbott 1982;Pauldrach et al 1986;Lamers & Cassinelli 1999;Noebauer & Sim 2015;Gormaz-Matamala et al 2019;Lattimer & Cranmer 2021).…”