Analytical Solutions for Radiation-Driven Winds in Massive Stars II: The $delta$-slow Regime. (arXiv:2104.03263v1 [astro-ph.SR])

Analytical Solutions for Radiation-Driven Winds in Massive Stars II: The $delta$-slow Regime. (arXiv:2104.03263v1 [astro-ph.SR])
<a href="http://arxiv.org/find/astro-ph/1/au:+Araya_I/0/1/0/all/0/1">I. Araya</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Christen_A/0/1/0/all/0/1">A. Christen</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Cure_M/0/1/0/all/0/1">M. Cur&#xe9;</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Cidale_L/0/1/0/all/0/1">L. S. Cidale</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Venero_R/0/1/0/all/0/1">R. O. J. Venero</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Arcos_C/0/1/0/all/0/1">C. Arcos</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Gormaz_Matamala_A/0/1/0/all/0/1">A. C. Gormaz-Matamala</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Haucke_M/0/1/0/all/0/1">M. Haucke</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Escarate_P/0/1/0/all/0/1">P. Esc&#xe1;rate</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Claveria_H/0/1/0/all/0/1">H. Claver&#xed;a</a>

Accurate mass-loss rates and terminal velocities from massive stars winds are
essential to obtain synthetic spectra from radiative transfer calculations and
to determine the evolutionary path of massive stars. From a theoretical point
of view, analytical expressions for the wind parameters and velocity profile
would have many advantages over numerical calculations that solve the complex
non-linear set of hydrodynamic equations. In a previous work, we obtained an
analytical description for the fast wind regime. Now, we propose an approximate
expression for the line-force in terms of new parameters and obtain a velocity
profile closed-form solution (in terms of the Lambert $W$ function) for the
$delta$-slow regime. Using this analytical velocity profile, we were able to
obtain the mass-loss rates based on the m-CAK theory. Moreover, we established
a relation between this new set of line-force parameters with the known stellar
and m-CAK line-force parameters. To this purpose, we calculated a grid of
numerical hydrodynamical models and performed a multivariate multiple
regression. The numerical and our descriptions lead to good agreement between
their values.

Accurate mass-loss rates and terminal velocities from massive stars winds are
essential to obtain synthetic spectra from radiative transfer calculations and
to determine the evolutionary path of massive stars. From a theoretical point
of view, analytical expressions for the wind parameters and velocity profile
would have many advantages over numerical calculations that solve the complex
non-linear set of hydrodynamic equations. In a previous work, we obtained an
analytical description for the fast wind regime. Now, we propose an approximate
expression for the line-force in terms of new parameters and obtain a velocity
profile closed-form solution (in terms of the Lambert $W$ function) for the
$delta$-slow regime. Using this analytical velocity profile, we were able to
obtain the mass-loss rates based on the m-CAK theory. Moreover, we established
a relation between this new set of line-force parameters with the known stellar
and m-CAK line-force parameters. To this purpose, we calculated a grid of
numerical hydrodynamical models and performed a multivariate multiple
regression. The numerical and our descriptions lead to good agreement between
their values.

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