2-dimensional models of rapidly rotating stars

I. W. Roxburgh

doi:doi:10.1051/0004-6361:20065109

Free access

Issue		A&A Volume 454, Number 3, August II 2006


Page(s)		883 - 888
Section		Stellar structure and evolution
DOI		http://dx.doi.org/10.1051/0004-6361:20065109

A&A 454, 883-888 (2006)
DOI: 10.1051/0004-6361:20065109

II. Hydrostatic and acoustic models with $\mathsf{\Omega=\Omega(r,\theta)}$

I. W. Roxburgh^{1, 2}

¹ Astronomy Unit, Queen Mary, University of London, Mile End Road, London E1 4NS, UK
e-mail: I.W.Roxburgh@qmul.ac.uk
² LESIA, Observatoire de Paris, Place Jules Janssen, 92195 Meudon Cedex, France

(Received 28 February 2006 / Accepted 23 April 2006)

Abstract
Aims.We show how to construct 2-dimensional models of rapidly rotating stars in hydrostatic equilibrium for any $\Omega(r,\theta)$ , given the density $\rho_{\rm m}(r)$ along any one angle $\theta_{\rm m}$ . If the hydrogen abundance $X_{\rm m}(r)$ is given on $\theta_{\rm m}$ then the adiabatic exponent $\Gamma_1(r,\theta)$ can by determined, yielding a self consistent acoustic model that can be used to investigate the oscillation properties of rapidly rotating stars.
Methods.The system of equations governing the hydrostatic structure is solved by iteration using the method of characteristics and spectral expansion, subject to the condition that $\rho(r,\theta)=\rho_{\rm m}(r)$ on $\theta=\theta_{\rm m}$ . $\Gamma_1(r,\theta)$ is calculated from the equation of state under the assumption that $X(r,\theta_{\rm m})=X_{\rm m}(r)$ and is constant on surfaces of constant entropy. Alternatively $\Gamma_1$ can be approximated by taking X constant in the equation of state and equal to the surface value.
Results.Results are presented for an evolved main sequence star of $2~M_\odot$ with the angular velocity a function only of radius $\Omega=\Omega(r)$ , evolved to a central hydrogen abundance of $X_{\rm c}=0.35$ . The model is first calculated using a spherically averaged stellar evolution code, where the averaged centrifugal force $2\Omega^2 r/3$ is added to gravity. The resulting $\rho_{\rm m}(r), X_{\rm m}(r)$ are then used as input to determine the 2-dimensional model.
Conclusions.The procedure described here gives self consistent hydrostatic and acoustic models of rapidly rotating stars for any $\Omega(r,\theta)$ .

Key words: stars: rotation -- stars: evolution

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