Gravity darkening in stars with surface differential rotation
Abstract
Context. The interpretation of stellar apparent fundamental parameters (viewingangle dependent) requires that they be treated consistently with the characteristics of their surface rotation law.
Aims: We aim to develop a model to determine the distribution of the effective temperature and gravity, which explicitly depend on the surface differential rotation law and on the concomitant stellar external geometry.
Methods: The basic assumptions in this model are: a) the external stellar layers are in radiative equilibrium; b) the emergent bolometric flux is antiparallel with the effective gravity; c) the angular velocity in the surface obeys relations like Ω(θ) = Ω_{o} [ 1 + αΥ(θ,k) ] where Υ(θ,k) = cos^{k}θ or sin^{k}θ, and where (α,k) are free parameters.
Results: The effective temperature varies with colatitude θ, with amplitudes that depend on the differentialrotation law through the surface effective gravity and the gravitydarkening function (GDF). Although the derived expressions can be treated numerically, for some low integer values of k, analytical forms of the integral of characteristic curves, on which the determination of the GDF relies, are obtained. The effects of the quantities (η,α,k) (η = ratio between centrifugal and gravitational accelerations at the equator) on the determination of the Vsini parameter and on the gravitydarkening exponent are studied. Depending on the values of (η,α,k) the velocity V in the derived Vsini may strongly deviate from the equatorial rotational velocity. It is shown that the von Zeipel'slike gravitydarkening exponent β_{1} depends on all parameters (η,α,k) and that its value also depends on the viewingangle I. Hence, there no unique interpretation of this exponent determined empirically in terms of (I,α).
Conclusions: We stress that the data on rotating stars should be analyzed by taking into account the rotational effects through the GDF, by assuming k = 2 as a first approximation. Instead of the classic pair (η,β_{1}), it would be more useful to determine the quantities (η,α,I) to characterize stellar rotation.
 Publication:
 Astronomy and Astrophysics
 Pub Date:
 October 2017
 DOI:
 10.1051/00046361/201730818
 arXiv:
 arXiv:1705.06485
 Bibcode:
 2017A&A...606A..32Z
 Keywords:

 stars: rotation;
 Astrophysics  Solar and Stellar Astrophysics
 EPrint:
 A&