Research Note

Visibilities and bolometric corrections for stellar oscillation modes observed by Kepler^⋆

¹ CNRS, Institut de Recherche en Astrophysique et Planétologie, 14 avenue Édouard Belin, 31400 Toulouse, France
e-mail: jballot@ast.obs-mip.fr
² Université de Toulouse, UPS-OMP, IRAP, Toulouse, France
³ Observatoire de Paris, LESIA, CNRS UMR 8109, Université Pierre et Marie Curie, Université Denis Diderot, 5 place J. Janssen, 92195 Meudon, France
⁴ Observatoire de Paris, GEPI, CNRS UMR 8111, Université Denis Diderot, 5 place J. Janssen, 92195 Meudon Principal Cedex, France

Received: 29 November 2010
Accepted: 23 May 2011

Abstract

Context.Kepler produces a large amount of data used for asteroseismological analyses, particularly of solar-like stars and red giants. The mode amplitudes observed in the Kepler spectral band have to be converted into bolometric amplitudes to be compared to models.

Aims. We give a simple bolometric correction for the amplitudes of radial modes observed with Kepler, as well as the relative visibilities of non-radial modes.

Methods. We numerically compute the bolometric correction c_K−bol and mode visibilities for different effective temperatures T_eff within the range 4000–7500 K, using a similar approach to a recent one from the literature.

Results. We derive a law for the correction to bolometric values: c_K − bol = 1 + a₁(T_eff − T_o) + a₂(T_eff − T_o)², with T_o = 5934 K, a₁ = 1.349 × 10^-4 K^-1, and a₂ =  −3.120 × 10^-9 K^-2 or, alternatively, as the power law c_K − bol = (T_eff/T_o)^α with α = 0.80. We give tabulated values for the mode visibilities based on limb-darkening (LD), computed from ATLAS9 model atmospheres for T_eff ∈  [4000,7500]  K, log g ∈  [2.5,4.5] , and [M/H] ∈  [ − 1.0, + 1.0] . We show that using LD profiles already integrated over the spectral band provides quick and good approximations for visibilities. We point out the limits of these classical visibility estimations.