Testing the forward modeling approach in asteroseismology^*

I. Seismic solutions for the hot B subdwarf Balloon 090100001 with and without a priori mode identification

¹ Laboratoire d'Astrophysique de Toulouse-Tarbes, Université de Toulouse, CNRS, 14 av. E. Belin, 31400 Toulouse, France e-mail: [valerie.vangrootel;stephane,charpinet]@ast.obs-mip.fr
² Département de Physique, Université de Montréal, CP 6128, Succursale Centre-Ville, Montréal, QC H3C 3J7, Canada e-mail: [fontaine;brassard]@astro.umontreal.ca
³ Steward Observatory, University of Arizona, 933 North Cherry Av., Tucson, AZ 85721, USA e-mail: bgreen@as.arizona.edu
⁴ Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA e-mail: chayer@stsci.edu
⁵ ESO, Karl-Schwarzschild-Str. 2, 85748 Garching bei München, Germany e-mail: srandall@eso.org

Received: 28 March 2008
Accepted: 1 July 2008

Abstract

Context. Balloon 090100001, the brightest of the known pulsating hot B subdwarfs, exhibits simultaneoulsy both short- and long-period pulsation modes, and shows relatively large amplitudes for its dominant modes. For these reasons, it has been studied extensively over the past few years, including a successful experiment carried out at the Canada-France-Hawaii Telescope to pin down or constrain the value of the degree index of several pulsation modes through multicolor photometry.

Aims. The primary goal of this paper is to take advantage of such partial mode identification to test the robustness of our standard approach to the asteroseismology of pulsating subdwarf B stars. The latter is based on the forward approach whereby a model that best matches the observed periods is searched for in parameter space with no a priori assumption about mode identification. When successful, this method leads to the determination of the global structural parameters of the pulsator. As a bonus, it also leads, after the fact, to complete mode identification. For the first time, with the availability of partial mode identification for Balloon 090100001, we are able to evaluate the sensitivity of the inferred seismic model to possible uncertainty in mode identification.

Methods. We carry out a number of exercises based on the double optimization technique that we developed within the framework of the forward modeling approach in asteroseismology. We use the set of ten periods corresponding to the independent pulsation modes for which values of have been either formally identified or constrained through multicolor photometry in Balloon 090100001. These exercises differ in that they assume different a priori mode identification.

Results. Our primary result is that the asteroseismic solution stands very robust, whether or not external constraints on the values of the degree are used. Although this may come as a small surprise, the test proves to be conclusive, and small differences in mode identification among the ten modes do not affect in any significant way, at the typical accuracy presently achieved, the final emergent seismic model. This is due to the structure of the p-mode pulsation spectra in sdB stars. In all cases, the inferred structural parameters of Balloon 090100001 remain practically unchanged. They correspond, and this constitutes our second important result, to a star beyond the TAEHB with T_eff = 28 000 ± 1 200 K, log g = 5.383 ± 0.004, = 0.432 ± 0.015, and = -4.89 ± 0.14. Other structural parameters are also derived.