Testing the asymptotic relation for period spacings from mixed modes of red giants observed with the Kepler mission

¹ Instituut voor Sterrenkunde, KU Leuven, Celestijnenlaan 200D, 3001 Leuven, Belgium
e-mail: bram.buysschaert@ster.kuleuven.be
² Stellar Astrophysics Centre, Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, 8000 Aarhus C, Denmark
³ LESIA, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Universités, UPMC Univ. Paris 6, Univ. Paris Diderot, Sorbonne Paris Cité, France
⁴ Laboratoire AIM, CEA/DSM − CNRS − Univ. Paris Diderot − IRFU/SAp, Centre de Saclay, 91191 Gif-sur-Yvette Cedex, France
⁵ Instituto de Astrofisica de Canarias, 38205, La Laguna, Tenerife, Spain
⁶ Univ. de La Laguna, Dept. de Astrofisica, 38206, La Laguna, Tenerife, Spain
⁷ Dept. of Astrophysics, IMAPP, Radboud University Nijmegen, 6500 GL Nijmegen, The Netherlands
⁸ Sydney Institute for Astronomy (SIfA), School of Physics, University of Sydney, 2006, Australia

Received: 24 July 2015
Accepted: 3 February 2016

Abstract

Context. Dipole mixed pulsation modes of consecutive radial order have been detected for thousands of low-mass red-giant stars with the NASA space telescope Kepler. These modes have the potential to reveal information on the physics of the deep stellar interior.

Aims. Different methods have been proposed to derive an observed value for the gravity-mode period spacing, the most prominent one relying on a relation derived from asymptotic pulsation theory applied to the gravity-mode character of the mixed modes. Our aim is to compare results based on this asymptotic relation with those derived from an empirical approach for three pulsating red-giant stars.

Methods. We developed a data-driven method to perform frequency extraction and mode identification. Next, we used the identified dipole mixed modes to determine the gravity-mode period spacing by means of an empirical method and by means of the asymptotic relation. In our methodology we consider the phase offset, ϵ_g, of the asymptotic relation as a free parameter.

Results. Using the frequencies of the identified dipole mixed modes for each star in the sample, we derived a value for the gravity-mode period spacing using the two different methods. These values differ by less than 5%. The average precision we achieved for the period spacing derived from the asymptotic relation is better than 1%, while that of our data-driven approach is 3%.

Conclusions. Good agreement is found between values for the period spacing derived from the asymptotic relation and from the empirical method. The achieved uncertainties are small, but do not support the ultra-high precision claimed in the literature. The precision from our data-driven method is mostly affected by the differing number of observed dipole mixed modes. For the asymptotic relation, the phase offset, ϵ_g, remains ill defined, but enables a more robust analysis of both the asymptotic period spacing and the dimensionless coupling factor. However, its estimation might still offer a valuable observational diagnostic for future theoretical modeling.