A diagnostic diagram for γ Doradus variables and slowly pulsating B-type stars

¹ LESIA, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Universités, UPMC Univ. Paris 06, Univ. Paris Diderot, Sorbonne Paris Cité, 5 Place Jules Janssen, 92195 Meudon, France
² Department of Astronomy, School of Science, The University of Tokyo, 7–3–1 Hongo, Bunkyo-ku, Tokyo 113–0033, Japan
e-mail: takata@astron.s.u-tokyo.ac.jp
³ Astronomical Institute, Graduate School of Science, Tohoku University, Sendai 980–8578, Japan
⁴ IRAP, Université de Toulouse, CNRS, UPS, CNES, 14 Avenue Édouard Belin, 31400 Toulouse, France
⁵ Stellar Astrophysics Centre, Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, 8000 Aarhus C, Denmark
⁶ STAR Institute, Université de Liège, Allée du 6 Août 19, 4000 Liège, Belgium

Received: 12 July 2019
Accepted: 3 February 2020

Abstract

Pulsating variables of γ Doradus type (γ Dor) and slowly pulsating B-type (SPB) stars are found on and near the main sequence with typical periods varying between one and several days, making them rather hard to detect from the ground. It is only with space missions such as CoRoT and Kepler that we became truly capable of determining their oscillation frequencies with enough precision to perform in-depth analyses. Here we present an efficient and easy-to-implement seismic tool, in which the frequency (ν) and the square root of the frequency difference ($\sqrt{\mathrm{\Delta }\nu }$) are plotted against each other as the abscissa and the ordinate, respectively. This allows us to immediately (1) perform mode identification; (2) estimate the average rotation rate and the characteristic period of gravity modes; and (3) recognise certain physical effects, including buoyancy glitches and avoided crossings. This diagnostic tool can only be applied to prograde sectoral g modes. To validate the tool presented here, we used stellar models and also applied it to three γ Dor (KIC 12066947, KIC 5608334 and KIC 4846809) and one SPB star (KIC 3459297), all observed with Kepler. Furthermore, we show that the rotation rates determined using this new tool are consistent with the results of previous studies.