Amplitude and frequency variations in PG 0101+039 from K2 photometry

A pulsating hot B subdwarf star in an unsynchronized binary system

¹ Institute for Frontiers in Astronomy and Astrophysics, Beijing Normal University, Beijing 102206, PR China
e-mail: xiaoyu.ma@mail.bnu.edu.cn; weikai.zong@bnu.edu.cn; jnfu@bnu.edu.cn
² Department of Astronomy, Beijing Normal University, Beijing 100875, PR China
³ Institut de Recherche en Astrophysique et Planétologie, CNRS, Université de Toulouse, CNES, 14 Avenue Édouard Belin, 31400 Toulouse, France
⁴ College of Science, Chongqing University of Posts and Telecommunications, Chongqing 400065, PR China

Received: 9 July 2023
Accepted: 18 September 2023

Abstract

Context. K2 photometry is suitable for the exploitation of mode variability on short timescales in hot B subdwarf stars and this technique is useful in constraining nonlinear quantities addressed by the stellar theory of high-order perturbation in the future.

Aims. We analyzed high-quality K2 data collected for PG 0101+039 over about 80 days and we extracted the frequency content of oscillation. We determined the star’s rotational and orbital properties, in addition to characterizing the dynamics of the amplitude and frequency.

Methods. The frequencies were extracted from light curves via a standard prewhitening technique. The binary information was obtained from variations both in brightness and radial velocities. The amplitude and frequency modulations (i.e., AMs and FMs) of the oscillation modes were measured by piece-wise light curves and characterized by a Markov chain Monte Carlo (MCMC) method.

Results. We extracted 137 independent frequencies in PG 0101+039 and derived period spacing of ∼252 s and 144 s for the dipole and quadruple modes, respectively. We derived rotation periods of ∼8.81 ± 0.06 days and ∼8.60 ± 0.16 days based on g- and p-mode multiplets, respectively, implying a marginally differential rotation with a probability of ∼60%. We find that the rotation period is much shorter than the orbital period of ∼0.57 d, indicating that this system is not synchronized. The AMs and FMs were found to be measurable for 44 frequencies with high enough amplitude, including 12 rotational components. We characterized their modulating patterns and found a clear correlation between the amplitude and frequency variation, linked to nonlinear resonant couplings. In general, the modulating scale and timescale are on the order of a few dozen of nanohertz and a few tens of days, respectively. These values can serve as important constraints on future calculations of nonlinear amplitude equations.

Conclusions. PG 0101+039 is an unsynchronized system containing a component whose amplitude and frequency variations are generally found to be on a shorter timescale than previously reported for other sdB pulsators. Those findings are essential to setting observational constraints on the nonlinear dynamics of resonant mode couplings and orbital solutions.