High-degree gravity modes in the single sdB star HD 4539

Abstract

HD 4539 (alias PG 0044+097 or EPIC 220641886) is a bright (V=10.2) long-period V1093 Her-type subdwarf B (sdB) pulsating star that was observed by the Kepler spacecraft in its secondary (K2) mission. We use the K2 light curve (78.7 days) to extract 169 pulsation frequencies, 124 with a robust detection. Most of these frequencies are found in the low-frequency region typical of gravity (g-)modes, but some higher frequencies corresponding to pressure (p-)modes are also detected. Therefore HD 4539 is a hybrid pulsator and both the deep and surface layers of the star can potentially be probed through asteroseismology. The lack of any frequency splitting in its amplitude spectrum suggests that HD 4539 has a rotation period longer than the K2 run and/or that it is seen pole-on. From asymptotic period spacing we see many high-degree modes, up to l=12, in the spectrum of HD 4539, with amplitudes as low as a few ppm. A large fraction of these modes can be identified and for ∼29% of them we obtain a unique and robust identification corresponding to l≤8. Our study includes also a new determination of the atmospheric parameters of the star. From low-resolution spectroscopy we obtain T eff =22,800±160 K, log g=5.20±0.02 and log(N (He)/N (H))=-2.34±0.05. By fitting the SED we obtain T eff =23,470 +650 −210 K, R =0.26±0.01 R and M =0.40±0.08 M . Moreover, from 11 high-resolution spectra we see the radial velocity variations caused by the stellar pulsations, with amplitudes of ≈150 m/s for the main modes, and we can exclude the presence of a companion with a minimum mass higher than a few Jupiter masses for orbital periods below ∼300 days.

Asteroseismic Observations of Hot Subdwarfs

“…Jeffery et al find the K2 light curve to show a dominant period around 10.8 h, with a variable amplitude, its first harmonic, and another period at 13.3 h. A preferred explanation is multi-periodic nonradial oscillation due to g-modes with very high radial order, although Jeffery et al note this presents difficulties for pulsation theory; alternative explanations fail for lack of radial-velocity evidence. Silvotti et al (2019) nicely illustrate the value of using spacecraft to obtain long time-base high precision photometry through their detection of pulsation in the bright (V 10.2) sdB star HD 4539 (PG 0044 + 097 and EPIC 220641886), a feat which Lynas-Gray (2012) fails to achieve with ground-based photometry using modest facilities. From the K2 light curve (78.7 days) Silvotti et al extract 169 pulsation frequencies, 124 having a robust detection; most are found in the low-frequency g-mode region but some higher frequency p-modes are also detected, implying that HD 4539 is a hybrid (DW Lyn) pulsator.…”

No close companions to a sample of bright sdB stars

“…Two stars, HD 4539 and PG 0342+026 (Fig. 1 and 2) show significant RV variations and indeed, after the Harps-N observations, both were found to vary also photometrically from K2 and T ESS observations respectively, due to g-mode pulsations (Silvotti et al, 2019;Sahoo et al, 2019).…”

“…In order to set upper limits to the mass of a companion, we computed a series of synthetic RV curves for different orbital periods and companion masses, assuming circular orbits and a stellar mass of 0.47 M ⊙ (0.40 M ⊙ only for HD 4539, Silvotti et al 2019), and compared these curves with the RV measurements.…”

“…For HD 4539, with 11 RV measurements, it was possible to partially subtract the contribution due to the pulsations (see Fig. 1 and Silvotti et al (2019) for more details).…”

LAMOST Observations in 15 \textit{K}2 Campaigns: I. Low resolution spectra from LAMOST DR6

“…The K2 mission collected photometry for more than 400,000 stars during 20 campaigns (C0, C1,..., C19). Those light curves are a treasure trove for many research areas, including exoplanets (Montet et al 2015), asteroseismology (Chen, & Li 2018;Silvotti et al 2019), and eclipsing binaries (Skarka et al 2019). Nevertheless, for many applications, an in-depth exploitation of these data requires the knowledge of precise atmospheric parameters.…”