skip to main content

Title: A new window to tidal asteroseismology: non-linearly excited stellar eigenmodes and the period spacing pattern in KOI-54

We revisit the tidally excited oscillations (TEOs) in the A-type main-sequence eccentric binary KOI-54, the prototype of heartbeat stars. Although the linear tidal response of the star is a series of orbital-harmonic frequencies which are not stellar eigenfrequencies, we show that the non-linearly excited non-orbital-harmonic TEOs are eigenmodes. By carefully choosing the modes which satisfy the mode-coupling selection rules, a period spacing (ΔP) pattern of quadrupole gravity modes (ΔP ≈ 2520–2535 s) can be discerned in the Fourier spectrum, with a detection significance level of $99.9{{\ \rm per\ cent}}$. The inferred period spacing value agrees remarkably well with the theoretical l = 2, m = 0 g modes from a stellar model with the measured mass, radius, and effective temperature. We also find that the two largest-amplitude TEOs at N = 90, 91 harmonics are very close to resonance with l = 2, m = 0 eigenmodes, and likely come from different stars. Previous works on tidal oscillations primarily focus on the modelling of TEO amplitudes and phases, the high sensitivity of TEO amplitude to the frequency detuning (tidal forcing frequency minus the closest stellar eigenfrequency) requires extremely dense grids of stellar models and prevents us from constraining the stellar physical parameters easily. This work, however, opens the window of real tidal asteroseismology by using the eigenfrequencies of the star inferred from the non-linear TEOs and possibly very-close-to-resonance linear TEOs. Our seismic modelling of these identified eigen g-modes shows that the best-matching stellar models have (M ≈ 2.20, 2.35 M⊙) and super-solar metallicity, in good agreement with previous measurements.

more » « less
Award ID(s):
Author(s) / Creator(s):
; ; ; ;
Publisher / Repository:
Oxford University Press
Date Published:
Journal Name:
Monthly Notices of the Royal Astronomical Society
Page Range / eLocation ID:
p. 437-446
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. null (Ed.)
    We study the principal core g-mode oscillation in hybrid stars containing quark matter and find that they have an unusually large frequency range (≈200–600 Hz) compared to ordinary neutron stars or self-bound quark stars of the same mass. Theoretical arguments and numerical calculations that trace this effect to the difference in the behavior of the equilibrium and adiabatic sound speeds in the mixed phase of quarks and nucleons are provided. We propose that the sensitivity of core g-mode oscillations to non-nucleonic matter in neutron stars could be due to the presence of a mixed quark-nucleon phase. Based on our analysis, we conclude that for binary mergers where one or both components may be a hybrid star, the fraction of tidal energy pumped into resonant g-modes in hybrid stars can exceed that of a normal neutron star by a factor of 2 to 3, although resonance occurs during the last stages of inspiral. A self-bound star, on the other hand, has a much weaker tidal overlap with the g-mode. The cumulative tidal phase error in hybrid stars, Δφ ≅ 0.5 rad, is comparable to that from tides in ordinary neutron stars, presenting a challenge in distinguishing between the two cases. However, should the principal g-mode be excited to sufficient amplitude for detection in a postmerger remnant with quark matter in its interior, its frequency would be a possible indication for the existence of non-nucleonic matter in neutron stars. 
    more » « less
  2. null (Ed.)
    ABSTRACT We report on the detection of pulsations of three pulsating subdwarf B stars observed by the Transiting Exoplanet Survey Satellite (TESS) satellite and our results of mode identification in these stars based on an asymptotic period relation. SB 459 (TIC 067584818), SB 815 (TIC 169285097), and PG 0342 + 026 (TIC 457168745) have been monitored during single sectors resulting in 27 d coverage. These data sets allowed for detecting, in each star, a few tens of frequencies that we interpreted as stellar oscillations. We found no multiplets, though we partially constrained mode geometry by means of period spacing, which recently became a key tool in analyses of pulsating subdwarf B stars. Standard routine that we have used allowed us to select candidates for trapped modes that surely bear signatures of non-uniform chemical profile inside the stars. We have also done statistical analysis using collected spectroscopic and asteroseismic data of previously known subdwarf B stars along with our three stars. Making use of high precision trigonometric parallaxes from the Gaia mission and spectral energy distributions we converted atmospheric parameters to stellar ones. Radii, masses, and luminosities are close to their canonical values for extreme horizontal branch stars. In particular, the stellar masses are close to the canonical one of 0.47 M⊙ for all three stars but uncertainties on the mass are large. The results of the analyses presented here will provide important constrains for asteroseismic modelling. 
    more » « less
  3. null (Ed.)
    Context. The recent arrival of continuous photometric observations of unprecedented quality from space missions has strongly promoted the study of pulsating stars and caused great interest in the stellar astrophysics community. In the particular case of pulsating white dwarfs, the TESS mission is taking asteroseismology of these compact stars to a higher level, emulating or even surpassing the performance of its predecessor, the Kepler mission. Aims. We present a detailed asteroseismological analysis of six GW Vir stars that includes the observations collected by the TESS mission. Methods. We processed and analyzed TESS observations of RX J2117+3412 (TIC 117070953), HS 2324+3944 (TIC 352444061), NGC 6905 (TIC 402913811), NGC 1501 (TIC 084306468), NGC 2371 (TIC 446005482), and K 1−16 (TIC 233689607). We carried out a detailed asteroseismological analysis of these stars on the basis of PG 1159 evolutionary models that take into account the complete evolution of the progenitor stars. We constrained the stellar mass of these stars by comparing the observed period spacing with the average of the computed period spacings, and we employed the individual observed periods to search for a representative seismological model when possible. Results. In total, we extracted 58 periodicities from the TESS light curves of these GW Vir stars using a standard prewhitening procedure to derive the potential pulsation frequencies. All the oscillation frequencies that we found are associated with g -mode pulsations, with periods spanning from ∼817 s to ∼2682 s. We find constant period spacings for all but one star (K 1−16), which allowed us to infer their stellar masses and constrain the harmonic degree ℓ of the modes. Based on rotational frequency splittings, we derive the rotation period of RX J2117+3412, obtaining a value in agreement with previous determinations. We performed period-to-period fit analyses on five of the six analyzed stars. For four stars (RX J2117+3412, HS 2324+3944, NGC 1501, and NGC 2371), we were able to find an asteroseismological model with masses that agree with the stellar mass values inferred from the period spacings and are generally compatible with the spectroscopic masses. Obtaining seismological models allowed us to estimate the seismological distance and compare it with the precise astrometric distance measured with Gaia . Finally, we find that the period spectrum of K 1−16 exhibits dramatic changes in frequency and amplitude that together with the scarcity of modes prevented us from meaningful seismological modeling of this star. Conclusions. The high-quality data collected by the TESS space mission, considered simultaneously with ground-based observations, provide very valuable input to the asteroseismology of GW Vir stars, similar to the case of other classes of pulsating white dwarf stars. The TESS mission, in conjunction with future space missions and upcoming surveys, will make impressive progress in white dwarf asteroseismology. 
    more » « less
  4. Abstract

    The evolution of many close binary and multiple star systems is defined by phases of mass exchange and interaction. As these systems evolve into contact, tidal dissipation is not always sufficient to bring them into circular, synchronous orbits. In these cases, encounters of increasing strength occur while the orbit remains eccentric. This paper focuses on the outcomes of close tidal passages in eccentric orbits. Close eccentric passages excite dynamical oscillations about the stars’ equilibrium configurations. These tidal oscillations arise from the transfer of orbital energy into oscillation mode energy. When these oscillations reach sufficient amplitude, they break near the stellar surface. The surface wave-breaking layer forms a shock-heated atmosphere that surrounds the object. The continuing oscillations in the star’s interior launch shocks that dissipate into the atmosphere, damping the tidal oscillations. We show that the rapid, nonlinear dissipation associated with the wave breaking of fundamental oscillation modes therefore comes with coupled mass loss to the wave-breaking atmosphere. The mass ratio is an important characteristic that defines the relative importance of mass loss and energy dissipation and therefore determines the fate of systems evolving under the influence of nonlinear dissipation. The outcome can be rapid tidal circularization (q≪ 1) or runaway mass exchange (q≫ 1).

    more » « less
  5. Abstract

    We study tidal dissipation in hot Jupiter host stars due to the nonlinear damping of tidally driveng-modes, extending the calculations of Essick & Weinberg to a wide variety of stellar host types. This process causes the planet’s orbit to decay and has potentially important consequences for the evolution and fate of hot Jupiters. Previous studies either only accounted for linear dissipation processes or assumed that the resonantly excited primary mode becomes strongly nonlinear and breaks as it approaches the stellar center. However, the great majority of hot Jupiter systems are in the weakly nonlinear regime in which the primary mode does not break but instead excites a sea of secondary modes via three-mode interactions. We simulate these nonlinear interactions and calculate the net mode dissipation for stars that range in mass from 0.5MM≤ 2.0Mand in age from the early main sequence to the subgiant phase. We find that the nonlinearly excited secondary modes can enhance the tidal dissipation by orders of magnitude compared to linear dissipation processes. For the stars withM≲ 1.0Mof nearly any age, we find that the orbital decay time is ≲100 Myr for orbital periodsPorb≲ 1 day. ForM≳ 1.2M, the orbital decay time only becomes short on the subgiant branch, where it can be ≲10 Myr forPorb≲ 2 days and result in significant transit time shifts. We discuss these results in the context of known hot Jupiter systems and examine the prospects for detecting their orbital decay with transit timing measurements.

    more » « less