G-mode Oscillations Research Articles

Temperature Effects on Core g-Modes of Neutron Stars

Neutron stars provide a unique physical laboratory in which to study the properties of matter at high density and temperature. We study a diagnostic of the composition of high-density matter, namely, g-mode oscillations, which are driven by buoyancy forces. These oscillations can be excited by tidal forces and couple to gravitational waves. We extend prior results for the g-mode spectrum of cold neutron star matter to high temperatures that are expected to be achieved in neutron star mergers using a parameterization for finite-temperature effects on equations of state recently proposed by Raithel, Özel and Psaltis. We find that the g-modes of canonical mass neutron stars (≈1.4M⊙) are suppressed at high temperatures, and core g-modes are supported only in the most massive (≥2M⊙) of hot neutron stars.

G -mode oscillations in hybrid stars: A tale of two sounds

We study the principal core g-mode oscillation in hybrid stars containing quark matter and find that they have an unusually large frequency range ($\approx$ 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 behaviour 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 2-3, 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, $\Delta\phi\cong$ 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 post-merger remnant with quark matter in its interior, its frequency would be a possible indication for the existence of non-nucleonic matter in neutron stars.

A comparison of the dynamical and model-derived parameters of the pulsating eclipsing binary KIC 9850387

Context. One-dimensional stellar evolutionary models incorporate interior mixing profiles as a simplification of multi-dimensional physical processes that have a significant impact on the evolution and lifetime of stars. As such, the proper calibration of interior mixing profiles is required for the reconciliation of observational parameters and theoretical predictions. The modelling and analysis of pulsating stars in eclipsing binary systems that display gravity-mode (g-mode) oscillations allows for the precise constraints on the interior mixing profiles through the combination of spectroscopic, binary and asteroseismic obervables. Aims. We aim to unravel the interior mixing profile of the pulsating eclipsing binary KIC 9850387 by comparing its dynamical parameters and the parameters derived through a combination of evolutionary and asteroseismic modelling. Methods. We created a grid of stellar evolutionary models using the stellar evolutionary code MESA and performed an isochrone-cloud (isocloud) based evolutionary modelling of the system. We then generated a grid of pulsational models using the stellar pulsation code GYRE based on the age constraints from the evolutionary modelling. Finally, we performed asteroseismic modelling of the observed ℓ = 1 and ℓ = 2 period-spacing patterns, utilising different combinations of observational constraints, merit functions, and asteroseismic observables to obtain strong constraints on the interior properties of the primary star. Results. Through a combination of asteroseismic modelling and dynamical constraints, we found that the system comprises two main-sequence components at an age of 1.2 ± 0.1 Gyr. We also observed that asteroseismic modelling provided stronger constraints on the interior properties than evolutionary modelling. Overall, we found high levels of interior mixing, when compared to similar studies, for the primary star. We posited that this is a result of intrinsic non-tidal mixing mechanisms due to a similar observed behaviour in single stars. We investigated the high-frequency regime of KIC 9850387 and found evidence of the surface effect due to the systematic frequency offset of the theoretical modes from the nearest observed modes. We also found evidence of rotational splitting in the form of a prograde-retrograde dipole g1 mode doublet with a missing zonal mode, implying an envelope rotational frequency that is three times higher than the core rotational frequency and about 20 times slower than the orbital frequency, but we note that this result is based completely on the rotational splitting of a single dipole mode. Conclusions. We find that the dynamical parameters and the parameters extracted from the asteroseismic modelling of period-spacing patterns are only barely compliant, reinforcing the need for homogeneous analyses of samples of pulsating eclipsing binaries that aim to calibrating interior mixing profiles.

Lifting the Veil on Quark Matter in Compact Stars with Core g-mode Oscillations

Abstract Compact stars containing quark matter may masquerade as neutron stars in the range of measured mass and radius, making it difficult to draw firm conclusions on the phase of matter inside the star. The sensitivity of core g-mode oscillations to the presence of a mixed phase may alleviate this difficulty. In hybrid stars that admit quark matter in a mixed phase, the g-mode frequency rises sharply due to a marked decrease in the equilibrium sound speed. Resonant excitation of g-modes can leave an imprint in the waveform of coalescing binary compact stars. We present analytic and numeric results to assess the sensitivity displayed by g-mode oscillations to quark matter in a homogeneous or mixed phase and also compute relevant damping times in quark matter due to viscosity.

Pulsational properties of ten new slowly pulsating B stars

Context. Slowly pulsating B (SPB) stars are upper main-sequence multi-periodic pulsators that show non-radial g-mode oscillations driven by the κ mechanism acting on the iron bump. These multi-periodic pulsators have great asteroseismic potential and can be employed for the calibration of stellar structure and evolution models of massive stars. Aims. We collected a sample of ten hitherto unidentified SPB stars with the aim of describing their pulsational properties and identifying pulsational modes. Methods. Photometric time series data from various surveys were collected and analyzed using diverse frequency search algorithms. We calculated astrophysical parameters and investigated the location of our sample stars in the log Teff vs. log L/L⊙ diagram. Current pulsational models were calculated and used for the identification of pulsational modes in our sample stars. An extensive grid of stellar models along with their g-mode eigenfrequencies was calculated and subsequently cross-matched with the observed pulsational frequencies. The best-fit models were then used in an attempt to constrain stellar parameters such as mass, age, metallicity, and convective overshoot. Results. We present detected frequencies, corresponding g-mode identifications, and the masses and ages of the stellar models producing the best frequency cross-matches. We partially succeeded in constraining stellar parameters, in particular concerning mass and age. Where applicable, rotation periods have been derived from the spacing of triplet component frequencies. No evolved SPB stars are present in our sample. We identify two candidate high-metallicity objects (HD 86424 and HD 163285), one young SPB star (HD 36999), and two candidate young SPB stars (HD 61712 and HD 61076). Conclusions. We demonstrate the feasibility of using ground-based observations to perform basic asteroseismological analyses of SPB stars. Our results significantly enlarge the sample of known SPB stars with reliable pulsational mode identifications, which provides important input parameters for modeling attempts aiming to investigate the internal processes at work in upper main-sequence stars.

Accretion-induced Collapse of Dark Matter Admixed White Dwarfs. II. Rotation and Gravitational-wave Signals

Abstract We present axisymmetric hydrodynamical simulations of accretion-induced collapse (AIC) of dark matter (DM) admixed rotating white dwarfs (WD) and their burst gravitational-wave (GW) signals. For initial WD models with the same central baryon density, the admixed DM is found to delay the plunge and bounce phases of AIC, and decrease the central density and mass of the protoneutron star (PNS) produced. The bounce time, central density, and PNS mass generally depend on two parameters, the admixed DM mass M DM and the ratio between the rotational kinetic and gravitational energies of the inner core at bounce . The emitted GWs have generic waveform shapes and the variation of their amplitudes h + show a degeneracy on and M DM. We found that the ratios between the GW amplitude peaks around bounce allow breaking of the degeneracy and extraction of both and M DM. Even within the uncertainties of the nuclear matter equation of state, a DM core can be inferred if its mass is greater than 0.03 M ⊙. We also discuss possible DM effects on the GW signals emitted by PNS g-mode oscillations. GWs may boost the possibility for the detection of AIC, as well as open a new window into the indirect detection of DM.

High-precision Asteroseismology in a Slowly Pulsating B Star: HD 50230

Abstract The slowly pulsating B star HD 50230, which is in fact a hybrid B-type pulsator, has been observed by CoRoT for at least 137 days. Nearly equidistant period spacing patterns are found among eight modes that are extracted from the oscillation spectrum with more than 500 frequencies. However, it is thought to be most likely accidental by Szewczuk et al. In the present work, we analyze the eight modes in depth with the χ 2-matching method. Based on the best-fitting model (model MA), we find that they can be well explained as sequences of consecutive dipolar (l, m) = (1, 0). The period discrepancies between observations and the best-fitting model are within 100 s except for the outlier, which is up to 300 s. Based on the calculated χ 2-minimization models, we find that, for pure g-mode oscillations, the buoyancy radius, Λ0, can be precisely measured with the χ 2-matching method between observations and calculations. It represents the “propagation time” of the g-mode from the stellar surface to the center. It is of Λ0 = 245.78 ± 0.59 μHz with a precision of 0.24%. In addition, we also find that HD 50230 is a metal-rich (Z init = 0.034–0.043) star with a mass of M = 6.15–6.27 M ⊙. It is still located in the hydrogen-burning phase with central hydrogen of X C = 0.298–0.316 (or ); therefore, it has a convective core with a radius of R cc = 0.525–0.536 R ⊙ (or ). In order to interpret the structure of the observed period spacing pattern well, the convective core overshooting (f ov = 0.0175–0.0200) and the extra diffusion mixing ( ) should be taken into account in theoretical models.

Characterizing the Gravitational Wave Signal from Core-collapse Supernovae

Abstract We study the gravitational wave (GW) signal from eight new 3D core-collapse supernova simulations. We show that the signal is dominated by f- and g-mode oscillations of the protoneutron star (PNS) and its frequency evolution encodes the contraction rate of the latter, which, in turn, is known to depend on the star’s mass, on the equation of state, and on transport properties in warm nuclear matter. A lower-frequency component of the signal, associated with the standing accretion shock instability, is found in only one of our models. Finally, we show that the energy radiated in GWs is proportional to the amount of turbulent energy accreted by the PNS.

A Linear and Quadratic Time–Frequency Analysis of Gravitational Waves from Core-collapse Supernovae

Abstract Recent core-collapse supernova (CCSN) simulations have predicted several distinct features in gravitational-wave (GW) spectrograms, including a ramp-up signature due to the g-mode oscillation of the protoneutron star (PNS) and an excess in the low-frequency domain (100 to ∼300 Hz) potentially induced by the standing accretion shock instability (SASI). These predictions motivated us to perform a sophisticated time–frequency analysis (TFA) of the GW signals, aimed at preparation for future observations. By reanalyzing a gravitational waveform obtained in a three-dimensional general-relativistic CCSN simulation, we show that both the spectrogram with an adequate window and the quadratic TFA separate the multimodal GW signatures much more clearly compared with a previous analysis. We find that the observed low-frequency excess during the SASI active phase is divided into two components, a stronger one at 130 Hz and an overtone at 260 Hz, both of which evolve quasistatically during the simulation time. We also identify a new mode with frequency varying from 700 to 600 Hz. Furthermore, we develop the quadratic TFA for the Stokes I, Q, U, and V parameters as a new tool to investigate the circular polarization of GWs. We demonstrate that the polarization states that randomly change with time after bounce are associated with the PNS g-mode oscillation, whereas a slowly changing polarization state in the low-frequency domain is connected to the PNS core oscillation. This study demonstrates the capability of sophisticated TFA to diagnose polarized CCSN GWs in order to explore their complex nature.

WDEC: A Code for Modeling White Dwarf Structure and Pulsations

Abstract The White Dwarf Evolution Code (WDEC), written in Fortran, makes models of white dwarf stars. It is fast, versatile, and includes the latest physics. The code evolves hot (∼100,000 K) input models down to a chosen effective temperature by relaxing the models to be solutions of the equations of stellar structure. The code can also be used to obtain g-mode oscillation modes for the models. WDEC has a long history going back to the late 1960s. Over the years, it has been updated and re-packaged for modern computer architectures and has specifically been used in computationally intensive asteroseismic fitting. Generations of white dwarf astronomers and dozens of publications have made use of the WDEC, although the last true instrument paper is the original one, published in 1975. This paper discusses the history of the code, necessary to understand why it works the way it does, details the physics and features in the code today, and points the reader to where to find the code and a user guide.

Equation of State Dependent Dynamics and Multi-messenger Signals from Stellar-mass Black Hole Formation

Abstract We investigate axisymmetric black hole (BH) formation and its gravitational wave (GW) and neutrino signals with self-consistent core-collapse supernova simulations of a non-rotating 40 M ⊙ progenitor star using the isotropic diffusion source approximation for the neutrino transport and a modified gravitational potential for general relativistic effects. We consider four different neutron star (NS) equations of state (EoS): LS220, SFHo, BHBΛϕ, and DD2, and study the impact of the EoS on BH formation dynamics and GW emission. We find that the BH formation time is sensitive to the EoS from 460 to >1300 ms and is delayed in multiple dimensions for ∼100–250 ms due to the finite entropy effects. Depending on the EoS, our simulations show the possibility that shock revival can occur along with the collapse of the proto-neutron star (PNS) to a BH. The gravitational waveforms contain four major features that are similar to previous studies but show extreme values: (1) a low-frequency signal (∼300–500 Hz) from core-bounce and prompt convection, (2) a strong signal from the PNS g-mode oscillation among other features, (3) a high-frequency signal from the PNS inner-core convection, and (4) signals from the standing accretion shock instability and convection. The peak frequency at the onset of BH formation reaches to ∼2.3 kHz. The characteristic amplitude of a 10 kpc object at peak frequency is detectable but close to the noise threshold of the Advanced LIGO and KAGRA, suggesting that the next-generation GW detector will need to improve the sensitivity at the kHz domain to better observe stellar-mass BH formation from core-collapse supernovae or failed supernovae.

Circular polarization of gravitational waves from non-rotating supernova cores: a new probe into the pre-explosion hydrodynamics

Abstract We present an analysis of the circular polarization of gravitational waves (GWs) using results from three-dimensional (3D), general relativistic (GR) core-collapse simulations of a non-rotating 15 M⊙ star. For the signal detection, we perform a coherent network analysis taking into account the four interferometers of LIGO Hanford, LIGO Livingston, VIRGO, and KAGRA. We focus on the Stokes V parameter, which directly characterizes the asymmetry of the GW circular polarization. We find that the amplitude of the GW polarization becomes bigger for our 3D-GR model that exhibits strong activity of the standing accretion shock instability (SASI). Our results suggest that the SASI-induced accretion flows to the proto-neutron star (PNS) lead to a characteristic, low-frequency modulation (100–200 Hz) in both the waveform and the GW circular polarization. By estimating the signal-to-noise ratio of the GW polarization, we demonstrate that the detection horizon of the circular polarization extends by more than a factor of several times farther comparing to that of the GW amplitude. Our results suggest that the GW circular polarization, if detected, could provide a new probe into the pre-explosion hydrodynamics such as the SASI activity and the g-mode oscillation of the PNS.

Self-trapping of g-mode oscillations in relativistic thin discs, revisited – II. Revision of boundary condition

In the previous paper, we have examined how the self-trapping of g-mode oscillations in geometrically thin relativistic discs is affected by the presence of uniform vertical magnetic fields. Discs considered are isothermal in the vertical direction and are truncated at a certain height by presence of hot corona. After the correction of simple analytical error, we showed that the self-trapping of axisymmetric g-mode oscillations in non-magnetized discs is destroyed by weak magnetic fields as Fu and Lai showed. In this paper, however, we re-examine the same problem by imposing a different, more relevant boundary condition on the disc-corona surface and find that the self-trapping of axisymmetric g-mode oscillations seems to still exist like in the case of non-magnetized discs.

A Parametric Study of the Acoustic Mechanism for Core-collapse Supernovae

Abstract We investigate the criterion for the acoustic mechanism to work successfully in core-collapse supernovae. The acoustic mechanism is an alternative to the neutrino-heating mechanism. It was proposed by Burrows et al., who claimed that acoustic waves emitted by g-mode oscillations in proto-neutron stars (PNS) energize a stalled shock wave and eventually induce an explosion. Previous works mainly studied to which extent the g-modes are excited in the PNS. In this paper, on the other hand, we investigate how strong the acoustic wave needs to be if it were to revive a stalled shock wave. By adding the acoustic power as a new axis, we draw a critical surface, which is an extension of the critical curve commonly employed in the context of neutrino heating. We perform both 1D and 2D parametrized simulations, in which we inject acoustic waves from the inner boundary. In order to quantify the power of acoustic waves, we use the extended Myers theory to take neutrino reactions into proper account. We find for the 1D simulations that rather large acoustic powers are required to relaunch the shock wave, since the additional heating provided by the secondary shocks developed from acoustic waves is partially canceled by the neutrino cooling that is also enhanced. In 2D, the required acoustic powers are consistent with those of Burrows et al. Our results seem to imply, however, that it is the sum of neutrino heating and acoustic powers that matters for shock revival.

Erratum: Self-trapping of g-mode oscillations in relativistic thin discs, revisited

Erratum: Self-trapping of g-mode oscillations in relativistic thin discs, revisited

An eLIMA model for the 67 s X-ray periodicity in CAL 83

Supersoft X-ray sources (SSSs) are characterized by their low effective temperatures and high X-ray luminosities. The soft X-ray emission can be explained by hydrogen nuclear burning on the surface of a white dwarf (WD) accreting at an extremely high rate. A peculiar 67 s periodicity (P67) was previously discovered in the XMM-Newton light curves of the SSS CAL 83. P67 was detected in X-ray light curves spanning 9 years, but exhibits variability of several seconds on time-scales as short as a few hours, and its properties are remarkably similar to those of dwarf nova oscillations (DNOs). DNOs are short time-scale modulations often observed in dwarf novae during outburst. DNOs are explained by the well established low-inertia mag- netic accretor (LIMA) model. In this paper, we show that P67 and its associated period variability can be satisfactorily explained by an application of the LIMA model to the more extreme environment in a SSS (eLIMA), contrary to another recent study at- tempting to explain P67 and its associated variability in terms of non-radial g-mode oscillations in the extended envelope of the rapidly accreting white dwarf in CAL 83. In the eLIMA model, P67 originates in an equatorial belt in the WD envelope at the boundary with the inner accretion disc, with the belt weakly coupled to the WD core by a 100 000 G magnetic field. New optical light curves obtained with the Sutherland High-speed Optical Camera (SHOC) are also presented, exhibiting quasi-periodic modulations on time-scales of 1000 s, compatible with the eLIMA framework.

Self-Trapping of G-Mode Oscillations in Relativistic Thin Disks, Revisited

We examine by a perturbation method how the self-trapping of g-mode oscillations in geometrically thin relativistic discs is affected by uniform vertical magnetic fields. Discs that we consider are isothermal in the vertical direction, but are truncated at a certain height by presence of hot coronae. We find that the characteristics of self-trapping of axisymmetric g-mode oscillations in non-magnetized discs are kept unchanged in magnetized discs at least till a strength of the fields, depending on vertical thickness of discs. These magnetic fields become stronger as the disc becomes thinner. This result suggests that trapped g-mode oscillations still remain as one of the possible candidates of quasi-periodic oscillations observed in black hole and neutron-star X-ray binaries (Okazaki, Kato & Fukue; Nowak et al.) in the cases where vertical magnetic fields in discs are weak.

Resonant tidal excitation of superfluid neutron stars in coalescing binaries

We study the resonant tidal excitation of g modes in coalescing superfluid neutron star (NS) binaries and investigate how such tidal driving impacts the gravitational-wave (GW) signal of the inspiral. Previous studies of this type treated the NS core as a normal fluid and thus did not account for its expected superfluidity. The source of buoyancy that supports the g modes is fundamentally different in the two cases: in a normal fluid core, the buoyancy is due to gradients in the proton-to-neutron fraction, whereas in a superfluid core it is due to gradients in the muon-to-electron fraction. The latter yields a stronger stratification and a superfluid NS therefore has a denser spectrum of g modes with frequencies above 10 Hz. As a result, many more g modes undergo resonant tidal excitation as the binary sweeps through the bandwidth of GW detectors such as LIGO. We find that ≃ 10 times more orbital energy is transferred into g-mode oscillations if the NS has a superfluid core rather than a normal fluid core. However, because this energy is transferred later in the inspiral when the orbital decay is faster, the accumulated phase error in the gravitational waveform is comparable for a superfluid and a normal fluid NS (∼10−3–10−2rad). A phase error of this magnitude is too small to be measured from a single event with the current generation of GW detectors.

Pulsation in pre-main sequence stars

AbstractAsteroseismology has been proven to be a successful tool to unravel details of the internal structure for different types of stars in various stages of evolution well after birth. We can now show that it has similar power for pre-main sequence (pre-MS) objects. Pre-MS stars with masses between ~1 and 6 solar masses that have recently been formed and gain their energy mainly from gravitational contraction can become vibrationally unstable during their evolution to the main sequence. Within the past ~15 years, several dozens of pulsating pre-MS stars were discovered using data obtained from ground and from space. Depending on their masses, pre-MS stars can show three different types of pulsations: (i) δ Scuti type p-mode pulsations, (ii) γ Doradus like g-mode oscillations and (iii) g-mode Slowly Pulsating B star pulsations.Our asteroseismic investigations yielded new insights into the connection between the pulsations and early stellar evolution: We revealed a relation between the stars' oscillatory behavior and their relative evolutionary stages that might lead us to a model-independent determination of the stars' fundamental parameters. With this we will be able to put constraints on theoretical models and help to answer some of the yet open questions in early stellar evolution.

Pulsations of Post-AGB Pre-White Dwarfs with Hydrogen-dominated Atmospheres*

It is shown by a fully non adiabatic analysis that pre-white dwarfs with hydrogen-dominated atmospheres in the range of T eff = 40 000 K - 300 000 K are pul-sationally unstable due to nuclear reactions in the hydrogen burning-shell against low-degree g-modes in the period range of about 40-200 s. It is also shown that the amount of hydrogen has a significant influence on the instability domain of such pre-white dwarfs in the Hertzsprung-Russel (H-R) diagram. Hence, the thickness of hydrogen-dominated envelopes may be well constrained by observing the presence of the g-mode oscillations.