Large Frequency Separation Research Articles

Evolution of dipolar mixed-mode coupling factor in red giant stars: impact of buoyancy spike

ABSTRACT Mixed modes observed in red giants allow for investigation of the stellar interior structures. One important feature in these structures is the buoyancy spike caused by the discontinuity of the chemical gradient left behind during the first dredge-up. The buoyancy spike emerges at the base of the convective zone in low-luminosity red giants and later becomes a glitch when the g-mode cavity expands to encompass the spike. Here, we study the impact of the buoyancy spike on the dipolar mixed modes using stellar models with different properties. We find that the applicability of the asymptotic formalisms for the coupling factor, q, varies depending on the location of the evanescent zone, relative to the position of the spike. Significant deviations between the value of q inferred from fitting the oscillation frequencies and either of the formalisms proposed in the literature are found in models with a large frequency separation in the interval 5–15 μHz, with evanescent zones located in a transition region that may be thin or thick. However, it is still possible to reconcile q with the predictions from the asymptotic formalisms, by choosing which formalism to use according to the value of q. For stars approaching the luminosity bump, the buoyancy spike becomes a glitch and strongly affects the mode frequencies. Fitting the frequencies without accounting for the glitch leads to unphysical variations in the inferred q, but we show that this is corrected when properly accounting for the glitch in the fitting.

Mixed-mode Asteroseismology of Red Giant Stars Through the Luminosity Bump

Most current models of low-mass red giant stars do not reproduce the observed position of the red giant branch luminosity bump, a diagnostic of the maximum extent of the convective envelope during the first dredge up. Global asteroseismic parameters, the large frequency separation and frequency of maximum oscillation power, measured for large samples of red giants, show that modeling convective overshoot below the convective envelope helps match the modeled luminosity bump positions to observations; however, these global parameters cannot be used to probe envelope overshoot in a star-by-star manner. Red giant mixed modes, which behave like acoustic modes at the surface and like gravity modes in the core, contain important information about the interior structure of the star, especially near the convective boundary. Therefore, these modes may be used to probe interior processes, such as overshoot. Using a grid of red giant models with varying mass, metallicity, surface gravity, overshoot treatment, and amount of envelope overshoot, we find that changing the overshoot amplitude (and prescription) of overshoot below the convection zone in red giant stellar models results in significant differences in the evolution of the models’ dipole mixed-mode oscillation frequencies, the average mixed-mode period spacing (〈ΔP〉), and gravity-mode phase offset term (ϵ g ).

Measuring Frequency and Period Separations in Red-giant Stars Using Machine Learning

Abstract Asteroseismology is used to infer the interior physics of stars. The Kepler and TESS space missions have provided a vast data set of red-giant lightcurves, which may be used for asteroseismic analysis. These data sets are expected to significantly grow with future missions such as PLATO, and efficient methods are therefore required to analyze these data rapidly. Here, we describe a machine-learning algorithm that identifies red giants from the raw oscillation spectra and captures p- and mixed-mode parameters from the red-giant power spectra. We report algorithmic inferences for large frequency separation (Δν), frequency at maximum amplitude ( ν max ), and period separation (ΔΠ) for an ensemble of stars. In addition, we have discovered ∼25 new probable red giants among 151,000 Kepler long-cadence stellar-oscillation spectra analyzed by this method, among which four are binary candidates that appear to possess red-giant counterparts. To validate the results of this method, we selected ∼3000 Kepler stars, at various evolutionary stages ranging from subgiants to red clumps, and compare inferences of Δν, ΔΠ, and ν max with estimates obtained using other techniques. The power of the machine-learning algorithm lies in its speed: It is able to accurately extract seismic parameters from 1000 spectra in ∼5 s on a modern computer (a single core of the Intel® Xeon® Platinum 8280 CPU).

All-optical dissipative discrete time crystals

Time crystals are periodic states exhibiting spontaneous symmetry breaking in either time-independent or periodically-driven quantum many-body systems. Spontaneous modification of discrete time-translation symmetry in periodically-forced physical systems can create a discrete time crystal (DTC) constituting a state of matter possessing properties like temporal rigid long-range order and coherence, which are inherently desirable for quantum computing and information processing. Despite their appeal, experimental demonstrations of DTCs are scarce and significant aspects of their behavior remain unexplored. Here, we report the experimental observation and theoretical investigation of DTCs in a Kerr-nonlinear optical microcavity. Empowered by the self-injection locking of two independent lasers with arbitrarily large frequency separation simultaneously to two same-family cavity modes and a dissipative Kerr soliton, this versatile platform enables realizing long-awaited phenomena such as defect-carrying DTCs and phase transitions. Combined with monolithic microfabrication, this room-temperature system paves the way for chip-scale time crystals supporting real-world applications outside sophisticated laboratories.

BESTP — An automated Bayesian modeling tool for asteroseismology

Asteroseismic observations are crucial to constrain stellar models with precision. Bayesian Estimation of STellar Parameters (BESTP) is a tool that utilizes Bayesian statistics and nested sampling Monte Carlo algorithm to search for the stellar models that best match a given set of classical and asteroseismic constraints from observations. The computation and evaluation of models are efficiently performed in an automated and multi-threaded way. To illustrate the capabilities of BESTP, we estimate fundamental stellar properties for the Sun and the red-giant star HD 222076. In both cases, we find models that are consistent with observations. We also evaluate the improvement in the precision of stellar parameters when the oscillation frequencies of individual modes are included as constraints, compared to the case when only the large frequency separation is included. For the solar case, the uncertainties of estimated masses, radii and ages are reduced by 0.7%, 0.3% and 8% respectively. For HD 222076, they are reduced even more noticeably by 2%, 0.5% and 4.7% respectively. We also note an improvement of 10% for the age of HD 222076 when the Gaia parallax is included as a constraint compared to the case when only the large separation is included as a constraint.

KIC 5197256: an eclipsing binary containing a δ Scuti variable star

This paper reports analysis of an eclipsing binary system KIC 5197256 with a δ Sct variable component. Utilizing light-curve modeling, several stellar parameters are derived, e.g., temperature, mass, and mass ratio. The O – C diagram is a straight line with a negative slope which means that its period is almost constant for about 2 yr. Frequency analyses are performed for the residual light curve after subtracting the binary variations. The frequency spectrum reveals that one component star is a δ Scuti variable. Large frequency separation is cross-identified with the histogram graph and the Fourier transform method. Based on the large separation and density relationship, the mean density of the δ Sct component is estimated to be 0.05 g⋅cm−3. Five frequencies with the same frequency spacing in the range of 25 d−1 – 34 d−1 are detected. Statistically, the pulsation amplitudes of δ Sct stars increase with decreasing of rotations, so we propose that KIC 5197256 might have a relatively large rotational velocity, and the frequency f 10 might be the rotation frequency.

Asteroseismology of evolved stars with EGGMiMoSA

Context.In the context of an ever increasing amount of highly precise data, thanks to the numerous space-borne missions, came a revolution in stellar physics. This data allowed asteroseismology to thrive and improve our general knowledge of stars. Important results were obtained about giant stars owing to the presence of ‘mixed modes’ in their oscillation spectra. These modes carry information about the whole stellar interior, enabling the comprehensive characterisation of their structure.Aims.The current study is part of a series of papers that provide a technique to coherently and robustly analyse the mixed-modes frequency spectra and characterise the stellar structure of stars on both the subgiant branch and red-giant branch (RGB). In this paper we aim at defining seismic indicators, relevant of the stellar structure, as well as studying their evolution along a grid of models.Methods.The proposed method, EGGMiMoSA, relies on the asymptotic description of mixed modes. It defines appropriate initial guesses for the parameters of the asymptotic formulation and uses a Levenberg-Marquardt minimisation scheme in order to adjust the complex mixed-modes pattern in a fast and robust way.Results.We are able to follow the evolution of the mixed-modes parameters along a grid of models from the subgiant phase to the RGB bump, therefore extending previous works. We show the impact of the stellar mass and composition on the evolution of these parameters. We observe that the evolution of the period spacing Δπ1, pressure offsetϵp, gravity offsetϵg, and coupling factorqas a function of the large frequency separation Δνis little affected by the chemical composition and that it follows two different regimes depending on the evolutionary stage. On the subgiant branch, the stellar models display a moderate core-envelope density contrast. Therefore, the evolution of Δπ1,ϵp,ϵg, andqsignificantly changes with the stellar mass. Furthermore, we demonstrate that, for a given metallicity and with proper measurements of the period spacing Δπ1and large frequency separation Δν, we may unambiguously constrain the stellar mass, radius and age of a subgiant star. Conversely, as the star reaches the red-giant branch, the core-envelope density contrast becomes very large. Consequently, the evolution ofϵp,ϵgandqas a function of Δνbecomes independent of the stellar mass. This is also true for Δπ1in stars with masses ≲1.8 M⊙because of core electron degeneracy. This degeneracy in Δπ1is lifted for higher masses, again allowing for a precise measurement of the stellar age. Overall, our computations qualitatively agree with previous observed and theoretical studies.Conclusions.The method provides automated measurements of the adjusted parameters along a grid of models and opens the way to the precise seismic characterisation of both subgiants and red giants. In the following papers of the series, we will explore further refinements to the technique as well as its application to observed stars.

Fundamental properties of a selected sample of Ap stars: Inferences from interferometric and asteroseismic constraints

Context. Magnetic fields influence the formation and evolution of stars and impact the observed stellar properties. magnetic A-type stars (Ap stars) are a prime example of this. Access to precise and accurate determinations of their stellar fundamental properties, such as masses and ages, is crucial to understand the origin and evolution of fossil magnetic fields. Aims. We propose using the radii and luminosities determined from interferometric measurements, in addition to seismic constraints when available, to infer fundamental properties of 14 Ap stars préviously characterised. Methods. We used a grid-based modelling approach, employing stellar models computed with the CESTAM stellar evolution code, and the parameter search performed with the AIMS optimisation method. The stellar model grid was built using a wide range of initial helium abundances and metallicities in order to avoid any bias originating from the initial chemical composition. The large frequency separations (Δν) of HR 1217 (HD 24712) and α Cir (HD 128898), two rapidly oscillating Ap stars of the sample, were used as seismic constraints. Results. We inferred the fundamental properties of the 14 stars in the sample. The overall results are consistent within 1σ with previous studies, however, the stellar masses inferred in this study are higher. This trend likely originates from the broader range of chemical compositions considered in this work. We show that the use of Δν in the modelling significantly improves our inferences, allowing us to set reasonable constraints on the initial metallicity which is, otherwise, unconstrained. This gives an indication of the efficiency of atomic diffusion in the atmospheres of roAp stars and opens the possibility of characterising the transport of chemical elements in their interiors.

Relations between the asteroseismic indices and stellar parameters of δ Scuti stars for two years of TESS mission

ABSTRACT We investigate the relationship between the asteroseismic indices and the physical quantities of 438 δ Scuti (DSCT) stars observed by the Transiting Exoplanet Survey Satellite (TESS) mission at 26 sectors. We study the scaling relations of stellar parameters (effective temperature, surface gravity, density, etc.) and asteroseismic indices such as fundamental frequency, large frequency separation (Δν), frequency of the highest peak in the spectrum, and the peak of the envelope of oscillation mode (νmax) for DSCT targets. Using an empirical relation and a 2D autocorrelation method, we determine the large frequency separation for targets. We obtain a highly positive correlation between the fundamental radial pressure mode and the large separation for one-third of targets. We find a scaling relation between the large separation and νmax as $\Delta \nu =0.49\nu _{\rm max}^{0.68}$, which is similar to that of the solar-like and red giant stars. We show a strong positive correlation between the effective temperature and νmax (Pearson correlation R = 0.65). We also obtain a very strong positive correlation (R = 0.86) between the effective temperature multiplying by the surface gravity and νmax.

Fundamental properties of stars from Kepler and Gaia data: parallax offset and revised scaling relations

ABSTRACT Data from the space missions Gaia, Kepler, CoRoT and TESS, make it possible to compare parallax and asteroseismic distances. From the ratio of two densities ρsca/ρπ, we obtain an empirical relation fΔν between the asteroseismic large frequency separation and mean density, which is important for more accurate stellar mass and radius. This expression for main-sequence (MS) and subgiant stars with K-band magnitude is very close to the one obtained from interior MS models by Yıldız, Çelik & Kayhan. We also discuss the effects of effective temperature and parallax offset as the source of the difference between asteroseismic and non-asteroseismic stellar parameters. We have obtained our best results for about 3500 red giants (RGs) by using 2MASS data and model values for fΔν from Sharma et al. Another unknown scaling parameter $f_{\nu _{\rm max}}$ comes from the relationship between the frequency of maximum amplitude and gravity. Using different combinations of $f_{\nu _{\rm max}}$ and the parallax offset, we find that the parallax offset is generally a function of distance. The situation where this slope disappears is accepted as the most reasonable solution. By a very careful comparison of asteroseismic and non-asteroseismic parameters, we obtain very precise values for the parallax offset and $f_{\nu _{\rm max}}$ for RGs of –0.0463 ± 0.0007 mas and 1.003 ± 0.001, respectively. Our results for mass and radius are in perfect agreement with those of APOKASC-2: the mass and radius of ∼3500 RGs are in the range of about 0.8–1.8 M⊙ (96 per cent) and 3.8–38 R⊙, respectively.

Asteroseismology of the heartbeat star KIC 5006817

This paper summarizes the project work on asteroseismology at the ERASMUS+ GATE 2020 Summer school on space satellite data. The aim was to do a global asteroseismic analysis of KIC 5006817 and quantify its stellar properties using the high-quality, state of the art space missions data. We employed the aperture photometry to analyze the data from the Kepler space telescope and the Transiting Exoplanet Survey Satellite (TESS). Using the lightkurve Python package, we have derived the asteroseismic parameters and calculated the stellar parameters using the scaling relations. Our analysis of KIC 5006817 confirmed its classification as a heartbeat binary. The rich oscillation spectrum facilitate estimating power excess ($\nu_{\rm max}$) at 145.50$\pm$0.50 $\mu$Hz and large frequency separation ($\Delta\nu$) to be 11.63$\pm$0.10 $\mu$Hz. Our results showed that the primary component is a low-luminosity, red-giant branch star with a mass, radius, surface gravity, and luminosity of 1.53$\pm$0.07 M$_\odot$, 5.91$\pm$0.12 R$_\odot$, 3.08$\pm$0.01 dex, and 19.66$\pm$0.73 L$_\odot$, respectively. The orbital period of the system is 94.83$\pm$0.05 d.

Radial oscillations of boson stars made of ultralight repulsive dark matter

We compute the lowest frequency radial oscillation modes of boson stars. It is assumed that the object is made of pseudo-Goldstone bosons subjected to a scalar potential that leads to a repulsive self-interaction force, and which is characterized by two unknown mass scales m (mass of the particle) and F (decay constant). First we integrate the Tolman-Oppenheimer-Volkoff equations for the hydrostatic equilibrium of the star, and then we solve the Sturm-Liouville boundary value problem for the perturbations using the shooting method. The effective potential that enters into the Schrödinger-like equation as well as several associated eigenfunctions are shown as well. Moreover, we found that the large frequency separation, i.e. the difference between consecutive modes, is proportional to the square root of the mass of the star and the cube of the mass scale defined by Λ≡mF.

The Hot Limit of Solar-like Oscillations From Kepler Photometry

Kepler short-cadence photometry of 2347 stars with effective temperatures in the range 6000 – 10000 K was used to search for the presence of solar-like oscillations. The aim is to establish the location of the hot end of the stochastic convective excitation mechanism and to what extent it may overlap the δ Scuti/γ Doradus instability region. A simple but effective autocorrelation method is described which is capable of detecting low-amplitude solar-like oscillations, but with significant risk of a false detection. The location of the frequency of maximum oscillation power, ν max , and the large frequency separation, ∆ν, is determined for 167 stars hotter than 6000 K, of which 70 are new detections. Results indicate that the hot edge of excitation of solar-like oscillations does not appear to extend into the δ Scuti/γ Doradus instability strip.

An ERP Study on the Auditory Stream Segregation in Cochlear Implant Simulations: Effects of Frequency Separation and Time Interval.

Auditory stream segregation is an important function of the auditory system, and the extent to which this function works has a major impact on listener's ability to recognize auditory objects in complex listening environments. However, cochlear implant (CI) listeners are poorly equipped for this challenge, mainly owing to the impoverished sensory information available via their implants. The purpose of this study was to examine two factors, i.e., frequency separation and time interval, affecting the auditory stream segregation in vocoder simulations simulating CI speech processing based on an event-related potential (ERP) experiment. The pure-tone stimuli were processed by a vocoding process, and presented to normal-hearing listeners in an ERP experiment. Experimental results showed that a large frequency separation or a short time interval led to a larger mismatch negativity (MMN) response. The MMN results in this work suggested that the degree of auditory stream segregation was affected by frequency separation and time interval, and MMN could serve as a potential index for future ERP studies on auditory stream segregation in CI users.

Asteroseismic masses of four evolved planet-hosting stars using SONG and TESS: resolving the retired A-star mass controversy

ABSTRACT The study of planet occurrence as a function of stellar mass is important for a better understanding of planet formation. Estimating stellar mass, especially in the red giant regime, is difficult. In particular, stellar masses of a sample of evolved planet-hosting stars based on spectroscopy and grid-based modelling have been put to question over the past decade with claims they were overestimated. Although efforts have been made in the past to reconcile this dispute using asteroseismology, results were inconclusive. In an attempt to resolve this controversy, we study four more evolved planet-hosting stars in this paper using asteroseismology, and we revisit previous results to make an informed study of the whole ensemble in a self-consistent way. For the four new stars, we measure their masses by locating their characteristic oscillation frequency, νmax, from their radial velocity time series observed by SONG. For two stars, we are also able to measure the large frequency separation, Δν, helped by extended SONG single-site and dual-site observations and new Transiting Exoplanet Survey Satellite observations. We establish the robustness of the νmax-only-based results by determining the stellar mass from Δν, and from both Δν and νmax. We then compare the seismic masses of the full ensemble of 16 stars with the spectroscopic masses from three different literature sources. We find an offset between the seismic and spectroscopic mass scales that is mass dependent, suggesting that the previously claimed overestimation of spectroscopic masses only affects stars more massive than about 1.6 M⊙.

Asteroseismology: Radial oscillations of neutron stars with realistic equation of state

We study radial oscillations of non-rotating neutron stars (NSs) in four-dimensional General Relativity. The interior of the NS was modelled within a recently proposed multicomponent realistic equation of state (EoS) with the induced surface tension (IST). In particular, we considered the IST EoS with two sets of model parameters, that both reproduce all the known properties of normal nuclear matter, give a high quality description of the proton flow constraint, hadron multiplicities created in nuclear-nuclear collisions, consistent with astrophysical observations and the observational data from the NS-NS merger. We computed the 12 lowest radial oscillation modes, their frequencies and corresponding eigenfunctions, as well as the large frequency separation for six selected fiducial NSs (with different radii and masses of 1.2, 1.5 and 1.9 solar masses) of the two distinct model sets. The calculated frequencies show their continuous growth with an increase of the NS central baryon density. Moreover, we found correlations between the behaviour of first eigenfunction calculated for the fundamental mode, the adiabatic index and the speed of sound profile, which could be used to probe the internal structure of NSs with the asteroseismology data.

On the multiplicity of axisymmetric Alfvén continuous spectra in tokamaks

Axisymmetric Alfvén continuous spectra are derived using the ideal MHD equations. The usual toroidal coupling effect due to the variation of the magnetic field strength is neglected, but the curvature coupling of the pressure fluctuation and the geodesic compressional effect are included. The cylindrical continuous spectrum of Alfvén waves splits into two branches due to these effects. The frequency separation of the two m = 2 branches is much smaller than that of the two m = 1 branches. It is likely that the experimentally observed modes with smaller frequency separation are related to the two m = 1 continuum branches, while the modes with large frequency separation have different poloidal numbers.

Floquet dynamics in the quantum measurement of mechanical motion

The radiation-pressure interaction between one or more laser fields and a mechanical oscillator gives rise to a wide range of phenomena: from sideband cooling and backaction-evading measurements to pondermotive and mechanical squeezing to entanglement and motional sideband asymmetry. In many protocols, such as dissipative mechanical squeezing, multiple lasers are utilized, giving rise to periodically driven optomechanical systems. Here we show that in this case, Floquet dynamics can arise due to presence of Kerr-type nonlinearities, which are ubiqitious in optomechanical systems. Specifically, employing multiple probe tones, we perform sideband asymmetry measurements, a macroscopic quantum effect, on a silicon optomechanical crystal sideband-cooled to 40% ground-state occupation. We show that the Floquet dynamics, resulting from the presence of multiple pump tones, gives rise to an artificially modified motional sideband asymmetry by redistributing thermal and quantum fluctuations among the initially independently scattered thermomechanical sidebands. For pump tones exhibiting large frequency separation, the dynamics is suppressed and accurate quantum noise thermometry demonstrated. We develop a theoretical model based on Floquet theory that accurately describes our observations. The resulting dynamics can be understood as resulting from a synthetic gauge field among the Fourier modes, which is created by the phase lag of the Kerr-type response. This novel phenomenon has wide-ranging implications for schemes utilizing several pumping tones, as commonly employed in backaction-evading measurements, dissipative optical squeezing, dissipative mechanical squeezing and quantum noise thermometry. Our observation may equally well be used for optomechanical Floquet engineering, e.g. generation of topological phases of sound by periodic time-modulation.

Signature of solargmodes in first-orderp-mode frequency shifts

Context.Solar gravity modes (gmodes) are buoyancy waves that are trapped in the solar radiative zone and have been very difficult to detect at the surface. Solargmodes would complement solar pressure modes (pmodes) in probing the central regions of the Sun, for example the rotation rate of the core.Aims.A detection ofgmodes using changes in the large frequency separation ofpmodes has recently been reported. However, it is unclear howpandgmodes interact. The aim of this study is to evaluate to what extentgmodes can perturb the frequencies ofpmodes.Methods.We computed the first-order perturbation to globalp-mode frequencies due to a flow field and perturbations to solar structure (e.g. density and sound speed) caused by agmode. We focused on long-periodgmodes and assumed that theg-mode perturbations are constant in time. The surface amplitude ofgmodes is assumed to be 1 mm s−1, which is close to the observational limit set by Doppler observations.Results.Gravity modes do perturbp-mode frequencies to first order if the harmonic degree of thegmode is even and if its azimuthal order is zero. The effect is extremely small. For dipole and quadrupolepmodes, all frequency shifts are smaller than 0.1 nHz, or 2 × 10−8in relative numbers. This is because the relative perturbation to solar structure quantities caused by agmode of realistic amplitude is of the order of 10−6–10−5. Additionally, we find that structural changes dominate over advection. Surprisingly, the interaction ofgandpmodes takes place to a large part near the surface, wherepmodes spend most of their propagation times andgmodes generate the largest relative changes to solar structure. This is due to the steep density stratification, which compensates the evanescent behaviour ofgmodes in the convection zone.Conclusions.It appears to be impossible to detectgmodes solely through their signature inp-mode frequency shifts. Whethergmodes leave a detectable signature inp-mode travel times under a given observational setup remains an open question.

EPIC 202843107: a close eclipsing binary containing a δ Scuti variable

This paper reports on the discovery that an eclipsing binary system, EPIC 202843107, has a δ Scuti variable component. The phased light curve from the Kepler space telescope presents a detached configuration. The binary modeling indicates that the two component stars have almost the same radius and may have experienced orbital circularization. Frequency analyses are performed for the residual light curve after subtracting the binary variations. The frequency spectrum reveals that one component star is a δ Scuti variable. A large frequency separation is cross-identified with the corresponding histogram, the Fourier transform and the echelle diagram method. The mean density of the δ Scuti component is estimated to be 0.09 g cm−3 based on the large separation and density relation. Systems like EPIC 202843107 are helpful to study the stellar evolution and physical state of binary stars.