Small Frequency Separations Research Articles

FIRST ASTEROSEISMIC LIMITS ON THE NATURE OF DARK MATTER

We report the first constraints on the properties of weakly interacting low-mass dark matter (DM) particles using asteroseismology. The additional energy transport mechanism due to accumulated asymmetric DM particles modifies the central temperature and density of low-mass stars and suppresses the convective core expected in 1.1-1.3 Ms stars even for an environmental DM density as low as the expected in the solar neighborhood. An asteroseismic modeling of the stars KIC 8006161, HD 52265 and Alpha Cen B revealed small frequency separations significantly deviated from the observations, leading to the exclusion of a region of the DM parameter space mass versus spin-dependent DM-proton scattering cross section comparable with present experimental constraints.

Evolutionary influences on the structure of red-giant acoustic oscillation spectra from 600d ofKeplerobservations

Context: The Kepler space mission is reaching continuous observing times long enough to start studying the fine structure of the observed p-mode spectra. Aims: In this paper, we aim to study the signature of stellar evolution on the radial and p-dominated l=2 modes in an ensemble of red giants that show solar-type oscillations. Results: We find that the phase shift of the central radial mode (eps_c) is significantly different for red giants at a given large frequency separation (Dnu_c) but which burn only H in a shell (RGB) than those that have already ignited core He burning. Even though not directly probing the stellar core the pair of local seismic observables (Dnu_c, eps_c) can be used as an evolutionary stage discriminator that turned out to be as reliable as the period spacing of the mixed dipole modes. We find a tight correlation between eps_c and Dnu_c for RGB stars and no indication that eps_c depends on other properties of these stars. It appears that the difference in eps_c between the two populations becomes if we use an average of several radial orders, instead of a local, i.e. only around the central radial mode, Dnu to determine the phase shift. This indicates that the information on the evolutionary stage is encoded locally, in the shape of the radial mode sequence. This shape turns out to be approximately symmetric around the central radial mode for RGB stars but asymmetric for core He burning stars. We computed radial modes for a sequence of RG models and find them to qualitatively confirm our findings. We also find that, at least in our models, the local Dnu is an at least as good and mostly better proxy for both the asymptotic spacing and the large separation scaled from the model density than the average Dnu. Finally, we investigate the signature of the evolutionary stage on the small frequency separation and quantify the mass dependency of this seismic parameter.

Fundamental properties of fiveKeplerstars using global asteroseismic quantities and ground-based observations

We present an asteroseismic study of the solar-like stars KIC 11395018, KIC 10273246, KIC 10920273, KIC 10339342, and KIC 11234888 using short-cadence time series of more than eight months from the Kepler satellite. For four of these stars, we derive atmospheric parameters from spectra acquired with the Nordic Optical Telescope. The global seismic quantities (average large frequency separation and frequency of maximum power), combined with the atmospheric parameters, yield the mean density and surface gravity with precisions of 2% and ~0.03 dex, respectively. We also determine the radius, mass, and age with precisions of 2-5%, 7-11%, and ~35%, respectively, using grid-based analyses. We determine asteroseismic distances to these stars with a precision better than 10%, and constrain the stellar inclination for three of the stars. An Li abundance analysis yields an independent estimate of the age, but this is inconsistent with the asteroseismically determined age for one of the stars. We compare the results from five different grid-based analyses, and we find that they all provide radius and mass values to within 2.4sigma. The absence of a metallicity constraint when the average large frequency separation is measured with a precision of 1% biases the fitted radius and mass for the stars with non-solar metallicity (metal-rich KIC 11395018 and metal-poor KIC 10273246), while including a metallicity constraint reduces the uncertainties in both of these parameters by almost a factor of two. We found that including the average small frequency separation improves the determination of the age only for KIC 11395018 and KIC 11234888, and for the latter this improvement was due to the lack of strong atmospheric constraints. (Abridged).

ASTEROSEISMIC DIAGRAMS FROM A SURVEY OF SOLAR-LIKE OSCILLATIONS WITH KEPLER

Photometric observations made by the NASA Kepler Mission have led to a dramatic increase in the number of main-sequence and subgiant stars with detected solar-like oscillations. We present an ensemble asteroseismic analysis of 76 solar-type stars. Using frequencies determined from the Kepler time-series photometry, we have measured three asteroseismic parameters that characterize the oscillations: the large frequency separation (\Delta \nu), the small frequency separation between modes of l=0 and l=2 (\delta \nu_02), and the dimensionless offset (\epsilon). These measurements allow us to construct asteroseismic diagrams, namely the so-called C-D diagram of \delta \nu_02 versus \Delta \nu, and the recently re-introduced {\epsilon} diagram. We compare the Kepler results with previously observed solar-type stars and with theoretical models. The positions of stars in these diagrams places constraints on their masses and ages. Additionally, we confirm the observational relationship between {\epsilon} and T_eff that allows for the unambiguous determination of radial order and should help resolve the problem of mode identification in F stars.

The diameter of the CoRoT target HD 49933

Context. The interpretation of stellar pulsations in terms of internal structure depends on the knowledge of the fundamental stellar parameters. Long-base interferometers permit us to determine very accurate stellar radii, which are independent constraints for stellar models that help us to locate the star in the HR diagram. Aims: Using a direct interferometric determination of the angular diameter and advanced three-dimensional (3D) modeling, we derive the radius of the CoRoT target HD 49933 and reduce the global stellar parameter space compatible with seismic data. Methods: The VEGA/CHARA spectro-interferometer is used to measure the angular diameter of the star. A 3D radiative hydrodynamical simulation of the surface is performed to compute the limb darkening and derive a reliable diameter from visibility curves. The other fundamental stellar parameters (mass, age, and Teff) are found by fitting the large and small p-mode frequency separations using a stellar evolution model that includes microscopic diffusion. Results: We obtain a limb-darkened angular diameter of {\theta}LD = 0.445 \pm 0.012 mas. With the Hipparcos parallax, we obtain a radius of R = 1.42 \pm 0.04 Rsun. The corresponding stellar evolution model that fits both large and small frequency separations has a mass of 1.20 \pm 0.08 Msun and an age of 2.7 Gy. The atmospheric parameters are Teff = 6640 \pm 100 K, log g = 4.21 \pm 0.14, and [Fe/H] = -0.38.

Solar-like oscillations from the depths of the red-giant star KIC 4351319 observed with Kepler

We present the results of the asteroseismic analysis of the red-giant star KIC 4351319 (TYC 3124-914-1), observed for 30 days in short-cadence mode with the Kepler satellite. The analysis has allowed us to determine the large and small frequency separations, and the frequency of maximum oscillation power. The high signal-to-noise ratio of the observations allowed us to identify 25 independent pulsation modes whose frequencies range approximately from 300 to 500 muHz. The observed oscillation frequencies together with the accurate determination of the atmospheric parameters (effective temperature, gravity and metallicity), provided by additional ground-based spectroscopic observations, enabled us to theoretically interpret the observed oscillation spectrum. KIC 4351319 appears to oscillate with a well defined solar-type p-modes pattern due to radial acoustic modes and non-radial nearly pure p modes. In addition, several non-radial mixed modes have been identified. Theoretical models well reproduce the observed oscillation frequencies and indicate that this star, located at the base of the ascending red-giant branch, is in the hydrogen-shell burning phase, with a mass of about 1.3 solar masses, a radius of about 3.4 solar radii and an age of about 5.6 Gyr. The main parameters of this star have been determined with an unprecedent level of precision for a red-giant star, with uncertainties of 2% for mass, 7% for age, 1% for radius, and 4% for luminosity.

Quantitative estimates of the constraints on solar-like models imposed by observables

Context. Seismic parameters such as the large Δ0 and small δ02 frequency separations are now being measured in a very large number of stars and begin to be used to test the physics of stellar models. Aims. We estimate the influence of different observed quantities (oscillation frequencies, interferometry, etc.) and the impact of their accuracy in constraining stellar model parameters. Methods. To relate the errors in observed quantities to the precision of the theoretical model parameters, we analyse the behaviour of the χ 2 fitting function around its minimum using the singular value decomposition (SVD) formalism. A new indicator called “weighting” quantifies the relative importance of observational constraints on the determination of each physical parameter individually. These tools are applied to a grid of evolutionary sequences for solar-like stellar models with varying age and mass, and to a real case: HD 49933 – a typical case for which seismic observations are available from space using CoRoT. Results. The mass M is always the best determined parameter. The new indicator “weighting” allows us to rank the importance of the different constraints: the mean large separation Δ0, the radius R/R� , the mean small separation δ02, the luminosity L/L� ,t he effective temperature Teff. If the metallicity and age parameters are known, for example in an open cluster, using either individual or mean frequency separations yields the same uncertainties for masses less than 1.1 M� . For HD 49933 the combination of M and Y0: M 2 Y0 is well determined because of their correlation. However, they are poorly constrained individually. The frequency difference δ01 ,i f known with an error of about 0.3%, can determine the size of the convective core overshooting with about 3% accuracy.

SOLAR-LIKE OSCILLATIONS IN KIC 11395018 AND KIC 11234888 FROM 8 MONTHS OFKEPLERDATA

We analyze the photometric short-cadence data obtained with the Kepler Mission during the first eight months of observations of two solar-type stars of spectral types G and F: KIC 11395018 and KIC 11234888 respectively, the latter having a lower signal-to-noise ratio compared to the former. We estimate global parameters of the acoustic (p) modes such as the average large and small frequency separations, the frequency of the maximum of the p-mode envelope and the average linewidth of the acoustic modes. We were able to identify and to measure 22 p-mode frequencies for the first star and 16 for the second one even though the signal-to-noise ratios of these stars are rather low. We also derive some information about the stellar rotation periods from the analyses of the low-frequency parts of the power spectral densities. A model-independent estimation of the mean density, mass and radius are obtained using the scaling laws. We emphasize the importance of continued observations for the stars with low signal-to-noise ratio for an improved characterization of the oscillation modes. Our results offer a preview of what will be possible for many stars with the long data sets obtained during the remainder of the mission.

Probing tiny convective cores with the acoustic modes of lowest degree

Solar-like oscillations are expected to be excited in stars of up to about 1.6 solar masses. Most of these stars will have convective cores during their main-sequence evolution. At the edges of these convective cores, there is a rapid variation in the sound speed, which influences the frequencies of acoustic oscillations. In this paper we build on earlier work to investigate the impact that these rapid structural variations have on different p-mode frequency combinations, involving modes of low degree. In particular, we adopt a different expression to describe the sound speed variation at the edge of the core, which we show more closely reproduces the profiles derived from the equilibrium models. We analyse the impact of this change on the frequency perturbation derived for radial modes. Moreover, we consider three different small frequency separations involving modes of degree l = 0,1,2,3, l = 0,1, and l = 0,2, and show that they are all significantly affected by the sharp sound speed variation at the edge of the core. In particular, we confirm that the frequency derivative of the diagnostic tool that combines modes of degree up to 3 can potentially be used to infer the amplitude of the relative sound speed variation directly at the edge of the core. We show that at high frequencies the other two diagnostic tools can be up to a few μHz smaller than what would be expected in the absence of the rapid structural variation at the edge of the core. Also, we show that the absolute values of their frequency derivatives are significantly increased, in a manner that strongly depends on stellar age.

ASTEROSEISMOLOGY OF RED GIANTS FROM THE FIRST FOUR MONTHS OFKEPLERDATA: GLOBAL OSCILLATION PARAMETERS FOR 800 STARS

We have studied solar-like oscillations in ~800 red-giant stars using Kepler long-cadence photometry. The sample includes stars ranging in evolution from the lower part of the red-giant branch to the Helium main sequence. We investigate the relation between the large frequency separation (Delta nu) and the frequency of maximum power (nu_max) and show that it is different for red giants than for main-sequence stars, which is consistent with evolutionary models and scaling relations. The distributions of nu_max and Delta nu are in qualitative agreement with a simple stellar population model of the Kepler field, including the first evidence for a secondary clump population characterized by M ~> 2 M_sun and nu_max ~ 40-110 muHz. We measured the small frequency separations delta nu_02 and delta nu_01 in over 400 stars and delta nu_03 in over 40. We present C-D diagrams for l=1, 2 and 3 and show that the frequency separation ratios delta nu_02/Delta nu and delta nu_01/Delta nu have opposite trends as a function of Delta nu. The data show a narrowing of the l=1 ridge towards lower nu_max, in agreement with models predicting more efficient mode trapping in stars with higher luminosity. We investigate the offset epsilon in the asymptotic relation and find a clear correlation with Delta nu, demonstrating that it is related to fundamental stellar parameters. Finally, we present the first amplitude-nu_max relation for Kepler red giants. We observe a lack of low-amplitude stars for nu_max ~> 110 muHz and find that, for a given nu_max between 40-110 muHz, stars with lower Delta nu (and consequently higher mass) tend to show lower amplitudes than stars with higher Delta nu.

Effects of rotational mixing on the asteroseismic properties of solar-type stars

<i>Context. <i/>Observations of solar-like oscillations obtained either from the ground or from space stimulated the study of the effects of various physical processes on the modelling of solar-type stars.<i>Aims. <i/>The influence of rotational mixing on the evolution and asteroseismic properties of solar-type stars is studied.<i>Methods. <i/>Global and asteroseismic properties of models of solar-type stars computed with and without a comprehensive treatment of shellular rotation are compared. The effects of internal magnetic fields are also discussed in the framework of the Tayler-Spruit dynamo.<i>Results. <i/>Rotational mixing changes the global properties of a solar-type star with a significant increase of the effective temperature resulting in a shift of the evolutionary track to the blue part of the HR diagram. These differences observed in the HR diagram are related to changes of the chemical composition, because rotational mixing counteracts the effects of atomic diffusion leading to larger helium surface abundances for rotating models than for non-rotating ones. Higher values of the large frequency separation are then found for rotating models than for non-rotating ones at the same evolutionary stage, because the increase of the effective temperature leads to a smaller radius and hence to an increase of the stellar mean density. In addition to changing the global properties of solar-type stars, rotational mixing also has a considerable impact on the structure and chemical composition of the central stellar layers by bringing fresh hydrogen fuel to the central stellar core, thereby enhancing the main-sequence lifetime. The increase of the central hydrogen abundance together with the change of the chemical profiles in the central layers result in a significant increase of the values of the small frequency separations and of the ratio of the small to large separations for models including shellular rotation. This increase is clearly seen for models with the same age sharing the same initial parameters except for the inclusion of rotation as well as for models with the same global stellar parameters and in particular the same location in the HR diagram. By computing rotating models of solar-type stars including the effects of a dynamo that possibly occurs in the radiative zone, we find that the efficiency of rotational mixing is strongly reduced when the effects of magnetic fields are taken into account, in contrast to what happens in massive stars.

Modelling the autocovariance of the power spectrum of a solar-type oscillator

Asteroseismology is able to conduct studies on the interiors of solar-type stars from the analysis of stellar acoustic spectra. However, such an analysis process often has to rely upon subjective choices made throughout. A recurring problem is to determine whether a signal in the acoustic spectrum originates from a radial or a dipolar oscillation mode. In order to overcome this problem, we present a procedure for modelling and fitting the autocovariance of the power spectrum which can be used to obtain global seismic parameters of solar-type stars, doing so in an automated fashion without the need to make subjective choices. From the set of retrievable global seismic parameters we emphasize the mean small frequency separation and, depending on the intrinsic characteristics of the power spectrum, the mean rotational frequency splitting. Since this procedure is automated, it can serve as a useful tool in the analysis of the more than one thousand solar-type stars expected to be observed as part of the Kepler Asteroseismic Investigation (KAI). We apply the aforementioned procedure to simulations of the Sun. Assuming different apparent magnitudes, we address the issues of how accurately and how precisely we can retrieve the several global seismic parameters were the Sun to be observed as part of the KAI.

Pulsations in the atmosphere of the roAp star HD 24712 - II. Theoretical models

We discuss pulsations of the rapidly oscillating Ap (roAp) star HD 24712 (HR 1217) based on nonadiabatic analyses taking into account the effect of dipole magnetic fields. We have found that all the pulsation modes appropriate for HD 24712 are damped; i.e., the kappa-mechanism excitation in the hydrogen ionization layers is not strong enough to excite high-order p-modes with periods consistent with observed ones, all of which are found to be above the acoustic cut-off frequencies of our models. The main (2.721 mHz) and the highest (2.806 mHz) frequencies are matched with modified $l=2$ and $l=3$ modes, respectively. The large frequency separation ($\approx 68 \mu$Hz) is reproduced by models which lay within the error box of HD 24712 on the HR diagram. The nearly equally spaced frequencies of HD 24712 indicate the small frequency separation to be as small as $\approx 0.5\mu$Hz. However, the small separation derived from theoretical $l=1$ and 2 modes are found to be larger than $\sim 3\mu$Hz. The problem of equal spacings could be resolved by assuming that the spacings correspond to pairs of $l=2$ and $l=0$ modes. The amplitude distribution on the stellar surface is strongly affected by the magnetic field resulting in the predominant concentration at the polar regions. Amplitudes and phases of radial-velocity variations for various spectral lines are converted to relations of amplitude/phase versus optical depth in the atmosphere. Oscillation phase delays gradually outward in the outermost layers indicating the presence of waves propagating outward. The phase changes steeply around $\log\tau\sim-3.5$, which supports a $T-\tau$ relation having a small temperature inversion there.

Effects of prior stimulus and prior perception on neural correlates of auditory stream segregation

We examined whether effects of prior experience are mediated by distinct brain processes from those processing current stimulus features. We recorded event-related potentials (ERPs) during an auditory stream segregation task that presented an adaptation sequence with a small, intermediate, or large frequency separation between low and high tones (Deltaf), followed by a test sequence with intermediate Deltaf. Perception of two streams during the test was facilitated by small prior Deltaf and by prior perception of two streams and was accompanied by more positive ERPs. The scalp topography of these perception-related changes in ERPs was different from that observed for ERP modulations due to increasing the current Deltaf. These results reveal complex interactions between stimulus-driven activity and temporal-context-based processes and suggest a complex set of brain areas involved in modulating perception based on current and previous experience.

High-frequency parasitic modes of superconducting gravimeters

The superconducting gravimeter (SG) has a long-period instrumental noise called the parasitic mode at periods around 100 s, whose precise mechanism has not yet been identified. In this paper, another instrumental noise is detected at much higher frequencies by analyzing the high-rate gravity channel of two SGs in Japan. This is also a parasitic oscillation, characterized by frequencies on the order of 1 Hz and very high Q values. Detailed spectra indicate that the noise actually consists of two modes with small frequency separations. Based on a simple theory on the rotational motions of the superconducting sphere in the gravity sensor, the observed modes are tentatively identified as rotational oscillations of the sphere about two orthogonal axes in the horizontal plane. Interactions between the parasitic modes are investigated using the spectra acquired on an earthquake, to conclude that the low-frequency parasitic mode is likely to be a rotational motion of the sphere about the vertical axis.

Bayesian Analysis of Solar Oscillations

A Bayesian probability based approach is applied to the problem of detecting and parameterizing oscillations in the upper solar atmosphere for the first time. Due to its statistical origin, this method provides a mechanism for determining the number of oscillations present, gives precise estimates of the oscillation parameters with a self-consistent statistical error analysis, and allows the oscillatory model signals to be reconstructed within these errors. A highly desirable feature of the Bayesian approach is the ability to resolve oscillations with extremely small frequency separations. The code is applied to SOHO/CDS (Solar and Heliospheric Observatory/Coronal Diagnostic Spectrometer) O V 629A observations and resolves four distinct P4, P5, P6 and P7 p-modes within the same sunspot transition region. This suggests that a spectrum of photospheric p-modes is able to propagate into the upper atmosphere of the Sun and Sun-like stars, and places precise observational constraints on models of umbral eigen modes.

Seismic analysis of 70 Ophiuchi A: A new quantity proposed

The basic intent of this paper is to model 70 Ophiuchi A using the latest asteroseismic observations as complementary constraints and to determine the fundamental parameters of the star. Additionally, we propose a new quantity to lift the degeneracy between the initial chemical composition and stellar age. Using the Yale stellar evolution code (YREC7), we construct a series of stellar evolutionary tracks for the mass range M = 0.85–0.93 M ⊙ with different composition Y i (0.26–0.30) and Z i (0.017–0.023). Along these tracks, we select a grid of stellar model candidates that fall within the error box in the HR diagram to calculate the theoretical frequencies, the large- and small-frequency separations using Guenther’s stellar pulsation code. Following the asymptotic formula of stellar p-modes, we define a quantity r 01 which is correlated with stellar age. Also, we test it by theoretical adiabatic frequencies of many models. Many detailed models of 70 Ophiuchi A are listed in Table 3. By combining all non-asteroseismic observations available for 70 Ophiuchi A with these seismological data, we think that Model 60, Model 125 and Model 126, listed in Table 3, are the optimum models presently. Meanwhile, we predict that the radius of this star is about 0.860–0.865 R ⊙ and the age is about 6.8–7.0 Gyr with mass 0.89–0.90 M ⊙. Additionally, we prove that the new quantity r 01 can be a useful indicator of stellar age.

The Complementary Roles of Interferometry and Asteroseismology in Determining the Mass of Solar‐Type Stars

How important is an independent diameter measurement for the determination of stellar parameters of solar-type stars? When coupled with seismic observables, how well can we determine the stellar mass? If we can determine the radius of the star to between 1% and 4%, how does this affect the theoretical uncertainties? Interferometry can provide an independent radius determination and it has been suggested that we should expect at least a 4% precision on such a measurement for nearby solar-type stars. This study aims to provide both qualitative and quantitive answers to these questions for a star such as our Sun, where seismic information will be available. We show that the importance of an independent radius measurement depends on the combination of observables available and the size of the measurement errors. It is important for determining all stellar parameters and in particular the mass, where a good radius measurement can even allow us to determine the mass with a precision better than 2%. Our results also show that measuring the small frequency separation significantly improves the determination of the evolutionary stage and the mixing-length parameter.

Seismology of Procyon A: determination of mode frequencies, amplitudes, lifetimes, and granulation noise

The F5 IV-V star Procyon A (aCMi) was observed in January 2001 by means of the high resolution spectrograph SARG operating with the TNG 3.5m Italian telescope (Telescopio Nazionale Galileo) at Canary Islands, exploiting the iodine cell technique. The time-series of about 950 spectra carried out during 6 observation nights and a preliminary data analysis were presented in Claudi et al. 2005. These measurements showed a significant excess of power between 0.5 and 1.5 mHz, with ~ 1 m/s peak amplitude. Here we present a more detailed analysis of the time-series, based on both radial velocity and line equivalent width analyses. From the power spectrum we found a typical p-mode frequency comb-like structure, identified with a good margin of certainty 11 frequencies in the interval 0.5-1400 mHz of modes with l=0,1,2 and 7< n < 22, and determined large and small frequency separations, Dn = 55.90 \pm 0.08 muHz and dnu_02=7.1 \pm 1.3 muHz, respectively. The mean amplitude per mode (l=0,1) at peak power results to be 0.45 \pm 0.07 m/s, twice larger than the solar one, and the mode lifetime 2 \pm 0.4 d, that indicates a non-coherent, stochastic source of mode excitation. Line equivalent width measurements do not show a significant excess of power in the examined spectral region but allowed us to infer an upper limit to the granulation noise.

Asteroseismic diagnostics of stellar convective cores

We present a detailed study of the small frequency separations as diagnostics of the mass of the convective core and evolutionary stage of solar-type stars. We demonstrate how the small separations can be combined to provide sensitive tests for the presence of convective overshoot at the edge of the core. These studies are focused on low-degree oscillation modes, the only modes expected to be detected in distant stars. Using simulated data with realistic errors, we find that the mass of the convective core can be estimated to within 5 per cent if the total stellar mass is known. Systematic errors arising due to uncertainty in the mass could be up to 20 per cent. The evolutionary stage of the star, determined in terms of the central hydrogen abundance using our proposed technique, however, is much less sensitive to the mass estimate.