Asymptotic and measured large frequency separations

With the space-borne missions CoRoT and Kepler, a large amount of asteroseismic data is now available. So-called global oscillation parameters are inferred to characterize the large sets of stars, to perform ensemble asteroseismology, and to derive scaling relations. The mean large separation is such a key parameter. It is therefore crucial to measure it with the highest accuracy. As the conditions of measurement of the large separation do not coincide with its theoretical definition, we revisit the asymptotic expressions used for analysing the observed oscillation spectra. Then, we examine the consequence of the difference between the observed and asymptotic values of the mean large separation. The analysis is focused on radial modes. We use series of radial-mode frequencies to compare the asymptotic and observational values of the large separation. We propose a simple formulation to correct the observed value of the large separation and then derive its asymptotic counterpart. We prove that, apart from glitches due to stellar structure discontinuities, the asymptotic expansion is valid from main-sequence stars to red giants. Our model shows that the asymptotic offset is close to 1/4, as in the theoretical development. High-quality solar-like oscillation spectra derived from precise photometric measurements are definitely better described with the second-order asymptotic expansion. The second-order term is responsible for the curvature observed in the \'echelle diagrams used for analysing the oscillation spectra and this curvature is responsible for the difference between the observed and asymptotic values of the large separation. Taking it into account yields a revision of the scaling relations providing more accurate asteroseismic estimates of the stellar mass and radius.Comment: accepted in A&

Oscillating red giants in the CoRoT exo-field: Asteroseismic mass and radius determination

Context. Observations and analysis of solar-type oscillations in red-giant stars is an emerging aspect of asteroseismic analysis with a number of open questions yet to be explored. Although stochastic oscillations have previously been detected in red giants from both radial velocity and photometric measurements, those data were either too short or had sampling that was not complete enough to perform a detailed data analysis of the variability. The quality and quantity of photometric data as provided by the CoRoT satellite is necessary to provide a breakthrough in observing p-mode oscillations in red giants. We have analyzed continuous photometric time-series of about 11 400 relatively faint stars obtained in the exofield of CoRoT during the first 150 days long-run campaign from May to October 2007. We find several hundred stars showing a clear power excess in a frequency and amplitude range expected for red-giant pulsators. In this paper we present first results on a sub-sample of these stars. Aims. Knowing reliable fundamental parameters like mass and radius is essential for detailed asteroseismic studies of red-giant stars. As the CoRoT exofield targets are relatively faint (11-16 mag) there are no (or only weak) constraints on the star's location in the H-R diagram. We therefore aim to extract information about such fundamental parameters solely from the available time series. Methods. We model the convective background noise and the power excess hump due to pulsation with a global model fit and deduce reliable estimates for the stellar mass and radius from scaling relations for the frequency of maximum oscillation power and the characteristic frequency separation.Comment: 10 pages, 7 figures, accepted for publication in A&

Comparison of High-degree Solar Acoustic Frequencies and Asymmetry between Velocity and Intensity Data

Using the local helioseismic technique of ring diagram we analyze the frequencies of high--degree f- and p-modes derived from both velocity and continuum intensity data observed by MDI. Fitting the spectra with asymmetric peak profiles, we find that the asymmetry associated with velocity line profiles is negative for all frequency ranges agreeing with previous observations while the asymmetry of the intensity profiles shows a complex and frequency dependent behavior. We also observe systematic frequency differences between intensity and velocity spectra at the high end of the frequency range, mostly above 4 mHz. We infer that this difference arises from the fitting of the intensity rather than the velocity spectra. We also show that the frequency differences between intensity and velocity do not vary significantly from the disk center to the limb when the spectra are fitted with the asymmetric profile and conclude that only a part of the background is correlated with the intensity oscillations.Comment: Accepted for publication in Astrophysical Journa

Solar-like oscillations of semiregular variables

Oscillations of the Sun and solar-like stars are believed to be excited stochastically by convection near the stellar surface. Theoretical modeling predicts that the resulting amplitude increases rapidly with the luminosity of the star. Thus one might expect oscillations of substantial amplitudes in red giants with high luminosities and vigorous convection. Here we present evidence that such oscillations may in fact have been detected in the so-called semiregular variables, extensive observations of which have been made by amateur astronomers in the American Association for Variable Star Observers (AAVSO). This may offer a new opportunity for studying the physical processes that give rise to the oscillations, possibly leading to further information about the properties of convection in these stars.Comment: Astrophys. J. Lett., in the press. Processed with aastex and emulateap

The universal red-giant oscillation pattern; an automated determination with CoRoT data

The CoRoT and Kepler satellites have provided thousands of red-giant oscillation spectra. The analysis of these spectra requires efficient methods for identifying all eigenmode parameters. The assumption of new scaling laws allows us to construct a theoretical oscillation pattern. We then obtain a highly precise determination of the large separation by correlating the observed patterns with this reference. We demonstrate that this pattern is universal and are able to unambiguously assign the eigenmode radial orders and angular degrees. This solves one of the current outstanding problems of asteroseismology hence allowing precise theoretical investigation of red-giant interiors.Comment: Accepted in A&A letter

Rotational Splittings with CoRoT, Expected Number of Detections and Measurement Accuracy

One of the main goal of the CoRoT experiment is to determine the internal rotation of stars. A seismic measure of rotation requires the detection and an accurate measurement of rotational splittings. Our ability to achieve this goal with CoRoT observations depends on the properties of the target star (in short: spectral type and distance) and will be discussed

Amplitudes and lifetimes of solar-like oscillations observed by CoRoT* Red-giant versus main-sequence stars

Context. The advent of space-borne missions such as CoRoT or Kepler providing photometric data has brought new possibilities for asteroseismology across the H-R diagram. Solar-like oscillations are now observed in many stars, including red giants and main- sequence stars. Aims. Based on several hundred identified pulsating red giants, we aim to characterize their oscillation amplitudes and widths. These observables are compared with those of main-sequence stars in order to test trends and scaling laws for these parameters for both main-sequence stars and red giants. Methods. An automated fitting procedure is used to analyze several hundred Fourier spectra. For each star, a modeled spectrum is fitted to the observed oscillation spectrum, and mode parameters are derived. Results. Amplitudes and widths of red-giant solar-like oscillations are estimated for several hundred modes of oscillation. Amplitudes are relatively high (several hundred ppm) and widths relatively small (very few tenths of a {\mu}Hz). Conclusions. Widths measured in main-sequence stars show a different variation with the effective temperature than red giants. A single scaling law is derived for mode amplitudes of both red giants and main-sequence stars versus their luminosity to mass ratio. However, our results suggest that two regimes may also be compatible with the observations.Comment: Accepted in A&A on 2011 February 8th, now includes corrections (results now more precise on \Gamma and A_max in Section 4.3 and 4.4, fig. 7 corrected consequently

Close to Uniform Prime Number Generation With Fewer Random Bits

In this paper, we analyze several variants of a simple method for generating prime numbers with fewer random bits. To generate a prime $p$ less than $x$, the basic idea is to fix a constant $q\propto x^{1-\varepsilon}$, pick a uniformly random $a<q$ coprime to $q$, and choose $p$ of the form $a+t\cdot q$, where only $t$ is updated if the primality test fails. We prove that variants of this approach provide prime generation algorithms requiring few random bits and whose output distribution is close to uniform, under less and less expensive assumptions: first a relatively strong conjecture by H.L. Montgomery, made precise by Friedlander and Granville; then the Extended Riemann Hypothesis; and finally fully unconditionally using the Barban-Davenport-Halberstam theorem. We argue that this approach has a number of desirable properties compared to previous algorithms.Comment: Full version of ICALP 2014 paper. Alternate version of IACR ePrint Report 2011/48

Models of red giants in the CoRoT asteroseismology fields combining asteroseismic and spectroscopic constraints

Context. The availability of asteroseismic constraints for a large sample of red giant stars from the CoRoT and Kepler missions paves the way for various statistical studies of the seismic properties of stellar populations. Aims. We use the first detailed spectroscopic study of 19 CoRoT red-giant stars (Morel et al 2014) to compare theoretical stellar evolution models to observations of the open cluster NGC 6633 and field stars. Methods. In order to explore the effects of rotation-induced mixing and thermohaline instability, we compare surface abundances of carbon isotopic ratio and lithium with stellar evolution predictions. These chemicals are sensitive to extra-mixing on the red-giant branch. Results. We estimate mass, radius, and distance for each star using the seismic constraints. We note that the Hipparcos and seismic distances are different. However, the uncertainties are such that this may not be significant. Although the seismic distances for the cluster members are self consistent they are somewhat larger than the Hipparcos distance. This is an issue that should be considered elsewhere. Models including thermohaline instability and rotation-induced mixing, together with the seismically determined masses can explain the chemical properties of red-giants targets. However, with this sample of stars we cannot perform stringent tests of the current stellar models. Tighter constraints on the physics of the models would require the measurement of the core and surface rotation rates, and of the period spacing of gravity-dominated mixed modes. A larger number of stars with longer times series, as provided by Kepler or expected with Plato, would help for ensemble asteroseismology.Comment: Accepted 03/05/201

The CoRoT target HD175726: an active star with weak solar-like oscillations

Context. The CoRoT short runs give us the opportunity to observe a large variety of late-type stars through their solar-like oscillations. We report observations of the star HD175726 that lasted for 27 days during the first short run of the mission. The time series reveals a high-activity signal and the power spectrum presents an excess due to solar-like oscillations with a low signal-to-noise ratio. Aims. Our aim is to identify the most efficient tools to extract as much information as possible from the power density spectrum. Methods. The most productive method appears to be the autocorrelation of the time series, calculated as the spectrum of the filtered spectrum. This method is efficient, very rapid computationally, and will be useful for the analysis of other targets, observed with CoRoT or with forthcoming missions such as Kepler and Plato. Results. The mean large separation has been measured to be 97.2+-0.5 microHz, slightly below the expected value determined from solar scaling laws.We also show strong evidence for variation of the large separation with frequency. The bolometric mode amplitude is only 1.7+-0.25 ppm for radial modes, which is 1.7 times less than expected. Due to the low signal-to-noise ratio, mode identification is not possible for the available data set of HD175726. Conclusions. This study shows the possibility of extracting a seismic signal despite a signal-to-noise ratio of only 0.37. The observation of such a target shows the efficiency of the CoRoT data, and the potential benefit of longer observing runs.Comment: 8 pages. Accepted in A&