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We present a new and highly efficient algorithm for computing a power spectrum made from evenly spaced data which combines the noise-reducing advantages of the weighted fit with the computational advantages of the Fast Fourier Transform (FFT). We apply this method to a 10-year data set of the solar p-mode oscillations obtained by the Birmingham Solar Oscillations Network (BiSON) and thereby uncover three new low-frequency modes. These are the l=2, n=5 and n=7 modes and the l=3, n=7 mode. In the case of the l=2, n=5 modes, this is believed to be the first such identification of this mode in the literature. The statistical weights needed for the method are derived from a combination of the real data and a sophisticated simulation of the instrument performance. Variations in the weights are due mainly to the differences in the noise characteristics of the various BiSON instruments, the change in those characteristics over time and the changing line-of-sight velocity between the stations and the Sun. It should be noted that a weighted data set will have a more time-dependent signal than an unweighted set and that, consequently, its frequency spectrum will be more susceptible to aliasing.

With the launch of the NASA Kepler spacecraft, the number of solar-like stars for which there are high-precision photometric observations available has increased considerably. In order to analyse the data from a large number of stars in a reasonable amount of time, automated pipelines are desirable. Here we present an extension of the OCTAVE (Birmingham–Sheffield Hallam) pipeline, which has been developed as part of the AsteroFLAG collaboration. While the first parts of the pipeline extracted overall oscillation parameters of the stars, here we present a significant extension to that pipeline designed in order to extract individual mode frequencies and amplitudes. The pipeline also attempts to label the detected modes by straightening and then identifying the ridges within the echelle diagrams in an automated manner. Tests have been performed on artificial stars and the pipeline is shown to return estimates of the mode frequencies that are in line with the input parameters. There does appear to be some positive bias in the returned value of the mode amplitudes which must be accounted for when employing the pipeline for real data.

We report on the results of the latest solarFLAG hare-and-hounds exercise, which was concerned with testing methods for extraction of frequencies of low-degree solar p modes from data collected by Sun-as-a-star observations. We have used the new solarFLAG simulator, which includes the effects of correlated mode excitation and correlations with background noise, to make artificial timeseries data that mimic Doppler velocity observations of the Sun as a star. The correlations give rise to asymmetry of mode peaks in the frequency power spectrum. Ten members of the group (the hounds) applied their ``peak bagging'' codes to a 3456-day dataset, and the estimated mode frequencies were returned to the hare (who was WJC) for comparison. Analysis of the results reveals a systematic bias in the estimated frequencies of modes above approximately 1.8 mHz. The bias is negative, meaning the estimated frequencies systematically underestimate the input frequencies. We identify two sources that are the dominant contributions to the frequency bias. Both sources involve failure to model accurately subtle aspects of the observed power spectral density in the part (window) of the frequency power spectrum that is being fitted. One source of bias arises from a failure to account for the power spectral density coming from all those modes whose frequencies lie outside the fitting windows. The other source arises from a failure to account for the power spectral density of the weak l=4 and 5 modes, which are often ignored in Sun-as-a-star analysis. The Sun-as-a-star peak-bagging codes need to allow for both sources, otherwise the frequencies are likely to be biased.

We introduce a modified version of a standard power spectrum `peak-bagging' technique which is designed to gain some of the advantages that fitting the entire low-degree p-mode power spectrum simultaneously would bring, but without the problems involved in fitting a model incorporating many hundreds of parameters. Employing Monte-Carlo simulations we show that by using this modified fitting code it is possible to determine the true background level in the vicinity of the p-mode peaks. In addition to this we show how small biases in other mode parameters, which are related to inaccurate estimates of the true background, are also consequently removed., 7 pages, 2 figures. To be published in a conference proceedings

We present results of fitting the 50-day time series of photometry of alpha Cen A taken by the WIRE satellite in 1999. Both power spectrum and autocovariance function (ACF) fitting techniques were used in an attempt to determine mode frequencies, rotational splittings, lifetimes and amplitudes of low-l p-modes. In all, using both techniques, we managed to fit 18 modes (seven l = 0, eight l = 1 and three l = 2) with frequencies determined to within 1 - 2 micro-Hz. These estimates are shown to be 0.6 +/- 0.3 micro-Hz lower, on average, than the frequencies determined from two other more recent studies (Bouchy & Carrier, 2002; Bedding et al. 2004) which used data gathered about 19 months after the WIRE observations. This could be indicative of an activity cycle, although due to the large uncertainty, more data would be needed to confirm this. Over a range of 1700 to 2650 micro-Hz we were also able to use the ACF fitting to determine an average lifetime of 3.9 +/- 1.4 days, and an average rotational splitting of 0.54 +/- 0.22 micro-Hz, which is the first ever reliable estimate of this parameter. In contrast to the ACF, the power spectrum fitting was shown to return significantly biased results for these parameters.

We report on results from the first solar Fitting at Low-Angular degree Group (solar FLAG) hare-and-hounds exercise. The group is concerned with the development of methods for extracting the parameters of low-l solar p mode data (`peak bagging'), collected by Sun-as-a-star observations. Accurate and precise estimation of the fundamental parameters of the p modes is a vital pre-requisite of all subsequent studies. Nine members of the FLAG (the `hounds') fitted an artificial 3456-d dataset. The dataset was made by the `hare' (WJC) to simulate full-disc Doppler velocity observations of the Sun. The rotational frequency splittings of the l=1, 2 and 3 modes were the first parameter estimates chosen for scrutiny. Significant differences were uncovered at l=2 and 3 between the fitted splittings of the hounds. Evidence is presented that suggests this unwanted bias had its origins in several effects. The most important came from the different way in which the hounds modeled the visibility ratio of the different rotationally split components. Our results suggest that accurate modelling of the ratios is vital to avoid the introduction of significant bias in the estimated splittings. This is of importance not only for studies of the Sun, but also of the solar analogues that will targets for asteroseismic campaigns.

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., Comment: 6 pages, 5 figures, accepted for publication in The Astrophysical Journal Letters

The evolved main-sequence Sun-like stars KIC 10273246 (F-type) and KIC 10920273 (G-type) were observed with the NASA Kepler satellite for approximately ten months with a duty cycle in excess of 90%. Such continuous and long observations are unprecedented for solar-type stars other than the Sun. We aimed mainly at extracting estimates of p-mode frequencies - as well as of other individual mode parameters - from the power spectra of the light curves of both stars, thus providing scope for a full seismic characterization. The light curves were corrected for instrumental effects in a manner independent of the Kepler Science Pipeline. Estimation of individual mode parameters was based both on the maximization of the likelihood of a model describing the power spectrum and on a classic prewhitening method. Finally, we employed a procedure for selecting frequency lists to be used in stellar modeling. A total of 30 and 21 modes of degree l=0,1,2 - spanning at least eight radial orders - have been identified for KIC 10273246 and KIC 10920273, respectively. Two avoided crossings (l=1 ridge) have been identified for KIC 10273246, whereas one avoided crossing plus another likely one have been identified for KIC 10920273. Good agreement is found between observed and predicted mode amplitudes for the F-type star KIC 10273246, based on a revised scaling relation. Estimates are given of the rotational periods, the parameters describing stellar granulation and the global asteroseismic parameters $\Delta\nu$ and $\nu_{\rm{max}}$., Comment: 15 pages, 15 figures, to be published in Astronomy & Astrophysics

We report on the first asteroseismic analysis of solar-type stars observed by Kepler. Observations of three G-type stars, made at one-minute cadence during the first 33.5d of science operations, reveal high signal-to-noise solar-like oscillation spectra in all three stars: About 20 modes of oscillation can clearly be distinguished in each star. We discuss the appearance of the oscillation spectra, including the presence of a possible signature of faculae, and the presence of mixed modes in one of the three stars., Comment: 5 pages, 4 figure, submitted to Astronomische Nachrichten

The primary science goal of the Kepler Mission is to provide a census of exoplanets in the solar neighborhood, including the identification and characterization of habitable Earth-like planets. The asteroseismic capabilities of the mission are being used to determine precise radii and ages for the target stars from their solar-like oscillations. Chaplin et al. (2010) published observations of three bright G-type stars, which were monitored during the first 33.5 days of science operations. One of these stars, the subgiant KIC 11026764, exhibits a characteristic pattern of oscillation frequencies suggesting that it has evolved significantly. We have derived asteroseismic estimates of the properties of KIC 11026764 from Kepler photometry combined with ground-based spectroscopic data. We present the results of detailed modeling for this star, employing a variety of independent codes and analyses that attempt to match the asteroseismic and spectroscopic constraints simultaneously. We determine both the radius and the age of KIC 11026764 with a precision near 1%, and an accuracy near 2% for the radius and 15% for the age. Continued observations of this star promise to reveal additional oscillation frequencies that will further improve the determination of its fundamental properties., Comment: 16 pages, 6 figures, 4 tables, ApJ in press

The Sun is a variable star whose magnetic activity varies most perceptibly on a timescale of approximately 11 years. However, significant variation is also observed on much shorter timescales. We observe a quasi-biennial (2 year) signal in the natural oscillation frequencies of the Sun. The oscillation frequencies are sensitive probes of the solar interior and so by studying them we can gain information about conditions beneath the solar surface. Our results point strongly to the 2 year signal being distinct and separate from, but nevertheless susceptible to the influence of, the main 11 year solar cycle., Comment: Accepted for publication in ApJL, 5 pages, 2 figures

Solar p-mode frequencies vary with solar activity. It is important to take this into account when comparing the frequencies observed from epochs that span different regions of the solar cycle. We present details of how to correct observed p-mode frequencies for the effects of the solar cycle. We describe three types of correction. The first allows mode frequencies to be corrected to a nominal activity level, such as the canonical quiet-Sun level. The second accounts for the effect on the observed mode frequencies, powers, and damping rates of the continually varying solar cycle and is pertinent to frequencies obtained from very long data sets. The third corrects for Sun-as-a-star observations not seeing all components of the modes. Suitable combinations of the three correction procedures allow the frequencies obtained from different sets of data to be compared and enable activity-independent inversions of the solar interior. As an example of how to apply the corrections we describe those used to produce a set of definitive Sun-as-a-star frequencies., Accepted for publication in A&A, 5 pages, 7 figures

We present a list of "best possible" estimates of low-degree p-mode frequencies, from 8640 days of observations made by the Birmingham Solar-Oscillations Network (BiSON). This is the longest stretch of helioseismic data ever used for this purpose, giving exquisite precision in the estimated frequencies. Every effort has been made in the analysis to ensure that the frequency estimates are also accurate. In addition to presenting the raw best-fitting frequencies from our "peak bagging" analysis, we also provide tables of corrected frequencies pertinent to the quiet-Sun and an intermediate level of solar activity., Accepted for publication in MNRAS; 5 pages, 3 tables

Mode fitting or "peak-bagging" is an important procedure in helioseismology allowing one to determine the various mode parameters of solar oscillations. Here we describe a way of reducing the systematic bias in the fits of certain mode parameters that are seen when using "local" fitting techniques to analyse the sun-as-a-star p-mode power spectrum. To do this we have developed a new "pseudo-global" fitting algorithm designed to gain the advantages of fitting the entire power spectrum, but without the problems involved in fitting a model incorporating many hundreds of parameters. We have performed a comparative analysis between the local and pseudo-global peak-bagging techniques by fitting the "limit" profiles of simulated helioseismic data. Results show that for asymmetric modes the traditional fitting technique returns systematically biased estimates of the central frequency parameter. This bias is significantly reduced when employing the pseudo-global routine. Similarly, we show that estimates of the background returned from the pseudo-global routine match the input values much more closely than the estimates from the local fitting method. We have also used the two fitting techniques to analyse a set of real solar data collected by the Global Oscillations at Low Frequencies (GOLF) instrument on board the ESA/NASA Solar and Heliospheric Observatory (SOHO) spacecraft. Similar differences between the estimated frequencies returned by the two techniques are seen when fitting both the real and simulated data. We show that the background fits returned by the pseudo-global routine more closely match the estimate of the background one can infer from interpolating between fits to the high and low frequency ends of the p-mode power spectrum.

For distant stars, as observed by the NASA Kepler satellite, parallax information is currently of fairly low quality and is not complete. This limits the precision with which the absolute sizes of the stars and their potential transiting planets can be determined by traditional methods. Asteroseismology will be used to aid the radius determination of stars observed during NASA's Kepler mission. We report on the recent asteroFLAG hare-and-hounds Exercise#2, where a group of `hares' simulated data of F-K main-sequence stars that a group of `hounds' sought to analyze, aimed at determining the stellar radii. Based on the asteroseismic large frequency spacing, obtained from simulations of 4-year time series data from the Kepler mission, we demonstrate that the stellar radii can be correctly and precisely determined, when combined with traditional stellar parameters from the Kepler Input Catalogue. The radii found by the various methods used by each independent hound generally agree with the true values of the artificial stars to within 3%, when the large frequency spacing is used. This is 5--10 times better than the results where seismology is not applied. These results give strong confidence that radius estimation can be performed to better than 3% for solar-like stars using automatic pipeline reduction. Even when the stellar distance and luminosity are unknown we can obtain the same level of agreement., 14 pages, 10 figures, accepted by ApJ

The number of main-sequence stars for which we can observe solar-like oscillations is expected to increase considerably with the short-cadence high-precision photometric observations from the NASA Kepler satellite. Because of this increase in number of stars, automated tools are needed to analyse these data in a reasonable amount of time. In the framework of the asteroFLAG consortium, we present an automated pipeline which extracts frequencies and other parameters of solar-like oscillations in main-sequence and subgiant stars. The pipeline uses only the timeseries data as input and does not require any other input information. Tests on 353 artificial stars reveal that we can obtain accurate frequencies and oscillation parameters for about three quarters of the stars. We conclude that our methods are well suited for the analysis of main-sequence stars, which show mainly p-mode oscillations., Comment: accepted by MNRAS

We make predictions of the detectability of low-frequency p modes. Estimates of the powers and damping times of these low-frequency modes are found by extrapolating the observed powers and widths of higher-frequency modes with large observed signal-to-noise ratios. The extrapolations predict that the low-frequency modes will have small signal-to-noise ratios and narrow widths in a frequency-power spectrum. Monte Carlo simulations were then performed where timeseries containing mode signals and normally distributed Gaussian noise were produced. The mode signals were simulated to have the powers and damping times predicted by the extrapolations. Various statistical tests were then performed on the frequency-amplitude spectra formed from these timeseries to investigate the fraction of spectra in which the modes could be detected. The results of these simulations were then compared to the number of p-modes candidates observed in real Sun-as-a-star data at low frequencies. The fraction of simulated spectra in which modes were detected decreases rapidly as the frequency of modes decreases and so the fraction of simulations in which the low-frequency modes were detected was very small. However, increasing the signal-to-noise (S/N) ratio of the low-frequency modes by a factor of 2 above the extrapolated values led to significantly more detections. Therefore efforts should continue to further improve the quality of solar data that is currently available., Comment: 9 pages, 6 figures, accepted for publication in Astronomische Nachrichten

We report on initial results from the first phase of Exercise 1 of the asteroFLAG hare and hounds. The asteroFLAG group is helping to prepare for the asteroseismology component of NASA's Kepler mission, and the first phase of Exercise 1 is concerned with testing extraction of estimates of the large and small frequency spacings of the low-degree p modes from Kepler-like artificial data. These seismic frequency spacings will provide key input for complementing the exoplanet search data., Comment: 11 pages, accepted for publication in Astronomische Nachrichten

In addition to the well-known 11-year solar cycle, the Sun's magnetic activity also shows significant variation on shorter time scales, e.g. between one and two years. We observe a quasi-biennial (2-year) signal in the solar p-mode oscillation frequencies, which are sensitive probes of the solar interior. The signal is visible in Sun-as-a-star data observed by different instruments and here we describe the results obtained using BiSON, GOLF, and VIRGO data. Our results imply that the 2-year signal is susceptible to the influence of the main 11-year solar cycle. However, the source of the signal appears to be separate from that of the 11-year cycle. We speculate as to whether it might be the signature of a second dynamo, located in the region of near-surface rotational shear., Comment: 6 pages, 2 figures, proceedings for SOHO-24/GONG 2010 conference, to be published in JPCS

We stand on the threshold of a critical expansion of asteroseismology of Sun-like stars, the study of stellar interiors by observation and analysis of their global acoustic modes of oscillation. The Sun-like oscillations give a very rich spectrum allowing the internal structure and dynamics to be probed down into the stellar cores to very high precision. Asteroseismic observations of many stars will allow multiple-point tests of crucial aspects of stellar evolution and dynamo theory. The aims of the asteroFLAG collaboration are to help the community to refine existing, and to develop new, methods for analysis of the asteroseismic data on the Sun-like oscillators.