Bayesian Asteroseismology of 23 Solar-Like Kepler Targets

We study 23 previously published Kepler targets to perform a consistent grid-based Bayesian asteroseismic analysis and compare our results to those obtained via the Asteroseismic Modelling Portal (AMP). We find differences in the derived stellar parameters of many targets and their uncertainties. While some of these differences can be attributed to systematic effects between stellar evolutionary models, we show that the different methodologies deliver incompatible uncertainties for some parameters. Using non-adiabatic models and our capability to measure surface effects, we also investigate the dependency of these surface effects on the stellar parameters. Our results suggest a dependence of the magnitude of the surface effect on the mixing length parameter which also, but only minimally, affects the determination of stellar parameters. While some stars in our sample show no surface effect at all, the most significant surface effects are found for stars that are close to the Sun's position in the HR diagram.Comment: 14 pages, 9 figures, accepted for publication in MNRA

On the detection of Lorentzian profiles in a power spectrum: A Bayesian approach using ignorance priors

Aims. Deriving accurate frequencies, amplitudes, and mode lifetimes from stochastically driven pulsation is challenging, more so, if one demands that realistic error estimates be given for all model fitting parameters. As has been shown by other authors, the traditional method of fitting Lorentzian profiles to the power spectrum of time-resolved photometric or spectroscopic data via the Maximum Likelihood Estimation (MLE) procedure delivers good approximations for these quantities. We, however, show that a conservative Bayesian approach allows one to treat the detection of modes with minimal assumptions (i.e., about the existence and identity of the modes). Methods. We derive a conservative Bayesian treatment for the probability of Lorentzian profiles being present in a power spectrum and describe an efficient implementation that evaluates the probability density distribution of parameters by using a Markov-Chain Monte Carlo (MCMC) technique. Results. Potentially superior to "best-fit" procedure like MLE, which only provides formal uncertainties, our method samples and approximates the actual probability distributions for all parameters involved. Moreover, it avoids shortcomings that make the MLE treatment susceptible to the built-in assumptions of a model that is fitted to the data. This is especially relevant when analyzing solar-type pulsation in stars other than the Sun where the observations are of lower quality and can be over-interpreted. As an example, we apply our technique to CoRoT observations of the solar-type pulsator HD 49933.Comment: 12 pages, 11 figures, accepted for publication in Astronomy and Astrophysic

Evidence for granulation in early A-type stars

Stars with spectral types earlier than about F0 on (or close) to the main sequence have long been believed to lack observable surface convection, although evolutionary models of A-type stars do predict very thin surface convective zones. We present evidence for granulation in two delta Scuti stars of spectral type A2: HD174936 and HD50844. Recent analyses of space-based CoRoT (Convection, Rotation, and planetary Transits) data revealed up to some 1000 frequencies in the photometry of these stars. The frequencies were interpreted as individual pulsation modes. If true, there must be large numbers of nonradial modes of very high degree l which should suffer cancellation effects in disk-integrated photometry (even of high space-based precision). The p-mode interpretation of all the frequencies in HD174936 and HD50844 depends on the assumption of white (frequency independent) noise. Our independent analyses of the data provide an alternative explanation: most of the peaks in the Fourier spectra are the signature of non-white granulation background noise, and less than about 100 of the frequencies are actual stellar p-modes in each star. We find granulation time scales which are consistent with scaling relations that describe cooler stars with known surface convection. If the granulation interpretation is correct, the hundreds of low-amplitude Fourier peaks reported in recent studies are falsely interpreted as independent pulsation modes and a significantly lower number of frequencies are associated with pulsation, consistent with only modes of low degree.Comment: accepted by ApJ

Asteroseismic surface gravity for evolved stars

Context: Asteroseismic surface gravity values can be of importance in determining spectroscopic stellar parameters. The independent log(g) value from asteroseismology can be used as a fixed value in the spectroscopic analysis to reduce uncertainties due to the fact that log(g) and effective temperature can not be determined independently from spectra. Since 2012, a combined analysis of seismically and spectroscopically derived stellar properties is ongoing for a large survey with SDSS/APOGEE and Kepler. Therefore, knowledge of any potential biases and uncertainties in asteroseismic log(g) values is now becoming important. Aims: The seismic parameter needed to derive log(g) is the frequency of maximum oscillation power (nu_max). Here, we investigate the influence of nu_max derived with different methods on the derived log(g) values. The large frequency separation between modes of the same degree and consecutive radial orders (Dnu) is often used as an additional constraint for the determination of log(g). Additionally, we checked the influence of small corrections applied to Dnu on the derived values of log(g). Methods We use methods extensively described in the literature to determine nu_max and Dnu together with seismic scaling relations and grid-based modeling to derive log(g). Results: We find that different approaches to derive oscillation parameters give results for log(g) with small, but different, biases for red-clump and red-giant-branch stars. These biases are well within the quoted uncertainties of ~0.01 dex (cgs). Corrections suggested in the literature to the Dnu scaling relation have no significant effect on log(g). However somewhat unexpectedly, method specific solar reference values induce biases of the order of the uncertainties, which is not the case when canonical solar reference values are used.Comment: 8 pages, 5 figures, accepted for publication by A&

Solar-type oscillations on the giant branch

Gegen Ende ihres Lebens dehnen sich sonnenähnliche Sterne erheblich aus und werden zu Roten Riesen. Dabei zeigen sie, so wie auch die Sonne selbst, stark gedämpfte Oszillationen, die durch die turbulenten konvektiven Strömungen in ihren äußeren Hüllen angeregt werden. Diese Schwingungen ermöglichen die seismologische Erkundung der inneren Sternstruktur und erlauben unter anderem die Bestimmung des Sternalters aufgrund der Ausdehnung des Kerns. Bisher war es nicht geklärt, ob man bei Roten Riesen, ähnlich wie bei sonnenähnlichen Sternen, radiale und nicht-radiale Schwingungen beobachtet, deren Lebenszeiten signifikant länger sind als bei sonnenähnlichen Sternen, oder nur radiale Oszillationen mit Lebenszeiten vergleichbar zu den in sonnenähnlichen Sternen. Letzteres würde die aus den beobachtbaren Schwingungen ableitbaren Informationen erheblich einschränken. Zu Beginn meiner Arbeit gab es noch keine allgemein anerkannte Theorie welche die zeitliche Entwicklung von Konvektion berücksichtigt und damit die Anregung und Dämpfung von sonnenähnlicher Pulsation erklärt. Weiters beschränkten sich die Beobachtungen hauptsächlich auf den Nachweis von sonnenähnlicher Pulsation. Aber das Interesse und das Potenzial zur Untersuchung der Struktur dieser Sterne waren groß, sodass die kanadische Weltraummission MOST und das europäische Satellitenprojekt CoRoT Programme zur Beobachtung von sonnenähnlich pulsierenden Roten Riesen entwickelten. Ein Teil dieser Arbeit beschäftigt sich mit dem Nachweis von radialen und nicht-radialen Schwingungen in der 28 Tage langen MOST Präzisionsphotometrie des G9.5 Riesen ε Oph. Die Oszillationsfrequenzen wurden unter der Annahme von relativ stabilen Schwingungen, d.h. unter der Annahme von langen Lebenszeiten, extrahiert. Deren Signifikanz wurde bezüglich des lokalen Hintergrundrauschens bewertet, welches durch die stellare Oberflächengranulation verursacht wird und mit Hilfe eines einfachen Potenzgesetzes berechnet werden kann. Die beobachteten Frequenzen wurden mit Modellfrequenzen aus einem umfangreichen Gitter von Sternmodellen verglichen, um Modelle zu identifizieren, deren Eigenfrequenzen möglichst gut mit den beobachteten übereinstimmen. Das am besten passende Modell erklärt 18 der 21 beobachteten Frequenzen als radiale und nicht-radiale Oszillationen und liegt innerhalb der ±1σ Fehlergrenzen von ε Oph’s Position im H-R Diagram und dessen interferometrisch bestimmten Radius. Aufgrund des relativ kurzen Datensatzes waren die Lebenszeiten der Schwingungen nicht direkt messbar. Die Streuung der beobachteten Frequenzen um die Modellfrequenzen deutet jedoch auf eine durchschnittliche Lebenszeit von 10 bis 20 Tagen hin. Diese Interpretation ist aber kontroversiell. So behaupten etwa Barban et.al. (2007), im gleichen Datensatz von ε Oph nur radiale Schwingungen mit sehr kurzen Lebenszeiten nachweisen zu können. Deren Resultat widerspricht somit meinem und stellt generell das asteroseismologische Potential von Roten Riesen in Frage. Diese Unklarheit konnte mit Hilfe der ersten 150 Tage langen Beobachtungskampagne von CoRoT beseitigt werden. Mehr als 300 Sterne wurden gefunden, die ein für Rote Riesen typisches Granulations- und Pulsationsverhalten zeigen. Mit Hilfe einer halbautomatischen Prozedur konnten die pulsierenden Roten Riesen unter den ca. 11000 beobachteten Sternen identifiziert werden. Exemplarisch für die große Zahl von neu entdeckten pulsierenden Roten Riesen habe ich zwei Sterne genauer untersucht. In einem ersten Schritt wurden die Fourierspektren mit Hilfe eines Potenzgesetzes bezüglich des stellaren Hintergrundsignals korrigiert. Die residualen Fourierspektren zeigen ein klares Muster aus radialen und nicht-radialen Oszillationen, deren Frequenzen mit Hilfe von Lorentzprofilen ermittelt wurden. Eine erste Abschätzung über die stellaren Massen und Radien ließ sich aus den globalen Pulsationsparametern ableiten. Im Fall der beiden CoRoT Sterne wurden Modelle gefunden, die alle 13 bzw. 12 extrahierten Frequenzen innerhalb der Beobachtungsfehler als radiale und nicht-radiale Schwingungen erklären. Weiters deuten die schmalen Profile der beobachteten Pulsationsmoden und die relative Stabilität des Signals in einer Zeit-Frequenzanalyse darauf hin, dass die Lebenszeiten der Schwingungen bei etwa 20 bis 50 Tagen liegen. Als wichtigste Resultate meiner Arbeit sehe ich: 1. Die Entscheidung der Kontroverse um die Existenz von nicht-radialen Pulsationsmoden in Roten Riesen. 2. Die Lebenszeiten dieser Schwingungen sind erheblich länger als bei sonnenähnlichen Sternen. 3. Die beobachteten Oszillationen lassen sich durch Frequenzen von Modellen Roter Riesen eindeutig erklären. Dies unterstreicht das große asteroseismologische Potenzial dieser Sterne und liefert einen Beitrag zum besseren Verständnis der späten Stadien in der Sternentwicklung.Towards the end of their lives, stars like the Sun greatly expand and become red giants. Like the Sun, they show strongly damped oscillations stochastically excited by the turbulent convective motions in their outer envelopes. These oscillation frequencies provide great potential for seismic probing of the internal structure of red-giant stars, and allow to determine, e.g., the stellar age. It has been unknown whether red giants exhibit radial and nonradial oscillations as it is known for sun-like stars but with significantly longer lifetimes, or radial modes only with lifetimes comparable to those of sun-like stars. In the second case this would seriously limit the asteroseismically deducible information. At the beginning of this study, no commonly accepted theory taking into account the temporal evolution of convection was available which is necessary to explain the driving and damping of solar-type oscillations. Furthermore, the observations were still in their infancy. But the interest and potential to investigate the structure of red giants was high, and both the Canadian space mission MOST and the European satellite CoRoT developed programs to observe pulsating red giants. Here I report on the detection of both radial and nonradial oscillations in the 28 days long high-precision MOST photometry of the G9.5 giant ε Oph. I have extracted the mode frequencies assuming the signal to be relatively stable, i.e. assuming the lifetimes to be long. Their significance was evaluated with respect to a simple power law model fit representing the local background noise due to intrinsic surface granulation. The extracted frequencies were then compared to those of an extensive grid of stellar models in order to search for models whose oscillation spectra best matches the observed frequencies. The best fit model explains 18 of the 21 observed frequencies as radial and nonradial p modes. It is located within ±1σ of ε Oph’s position in the H-R diagram and its interferometrically determined radius. The lifetimes of the observed oscillations are not directly accessible due to the relatively short data set. But the small scatter of the frequencies about the model predicted frequencies indicates that the average lifetime could be as long as 10 to 20 days. This interpretation is quite controversial. For example, Barban et. al. (2007) claimed to find short living radial modes only in the same data set of ε Oph. Consequently, their findings strongly contradicts my result and questions the asteroseismic potential of red giants in general. This ambiguity could be solved by the first 150 days long-run observations of CoRoT. More than 300 stars have been identified showing a granulation and pulsation signal in a frequency and amplitude range typical for solar-type pulsation in red giants. A semi-automatic method was used to identify the red-giant candidates among the about 11000 exofield targets. Exemplary for the large number of CoRoT red-giant pulsators I have analyzed two stars in detail. In a first step, their power spectra are corrected for the intrinsic background signal using power law model fits. The residual power spectra show a clear pattern of radial and nonradial modes and Lorentzian profile fits are used to extract the frequencies of 12 and 13 p modes, respectively. First estimates for the stellar mass and radii are determined from global pulsation parameter. In case of the two CoRoT stars, I found red-giant models whose oscillation spectra match all observed frequencies as radial and nonradial modes with an angular degree of up to and including 3. Furthermore, the narrow profiles of the observed modes and the relative stability of these modes in a time-frequency analysis indicates that the mode lifetimes are of the order of 20 to 50 days. As the main result of this thesis I conclude: 1. To resolve the controversy about the existence of nonradial modes in red giants. 2. Their lifetimes are significantly longer than those in sun-like stars. 3. The observable oscillations are consistent with theoretical eigenspectra of red-giant models. This finally approves the high asteroseismic potential of red-giant stars and will contribute to a better understanding of the late stages of stellar evolution

Atmospheric parameters of 82 red giants in the Kepler field

Context: Accurate fundamental parameters of stars are essential for the asteroseismic analysis of data from the NASA Kepler mission. Aims: We aim at determining accurate atmospheric parameters and the abundance pattern for a sample of 82 red giants that are targets for the Kepler mission. Methods: We have used high-resolution, high signal-to-noise spectra from three different spectrographs. We used the iterative spectral synthesis method VWA to derive the fundamental parameters from carefully selected high-quality iron lines. After determination of the fundamental parameters, abundances of 13 elements were measured using equivalent widths of the spectral lines. Results: We identify discrepancies in log g and [Fe/H], compared to the parameters based on photometric indices in the Kepler Input Catalogue (larger than 2.0 dex for log g and [Fe/H] for individual stars). The Teff found from spectroscopy and photometry shows good agreement within the uncertainties. We find good agreement between the spectroscopic log g and the log g derived from asteroseismology. Also, we see indications of a potential metallicity effect on the stellar oscillations. Conclusions: We have determined the fundamental parameters and element abundances of 82 red giants. The large discrepancies between the spectroscopic log g and [Fe/H] and values in the Kepler Input Catalogue emphasize the need for further detailed spectroscopic follow-up of the Kepler targets in order to produce reliable results from the asteroseismic analysis.Comment: 16 Pages, 12 Figures, accepted for publication in A&

The nature of p-modes and granulation in HD 49933 observed by CoRoT

Context: Recent observations of HD49933 by the space-photometric mission CoRoT provide photometric evidence of solar type oscillations in a star other than our Sun. The first published reduction, analysis, and interpretation of the CoRoT data yielded a spectrum of p-modes with l = 0, 1, and 2. Aims: We present our own analysis of the CoRoT data in an attempt to compare the detected pulsation modes with eigenfrequencies of models that are consistent with the observed luminosity and surface temperature. Methods: We used the Gruberbauer et al. frequency set derived based on a more conservative Bayesian analysis with ignorance priors and fit models from a dense grid of model spectra. We also introduce a Bayesian approach to searching and quantifying the best model fits to the observed oscillation spectra. Results: We identify 26 frequencies as radial and dipolar modes. Our best fitting model has solar composition and coincides within the error box with the spectroscopically determined position of HD49933 in the H-R diagram. We also show that lower-than-solar Z models have a lower probability of matching the observations than the solar metallicity models. To quantify the effect of the deficiencies in modeling the stellar surface layers in our analysis, we compare adiabatic and nonadiabatic model fits and find that the latter reproduces the observed frequencies better.Comment: accepted to be published in A&A, 9 pages, 5 figure