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Register a new userA fresh look at the seismic spectrum of HD49933: analysis of 180 days of CoRoT photometry
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Solar-like oscillations have now been observed in several stars, thanks to ground-based spectroscopic observations and space-borne photometry. CoRoT, which has been in orbit since December 2006, has observed the star HD49933 twice. The oscillation spectrum of this star has proven difficult to interpret. Thanks to a new timeseries provided by CoRoT, we aim to provide a robust description of the oscillations in HD49933, i.e., to identify the degrees of the observed modes, and to measure mode frequencies, widths, amplitudes and the average rotational splitting. Several methods were used to model the Fourier spectrum: Maximum Likelihood Estimators and Bayesian analysis using Markov Chain Monte-Carlo techniques. The different methods yield consistent result, and allow us to make a robust identification of the modes and to extract precise mode parameters. Only the rotational splitting remains difficult to estimate precisely, but is clearly relatively large (several microHz in size).
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The frequency ratios and of HD 49933 exhibit an increase at high frequencies. This behavior also exists in the ratios of other stars, which is considered to result from the low signal-to-noise ratio and the larger line width at the high-frequency end and could not be predicted by stellar models in previous work. Our calculations show that the behavior not only can be reproduced by stellar models, but can be predicted by asymptotic formulas of the ratios. The frequency ratios of the Sun, too, can be reproduced well by the asymptotic formulas. The increased behavior derives from the fact that the gradient of mean molecular weight at the bottom of the radiative region hinders the propagation of p-modes, while the hindrance does not exist in the convective core. This behavior should exist in the ratios of stars with a large convective core. The characteristic of the ratios at high frequencies provides a strict constraint on stellar models and aids in determining the size of the convective core and the extent of overshooting. Observational constraints point to a star with $M=1.28pm0.01 M_{odot}$, $R=1.458pm0.005 R_{odot}$, $t=1.83pm0.1$ Gyr, $r_{cc}=0.16pm0.02 R_{odot}$, $alpha=1.85pm0.05$, and $delta_{ov}=0.6pm0.2$ for HD 49933.
Let $G$ be a countable cancellative amenable semigroup and let $(F_n)$ be a (left) F{o}lner sequence in $G$. We introduce the notion of an $(F_n)$-normal element of ${0,1}^G$. When $G$ = $(mathbb N,+)$ and $F_n = {1,2,...,n}$, the $(F_n)$-normality coincides with the classical notion. We prove that: $bullet$ If $(F_n)$ is a F{o}lner sequence in $G$, such that for every $alphain(0,1)$ we have $sum_n alpha^{|F_n|}<infty$, then almost every $xin{0,1}^G$ is $(F_n)$-normal. $bullet$ For any F{o}lner sequence $(F_n)$ in $G$, there exists an Cham-per-nowne-like $(F_n)$-normal set. $bullet$ There is a natural class of nice F{o}lner sequences in $(mathbb N,times)$. There exists a Champernowne-like set which is $(F_n)$-normal for every nice F{o}lner sq. $bullet$ Let $Asubsetmathbb N$ be a classical normal set. Then, for any F{o}lner sequence $(K_n)$ in $(mathbb N,times)$ there exists a set $E$ of $(K_n)$-density $1$, such that for any finite subset ${n_1,n_2,dots,n_k}subset E$, the intersection $A/{n_1}cap A/{n_2}capldotscap A/{n_k}$ has positive upper density in $(mathbb N,+)$. As a consequence, $A$ contains arbitrarily long geometric progressions, and, more generally, arbitrarily long geo-arithmetic configurations of the form ${a(b+ic)^j,0le i,jle k}$. $bullet$ For any F{o}lner sq $(F_n)$ in $(mathbb N,+)$ there exist uncountably many $(F_n)$-normal Liouville numbers. $bullet$ For any nice F{o}lner sequence $(F_n)$ in $(mathbb N,times)$ there exist uncountably many $(F_n)$-normal Liouville numbers.
It has also been suggested that the detection of a wealth of very low amplitude modes in Delta Sct stars was only a matter of signal--to--noise ratio. Access to this treasure, impossible from the ground, is one of the scientific aims of the space mission CoRoT, a space mission developed and operated by CNES. This work presents the results obtained on HD 50844: the 140,016 datapoints were analysed using independent approaches and several checks performed. A level of 10^{-5} mag was reached in the amplitude spectra of the CoRoT timeseries. The frequency analysis of the CoRoT timeseries revealed hundreds of terms in the frequency range 0--30 d^{-1}. All the cross--checks confirmed this new result. The initial guess that Delta Sct stars have a very rich frequency content is confirmed. The spectroscopic mode identification gives theoretical support since very high--degree modes (up to ell=14) are identified. We also prove that cancellation effects are not sufficient in removing the flux variations associated to these modes at the noise level of the CoRoT measurements. The ground--based observations indicate that HD 50844 is an evolved star that is slightly underabundant in heavy elements, located on the Terminal Age Main Sequence. Probably due to this unfavourable evolutionary status, no clear regular distribution is observed in the frequency set. The predominant term (f_1=6.92 d^{-1}) has been identified as the fundamental radial mode combining ground-based photometric and spectroscopic data. This work is also based on observations made with ESO telescopes under the ESO Large Programme LP178.D-0361 and on data collected at the Observatorio de Sierra Nevada, at the Observatorio Astronomico Nacional San Pedro Martir, and at the Piszkesteto Mountain Station of Konkoly Observatory.
An alternative approach to the calculation of tunneling actions, that control the exponential suppression of the decay of metastable phases, is presented. The new method circumvents the use of bounces in Euclidean space by introducing an auxiliary function, a tunneling potential $V_t$ that connects smoothly the metastable and stable phases of the field potential $V$. The tunneling action is obtained as the integral in field space of an action density that is a simple function of $V_t$ and $V$. This compact expression can be considered as a generalization of the thin-wall action to arbitrary potentials and allows a fast numerical evaluation with a precision below the percent level for typical potentials. The method can also be used to generate potentials with analytic tunneling solutions.
Solar analogues are important stars to study for understanding the properties of the Sun. Evolutionary modeling, combined with seismic and spectroscopic analysis, becomes a powerful method to characterize stellar intrinsic parameters, such as mass, radius, metallicity and age.However, these characteristics, relevant for other aspects of astrophysics or exoplanetary system physics for example, are difficult to obtain with a high precision and/or accuracy. The goal of this study is to characterize the two solar analogues HD42618 and HD43587, observed by CoRoT. In particular, we aim to infer precise mass, radius, and age, using evolutionary modeling constrained by spectroscopic, photometric, and seismic analysis. These stars show evidences of being older than the Sun but with a relatively large lithium abundance. We present the seismic analysis of HD42618, and the modeling of the two solar analogs HD42618 andHD43587 using the CESTAM stellar evolution code. Models were computed to reproduce the spectroscopic (effective temperature and metallicity) and seismic (mode frequencies) data,and the luminosity of the stars, based on Gaia parallaxes. We infer very similar values of mass and radius for both stars compared to the literature, within the uncertainties, and reproduce correctly the seismic constraints. For HD42618, the modeling shows it is slightly less massive and older than the Sun. For HD43587, it confirms it is more massive and older than the Sun,in agreement with previous results. The use of chemical clocks improves the reliability of our age estimates.
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