The space-borne missions CoRoT and Kepler are indiscreet. With their asteroseismic programs, they tell us what is hidden deep inside the stars. Waves excited just below the stellar surface travel throughout the stellar interior and unveil many secret
s: how old is the star, how big, how massive, how fast (or slow) its core is dancing. This paper intends to emph{paparazze} the red giants according to the seismic pictures we have from their interiors.
The solar granulation is known for a long time to be a surface manifestation of convection. Thanks to the current space-borne missions CoRoT and Kepler, it is now possible to observe in disk-integrated intensity the signature of this phenomena in a g
rowing number of stars. The space-based photometric measurements show that the global brightness fluctuations and the lifetime associated with granulation obeys characteristic scaling relations. We thus aim at providing a simple theoretical modeling to reproduce these scaling relations and subsequently at inferring the physical properties of granulation properties across the HR diagram. We develop a simple 1D theoretical model that enable us to test any prescription concerning the time-correlation between granules. The input parameters of the model are extracted from 3D hydrodynamical models of the surface layers of stars, and the free parameters involved in the model are calibrated with solar observations. Two different prescriptions for representing the eddy time-correlation in the Fourier space are compared: a Lorentzian and an exponential form. Finally, we compare our theoretical prediction with a 3D radiative hydrodynamical (RHD) numerical modeling of stellar granulation (ab-initio approach). Provided that the free parameters are appropriately adjusted, our theoretical model satisfactorily reproduces the shape and the amplitude of the observed solar granulation spectrum. The best agreement is obtained with an exponential form. Furthermore, our theoretical model results in granulation spectra that consistently agree with the these calculated on the basis of the ab-initio approach with two 3D RHD models. Comparison between theoretical granulation spectra calculated with the present model and high precision photometry measurements of stellar granulation is undertaken in a companion paper.
A large set of stars observed by CoRoT and Kepler shows clear evidence for the presence of a stellar background, which is interpreted to arise from surface convection, i.e., granulation. These observations show that the characteristic time-scale (tau
_eff) and the root-mean-square (rms) brightness fluctuations (sigma) associated with the granulation scale as a function of the peak frequency (nu_max) of the solar-like oscillations. We aim at providing a theoretical background to the observed scaling relations based on a model developed in the companion paper. We computed for each 3D model the theoretical power density spectrum (PDS) associated with the granulation as seen in disk-integrated intensity on the basis of the theoretical model. For each PDS we derived tau_eff and sigma and compared these theoretical values with the theoretical scaling relations derived from the theoretical model and the Kepler measurements. We derive theoretical scaling relations for tau_eff and sigma, which show the same dependence on nu_max as the observed scaling relations. In addition, we show that these quantities also scale as a function of the turbulent Mach number (Ma) estimated at the photosphere. The theoretical scaling relations for tau_eff and sigma match the observations well on a global scale. Our modelling provides additional theoretical support for the observed variations of sigma and tau_eff with nu_m max. It also highlights the important role of Ma in controlling the properties of the stellar granulation. However, the observations made with Kepler on a wide variety of stars cannot confirm the dependence of our scaling relations on Ma. Measurements of the granulation background and detections of solar-like oscillations in a statistically sufficient number of cool dwarf stars will be required for confirming the dependence of the theoretical scaling relations with Ma.
Scaling relations between asteroseismic quantities and stellar parameters are essential tools for studying stellar structure and evolution. We will address two of them, namely, the relation between the large frequency separation ($Delta u$) and the
mean density ($bar{rho}$) as well as the relation between the frequency of the maximum in the power spectrum of solar-like oscillations ($ u_{rm max}$) and the cut-off frequency ($ u_{rm c}$). For the first relation, we will consider the possible sources of uncertainties and explore them with the help of a grid of stellar models. For the second one, we will show that the basic physical picture is understood and that departure from the observed relation arises from the complexity of non-adiabatic processes involving time-dependent treatment of convection. This will be further discussed on the basis of a set of 3D hydrodynamical simulation of surface convection.
A growing number of solar-like oscillations has been detected in red giant stars thanks to CoRoT and Kepler space-crafts. The seismic data gathered by CoRoT on red giant stars allow us to test mode driving theory in physical conditions different from
main-sequence stars. Using a set of 3D hydrodynamical models representative of the upper layers of sub- and red giant stars, we computed the acoustic mode energy supply rate (Pmax). Assuming adiabatic pulsations and using global stellar models that assume that the surface stratification comes from the 3D hydrodynamical models, we computed the mode amplitude in terms of surface velocity. This was converted into intensity fluctuations using either a simplified adiabatic scaling relation or a non-adiabatic one. From L and M (the luminosity and mass), the energy supply rate Pmax is found to scale as (L/M)^2.6 for both main-sequence and red giant stars, extending previous results. The theoretical amplitudes in velocity under-estimate the Doppler velocity measurements obtained so far from the ground for red giant stars by about 30%. In terms of intensity, the theoretical scaling law based on the adiabatic intensity-velocity scaling relation results in an under-estimation by a factor of about 2.5 with respect to the CoRoT seismic measurements. On the other hand, using the non-adiabatic intensity-velocity relation significantly reduces the discrepancy with the CoRoT data. The theoretical amplitudes remain 40% below, however, the CoRoT measurements. Our results show that scaling relations of mode amplitudes cannot be simply extended from main-sequence to red giant stars in terms of intensity on the basis of adiabatic relations because non-adiabatic effects for red giant stars are important and cannot be neglected. We discuss possible reasons for the remaining differences.
The star HD 52265 is a G0V metal-rich exoplanet-host star observed in the seismology field of the CoRoT space telescope from November 2008 to March 2009. The satellite collected 117 days of high-precision photometric data on this star, showing that i
t presents solar-like oscillations. HD 52265 was also observed in spectroscopy with the Narval spectrograph at the same epoch. We characterise HD 52265 using both spectroscopic and seismic data. The fundamental stellar parameters of HD 52265 were derived with the semi-automatic software VWA, and the projected rotational velocity was estimated by fitting synthetic profiles to isolated lines in the observed spectrum. The parameters of the observed p modes were determined with a maximum-likelihood estimation. We performed a global fit of the oscillation spectrum, over about ten radial orders, for degrees l=0 to 2. We also derived the properties of the granulation, and analysed a signature of the rotation induced by the photospheric magnetic activity. Precise determinations of fundamental parameters have been obtained: Teff = 6100 +- 60 K, log g = 4.35 +- 0.09, [M/H] = 0.19 +- 0.05, as well as vsini = 3.6 +0.3 -1.0 km/s. We have measured a mean rotation period P_rot = 12.3 +- 0.15 days, and find a signature of differential rotation. The frequencies of 31 modes are reported in the range 1500-2550 micro-Hz. The large separation exhibits a clear modulation around the mean value <Dnu> = 98.3 +- 0.1 micro-Hz. Mode widths vary with frequency along an S-shape with a clear local maximum around 1800 micro-Hz. We deduce lifetimes ranging between 0.5 and 3 days for these modes. Finally, we find a maximal bolometric amplitude of about 3.96 +- 0.24 ppm for radial modes.
For more than ten years, solar-like oscillations have been detected and frequencies measured for a growing number of stars with various characteristics (e.g. different evolutionary stages, effective temperatures, gravities, metal abundances ...). E
xcitation of such oscillations is attributed to turbulent convection and takes place in the uppermost part of the convective envelope. Since the pioneering work of Goldreich & Keely (1977), more sophisticated theoretical models of stochastic excitation were developed, which differ from each other both by the way turbulent convection is modeled and by the assumed sources of excitation. We review here these different models and their underlying approximations and assumptions. We emphasize how the computed mode excitation rates crucially depend on the way turbulent convection is described but also on the stratification and the metal abundance of the upper layers of the star. In turn we will show how the seismic measurements collected so far allow us to infer properties of turbulent convection in stars.
From the seismic data obtained by CoRoT for the star HD 49933 it is possible, as for the Sun, to constrain models of the excitation of acoustic modes by turbulent convection. We compare a stochastic excitation model described in Paper I (arXiv:0910.4
027) with the asteroseismology data for HD 49933, a star that is rather metal poor and significantly hotter than the Sun. Using the mode linewidths measured by CoRoT for HD 49933 and the theoretical mode excitation rates computed in Paper I, we derive the expected surface velocity amplitudes of the acoustic modes detected in HD 49933. Using a calibrated quasi-adiabatic approximation relating the mode amplitudes in intensity to those in velocity, we derive the expected values of the mode amplitude in intensity. Our amplitude calculations are within 1-sigma error bars of the mode surface velocity spectrum derived with the HARPS spectrograph. The same is found with the mode amplitudes in intensity derived for HD 49933 from the CoRoT data. On the other hand, at high frequency, our calculations significantly depart from the CoRoT and HARPS measurements. We show that assuming a solar metal abundance rather than the actual metal abundance of the star would result in a larger discrepancy with the seismic data. Furthermore, calculations that assume the ``new solar chemical mixture are in better agreement with the seismic data than those that assume the ``old solar chemical mixture. These results validate, in the case of a star significantly hotter than the Sun and Alpha Cen A, the main assumptions in the model of stochastic excitation. However, the discrepancies seen at high frequency highlight some deficiencies of the modelling, whose origin remains to be understood.
Solar-like oscillations are stochastically excited by turbulent convection at the surface layers of the stars. We study the role of the surface metal abundance on the efficiency of the stochastic driving in the case of the CoRoT target HD 49933. We c
ompute two 3D hydrodynamical simulations representative -- in effective temperature and gravity -- of the surface layers of the CoRoT target HD 49933, a star that is rather metal poor and significantly hotter compared to the Sun. One 3D simulation has a solar metal abundance and the other has a surface iron-to-hydrogen, [Fe/H], abundance ten times smaller. For each 3D simulation we match an associated global 1D model and we compute the associated acoustic modes using a theoretical model of stochastic excitation validated in the case of the Sun and Alpha Cen A. The rate at which energy is supplied per unit time into the acoustic modes associated with the 3D simulation with [Fe/H]=-1 are found about three times smaller than those associated with the 3D simulation with [Fe/H]=0. As shown here, these differences are related to the fact that low metallicity implies surface layers with a higher mean density. In turn, a higher mean density favors smaller convective velocities and hence less efficient driving of the acoustic modes. Our result shows the importance of taking the surface metal abundance into account in the modeling of the mode driving by turbulent convection. A comparison with observational data is presented in a companion paper using seismic data obtained for the CoRoT target HD 49933.
Context: The F8 star HD 181906 (effective temperature ~6300K) was observed for 156 days by the CoRoT satellite during the first long run in the centre direction. Analysis of the data reveals a spectrum of solar-like acoustic oscillations. However, th
e faintness of the target (m_v=7.65) means the signal-to-noise (S/N) in the acoustic modes is quite low, and this low S/N leads to complications in the analysis. Aims: To extract global variables of the star as well as key parameters of the p modes observed in the power spectrum of the lightcurve. Methods: The power spectrum of the lightcurve, a wavelet transform and spot fitting have been used to obtain the average rotation rate of the star and its inclination angle. Then, the autocorrelation of the power spectrum and the power spectrum of the power spectrum were used to properly determine the large separation. Finally, estimations of the mode parameters have been done by maximizing the likelihood of a global fit, where several modes were fit simultaneously. Results: We have been able to infer the mean surface rotation rate of the star (~4 microHz) with indications of the presence of surface differential rotation, the large separation of the p modes (~87 microHz), and therefore also the ridges corresponding to overtones of the acoustic modes.
