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.
We present an overview of the current status of our efforts to derive the microturbulence and macroturbulence parameters (ximic and ximac) from the CIFIST grid of CO5BOLD 3D model atmospheres as a function of the basic stellar parameters Teff, log g,
and [M/H]. The latest results for the Sun and Procyon show that the derived microturbulence parameter depends significantly on the numerical resolution of the underlying 3D simulation, confirming that `low-resolution models tend to underestimate the true value of ximic. Extending the investigation to twelve further simulations with different Teff, log g, and [M/H], we obtain a first impression of the predicted trend of ximic over the Hertzsprung-Russell diagram: in agreement with empirical evidence, microturbulence increases towards higher effective temperature and lower gravity. The metallicity dependence of ximic must be interpreted with care, since it also reflects the deviation between the 1D and 3D photospheric temperature stratifications that increases systematically towards lower metallicity.
In this work we have used 3D hydrodynamical (CO5BOLD) and 1D hydrostatic (LHD) stellar atmosphere models to study the importance of convection and horizontal temperature inhomogeneities in stellar abundance work related to late-type giants. We have f
ound that for a number of key elements, such as Na, Mg, Si, Ca, Ti, Fe, Ni, Zn, Ba, Eu, differences in abundances predicted by 3D and 1D models are typically minor (< 0.1 dex) at solar metallicity. However, at [M/H] = -3 they become larger and reach to -0.5...-0.8 dex. In case of neutral atoms and fixed metallicity, the largest abundance differences were obtained for the spectral lines with lowest excitation potential, while for ionized species the largest 3D-1D abundance differences were found for lines of highest excitation potential. The large abundance differences at low metallicity are caused by large horizontal temperature fluctuations and lower mean temperature in the outer layers of the 3D hydrodynamical model compared with its 1D counterpart.
The use of hydrodynamical simulations, the selection of atomic data, and the computation of deviations from local thermodynamical equilibrium for the analysis of the solar spectra have implied a downward revision of the solar metallicity. We are in t
he process of using the latest simulations computed with the CO5BOLD code to reassess the solar chemical composition. We determine the solar photospheric carbon abundance by using a radiation-hydrodynamical CO5BOLD model, and compute the departures from local thermodynamical equilibrium by using the Kiel code. We measure equivalent widths of atomic CI lines on high resolution, high signal-to-noise ratio solar atlases. Deviations from local thermodynamic equilibrium are computed in 1D with the Kiel code. Our recommended value for the solar carbon abundance, relies on 98 independent measurements of observed lines and is A(C)=8.50+-0.06, the quoted error is the sum of statistical and systematic error. Combined with our recent results for the solar oxygen and nitrogen abundances this implies a solar metallicity of Z=0.0154 and Z/X=0.0211. Our analysis implies a solar carbon abundance which is about 0.1 dex higher than what was found in previous analysis based on different 3D hydrodynamical computations. The difference is partly driven by our equivalent width measurements (we measure, on average, larger equivalent widths with respect to the other work based on a 3D model), in part it is likely due to the different properties of the hydrodynamical simulations and the spectrum synthesis code. The solar metallicity we obtain from the CO5BOLD analyses is in slightly better agreement with the constraints of helioseismology than the previous 3D abundance results. (Abridged)
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.
We present an investigation of the velocity fields in early to late M-type star hydrodynamic models, and we simulate their influence on FeH molecular line shapes. The M star model parameters range between log g of 3.0 - 5.0 and Teff of 2500 K and 400
0 K. Our aim is to characterize the Teff- and log g -dependence of the velocity fields and express them in terms of micro- and macro-turbulent velocities in the one dimensional sense. We present also a direct comparison between 3D hydrodynamical velocity fields and 1D turbulent velocities. The velocity fields strongly affect the line shapes of FeH, and it is our goal to give a rough estimate for the log g and Teff parameter range in which 3D spectral synthesis is necessary and where 1D synthesis suffices. In order to calculate M-star structure models we employ the 3D radiative-hydrodynamics (RHD) code CO5BOLD. The spectral synthesis on these models is performed with the line synthesis code LINFOR3D. We describe the 3D velocity fields in terms of a Gaussian standard deviation and project them onto the line of sight to include geometrical and limb-darkening effects. The micro- and macro-turbulent velocities are determined with the Curve of Growth method and convolution with a Gaussian velocity profile, respectively. To characterize the log g and Teff dependence of FeH lines, the equivalent width, line width, and line depth are regarded. The velocity fields in M-stars strongly depend on log g and Teff. They become stronger with decreasing log g and increasing Teff.
We present an investigation of velocity fields in early to late M-type hydrodynamic stellar atmosphere models. These velocities will be expressed in classical terms of micro- and macro-turbulent velocities for usage in 1D spectral synthesis. The M-st
ar model parameters range between log g of 3.0 - 5.0 and Teff of 2500 K - 4000 K. We characterize the Teff- and log g-dependence of the hydrodynamical velocity fields in these models with a binning method, and for the determination of micro-turbulent velocities, the Curve of Growth method is used. The macro-turbulent velocities are obtained by convolutions with Gaussian profiles. Velocity fields in M-stars strongly depend on log g and Teff. Their velocity amplitudes increase with decreasing log g and increasing Teff. The 3D hydrodynamical and 1D macro-turbulent velocities range from ~100 m/s for cool high gravity models to ~ 800 m/s - 1000 m/s for hot models or models with low log g. The micro-turbulent velocities range in the order of ~100 m/s for cool models, to ~600 m/s for hot or low log g models. Our M-star structure models are calculated with the 3D radiative-hydrodynamics (RHD) code CO5BOLD. The spectral synthesis on these models is performed with the line synthesis code LINFOR3D.
We present synthetic FeH band spectra in the z-filter range for several M-dwarf models with logg=3.0-5.0 [cgs] and Teff=2800K -3450K. Our aim is to characterize convective velocities in M-dwarfs and to give a rough estimate of the range in which 3D-a
tmosphere treatment is necessary and where 1D-atmosphere models suffice for the interpretation of molecular spectral features. This is also important in order to distinguish between the velocity-broadening and the rotational- or Zeeman-broadening. The synthetic spectra were calculated using 3D CO5BOLD radiative-hydrodynamic (RHD) models and the line synthesis code LINFOR3D. We used complete 3D-models and high resolution 3D spectral synthesis for the detailed study of some well isolated FeH lines. The FeH line strength shows a dependence on surface gravity and effective temperature and could be employed to measure both quantities in M-type objects. The line width is related to the velocity-field in the model stars, which depends strongly on surface gravity. Furthermore, we investigate the velocity-field in the 3D M-dwarf models together with the related micro- and macro-turbulent velocities in the 1D case. We also search for effects on the lineshapes.
