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Register a new userStellar granulation as seen in disk-integrated intensity. II. Theoretical scaling relations compared with observations
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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.
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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 growing 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.
The granulation background seen in the power spectrum of a solar-like oscillator poses a serious challenge for extracting precise and detailed information about the stellar oscillations. Using a 3D hydrodynamical simulation of the Sun computed with CO$^5$BOLD, we investigate various background models to infer, using a Bayesian methodology, which one provides the best fit to the background in the simulated power spectrum. We find that the best fit is provided by an expression including the overall power level and two characteristic frequencies, one with an exponent of 2 and one with a free exponent taking on a value around 6. We assess the impact of the 3D hydro-code on this result by repeating the analysis with a simulation from Stagger and find that the main conclusion is unchanged. However, the details of the resulting best fits differ slightly between the two codes, but we explain this difference by studying the effect of the spatial resolution and the duration of the simulation on the fit. Additionally, we look into the impact of adding white noise to the simulated time series as a simple way to mimic a real star. We find that, as long as the noise level is not too low, the results are consistent with the no-noise case.
A large fraction of cool, low-mass stars exhibit brightness fluctuations that arise from a combination of convective granulation, acoustic oscillations, magnetic activity, and stellar rotation. Much of the short-timescale variability takes the form of stochastic noise, whose presence may limit the progress of extrasolar planet detection and characterization. In order to lay the groundwork for extracting useful information from these quasi-random signals, we focus on the origin of the granulation-driven component of the variability. We apply existing theoretical scaling relations to predict the star-integrated variability amplitudes for 508 stars with photometric light curves measured by the Kepler mission. We also derive an empirical correction factor that aims to account for the suppression of convection in F-dwarf stars with magnetic activity and shallow convection zones. So that we can make predictions of specific observational quantities, we performed Monte Carlo simulations of granulation light curves using a Lorentzian power spectrum. These simulations allowed us to reproduce the so-called flicker floor (i.e., a lower bound in the relationship between the full light-curve range and power in short-timescale fluctuations) that was found in the Kepler data. The Monte Carlo model also enabled us to convert the modeled fluctuation variance into a flicker amplitude directly comparable with observations. When the magnetic suppression factor described above is applied, the model reproduces the observed correlation between stellar surface gravity and flicker amplitude. Observationally validated models like these provide new and complementary evidence for a possible impact of magnetic activity on the properties of near-surface convection.
We have investigated a time series of continuum intensity maps and corresponding Dopplergrams of granulation in a very quiet solar region at the disk center, recorded with the Imaging Magnetograph eXperiment (IMaX) on board the balloon-borne solar observatory Sunrise. We find that granules frequently show substructure in the form of lanes composed of a leading bright rim and a trailing dark edge, which move together from the boundary of a granule into the granule itself. We find strikingly similar events in synthesized intensity maps from an ab initio numerical simulation of solar surface convection. From cross sections through the computational domain of the simulation, we conclude that these `granular lanes are the visible signature of (horizontally oriented) vortex tubes. The characteristic optical appearance of vortex tubes at the solar surface is explained. We propose that the observed vortex tubes may represent only the large-scale end of a hierarchy of vortex tubes existing near the solar surface.
We explore how the slopes and scatters of the scaling relations of disk galaxies (Vm-L[-M], R-L[-M], and Vm-R) do change when moving from B to K bands and to stellar and baryonic quantities. For our compiled sample of 76 normal, non-interacting high and low surface brightness galaxies, we find some changes, which evidence evolution effects, mainly related to gas infall and star formation (SF). We also explore correlations among the (B-K) color, stellar mass fraction fs, mass M (luminosity L), and surface density (SB), as well as correlations among the residuals of the scaling relations. Some of our findings are: (i) the scale length Rb is a third parameter in the baryonic TF relation and the residuals of this relation follow a trend (slope ~-0.15) with the residuals of the Rb-Mb relation; for the stellar and K band cases, R is not anymore a third parameter and the mentioned trend disappears; (ii) among the TFRs, the B-band TFR is the most scattered; in this case, the color is a third parameter; (iii) the LSB galaxies break some observed trends, which suggest a threshold in the gas surface density Sg, below which the SF becomes independent of the gas infall rate and Sg. Our results are interpreted and discussed in the light of LCDM-based models of galaxy evolution. The models explain not only the baryonic scaling relations, but also most of the processes responsible for the observed changes in the slopes, scatters, and correlations among the residuals when changing to stellar and luminous quantities. The baryon fraction is required to be smaller than 0.05 on average. We detect some potential difficulties for the models: the observed color-M and surface density-M correlations are steeper, and the intrinsic scatter in the baryonic TFR is smaller than those predicted. [abridged]
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