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Register a new userAn observational correlation between stellar brightness variations and surface gravity
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Authors
Fabienne A. Bastien
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Surface gravity is one of a stars basic properties, but it is difficult to measure accurately, with typical uncertainties of 25-50 per cent if measured spectroscopically and 90-150 per cent photometrically. Asteroseismology measures gravity with an uncertainty of about two per cent but is restricted to relatively small samples of bright stars, most of which are giants. The availability of high-precision measurements of brightness variations for >150,000 stars provides an opportunity to investigate whether the variations can be used to determine surface gravities. The Fourier power of granulation on a stars surface correlates physically with surface gravity; if brightness variations on timescales of hours arise from granulation, then such variations should correlate with surface gravity. Here we report an analysis of archival data that reveals an observational correlation between surface gravity and the root-mean-square brightness variations on timescales of less than eight hours for stars with temperatures of 4500-6750K, log of surface gravities of 2.5-4.5 (cgs units), and having overall brightness variations <3 parts per thousand. A straightforward observation of optical brightness variations therefore allows a determination of the surface gravity with a precision of <25 percent for inactive Sun-like stars at main-sequence to giant stages of evolution.
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Comparing solar and stellar brightness variations is hampered by the difference in spectral passbands used in observations as well as by the possible difference in the inclination of their rotation axes from the line of sight. We calculate the rotational variability of the Sun as it would be measured in passbands used for stellar observations. In particular, we consider the filter systems used by the CoRoT, $Kepler$, TESS, and $Gaia$ space missions. We also quantify the effect of the inclination of the rotation axis on the solar rotational variability. We employ the Spectral And Total Irradiance REconstructions (SATIRE) model to calculate solar brightness variations in different filter systems as observed from the ecliptic plane. We then combine the simulations of the surface distribution of the magnetic features at different inclinations using a surface flux transport model (SFTM) with the SATIRE calculations to compute the dependence of the variability on the inclination. For an ecliptic-bound observer, the amplitude of the solar rotational variability, as observed in the total solar irradiance (TSI) is 0.68 mmag (averaged over solar cycles 21-24). We obtained corresponding amplitudes in the $Kepler$ (0.74 mmag), CoRoT (0.73 mmag), TESS (0.62 mmag), $Gaia~ $ (0.74 mmag), $Gaia~ G_{RP}$ (0.62 mmag), and ), $Gaia~ G_{BP}$ (0.86 mmag) passbands. Decreasing the inclination of the rotation axis decreases the rotational variability. For a sample of randomly inclined stars, the variability is on average 15% lower in all filter systems considered in this work. This almost compensates for the difference in the amplitudes of the variability in TSI and $Kepler$ passbands, making the amplitudes derived from the TSI records an ideal representation of the solar rotational variability for comparison to $Kepler$ stars with unknown inclinations.
It has been demonstrated that the time variability of a stars brightness at different frequencies can be used to infer its surface gravity, radius, mass, and age. With large samples of light curves now available from Kepler and K2, and upcoming surveys like TESS, we wish to quantify the overall information content of this data and identify where the information resides. As a first look into this question we ask which stellar parameters we can predict from the brightness variations in red-giant stars data and to what precision, using a data-driven model. We demonstrate that the long-cadence (30-minute) Kepler light curves for 2000 red-giant stars can be used to predict their $T_{rm eff}$ and $log g$. Our inference makes use of a data-driven model of a part of the autocorrelation function (ACF) of the light curve, where we posit a polynomial relationship between stellar parameters and the ACF pixel values. We find that this model, trained using 1000 stars, can be used to recover the temperature $T_{rm eff}$ to $<$100 K, the surface gravity to $<$ 0.1 dex, and the asteroseismic power-spectrum parameters $rm u_{max}$ and $rm Delta{ u}$ to $<11$ $mu$Hz and $<0.9$ $mu$Hz ($lesssim$ 15%). We recover $T_{rm eff}$ from range of time-lags 0.045 $<$ $T_{rm lag}$ $<$ 370 days and the $log g$, $rm u_{max}$ and $rm Delta{ u}$ from the range 0.045 $<$ $T_{rm lag}$ $<$ 35 days. We do not discover any information about stellar metallicity. The information content of the data about each parameter is empirically quantified using this method, enabling comparisons to theoretical expectations about convective granulation.
We have determined new statistical relations to estimate the fundamental atmospheric parameters of effective temperature and surface gravity, using MK spectral classification, and vice versa. The relations were constructed based on the published calibration tables (for main sequence stars) and observational data from stellar spectral atlases (for giants and supergiants). These new relations were applied to field giants with known atmospheric parameters, and the results of the comparison of our estimations with available spectral classification had been quite satisfactory.
Context. Comparison studies of Sun-like stars with the Sun suggest an anomalously low photometric variability of the Sun compared to Sun-like stars with similar magnetic activity. Comprehensive understanding of stellar variability is needed, to find a physical reasoning for this observation. Aims. We investigate the effect of metallicity and effective temperature on the photometric brightness change of Sun-like stars seen at different inclinations. The considered range of fundamental stellar parameters is sufficiently small so the stars, investigated here, still count as Sun-like or even as solar twins. Methods. To model the brightness change of stars with solar magnetic activity, we extend a well established model of solar brightness variations, SATIRE (which stands for Spectral And Total Irradiance Reconstruction), which is based on solar spectra, to stars with different fundamental parameters. For that we calculate stellar spectra for different metallicities and effective temperature using the radiative transfer code ATLAS9. Results. We show that even a small change (e.g. within the observational error range) of metallicity or effective temperature significantly affects the photometric brightness change compared to the Sun. We find that for Sun-like stars, the amplitude of the brightness variations obtained for Stromgren (b + y)/2 reaches a local minimum for fundamental stellar parameters close to the solar metallicity and effective temperature. Moreover, our results show that the effect of inclination decreases for metallicity values greater than the solar metallicity. Overall, we find that an exact determination of fundamental stellar parameters is crucially important for understanding stellar brightness changes.
The Rastall gravity is a modification of Einsteins general relativity, in which the energy-momentum conservation is not satisfied and depends on the gradient of the Ricci curvature. It is in dispute whether the Rastall gravity is equivalent to the general relativity (GR). In this work, we constrain the theory using the rotation curves of Low Surface Brightness (LSB) spiral galaxies. Through fitting the rotation curves of LSB galaxies, we obtain the parameter $beta$ of the Rastall gravity. The $beta$ values of LSB galaxies satisfy Weak Energy Condition (WEC) and Strong Energy Condition(SEC). Combining the $beta$ values of type Ia supernovae and gravitational lensing of elliptical galaxies on the Rastall gravity, we conclude that the Rastall gravity is equivalent to the general relativity.
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