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Kepler Mission results are rapidly contributing to fundamentally new discoveries in both the exoplanet and asteroseismology fields. The data returned from Kepler are unique in terms of the number of stars observed, precision of photometry for time series observations, and the temporal extent of high duty cycle observations. As the first mission to provide extensive time series measurements on thousands of stars over months to years at a level hitherto possible only for the Sun, the results from Kepler will vastly increase our knowledge of stellar variability for quiet solar-type stars. Here we report on the stellar noise inferred on the timescale of a few hours of most interest for detection of exoplanets via transits. By design the data from moderately bright Kepler stars are expected to have roughly comparable levels of noise intrinsic to the stars and arising from a combination of fundamental limitations such as Poisson statistics and any instrument noise. The noise levels attained by Kepler on-orbit exceed by some 50% the target levels for solar-type, quiet stars. We provide a decomposition of observed noise for an ensemble of 12th magnitude stars arising from fundamental terms (Poisson and readout noise), added noise due to the instrument and that intrinsic to the stars. The largest factor in the modestly higher than anticipated noise follows from intrinsic stellar noise. We show that using stellar parameters from galactic stellar synthesis models, and projections to stellar rotation, activity and hence noise levels reproduces the primary intrinsic stellar noise features.
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We have modified the graphical user interfaced close binary system analysis program CurveFit to the form WinKepler and applied it to 16 representative planetary candidate light curves found in the NASA Exoplanet Archive (NEA) at the Caltech website http://exoplanetarchive.ipac.caltech.edu, with an aim to compare different analytical approaches. WinKepler has parameter options for a realistic physical model, including gravity-brightening and structural parameters derived from the relevant Radau equation. We tested our best-fitting parameter-sets for formal determinacy and adequacy. A primary aim is to compare our parameters with those listed in the NEA. Although there are trends of agreement, small differences in the main parameter values are found in some cases, and there may be some relative bias towards a 90 degrees value for the NEA inclinations. These are assessed against realistic error estimates. Photometric variability from causes other than planetary transits affects at least 6 of the data-sets studied; with small pulsational behaviour found in 3 of those. For the false positive KOI 4.01, we found that the eclipses could be modelled by a faint background classical Algol as effectively as by a transiting exoplanet. Our empirical checks of limb-darkening, in the cases of KOI 1.01 and 12.01, revealed that the assigned stellar temperatures are probably incorrect. For KOI 13.01, our empirical mass-ratio differs by about 7% from that of Mislis and Hodgkin (2012), who neglected structural effects and higher order terms in the tidal distortion. Such detailed parameter evaluation, additional to the usual main geometric ones, provides an additional objective for this work.
With recent advances in modelling stars using high-precision asteroseismology, the systematic effects associated with our assumptions of stellar helium abundance ($Y$) and the mixing-length theory parameter ($alpha_mathrm{MLT}$) are becoming more important. We apply a new method to improve the inference of stellar parameters for a sample of Kepler dwarfs and subgiants across a narrow mass range ($0.8 < M < 1.2,mathrm{M_odot}$). In this method, we include a statistical treatment of $Y$ and the $alpha_mathrm{MLT}$. We develop a hierarchical Bayesian model to encode information about the distribution of $Y$ and $alpha_mathrm{MLT}$ in the population, fitting a linear helium enrichment law including an intrinsic spread around this relation and normal distribution in $alpha_mathrm{MLT}$. We test various levels of pooling parameters, with and without solar data as a calibrator. When including the Sun as a star, we find the gradient for the enrichment law, $Delta Y / Delta Z = 1.05^{+0.28}_{-0.25}$ and the mean $alpha_mathrm{MLT}$ in the population, $mu_alpha = 1.90^{+0.10}_{-0.09}$. While accounting for the uncertainty in $Y$ and $alpha_mathrm{MLT}$, we are still able to report statistical uncertainties of 2.5 per cent in mass, 1.2 per cent in radius, and 12 per cent in age. Our method can also be applied to larger samples which will lead to improved constraints on both the population level inference and the star-by-star fundamental parameters.
As a response to the white paper call, we propose to turn Kepler to the South Ecliptic Pole (SEP) and observe thousands of large amplitude variables for years with high cadence in the frame of the Kepler-SEP Mission. The degraded pointing stability will still allow observing these stars with reasonable (probably better than mmag) accuracy. Long-term continuous monitoring already proved to be extremely helpful to investigate several areas of stellar astrophysics. Space-based missions opened a new window to the dynamics of pulsation in several class of pulsating variable stars and facilitated detailed studies of eclipsing binaries. The main aim of this mission is to better understand the fascinating dynamics behind various stellar pulsational phenomena (resonances, mode coupling, chaos, mode selection) and interior physics (turbulent convection, opacities). This will also improve the applicability of these astrophysical tools for distance measurements, population and stellar evolution studies. We investigated the pragmatic details of such a mission and found a number of advantages: minimal reprogramming of the flight software, a favorable field of view, access to both galactic and LMC objects. However, the main advantage of the SEP field comes from the large sample of well classified targets, mainly through OGLE. Synergies and significant overlap (spatial, temporal and in brightness) with both ground- (OGLE, LSST) and space-based missions (GAIA, TESS) will greatly enhance the scientific value of the Kepler-SEP mission. GAIA will allow full characterization of the distance indicators. TESS will continuously monitor this field for at least one year, and together with the proposed mission provide long time series that cannot be obtained by other means. If Kepler-SEP program is successful, there is a possibility to place one of the so-called LSST deep-drilling fields in this region.
We report the latest statistical analyses of superflares on solar-type (G-type main-sequence; effective temperature is 5100 - 6000 K) stars using all of the $Kepler$ primary mission data, and $Gaia$-DR2 (Data Release 2) catalog. We updated the flare detection method from our previous studies by using high-pass filter to remove rotational variations caused by starspots. We also examined the sample biases on the frequency of superflares, taking into account gyrochronology and flare detection completeness. The sample size of solar-type stars and Sun-like stars (effective temperature is 5600 - 6000 K and rotation period is over 20 days in solar-type stars) are $sim$4 and $sim$12 times, respectively, compared with Notsu et al. (2019, ApJ, 876, 58). As a result, we found 2341 superflares on 265 solar-type stars, and 26 superflares on 15 Sun-like stars: the former increased from 527 to 2341 and the latter from 3 to 26 events compared with our previous study. This enabled us to have a more well-established view on the statistical properties of superflares. The observed upper limit of the flare energy decreases as the rotation period increases in solar-type stars. The frequency of superflares decreases as the stellar rotation period increases. The maximum energy we found on Sun-like stars is $4 times 10^{34}$ erg. Our analysis of Sun-like stars suggest that the Sun can cause superflares with energies of $sim 7 times 10^{33}$ erg ($sim$X700-class flares) and $sim 1 times 10^{34}$ erg ($sim$X1000-class flares) once every $sim$3,000 years and $sim$6,000 years, respectively.
The stellar magnetic field plays a crucial role in the star internal mechanisms, as in the interactions with its environment. The study of starspots provides information about the stellar magnetic field, and can characterise the cycle. Moreover, the analysis of solar-type stars is also useful to shed light onto the origin of the solar magnetic field. The objective of this work is to characterise the magnetic activity of stars. Here, we studied two solar-type stars Kepler-17 and Kepler-63 using two methods to estimate the magnetic cycle length. The first one characterises the spots (radius, intensity, and location) by fitting the small variations in the light curve of a star caused by the occultation of a spot during a planetary transit. This approach yields the number of spots present in the stellar surface and the flux deficit subtracted from the star by their presence during each transit. The second method estimates the activity from the excess in the residuals of the transit lightcurves. This excess is obtained by subtracting a spotless model transit from the lightcurve, and then integrating all the residuals during the transit. The presence of long term periodicity is estimated in both time series. With the first method, we obtained $P_{rm cycle}$ = 1.12 $pm$ 0.16 yr (Kepler-17) and $P_{rm cycle}$ = 1.27 $pm$ 0.16 yr (Kepler-63), and for the second approach the values are 1.35 $pm$ 0.27 yr and 1.27 $pm$ 0.12 yr, respectively. The results of both methods agree with each other and confirm their robustness.
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