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Observations of very low-mass stars with Kepler represent an excellent opportunity to search for planetary transits and to characterize optical photometric variability at the cool end of the stellar mass distribution. In this paper, we present low-resolution red optical spectra that allow us to identify 18 very low-mass stars that have Kepler light curves available in the public archive. Spectral types of these targets are found to lie in the range dM4.5--dM8.5, implying spectrophotometric distances from 17 pc to 80 pc. Limits to the presence of transiting planets are placed from modelling of the Kepler light curves. We find that the size of the planets detectable by Kepler around these small stars typically lie in the range 1 to 5 Earth radii within the habitable regions (P$le$10 days). We identify one candidate transit with a period of 1.26 days that resembles the signal produced by a planet slightly smaller than the Moon. However, our pixel by pixel analysis of the Kepler data shows that the signal most likely arises from a background contaminating eclipsing binary. For 11 of these objects reliable photometric periods shorter than 7 days are derived, and are interpreted as rotational modulation of magnetic cool spots. For 3 objects we find possible photometric periods longer than 50 days that require confirmation. H$_alpha$ emission measurements and flare rates are used as a proxies for chromospheric activity and transversal velocities are used as an indicator of dynamical ages. These data allow us to discuss the relationship between magnetic activity and detectability of planetary transits around very low-mass stars. We show that Super-Earth planets with sizes around 2 Earth radii are detectable with Kepler around about two thirds of the stars in our sample, independently from their level of chromospheric activity.
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We present calculations of the occurrence rate of small close-in planets around low mass dwarf stars using the known planet populations from the $Kepler$ and $K2$ missions. Applying completeness corrections clearly reveals the radius valley in the maximum a-posteriori occurrence rates as a function of orbital separation and planet radius. We measure the slope of the valley to be $r_{p,text{valley}} propto F^{-0.060pm 0.025}$ which bears the opposite sign from that measured around Sun-like stars thus suggesting that thermally driven atmospheric mass loss may not dominate the evolution of planets in the low stellar mass regime or that we are witnessing the emergence of a separate channel of planet formation. The latter notion is supported by the relative occurrence of rocky to non-rocky planets increasing from $0.5pm 0.1$ around mid-K dwarfs to $8.5pm 4.6$ around mid-M dwarfs. Furthermore, the center of the radius valley at $1.54pm 0.16$ R$_{oplus}$ is shown to shift to smaller sizes with decreasing stellar mass in agreement with physical models of photoevaporation, core-powered mass loss, and gas-poor formation. Although current measurements are insufficient to robustly identify the dominant formation pathway of the radius valley, such inferences may be obtained by $TESS$ with $mathcal{O}(85,000)$ mid-to-late M dwarfs observed with 2-minute cadence. The measurements presented herein also precisely designate the subset of planetary orbital periods and radii that should be targeted in radial velocity surveys to resolve the rocky to non-rocky transition around low mass stars.
We conduct a pebble-driven planet population synthesis study to investigate the formation of planets around very low-mass stars and brown dwarfs, in the (sub)stellar mass range between $0.01 M_{odot}$ and $0.1 M_{odot}$. Based on the extrapolation of numerical simulations of planetesimal formation by the streaming instability, we obtain the characteristic mass of the planetesimals and the initial masses of the protoplanets (largest bodies from the planetesimal size distributions), in either the early self-gravitating phase or the later non-self-gravitating phase of the protoplanetary disk evolution. We find that the initial protoplanets form with masses that increase with host mass, orbital distance and decrease with disk age. Around late M-dwarfs of $0.1 M_{odot}$, these protoplanets can grow up to Earth-mass planets by pebble accretion. However, around brown dwarfs of $0.01 M_{odot}$, planets do not grow larger than Mars mass when the initial protoplanets are born early in self-gravitating disks, and their growth stalls at around $0.01$ Earth-mass when they are born late in non-self-gravitating disks. Around these low mass stars and brown dwarfs, we find no channel for gas giant planet formation because the solid cores remain too small. When the initial protoplanets form only at the water-ice line, the final planets typically have ${gtrsim} 15%$ water mass fraction. Alternatively, when the initial protoplanets form log-uniformly distributed over the entire protoplanetary disk, the final planets are either very water-rich (water mass fraction ${gtrsim}15%$) or entirely rocky (water mass fraction ${lesssim}5%$).
Very-low-mass stars can develop secularly unstable hydrogen-burning shells late in their life. Since the thermal pulses that go along are driven at the bottoms of very shallow envelopes, the stars luminosities and effective temperatures react strongly during a pulse cycle. Towards the end of the Galaxys stelliferous era, the hydrogen-shell flashing very-low-mass single stars should inflict an intricate light-show performed by the large population of previously inconspicuous dim stars. Unfortunately, this natural spectacle will discharge too late for mankind to indulge in. Not all is hopeless, though: In the case of close binary-star evolution, hydrogen-shell flashes of mass-stripped, very-low mass binary components can develop in a fraction of a Hubble time. Therefore, the Galaxy should be able put forth a few candidates that are going to evolve through a H-shell flash in a humanity-compatible time frame.
We report the discovery of Kepler-77b (alias KOI-127.01), a Saturn-mass transiting planet in a 3.6-day orbit around a metal-rich solar-like star. We combined the publicly available Kepler photometry (quarters 1-13) with high-resolution spectroscopy from the Sandiford@McDonald and FIES@NOT spectrographs. We derived the system parameters via a simultaneous joint fit to the photometric and radial velocity measurements. Our analysis is based on the Bayesian approach and is carried out by sampling the parameter posterior distributions using a Markov chain Monte Carlo simulation. Kepler-77b is a moderately inflated planet with a mass of Mp=0.430+/-0.032 Mjup, a radius of Rp=0.960+/-0.016 Rjup, and a bulk density of 0.603+/-0.055 g/cm^3. It orbits a slowly rotating (P=36+/-6 days) G5V star with M*=0.95+/-0.04 Msun, R*=0.99+/-0.02 Rsun, Teff=5520+/-60 K, [M/H]=0.20+/-0.05, that has an age of 7.5+/-2.0 Gyr. The lack of detectable planetary occultation with a depth higher than about 10 ppm implies a planet geometric and Bond albedo of Ag<0.087+/-0.008 and Ab<0.058+/-0.006, respectively, placing Kepler-77b among the gas-giant planets with the lowest albedo known so far. We found neither additional planetary transit signals nor transit-timing variations at a level of about 0.5 minutes, in accordance with the trend that close-in gas giant planets seem to belong to single-planet systems. The 106 transits observed in short-cadence mode by Kepler for nearly 1.2 years show no detectable signatures of the planets passage in front of starspots. We explored the implications of the absence of detectable spot-crossing events for the inclination of the stellar spin-axis, the sky-projected spin-orbit obliquity, and the latitude of magnetically active regions.
We briefly review the main physical and structural properties of Very Low-Mass stars. The most important improvements in the physical inputs required for the stellar models computations are also discussed. We show some comparisons with observational measurements concerning both the Color-Magnitude diagrams, mass-luminosity relations and mass-radius one, in order to disclose the level of agreement between the present theoretical framework and observations.
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