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To date, only 18 exoplanets with radial velocity (RV) semi-amplitudes $<2$ m/s have had their masses directly constrained. The biggest obstacle to RV detection of such exoplanets is variability intrinsic to stars themselves, e.g. nuisance signals arising from surface magnetic activity such as rotating spots and plages, which can drown out or even mimic planetary RV signals. We use Kepler-37 - known to host three transiting planets, one of which, Kepler-37d, should be on the cusp of RV detectability with modern spectrographs - as a case study in disentangling planetary and stellar activity signals. We show how two different statistical techniques - one seeking to identify activity signals in stellar spectra, and another to model activity signals in extracted RVs and activity indicators - can enable detection of the hitherto elusive Kepler-37d. Moreover, we show that these two approaches can be complementary, and in combination, facilitate a definitive detection and precise characterisation of Kepler-37d. Its RV semi-amplitude of $1.22pm0.31$ m/s (mass $5.4pm1.4$ $M_oplus$) is formally consistent with TOI-178bs $1.05^{+0.25}_{-0.30}$ m/s, the latter being the smallest detected RV signal of any transiting planet to date, though dynamical simulations suggest Kepler-37ds mass may be on the lower end of our $1sigma$ credible interval. Its consequent density is consistent with either a water-world or that of a gaseous envelope ($sim0.4%$ by mass) surrounding a rocky core. Based on RV modelling and a re-analysis of Kepler-37 TTVs, we also argue that the putative (non-transiting) planet Kepler-37e should probably be stripped of its confirmed status.
We present a comprehensive analysis of 10 years of HARPS radial velocities of the K2V dwarf star HD 13808, which has previously been reported to host two unconfirmed planet candidates. We use the state-of-the-art nested sampling algorithm PolyChord t
Radial velocity perturbations induced by stellar surface inhomogeneities including spots, plages and granules currently limit the detection of Earth-twins using Doppler spectroscopy. Such stellar noise is poorly understood for stars other than the Su
We present high-precision linear polarization observations of four bright hot Jupiter systems ($tau$ Boo, HD 179949, HD 189733 and 51 Peg) and use the data to search for polarized reflected light from the planets. The data for 51 Peg are consistent w
[Abridged] Context. Stellar activity is an important source of systematic errors and uncertainties in the characterization of exoplanets. Most of the techniques used to correct for this activity focus on an ad hoc data reduction. Aims. We have develo
Studies of exoplanet demographics require large samples and precise constraints on exoplanet host stars. Using the homogeneous Kepler stellar properties derived using Gaia Data Release 2 by Berger et al. (2020), we re-compute Kepler planet radii and