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Register a new userFriends and Foes: Conditional Occurrence Rates of Exoplanet Companions and their Impact on Radial Velocity Follow-up Surveys
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Population studies of Keplers multi-planet systems have revealed a surprising degree of structure in their underlying architectures. Information from a detected transiting planet can be combined with a population model to make predictions about the presence and properties of additional planets in the system. Using a statistical model for the distribution of planetary systems (He et al. 2020; arXiv:2007.14473), we compute the conditional occurrence of planets as a function of the period and radius of Kepler--detectable planets. About half ($0.52 pm 0.03$) of the time, the detected planet is not the planet with the largest semi-amplitude $K$ in the system, so efforts to measure the mass of the transiting planet with RV follow-up will have to contend with additional planetary signals in the data. We simulate RV observations to show that assuming a single--planet model to measure the $K$ of the transiting planet often requires significantly more observations than in the ideal case with no additional planets, due to the systematic errors from unseen planet companions. Our results show that planets around 10-day periods with $K$ close to the single--measurement RV precision ($sigma_{1,rm obs}$) typically require $sim 100$ observations to measure their $K$ to within 20% error. For a next generation RV instrument achieving $sigma_{1,rm obs} = 10$ cm/s, about $sim 200$ ($600$) observations are needed to measure the $K$ of a transiting Venus in a Kepler--like system to better than 20% (10%) error, which is $sim 2.3$ times as many as what would be necessary for a Venus without any planetary companions.
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We present an extension of the formalism recently proposed by Pepper & Gaudi to evaluate the yield of transit surveys in homogeneous stellar systems, incorporating the impact of correlated noise on transit time-scales on the detectability of transits, and simultaneously incorporating the magnitude limits imposed by the need for radial velocity follow-up of transit candidates. New expressions are derived for the different contributions to the noise budget on transit time-scales and the least-squares detection statistic for box-shaped transits, and their behaviour as a function of stellar mass is re-examined. Correlated noise that is constant with apparent stellar magnitude implies a steep decrease in detection probability at the high mass end which, when considered jointly with the radial velocity requirements, can severely limit the potential of otherwise promising surveys in star clusters. However, we find that small-aperture, wide field surveys may detect hot Neptunes whose radial velocity signal can be measured with present-day instrumentation in very nearby (<100 pc) clusters.
Radial Velocity follow-up is essential to establish or exclude the planetary nature of a transiting companion as well as to accurately determine its mass. Here we present some elements of an efficient Doppler follow-up strategy, based on high-resolution spectroscopy, devoted to the characterization of transiting candidates. Some aspects and results of the radial velocity follow-up of the CoRoT space mission are presented in order to illustrate the strategy used to deal with the zoo of transiting candidates.
We infer the number of planets-per-star as a function of orbital period and planet size using $Kepler$ archival data products with updated stellar properties from the $Gaia$ Data Release 2. Using hierarchical Bayesian modeling and Hamiltonian Monte Carlo, we incorporate planet radius uncertainties into an inhomogeneous Poisson point process model. We demonstrate that this model captures the general features of the outcome of the planet formation and evolution around GK stars, and provides an infrastructure to use the $Kepler$ results to constrain analytic planet distribution models. We report an increased mean and variance in the marginal posterior distributions for the number of planets per $GK$ star when including planet radius measurement uncertainties. We estimate the number of planets-per-$GK$ star between 0.75 and 2.5 $R_{oplus}$ and 50 to 300 day orbital periods to have a $68%$ credible interval of $0.49$ to $0.77$ and a posterior mean of $0.63$. This posterior has a smaller mean and a larger variance than the occurrence rate calculated in this work and in Burke et al. (2015) for the same parameter space using the $Q1-Q16$ (previous $Kepler$ planet candidate and stellar catalog). We attribute the smaller mean to many of the instrumental false positives at longer orbital periods being removed from the $DR25$ catalog. We find that the accuracy and precision of our hierarchical Bayesian model posterior distributions are less sensitive to the total number of planets in the sample, and more so on the characteristics of the catalog completeness and reliability and the span of the planet parameter space.
There is mounting evidence for the binary nature of the progenitors of gamma-ray bursts (GRBs). For a long GRB, the induced gravitational collapse (IGC) paradigm proposes as progenitor, or in-state, a tight binary system composed of a carbon-oxygen core (CO$_{core}$) undergoing a supernova (SN) explosion which triggers hypercritical accretion onto a neutron star (NS) companion. For a short GRB, a NS-NS merger is traditionally adopted as the progenitor. We divide long and short GRBs into two sub-classes, depending on whether or not a black hole (BH) is formed in the merger or in the hypercritical accretion process exceeding the NS critical mass. For long bursts, when no BH is formed we have the sub-class of X-ray flashes (XRFs), with isotropic energy $E_{iso}lesssim10^{52}$ erg and rest-frame spectral peak energy $E_{p,i}lesssim200$ keV. When a BH is formed we have the sub-class of binary-driven hypernovae (BdHNe), with $E_{iso}gtrsim10^{52}$ erg and $E_{p,i}gtrsim200$ keV. In analogy, short bursts are similarly divided into two sub-classes. When no BH is formed, short gamma-ray flashes (S-GRFs) occur, with $E_{iso}lesssim10^{52}$ erg and $E_{p,i}lesssim2$ MeV. When a BH is formed, the authentic short GRBs (S-GRBs) occur, with $E_{iso}gtrsim10^{52}$ erg and $E_{p,i}gtrsim2$ MeV. We give examples and observational signatures of these four sub-classes and their rate of occurrence. From their respective rates it is possible that in-states of S-GRFs and S-GRBs originate from the out-states of XRFs. We indicate two additional progenitor systems: white dwarf-NS and BH-NS. These systems have hybrid features between long and short bursts. In the case of S-GRBs and BdHNe evidence is given of the coincidence of the onset of the high energy GeV emission with the birth of a Kerr BH.
Close binaries suppress the formation of circumstellar (S-type) planets and therefore significantly bias the inferred planet occurrence rates and statistical trends. After compiling various radial velocity and high-resolution imaging surveys, we determine that binaries with a < 1 au fully suppress S-type planets, binaries with a = 10 au host close planets at 15% the occurrence rate of single stars, and wide binaries with a > 200 au have a negligible effect on close planet formation. We show that F = 43% +/- 7% of solar-type primaries do not host close planets due to suppression by close stellar companions. By removing spectroscopic binaries from their samples, radial velocity surveys for giant planets boost their detection rates by a factor of 1/(1-F) = 1.8 +/- 0.2 compared to transiting surveys. This selection bias fully accounts for the discrepancy in hot Jupiter occurrence rates inferred from these two detection methods. Correcting for both planet suppression by close binaries and transit dilution by wide binaries, the occurrence rate of small planets orbiting single G-dwarfs is 2.1 +/- 0.3 times larger than the rate inferred from all G-dwarfs in the Kepler survey. Additionally, about half (but not all) of the observed increase in small, short-period planets toward low-mass hosts can be explained by the corresponding decrease in the binary fraction. Finally, we demonstrate that the apparent enhancement of wide stellar companions to hot Jupiter hosts is due to multiple selection effects. Very close binaries, brown dwarf companions, and massive planets with M_2 > 7 M_J within a < 0.2 au preferentially have metal-poor hosts and wide tertiary companions, but genuine hot Jupiters with M_p = 0.2-4 M_J that formed via core accretion instead favor metal-rich hosts and do not exhibit a statistically significant excess of wide stellar companions.
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