No Arabic abstract
Methods used to detect giant exoplanets can be broadly divided into two categories: indirect and direct. Indirect methods are more sensitive to planets with a small orbital period, whereas direct detection is more sensitive to planets orbiting at a large distance from their host star. %, and thus on long orbital period. This dichotomy makes it difficult to combine the two techniques on a single target at once. Simultaneous measurements made by direct and indirect techniques offer the possibility of determining the mass and luminosity of planets and a method of testing formation models. Here, we aim to show how long-baseline interferometric observations guided by radial-velocity can be used in such a way. We observed the recently-discovered giant planet $beta$ Pictoris c with GRAVITY, mounted on the Very Large Telescope Interferometer (VLTI). This study constitutes the first direct confirmation of a planet discovered through radial velocity. We find that the planet has a temperature of $T = 1250pm50$,K and a dynamical mass of $M = 8.2pm0.8,M_{rm Jup}$. At $18.5pm2.5$,Myr, this puts $beta$ Pic c close to a hot start track, which is usually associated with formation via disk instability. Conversely, the planet orbits at a distance of 2.7,au, which is too close for disk instability to occur. The low apparent magnitude ($M_{rm K} = 14.3 pm 0.1$) favours a core accretion scenario. We suggest that this apparent contradiction is a sign of hot core accretion, for example, due to the mass of the planetary core or the existence of a high-temperature accretion shock during formation.
Planet yield calculations may be used to inform the target selection strategy and science operations of space observatories. Forthcoming and proposed NASA missions, such as the Wide-Field Infrared Survey Telescope (WFIRST), the Habitable Exoplanet Imaging Mission (HabEx), and the Large UV/Optical/IR Surveyor (LUVOIR), are expected to be equipped with sensitive coronagraphs and/or starshades. We are developing a suite of numerical simulations to quantify the extent to which ground-based radial velocity (RV) surveys could boost the detection efficiency of direct imaging missions. In this paper, we discuss the first step in the process of estimating planet yields: generating synthetic planetary systems consistent with observed occurrence rates from multiple detection methods. In an attempt to self-consistently populate stars with orbiting planets, it is found that naive extrapolation of occurrence rates (mass, semi-major axis) results in an unrealistically large number-density of Neptune-mass planets beyond the ice-line ($a gtrsim 5$au), causing dynamic interactions that would destabilize orbits. We impose a stability criterion for multi-planet systems based on mutual Hill radii separation. Considering the influence of compact configurations containing Jovian-mass and Neptune-mass planets results in a marked suppression in the number of terrestrial planets that can exist at large radii. This result has a pronounced impact on planet yield calculations particularly in regions accessible to high-contrast imaging and microlensing. The dynamically compact configurations and occurrence rates that we develop may be incorporated as input into joint RV and direct imaging yield calculations to place meaningful limits on the number of detectable planets with future missions.
We present results from a data challenge posed to the radial velocity (RV) community: namely, to quantify the Bayesian evidence for n={0,1,2,3} planets in a set of synthetically generated RV datasets containing a range of planet signals. Participating teams were provided the same likelihood function and set of priors to use in their analysis. They applied a variety of methods to estimate Z, the marginal likelihood for each n-planet model, including cross-validation, the Laplace approximation, importance sampling, and nested sampling. We found the dispersion in Z across different methods grew with increasing n-planet models: ~3 for 0-planets, ~10 for 1-planet, ~100-1000 for 2-planets, and >10,000 for 3-planets. Most internal estimates of uncertainty in Z for individual methods significantly underestimated the observed dispersion across all methods. Methods that adopted a Monte Carlo approach by comparing estimates from multiple runs yielded plausible uncertainties. Finally, two classes of numerical algorithms (those based on importance and nested samplers) arrived at similar conclusions regarding the ratio of Zs for n and (n+1)-planet models. One analytic method (the Laplace approximation) demonstrated comparable performance. We express both optimism and caution: we demonstrate that it is practical to perform rigorous Bayesian model comparison for <=3-planet models, yet robust planet discoveries require researchers to better understand the uncertainty in Z and its connections to model selection.
We present a comprehensive orbital analysis to the exoplanets $beta$ Pictoris b and c that resolves previously reported tensions between the dynamical and evolutionary mass constraints on $beta$ Pic b. We use the MCMC orbit code orvara to fit fifteen years of radial velocities and relative astrometry (including recent GRAVITY measurements), absolute astrometry from Hipparcos and Gaia, and a single relative radial velocity measurement between $beta$ Pic A and b. We measure model-independent masses of $9.3^{+2.6}_{-2.5}, M_{rm Jup}$ for $beta$ Pic b and $8.3pm 1.0,M_{rm Jup}$ for $beta$ Pic c. These masses are robust to modest changes to the input data selection. We find a well-constrained eccentricity of $0.119 pm 0.008$ for $beta$ Pic b, and an eccentricity of $0.21^{+0.16}_{-0.09}$ for $beta$ Pic c, with the two orbital planes aligned to within $sim$0.5$^circ$. Both planets masses are within $sim$1$sigma$ of the predictions of hot-start evolutionary models and exclude cold starts. We validate our approach on $N$-body synthetic data integrated using REBOUND. We show that orvara can account for three-body effects in the $beta$ Pic system down to a level $sim$5 times smaller than the GRAVITY uncertainties. Systematics in the masses and orbital parameters from orvaras approximate treatment of multiplanet orbits are a factor of $sim$5 smaller than the uncertainties we derive here. Future GRAVITY observations will improve the constraints on $beta$ Pic cs mass and (especially) eccentricity, but improved constraints on the mass of $beta$ Pic b will likely require years of additional RV monitoring and improved precision from future Gaia data releases.
High-contrast medium resolution spectroscopy has been used to detect molecules such as water and carbon monoxide in the atmospheres of gas giant exoplanets. In this work, we show how it can be used to derive radial velocity (RV) measurements of directly imaged exoplanets. Improving upon the traditional cross-correlation technique, we develop a new likelihood based on joint forward modelling of the planetary signal and the starlight background (i.e., speckles). After marginalizing over the starlight model, we infer the barycentric RV of HR 8799 b and c in 2010 yielding -9.2 +- 0.5 km/s and -11.6 +- 0.5 km/s respectively. These RV measurements help to constrain the 3D orientation of the orbit of the planet by resolving the degeneracy in the longitude of ascending node. Assuming coplanar orbits for HR 8799 b and c, but not including d and e, we estimate Omega = 89 (+27,-17) deg and i = 20.8 (4.5,-3.7) deg.
Young giant exoplanets are a unique laboratory for understanding cool, low-gravity atmospheres. A quintessential example is the massive extrasolar planet $beta$ Pic b, which is 9 AU from and embedded in the debris disk of the young nearby A6V star $beta$ Pictoris. We observed the system with first light of the Magellan Adaptive Optics (MagAO) system. In Paper I we presented the first CCD detection of this planet with MagAO+VisAO. Here we present four MagAO+Clio images of $beta$ Pic b at 3.1 $mu$m, 3.3 $mu$m, $L^prime$, and $M^prime$, including the first observation in the fundamental CH$_4$ band. To remove systematic errors from the spectral energy distribution (SED), we re-calibrate the literature photometry and combine it with our own data, for a total of 22 independent measurements at 16 passbands from 0.99--4.8 $mu$m. Atmosphere models demonstrate the planet is cloudy but are degenerate in effective temperature and radius. The measured SED now covers $>$80% of the planets energy, so we approach the bolometric luminosity empirically. We calculate the luminosity by extending the measured SED with a blackbody and integrating to find log($L_{bol}$/$L_{Sun}$) $= -3.78pm0.03$. From our bolometric luminosity and an age of 23$pm$3 Myr, hot-start evolutionary tracks give a mass of 12.7$pm$0.3 $M_{Jup}$, radius of 1.45$pm$0.02 $R_{Jup}$, and $T_{eff}$ of 1708$pm$23 K (model-dependent errors not included). Our empirically-determined luminosity is in agreement with values from atmospheric models (typically $-3.8$ dex), but brighter than values from the field-dwarf bolometric correction (typically $-3.9$ dex), illustrating the limitations in comparing young exoplanets to old brown dwarfs.