No Arabic abstract
Many warm Jupiters (WJs) have substantial eccentricities, which are linked to their formation and migration histories. This paper explores eccentricity excitation of WJs due to planet-planet scattering, beginning with 3-4 planets in unstable orbits, with the innermost planet placed in the range (0.1 - 1)AU. Such a setup is consistent with either in-situ formation or arrival at sub-AU orbits due to disk migration. Most previous N-body experiments have focused on cold Jupiters at several AU, where scattering results in planet ejections, efficiently exciting the eccentricities of surviving planets. In contrast, scattering at sub-AU distances results in a mixture of collisions and ejections, and the final eccentricities of surviving planets are unclear. We conduct scattering experiments for a range of planet masses and initial spacings, including the effect of general relativistic apsidal precession, and systematically catalogue the scattering outcomes and properties of surviving planets. A comparable number of one-planet and two-planet systems are produced. Two-planet systems arise exclusively through planet-planet collisions, and tend to have low eccentricities/mutual inclinations and compact configurations. One-planet systems arise through a combination of ejections and collisions, resulting in higher eccentricities. The observed eccentricity distribution of solitary WJs (lacking detection of a giant planet companion) is consistent with roughly 60% of the systems having undergone in-situ scattering, and the remaining experiencing a quiescent history.
Observations have confirmed the existence of multiple-planet systems containing a hot Jupiter and smaller planetary companions. Examples include WASP-47, Kepler-730, and TOI-1130. We examine the plausibility of forming such systems in situ using $N$-body simulations that include a realistic treatment of collisions, an evolving protoplanetary disc and eccentricity/inclination damping of planetary embryos. Initial conditions are constructed using two different models for the core of the giant planet: a seed-model and an equal-mass-model. The former has a more massive protoplanet placed among multiple small embryos in a compact configuration. The latter consists only of equal-mass embryos. Simulations of the seed-model lead to the formation of systems containing a hot Jupiter and super-Earths. The evolution consistently follows four distinct phases: early giant impacts; runaway gas accretion onto the seed protoplanet; disc damping-dominated evolution of the embryos orbiting exterior to the giant; a late chaotic phase after dispersal of the gas disc. Approximately 1% of the equal-mass simulations form a giant and follow the same four-phase evolution. Synthetic transit observations of the equal-mass simulations provide an occurrence rate of 0.26% for systems containing a hot Jupiter and an inner super-Earth, similar to the 0.2% occurrence rate from actual transit surveys, but simulated hot Jupiters are rarely detected as single transiting planets, in disagreement with observations. A subset of our simulations form two close-in giants, similar to the WASP-148 system. The scenario explored here provides a viable pathway for forming systems with unusual architectures, but does not apply to the majority of hot Jupiters.
Recent observations by the {it Juno} spacecraft have revealed that the tidal Love number $k_2$ of Jupiter is $4%$ lower than the hydrostatic value. We present a simple calculation of the dynamical Love number of Jupiter that explains the observed anomaly. The Love number is usually dominated by the response of the (rotation-modified) f-modes of the planet. Our method also allows for efficient computation of high-order dynamical Love numbers. While the inertial-mode contributions to the Love numbers are negligible, a sufficiently strong stratification in a large region of the planets interior would induce significant g-mode responses and influence the measured Love numbers.
We report the first results from a search for transiting warm Jupiter exoplanets - gas giant planets receiving stellar irradiation below about $10^8$ erg s$^{-1}$ cm$^{-2}$, equivalent to orbital periods beyond about 10 days around Sun-like stars. We have discovered two transiting warm Jupiter exoplanets initially identified as transiting candidates in ${it K2}$ photometry. K2-114b has a mass of $1.85^{+0.23}_{-0.22} M_J$, a radius of $0.942^{+0.032}_{-0.020} R_J$, and an orbital period of 11.4 days. K2-115b has a mass of $0.84^{+0.18}_{-0.20} M_J$, a radius of $1.115^{+0.057}_{-0.061} R_J$, and an orbital period of 20.3 days. Both planets are among the longest period transiting gas giant planets with a measured mass, and they are orbiting relatively old host stars. Both planets are not inflated as their radii are consistent with theoretical expectations. Their position in the planet radius - stellar irradiation diagram is consistent with the scenario where the radius - irradiation correlation levels off below about 10$^8$ erg s$^{-1}$ cm$^{-2}$, suggesting that for warm Jupiters the stellar irradiation does not play a significant role in determining the planet radius. We also report our identification of another ${it K2}$ transiting warm Jupiter candidate, EPIC 212504617, as a false positive.
Torques from a mutually inclined perturber can change a transiting planets impact parameter, resulting in variations in the transit shape and duration. Detection of and upper limits on changes in impact parameter yield valuable constraints on a planetary systems three dimensional architecture. Constraints for warm Jupiters are particularly interesting because they allow us to test origins theories that invoke a mutually inclined perturber. Because of warm Jupiters high signal-to-noise transits, changes in impact parameter are feasible to detect. However, here we show that allowing the impact parameter to vary uniformly and independently from transit to transit leads to incorrect inferences about the change, propagating to incorrect inferences about the perturber. We demonstrate that an appropriate prior on the change in impact parameter mitigates this problem. We apply our approach to eight systems from the literature and find evidence for changes in impact parameter for warm Jupiter Kepler-46b. We conclude with our recommendations for light curve fitting, including when to fit impact parameters vs. transit durations.
We use N-body simulations of star cluster evolution to explore the hypothesis that short-lived radioactive isotopes found in meteorites, such as 26-Al, were delivered to the Suns protoplanetary disc from a supernova at the epoch of Solar System formation. We cover a range of star cluster formation parameter space and model both clusters with primordial substructure, and those with smooth profiles. We also adopt different initial virial ratios - from cool, collapsing clusters to warm, expanding associations. In each cluster we place the same stellar population; the clusters each have 2100 stars, and contain one massive 25M_Sun star which is expected to explode as a supernova at about 6.6Myr. We determine the number of Solar (G)-type stars that are within 0.1 - 0.3pc of the 25M_Sun star at the time of the supernova, which is the distance required to enrich the protoplanetary disc with the 26-Al abundances found in meteorites. We then determine how many of these G-dwarfs are unperturbed `singletons; stars which are never in close binaries, nor suffer sub-100au encounters, and which also do not suffer strong dynamical perturbations. The evolution of a suite of twenty initially identical clusters is highly stochastic, with the supernova enriching over 10 G-dwarfs in some clusters, and none at all in others. Typically only ~25 per cent of clusters contain enriched, unperturbed singletons, and usually only 1 - 2 per cluster (from a total of 96 G-dwarfs in each cluster). The initial conditions for star formation do not strongly affect the results, although a higher fraction of supervirial (expanding) clusters would contain enriched G-dwarfs if the supernova occurred earlier than 6.6Myr. If we sum together simulations with identical initial conditions, then ~1 per cent of all G-dwarfs in our simulations are enriched, unperturbed singletons.