[en] We describe statistical methods for measuring the exoplanet multiplicity function (the fraction of host stars containing a given number of planets) and inclination distribution from transit and radial-velocity (RV) surveys. The analysis is based on the approximation of separability—that the distribution of planetary parameters in an n-planet system is the product of identical 1-planet distributions. We review the evidence that separability is a valid approximation for exoplanets and conclude that it captures many, but not all, of the known characteristics of multi-planet systems. We show how to relate the observable multiplicity function in surveys with similar host-star populations but different sensitivities. We also show how to correct for geometrical selection effects to derive the multiplicity function from transit surveys if the distribution of relative inclinations is known. Applying these tools to the Kepler transit survey and to RV surveys, we find that (1) the Kepler data alone do not constrain the mean inclination of multi-planet systems; even spherical distributions are allowed by the data but only if a small fraction of host stars contain large planet populations (∼> 30); (2) comparing the Kepler and RV surveys shows that the mean inclination of multi-planet systems is less than 5°; and (3) the multiplicity function of the Kepler planets is not well determined by the present data.

[en] Upcoming direct-imaging experiments may detect a new class of long-period, highly luminous, tidally powered extrasolar gas giants. Even though they are hosted by ∼ Gyr-'old' main-sequence stars, they can be as 'hot' as young Jupiters at ∼100 Myr, the prime targets of direct-imaging surveys. They are on years-long orbits and presently migrating to 'feed' the 'hot Jupiters'. They are expected from 'high-e' migration mechanisms, in which Jupiters are excited to highly eccentric orbits and then shrink semimajor axis by a factor of ∼10-100 due to tidal dissipation at close periastron passages. The dissipated orbital energy is converted to heat, and if it is deposited deep enough into the atmosphere, the planet likely radiates steadily at luminosity L ∼ 100-1000 L_Jup(2 × 10^–7-2 × 10^–6 L_☉) during a typical ∼ Gyr migration timescale. Their large orbital separations and expected high planet-to-star flux ratios in IR make them potentially accessible to high-contrast imaging instruments on 10 m class telescopes. ∼10 such planets are expected to exist around FGK dwarfs within ∼50 pc. Long-period radial velocity planets are viable candidates, and the highly eccentric planet HD 20782b at maximum angular separation ∼0.''08 is a promising candidate. Directly imaging these tidally powered Jupiters would enable a direct test of high-e migration mechanisms. Once detected, the luminosity would provide a direct measurement of the migration rate, and together with mass (and possibly radius) estimate, they would serve as a laboratory to study planetary spectral formation and tidal physics.

[en] With 16-month of Kepler data, 15 long-period (40-265 days) eclipsing binaries on highly eccentric orbits (minimum e between 0.5 and 0.85) are identified from their closely separated primary and secondary eclipses (Δt_I,II = 3-10 days). These systems confirm the existence of a previously hinted binary population situated near a constant angular momentum track at P(1 – e ²)^3/2 ∼ 15 days, close to the tidal circularization period P_circ. They may be presently migrating due to tidal dissipation and form a steady-state 'flow' (∼1% of stars) feeding the close-binary population (few % of stars). If so, future Kepler data releases will reveal a growing number (dozens) of systems at longer periods, following dN/dlgP ∝ P ^1/3 with increasing eccentricities reaching e → 0.98 for P → 1000 days. Radial-velocity follow-up of long-period eclipsing binaries with no secondary eclipses could offer a significantly larger sample. Orders of magnitude more (hundreds) may reveal their presence from periodic 'eccentricity pulses', such as tidal ellipsoidal variations near pericenter passages. Several new few-day-long eccentricity-pulse candidates with long periods (P = 25-80 days) are reported.

[en] An important class of formation theories for hot Jupiters involves the excitation of extreme orbital eccentricity (e = 0.99 or even larger) followed by tidal dissipation at periastron passage that eventually circularizes the planetary orbit at a period less than 10 days. In a steady state, this mechanism requires the existence of a significant population of super-eccentric (e > 0.9) migrating Jupiters with long orbital periods and periastron distances of only a few stellar radii. For these super-eccentric planets, the periastron is fixed due to conservation of orbital angular momentum and the energy dissipated per orbit is constant, implying that the rate of change in semi-major axis a is a-dot ∝a^1/2 and consequently the number distribution satisfies dN/d log a∝a^1/2. If this formation process produces most hot Jupiters, Kepler should detect several super-eccentric migrating progenitors of hot Jupiters, allowing for a test of high-eccentricity migration scenarios.

[en] We infer the period (P) and size (R_p ) distribution of Kepler transiting planet candidates with R_p ≥ 1 R _⊕ and P < 250 days hosted by solar-type stars. The planet detection efficiency is computed by using measured noise and the observed time spans of the light curves for ∼120,000 Kepler target stars. We focus on deriving the shape of planet periods and radius distribution functions. We find that for orbital periods P > 10 days, the planet frequency dN_p /dlog P for 'Neptune-size' planets (R_p = 4-8 R _⊕) increases with period as ∝P ^0.7±0.1. In contrast, dN_p /dlog P for 'super-Earth-size' (2-4 R _⊕) as well as 'Earth-size' (1-2 R _⊕) planets are consistent with a nearly flat distribution as a function of period (∝P ^0.11±0.05 and ∝P ^{–0.10±0.12}, respectively), and the normalizations are remarkably similar (within a factor of ∼1.5 at 50 days). Planet size distribution evolves with period, and generally the relative fractions for big planets (∼3-10 R _⊕) increase with period. The shape of the distribution function is not sensitive to changes in the selection criteria of the sample. The implied nearly flat or rising planet frequency at long periods appears to be in disagreement with the sharp decline at ∼100 days in planet frequency for low-mass planets (planet mass m_p < 30 M _⊕) recently suggested by the HARPS survey. Within 250 days, the cumulative frequencies for Earth-size and super-Earth-size planets are remarkably similar (∼28% and 25%), while Neptune-size and Jupiter-size planets are ∼7% and ∼3%, respectively. A major potential uncertainty arises from the unphysical impact parameter distribution of the candidates.

[en] We present the first measurement of the planet frequency beyond the 'snow line', for the planet-to-star mass-ratio interval -4.5 < log q < -2, corresponding to the range of ice giants to gas giants. We find (d²N_pl)/(d log q d log s) = (0.36±0.15) dex^-2 at the mean mass ratio q = 5 x 10^-4 with no discernible deviation from a flat (Oepik's law) distribution in log-projected separation s. The determination is based on a sample of six planets detected from intensive follow-up observations of high-magnification (A>200) microlensing events during 2005-2008. The sampled host stars have a typical mass M_host ∼ 0.5 M _sun, and detection is sensitive to planets over a range of planet-star-projected separations (s ^-1_max R _E, s_max R _E), where R _E ∼ 3.5 AU(M_host/M_sun)^1/2 is the Einstein radius and s _max ∼ (q/10^-4.3)^1/3. This corresponds to deprojected separations roughly three times the 'snow line'. We show that the observations of these events have the properties of a 'controlled experiment', which is what permits measurement of absolute planet frequency. High-magnification events are rare, but the survey-plus-follow-up high-magnification channel is very efficient: half of all high-mag events were successfully monitored and half of these yielded planet detections. The extremely high sensitivity of high-mag events leads to a policy of monitoring them as intensively as possible, independent of whether they show evidence of planets. This is what allows us to construct an unbiased sample. The planet frequency derived from microlensing is a factor 8 larger than the one derived from Doppler studies at factor ∼25 smaller star-planet separations (i.e., periods 2-2000 days). However, this difference is basically consistent with the gradient derived from Doppler studies (when extrapolated well beyond the separations from which it is measured). This suggests a universal separation distribution across 2 dex in planet-star separation, 2 dex in mass ratio, and 0.3 dex in host mass. Finally, if all planetary systems were 'analogs' of the solar system, our sample would have yielded 18.2 planets (11.4 'Jupiters', 6.4 'Saturns', 0.3 'Uranuses', 0.2 'Neptunes') including 6.1 systems with two or more planet detections. This compares to six planets including one two-planet system in the actual sample, implying a first estimate of 1/6 for the frequency of solar-like systems.

[en] We analyze the extreme high-magnification microlensing event OGLE-2008-BLG-279, which peaked at a maximum magnification of A ∼ 1600 on 2008 May 30. The peak of this event exhibits both finite-source effects and terrestrial parallax, from which we determine the mass of the lens, M_l = 0.64 ± 0.10 M _sun, and its distance, D_l = 4.0 ± 0.6 kpc. We rule out Jupiter-mass planetary companions to the lens star for projected separations in the range 0.5-20 AU. More generally, we find that this event was sensitive to planets with masses as small as 0.2 M₊≅2 M_Mars with projected separations near the Einstein ring (∼3 AU).

[en] We combine all available information to constrain the nature of OGLE-2005-BLG-071Lb, the second planet discovered by microlensing and the first in a high-magnification event. These include photometric and astrometric measurements from the Hubble Space Telescope, as well as constraints from higher order effects extracted from the ground-based light curve, such as microlens parallax, planetary orbital motion, and finite-source effects. Our primary analysis leads to the conclusion that the host of Jovian planet OGLE-2005-BLG-071Lb is an M dwarf in the foreground disk with mass M = 0.46 ± 0.04 M_sun, distance D_l = 3.2 ± 0.4 kpc, and thick-disk kinematics v_LSR ∼ 103 km s^-1. From the best-fit model, the planet has mass M_p = 3.8 ± 0.4 M_Jupiter, lies at a projected separation r_perpendicular = 3.6 ± 0.2AU from its host, and so has an equilibrium temperature of T ∼ 55 K, that is, similar to Neptune. A degenerate model gives similar planetary mass M_p = 3.4 ± 0.4 M_Jupiter with a smaller projected separation, r_perpendicular = 2.1 ± 0.1AU, and higher equilibrium temperature, T ∼ 71 K. These results from the primary analysis suggest that OGLE-2005-BLG-071Lb is likely to be the most massive planet yet discovered that is hosted by an M dwarf. However, the formation of such high-mass planetary companions in the outer regions of M dwarf planetary systems is predicted to be unlikely within the core-accretion scenario. There are a number of caveats to this primary analysis, which assumes (based on real but limited evidence) that the unlensed light coincident with the source is actually due to the lens, that is, the planetary host. However, these caveats could mostly be resolved by a single astrometric measurement a few years after the event.

[en] We report the detection of sub-Saturn-mass planet MOA-2008-BLG-310Lb and argue that it is the strongest candidate yet for a bulge planet. Deviations from the single-lens fit are smoothed out by finite-source effects and therefore are not immediately apparent from the light curve. Nevertheless, we find that a model in which the primary has a planetary companion is favored over the single-lens model by Δχ² ∼ 880 for an additional 3 degrees of freedom. Detailed analysis yields a planet/star mass ratio q = (3.3 ± 0.3) x 10^-4 and an angular separation between the planet and star within 10% of the angular Einstein radius. The small angular Einstein radius, θ_E = 0.155 ± 0.011 mas, constrains the distance to the lens to be D_L >6.0 kpc if it is a star (M_L >0.08 M_sun). This is the only microlensing exoplanet host discovered so far that must be in the bulge if it is a star. By analyzing VLT NACO adaptive optics images taken near the baseline of the event, we detect additional blended light that is aligned to within 130 mas of the lensed source. This light is plausibly from the lens, but could also be due to a companion to the lens or source, or possibly an unassociated star. If the blended light is indeed due to the lens, we can estimate the mass of the lens, M_L = 0.67 ± 0.14 M_sun, planet mass m = 74 ± 17 M₊, and projected separation between the planet and host, 1.25 ± 0.10 AU, putting it right on the 'snow line'. If not, then the planet has lower mass, is closer to its host and is colder. To distinguish among these possibilities on reasonable timescales would require obtaining Hubble Space Telescope images almost immediately, before the source-lens relative motion of μ= 5 mas yr^-1 causes them to separate substantially.

[en] We propose a stringent observational test on the formation of warm Jupiters (gas-giant planets with 10 days ≲ P ≲ 100 days) by high-eccentricity (high-e) migration mechanisms. Unlike hot Jupiters, the majority of observed warm Jupiters have pericenter distances too large to allow efficient tidal dissipation to induce migration. To access the close pericenter required for migration during a Kozai-Lidov cycle, they must be accompanied by a strong enough perturber to overcome the precession caused by general relativity, placing a strong upper limit on the perturber's separation. For a warm Jupiter at a ∼ 0.2 AU, a Jupiter-mass (solar-mass) perturber is required to be ≲ 3 AU (≲ 30 AU) and can be identified observationally. Among warm Jupiters detected by radial velocities (RVs), ≳ 50% (5 out of 9) with large eccentricities (e ≳ 0.4) have known Jovian companions satisfying this necessary condition for high-e migration. In contrast, ≲ 20% (3 out of 17) of the low-e (e ≲ 0.2) warm Jupiters have detected additional Jovian companions, suggesting that high-e migration with planetary perturbers may not be the dominant formation channel. Complete, long-term RV follow-ups of the warm-Jupiter population will allow a firm upper limit to be put on the fraction of these planets formed by high-e migration. Transiting warm Jupiters showing spin-orbit misalignments will be interesting to apply our test. If the misalignments are solely due to high-e migration as commonly suggested, we expect that the majority of warm Jupiters with low-e (e ≲ 0.2) are not misaligned, in contrast with low-e hot Jupiters