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Microlensing is the only technique likely, within the next 5 years, to constrain the frequency of Jupiter-analogs. The PLANET collaboration has monitored nearly 100 microlensing events of which more than 20 have sensitivity to the perturbations that would be caused by a Jovian-mass companion to the primary lens. No clear signatures of such planets have been detected. These null results indicate that Jupiter mass planets with separations of 1.5-3 AU occur in less than 1/3 of systems. A similar limit applies to planets of 3 Jupiter masses between 1-4 AU.
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We analyze five years of PLANET photometry of microlensing events toward the Galactic bulge to search for the short-duration deviations from single lens light curves that are indicative of the presence of planetary companions to the primary microlenses. Using strict event selection criteria, we construct a well defined sample of 43 intensively monitored events. We search for planetary perturbations in these events over a densely sampled region of parameter space spanning two decades in mass ratio and projected separation, but find no viable planetary candidates. By combining the detection efficiencies of the events, we find that, at 95% confidence, less than 25% of our primary lenses have companions with mass ratio q=0.01 and separations in the lensing zone, 0.6-1.6 Einstein ring radii. Using a model of the mass, velocity and spatial distribution of bulge lenses, we infer that the majority of our lenses are likely M dwarfs in the Galactic bulge. We conclude that less than 33% of M-dwarfs in the Galactic bulge have Jupiter-mass companions between 1.5 and 4 AU, and less than 45% have 3 Jupiter-mass companions between 1 and 7 AU, the first significant limits on planetary companions to M-dwarfs. We consider the effects of the finite size of the source stars and changing our detection criterion, but find that these do not alter our conclusions substantially.
The Anglo-Australian Planet Search has now accumulated 12 years of radial-velocity data with long-term instrumental precision better than 3 m/s. In this paper, we expand on earlier simulation work, to probe the frequency of near-circular, long-period gas-giant planets residing at orbital distances of 3-6 AU -- the so-called Jupiter analogs. We present the first comprehensive analysis of the frequency of these objects based on radial-velocity data. We find that 3.3% of stars in our sample host Jupiter analogs; detailed, star-by-star simulations show that no more than 37% of stars host a giant planet between 3-6 AU.
We show that Earth mass planets orbiting stars in the Galactic disk and bulge can be detected by monitoring microlensed stars in the Galactic bulge. The star and its planet act as a binary lens which generates a lightcurve which can differ substantially from the lightcurve due only to the star itself. We show that the planetary signal remains detectable for planetary masses as small as an Earth mass when realistic source star sizes are included in the lightcurve calculation. These planets are detectable if they reside in the ``lensing zone which is centered between 1 and 4 AU from the lensing star and spans about a factor of 2 in distance. If we require a minimum deviation of 4% from the standard point-lens microlensing lightcurve, then we find that more than 2% of all $mearth$ planets and 10% of all $10mearth$ in the lensing zone can be detected. If a third of all lenses have no planets, a third have $1mearth$ planets and the remaining third have $10mearth$ planets then we estimate that an aggressive ground based microlensing planet search program could find one earth mass planet and half a dozen $10mearth$ planets per year.
Type-II migration of giant planets has a speed proportional to the discs viscosity for values of the alpha viscosity parameter larger than 1.e-4 . At lower viscosities previous studies, based on 2D simulations have shown that migration can be very chaotic and often characterized by phases of fast migration. The reason is that in low-viscosity discs vortices appear due to the Rossby-wave instability at the edges of the gap opened by the planet. Migration is then determined by vortex-planet interactions. Our aim is to study migration in low viscosity 3D discs. We performed numerical simulations using 2D (including self-gravity) and 3D codes. After selecting disc masses for which self-gravity is not important, 3D simulations without self-gravity can be safely used. In our nominal simulation only numerical viscosity is present. We then performed simulations with prescribed viscosity to assess the threshold below which the new migration processes appear. We show that for alpha viscosity <= 1.e-5 two migration modes are possible which differ from classical Type-II migration, in the sense that they are not proportional to the discs viscosity. The first occurs when the gap opened by the planet is not very deep. This occurs in 3D simulations and/or when a big vortex forms at the outer edge of the planetary gap, diffusing material into the gap. We call this type of migration vortex-driven migration. This migration is very slow and cannot continue indefinitely, because eventually the vortex dissolves. The second migration mode occurs when the gap is deep so that the planets eccentricity grows to a value ~0.2 due to inefficient eccentricity damping by corotation resonances. This second, faster migration mode appears to be typical of 2D models in discs with slower damping of temperatures perturbations.
In the core-accretion model the nominal runaway gas-accretion phase brings most planets to multiple Jupiter masses. However, known giant planets are predominantly Jupiter-mass bodies. Obtaining longer timescales for gas accretion may require using realistic equations of states, or accounting for the dynamics of the circumplanetary disk (CPD) in low-viscosity regime, or both. Here we explore the second way using global, three-dimensional isothermal hydrodynamical simulations with 8 levels of nested grids around the planet. In our simulations the vertical inflow from the circumstellar disk (CSD) to the CPD determines the shape of the CPD and its accretion rate. Even without prescribed viscosity Jupiters mass-doubling time is $sim 10^4$ years, assuming the planet at 5.2 AU and a Minimum Mass Solar Nebula. However, we show that this high accretion rate is due to resolution-dependent numerical viscosity. Furthermore, we consider the scenario of a layered CSD, viscous only in its surface layer, and an inviscid CPD. We identify two planet-accretion mechanisms that are independent of the viscosity in the CPD: (i) the polar inflow -- defined as a part of the vertical inflow with a centrifugal radius smaller than 2 Jupiter-radii and (ii) the torque exerted by the star on the CPD. In the limit of zero effective viscosity, these two mechanisms would produce an accretion rate 40 times smaller than in the simulation.
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