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Andrew Gould
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The frequency of microlensing planet detections, particularly in difficult-to-model high-magnification events, is increasing. Their analysis can require tens of thousands of processor hours or more, primarily because of the high density and high precision of measurements whose modeling requires time-consuming finite-source calculations. I show that a large fraction of these measurements, those that lie at least one source diameter from a caustic or the extension from a cusp, can be modeled using a very simple hexadecapole approximation, which is one to several orders of magnitude faster than full-fledged finite-source calculations. Moreover, by restricting the regions that actually require finite-source calculations to a few isolated `caustic features, the hexadecapole approximation will, for the first time, permit the powerful `magnification-map approach to be applied to events for which the planets orbital motion is important.
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The exoplanet detection rate from gravitational microlensing has grown significantly in recent years thanks to a great enhancement of resources and improved observational strategy. Current observatories include ground-based wide-field and/or robotic world-wide networks of telescopes, as well as space-based observatories such as satellites Spitzer or Kepler/K2. This results in a large quantity of data to be processed and analyzed, which is a challenge for modeling codes because of the complexity of the parameter space to be explored, and the intensive computations required to evaluate the models. In this work, I present a method that allows to compute the quadrupole and hexadecapole approximation of the finite-source magnification with more efficiency that previously available codes, with routines about x6 and x4 faster respectively. The quadrupole takes just about twice the time of a point-source evaluation, which advocates for generalizing its use to large portion of the light curves. The corresponding routines are available as open-source python codes.
Four planets have recently been discovered by gravitational microlensing. The most recent of these discoveries is the lowest-mass planet known to exist around a normal star. The detection of planets in gravitational microlensing events was predicted over a decade ago. Microlensing is now a mature field of astrophysical research and the recent planet detections herald a new chapter in the hunt for low mass extra-solar planets. This paper reviews the basic theory of planetary microlensing, describes the experiments currently in operation for the detection and observation of microlensing events and compares the characteristics of the planetary systems found to date by microlensing. Some proposed schemes for improving the detection rate of planets via microlensing are also discussed.
MOA-2006-BLG-074 was selected as one of the most promising planetary candidates in a retrospective analysis of the MOA collaboration: its asymmetric high-magnification peak can be perfectly explained by a source passing across a central caustic deformed by a small planet. However, after a detailed analysis of the residuals, we have realized that a single lens and a source orbiting with a faint companion provides a more satisfactory explanation for all the observed deviations from a Paczynski curve and the only physically acceptable interpretation. Indeed the orbital motion of the source is constrained enough to allow a very good characterization of the binary source from the microlensing light curve. The case of MOA-2006-BLG-074 suggests that the so-called xallarap effect must be taken seriously in any attempts to obtain accurate planetary demographics from microlensing surveys.
We conduct the first microlensing simulation in the context of planet formation model. The planet population is taken from the Ida & Lin core accretion model for $0.3M_odot$ stars. With $6690$ microlensing events, we find for a simplified Korea Microlensing Telescopes Network (KMTNet) the fraction of planetary events is $2.9%$ , out of which $5.5%$ show multiple-planet signatures. The number of super-Earths, super-Neptunes and super-Jupiters detected are expected to be almost equal. Our simulation shows that high-magnification events and massive planets are favored by planet detections, which is consistent with previous expectation. However, we notice that extremely high-magnification events are less sensitive to planets, which is possibly because the 10 min sampling of KMTNet is not intensive enough to capture the subtle anomalies that occur near the peak. This suggests that while KMTNet observations can be systematically analyzed without reference to any follow-up data, follow-up observations will be essential in extracting the full science potential of very high-magnification events. The uniformly high-cadence observations expected for KMTNet also result in $sim 55%$ of all detected planets being non-caustic-crossing, and more low-mass planets even down to Mars-mass being detected via planetary caustics. We also find that the distributions of orbital inclinations and planet mass ratios in multiple-planet events agree with the intrinsic distributions.
The validity of the widely used linear mixing approximation for the equations of state (EOS) of planetary ices is investigated at pressure-temperature conditions typical for the interior of Uranus and Neptune. The basis of this study are ab initio data ranging up to 1000 GPa and 20 000 K calculated via density functional theory molecular dynamics simulations. In particular, we calculate a new EOS for methane and EOS data for the 1:1 binary mixtures of methane, ammonia, and water, as well as their 2:1:4 ternary mixture. Additionally, the self-diffusion coefficients in the ternary mixture are calculated along three different Uranus interior profiles and compared to the values of the pure compounds. We find that deviations of the linear mixing approximation from the results of the real mixture are generally small; for the thermal EOS they amount to 4% or less. The diffusion coefficients in the mixture agree with those of the pure compounds within 20% or better. Finally, a new adiabatic model of Uranus with an inner layer of almost pure ices is developed. The model is consistent with the gravity field data and results in a rather cold interior ($mathrm{T_{core}} mathtt{sim}$ 4000 K).
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