OGLE-2012-BLG-0455/MOA-2012-BLG-206: Microlensing event with ambiguity in planetary interpretations caused by incomplete coverage of planetary signal

Characterizing a microlensing planet is done from modeling an observed lensing light curve. In this process, it is often confronted that solutions of different lensing parameters result in similar light curves, causing difficulties in uniquely interpreting the lens system, and thus understanding the causes of different types of degeneracy is important. In this work, we show that incomplete coverage of a planetary perturbation can result in degenerate solutions even for events where the planetary signal is detected with a high level of statistical significance. We demonstrate the degeneracy for an actually observed event OGLE-2012-BLG-0455/MOA-2012-BLG-206. The peak of this high-magnification event $(A_{\rm max}\sim400)$ exhibits very strong deviation from a point-lens model with $\Delta\chi^{2}\gtrsim4000$ for data sets with a total number of measurement 6963. From detailed modeling of the light curve, we find that the deviation can be explained by four distinct solutions, i.e., two very different sets of solutions, each with a two-fold degeneracy. While the two-fold (so-called "close/wide") degeneracy is well-understood, the degeneracy between the radically different solutions is not previously known. The model light curves of this degeneracy differ substantially in the parts that were not covered by observation, indicating that the degeneracy is caused by the incomplete coverage of the perturbation. It is expected that the frequency of the degeneracy introduced in this work will be greatly reduced with the improvement of the current lensing survey and follow-up experiments and the advent of new surveys.Comment: 5 pages, 3 figures, ApJ accepte

A Low-Mass Planet with a Possible Sub-Stellar-Mass Host in Microlensing Event MOA-2007-BLG-192

We report the detection of an extrasolar planet of mass ratio q ~ 2 x 10^(-4) in microlensing event MOA-2007-BLG-192. The best fit microlensing model shows both the microlensing parallax and finite source effects, and these can be combined to obtain the lens masses of M = 0.060 (+0.028 -0.021) M_sun for the primary and m = 3.3 (+4.9 -1.6) M_earth for the planet. However, the observational coverage of the planetary deviation is sparse and incomplete, and the radius of the source was estimated without the benefit of a source star color measurement. As a result, the 2-sigma limits on the mass ratio and finite source measurements are weak. Nevertheless, the microlensing parallax signal clearly favors a sub-stellar mass planetary host, and the measurement of finite source effects in the light curve supports this conclusion. Adaptive optics images taken with the Very Large Telescope (VLT) NACO instrument are consistent with a lens star that is either a brown dwarf or a star at the bottom of the main sequence. Follow-up VLT and/or Hubble Space Telescope (HST) observations will either confirm that the primary is a brown dwarf or detect the low-mass lens star and enable a precise determination of its mass. In either case, the lens star, MOA-2007-BLG-192L, is the lowest mass primary known to have a companion with a planetary mass ratio, and the planet, MOA-2007-BLG-192Lb, is probably the lowest mass exoplanet found to date, aside from the lowest mass pulsar planet.Comment: Accepted for publication in the Astrophysical Journal. Scheduled for the Sept. 1, 2008 issu

Microlensing Event MOA-2007-BLG-400: Exhuming the Buried Signature of a Cool, Jovian-Mass Planet

We report the detection of the cool, Jovian-mass planet MOA-2007-BLG-400Lb. The planet was detected in a high-magnification microlensing event (with peak magnification A_max = 628) in which the primary lens transited the source, resulting in a dramatic smoothing of the peak of the event. The angular extent of the region of perturbation due to the planet is significantly smaller than the angular size of the source, and as a result the planetary signature is also smoothed out by the finite source size. Thus the deviation from a single-lens fit is broad and relatively weak (~ few percent). Nevertheless, we demonstrate that the planetary nature of the deviation can be unambiguously ascertained from the gross features of the residuals, and detailed analysis yields a fairly precise planet/star mass ratio of q = 0.0026+/-0.0004, in accord with the large significance (\Delta\chi^2=1070) of the detection. The planet/star projected separation is subject to a strong close/wide degeneracy, leading to two indistinguishable solutions that differ in separation by a factor of ~8.5. Upper limits on flux from the lens constrain its mass to be M < 0.75 M_Sun (assuming it is a main-sequence star). A Bayesian analysis that includes all available observational constraints indicates a primary in the Galactic bulge with a mass of ~0.2-0.5 M_Sun and thus a planet mass of ~ 0.5-1.3 M_Jupiter. The separation and equilibrium temperature are ~0.6-1.1AU (~5.3-9.7AU) and ~103K (~34K) for the close (wide) solution. If the primary is a main-sequence star, follow-up observations would enable the detection of its light and so a measurement of its mass and distance.Comment: 30 pages, 6 figures, Submitted to Ap

Density functional formalism in the canonical ensemble

Density functional theory, when applied to systems with $T\neq 0$, is based on the grand canonical extension of the Hohenberg-Kohn-Sham theorem due to Mermin (HKSM theorem). While a straightforward canonical ensemble generalization fails, work in nanopore systems could certainly benefit from such extension. We show that, if the asymptotic behaviour of the canonical distribution functions is taken into account, the HKSM theorem can be extended to the canonical ensemble. We generate $N$-modified correlation and distribution functions hierarchies and prove that, if they are employed, either a modified external field or the density profiles can be indistinctly used as independent variables. We also write down the $N$% -modified free energy functional and prove that its minimum is reached when the equilibrium values of the new hierarchy are used. This completes the extension of the HKSM theorem.Comment: revtex, to be submitted to Phys. Rev. Let

MOA-2011-BLG-293Lb: A test of pure survey microlensing planet detections

Because of the development of large-format, wide-field cameras, microlensing surveys are now able to monitor millions of stars with sufficient cadence to detect planets. These new discoveries will span the full range of significance levels including planetary signals too small to be distinguished from the noise. At present, we do not understand where the threshold is for detecting planets. MOA-2011-BLG-293Lb is the first planet to be published from the new surveys, and it also has substantial followup observations. This planet is robustly detected in survey+followup data (Delta chi^2 ~ 5400). The planet/host mass ratio is q=5.3+/- 0.2*10^{-3}. The best fit projected separation is s=0.548+/- 0.005 Einstein radii. However, due to the s-->s^{-1} degeneracy, projected separations of s^{-1} are only marginally disfavored at Delta chi^2=3. A Bayesian estimate of the host mass gives M_L = 0.43^{+0.27}_{-0.17} M_Sun, with a sharp upper limit of M_L < 1.2 M_Sun from upper limits on the lens flux. Hence, the planet mass is m_p=2.4^{+1.5}_{-0.9} M_Jup, and the physical projected separation is either r_perp = ~1.0 AU or r_perp = ~3.4 AU. We show that survey data alone predict this solution and are able to characterize the planet, but the Delta chi^2 is much smaller (Delta chi^2~500) than with the followup data. The Delta chi^2 for the survey data alone is smaller than for any other securely detected planet. This event suggests a means to probe the detection threshold, by analyzing a large sample of events like MOA-2011-BLG-293, which have both followup data and high cadence survey data, to provide a guide for the interpretation of pure survey microlensing data.Comment: 29 pages, 6 figures, Replaced 7/3/12 with the version accepted to Ap

OGLE-2009-BLG-023/MOA-2009-BLG-028: Characterization of a Binary Microlensing Event Based on Survey Data

We report the result of the analysis of the light curve of a caustic-crossing binary-lens microlensing event OGLE-2009-BLG-023/MOA-2009-BLG-028. Even though the event was observed solely by survey experiments, we could uniquely determine the mass of the lens and distance to it by simultaneously measuring the Einstein radius and lens parallax. From this, we find that the lens system is composed of M-type dwarfs with masses $(0.50\pm 0.07) \ M_\odot$ and $(0.15\pm 0.02)\ M_\odot$ located in the Galactic disk with a distance of $\sim 1.8$ kpc toward the Galactic bulge direction. The event demonstrates that physical lens parameters of binary-lens events can be routinely determined from future high-cadence lensing surveys and thus microlensing can provide a new way to study Galactic binaries.Comment: 8 pages, 5 figure