Lattice density-functional theory of surface melting: the effect of a square-gradient correction

I use the method of classical density-functional theory in the weighted-density approximation of Tarazona to investigate the phase diagram and the interface structure of a two-dimensional lattice-gas model with three phases -- vapour, liquid, and triangular solid. While a straightforward mean-field treatment of the interparticle attraction is unable to give a stable liquid phase, the correct phase diagram is obtained when including a suitably chosen square-gradient term in the system grand potential. Taken this theory for granted, I further examine the structure of the solid-vapour interface as the triple point is approached from low temperature. Surprisingly, a novel phase (rather than the liquid) is found to grow at the interface, exhibiting an unusually long modulation along the interface normal. The conventional surface-melting behaviour is recovered only by artificially restricting the symmetries being available to the density field.Comment: 16 pages, 6 figure

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

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

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

Determining the Physical Lens Parameters of the Binary Gravitational Microlensing Event MOA-2009-BLG-016

We report the result of the analysis of the light curve of the microlensing event MOA-2009-BLG-016. The light curve is characterized by a short-duration anomaly near the peak and an overall asymmetry. We find that the peak anomaly is due to a binary companion to the primary lens and the asymmetry of the light curve is explained by the parallax effect caused by the acceleration of the observer over the course of the event due to the orbital motion of the Earth around the Sun. In addition, we detect evidence for the effect of the finite size of the source near the peak of the event, which allows us to measure the angular Einstein radius of the lens system. The Einstein radius combined with the microlens parallax allows us to determine the total mass of the lens and the distance to the lens. We identify three distinct classes of degenerate solutions for the binary lens parameters, where two are manifestations of the previously identified degeneracies of close/wide binaries and positive/negative impact parameters, while the third class is caused by the symmetric cycloid shape of the caustic. We find that, for the best-fit solution, the estimated mass of the lower-mass component of the binary is (0.04 +- 0.01) M_sun, implying a brown-dwarf companion. However, there exists a solution that is worse only by \Delta\chi^2 ~ 3 for which the mass of the secondary is above the hydrogen-burning limit. Unfortunately, resolving these two degenerate solutions will be difficult as the relative lens-source proper motions for both are similar and small (~ 1 mas/yr) and thus the lens will remain blended with the source for the next several decades.Comment: 7 pages, 2 tables, and 5 figure