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

MOA 2003-BLG-37: A Bulge Jerk-Parallax Microlens Degeneracy

We analyze the Galactic bulge microlensing event MOA-2003-BLG-37. Although the Einstein timescale is relatively short, t_e=43 days, the lightcurve displays deviations consistent with parallax effects due to the Earth's accelerated motion. We show that the chi^2 surface has four distinct local minima that are induced by the ``jerk-parallax'' degeneracy, with pairs of solutions having projected Einstein radii, \tilde r_e = 1.76 AU and 1.28 AU, respectively. This is the second event displaying such a degeneracy and the first toward the Galactic bulge. For both events, the jerk-parallax formalism accurately describes the offsets between the different solutions, giving hope that when extra solutions exist in future events, they can easily be found. However, the morphologies of the chi^2 surfaces for the two events are quite different, implying that much remains to be understood about this degeneracy.Comment: 19 pages, 3 figures, 1 table, ApJ, in press, 1 July 200

On Planetary Companions to the MACHO-98-BLG-35 Microlens Star

We present observations of microlensing event MACHO-98-BLG-35 which reached a peak magnification factor of almost 80. These observations by the Microlensing Planet Search (MPS) and the MOA Collaborations place strong constraints on the possible planetary system of the lens star and show intriguing evidence for a low mass planet with a mass fraction $4\times 10^{-5} \leq \epsilon \leq 2\times 10^{-4}$. A giant planet with $\epsilon = 10^{-3}$ is excluded from 95% of the region between 0.4 and 2.5 $R_E$ from the lens star, where $R_E$ is the Einstein ring radius of the lens. This exclusion region is more extensive than the generic "lensing zone" which is $0.6 - 1.6 R_E$. For smaller mass planets, we can exclude 57% of the "lensing zone" for $\epsilon = 10^{-4}$ and 14% of the lensing zone for $\epsilon = 10^{-5}$. The mass fraction $\epsilon = 10^{-5}$ corresponds to an Earth mass planet for a lensing star of mass \sim 0.3 \msun. A number of similar events will provide statistically significant constraints on the prevalence of Earth mass planets. In order to put our limits in more familiar terms, we have compared our results to those expected for a Solar System clone averaging over possible lens system distances and orientations. We find that such a system is ruled out at the 90% confidence level. A copy of the Solar System with Jupiter replaced by a second Saturn mass planet can be ruled out at 70% confidence. Our low mass planetary signal (few Earth masses to Neptune mass) is significant at the $4.5\sigma$ confidence level. If this planetary interpretation is correct, the MACHO-98-BLG-35 lens system constitutes the first detection of a low mass planet orbiting an ordinary star without gas giant planets.Comment: ApJ, April 1, 2000; 27 pages including 8 color postscript figure

OGLE-2005-BLG-071Lb, the Most Massive M-Dwarf Planetary Companion?

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 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 Msun, distance D_l = 3.3 +/- 0.4 kpc, and thick-disk kinematics v_LSR ~ 103 km/s. From the best-fit model, the planet has mass M_p = 3.8 +/- 0.4 M_Jup, lies at a projected separation r_perp = 3.6 +/- 0.2 AU from its host and so has an equilibrium temperature of T ~ 55 K, i.e., similar to Neptune. A degenerate model less favored by \Delta\chi^2 = 2.1 (or 2.2, depending on the sign of the impact parameter) gives similar planetary mass M_p = 3.4 +/- 0.4 M_Jup with a smaller projected separation, r_\perp = 2.1 +/- 0.1 AU, 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.Comment: 51 pages, 12 figures, 3 tables, Published in Ap

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

The Extreme Microlensing Event OGLE-2007-BLG-224: Terrestrial Parallax Observation of a Thick-Disk Brown Dwarf

Parallax is the most fundamental technique to measure distances to astronomical objects. Although terrestrial parallax was pioneered over 2000 years ago by Hipparchus (ca. 140 BCE) to measure the distance to the Moon, the baseline of the Earth is so small that terrestrial parallax can generally only be applied to objects in the Solar System. However, there exists a class of extreme gravitational microlensing events in which the effects of terrestrial parallax can be readily detected and so permit the measurement of the distance, mass, and transverse velocity of the lens. Here we report observations of the first such extreme microlensing event OGLE-2007-BLG-224, from which we infer that the lens is a brown dwarf of mass M=0.056 +- 0.004 Msun, with a distance of 525 +- 40 pc and a transverse velocity of 113 +- 21 km/s. The velocity places the lens in the thick disk, making this the lowest-mass thick-disk brown dwarf detected so far. Follow-up observations may allow one to observe the light from the brown dwarf itself, thus serving as an important constraint for evolutionary models of these objects and potentially opening a new window on sub-stellar objects. The low a priori probability of detecting a thick-disk brown dwarf in this event, when combined with additional evidence from other observations, suggests that old substellar objects may be more common than previously assumed.Comment: ApJ Letters, in press, 15 pages including 2 figure

Microlensing optical depth towards the Galactic bulge from MOA observations during 2000 with Difference Image Analysis

We analyze the data of the gravitational microlensing survey carried out by by the MOA group during 2000 towards the Galactic Bulge (GB). Our observations are designed to detect efficiently high magnification events with faint source stars and short timescale events, by increasing the the sampling rate up to 6 times per night and using Difference Image Analysis (DIA). We detect 28 microlensing candidates in 12 GB fields corresponding to 16 deg^2. We use Monte Carlo simulations to estimate our microlensing event detection efficiency, where we construct the I-band extinction map of our GB fields in order to find dereddened magnitudes. We find a systematic bias and large uncertainty in the measured value of the timescale $t_{\rm Eout}$ in our simulations. They are associated with blending and unresolved sources, and are allowed for in our measurements. We compute an optical depth tau = 2.59_{-0.64}^{+0.84} \times 10^{-6} towards the GB for events with timescales 0.3<t_E<200 days. We consider disk-disk lensing, and obtain an optical depth tau_{bulge} = 3.36_{-0.81}^{+1.11} \times 10^{-6}[0.77/(1-f_{disk})] for the bulge component assuming a 23% stellar contribution from disk stars. These observed optical depths are consistent with previous measurements by the MACHO and OGLE groups, and still higher than those predicted by existing Galactic models. We present the timescale distribution of the observed events, and find there are no significant short events of a few days, in spite of our high detection efficiency for short timescale events down to t_E = 0.3 days. We find that half of all our detected events have high magnification (>10). These events are useful for studies of extra-solar planets.Comment: 65 pages and 30 figures, accepted for publication in ApJ. A systematic bias and uncertainty in the optical depth measurement has been quantified by simulation

Interpretation of Strong Short-Term Central Perturbations in the Light Curves of Moderate-Magnification Microlensing Events

To improve the planet detection efficiency, current planetary microlensing experiments are focused on high-magnification events searching for planetary signals near the peak of lensing light curves. However, it is known that central perturbations can also be produced by binary companions and thus it is important to distinguish planetary signals from those induced by binary companions. In this paper, we analyze the light curves of microlensing events OGLE-2007-BLG-137/MOA-2007-BLG-091, OGLE-2007-BLG-355/MOA-2007-BLG-278, and MOA-2007-BLG-199/OGLE-2007-BLG-419, for all of which exhibit short-term perturbations near the peaks of the light curves. From detailed modeling of the light curves, we find that the perturbations of the events are caused by binary companions rather than planets. From close examination of the light curves combined with the underlying physical geometry of the lens system obtained from modeling, we find that the short time-scale caustic-crossing feature occurring at a low or a moderate base magnification with an additional secondary perturbation is a typical feature of binary-lens events and thus can be used for the discrimination between the binary and planetary interpretations.Comment: 17 pages, 4 figures, 1 tabl