B. S. Gaudi

Detection of rotation in a binary microlens : PLANET photometry of MACHO 97-BLG-41

We analyze PLANET collaboration data for MACHO 97-BLG-41, the only microlensing event observed to date in which the source transits two disjoint caustics. The PLANET data, consisting of 46 V -band and 325 I-band observations from —ve southern observatories, span a period from the initial alert until the end of the event. Our data are incompatible with a static binary lens, but are well —tted by a rotating binary lens of mass ratio q \ 0.34 and angular separation d B 0.5 (in units of the Einstein ring radius), in which the binary separation changes in size by dd \( 0.070 ^ 0.009 and in orientation by during the 35.17 days between the separate caustic transits. We use this measurement, dh \ 5i.61^ 0i.36 combined with other observational constraints, to derive the —rst kinematic estimate of the mass, dis- tance, and period of a binary microlens. The relative probability distributions for these parameters peak at a total lens mass M D 0.3 (M-dwarf binary system), lens distance kpc, and binary period M _ D L D 5.5 P D 1.5 yr. The robustness of our model is demonstrated by its striking agreement with MACHO/ GMAN data that cover several sharp features in the light curve not probed by the PLANET obser- vations, and which did not enter our modeling procedure in any way. Available data sets thus indicate that the light curve of MACHO 97-BLG-41 can be modeled as a source crossing two caustics of a physi- cally realistic rotating binary. Thus, contrary to a recent suggestion, the additional eUects of a postulated planetary companion to the binary lens are not required. Subject headings: binaries: generalgravitational lensingplanetary systems

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 (approximately 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 , in accord with the large significance () 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 ? (assuming that 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 ? and thus a planet mass of ~0.5-1.3 M Jup. The separation and equilibrium temperature are ~5.3-9.7 AU (~0.6-1.1 AU) and ~34 K (~103 K) for the wide (close) 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.

Combined Analysis of the Binary Lens Caustic-crossing Event MACHO 98-SMC-1

We fit the data for the binary lens microlensing event MACHO 98-SMC-1 from five different microlensing collaborations and find two distinct solutions characterized by binary separation d and mass ratio q: (d,q) = (0.54,0.50) and (d,q) = (3.65,0.36), where d is in units of the Einstein radius. However, the relative proper motion of the lens is very similar in the two solutions, 1.30 km s-1 kpc-1 and 1.48 km s-1 kpc-1, thus confirming that the lens is in the Small Magellanic Cloud. The close binary can be either rotating or approximately static but the wide binary must be rotating at close to its maximum allowed rate to be consistent with all the data. We measure limb-darkening coefficients for five bands ranging from I to V. As expected, these progressively decrease with rising wavelength. This is the first measurement of limb darkening for a metal-poor A star.

Deep MMT* Transit Survey of the Open Cluster M37. II. Variable Stars

We have conducted a deep (15 r 23), 20 night survey for transiting planets in the intermediate-age (~550 Myr) open cluster M37 (NGC 2099) using the Megacam wide-field mosaic CCD camera on the 6.5 m MMT. In this paper we present a catalog and light curves for 1445 variable stars; 1430 (99%) of these are new discoveries. We have discovered 20 new eclipsing binaries and 31 new short-period (P < 1 day ) pulsating stars. The bulk of the variables are most likely rapidly rotating young low-mass stars, including a substantial number (500) that are members of the cluster. We identify and analyze five particularly interesting individual variables, including a previously identified variable that we suggest is probably a hybrid γ Doradus/δ Scuti pulsator, two possible quiescent cataclysmic variables, a detached eclipsing binary (DEB) with at least one γ Doradus pulsating component (only the second such variable found in an eclipsing binary), and a low-mass (MP ~ MS ~ 0.6 M☉) DEB that is a possible cluster member. A preliminary determination of the physical parameters for the DEB+γ Doradus system yields MP = 1.58 ± 0.04 M☉, MS = 1.58 ± 0.04 M☉, RP = 1.39 ± 0.07 R☉, and RS = 1.38 ± 0.07 R☉.

Masses and Orbital Constraints for the OGLE-2006-BLG-109Lb,c Jupiter/Saturn Analog Planetary System

We present a new analysis of the Jupiter+Saturn analog system, OGLE-2006-BLG-109Lb,c, which was the first double planet system discovered with the gravitational microlensing method. This is the only multi-planet system discovered by any method with measured masses for the star and both planets. In addition to the signatures of two planets, this event also exhibits a microlensing parallax signature and finite source effects that provide a direct measure of the masses of the star and planets, and the expected brightness of the host star is confirmed by Keck AO imaging, yielding masses of , Mb = 231 ± 19 M ⊕, and Mc = 86 ± 7 M ⊕. The Saturn-analog planet in this system had a planetary light-curve deviation that lasted for 11 days, and as a result, the effects of the orbital motion are visible in the microlensing light curve. We find that four of the six orbital parameters are tightly constrained and that a fifth parameter, the orbital acceleration, is weakly constrained. No orbital information is available for the Jupiter-analog planet, but its presence helps to constrain the orbital motion of the Saturn-analog planet. Assuming co-planar orbits, we find an orbital eccentricity of and an orbital inclination of . The 95% confidence level lower limit on the inclination of i > 49° implies that this planetary system can be detected and studied via radial velocity measurements using a telescope of 30 m aperture.

MOA-2011-BLG-293Lb: A TEST OF PURE SURVEY MICROLENSING PLANET DETECTIONS

Mathematical and Physical Sciences: 1st Place (The Ohio State University Edward F. Hayes Graduate Research Forum)

A Complete Set of Solutions for Caustic Crossing Binary Microlensing Events

We present a method to analyze binary lens microlensing light curves with one well-sampled fold caustic crossing. In general, the surface of s2 shows extremely complicated behavior over the nine- parameter space that characterizes binary lenses. This makes it difficult to systematically search the space and verify that a given local minimum is a global minimum. We show that for events with well- monitored caustics, the caustic crossing region can be isolated from the rest of the light curve and easily —tted to a —ve-parameter function. Four of these caustic crossing parameters can then be used to con- strain the search in the larger nine-parameter space. This allows a systematic search for all solutions and thus identi—cation of all local minima. We illustrate this technique using the PLANET data for MACHO 98-SMC-1, an excellent and publicly available caustic crossing data set. We show that a very broad range of parameter combinations are compatible with the PLANET data set, demonstrating that observations of binary lens light curves with a sampling of only one caustic crossing do not yield unique solutions. The corollary to this is that the time of the second caustic crossing cannot be reliably predict- ed on the basis of early data including the —rst caustic crossing alone. We investigate the requirements for determination of a unique solution and —nd that occasional observations of the —rst caustic crossing may be sufficient to derive a complete solution. Subject headings: astrometrydark mattergravitational lensing

PLANET Observations of Microlensing Event OGLE-1999-BUL-23: Limb-darkening Measurement of the Source Star

We present PLANET observations of OGLE-1999-BUL-23, a binary-lens microlensing event toward the Galactic bulge. PLANET observations in the I and V bands cover the event from just before the first caustic crossing until the end of the event. In particular, a densely sampled second caustic crossing enables us to derive the linear limb-darkening coefficients of the source star : and c(V) = 0.786(-0.078)(+0.080) c(I) = 0.632(-0.037)(+0.047). Combined analysis of the light curve and the color-magnitude diagram suggests that the source star is a G/K subgiant in the Galactic bulge (T-eff similar or equal to 4800 K). The resulting linear limb-darkening coefficient of the source is consistent with theoretical predictions, although it is likely that nonlinearity of the stellar surface brightness profile complicates the interpretation, especially for the I band. The global light curve fit to the data indicates that the event is due to a binary lens of a mass ratio q similar or equal to 0.39 and a projected separation d similar or equal to 2.42. The lens/source relative proper motion is (22.8 +/- 1.5) km s(-1) kpc(-1), typical of bulge/bulge or bulge/disk events.

DEEP MMT TRANSIT SURVEY OF THE OPEN CLUSTER M37. III. STELLAR ROTATION AT 550 Myr

In the course of conducting a deep (14.5 r 23), 20 night survey for transiting planets in the rich ~550 Myr old open cluster M37, we have measured the rotation periods of 575 stars, which lie near the cluster main sequence, with masses 0.2 M ? M 1.3 M ?. This is the largest sample of rotation periods for a cluster older than 500 Myr. Using this rich sample we investigate a number of relations between rotation period, color, and the amplitude of photometric variability. Stars with M 0.8 M ? show a tight correlation between period and mass with heavier stars rotating more rapidly. There is a group of four stars with P > 15 days that fall well above this relation, which, if real, would present a significant challenge to theories of stellar angular momentum evolution. Below 0.8 M ?, the stars continue to follow the period-mass correlation but with a broad tail of rapid rotators that expands to shorter periods with decreasing mass. We combine these results with observations of other open clusters to test the standard theory of lower main-sequence stellar angular momentum evolution. We find that the model reproduces the observations for solar-mass stars, but discrepancies are apparent for stars with 0.6 M 1.0 M ?. We also find that for late K through early M dwarf stars in this cluster, rapid rotators tend to be bluer than slow rotators in B ? V but redder than slow rotators in V ? IC . This result supports the hypothesis that the significant discrepancy between the observed and predicted temperatures and radii of low-mass main-sequence stars is due to stellar activity.

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

Parallax is the most fundamental technique for measuring distances to astronomical objects. Although terrestrial parallax was pioneered over 2000 years ago by Hipparchus (ca. 140 B.C.E.) 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 M ☉, with a distance of 525 ± 40 pc and a transverse velocity of 113 ± 21 km s–1. 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 substellar 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.