P. Vermaak

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

First microlens mass measurement: Planet photometry of EROS BLG-2000-5

We analyze PLANET photometric observations of the caustic-crossing binary lens microlensing event, EROS BLG-2000-5, and find that modeling the observed light curve requires incorporation of the microlens parallax and the binary orbital motion. The projected Einstein radius (E = 3.61 ± 0.11 AU) is derived from the measurement of the microlens parallax, and we are also able to infer the angular Einstein radius (θE = 1.38 ± 0.12 mas) from the finite source effect on the light curve, combined with an estimate of the angular size of the source given by the source position in a color-magnitude diagram. The lens mass, M = 0.612 ± 0.057 M☉, is found by combining these two quantities. This is the first time that parallax effects are detected for a caustic-crossing event and also the first time that the lens mass degeneracy has been completely broken through photometric monitoring alone. The combination of E and θE also allows us to conclude that the lens lies in the near side of the disk, within 2.6 kpc of the Sun, while the radial velocity measurement indicates that the source is a Galactic bulge giant.

Microlensing Constraints on the Frequency of Jupiter-Mass Companions: Analysis of 5 Years of PLANET Photometry

We analyze 5 years of PLANET photometry of microlensing events toward the Galactic bulge to search for the short-duration deviations from single-lens light curves that are indicative of the presence of planetary companions to the primary microlenses. Using strict event-selection criteria, we construct a well-defined sample of 43 intensively monitored events. We search for planetary perturbations in these events over a densely sampled region of parameter space spanning two decades in mass ratio and projected separation, but find no viable planetary candidates. By combining the detection efficiencies of the events, we find that, at 95% confidence, less than 25% of our primary lenses have companions with mass ratio q = 10-2 and separations in the lensing zone, [0.6-1.6]θE, where θE is the Einstein ring radius. Using a model of the mass, velocity, and spatial distribution of bulge lenses, we infer that the majority of our lenses are likely M dwarfs in the Galactic bulge. We conclude that less than 33% of M dwarfs in the Galactic bulge have companions with mass mp = MJ between 1.5 and 4 AU, and less than 45% have companions with mp = 3MJ between 1 and 7 AU, the first significant limits on planetary companions to M dwarfs. We consider the effects of the finite size of the source stars and changing our detection criterion, but find that these do not alter our conclusions substantially.

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.

Limb Darkening of a K Giant in the Galactic Bulge: PLANET Photometry of MACHO 97-BLG-28

We present the PLANET photometric data set10 for the binary-lens microlensing event MACHO 97- BLG-28, consisting of 696 I- and V -band measurements, and analyze it to determine the radial surface brightness pro—le of the Galactic bulge source star. The microlensed source, demonstrated to be a K giant by our independent spectroscopy, crossed an isolated cusp of the central caustic of the lensing binary, generating a sharp peak in the light curve that was well-resolved by dense (3¨30 minute) and continuous monitoring from PLANET sites in Chile, South Africa, and Australia. This is the —rst time that such a cusp crossing has been observed. Analysis of the PLANET data set has produced a measure- ment of the square-root limb-darkening coefficients of the source star in the I and V bands; the resulting stellar pro—les are in excellent agreement with those predicted by stellar atmospheric models for K giants. The limb-darkening coefficients presented here are the —rst derived from microlensing. They are also among the —rst found for normal giants by any technique and the —rst for any star as distant as the Galactic bulge. Modeling of our light curve for MACHO 97-BLG-28 indicates that the lensing binary has a mass ratio q \ 0.23 and an (instantaneous) separation in units of the angular Einstein ring radius of d \ 0.69. For a lens in the Galactic bulge, this corresponds to a typical stellar binary with a projected separation between 1 and 2 AU. If the lens lies closer (i.e., in the Galactic disk), the separation is smaller, and one or both of the lens objects is in the brown dwarf regime. Assuming that the source is a bulge K2 giant at 8 kpc, the relative lens-source proper motion is k \ 19.4 ^ 2.6 km s~1 kpc~1, consistent with a disk or bulge lens. If the nonlensed blended light is due to a single star, it is likely to be a young white dwarf in the bulge, consistent with the blended light coming from the lens itself. Subject headings: binaries: visualgravitational lensingstars: fundamental parameters ¨ stars: late-type

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.

The relative lens-source proper motion in MACHO 98-SMC-1

We present photometric and spectroscopic data for the second microlensing event seen toward the Small Magellanic Cloud (SMC), MACHO 98-SMC-1. The lens is a binary. We resolve the caustic crossing and find that the source took 2 Δt=8.5 hr to transit the caustic. We measure the source temperature Teff=8000 K both spectroscopically and from the color, (V-I)0~0.22. We find two acceptable binary-lens models. In the first, the source crosses the caustic at =432 and the unmagnified source magnitude is Is=22.15. The angle implies that the lens crosses the source radius in time t*=Δt=2.92 hr. The magnitude (together with the temperature) implies that the angular radius of the source is θ*=0.089 μas. Hence, the proper motion is μ=θ*/t*=1.26 km s-1 kpc-1. For the second solution, the corresponding parameters are =306, Is=21.81, t*=2.15 hr, θ*=0.104 μas, and μ=θ*/t*=2.00 km s-1 kpc-1. Both proper-motion estimates are slower than 99.5% of the proper motions expected for halo lenses. Both are consistent with an ordinary binary lens moving at ~75-120 km s-1 within the SMC itself. We conclude that the lens is most likely in the SMC proper.

High-Precision Limb-Darkening Measurement of a K3 Giant Using Microlensing

We obtain high-precision limb-darkening measurements in five bands (V, VE, IE, I, and H) for the K3 III (Teff = 4200 K, [Fe/H] = +0.3, log g = 2.3) source of the Galactic bulge microlensing event EROS BLG-2000-5. These measurements are inconsistent with the predictions of atmospheric models at higher than 10 σ. While the disagreement is present in all bands, it is most apparent in I, IE, and VE, in part because the data are better and in part because the intrinsic disagreement is stronger. We find that when limb-darkening profiles are normalized to have unit total flux, the I-band models for a broad range of temperatures all cross each other at a common point. The solar profile also passes through this point. However, the profile as measured by microlensing does not. We hypothesize that the models have incorporated some aspect of solar physics that is not shared by giant atmospheres.

Limits on the Abundance of Galactic Planets From 5 Years of PLANET Observations

We search for signatures of planets in 43 intensively monitored microlensing events that were observed between 1995 and 1999. Planets would be expected to cause a short-duration (∼1 day) deviation on the smooth, symmetric light curve produced by a single lens. We find no such anomalies and infer that less than one-third of the ∼0.3 stars that typically comprise the lens population have Jupiter mass companions with semimajor axes in M, the range of . Since orbital periods of planets at these radii are 3–15 yr, the outer portion of 1.5 AU ! a ! 4A U this region is currently difficult to probe with any other technique. Subject headings: gravitational lensing — planetary systems — stars: late-type — stars: low-mass, brown dwarfs — techniques: photometric On-line material: color figure