Robyn A. Allsman

The MACHO Project: Microlensing Results from 5.7 Years of Large Magellanic Cloud Observations

We report on our search for microlensing toward the Large Magellanic Cloud (LMC). Analysis of 5.7 yr of photometry on 11.9 million stars in the LMC reveals 13-17 microlensing events. A detailed treatment of our detection efficiency shows that this is significantly more than the ~2-4 events expected from lensing by known stellar populations. The timescales () of the events range from 34 to 230 days. We estimate the microlensing optical depth toward the LMC from events with 2 < < 400 days to be τ = 1.2 × 10-7, with an additional 20% to 30% of systematic error. The spatial distribution of events is mildly inconsistent with LMC/LMC disk self-lensing, but is consistent with an extended lens distribution such as a Milky Way or LMC halo. Interpreted in the context of a Galactic dark matter halo, consisting partially of compact objects, a maximum-likelihood analysis gives a MACHO halo fraction of 20% for a typical halo model with a 95% confidence interval of 8%-50%. A 100% MACHO halo is ruled out at the 95% confidence level for all except our most extreme halo model. Interpreted as a Galactic halo population, the most likely MACHO mass is between 0.15 and 0.9 M☉, depending on the halo model, and the total mass in MACHOs out to 50 kpc is found to be 9 × 1010 M☉, independent of the halo model. These results are marginally consistent with our previous results, but are lower by about a factor of 2. This is mostly due to Poisson noise, because with 3.4 times more exposure and increased sensitivity to long-timescale events, we did not find the expected factor of ~4 more events. In addition to a larger data set, this work also includes an improved efficiency determination, improved likelihood analysis, and more thorough testing of systematic errors, especially with respect to the treatment of potential backgrounds to microlensing. We note that an important source of background are supernovae (SNe) in galaxies behind the LMC.

The macho project: 45 candidate microlensing events from the first-year Galactic bulge data

We report the detection of 45 candidate microlensing events in fields toward the Galactic bulge. These come from the analysis of 24 fields containing 12.6 million stars observed for 190 days in 1993. Many of these events are of extremely high signal-to-noise ratio and are remarkable examples of gravitational microlensing. The distribution of peak magnifications is shown to be consistent with the microlensing interpretation of these events. Using a subsample of 1.3 million {open_quotes}clump giant{close_quotes} stars whose distance and detection efficiency are well known, we find 13 events and estimate the microlensing optical depth toward the Galactic bulge as {tau}{sub bulge}=3.9{sub {minus}1.2}{sup +1.8}{times}10{sup {minus}6} averaged over an area of {approximately}12deg{sup 2} centered at Galactic coordinates l=2.55{degree} and b=3.64{degree}. This is similar to the value reported by the OGLE collaboration and is marginally higher than current theoretical models for {tau}{sub bulge}. The optical depth is also seen to increase significantly for decreasing {vert_bar}b{vert_bar}. These results demonstrate that obtaining large numbers of microlensing events toward the Galactic bulge is feasible, and that the study of such events will have important consequences for the structure of the Galaxy and its dark halo. {copyright} {ital 1997} {ital The American Astronomical Society}

The MACHO Project: Microlensing Optical Depth toward the Galactic Bulge from Difference Image Analysis

We present the microlensing optical depth toward the Galactic bulge based on the detection of 99 events found in our Difference Image Analysis (DIA) survey. This analysis encompasses 3 yr of data, covering ~17 million stars in ~4 deg2, to a source-star baseline magnitude limit of V = 23. The DIA technique improves the quality of photometry in crowded fields, and allows us to detect more microlensing events with faint source stars. We find that this method increases the number of detection events by 85% compared with the standard analysis technique. DIA light curves of the events are presented, and the microlensing fit parameters are given. The total microlensing optical depth is estimated to be τtotal = 2.43 × 10-6, averaged over eight fields centered at l = 268 and b = -335. For the bulge component, we find τbulge = 3.23 × 10-6, assuming a 25% stellar contribution from disk sources. These optical depths are in good agreement with the past determinations of the MACHO and OGLE groups, and are higher than predicted by contemporary Galactic models. We show that our observed event timescale distribution is consistent with the distribution expected from normal mass stars, if we adopt the Scalo stellar mass function as our lens mass function. However, we note that since there is still disagreement about the exact form of the stellar mass function, there is uncertainty in this conclusion. Based on our event timescale distribution, we find no evidence for the existence of a large population of brown dwarfs in the direction of the Galactic bulge.

MACHO Alert 95-30: First Real-Time Observation of Extended Source Effects in Gravitational Microlensing

We present analysis of MACHO Alert 95-30, a dramatic gravitational microlensing event toward the Galactic bulge whose peak magnification departs significantly from the standard point-source microlensing model. Alert 95-30 was observed in real time by the Global Microlensing Alert Network (GMAN), which obtained densely sampled photometric and spectroscopic data throughout the event. We interpret the light-curve fine structure as indicating transit of the lens across the extended face of the source star. This signifies resolution of a star several kiloparsecs distant. We find a lens angular impact parameter θmin/θsource = 0.715 ± 0.003. This information, along with the radius and distance of the source, provides an additional constraint on the lensing system. Spectroscopic and photometric data indicate the source is a M4 III star of radius 61 ± 12 R☉, located on the far side of the bulge at ~9 kpc. We derive a lens angular velocity, relative to the source, of 21.5 ± 2.9 km s-1 kpc-1, where the error is dominated by uncertainty in the angular size of the source star. Likelihood analysis yields a median lens mass of 0.67 -->+ 2.53−0.46 M☉, located with 80% probability in the Galactic bulge at a distance of 6.93 -->+ 1.56−2.25 kpc. If the lens is a main-sequence star, we can include constraints on the lens luminosity. This modifies our estimates to Mlens=0.53 -->+ 0.52−0.35 M☉ and Dlens=6.57 -->+ 0.99−2.25 kpc. Spectra taken during the event show that the absorption-line equivalent widths of Hα and the TiO bands near 6700 A vary, as predicted for microlensing of an extended source. This is most likely due to center-to-limb variation in the stellar spectral lines. The observed spectral changes further support our microlensing interpretation. These data demonstrate the feasibility of using microlensing limb crossings as a tool to probe stellar atmospheres directly.

EROS and MACHO Combined Limits on Planetary Mass Dark Matter in the Galactic Halo

The EROS and MACHO collaborations have each published upper limits on the amount of planetary-mass dark matter in the Galactic halo obtained from gravitational microlensing searches. In this Letter, the two limits are combined to give a much stronger constraint on the abundance of low-mass MACHOs. Specifically, objects with masses 10−7 Mm10−3 M make up less than 25% of the halo dark matter for most models considered, and less than 10% of a standard spherical halo is made of MACHOs in the 3.5×10−7 MThe EROS and MACHO collaborations have each published upper limits on the amount of planetary mass dark matter in the Galactic Halo obtained from gravitational microlensing searches. In this paper the two limits are combined to give a much stronger constraint on the abundance of low mass MACHOs.

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.

Calibration of the MACHO photometry database

The MACHO Project is a microlensing survey that monitors the brightnesses of -60 million stars in the Large Magellanic Cloud (LMC), Small Magellanic Cloud, and Galactic bulge. The database presently contains more photometric measurements than previously recorded in the history of astronomy. We describe the calibration of the MACHO two-color photometry and transformation to the standard Kron-Cousins V and R system. This allows for proper comparison with all other observations on the Kron-Cousins standard system. The highest precision calibrations are for -9 million stars in the LMC bar. For these stars, independent photometric measurements in field-overlap regions indicate standard deviations crv = cry = 0.020 mag. Calibrated MACHO photometry data are compared with published photometric sequences and with new Hubble Space Telescope observations. We additionally describe the first application of these calibrated data: the construction of the “efficiency” color-magnitude diagram which will be used to calculate our experimental sensitivity for detecting microlensing in the LMC. Subject headings: astronomical databases: surveys astronomical methods: data analysis astronomical techniques: photometricThe MACHO Project is a microlensing survey that monitors the brightnesses of ~60 million stars in the Large Magellanic Cloud (LMC), Small Magellanic Cloud, and Galactic bulge. Our database presently contains about 80 billion photometric measurements, a significant fraction of all astronomical photometry. We describe the calibration of MACHO two-color photometry and transformation to the standard Kron-Cousins V and R system. Calibrated MACHO photometry may be properly compared with all other observations on the Kron-Cousins standard system, enhancing the astrophysical value of these data. For ~9 million stars in the LMC bar, independent photometric measurements of ~20,000 stars with V 18 mag in field-overlap regions demonstrate an internal precision σV = 0.021, σR = 0.019, σV-R = 0.028 mag. The accuracy of the zero point in this calibration is estimated to be ±0.035 mag for stars with colors in the range –0.1 mag < V-R < 1.2 mag. A comparison of calibrated MACHO photometry with published photometric sequences and new Hubble Space Telescope observations shows agreement. The current calibration zero-point uncertainty for the remainder of the MACHO photometry database is estimated to be ±0.10 mag in V or R and ±0.04 mag in V–R. We describe the first application of calibrated MACHO data: the construction of a color-magnitude diagram used to calculate our experimental sensitivity for detecting microlensing in the LMC.

Binary Microlensing Events from the MACHO Project

We present the light curves of 21 gravitational microlensing events from the first six years of the MACHO Project gravitational microlensing survey that are likely examples of lensing by binary systems. These events were manually selected from a total sample of ~350 candidate microlensing events that were either detected by the MACHO Alert System or discovered through retrospective analyses of the MACHO database. At least 14 of these 21 events exhibit strong (caustic) features, and four of the events are well fit with lensing by large mass ratio (brown dwarf or planetary) systems, although these fits are not necessarily unique. The total binary event rate is roughly consistent with predictions based upon our knowledge of the properties of binary stars, but a precise comparison cannot be made without a determination of our binary lens event detection efficiency. Toward the Galactic bulge, we find a ratio of caustic crossing to noncaustic crossing binary lensing events of 12?:?4, excluding one event for which we present two fits. This suggests significant incompleteness in our ability to detect and characterize noncaustic crossing binary lensing. The distribution of mass ratios, N(q), for these binary lenses appears relatively flat. We are also able to reliably measure source-face crossing times in four of the bulge caustic crossing events, and recover from them a distribution of lens proper motions, masses, and distances consistent with a population of Galactic bulge lenses at a distance of 7 ? 1 kpc. This analysis yields two systems with companions of ~0.05 M?.We present the lightcurves of 21 gravitational microlensing events from the first six years of the MACHO Project gravitational microlensing survey which are likely examples of lensing by binary systems. These events were manually selected from a total sample of ~350 candidate microlensing events which were either detected by the MACHO Alert System or discovered through retrospective analyses of the MACHO database. At least 14 of these 21 events exhibit strong (caustic) features, and 4 of the events are well fit with lensing by large mass ratio (brown dwarf or planetary) systems, although these fits are not necessarily unique. The total binary event rate is roughly consistent with predictions based upon our knowledge of the properties of binary stars, but a precise comparison cannot be made without a determination of our binary lens event detection efficiency. Towards the Galactic bulge, we find a ratio of caustic crossing to non-caustic crossing binary lensing events of 12:4, excluding one event for which we present 2 fits. This suggests significant incompleteness in our ability to detect and characterize non-caustic crossing binary lensing. The distribution of mass ratios, N(q), for these binary lenses appears relatively flat. We are also able to reliably measure source-face crossing times in 4 of the bulge caustic crossing events, and recover from them a distribution of lens proper motions, masses, and distances consistent with a population of Galactic bulge lenses at a distance of 7 +/- 1 kpc. This analysis yields 2 systems with companions of ~0.05 M_sun.

THE MACHO PROJECT LARGE MAGELLANIC CLOUD VARIABLE-STAR INVENTORY. IX. FREQUENCY ANALYSIS OF THE FIRST-OVERTONE RR LYRAE STARS AND THE INDICATION FOR NONRADIAL PULSATIONS

More than 1300 variables classified provisionally as first-overtone RR Lyrae pulsators in the MACHO variable-star database of the Large Magellanic Cloud (LMC) have been subjected to standard frequency analysis. Based on the remnant power in the prewhitened spectra, we found 70% of the total population to be monoperiodic. The remaining 30% (411 stars) are classified as one of nine types according to their frequency spectra. Several types of RR Lyrae pulsational behavior are clearly identified here for the first time. Together with the earlier discovered double-mode (fundamental and first-overtone) variables, this study increased the number of known double-mode stars in the LMC to 181. During the total 6.5 yr time span of the data, 10% of the stars showed strong period changes. The size, and in general also the patterns of the period changes, exclude a simple evolutionary explanation. We also discovered two additional types of multifrequency pulsators with low occurrence rates of 2% for each. In the first type, there remains one closely spaced component after prewhitening by the main pulsation frequency. In the second type, the number of remnant components is two; they are also closely spaced, and are symmetric in their frequency spacing relative to the central component. This latter type of variables are associated with their relatives among the fundamental pulsators, known as Blazhko variables. Their high frequency (≈20%) among the fundamental-mode variables versus the low occurrence rate of their first-overtone counterparts makes it more difficult to explain the Blazhko phenomenon by any theory depending mainly on the role of aspect angle or magnetic field. None of the current theoretical models are able to explain the observed close frequency components without invoking nonradial pulsation components in these stars.

The MACHO project LMC variable star inventory. 1: Beat Cepheids-conclusive evidence for the excitation of the second overtone in classical Cepheids

We report the discovery of 45 beat Cepheids in the Large Magellanic Cloud (LMC) using the MACHO Project photometry database. The variables which are pulsating simultaneously in two radial modes are shown to break cleanly into two period-ratio groups, providing the first unambiguous evidence that the second overtone is indeed excited in real Cepheids. Thirty stars are beating in the fundamental and first overtone mode (F/1H, with a period ratio in the neighborhood of 0.72), and fifteen stars are beating in the first and second overtone (1H/2H, with a period ratio near 0.80). The F/1H period ratios are systematically higher than known Galactic beat Cepheids, indicating a metallicity dependence whose sense is in agreement with theory. Beat Cepheids in the LMC are found to select the 1H/2H mode for fundamental periods shorter than 1.25 days. We find the fraction of Cepheids excited in two modes to be about 20\% for stars with fundamental periods shorter than 2.5 days. We fail to confirm any of the proposed beat Cepheid candidates common to our sample from the surveys of Andreasen (1987) and Andreasen \& Petersen (1987). We also present finder charts and find several of the beat Cepheids to be in or near LMC clusters.