David Randall Alves

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.

K-band calibration of the red clump luminosity

The average near-infrared (K-band) luminosity of 238 Hipparcos red clump giants is derived and then used to measure the distance to the Galactic center. These Hipparcos red clump giants have been previously employed as I-band standard candles. The advantage of the K-band is a decreased sensitivity to reddening and perhaps a reduced systematic dependence on metallicity. In order to investigate the latter, and also to refer our calibration to a known metallicity zero point, we restrict our sample of red clump calibrators to those with abundances derived from high-resolution spectroscopic data. The mean metallicity of the sample is [Fe/H] = -0.18 dex (σ = 0.17 dex). The data are consistent with no correlation between MK and [Fe/H] and only weakly constrain the slope of this relation. The luminosity function of the sample peaks at MK = -1.61 ± 0.03 mag. Next, we assemble published optical and near-infrared photometry for ~20 red clump giants in a Baades window field with a mean metallicity of [Fe/H] = -0.17 ± 0.09 dex, which is nearly identical to that of the Hipparcos red clump. Assuming that the average (V-I)0 and (V-K)0 colors of these two red clumps are the same, the extinctions in the Baades window field are found to be AV = 1.56, AI = 0.87, and AK = 0.15, in agreement with previous estimates. We derive the distance to the Galactic center: (m - M)0 = 14.58 ± 0.11 mag, or R = 8.24 ± 0.42 kpc. The uncertainty in this distance measurement is dominated by the small number of Baades window red clump giants examined here.

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.

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 Large Magellanic Cloud Variable Star Inventory. XI. Frequency Analysis of the Fundamental-Mode RR Lyrae Stars

We have frequency-analyzed 6391 variables classified earlier as fundamental-mode RR Lyrae (RR0) stars in the MACHO database on the Large Magellanic Cloud (LMC). The overwhelming majority (i.e., 96%) of these variables have been proved to be indeed RR0 stars, whereas the remaining ones have fallen into one of the following categories: single- and double-mode Cepheids, binaries, first-overtone and double-mode RR Lyrae stars, and nonclassified variables. Special attention has been paid to the properties of the amplitude- and phase-modulated RR0 stars (the Blazhko stars). We found altogether 731 Blazhko variables showing either a doublet or an equidistant triplet pattern at the main pulsation component in their frequency spectra. This sample overwhelmingly exceeds the number of Blazhko stars known in all other systems combined. The incidence rate of the Blazhko variables among the RR0 stars in the LMC is 11.9%, which is 3 times higher than their rate among the first-overtone RR Lyrae stars. No difference is found in the average brightness between the single-mode and Blazhko variables. However, the latter ones show a somewhat lower degree of skewness in their average light curves and a concomitant lower total amplitude in their modulation-free light curves. From the frequency spectra we found that variables with larger modulation amplitudes at the higher frequency side of the main pulsation component are 3 times more common than the ones showing the opposite amplitude pattern. A search for a modulation component with the Blazhko period in the average brightness of the individual variables showed the existence of such a modulation with an overall amplitude of ≈0.006 mag. On the other hand, a similar search for quadruple modulation patterns around the main pulsation component has failed to clearly detect such components at the ≈0.004 mag level. This means that the amplitudes of the quadruple components (if they exist) should be, on average, at least 10 times smaller than those of the triplet components. This finding and the existence of Blazhko variables with highly asymmetric modulation amplitudes not only question the validity of the magnetic oblique rotator model but also put stringent constraints on models based on mode-coupling theories.

Direct detection of a microlens in the Milky Way

The nature of dark matter remains mysterious, with luminous material accounting for at most ∼25 per cent of the baryons in the Universe. We accordingly undertook a survey looking for the microlensing of stars in the Large Magellanic Cloud (LMC) to determine the fraction of Galactic dark matter contained in massive compact halo objects (MACHOs). The presence of the dark matter would be revealed by gravitational lensing of the light from an LMC star as the foreground dark matter moves across the line of sight. The duration of the lensing event is the key observable parameter, but gives non-unique solutions when attempting to estimate the mass, distance and transverse velocity of the lens. The survey results to date indicate that between 8 and 50 per cent of the baryonic mass of the Galactic halo is in the form of MACHOs (ref. 3), but removing the degeneracy by identifying a lensing object would tighten the constraints on the mass in MACHOs. Here we report a direct image of a microlens, revealing it to be a nearby low-mass star in the disk of the Milky Way. This is consistent with the expected frequency of nearby stars acting as lenses, and demonstrates a direct determination of a lens mass from a microlensing event. Complete solutions such as this for halo microlensing events will probe directly the nature of the MACHOs.

Gravitational Microlensing Events Due to Stellar-Mass Black Holes

We present an analysis of the longest timescale microlensing events discovered by the MACHO Collaboration during a 7 year survey of the Galactic bulge. We find six events that exhibit very strong microlensing parallax signals due, in part, to accurate photometric data from the GMAN and MPS collaborations. The microlensing parallax fit parameters are used in a likelihood analysis, which is able to estimate the distances and masses of the lens objects based on a standard model of the Galactic velocity distribution. This analysis indicates that the most likely masses of five of the six lenses are greater than 1 M☉, which suggests that a substantial fraction of the Galactic lenses may be massive stellar remnants. This could explain the observed excess of long-timescale microlensing events. The lenses for events MACHO-96-BLG-5 and MACHO-98-BLG-6 are the most massive, with mass estimates of M/M☉ = 6 and M/M☉ = 6, respectively. The observed upper limits on the absolute brightness of main-sequence stars for these lenses are less than 1 L☉, so both lenses are black hole candidates. The black hole interpretation is also favored by a likelihood analysis with a Bayesian prior using a conventional model for the lens mass function. We consider the possibility that the source stars for some of these six events may lie in the foreground Galactic disk or in the Sagittarius (Sgr) dwarf galaxy behind the bulge, but we find that bulge sources are likely to dominate our microlensing parallax event sample. Future Hubble Space Telescope observations of these events can either confirm the black hole lens hypothesis or detect the lens stars and provide a direct measurement of their masses. Future observations of similar events by the Space Interferometry Mission or the Keck or VLT interferometers, as explained by Delplancke, Gorski, & Richichi, will allow direct measurements of the lens masses for stellar remnant lenses as well.