Mark Robin Pratt

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 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.

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.

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.

EXPERIMENTAL LIMITS ON THE DARK MATTER HALO OF THE GALAXY FROM GRAVITATIONAL MICROLENSING

We monitored 8.6{times}10{sup 6} stars in the Large Magellanic Cloud for 1.1 years and have found three events consistent with gravitational microlensing. We place strong constraints on Galactic halo lensing objects in the mass range 10{sup {minus}4}{ital M}{sub {circle_dot}} to 10{sup {minus}1}{ital M}{sub {circle_dot}}. Three events are fewer than expected for a standard spherical halo of objects in this mass range, but appear to exceed the number expected from known Galactic populations. Fitting a naive spherical halo model to our data yields a MACHO fraction {ital f} of massive compact halo objects (MACHOs), {ital f}=0.19{sub {minus}0.10}{sup +0.16}, a total MACHO mass (inside 50 kpc) of 7.6{sub {minus}4}{sup +6}{times}10{sup 10}{ital M}{sub {circle_dot}}, and a microlensing optical depth 8.8{sub {minus}5}{sup +7}{times}10{sup {minus}8} (68% C.L.).

Macho project limits on black hole dark matter in the 1-30 M⊙ range

We report on a search for long-duration microlensing events toward the Large Magellanic Cloud. We find none and therefore put limits on the contribution of high-mass objects to the Galactic dark matter. At a 95% confidence level, we exclude objects in the mass range of 0.3-30.0 M☉ from contributing more than 4 × 1011 M☉ to the Galactic halo. Combined with earlier results, this means that objects with masses under 30 M☉ cannot make up the entire dark matter halo if the halo is of typical size. For a typical dark halo, objects with masses under 10 M☉ contribute less than 40% of the dark matter.We report on a search for long duration microlensing events towards the Large Magellanic Cloud. We find none, and therefore put limits on the contribution of high mass objects to the Galactic dark matter. At 95% confidence level we exclude objects in the mass range 0.3 solar masses to 30.0 solar masses from contributing more than 4 times 10^11 solar masses to the Galactic halo. Combined with earlier results, this means that objects with masses under 30 solar masses cannot make up the entire dark matter halo if the halo is of typical size. For a typical dark halo, objects with masses under 10 solar masses contribute less than 40% of the dark matter.

The Macho Project LMC Variable Star Inventory. X. The R Coronae Borealis Stars

We report the discovery of eight new R Coronae Borealis (RCB) stars in the Large Magellanic Cloud (LMC) using the MACHO project photometry database. The discovery of these new stars increases the number of known RCB stars in the LMC to thirteen. We have also discovered four stars similar to the Galactic variable DY Per. These stars decline much more slowly and are cooler than the RCB stars. The absolute luminosities of the Galactic RCB stars are unknown since there is no direct measurement of the distance to any Galactic RCB star. Hence, the importance of the LMC RCB stars. We find a much larger range of absolute magnitudes (MV = -2.5 to -5 mag) than inferred from the small pre-MACHO sample of LMC RCB stars. It is likely that there is a temperature-MV relationship with the cooler stars being intrinsically fainter. Cool (~5000 K) RCB stars are much more common than previously thought based on the Galactic RCB star sample. Using the fairly complete sample of RCB stars discovered in the MACHO fields, we have estimated the likely number of RCB stars in the Galaxy to be ~3200. The SMC MACHO fields were also searched for RCB stars, but none were found.

Variability-selected Quasars in MACHO Project Magellanic Cloud Fields

We present 47 spectroscopically confirmed quasars discovered behind the Magellanic Clouds identified via photometric variability in the MACHO database. Thirty-eight quasars lie behind the Large Magellanic Cloud and nine behind the Small Magellanic Cloud, more than tripling the number of quasars previously known in this region. The quasars cover the redshift interval 0.2 < z < 2.8 and have apparent mean magnitudes 16.6 ≤ ≤ 20.1. We discuss the details of quasar candidate selection based on time variability in the MACHO database and present results of spectroscopic follow-up observations. Our follow-up detection efficiency was 20%; the primary contaminants were emission-line Be stars in Magellanic Clouds. For the 47 quasars discovered behind the Magellanic Clouds, plus an additional 12 objects previously identified in this region, we present 7.5 yr MACHO V- and R-band light curves with average sampling times of 2–10 days.