M. J. Lehner

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.

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.).

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.

Repetitive patterns in rapid optical variations in the nearby black-hole binary V404 Cygni.

How black holes accrete surrounding matter is a fundamental yet unsolved question in astrophysics. It is generally believed that matter is absorbed into black holes via accretion disks, the state of which depends primarily on the mass-accretion rate. When this rate approaches the critical rate (the Eddington limit), thermal instability is supposed to occur in the inner disk, causing repetitive patterns of large-amplitude X-ray variability (oscillations) on timescales of minutes to hours. In fact, such oscillations have been observed only in sources with a high mass-accretion rate, such as GRS 1915+105 (refs 2, 3). These large-amplitude, relatively slow timescale, phenomena are thought to have physical origins distinct from those of X-ray or optical variations with small amplitudes and fast timescales (less than about 10 seconds) often observed in other black-hole binaries—for example, XTE J1118+480 (ref. 4) and GX 339−4 (ref. 5). Here we report an extensive multi-colour optical photometric data set of V404 Cygni, an X-ray transient source containing a black hole of nine solar masses (and a companion star) at a distance of 2.4 kiloparsecs (ref. 8). Our data show that optical oscillations on timescales of 100 seconds to 2.5 hours can occur at mass-accretion rates more than ten times lower than previously thought. This suggests that the accretion rate is not the critical parameter for inducing inner-disk instabilities. Instead, we propose that a long orbital period is a key condition for these large-amplitude oscillations, because the outer part of the large disk in binaries with long orbital periods will have surface densities too low to maintain sustained mass accretion to the inner part of the disk. The lack of sustained accretion—not the actual rate—would then be the critical factor causing large-amplitude oscillations in long-period systems.

The Taos Project:upper bounds on the population of small kuiper belt objects and tests of models of formation and evolution of the outer solar system

We have analyzed the first 3.75 years of data from the Taiwanese American Occultation Survey (TAOS). TAOS monitors bright stars to search for occultations by Kuiper Belt objects (KBOs). This data set comprises 5 × 10^5 star hours of multi-telescope photometric data taken at 4 or 5 Hz. No events consistent with KBO occultations were found in this data set. We compute the number of events expected for the Kuiper Belt formation and evolution models of Pan & Sari, Kenyon & Bromley, Benavidez & Campo Bagatin, and Fraser. A comparison with the upper limits we derive from our data constrains the parameter space of these models. This is the first detailed comparison of models of the KBO size distribution with data from an occultation survey. Our results suggest that the KBO population is composed of objects with low internal strength and that planetary migration played a role in the shaping of the size distribution.

The MACHO project Hubble Space Telescope follow-up: Preliminary results on the location of the large magellanic cloud microlensing source stars

We attempt to determine whether the MACHO microlensing source stars are drawn from the average population of the LMC or from a population behind the LMC by examining the Hubble Space Telescope (HST) color-magnitude diagram (CMD) of microlensing source stars. We present WFPC2 HST photometry of eight MACHO microlensing source stars and the surrounding fields in the LMC. The microlensing source stars are identified by deriving accurate centroids in the ground-based MACHO images using difference image analysis (DIA) and then transforming the DIA coordinates to the HST frame. We consider in detail a model for the background population of source stars based on that presented by Zhao, Graff, & Guhathakurta. In this model, the source stars have an additional reddening of = 0.13 mag and a slightly larger distance modulus, ~ 0.3 mag, than the average LMC population. We also investigate a series of source star models, varying the relative fraction of source stars drawn from the average and background populations and the displacement of the background population from the LMC. Because of the small number of analyzed events, the distribution of probabilities of different models is rather flat. A shallow maximum occurs at a fraction sLMC ~ 0.8 of the source stars in the LMC. This is consistent with the interpretation that a significant fraction of observed microlensing events are due to lenses in the Milky Way halo, but does not definitively exclude other models.

Detectability of Occultations of Stars by Objects in the Kuiper Belt and Oort Cloud

The serendipitous detection of stellar occultations by outer solar system objects is a powerful method for ascertaining the small end (r 15 km) of the size distribution of Kuiper Belt objects and may potentially allow the exploration of objects as far out as the Oort Cloud. The design and implementation of an occultation survey is aided by a detailed understanding of how diffraction and observational parameters affect the detection of occultation events. In this study, stellar occultations are simulated, accounting for diffraction effects, finite source sizes, finite bandwidths, stellar spectra, sampling, and signal-to-noise ratios. Finally, the possibility of detecting small outer solar system objects from the Kuiper Belt all the way out to the Oort Cloud is explored for three photometric systems: a proposed space telescope, Whipple, the Taiwanese-American Occultation Survey, and the MMT.

The MACHO Project Large Magellanic Cloud Variable-Star Inventory. XIII. Fourier Parameters for the First-Overtone RR Lyrae Variables and the LMC Distance

Shapes of RR Lyrae light curves can be described in terms of Fourier coefficients that past research has linked with physical characteristics such as luminosity, mass, and temperature. Fourier coefficients have been derived for the V and R light curves of 785 overtone RR Lyrae variables in 16 MACHO fields near the bar of the LMC. In general, the Fourier phase differences 21, 31, and 41 increase and the amplitude ratio R21 decreases with increasing period. The coefficients for both the V and R magnitudes follow these patterns, but the phase differences for the R curves are on average slightly greater, and their amplitudes are about 20% smaller, than the ones for the V curves. The 31 and R21 coefficients have been compared with those of the first-overtone RR Lyrae variables in the Galactic globular clusters NGC 6441, M107, M5, M3, M2, ω Centauri, and M68. The results indicate that many of the LMC variables have properties similar to the ones in M2, M3, M5, and the Oosterhoff type I variables in ω Cen, but they are different from the Oosterhoff type II variables in ω Cen. Equations derived from hydrodynamic pulsation models have been used to calculate the luminosity and temperature for the 330 bona fide first-overtone variables. The results indicate that they have log L in the range 1.6–1.8 L⊙ and log Teff between 3.85 and 3.87. Based on these temperatures, a mean color excess E(V-R) = 0.08 mag, equivalent to E(B-V) = 0.14 mag, has been estimated for these 330 stars. The 80 M5-like variables (selected according to their location in the 31–log P plot) are used to determine an LMC distance. After correcting for the effects of extinction and crowding, a mean apparent magnitude V0 = 18.99 ± 0.02 (statistical) ±0.16 (systematic) has been estimated for these 80 stars. Combining this with a mean absolute magnitude MV = 0.56 ± 0.06 for M5-like stars derived from Baade-Wesselink analyses, main-sequence fitting, Fourier parameters, and the trigonometric parallax of RR Lyrae, we derive an LMC distance modulus μ = 18.43 ± 0.06 (statistical) ±0.16 (systematic) mag. The large systematic error arises from the difficulties of correcting for interstellar extinction and for crowding.