Optical Gravitational Lensing Experiment OGLE-1999-BUL-32: the longest ever microlensing event – evidence for a stellar mass black hole?

We describe the discovery of the longest microlensing event ever observed, OGLE-1999-BUL-32, also independently identified by the MACHO collaboration as MACHO-99-BLG-22. This unique event has an Einstein radius crossing time of 640 d. The high-quality data obtained with difference image analysis shows a small but significant parallax signature. This parallax effect allows one to determine the Einstein radius projected on to the observer plane as     . The transverse velocity projected on to the observer plane is about 79 km s⁻¹. We argue that the lens is likely to have a mass of at least a few solar masses, i.e. it could be a stellar black hole. The black hole hypothesis can be tested using the astrometric microlensing signature with the soon-to-be installed Advanced Camera for Surveys on board the Hubble Space Telescope . Deep X-ray and radio images may also be useful for revealing the nature of the object.     

On the prospect of inferring the halo structure and the masses of dark objects through parallax microlensing

We study the proposed use of parallax microlensing in the direction of the Large Magellanic Cloud (LMC) to separate the effects of the mass function of dark massive halo objects (MHOs or 'machos') on the one hand, and their spatial distribution and kinematics on the other. This disentanglement is supposed to allow a much better determination of the two than could be achieved entirely on the basis of the durations of events. We restrict our treatment to the same class of power-law spherical models for the halo of MHOs studied in a previous paper by Marković 38 Sommer-Larsen, and assume that one can eliminate microlensing events caused by massive objects outside the halo (e.g., the LMC halo). Whereas the duration-based error in the average MHO mass, μ¯ ≡  M ¯/M, exceeds (at N  = 100 events) μ¯ by a factor of 2 or more, parallax microlensing remarkably brings it down to 15–20 per cent of μ¯, regardless of the shape of the mass function. In addition, the slope α of the mass function, d n /dμ ∝ μ^α, can be inferred relatively accurately (σ_α < 0.4) for a broader range, −3 < α < 0. The improvement in the inference of the halo structure is also significant: the index γ of the density profile ( ρ ∼  R ^−γ) can be obtained with the error σ_γ < 0.4. While in a typical situation the errors for the parameters specifying the velocity dispersion profile are of about the same magnitude as the parameters themselves, virtually all the uncertainty is 'concentrated' in linear combinations of the parameters that may have little influence on the profile, thus allowing its reasonably accurate inference.     

Repeating microlensing events in the OGLE data

Microlensing events are usually selected among single-peaked non-repeating light curves in order to avoid confusion with variable stars. However, a microlensing event may exhibit a second microlensing brightening episode when the source or/and the lens is a binary system. A careful analysis of these repeating events provides an independent way to study the statistics of wide binary stars and to detect extrasolar planets. Previous theoretical studies predicted that 0.5–2 per cent of events should repeat due to wide binary lenses. We present a systematic search for such events in about 4000 light curves of microlensing candidates detected by the Optical Gravitational Lensing Experiment (OGLE) towards the Galactic bulge from 1992 to 2007. The search reveals a total of 19 repeating candidates, with six clearly due to a wide binary lens. As a by-product, we find that 64 events (∼2 per cent of the total OGLE-III sample) have been misclassified as microlensing; these misclassified events are mostly nova or other types of eruptive stars. The number and importance of repeating events will increase considerably when the next-generation wide-field microlensing experiments become fully operational in the future.     

A systematic fitting scheme for caustic-crossing microlensing events

We outline a method for fitting binary-lens caustic-crossing microlensing events based on the alternative model parametrization proposed and detailed by Cassan. As an illustration of our methodology, we present an analysis of OGLE-2007-BLG-472, a double-peaked Galactic microlensing event with a source crossing the whole caustic structure in less than three days. In order to identify all possible models we conduct an extensive search of the parameter space, followed by a refinement of the parameters with a Markov Chain Monte Carlo algorithm. We find a number of low-  χ²  regions in the parameter space, which lead to several distinct competitive best models. We examine the parameters for each of them, and estimate their physical properties. We find that our fitting strategy locates several minima that are difficult to find with other modelling strategies and is therefore a more appropriate method to fit this type of event.     

Constraints on Jupiters from observations of Galactic bulge microlensing events during 2000

We present observations of eight Galactic bulge microlensing events taken with the 1.0-m Jacobus Kapteyn Telescope (JKT) on La Palma during 2000 June and July. The JKT observing schedule was optimized using a prioritizing algorithm to automatically update the target list. For most of these events we have sampled the light curves at times where no information was available from the OGLE alert team. We assume a point-source point-lens (PSPL) model and perform a maximum likelihood fit to both our data and the OGLE data to constrain the event parameters of the fit. We then refit the data assuming a binary lens and proceed to calculate the probability of detecting planets with mass ratio   q = 10⁻³  . We have seen no clear signatures of planetary deviations on any of the eight events and we quantify constraints on the presence of planetary companions to the lensing stars. For two well-observed events, 2000BUL31 and 2000BUL33, our detection probabilities peak at ∼30 and ∼20 per cent respectively for   q = 10⁻³  and   a ∼ R _E  for a  Δχ²  threshold value of 60.     

Pixel lensing as a way to detect extrasolar planets in M31

We study the possibility to detect extrasolar planets in M31 through pixel-lensing observations. Using a Monte Carlo approach, we select the physical parameters of the binary lens system, a star hosting a planet, and we calculate the pixel-lensing light curve taking into account the finite source effects. Indeed, their inclusion is crucial since the sources in M31 microlensing events are mainly giant stars. Light curves with detectable planetary features are selected by looking for significant deviations from the corresponding Paczyński shapes. We find that the time-scale of planetary deviations in light curves increase (up to 3–4 d) as the source size increases. This means that only few exposures per day, depending also on the required accuracy, may be sufficient to reveal in the light curve a planetary companion. Although the mean planet mass for the selected events is about     , even small mass planets  ( M _P < 20 M_⊕)  can cause significant deviations, at least in the observations with large telescopes. However, even in the former case, the probability to find detectable planetary features in pixel-lensing light curves is at most a few per cent of the detectable events, and therefore many events have to be collected in order to detect an extrasolar planet in M31. Our analysis also supports the claim that the anomaly found in the candidate event PA-99-N2 towards M31 can be explained by a companion object orbiting the lens star.     

On the parallax of WD 0346++246: a halo white dwarf candidate

We present a parallax measurement for the very cool degenerate WD 0346+246, the serendipitous discovery of which was reported by Hambly et al. We find an absolute parallax of 36±5 mas, yielding a distance estimate of 28±4 pc. The resulting absolute visual magnitude of the object is M _V =16.8±0.3, making it the second-lowest luminosity white dwarf currently known. We use the distance estimate and measured proper motion to show that the object has kinematics consistent with membership of the Galactic halo. WD 0346+246 is therefore by far the coolest and least luminous of only a handful of plausible halo white dwarf candidates. As such, the object has relevance to the ongoing debate concerning the results of microlensing experiments and the nature of any baryonic dark matter component to the Galactic halo residing in stellar remnants.     

On the probability of microlensing in gamma-ray burst afterglows

The declining light curve of the optical afterglow of gamma-ray burst (GRB) GRB000301C showed rapid variability with one particularly bright feature at about t − t ₀=3.8 d. This event was interpreted as gravitational microlensing by Garnavich, Loeb & Stanek and subsequently used to derive constraints on the structure of the GRB optical afterglow. In this paper, we use these structural parameters to calculate the probability of such a microlensing event in a realistic scenario, where all compact objects in the universe are associated with observable galaxies. For GRB000301C at a redshift of z =2.04, the a posteriori probability for a microlensing event with an amplitude of Δ m 0.95 mag (as observed) is 0.7 per cent (2.7 per cent) for the most plausible scenario of a flat Λ-dominated Friedmann–Robertson–Walker (FRW) universe with Ω_m=0.3 and a fraction f ∗=0.2 (1.0) of dark matter in the form of compact objects. If we lower the magnification threshold to Δ m 0.10 mag, the probabilities for microlensing events of GRB afterglows increase to 17 per cent (57 per cent). We emphasize that this low probability for a microlensing signature of almost 1 mag does not exclude that the observed event in the afterglow light curve of GRB000301C was caused by microlensing, especially in light of the fact that a galaxy was found within 2 arcsec from the GRB. In that case, however, a more robust upper limit on the a posteriori probability of ≈5 per cent is found. It does show, however, that it will not be easy to create a large sample of strong GRB afterglow microlensing events for statistical studies of their physical conditions on microarcsec scales.     

An Inventory of Gravitational Microlenses Toward the Galactic Bulge

Although microlensing experiments toward the Galactic bulge were originally initiated to check the feasibility of the experiments, they have now become an important tool which allows one to investigate Galactic matter composition. However, previous determination of the lens mass function was not based on the actual number of lenses even for the well-determined population of stellar lenses, but rather on arbitrarily assumed functional forms such as power laws, and thus the derived mass functions were subject to large uncertainties. In this paper, we take a different approach in which we first estimate the event rate distribution expected from observationally well-constrained populations of lenses, and then test other possible lens populations. By comparing the determined event rate distribution Γ( t _E) for various mass function models of lens populations with the observed distribution, we find that stars and white dwarfs explain just ∼ 50 per cent of the total observed events even including very faint stars just above the hydrogen-burning limit. Additionally, the expected time-scale distribution of events caused by these known populations of lenses deviates significantly from the observed distribution, especially in the short time-scale region. However, if the rest of the dynamical mass of the bulge (∼ 2.1 × 10¹⁰ M) is composed of brown dwarfs, the expected event rate distribution matches the observation well.     

Chromatic and spectroscopic signatures of microlensing events as a tool for the gravitational imaging of stars

The detection of microlensing events from stars in the Large Magellanic Cloud and in the Galactic bulge raises important constraints on the distribution of dark matter and on galactic structure, although some events may be the result of a new type of intrinsic variability. When lenses are relatively close to the sources, we predict that chromatic and spectroscopic effects are likely to appear for a significant fraction of the microlensing events. These effects are due to the differential amplification of the limb and the centre of the stellar disc, and present a systematic dependence with wavelength and time that provides an unambiguous signature of a microlensing event (as opposed to a new type of intrinsic stellar variability). We present detailed predictions of the effects, using realistic model atmospheres. The observations of these effects provide a direct constraint on stellar atmospheres, allowing a three-dimensional reconstruction or imaging of its structure, a unique tool with which to test the current models of stellar atmospheres.     

Microlensing in dark matter haloes

Using eight dark matter haloes extracted from fully self-consistent cosmological N -body simulations, we perform microlensing experiments. A hypothetical observer is placed at a distance of 8.5 kpc from the centre of the halo measuring optical depths, event durations and event rates towards the direction of the Large Magellanic Cloud. We simulate 1600 microlensing experiments for each halo. Assuming that the whole halo consists of massive astronomical compact halo objects (MACHOs),   f = 1.0  , and a single MACHO mass is   m _M= 1.0 M_⊙  , the simulations yield mean values of  τ= 4.7^+5.0_−2.2× 10⁻⁷  and  Γ= 1.6^+1.3_−0.6× 10⁻⁶  events star⁻¹ yr⁻¹. We find that triaxiality and substructure can have major effects on the measured values so that τ and Γ values of up to three times the mean can be found. If we fit our values of τ and Γ to the MACHO collaboration observations, we find   f = 0.23^+0.15_−0.13  and   m _M= 0.44^+0.24_−0.16  . Five out of the eight haloes under investigation produce f and m _M values mainly concentrated within these bounds.     

On the intrinsic bias in detecting caustic crossings between Galactic halo and self-lensing events in the Magellanic Clouds

In this paper, we investigate the intrinsic bias in detecting caustic crossings between the Galactic halo and self-lensing gravitational microlensing events in the Magellanic Clouds. For this, we determine the region for optimal caustic-crossing detection in the parameter space of the physical binary separations, ℓ, and the total binary lens mass, M , and find that the optimal regions for both populations of events are similar to each other. In particular, if the Galactic halo is composed of lenses with the claimed average mass of 〈 M 〉∼0.5 M_⊙, the optimal binary separation range of Galactic halo events of 3.5 au≲ℓ≲14 au matches well with that of a Magellanic Cloud self-lensing event caused by a binary lens with a total mass of M ∼1 M_⊙; well within the mass range of the most probable lens population of stars in the Magellanic Clouds. Therefore, our computation implies that if the binary fractions and the distributions of binary separations of the two populations of lenses are not significantly different from each other, there is no strong detection bias against Galactic halo caustic-crossing events.     

The microlensing rate and mass function versus dynamics of the Galactic bar

With the steady increase of the sample size of observed microlenses towards the central regions of the Galaxy, the main source of the uncertainty in the lens mass will shift from the simple Poisson noise to the intrinsic non-uniqueness of our dynamical models of the inner Galaxy, particularly the Galactic bar. We use a set of simple self-consistent bar models to investigate how the microlensing event rate varies as a function of axis ratio, bar angle and velocity distribution. The non-uniqueness of the velocity distribution of the bar model adds a significant uncertainty (by about a factor of 1.5) to any prediction of the lens mass. Kinematic data and self-consistent models are critical to lift the non-uniqueness. We discuss the implications of these results for the interpretation of microlensing observations of the Galactic bulge. In particular we show that Freeman bar models scaled to the mass of the Galactic bulge/bar imply a typical lens mass of around 0.8 M⊙, a factor of 3–5 times larger than the value from other models.     

Real-time difference imaging analysis of MOA Galactic bulge observations during 2000

We describe observations carried out by the MOA group of the Galactic bulge during 2000 that were designed to detect efficiently gravitational microlensing of faint stars in which the magnification is high and/or of short duration. These events are particularly useful for studies of extrasolar planets and faint stars. Approximately 17 deg² were monitored at a sampling rate of up to six times per night. The images were analysed in real time using a difference imaging technique. 20 microlensing candidates were detected, of which eight were alerted to the microlensing community whilst in progress. Approximately half of the candidates had high magnifications (≳10), at least one had very high magnification (≳50), and one exhibited a clear parallax effect. The details of these events are reported here, together with details of the on-line difference imaging technique. Some nova-like events were also observed and these are described, together with one asteroid.     

Interferometric visibility and closure phase of microlensing events with finite source size

Interferometers from the ground and space will be able to resolve the two images in a microlensing event. This will at least partially lift the inherent degeneracy between physical parameters in microlensing events. To increase the signal-to-noise ratio, intrinsically bright events with large magnifications will be preferentially selected as targets. These events may be influenced by finite source size effects both photometrically and astrometrically. Using observed finite source size events as examples, we show that the fringe visibility can be affected by ∼5–10 per cent, and the closure phase by a few degrees – readily detectable by ground and space interferometers. Such detections will offer unique information about the lens–source trajectory relative to the baseline of the interferometers. Combined with photometric finite source size effects, interferometry offers a way to measure the angular sizes of the source and the Einstein radius accurately. Limb-darkening changes the visibility by a small amount compared with a source with uniform surface brightness, marginally detectable with ground-based instruments. We discuss the implications of our results for the plans to make interferometric observations of future microlensing events.     

Contribution to the search for binaries among Am stars – VIII. New spectroscopic orbits of eight systems and statistical study of a sample of 91 Am stars

Red clump giant (RCG) stars can be used as distance indicators to trace the mass distribution of the Galactic bar. We use RCG stars from 44 bulge fields from the OGLE-II microlensing collaboration data base to constrain analytic triaxial models for the Galactic bar. We find the bar major-axis is oriented at an angle of 24°–27° to the Sun–Galactic Centre line-of-sight. The ratio of semimajor and semiminor bar axis scalelengths in the Galactic plane   x ₀, y ₀  , and vertical bar scalelength z ₀, is   x ₀ :  y ₀ :  z ₀= 10 : 3.5 : 2.6  , suggesting a slightly more prolate bar structure than the working model of Gerhard which gives the scalelength ratios as   x ₀ :  y ₀ :  z ₀= 10 : 4 : 3  .     

Detection of stellar spots from the observations of caustic-crossing binary-lens gravitational microlensing events

Recently, Heyrovský & Sasselov investigated the sensitivity of single-lens gravitational microlensing event light curves to spots and found that, during source transit, spots can cause deviations in amplification larger than 2 per cent, and thus be detectable. In this paper, we explore the feasibility of spot detection from the observations of binary-lens microlensing events instead of single-lens events. For this we investigate the sensitivity of binary-lens event light curves to spots and compare it with that of single-lens events. From this investigation, we find that during caustic crossings the fractional amplification deviations of light curves from those of spotless source events are equivalent to those of single-lens events, implying that spots can also be detected with a similar photometric precision to that required for spot detection by observing single-lens events. We discuss the relative advantages of observing binary-lens events over the observations of single-lens events in detecting stellar spots.     

Dark haloes of spiral galaxies: ISO photometry

We exclude hydrogen-burning stars, of any mass above the hydrogen-burning limit and any metallicity, as significant contributors to the massive haloes deduced from rotation curves to dominate the outer parts of spiral galaxies. We present and analyse images of four nearly edge-on bulgeless spiral galaxies (UGC 711, NGC 2915, UGC 12426, UGC 1459) obtained with ISOCAM (The CAMera instrument on board the Infrared Space Observatory ) at 14.5 and 6.75 μm. Our sensitivity limit for detection of any diffuse infrared emission associated with the dark haloes in these galaxies is a few tens of μJy per 6 × 6 arcsec² pixel, with this limit currently set by remaining difficulties in modelling the non-linear behaviour of the detectors. All four galaxies show zero detected signal from extended non-disc emission, consistent with zero halo-like luminosity density distribution. The 95 per cent upper limit on any emission, for NGC 2915 in particular, allows us to exclude very low mass main-sequence stars ( M  > 0.08 M⊙) and young brown dwarfs (≲1 Gyr) as significant contributors to dark matter in galactic haloes. Combining our results with those of the Galactic microlensing surveys, which exclude objects with M  < 0.01 M⊙, excludes almost the entire possible mass range of compact baryonic objects from contributing to Galactic dark matter.     

A measurement of the transverse velocity of Q2237+0305

Determination of microlensing parameters in the gravitationally lensed quasar Q2237+0305 from the statistics of high-magnification events will require monitoring for more than 100 years (Wambsganss, Paczynski & Schneider). However, we show that the effective transverse velocity of the lensing galaxy can be determined on a more realistic time-scale through consideration of the distribution of light-curve derivatives. The 10 years of existing monitoring data for Q2237+0305 are analysed. These data display strong evidence for microlensing that is not associated with a high-magnification event. An upper limit of v _t<500 km s⁻¹ is obtained for the galactic transverse velocity, which is smaller than previously assumed values. The analysis suggests that the observed microlensing variation may be predominantly due to stellar proper motions. The statistical significance of the results obtained from our method will be increased by the addition of data points from current and future monitoring campaigns. However, reduced photometric errors will be more valuable than an increased sampling rate.     

Short time-scale fluctuations in the difference light curves of QSO 0957+561A,B: microlensing or noise?

From optical R -band data of the double quasar QSO 0957+561A,B, we made two new difference light curves (with an overlap of about 330 d between the time-shifted light curve for the A image and the magnitude-shifted light curve for the B image). We observed noisy behaviours around the zero line and no short time-scale events (with a duration of months), where the term 'event' refers to a prominent feature that may be a result of microlensing or another source of variability. Only one event lasting two weeks and rising −33 mmag was found . Measured constraints on the possible microlensing variability can be used to obtain information on the granularity of the dark matter in the main lensing galaxy and the size of the source. In addition, one can also test the ability of the observational noise to cause the rms averages and the local features of the difference signals. We focused on this last issue. The combined photometries were related to a process consisting of an intrinsic signal plus a Gaussian observational noise. The intrinsic signal has been assumed to be either a smooth function (polynomial), a smooth function plus a stationary noise process, or a correlated stationary process . Using these three pictures without microlensing, we derived some models totally consistent with the observations. We finally discussed the sensitivity of our telescope (at Teide Observatory) to several classes of microlensing variability.