Parallax microlensing events in the OGLE II data base toward the Galactic bulge

We present a systematic search for parallax microlensing events among a total of 512 microlensing candidates in the OGLE II data base for the  1997–1999  seasons. We fit each microlensing candidate with both the standard microlensing model and a parallax model that accounts for the Earth's motion around the Sun. We then search for the parallax signature by comparing the χ ² of the standard and parallax models. For the events which show a significant improvement, we further use the 'duration' of the event and the signal-to-noise ratio as criteria to separate true parallax events from other noisy microlensing events. We have discovered one convincing new candidate, sc33_4505, and seven other marginal cases. The convincing candidate (sc33_4505) is caused by a slow-moving, and likely low-mass, object, similar to other known parallax events. We found that irregular sampling and gaps between observing seasons hamper the recovery of parallax events. We have also searched for long-duration events that do not show parallax signatures. The lack of parallax effects in a microlensing event puts a lower limit on the Einstein radius projected on to the observer plane, which in turn imposes a lower limit on the lens mass divided by the relative lens–source parallax. Most of the constraints are however quite weak.     

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.     

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.     

Measuring Microlensing Parallax via Simultaneous Observations from Chinese Space Station Telescope and Roman Telescope

Simultaneous observations from two spatially well-separated telescopes can lead to measurements of the microlensing parallax parameter,an important quantity tow...     

Gravitational microlensing of gamma-ray bursts at medium optical depth

Gravitational lensing of a gamma-ray burst (GRB) by a single point mass will produce a second, delayed signal. Several authors have discussed using microlensed GRBs to probe a possible cosmological population of compact objects. We analyse a closely related phenomenon: the effect of microlensing by low to medium optical depth in compact objects on the averaged observed light curve of a sample of GRBs. We discuss the cumulative measured flux as a function of time resulting from delays caused by microlensing by cosmological compact objects. The time-scale and curvature of this function describe unique values for the compact object mass and optical depth. For GRBs with durations larger than the detector resolution, limits could be placed on the mass and optical depth of cosmological compact objects. The method does not rely on the separation of lensed bursts from those that are spatially coincident.     

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.     

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.     

Microlensing by halo MACHOs with a spatially varying mass function

The main aim of microlensing experiments is to evaluate the mean mass of massive compact halo objects (MACHOs) and the mass fraction of the Galactic halo made by this type of dark matter. Statistical analysis shows that by considering a Dirac-Delta mass function (MF) for the MACHOs, their mean mass is about that of a white dwarf star. This result is, however, in discrepancy with other observations such as those of non-observed expected white dwarfs in the Galactic halo which give rise to metal abundance, polluting the interstellar medium by their evolution. Here we use the hypothesis of the spatially varying MF of MACHOs, proposed by Kerins and Evans to interpret microlensing events. In this model, massive lenses with a lower population contribute to the microlensing events more frequently than do dominant brown dwarfs. This effect causes the mean mass of the observed lenses to be larger than the mean mass of all the lenses. A likelihood analysis is performed to find the best parameters of the spatially varying MF that are compatible with the duration distribution of Large Magellanic Cloud microlensing candidates of the MACHO experiment.     

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.     

Gravitational lensing of type Ia supernovae by galaxy clusters

We propose a method to remove the mass-sheet degeneracy that arises when the mass of galaxy clusters is inferred from gravitational shear. The method utilizes high-redshift standard candles that undergo weak lensing. Natural candidates for such standard candles are type Ia supernovae (SNe Ia).
When corrected with the light-curve shape (LCS), the peak magnitude of SNe Ia provides a standard candle with an uncertainty in apparent magnitude of Δ m ≃0.1–0.2. Gravitational magnification of a background SN Ia by an intervening cluster would cause a mismatch between the observed SN Ia peak magnitude compared with that expected from its LCS and redshift. The average detection rate for SNe Ia with a significant mismatch of ≥2Δ m behind a cluster at z ≃0.05–0.15 is about 1–2 supernovae per cluster per year at J , I , R ≲25–26.
Since SNe are point-like sources for a limited period, they can experience significant microlensing by massive compact halo objects (MACHOs) in the intracluster medium. Microlensing events caused by MACHOs of ∼10⁻⁴ M⊙ are expected to have time-scales similar to that of the SN light curve. Both the magnification curve by a MACHO and the light curve of a SN Ia have characteristic shapes that allow us to separate them. Microlensing events caused by MACHOs of smaller mass can unambiguously be identified in the SN light curve if the latter is continuously monitored. The average number of identifiable microlensing events per nearby cluster ( z ≲0.05) per year is ∼0.02 ( f /0.01), where f is the fraction of the cluster mass in MACHOs of masses 10⁻⁷< M _macho/M⊙<10⁻⁴.     

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.     

Planetary microlensing signals from the orbital motion of the source star around the common barycentre

With several detections, the technique of gravitational microlensing has proven useful for studying planets that orbit stars at Galactic distances, and it can even be applied to detect planets in neighbouring galaxies. So far, planet detections by microlensing have been considered to result from a change in the bending of light and the resulting magnification caused by a planet around the foreground lens star. However, in complete analogy to the annual parallax effect caused by the revolution of the Earth around the Sun, the motion of the source star around the common barycentre with an orbiting planet can also lead to observable deviations in microlensing light curves that can provide evidence for the unseen companion. We discuss this effect in some detail and study the prospects of microlensing observations for revealing planets through this alternative detection channel. Given that small distances between lens and source star are favoured, and that the effect becomes nearly independent of the source distance, planets would remain detectable even if their host star is located outside the Milky Way with a sufficiently good photometry (exceeding present-day technology) being possible. From synthetic light curves arising from a Monte Carlo simulation, we find that the chances for such detections are not overwhelming and appear practically limited to the most massive planets (at least with current observational set-ups), but they are large enough for leaving the possibility that one or the other signal has already been observed. However, it may remain undetermined whether the planet actually orbits the source star or rather the lens star, which leaves us with an ambiguity not only with respect to its location, but also to its properties.     

ECHA J0843.3–7905: Discovery of an ''old'' classical T Tauri star in the η Chamaeleontis cluster

Cold, dense clouds of gas have been proposed to explain the dark matter in Galactic haloes, and have also been invoked in the Galactic disc as an explanation for the excess faint submillimetre sources detected by SCUBA. Even if their dust-to-gas ratio is only a small percentage of that in conventional gas clouds, these dense systems would be opaque to visible radiation. We examine the possibility that the data sets of microlensing experiments searching for massive compact halo objects can also be used to search for occultation signatures by such clouds. We compute the rate and time-scale distribution of stellar transits by clouds in the Galactic disc and halo. We find that, for cloud parameters typically advocated by theoretical models, thousands of transit events should already exist within microlensing survey data sets. We examine the seasonal modulation in the rate caused by the Earth's orbital motion and find it provides an excellent probe of whether detected clouds are of disc or halo origin.     

Stochastic distributions of lens and source properties for observed galactic microlensing events

A comprehensive new approach is presented for deriving probability densities of physical properties characterizing the lens and source that constitute an observed galactic microlensing event. While previously encountered problems are overcome, constraints from event anomalies and model parameter uncertainties can be incorporated into the estimates. Probability densities for given events need to be carefully distinguished from the statistical distribution of the same parameters among the underlying population from which the actual lenses and sources are drawn. Using given model distributions of the mass spectrum, the mass density, and the velocity distribution of Galactic disc and bulge constituents, probability densities of lens mass, distance, and the effective lens–source velocities are derived, where the effect on the distribution that arises from additional observations of annual parallax or finite-source effects, or the absence of significant effects, is shown. The presented formalism can also be used to calculate probabilities for the lens to belong to one or another population and to estimate parameters that characterize anomalies. Finally, it is shown how detection efficiency maps for binary-lens companions in the physical parameters, such as companion mass and orbital semimajor axis, arise from values determined for the mass ratio and dimensionless projected separation parameter, including the deprojection of the orbital motion for elliptical orbits. Compared to the naive estimate based on 'typical values', the detection efficiency for low-mass companions is increased by mixing in higher detection efficiencies for smaller mass ratios (i.e. smaller masses of the primary).     

A small source in Q2237+0305?

Microlensing in Q2237+0305 between 1985 and 1995 has been interpreted in two different ways. First, the observed variations can be explained through microlensing by stellar mass objects of a continuum source with dimensions significantly smaller than the microlens Einstein Radius ( ₀), but consistent with that expected for thermal accretion discs . However, other studies have shown that models having sources as large as 5 ₀ can reproduce the observed variation . In this paper we present evidence in favour of a small source. Our approach uses the distribution of microlensed light-curve derivatives to place statistical limits (as a function of source size) on the number of microlens Einstein radii crossed by the source during the monitoring period. In contrast with previous analyses, our results are therefore not dependent on an assumed time-scale. Limits on the source size are obtained from two separate light-curve features. First, recently published monitoring data show large variations (0.81.5 mag) between image brightnesses over a period of 700 d or 15 per cent of the monitoring period. Secondly, the 1988 peak in the image A light curve had a duration that is a small fraction (0.02) of the monitoring period. Such rapid microlensing rises and short microlensing peaks only occur for small sources. We find that the observed large, rapid variation limits the source size to be <0.2 ₀ (95 per cent confidence). The width of the light-curve peak provides a stronger constraint of <0.025 ₀ (99 per cent confidence). The Einstein radius (projected into the source plane) of the average microlens mass m in Q2237+0305 is The interpretation that stars are responsible for microlensing in Q2237+0305 therefore results in limits on the continuum source size that are consistent with current accretion disc theory.     

Microlensing of an extended source by a power-law mass distribution

Microlensing promises to be a powerful tool for studying distant galaxies and quasars. As the data and models improve, there are systematic effects that need to be explored. Quasar continuum and broad-line regions may respond differently to microlensing due to their different sizes; to understand this effect, we study microlensing of finite sources by a mass function of stars. We find that microlensing is insensitive to the slope of the mass function but does depend on the mass range. For negative-parity images, diluting the stellar population with dark matter increases the magnification dispersion for small sources and decreases it for large sources. This implies that the quasar continuum and broad-line regions may experience very different microlensing in negative-parity lensed images. We confirm earlier conclusions that the surface brightness profile and geometry of the source have little effect on microlensing. Finally, we consider non-circular sources. We show that elliptical sources that are aligned with the direction of shear have larger magnification dispersions than sources with perpendicular alignment, an effect that becomes more prominent as the ellipticity increases. Elongated sources can lead to more rapid variability than circular sources, which raises the prospect of using microlensing to probe source shape.     

Search for exotic matter from gravitational microlensing observations of stars

We consider small-scale spheroidal clusters of weakly interacting massive particles in our Galaxy as non-compact gravitational microlenses and predict the appearance of caustics in the plane of a lensed source. The crossing of these caustics by a lensed star can produce a large variety of light curves, including some observed in actual microlensing events that have been interpreted as manifestations of binary gravitational lenses. We consider also observable effects during the gravitational microlensing of stars of non-zero angular size with a given brightness distribution across their disks by such an exotic objects as natural wormholes and objects whose space-time environment is described with the NUT metric. We demonstrate that, under certain conditions, the microlensing light curves, chromatic and polarizational effects due to the properties of the lens and the star disk brightness distributions can differ considerably from those observed for a Schwarzschild gravitational lens, so that their analysis can facilitate the identification of such objects.     

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.     

The distribution of microlensed light-curve derivatives: the relationship between stellar proper motions and transverse velocity

We present a method for computing the probability distribution of microlensed light-curve derivatives both in the case of a static lens with a transverse velocity, and in the case of microlensing that is produced through stellar proper motions. The distributions are closely related in form, and can be considered equivalent after appropriate scaling of the input transverse velocity. The comparison of the distributions in this manner provides a consistent way to consider the relative contribution to microlensing (both large and small fluctuations) of the two classes of motion, a problem that is otherwise an extremely expensive computational exercise. We find that the relative contribution of stellar proper motions to the microlensing rate is independent of the mass function assumed for the microlenses, but is a function of optical depth and shear. We find that stellar proper motions produce a higher overall microlensing rate than a transverse velocity of the same magnitude. This effect becomes more pronounced at higher optical depth. With the introduction of shear, the relative rates of microlensing become dependent on the direction of the transverse velocity. This may have important consequences in the case of quadruply lensed quasars such as Q2237+0305, where the alignment of the shear vector with the source trajectory varies between images.