Observed Microlensing Events Research Articles

Constraints from microlensing experiments on clustered primordial black holes

Abstract It has recently been proposed that massive primordial black holes (PBH) could constitute all of the dark matter, providing a novel scenario of structure formation, with early reionization and a rapid growth of the massive black holes at the center of galaxies and dark matter halos. The scenario arises from broad peaks in the primordial power spectrum that give both a spatially clustered and an extended mass distribution of PBH. The constraints from the observed microlensing events on the extended mass function have already been addressed. Here we study the impact of spatial clustering on the microlensing constraints. We find that the bounds can be relaxed significantly for relatively broad mass distributions if the number of primordial black holes within each cluster is typically above one hundred. On the other hand, even if they arise from individual black holes within the cluster, the bounds from CMB anisotropies are less stringent due to the enhanced black hole velocity in such dense clusters. This way, the window between a few and ten solar masses has opened up for PBH to comprise the totality of the dark matter.

MICROLENSING PARALLAX FOR OBSERVERS IN HELIOCENTRIC MOTION

ABSTRACT Motivated by the ongoing Spitzer observational campaign, and the forthcoming K2 one, we revisit, working in an heliocentric reference frame, the geometrical foundation for the analysis of the microlensing parallax, as measured with the simultaneous observation of the same microlensing event from two observers with relative distance of order au. For the case of observers at rest, we discuss the well-known fourfold microlensing parallax degeneracy and determine an equation for the degenerate directions of the lens trajectory. For the case of observers in motion, we write down an extension of the Gould relationship between the microlensing parallax and the observable quantities and, at the same time, highlight the functional dependence of these same quantities from the timescale of the underlying microlensing event. Furthermore, through a series of examples, we show the importance of taking into account themotion of the observers to correctly recover the parameters of the underlying microlensing event. In particular, we discuss the cases of the amplitude of the microlensing parallax and that of the difference of the timescales between the observed microlensing events, which are key to understand the breaking of the microlensing parallax degeneracy. Finally, we consider the case of the simultaneous observation of the same microlensing event from the ground and two satellites, a case relevant for the expected joint K2 and Spitzer observational programs in 2016.

Are the Distribution of Einstein Crossing Times of Galactic Microlensing Events Bimodal?

The observed distribution of a blending-corrected sample of Einstein ring crossing times, , for microlensing events toward the galactic bulge/bar are analyzed. An inspection of the distribution of crossing times suggests that it may be bimodal, indicating that two populations of lenses could be responsible for observed microlensing events. Given the possibility that microlensing in this direction can be due to the two most common classes of stars, main-sequence and white dwarf, we analyze and show via Monte Carlo simulations that the observed bimodality of can be derived from their accepted mass functions, and the density distributions of both stellar populations in the galactic disk and bulge/bar, with a transverse velocity distribution that is consistent with the density distribution. Kolmogorov-Smirnov (KS) one sample tests shows that a white dwarf population of about 25% of all stars in the galaxy agrees well with the observed bimodality with a KS significance level greater than 97%. This is an expanded and updated version of a previous investigation (Wickramasinghe, Neusima, & Struble, in Mao 2008). A power-point version of the talk, with introductory figures, is found at: https://sites.google.com/site/rhkochconference/agenda-1/program.

MICROLENSING-BASED ESTIMATE OF THE MASS FRACTION IN COMPACT OBJECTS IN LENS GALAXIES

We estimate the fraction of mass that is composed of compact objects in gravitational lens galaxies. This study is based on microlensing measurements (obtained from the literature) of a sample of 29 quasar image pairs seen through 20 lens galaxies. We determine the baseline for no microlensing magnification between two images from the ratios of emission line fluxes. Relative to this baseline, the ratio between the continua of the two images gives the difference in microlensing magnification. The histogram of observed microlensing events peaks close to no magnification and is concentrated below 0.6 magnitudes, although two events of high magnification, $\Delta m \sim 1.5$, are also present. We study the likelihood of the microlensing measurements using frequency distributions obtained from simulated microlensing magnification maps for different values of the fraction of mass in compact objects, $\alpha$. The concentration of microlensing measurements close to $\Delta m \sim 0$ can be explained only by simulations corresponding to very low values of $\alpha$ (10% or less). A maximum likelihood test yields $\alpha=0.05_{-0.03}^{+0.09}$ (90% confidence interval) for a quasar continuum source of intrinsic size $r_{s_0}\sim 2.6 \cdot 10^{15} \rm cm$. Regarding the current controversy about Milky Way/LMC and M31 microlensing studies, our work supports the hypothesis of a very low content in MACHOS (Massive Compact Halo Objects).

Do Low Luminosity Stars Matter?

AbstractHistorically, low luminosity stars have attracted very little attention, in part because they are difficult to see except with large telescopes, however, by neglecting to study them we are leaving out the vast majority of stars in the Universe. Low mass stars evolve very slowly, it takes them trillions of years to burn their hydrogen, after which, they just turn into a He white dwarf, without ever going through the red giant phase. This lack of observable evolution partly explains the lack of interest in them. The search for the “missing mass” in the galactic plane turned things around and during the 60s and 70s the search for large M/L objects placed M-dwarfs and cool WDs among objects of astrophysical interest. New fields of astronomical research, like BDs and exoplanets appeared as spin-offs from efforts to find the “missing mass”. The search for halo white dwarfs, believed to be responsible for the observed microlensing events, is pursued by several groups. The progress in these last few years has been tremendous, here I present highlights some of the great successes in the field and point to some of the still unsolved issues.

Parameter degeneracies and (un)predictability of gravitational microlensing events

(abridged) Some difficulties in determining the physical properties that lead to observed anomalies in microlensing light curves, such as the mass and separation of extra-solar planets orbiting the lens star, or the relative source-lens parallax, are already anchored in factors that limit the amount of information available from ordinary events and in the adopted parametrization. Moreover, a real-time detection of deviations from an ordinary light curve while these are still in progress can only be done against a known model of the latter, and such is also required for properly prioritizing ongoing events for monitoring in order to maximize scientific returns. Despite the fact that ordinary microlensing light curves are described by an analytic function that only involves a handful of parameters, modelling these is far less trivial than one might be tempted to think. A well-known degeneracy for small impacts, and another one for the initial rise of an event, makes an interprediction of different phases impossible, while determining a complete set of model parameters requires the assessment of the fundamental characteristics of all these phases. While the wing of the light curve provides valuable information about the time-scale that absorbs the physical properties, the peak flux of the event can be meaningfully predicted only after about a third of the total magnification has been reached. Parametrizations based on observable features not only ease modelling by bringing the covariance matrix close to diagonal form, but also allow good predictions of the measured flux without the need to determine all parameters accurately. Campaigns intending to infer planet populations from observed microlensing events need to invest some time into acquiring data that allows to properly determine the magnification function.

Testing LMC Microlensing Scenarios: The Discrimination Power of the SuperMACHO Microlensing Survey

Characterizing the nature and spatial distribution of the lensing objects that produce the previously measured microlensing optical depth toward the Large Magellanic Cloud (LMC) remains an open problem. We present an appraisal of the ability of the SuperMACHO Project, a next-generation microlensing survey directed toward the LMC, to discriminate between various proposed lensing populations. We consider two scenarios: lensing by a uniform foreground screen of objects and self-lensing by LMC stars. The optical depth for screen lensing is essentially constant across the face of the LMC, whereas the optical depth for self-lensing shows a strong spatial dependence. We have carried out extensive simulations, based on data obtained during the first year of the project, to assess the SuperMACHO survey's ability to discriminate between these two scenarios. In our simulations we predict the expected number of observed microlensing events for various LMC models for each of our fields by adding artificial stars to the images and estimating the spatial and temporal efficiency of detecting microlensing events using Monte Carlo methods. We find that the event rate itself shows significant sensitivity to the choice of the LMC luminosity function, limiting the conclusions that can be drawn from the absolute rate. If instead we determine the differential event rate across the LMC, we will decrease the impact of these systematic biases and render our conclusions more robust. With this approach the SuperMACHO Project should be able to distinguish between the two categories of lens populations. This will provide important constraints on the nature of the lensing objects and their contributions to the Galactic dark matter halo.

LMC self-lensing from a new perspective

We present a new analysis on the issue of the location of the observed microlensing events in direction of the Large Magellanic Cloud (LMC). This is carried out starting from a recently drawn coherent picture of the geometrical structure and dynamics of the LMC disk and by considering different configurations for the LMC bar. In this framework it clearly emerges that the spatial distribution of the events observed so far shows a near--far asymmetry. This turns out to be compatible with the optical depth calculated for the LMC halo objects. In this perspective, our main conclusion, supported by a statistical analysis on the outcome of an evaluation of the microlensing rate, is that self lensing can not account for all the observed events. Finally we propose a general inequality to calculate quickly an upper limit to the optical depth along a line of view through the LMC center.

Monte Carlo simulations of the halo white dwarf population

The interpretation of microlensing results towards the Large Magellanic Cloud (LMC) still remains controversial. While white dwarfs have been proposed to explain these results and, hence, to contribute significantly to the mass budget of our Galaxy, there are also several constraints on the role played by white dwarfs. In this paper we analyze self-consistently and simultaneously four different results, namely, the local halo white dwarf luminosity function, the microlensing results reported by the MACHO team towards the LMC, the results of Hubble Deep Field (HDF) and the results of the EROS experiment, for several initial mass functions and halo ages. We find that the proposed log-normal initial mass functions do not contribute to solve the problem posed by the observed microlensing events and, moreover, they overproduce white dwarfs when compared to the results of the HDF and of the EROS survey. We also find that the contribution of hydrogen-rich white dwarfs to the dynamical mass of the halo of the Galaxy cannot be more than ∼4%.

Gravitational microlensing in NUT space

We study the theoretical signature of magnetic masses on the light curve of gravitational microlensing effect in NUT space. The light curves for microlensing events in NUT space are presented and contrasted with those due to lensing produced by normal matter. In the next step, associating magnetic mass to massive astrophysical compact objects (MACHOs), we try to see its effect on the light curves of microlensing candidates observered by the MACHO group. Presence or absence of this feature in the observed microlensing events can shed light on the question of the existence of magnetic masses in the Universe.

Microlensing by natural wormholes: Theory and simulations

We provide an in depth study of the theoretical peculiarities that arise in effective negative mass lensing, both for the case of a point mass lens and source, and for extended source situations. We describe novel observational signatures arising in the case of a source lensed by a negative mass. We show that a negative mass lens produces total or partial eclipse of the source in the umbra region and also show that the usual Shapiro time delay is replaced with an equivalent time gain. We describe these features both theoretically, as well as through numerical simulations. We provide negative mass microlensing simulations for various intensity profiles and discuss the differences between them. The light curves for microlensing events are presented and contrasted with those due to lensing produced by normal matter. Presence or absence of these features in the observed microlensing events can shed light on the existence of natural wormholes in the Universe.

Resolving gravitational microlensing events with long-baseline optical interferometry

Until now, the detailed interpretation of the observed microlensing events has suffered from the fact that the physical parameters of the phenomenon cannot be uniquely determined from the available astronomical measurements, i.e. the photometric lightcurves. The situation will change in the near-future with the availability of long-baseline, sensitive optical interferometers, which should be able to resolve the images of the lensed objects into their components. For this, it will be necessary to achieve a milliarcsecond resolution on sources with typical magnitudes K . Indeed, brighter events have never been observed up to now by micro-lensing surveys. We discuss the possibilities opened by the use of long baseline interferometry in general, and in particular for one such facility, the ESO VLT Interferometer, which will attain the required performance. We discuss the expected accuracy and limiting magnitude of such measurements. On the basis of the database of the events detected by the OGLE experiment, we estimate the number of microlenses that could be available for measurements by the VLTI. We find that at least several tens of events could be observed each year. In conjunction with the photometric data, our ability to measure the angular separation between the microlensed images will enable a direct and unambiguous determination of both their masses and locations.

The MACHO ProjectHubble Space TelescopeFollow‐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 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 = 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. Due to the small number of analyzed events the distribution of probabilities of different models is rather flat. A shallow maximum occurs at a fraction s_LMC ~ 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.

Baryonic dark matter and machos

A brief description of the status of baryons in the Universe is given, along with recent results from the MACHO collaboration and their meaning. A dark matter halo consisting of baryons in the form of Machos is ruled out, leaving an elementary particle as the prime candidate for the dark matter. The observed microlensing events may make up around 20% of the dark matter in the Milky Way, or may indicate an otherwise undetected component of the Large Magellanic Cloud.

Magnitude Bias of Microlensed Sources toward the Large Magellanic Cloud.

There are lines of evidence suggesting that some of the observed microlensing events in the direction of the Large Magellanic Cloud (LMC) are caused by ordinary star lenses as opposed to dark MACHOs in the Galactic halo. Efficient lensing by ordinary stars generally requires the presence of one or more additional concentrations of stars along the line of sight to the LMC disk. If such a population behind the LMC disk exists, then the source stars (for lensing by LMC disk objects) will be drawn preferentially from the background population and will show systematic differences from LMC field stars. One such difference is that the (lensed) source stars will be farther away than the average LMC field stars, and this should be reflected in their apparent baseline magnitudes. We focus on red clump stars; these should appear in the color-magnitude diagram at a few tenths of a magnitude fainter than the field red clump. Suggestively, one of the two near-clump confirmed events, MACHO-LMC-1, is a few tenths of magnitude fainter than the clump.

A New Argument against an Intervening Stellar Population toward the Large Magellanic Cloud

Zaritsky & Lin have claimed detection of an intervening population of stars toward the Large Magellanic Cloud (LMC), which, they believe, could account for a substantial fraction of the observed microlensing events. I show that the observed timescales of these events imply that if such an intervening population were composed of ordinary stars that gave rise to a significant fraction of the microlensing events, then the population could not be associated with the LMC. I present two independent statistical arguments which together essentially rule out such a chance alignment of unassociated structures. On the other hand, if the intervening structure is associated with the LMC, I show that of order half the mass in this structure is in substellar objects, which would make it unlike any known stellar population.

ΩBand Ω0from MACHOs and Local Group Dynamics

We obtain restrictions on the universal baryon fraction, fB ≡ ΩB/Ω0, by assuming that the observed microlensing events toward the Large Magellanic Cloud are due to baryonic MACHOs in the halo of the Galaxy and by extracting a bound to the total mass of the Milky Way from the motion of tracer galaxies in the Local Group. We find a lower bound fB > 0.29+0.18-0.15. Consistency with the predictions of primordial nucleosynthesis leads to the further constraint on the total mass density, Ω0 0.2.

The abundance of brown dwarfs

The amount of mass contained in low-mass objects is investigated anew. Instead of using a mass±luminosity relation to convert a luminosity function to a mass function, I predict the mass±luminosity relation from assumed mass functions and the luminosity functions of Jahreiss & Wielen and Gould, Bahcall & Flynn. Comparison of the resulting mass± luminosity relations with data for binary stars constrains the permissible mass functions. If the mass function is assumed to be a power law, the best-fitting slope lies either side of the critical slope, a ˆ 22, below which the mass in low-mass objects is divergent, depending on the luminosity function adopted. If these power-law mass functions are truncated at 0.001 M(, the contribution to the local density from stars lies between 0.013 and 0.10 M( pc 23 depending on the mass at which the mass function is normalized and the adopted value of a . Recent dynamical estimates of the local mass density rule out stellar mass densities above , 0:05 M( pc: Hence, power laws steeper than a ˆ 22 that extend down to 0.001 M( are allowed only if one adopts an implausible normalization of the mass function. If the mass function is generalized from a power law to a low-order polynomial in log(M), the mass in stars with M , 0:1 M( is either negligible or strongly divergent, depending on the order of the polynomial adopted. Key words: stars: luminosity function, mass function. 1 I N T R O D U C T I O N The abundance in galaxies of low-mass objects is of fundamental importance because we know that near the Sun at least half of the mass density of the Galaxy is made up of stars fainter than MV ˆ 10, and uncertainty in the expected mass-to-light ratio of the Galactic disc is dominated by uncertainty in the number of stars with MV * 16, which are extremely hard to detect despite being intrinsically numerous. The traditional way to determine the density of the lowest-mass stars is the use of a wide-field proper-motion survey to pick up faint but nearby stars, for which photometry and perhaps parallaxes can be obtained. More recently, two alternative strategies have become available: (i) searches for gravitational microlensing events, and (ii) narrow-field surveys to identify extremely red stars. Microlensing surveys detect stars through their gravitational fields rather than their radiation, so microlensing surveys should provide a powerful probe of the mass contained in low-mass stars. Unfortunately, there are two large problems. First, to obtain even the projected density of deflectors along lines of sight towards the survey stars, one must know how the deflectors are distributed along the line of sight. Secondly, to determine the mass function of the deflectors one requires a model of their kinematics. In consequence of these difficulties, there is no consensus regarding the nature of the deflectors that have caused the observed microlensing events towards either the Galactic Centre or the Magellanic Clouds. The work with the Hubble Space Telescope (HST) of Gould, Bahcall & Flynn (1997, hereafter GBF) and Gould, Flynn & Bahcall (1998) pushes the strategy of counting extremely red stars to its ultimate form, in which the limiting magnitude of the survey becomes extremely faint and the field becomes very narrow. Consequently, most objects detected are of low luminosity and rather distant , 2 kpc† (as are objects detected by microlensing surveys), and it is a non-trivial task, that involves the adoption of a large-scale model of the Galaxy, to infer the local luminosity function from the data. Despite these difficulties, the luminosity function of the Galactic disc is now well determined at MV & 13 and is usefully constrained down to MV , 19 ± see Fig. 1. This paper is concerned with the problem of converting a known luminosity function into a mass function. The conventional procedure involves the adoption of some mass±luminosity relation. The mass±luminosity relation for cool stars is complex and hard to determine either theoretically or observationally, while we expect, a priori, that the mass function is simple. Therefore, following Kroupa, Tout & Gilmore (1990) I assume plausible mass functions and use measured luminosity functions to infer mass±luminosity relations. Comparison of these inferred relations with the data for binary stars clarifies the amount of mass that may

Spectroscopy of MACHO 97-SMC-1: Self-Lensing within the Small Magellanic Cloud

More than a dozen microlensing events have been detected so far toward the LMC, and two have been detected toward the SMC. If all of the lenses are in the Galactic halo, both the LMC and the SMC events are expected to have similar timescales. However, the first event toward the SMC, MACHO 97-SMC-1, had a timescale of 123 days, which is much larger than the typical timescale for the LMC events. Since the observed timescale of the SMC event would need the mass of the halo lens to be ~3 M☉, it has been argued earlier that the lens must be within the SMC, which we spectroscopically confirm in this Letter. From optical depth estimates, we first show that the stars within the SMC play a dominant role as gravitational lenses and can fully account for the observed microlensing events, mainly due to its large physical depth. We also show that if the lenses are within the Magellanic Clouds, then the SMC events should be longer in duration than the LMC events, a fact that is consistent with the observations. The timescale of the event implies that the mass of the lens is 2 M☉ if it is in the Milky Way disk or halo, in which case the lens, if it is a normal star, is expected to be bright and should reveal itself in the spectrum. Here, we present an optical spectrum of MACHO 97-SMC-1 obtained in 1997 May that shows that the source is a main-sequence B star. There is no trace of any contribution from the lens, which suggests that the lens is not in the Milky Way disk or halo but is a low-mass star within the SMC. The other alternative, that the lens could be a black hole in the Galactic halo, cannot be ruled out from the spectrum alone, but this is disfavored by the timescales of the LMC events. It is worth noting here that MACHO SMC-98-1 is the only other observed event toward the SMC. This was a binary lens event for which the caustic crossing timescale as observed by the PLANET, MACHO, EROS, and OGLE collaborations suggests that the lens is within the SMC. Furthermore, the only LMC event for which we have independent information on the location of the lens is the binary lens event MACHO LMC-9, where the caustic crossing timescale suggests the lens to be within the LMC. Thus, our current knowledge of the events indicates that all three microlensing events toward the Magellanic Clouds for which we have independent knowledge of the location of the lenses are due to self-lensing within the Magellanic Clouds.

Emission from Isolated Black Holes and MACHO[CLC]s[/CLC] Accreting from the Interstellar Medium

Adopting the advection-dominated accretion flow (ADAF) model, we have reexamined the radiation emitted by isolated stellar-mass black holes accreting from the interstellar medium of our Galaxy. Two distinct types of black holes are given consideration: (1) remnants of conventional massive star evolution (remnant black holes [RBHs], mass ~10 M☉) and (2) low-mass objects that possibly constitute the dark halo and cause the observed microlensing events (MACHOBHs, mass ~0.5 M☉). In contrast to previous studies incorporating spherical accretion models, the characteristic hard X-ray emission from ADAFs serves as an important observational signature. Standard estimates for the present density of RBHs suggest that a fair number of objects, either in nearby molecular clouds (such as Orion) or in the general Galactic disk, may be detected by near-future X-ray instruments. Their observation may also be feasible at lower frequencies, particularly in the infrared and optical bands. On the other hand, the smaller mass and larger velocity on average of MACHOBHs compared with RBHs make them unlikely to be observable in the foreseeable future.