We show that quasar microlensing magnification statistics induced by a population of point microlenses distributed according to a mass-spectrum can be very well approximated by that of a single-mass, "monochromatic", population. When the spatial resolution (physically defined by the source size) is small as compared with the Einstein radius, the mass of the monochromatic population matches the geometric mean of the mass-spectrum. Otherwise, the best-fit mass can be larger. Taking into account the degeneracy with the geometric mean, the interpretation of quasar microlensing observations under the hypothesis of a mixed population of primordial black holes and stars, makes the existence of a significant population of intermediate mass black holes ($\sim$ 100$M_\odot$) unlikely but allows, within a two-$σ$ confidence interval, the presence of a large population ($\gtrsim 40\%$ of the total mass) of substellar black holes ($\sim$ 0.01$M_\odot$).
We investigate the effect of microlensing on the standardisation of strongly lensed Type Ia supernovae (GLSNe Ia). We present predictions for the amount of scatter induced by microlensing across a range of plausible strong lens macromodels. We find that lensed images in regions of low convergence, shear and stellar density are standardisable, where the microlensing scatter is < 0.15 magnitudes, comparable to the intrinsic dispersion of for a typical SN Ia. These standardisable configurations correspond to asymmetric lenses with an image located far outside the Einstein radius of the lens. Symm…
With the increase in the number of observed gravitational wave (GW) signals, detecting strongly lensed GWs by galaxies has become a real possibility. Lens galaxies also contain microlenses (e.g., stars and black holes), introducing further frequency-dependent modulations in the strongly lensed GW signal within the LIGO frequency range. The multiple lensed signals in a given lens system have different underlying macro-magnifications ($|μ|$) and are located in varied microlens densities ($Σ_\bullet$), leading to different levels of microlensing distortions. This work quantifies the fraction of s…
The idea that dark matter can be made of intermediate-mass primordial black holes in the $10M_\odot \lesssim M \lesssim 200M_\odot$ range has recently been reconsidered, particularly in the light of the detection of gravitational waves by the LIGO experiment. The existence of even a small fraction of dark matter in black holes should nevertheless result in noticeable quasar gravitational microlensing. Quasar microlensing is sensitive to any type of compact objects in the lens galaxy, to their abundance, and to their mass. We have analyzed optical and X-ray microlensing data from 24 gravitation…
We present estimates for the size and the logarithmic slope of the disk temperature profile of the lensed quasar Q2237+0305, independent of the component velocities. These estimates are based on six epochs of multi-wavelength narrowband images from the Nordic Optical Telescope. For each pair of lensed images and each photometric band, we determine the microlensing amplitude and chromaticity using pre-existing mid-IR photometry to define the baseline for no microlensing magnification. A statistical comparison of the combined microlensing data (6 epochs $\times$ 5 narrow bands $\times$ 6 image p…
Gravitational microlensing is a powerful tool for probing the physical properties of quasar accretion disks and properties of the lens galaxy such as its dark matter fraction and mean stellar mass. Unfortunately the number of lensed quasars ($\sim 90$) exceeds our monitoring capabilities. Thus, estimating their microlensing properties is important for identifying good microlensing candidates as well as for the expectations of future surveys. In this work we estimate the microlensing properties of a sample of 87 lensed quasars. While the median Einstein radius crossing time scale is 20.6 years,…
The recent discovery of gravitational waves from mergers of $\sim 10 \, M_{\odot}$ black hole binaries has stimulated interested in Primordial Black Hole dark matter in this mass range. Microlensing and dynamical constraints exclude all of the dark matter being in compact objects with a delta function mass function in the range $10^{-7} \lesssim M/ M_{\odot} \lesssim 10^{5}$. However it has been argued that all of the dark matter could be composed of compact objects in this range with an extended mass function. We explicitly recalculate the microlensing and dynamical constraints for compact ob…
The dark matter enclosed in a density perturbation with a large initial amplitude (delta-rho/rho > 1e-3) collapses shortly after recombination and forms an ultracompact minihalo (UCMH). Their high central densities make UCMHs especially suitable for detection via astrometric microlensing: as the UCMH moves, it changes the apparent position of background stars. A UCMH with a mass larger than a few solar masses can produce a distinctive astrometric microlensing signal that is detectable by the space astrometry mission Gaia. If Gaia does not detect gravitational lensing by any UCMHs, then it esta…
Microlensing observations toward globular clusters could be very useful to probe their low mass star and brown dwarf content. Using the large set of microlensing events detected so far toward the Galactic centre we investigated whether for some of the observed events the lenses are located in the Galactic globular clusters. Indeed, we found that in four cases some events might be due to lenses located in the globular clusters themselves. Moreover, we discuss a microlensing event found in M22. Using the adaptive optics system NACO at ESO VLT it was possible to identify the lens, which turned ou…
AMPM I. A Targeted Search for Asteroid Mass Primordial Black Hole Microlenses
Swinburne University of Technology（斯威本科技大学）；ARC Centre of Excellence for Dark Matter Particle Physics（暗物质粒子物理卓越研究中心）；Research School of Astronomy and Astrophysics Australian National University（澳大利亚国立大学天体与天体物理学研究学院）；NSF NOIRLab National Optical-Infrared Astronomy Research Laboratory（美国国家光学红外天文研究实验室）；Cerro Tololo Inter-American Observatory（塞罗托洛洛美洲际观测台）
We present an analysis of the large set of microlensing events detected so far toward the Galactic center with the purpose of investigating whether some of the dark lenses are located in Galactic globular clusters. We find that in four cases some events might indeed be due to lenses located in the globular clusters themselves. We also give a rough estimate for the average lens mass of the events being highly aligned with Galactic globular cluster centers and find that, under reasonable assumptions, the deflectors could most probably be either brown dwarfs, M-stars or stellar remnants.
There has recently been interest in multi-Solar mass Primordial Black Holes (PBHs) as a dark matter (DM) candidate. There are various microlensing, dynamical and accretion constraints on the abundance of PBHs in this mass range. Taken at face value these constraints exclude multi-Solar mass PBHs making up all of the DM for both delta-function and extended mass functions. However the stellar microlensing event rate depends on the density and velocity distribution of the compact objects along the line of sight to the Magellanic Clouds. We study the dependence of the constraints on the local dark…
Stellar microlensing observations tightly constrain compact object dark matter in the mass range $(10^{-11} - 10^{3}) M_{\odot}$. Primordial Black Holes (PBHs) form clusters, and it has been argued that these microlensing constraints are consequently weakened or evaded. For the most commonly studied PBH formation mechanism, the collapse of large gaussian curvature perturbations generated by inflation, the clusters are sufficiently extended that the PBHs within them act as individual lenses. We find that if the typical mass of the clusters is sufficiently large, $ \gtrsim 10^{6} M_{\odot}$, the…
When an image of a strongly lensed quasar is microlensed, the different components of its spectrum are expected to be differentially magnified owing to the different sizes of the corresponding emitting region. Chromatic changes are expected to be observed in the continuum while the emission lines should be deformed as a function of the size, geometry and kinematics of the regions from which they originate. Microlensing of the emission lines has been reported only in a handful of systems so far. In this paper we search for microlensing deformations of the optical spectra of pairs of images in 1…
Primordial black holes (PBHs) have long been suggested as a viable candidate for the elusive dark matter (DM). The abundance of such PBHs has been constrained using a number of astrophysical observations, except for a hitherto unexplored mass window of $M_{\rm PBH}=[10^{-14},10^{-9}]M_\odot$. Here we carry out a dense-cadence (2~min sampling rate), 7 hour-long observation of the Andromeda galaxy (M31) with the Subaru Hyper Suprime-Cam to search for microlensing of stars in M31 by PBHs lying in the halo regions of the Milky Way (MW) and M31. Given our simultaneous monitoring of tens of millions…
We report on a program of spectroscopic observations of gravitationally-lensed QSOs with multiple images. We seek to establish whether microlensing is occurring in each QSO image using only single-epoch observations. We calculate flux ratios for the cores of emission lines in image pairs to set a baseline for no microlensing. The offset of the continuum flux ratios relative to this baseline yields the microlensing magnification free from extinction, as extinction affects the continuum and the lines equally. When we find chromatic microlensing, we attempt to constrain the size of the QSO accret…
The Chandra observations of several gravitationally lensed quasars show evidence for flux and spectral variability of the X-ray emission that is uncorrelated between images and is thought to result from the microlensing by stars in the lensing galaxy. We report here on the most detailed modeling of such systems to date, including simulations of the emission of the Fe K-alpha fluorescent radiation from the accretion disk with a general relativistic ray tracing code, the use of realistic microlensing magnification maps derived from inverse ray shooting calculations, and the simulation of the lin…
We present four new seasons of optical monitoring data and six epochs of X-ray photometry for the doubly-imaged lensed quasar Q J0158-4325. The high-amplitude, short-period microlensing variability for which this system is known has historically precluded a time delay measurement by conventional methods. We attempt to circumvent this limitation by application of a Monte Carlo microlensing analysis technique, but we are only able to prove that the delay must have the expected sign (image A leads image B). Despite our failure to robustly measure the time delay, we successfully model the microlen…
We present V and R photometry of the gravitationally lensed quasars WFI2033-4723 and HE0047-1756. The data were taken by the MiNDSTEp collaboration with the 1.54 m Danish telescope at the ESO La Silla observatory from 2008 to 2012. Differential photometry has been carried out using the image subtraction method as implemented in the HOTPAnTS package, additionally using GALFIT for quasar photometry. The quasar WFI2033-4723 showed brightness variations of order 0.5 mag in V and R during the campaign. The two lensed components of quasar HE0047-1756 varied by 0.2-0.3 mag within five years. We provi…
Gravitational microlensing is one of the few means of finding primordial black holes (PBHs), if they exist. Recent LIGO detections of 30 Msun black holes have re-invigorated the search for PBHs in the 10-100 Msun mass regime. Unfortunately, individual PBH microlensing events cannot easily be distinguished from stellar lensing events from photometry alone. However, the distribution of microlensing timescales (tE, the Einstein radius crossing time) can be analyzed in a statistical sense using models of the Milky Way with and without PBHs. While previous works have presented both theoretical mode…
Cosmological gravitational microlensing has been proven to be a powerful tool to constrain the structure of multiply imaged quasars, especially the accretion disc and central supermassive black-hole system. However, the derived constraints on models may be affected by large systematic errors introduced in the various stages of modelling, namely, the macromodels, the microlensing magnification maps, and the convolution with realistic disc profiles. In particular, it has been known that different macromodels of the galaxy lens that fit the observations equally well, can lead to different values …
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 m…
We use archival data of NASA's Chandra X-ray telescope to compile an X-ray light curve of all four images of the quadruply lensed quasar Q2237+0305 (z=1.695) from January 2006 to January 2007. We fit simulated point spread functions to the four individual quasar images using Cash's C-statistic to account for the Poisson nature of the X-ray signal. The quasar images display strong flux variations up to a factor of ~4 within one month. We can disentangle the intrinsic quasar variability from flux variations due to gravitational microlensing by looking at the flux ratios of the individual quasar …
The National Research Centre Kurchatov Institute（库尔恰托夫国家研究中心）；Space Research Institute, Russian Academy of Sciences（俄罗斯科学院空间研究所）；Lebedev Physical Institute, Russian Academy of Sciences（俄罗斯科学院列别捷夫物理研究所）；National Research Nuclear University (MEPhI)（国立核研究大学（莫斯科工程物理学院））；Novosibirsk State University（新西伯利亚国立大学）；Sternberg Astronomical Institute, Moscow State University（莫斯科大学斯登伯格天文研究所）
Primordial Black Holes (PBHs) remain a Dark Matter (DM) candidate of the Standard Model of Particle Physics. Previously, we proposed a new method of constraining the remaining PBH DM mass range using microlensing of stars monitored by NASA's Kepler mission. We improve this analysis using a more accurate treatment of the population of the Kepler source stars, their variability and limb-darkening. We extend the theoretically detectable PBH DM mass range down to $2\times10^{-10} M_\sun$, two orders of magnitude below current limits and one third order of magnitude below our previous estimate. We …
If the Dark Matter consists of primordial black holes (PBHs), we show that gravitational lensing of stars being monitored by NASA's Kepler search for extra-solar planets can cause significant numbers of detectable microlensing events. A search through the roughly 150,000 lightcurves would result in large numbers of detectable events for PBHs in the mass range $5 \ten{-10}\msun$ to $\aten{-4}\msun$. Non-detection of these events would close almost two orders of magnitude of the mass window for PBH dark matter. The microlensing rate is higher than previously noticed due to a combination of the e…
We propose to use the flux variability of lensed quasar images induced by gravitational microlensing to measure the transverse peculiar velocity of lens galaxies over a wide range of redshift. Microlensing variability is caused by the motions of the observer, the lens galaxy (including the motion of the stars within the galaxy), and the source; hence, its frequency is directly related to the galaxy's transverse peculiar velocity. The idea is to count time-event rates (e.g., peak or caustic crossing rates) in the observed microlensing light curves of lensed quasars that can be compared with mod…
Measuring time delays between the multiple images of gravitationally lensed quasars is now recognized as a competitive way to constrain the cosmological parameters, and it is complementary with other cosmological probes. This requires long and well sampled optical light curves of numerous lensed quasars, such as those obtained by the COSMOGRAIL collaboration. High-quality data from our monitoring campaign call for novel numerical techniques to robustly measure the delays, as well as the associated random and systematic uncertainties, even in the presence of microlensing variations. We propose …
Recent quasar microlensing observations have constrained the sizes of X-ray emission regions to be within about 10 gravitational radii of the central supermassive black hole. Therefore, the X-ray emission from lensed quasars is first strongly lensed by the black hole before it is lensed by the foreground galaxy and star fields. We present a scheme that combines the initial strong lensing of a Kerr black hole with standard linearized microlensing by intervening stars. We find that X-ray microlensed light curves incorporating Kerr strong gravity can differ significantly from standard curves. The…
Recent observations of gravitational waves motivate investigations for the existence of Primordial Black Holes (PBHs). We propose the observation of gravitational microlensing of distant quasars for the range of infrared to the submillimeter wavelengths by sub-lunar PBHs as lenses. The advantage of observations in the longer wavelengths, comparable to the Schwarzschild radius of the lens (i.e. $R_{\rm sch}\simeq λ$) is the detection of the wave optics features of the gravitational microlensing. The observation of diffraction pattern in the microlensing light curve of a quasar can break the deg…
We show that observation of the time-dependent effect of microlensing of relativistically broadened emission lines (such as e.g. the Fe Kalpha line in X-rays) in strongly lensed quasars could provide data on celestial mechanics of circular orbits in the direct vicinity of the horizon of supermassive black holes. This information can be extracted from the observation of evolution of red / blue edge of the magnified line just before and just after the period of crossing of the innermost stable circular orbit by the microlensing caustic. The functional form of this evolution is insensitive to num…
The discovery of black-hole-binary mergers through their gravitational wave (GW) emission has reopened the exciting possibility that dark matter is made, at least partly, of primordial black holes (PBHs). However, this scenario is challenged by many observational probes that set bounds on the relative PBH abundance across a broad range of viable PBH masses. Among these bounds, the ones coming from microlensing surveys lead to the strongest constraints in the mass range from $\sim 10^{-10}$ to a few M$_{\odot}$. The upper part of this range precisely corresponds to the mass window inside which …
We present three complete seasons and two half-seasons of SDSS r-band photometry of the gravitationally lensed quasar SBS 0909+532 from the U.S. Naval Observatory, as well as two seasons each of SDSS g-band and r-band monitoring from the Liverpool Robotic Telescope. Using Monte Carlo simulations to simultaneously measure the system's time delay and model the r-band microlensing variability, we confirm and significantly refine the precision of the system's time delay to Δt_{AB} = 50^{+2}_{-4} days, where the stated uncertainties represent the bounds of the formal 1σ confidence interval. There m…
Microlensing Signatures of Dyson Sphere-like Structures around Primordial Black Holes as Technosignatures of Extraterrestrial Advanced Civilizations
Sharif University of Technology（谢里夫理工大学）；Research Center for High Energy Physics, Department of Physics, Sharif University of Technology（谢里夫理工大学物理系高能物理研究中心）
Supernova microlensing as a probe of ultracompact minihalos and primordial cosmology
Institute for Particle Physics Phenomenology, Department of Physics, Durham University（达勒姆大学粒子物理现象学研究所）；Center for Particle Cosmology, Department of Physics and Astronomy, University of Pennsylvania（宾夕法尼亚大学天体物理学与宇宙学中心）；Max Planck Institute for Gravitational Physics (Albert Einstein Institute)（马克斯·普朗克引力物理研究所（阿尔伯特·爱因斯坦研究所））；Instituto de Física Teórica UAM/CSIC（马德里自治大学/西班牙国家研究委员会理论物理研究所）
该研究提出利用超新星微引力透镜搜寻超致密小暗晕等延展暗结构，计算其探测效率并可约束原初功率谱，有望借助Vera C. Rubin天文台的LSST超新星样本成为早期宇宙物理的互补探针。
The accretion of dark matter around the primordial black holes (PBHs) could lead to the formation of surrounding minihalos, whose mass can be several orders of magnitude higher than the central PBH mass. The gravitational microlensing produced by such dressed PBHs could be quite different from that of the bare PBHs, which may significantly affect the constraints on the PBH abundance. In this paper, we study the gravitational microlensing produced by dressed PBHs in detail. We find that all the microlensing effects by dressed PBHs have asymptotic behavior depending on the minihalo size, which c…
The aim of this paper is to provide a plausible explanation for the large amplitude microlensing events observed in the cluster lensed quasar system SDSS J1004+4112. The microlensed quasar images appear to lie well clear of the stellar population of the cluster, raising the possibility that the cluster dark matter is composed of compact bodies which are responsible for the observed microlensing. In the first part of the paper we establish the exact structure of the difference light curves attributed to microlensing from photometric monitoring programmes in the literature. We then show from mea…
The recent Sumi et al (2010, 2011) detection of free roaming planet mass MACHOs in cosmologically significant numbers recalls their original detection in quasar microlening studies (Schild 1996, Colley and Schild 2003). We consider the microlensing signature of such a population, and find that the nano-lensing (microlensing) would be well characterized by a statistical microlensing theory published previously by Refsdal and Stabel (1991). Comparison of the observed First Lens microlensing amplitudes with the theoretical prediction gives close agreement and a methodology for determining the slo…
Cosmological gravitational microlensing is a useful technique for understanding the structure of the inner parts of a quasar, especially the accretion disk and the central supermassive black hole. So far, most of the cosmological microlensing studies have focused on single objects from ~90 currently known lensed quasars. However, present and planned all-sky surveys are expected to discover thousands of new lensed systems. Using a graphics processing unit (GPU) accelerated ray-shooting code, we have generated 2550 magnification maps uniformly across the convergence (κ) and shear (γ) parameter s…
Microlensing of stars, e.g. in the Galactic bulge and Andromeda galaxy (M31), is among the most robust, powerful method to constrain primordial black holes (PBHs) that are a viable candidate of dark matter. If PBHs are in the mass range $M_{\rm PBH} \lower.5ex\hbox{$\; \buildrel < \over \sim \;$} 10^{-10}M_\odot$, its Schwarzschild radius ($r_{\rm Sch}$) becomes comparable with or shorter than optical wavelength ($λ)$ used in a microlensing search, and in this regime the wave optics effect on microlensing needs to be taken into account. For a lensing PBH with mass satisfying $r_{\rm Sch}\sim λ…
AMPM II. A Lunar-Mass Primordial Black Hole Microlensing Candidate in the Milky Way Halo
Swinburne University of Technology（斯威本科技大学）；ARC Centre of Excellence for Dark Matter Particle Physics（暗物质粒子物理卓越研究中心）；Australian National University（澳大利亚国立大学）；NSF NOIRLab National Optical-Infrared Astronomy Research Laboratory（美国国家光学红外天文研究实验室）；Cerro Tololo Inter-American Observatory（塞罗托洛美洲际天文台）
We present the results of 15 years of monitoring lensed quasars, which was conducted by the COSMOGRAIL programme at the Leonhard Euler 1.2m Swiss Telescope. The decade-long light curves of 23 lensed systems are presented for the first time. We complement our data set with other monitoring data available in the literature to measure the time delays in 18 systems, among which nine reach a relative precision better than 15% for at least one time delay. To achieve this, we developed an automated version of the curve-shifting toolbox PyCS to ensure robust estimation of the time delay in the presenc…
Sub-parsec binary massive black holes (BBHs) are long anticipated to exist in many QSOs but remain observationally elusive. In this paper, we propose a novel method to probe sub-parsec BBHs through microlensing of lensed QSOs. If a QSO hosts a sub-parsec BBH in its center, it is expected that the BBH is surrounded by a circum-binary disk, each component of the BBH is surrounded by a small accretion disk, and a gap is opened by the secondary component in between the circum-binary disk and the two small disks. Assuming such a BBH structure, we generate mock microlensing light curves for some QSO…
We present an improved inverse ray-shooting code based on GPUs for generating microlensing magnification maps. In addition to introducing GPUs for acceleration, we put the efforts in two aspects: (i) A standard circular lens plane is replaced by a rectangular one to reduce the number of unnecessary lenses as a result of an extremely prolate rectangular image plane. (ii) Interpolation method is applied in our implementation which has achieved an significant acceleration when dealing with large number of lenses and light rays required by high resolution maps. With these applications, we have gre…
We constrain the abundance of primordial black holes (PBH) using 2622 microlensing events obtained from 5-years observations of stars in the Galactic bulge by the Optical Gravitational Lensing Experiment (OGLE). The majority of microlensing events display a single or at least continuous population that has a peak around the light curve timescale $t_{\rm E}\simeq 20~{\rm days}$ and a wide distribution over the range $t_{\rm E}\simeq [1, 300]~{\rm days}$, while the data also indicates a second population of 6 ultrashort-timescale events in $t_{\rm E}\simeq [0.1,0.3]~{\rm days}$, which are advoca…
We investigate gravitational microlensing signals produced by a spatially extended object transiting in front of a finite-sized source star. The most interesting features arise for lens and source sizes comparable to the Einstein radius of the setup. Using this information, we obtain constraints from the Subaru-HSC survey of M31 on the dark matter populations of NFW subhalos and boson stars of asteroid to Earth masses. These lens profiles capture the qualitative behavior of a wide range of dark matter substructures. We find that deviations from constraints on point-like lenses (e.g. primordial…
