Lensing Events Research Articles

Predictions of the Nancy Grace Roman Space Telescope Galactic Exoplanet Survey. II. Free-floating Planet Detection Rates*

Abstract The Nancy Grace Roman Space Telescope (Roman) will perform a Galactic Exoplanet Survey (RGES) to discover bound exoplanets with semimajor axes greater than 1 au using gravitational microlensing. Roman will even be sensitive to planetary-mass objects that are not gravitationally bound to any host star. Such free-floating planetary-mass objects (FFPs) will be detected as isolated microlensing events with timescales shorter than a few days. A measurement of the abundance and mass function of FFPs is a powerful diagnostic of the formation and evolution of planetary systems, as well as the physics of the formation of isolated objects via direct collapse. We show that Roman will be sensitive to FFP lenses that have masses from that of Mars (0.1 M ⊕) to gas giants (M ≳ 100 M ⊕) as isolated lensing events with timescales from a few hours to several tens of days, respectively. We investigate the impact of the detection criteria on the survey, especially in the presence of finite-source effects for low-mass lenses. The number of detections will depend on the abundance of such FFPs as a function of mass, which is at present poorly constrained. Assuming that FFPs follow the fiducial mass function of cold, bound planets adapted from Cassan et al., we estimate that Roman will detect ∼250 FFPs with masses down to that of Mars (including ∼60 with masses ≤ M ⊕). We also predict that Roman will improve the upper limits on FFP populations by at least an order of magnitude compared to currently existing constraints.

Lensed or not lensed: determining lensing magnifications for binary neutron star mergers from a single detection

ABSTRACT Advanced LIGO and Advanced Virgo could observe the first lensed gravitational wave sources in the coming years, while the future Einstein Telescope could observe hundreds of lensed events. It is, therefore, crucial to develop methodologies to distinguish between lensed from unlensed gravitational-wave observations. A lensed signal not identified as such will lead to biases during the interpretation of the source. In particular, sources will appear to have intrinsically higher masses. No robust method currently exists to distinguish between the magnification bias caused by lensing and intrinsically high-mass sources. In this work, we show how to recognize lensed and unlensed binary neutron star systems through the measurement of their tidal effects for highly magnified sources as a proof-of-principle. The proposed method could be used to identify lensed binary neutron stars that are the chief candidate for lensing cosmography studies. We apply our method on GW190425, finding no evidence in favour of lensing, mainly due to the poor measurement of the event’s tidal effects. However, we expect that future detections with better tidal measurements can yield better constraints.

A Free-floating or Wide-orbit Planet in the Microlensing Event OGLE-2019-BLG-0551

Abstract High-cadence observations of the Galactic bulge by the microlensing surveys led to the discovery of a handful of extremely short-timescale microlensing events that can be attributed to free-floating or wide-orbit planets. Here, we report the discovery of another strong free-floating planet candidate, which was found from the analysis of the gravitational microlensing event OGLE-2019-BLG-0551. The light curve of the event is characterized by a very short duration (≲3 days) and a very small amplitude (≲0.1 mag). From modeling of the light curve, we find that the Einstein timescale, day, is much shorter, and the angular Einstein radius, μas, is much smaller than those of typical lensing events produced by stellar-mass lenses ( days, mas), indicating that the lens is very likely to be a planetary-mass object. We conduct an extensive search for possible signatures of a companion star in the light curve of the event, finding no significant evidence for the putative host star. For the first time, we also demonstrate that the angular Einstein radius of the lens does not depend on blending in the low-magnification events with strong finite source effects.

High accuracy on H0 constraints from gravitational wave lensing events

In light of the newly opened and rapidly growing gravitational waves window in multi-messenger astronomy, in order to fully take advantage of the new opportunities we are provided with, new ideas are required for a better and deeper employ of the state-of-the-art probes we handle. Following this goal, here we suggest a method to constrain the cosmological background, and the Hubble constant in particular, by future observations of gravitationally lensed radiation emitted by a single source in both the gravitational wave and the electromagnetic regimes. The lensing of the gravitational wave radiation, in fact, can leave a clear imprinting in the corresponding waveform, and we want to analyze if such kind of measurements can be successfully employed to better constrain the cosmological background. Thus, by making use of wave optics for the gravitational wave lensed signal, and of standard geometrical optics approximation for the electromagnetic one, we study the impact of different cosmological parameters on the value of the arrival time delay due to gravitational lensing, given specific gravitational wave frequencies, mass models of the lens, and redshifts and positions (with respect to the lens) of the source. Although the rate of lensing of gravitational waves is expected to be low, we show that even one single lensing event, combined with a prior on $\Omega_m$ from \textit{Planck}, could provide us with an uncertainty on $H_0$ comparable with present independent probes in a "pessimistic" scenario (with a pulsar population similar to present Pulsar Timing Array state), and of two orders smaller in an optimistic one (with a number of observed pulsars as large as that expected from the Square Kilometer Array). Thus, its role in the solution of the Hubble tension could be decisive.

Repeated gravitational lensing of gravitational waves in hierarchical black hole triples

We consider binary black holes (BBHs) in a hierarchical triple system where a more compact, less-massive binary is emitting detectable gravitational waves (GWs), and the tertiary is a supermassive BH at the center of a nuclear star cluster. As previous works have shown, the orbital motion of the outer binary can generate a detectable relativistic Doppler boost of the GWs emitted by the orbiting inner binary. We show here that for outer-binary orbits with a period of order one year, there can be a non-negligible probability for repeated gravitational lensing of the GWs emitted by the inner binary. Repeating gravitational lensing events could be detected by the LISA observatory as periodic GW amplitude spikes before the BBH enters the LIGO band. Such a detection would confirm the origin of some BBH mergers in nuclear star clusters. GW lensing also offers new testing grounds for strong gravity.

Candidate Brown-dwarf Microlensing Events with Very Short Timescales and Small Angular Einstein Radii

Abstract Short-timescale microlensing events are likely to be produced by substellar brown dwarfs (BDs), but it is difficult to securely identify BD lenses based on only event timescales because short-timescale events can also be produced by stellar lenses with high relative lens-source proper motions. In this paper, we report three strong candidate BD-lens events found from the search for lensing events not only with short timescales ( ) but also with very small angular Einstein radii ( ) among the events that have been found in the 2016–2019 observing seasons. These events include MOA-2017-BLG-147, MOA-2017-BLG-241, and MOA-2019-BLG-256, in which the first two events are produced by single lenses and the last event is produced by a binary lens. From the Monte Carlo simulations of Galactic events conducted with the combined and constraint, it is estimated that the lens masses of the individual events are , , and and the probability of the lens mass smaller than the lower limit of stars is ∼80% for all events. We point out that routine lens mass measurements of short-timescale lensing events require survey-mode space-based observations.

OGLE-2016-BLG-1227L: A Wide-separation Planet from a Very Short-timescale Microlensing Event

Abstract We present the analysis of the microlensing event OGLE-2016-BLG-1227. The light curve of this short-duration event appears to be a single-lens event affected by severe finite-source effects. Analysis of the light curve based on a single-lens single-source (1L1S) model yields very small values of the event timescale, days, and the angular Einstein radius, mas, making the lens a candidate of a free-floating planet. Close inspection reveals that the 1L1S solution leaves small residuals with an amplitude of ΔI ≲ 0.03 mag. We find that the residuals are explained by the existence of an additional widely separated heavier lens component, indicating that the lens is a wide-separation planetary system rather than a free-floating planet. From Bayesian analysis, it is estimated that the planet has a mass of and it is orbiting a low-mass host star with a mass of located with a projected separation of au. The planetary system is located in the Galactic bulge with a line-of-sight separation from the source star of kpc. The event shows that there is a range of deviations in the signatures of host stars for apparently isolated planetary lensing events and that it is possible to identify a host even when a deviation is subtle.

Model-independent Estimations for the Cosmic Curvature from the Latest Strong Gravitational Lensing Systems

Abstract Model-independent measurements for the cosmic spatial curvature, which is related to the nature of cosmic spacetime geometry, play an important role in cosmology. On the basis of the distance sum rule in the Friedmann–Lemaître–Robertson–Walker metric, (distance ratio) measurements of strong gravitational lensing (SGL) systems, together with distances from SNe Ia observations, have been proposed to directly estimate the spatial curvature without any assumptions for the theories of gravity and contents of the universe. However, previous studies indicated that a spatially closed universe was strongly preferred. In this paper, we re-estimate the cosmic curvature with the latest SGL data, which includes 163 well-measured systems. In addition, possible factors, e.g., a combination of SGL data from different surveys and stellar masses of the lens galaxy, which might affect estimations for the spatial curvature, are considered in our analysis. We find that, except for the case where only SGL systems from the Sloan Lens ACS Survey are considered, a spatially flat universe is consistently favored at very high confidence levels by the latest observations. It has been suggested that an increasing number of well-measured strong lensing events might significantly reduce the bias of estimation for the cosmic curvature.

Fast Computational Convolution Methods for Extended Source Effects in Microlensing Light Curves

Abstract Extended source effects can be seen in gravitational lensing events when sources cross critical lines. Such events probe the stellar intensity profile and could be used to measure limb-darkening coefficients to test stellar model predictions. A database of accurately measured stellar profiles is needed to correctly subtract the stellar flux in planetary transient events. The amount of data that is being produced and that will be produced in current and future microlensing surveys, from both space and ground, requires algorithms that can quickly compute light curves for different source-lens configurations. Based on the convolution method, we describe a general formalism to compute those curves for single lenses. We develop approximations in terms of quadratures of elliptic integrals that we integrate by solving the associated first-order differential equations. We construct analytic solutions for a limb darkening and, for the first time, for a parabolic profile that are accurate at the ∼1%–3% and 0.5% level, respectively. These solutions can be computed orders of magnitude faster than other integration routines. They can be implemented in pipelines processing large data sets to extract stellar parameters in real time.

SHALOS: StatisticalHerschel-ATLAS lensed objects selection

Context. The statistical analysis of large sample of strong lensing events can be a powerful tool to extract astrophysical or cosmological valuable information. Their selection using submillimetre galaxies has been demonstrated to be very effective with more than ∼200 proposed candidates in the case ofHerschel-ATLAS data and several tens in the case of the South Pole Telescope. However, the number of confirmed events is still relatively low, i.e. a few tens, mostly because of the lengthy observational validation process on individual events.Aims. In this work we propose a new methodology with a statistical selection approach to increase by a factor of ∼5 the number of such events within theHerschel-ATLAS data set. Although the methodology can be applied to address several selection problems, it has particular benefits in the case of the identification of strongly lensed galaxies: objectivity, minimal initial constrains in the main parameter space, and preservation of statistical properties.Methods. The proposed methodology is based on the Bhattacharyya distance as a measure of the similarity between probability distributions of properties of two different cross-matched galaxies. The particular implementation for the aim of this work is called SHALOS and it combines the information of four different properties of the pair of galaxies: angular separation, luminosity percentile, redshift, and the ratio of the optical to the submillimetre flux densities.Results. The SHALOS method provides a ranked list of strongly lensed galaxies. The number of candidates within ∼340 deg2of theHerschel-ATLAS surveyed area for the final associated probability,Ptot > 0.7, is 447 and they have an estimated mean amplification factor of 3.12 for a halo with a typical cluster mass. Additional statistical properties of the SHALOS candidates, as the correlation function or the source number counts, are in agreement with previous results indicating the statistical lensing nature of the selected sample.

Primordial Black Hole Microlensing: The Einstein Crossing Time Distribution

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 models and observational constrains for PBHs (e.g. Calcino et al. 2018; Niikura et al. 2019), surprisingly, they rarely show the observed quantity -- the tE distribution -- for different abundances of PBHs relative to the total dark matter mass (fPBH). We present a simple calculation of how the tE distribution changes between models with and without PBHs.

Search for Gravitational Lensing Signatures in LIGO-Virgo Binary Black Hole Events

Abstract We search for signatures of gravitational lensing in the binary black hole events detected by Advanced LIGO and Virgo during their first two observational runs. In particular, we look for three effects: (1) evidence of lensing magnification in the individual signals due to galaxy lenses, (2) evidence of multiple images due to strong lensing by galaxies, and (3) evidence of wave optics effects due to point-mass lens. We find no compelling evidence of any of these signatures in the observed gravitational wave signals. However, as the sensitivities of gravitational wave detectors improve in the future, detecting lensed events may become quite likely.

Optical analysis of a CMB cosmic string candidate

The complexity of the cosmological scenario regarding cosmic strings (CSs) stands still in the way of a complete understanding. We describe here a promising strategy for the possible detection of these elusive physical entities. It is based on the search of strong gravitational lensing events in the location area of the CS candidate (CSc-1), which was declared in a previous work by CMB analysis. Using photometric and geometric criteria, we identified pairs of candidates of lensed galaxies (LGCs) in the "string field" (SF), which were then compared with the average density of background galaxy pairs in a set of "control fields" (CFs). We found an excess of $22\%$ (per sq. deg.) of the LGCs in SF, which exceeds the estimated cosmic dispersion. We also found that the number of LGCs is in excess of $29.2\%$ in the angular separation bin $[8'', 9'']$. Finally, we analysed the possibility of a preferred orientation of the line connecting the centres of the LGCs. The orientation is statistically significant for an angular separation bin $[4'',6'']$. Therefore, we found two "windows" for the preferred angular separation for LGCs along the possible CS. However, the confirmation of the gravitational lensing origin of our LGCs requires spectroscopic observations which seem to be justified by the present results. We plan to acquire their spectra as well as to continue the study of the spectral and morphological features of the LGCs in the CSc-1 field and to analyse the other CS-candidates using the same strategy.

Constraining magnetic fields through plasma lensing: application to the Black Widow pulsar

In regions with strongly varying electron density, radio emission can be magnified significantly by plasma lensing. In the presence of magnetic fields, magnification in time and frequency will be different for two circular polarizations. We show how these effects can be used to measure or constrain the magnetic field parallel to the line of sight, $B_\parallel$, as well as its spatial structure, $\sigma_{B_\parallel}$, in the lensing region. In addition, we discuss how generalized Faraday rotation can constrain the strength of the perpendicular field, $B_\perp$. We attempt to make such measurements for the Black Widow pulsar, PSR~B1957+20, in which plasma lensing was recently discovered. For this system, pressure equilibrium suggests $B\gtrsim 20\,$G at the interface between the pulsar and companion winds, where the radio eclipse starts and ends, and where most lensing occurs. We find no evidence for large-scale magnetic fields, with, on average, $B_\parallel=0.02\pm0.09\,$G over the egress lensing region. From individual lensing events, we strongly constrain small scale magnetic structure to $\sigma_B<10\,$mG, thus excluding scenarios with a strong but rapidly varying field. Finally, from the lack of reduction of average circular polarization in the same region, we rule out a strong, quasi-transverse field. We cannot identify any plausible scenario in which a large magnetic field in this system is concealed, leaving the nature of the interface between the pulsar and companion winds an enigma. Our method can be applied to other sources showing plasma lensing, including other eclipsing pulsars and fast radio bursts, to study the local properties of the magnetic field.

Strong lensing of gamma ray bursts as a probe of compact dark matter

Compact dark matter has been efficiently constrained in the M <~ 10 M_sun mass range by null searches for microlensing of stars in nearby galaxies. Here we propose to probe the mass range M >~ 10 M_sun by seeking echoes in gamma-ray-burst light curves induced by strong lensing. We show that strong gravitational lensing of gamma ray bursts (GRBs) by massive compact halo objects (MACHOs) generates superimposed GRB images with a characteristic time delay of >~ 1 ms for M >~ 10 M_sun. Using dedicated simulations to capture the relevant phenomenology of the GRB prompt emission, we calculate the signal-to-noise ratio required to detect GRB lensing events as a function of the flux ratio and time delay between the lensed images. We then analyze existing data from the Fermi/GBM and Swift/BAT instruments to assess their constraining power on the compact dark matter fraction f_DM. We find that this data is noise limited, and therefore localization-based masking of background photons is a key ingredient. Future observatories with better sensitivity will be able to probe down to the f_ DM >~ 1% level across the 10 M_sun <~ M <~ 1000 M_sun mass range.

Detecting stellar lensing of gravitational waves with ground-based observatories

We investigate the ability of ground based gravitational wave observatories to detect gravitational wave lensing events caused by stellar mass lenses. We show that LIGO and Virgo possess the sensitivities required to detect lenses with masses as small as $\sim 30 M_\odot$ provided that the gravitational wave is observed with a signal-to-noise ratio of $\sim30$. Third generation observatories will allow detection of gravitational wave lenses with masses of $\sim 1 M_\odot$. Finally, we discuss the possibility of lensing by multiple stars, as is the case if the gravitational radiation is passing through galactic nucleus or a dense star cluster.

MOA-2016-BLG-319Lb: Microlensing Planet Subject to Rare Minor-image Perturbation Degeneracy in Determining Planet Parameters

Abstract We present the analysis of the planetary microlensing event MOA-2016-BLG-319. The event light curve is characterized by a brief (∼3 days) anomaly near the peak produced by minor-image perturbations. From modeling, we find two distinct solutions that describe the observed light curve almost equally as well. From the investigation of the lens-system configurations, we find that the confusion in the lensing solution is caused by the degeneracy between the two solutions resulting from the source passages on different sides of the planetary caustic. These degeneracies can be severe for major-image perturbations, but it is known that they are considerably less severe for minor-image perturbations. From the comparison of the lens-system configuration with those of two previously discovered planetary events, for which similar degeneracies were reported, we find that the degeneracies are caused by the special source trajectories that passed the star–planet axes at approximately right angles. By conducting a Bayesian analysis, it is estimated that the lens is a planetary system in which a giant planet with a mass ( ) is orbiting a low-mass M-dwarf host with a mass . Here the planet masses in and out of the parentheses represent the masses for the individual degenerate solutions. The projected host-planet separations are a ⊥ ∼ 0.95 and ∼1.05 au for the two solutions. The identified degeneracy indicates the need to check similar degeneracies in future analyses of planetary lensing events with minor-image perturbations.

Toward the Measurement of the Mass of Isolated Neutron Stars: Prediction of Future Astrometric Microlensing Events by Pulsars

Abstract The mass of single neutron stars (NSs) can be measured using astrometric microlensing events. In such events, the center-of-light motion of a star lensed by an NS will deviate from the expected nonlensed motion and this deviation can be used to measure the mass of the NS. I search for future conjunctions between pulsars, with measured proper motion, and stars in the GAIA-DR2 catalog. I identify two candidate events of stars involving lensing by a foreground pulsar in which the estimated light deflection of the background star will deviate from the nonlensed motion by more than 10 μas. PSR J185635−375435 passed ≅4.″1 from a 19.4 G magnitude star on J2014.9 with an estimated deflection of 13 μas, while PSR J084606−353340 may pass ∼0.″2 from a 19.0 G magnitude star on J2022.9 with an estimated deflection of 91 μas. However, the proper motion of the second event is highly uncertain. Therefore, additional observations are required in order to verify this event. I briefly discuss the opposite case, in which a pulsar is being lensed by a star. Such events can be used to measure the stellar mass via pulsar timing measurements. I do not find good candidates for such events with predicted variations in the pulsar period derivative ( ), divided by 1 s, exceeding 10−20 s−1. Since only about 10% of the known pulsars have measured proper motions, there is potential for an increase in the number of predicted pulsar lensing events.

KMT-2016-BLG-2052L: Microlensing Binary Composed of M Dwarfs Revealed from a Very Long Timescale Event

Abstract We present the analysis of a binary microlensing event, KMT-2016-BLG-2052, for which the lensing-induced brightening of the source star lasted for two seasons. We determine the lens mass from the combined measurements of the microlens parallax, π E, and angular Einstein radius, θ E. The measured mass indicates that the lens is a binary composed of M dwarfs with masses of M 1 ∼ 0.34 M ⊙ and M 2 ∼ 0.17 M ⊙. The measured relative lens-source proper motion of μ ∼ 3.9 mas yr−1 is smaller than ∼5 mas yr−1 of typical Galactic lensing events, while the estimated angular Einstein radius of θ E ∼ 1.2 mas is substantially greater than the typical value of ∼0.5 mas. Therefore, it turns out that the long timescale of the event is caused by the combination of the slow μ and large θ E rather than the heavy mass of the lens. From the simulation of Galactic lensing events with very long timescales (t E ≳ 100 days), we find that the probabilities that long timescale events are produced by lenses with masses ≥1.0 M ⊙ and ≥3.0 M ⊙ are ∼19% and 2.6%, respectively, indicating that events produced by heavy lenses comprise a minor fraction of long timescale events. The results indicate that it is essential to determine lens masses by measuring both π E and θ E in order to firmly identify heavy stellar remnants, such as neutron stars and black holes.

Twenty years of photometric microlensing events predicted by Gaia DR2

Context. Gaia Data Release 2 (DR2) offers unparalleled precision on stars’ parallaxes and proper motions. This allows the prediction of microlensing events for which the lens stars (and any planets they possess) are nearby and may be well studied and characterised. Aims. We identify a number of potential microlensing events that will occur before the year 2035.5, 20 years from the Gaia DR2 reference epoch. Methods. We query Gaia DR2 for potential lenses within 100 pc, extract parallaxes and proper motions of the lenses and background sources, and identify potential lensing events. We estimate the lens masses from Priam effective temperatures and use these to calculate peak magnifications and the size of the Einstein radii relative to the lens stars’ habitable zones. Results. We identify seven future events with a probability &gt;10% of an alignment within one Einstein radius. Of particular interest is DR2 5918299904067162240 (WISE J175839.20–583931.6), magnitude G = 14.9, which will lens a G = 13.9 background star in early 2030, with a median 23% net magnification. Other pairs are typically fainter, hampering characterisation of the lens (if the lens is faint) or the ability to accurately measure the magnification (if the source is much fainter than the lens). Of timely interest is DR2 4116504399886241792 (2MASS J17392440–2327071), which will lens a background star in July 2020, albeit with weak net magnification (0.03%). Median magnifications for the other five high-probability events range from 0.3% to 5.3%. The Einstein radii for these lenses are one to ten times the radius of the habitable zone, allowing these lensing events to pick out cold planets around the ice line, and filling a gap between transit and current microlensing detections of planets around very low-mass stars. Conclusions. We provide a catalogue of the predicted events to aid future characterisation efforts. Current limitations include a lack of many high-proper-motion objects in Gaia DR2 and often large uncertainties on the proper motions of the background sources (or only two-parameter solutions). Both of these deficiencies will be rectified with Gaia DR3 in 2020. Further characterisation of the lenses is also warranted to better constrain their masses and predict the photometric magnifications.