Search

Strong gravitational lensing and microlensing of supernovae (SNe) are emerging as a new probe of cosmology and astrophysics in recent years. We provide an overview of this nascent research field, starting with a summary of the first discoveries of strongly lensed SNe. We describe the use of the time delays between multiple SN images as a way to measure cosmological distances and thus constrain cosmological parameters, particularly the Hubble constant, whose value is currently under heated debates. New methods for measuring the time delays in lensed SNe have been developed, and the sample of lensed SNe from the upcoming Rubin Observatory Legacy Survey of Space and Time (LSST) is expected to provide competitive cosmological constraints. Lensed SNe are also powerful astrophysical probes. We review the usage of lensed SNe to constrain SN progenitors, acquire high-z SN spectra through lensing magnifications, infer SN sizes via microlensing, and measure properties of dust in galaxies. The current challenge in the field is the rarity and difficulty in finding lensed SNe. We describe various methods and ongoing efforts to find these spectacular explosions, forecast the properties of the expected sample of lensed SNe from upcoming surveys particularly the LSST, and summarize the observational follow-up requirements to enable the various scientific studies. We anticipate the upcoming years to be exciting with a boom in lensed SN discoveries.

Gravitational lensing may render individual high-mass stars detectable out to cosmological distances, and several extremely magnified stars have in recent years been detected out to redshifts z≈6⁠. Here, we present Muspelheim, a model for the evolving spectral energy distributions of both metal-enriched and metal-free stars at high redshifts. Using this model, we argue that lensed stars will form a highly biased sample of the intrinsic distribution of stars across the Hertzsprung–Russell diagram, and that this bias will typically tend to favour the detection of lensed stars in evolved stages characterized by low effective temperatures, even though stars only spend a minor fraction of their lifetimes in such states. We also explore the prospects of detecting individual, lensed metal-free (Population III) stars at high redshifts using the James Webb Space Telescope (JWST). We find that very massive (≳ 100 M⁠⁠☉) Population III stars at z≳6 may potentially be detected by JWST in surveys covering large numbers of strong-lensing clusters, provided that the Population III stellar initial mass function is sufficiently top-heavy, that these stars evolve to effective temperatures ≤15000K, and that the cosmic star formation rate density of Pop III stars reaches ≳10-4 M⁠⁠☉ cMpc -3yr-1 at z≈6⁠–10. Various ways to distinguish metal-free lensed stars from metal-enriched ones are also discussed.

Gravitational lensing may render individual high-mass stars detectable out to cosmological distances, and several extremely magnified stars have in recent years been detected out to redshifts z≈6⁠. Here, we present Muspelheim, a model for the evolving spectral energy distributions of both metal-enriched and metal-free stars at high redshifts. Using this model, we argue that lensed stars will form a highly biased sample of the intrinsic distribution of stars across the Hertzsprung–Russell diagram, and that this bias will typically tend to favour the detection of lensed stars in evolved stages characterized by low effective temperatures, even though stars only spend a minor fraction of their lifetimes in such states. We also explore the prospects of detecting individual, lensed metal-free (Population III) stars at high redshifts using the James Webb Space Telescope (JWST). We find that very massive (≳ 100 M⁠⁠☉) Population III stars at z≳6 may potentially be detected by JWST in surveys covering large numbers of strong-lensing clusters, provided that the Population III stellar initial mass function is sufficiently top-heavy, that these stars evolve to effective temperatures ≤15000K, and that the cosmic star formation rate density of Pop III stars reaches ≳10-4 M⁠⁠☉ cMpc -3yr-1 at z≈6⁠–10. Various ways to distinguish metal-free lensed stars from metal-enriched ones are also discussed.

Gravitational lensing may render individual high-mass stars detectable out to cosmological distances, and several extremely magnified stars have in recent years been detected out to redshifts z≈6⁠. Here, we present Muspelheim, a model for the evolving spectral energy distributions of both metal-enriched and metal-free stars at high redshifts. Using this model, we argue that lensed stars will form a highly biased sample of the intrinsic distribution of stars across the Hertzsprung–Russell diagram, and that this bias will typically tend to favour the detection of lensed stars in evolved stages characterized by low effective temperatures, even though stars only spend a minor fraction of their lifetimes in such states. We also explore the prospects of detecting individual, lensed metal-free (Population III) stars at high redshifts using the James Webb Space Telescope (JWST). We find that very massive (≳ 100 M⁠⁠☉) Population III stars at z≳6 may potentially be detected by JWST in surveys covering large numbers of strong-lensing clusters, provided that the Population III stellar initial mass function is sufficiently top-heavy, that these stars evolve to effective temperatures ≤15000K, and that the cosmic star formation rate density of Pop III stars reaches ≳10-4 M⁠⁠☉ cMpc -3yr-1 at z≈6⁠–10. Various ways to distinguish metal-free lensed stars from metal-enriched ones are also discussed.

Gravitational lensing may render individual high-mass stars detectable out to cosmological distances, and several extremely magnified stars have in recent years been detected out to redshifts z≈6⁠. Here, we present Muspelheim, a model for the evolving spectral energy distributions of both metal-enriched and metal-free stars at high redshifts. Using this model, we argue that lensed stars will form a highly biased sample of the intrinsic distribution of stars across the Hertzsprung–Russell diagram, and that this bias will typically tend to favour the detection of lensed stars in evolved stages characterized by low effective temperatures, even though stars only spend a minor fraction of their lifetimes in such states. We also explore the prospects of detecting individual, lensed metal-free (Population III) stars at high redshifts using the James Webb Space Telescope (JWST). We find that very massive (≳ 100 M⁠⁠☉) Population III stars at z≳6 may potentially be detected by JWST in surveys covering large numbers of strong-lensing clusters, provided that the Population III stellar initial mass function is sufficiently top-heavy, that these stars evolve to effective temperatures ≤15000K, and that the cosmic star formation rate density of Pop III stars reaches ≳10-4 M⁠⁠☉ cMpc -3yr-1 at z≈6⁠–10. Various ways to distinguish metal-free lensed stars from metal-enriched ones are also discussed.

To better understand which sources contribute to optical passband fluxes of Q0957+561, we present and analyse light curves of the doubly imaged gravitationally lensed quasar from its discovery to 2023. After an early microlensing event, the difference light curves (describing delay-corrected flux ratios between the two quasar images) only show prominent microlensing gradients over the last 17 yr. In addition to these long time-scale gradients in the gr bands, we detect short time-scale, extrinsically induced differential variations that are highly correlated with the short time-scale intrinsic variability of the quasar in those bands. Both the accretion disc and the broad emission-line region (BELR) contribute to optical passband fluxes, and we also show that realistic contributions of the BELR account for the observed correlations in the gr bands. We would like to highlight that the BELR sources of optical passband fluxes of Q0957+561 should be taken into account when measuring accretion-disc source sizes from microlensing simulations.

We present JWST/NIRSpec observations of a highly magnified star candidate at a photometric redshift of zphot 4.8, previously detected in JWST/NIRCam imaging of the strong lensing (SL) cluster MACS J0647+7015 (z = 0.591). The spectroscopic observation allows us to precisely measure the redshift of the host arc at zspec = 4.758 ± 0.004, and the star’s spectrum displays clear Lyman- and Balmer-breaks commensurate with this redshift. A fit to the spectrum suggests a B-type super-giant star of surface temperature Teff,B 15 000 K with either a redder F-type companion (Teff,F 6 250 K) or significant dust attenuation (AV 0.82) along the line of sight. We also investigate the possibility that this object is a magnified young globular cluster rather than a single star. We show that the spectrum is in principle consistent with a star cluster, which could also accommodate the lack of flux variability between the two epochs. However, the lack of a counter image and the strong upper limit on the size of the object from lensing symmetry, r 0.5 pc, could indicate that this scenario is somewhat less likely – albeit not completely ruled out by the current data. The presented spectrum seen at a time when the Universe was only ∼1.2 Gyr old showcases the ability of JWST to study early stars through extreme lensing.

Along their path from source to observer, gravitational waves may be gravitationally lensed by massive objects leading to distortion in the signals. Searches for these distortions amongst the observed signals from the current detector network have already been carried out, though there have as yet been no confident detections. However, predictions of the observation rate of lensing suggest detection in the future is a realistic possibility. Therefore, preparations need to be made to thoroughly investigate the candidate lensed signals. In this work, we present some follow-up analyses that could be applied to assess the significance of such events and ascertain what information may be extracted about the lens-source system by applying these analyses to a number of O3 candidate events, even if these signals did not yield a high significance for any of the lensing hypotheses. These analyses cover the strong lensing, millilensing, and microlensing regimes. Applying these additional analyses does not lead to any additional evidence for lensing in the candidates that have been examined. However, it does provide important insight into potential avenues to deal with high-significance candidates in future observations.

We report the discovery of a transient seen in a strongly lensed arc at redshift zs = 1.2567 in Hubble Space Telescope imaging of the Abell 370 galaxy cluster. The transient is detected at 29.51 ± 0.14 AB mag in a WFC3/UVIS F200LP difference image made using observations from two different epochs, obtained in the framework of the Flashlights programme, and is also visible in the F350LP band (mF350LP ≈ 30.53 ± 0.76 AB mag). The transient is observed on the negative-parity side of the critical curve at a distance of ∼0.6 arcsec from it, greater than previous examples of lensed stars. The large distance from the critical curve yields a significantly smaller macromagnification, but our simulations show that bright, O/B-type supergiants can reach sufficiently high magnifications to be seen at the observed position and magnitude. In addition, the observed transient image is a trailing image with an observer-frame time delay of ∼+0.8 d from its expected counterpart, so that any transient lasting for longer than that should have also been seen on the minima side and is thus excluded. This, together with the blue colour we measure for the transient (mF200LP − mF350LP ≈ [−0.3, −1.6] AB), rules out most other transient candidates such as (kilo)novae, for example, and makes a lensed star the prime candidate. Assuming that the transient is indeed a lensed star as suggested, many more such events should be detected in the near future in cluster surveys with the Hubble Space Telescope and JWST.

Context. Brown dwarfs are transition objects between stars and planets that are still poorly understood, for which several competing mechanisms have been proposed to describe their formation. Mass measurements are generally difficult to carry out for isolated objects as well as for brown dwarfs orbiting low-mass stars, which are often too faint for a spectroscopic follow-up.Aims. Microlensing provides an alternative tool for the discovery and investigation of such faint systems. Here, we present an analysis of the microlensing event OGLE-2019-BLG-0033/MOA-2019-BLG-035, which is caused by a binary system composed of a brown dwarf orbiting a red dwarf.Methods. Thanks to extensive ground observations and the availability of space observations from Spitzer, it has been possible to obtain accurate estimates of all microlensing parameters, including the parallax, source radius, and orbital motion of the binary lens.Results. Following an accurate modeling process, we found that the lens is composed of a red dwarf with a mass of M-1 = 0.149 +/- 0.010 M-circle dot and a brown dwarf with a mass of M-2 = 0.0463 +/- 0.0031 M-circle dot at a projected separation of a(perpendicular to) = 0.585 au. The system has a peculiar velocity that is typical of old metal-poor populations in the thick disk. A percent-level precision in the mass measurement of brown dwarfs has been achieved only in a few microlensing events up to now, but will likely become more common in the future thanks to the Roman space telescope.

The observed magnifications and light curves of the quadruply imaged iPTF16geu supernova (SN) offers a unique opportunity to study a lens system with a variety of independent constraints. The four observed positions can be used to constrain the macrolens model. The magnifications and light curves at the four SN positions are more useful to constrain microlensing models. We define the macrolens model as a combination of a baryonic component that traces the observed light distribution, and a dark matter halo component. We constrained the macrolens model using the positional constraints given by the four observed images, and compared it with the best model obtained when magnification constraints were included. We found that the magnification cannot be explained by a macrolens model alone, and that contributions from substructures such as microlenses are needed to explain the observed magnifications. We considered microlens models based on the inferred stellar mass from the baryonic component of the macrolens model, and used the observed magnification and light curves to constrain the contribution from microlenses. We computed the likelihood of a variety of macro and micro lens models where we varied the dark matter halo, baryonic component, and microlens configurations. We used information about the position, magnification, and, for the first time, the light curves of the four observed SN images. We combined macrolens and microlens models in order to reproduce the observations; the four SN positions, magnifications, and lack of fluctuations in the light curves. After marginalizing over the model parameters, we found that larger stellar surface mass densities are preferred. This result suggests that the mass of the baryonic component is dominated by its stellar component. We conclude that microlensing from the baryonic component suffices to explain the observed flux ratios and light curves.

Context. Brown dwarfs are transition objects between stars and planets that are still poorly understood, for which several competing mechanisms have been proposed to describe their formation. Mass measurements are generally difficult to carry out for isolated objects as well as for brown dwarfs orbiting low-mass stars, which are often too faint for a spectroscopic follow-up.Aims. Microlensing provides an alternative tool for the discovery and investigation of such faint systems. Here, we present an analysis of the microlensing event OGLE-2019-BLG-0033/MOA-2019-BLG-035, which is caused by a binary system composed of a brown dwarf orbiting a red dwarf.Methods. Thanks to extensive ground observations and the availability of space observations from Spitzer, it has been possible to obtain accurate estimates of all microlensing parameters, including the parallax, source radius, and orbital motion of the binary lens.Results. Following an accurate modeling process, we found that the lens is composed of a red dwarf with a mass of M-1 = 0.149 +/- 0.010 M-circle dot and a brown dwarf with a mass of M-2 = 0.0463 +/- 0.0031 M-circle dot at a projected separation of a(perpendicular to) = 0.585 au. The system has a peculiar velocity that is typical of old metal-poor populations in the thick disk. A percent-level precision in the mass measurement of brown dwarfs has been achieved only in a few microlensing events up to now, but will likely become more common in the future thanks to the Roman space telescope.

When gravitational waves (GWs) pass through the nuclear star clusters of galactic lenses, they may be microlensed by the stars. Such microlensing can cause potentially observable beating patterns on the waveform due to waveform superposition and magnify the signal. On the one hand, the beating patterns and magnification could lead to the first detection of a microlensed GW. On the other hand, microlensing introduces a systematic error in strong lensing use-cases, such as localization and cosmography studies. By numerically solving the lensing diffraction integral, we show that diffraction effects are important when we consider GWs in the LIGO frequency band lensed by objects with masses ≲ 100M☉. We also show that the galaxy hosting the microlenses changes the lensing configuration qualitatively, so we cannot treat the microlenses as isolated point mass lenses when strong lensing is involved. We find that for stellar lenses with masses ∼1M☉, diffraction effects significantly suppress the microlensing magnification. Thus, our results suggest that GWs lensed by typical galaxy or galaxy cluster lenses may offer a relatively clean environment to study the lens system, free of contamination by stellar lenses, which can be advantageous for localization and cosmography studies.

We study light variability of gravitationally magnified high-redshift star clusters induced by a foreground population of microlenses. This arises as the incoherent superposition of light variations from many source stars traversing the random magnification pattern on the source plane. The light curve resembles a scale-invariant, Gaussian process on time-scales of years to decades, while exhibits rapid and frequent micro-caustic crossing flares of larger amplitudes on time-scales of days to months. For a concrete example, we study a young Lyman-continuum-leaking star cluster in the Sunburst Arc at z = 2.37. We show that one magnified image happens to be intervened by a foreground galaxy, and hence should exhibit a variable flux at the 1-$2{{\ \rm per\ cent}}$ level, which is measurable in space with ∼1-$3\,$ ks exposures on the Hubble Space Telescope and more easily with the James Webb Space Telescope, or even from the ground using a ∼4-m telescope without adaptive optics. Detailed measurement of this variability can help determine the absolute macro magnification and hence the intrinsic mass and length scales of the star cluster, test synthetic stellar population models, and probe multiplicity of massive stars. Furthermore, monitoring the other lensed images of the star cluster, which are free from significant intervention by foreground microlenses, can allow us to probe planetary to stellar mass compact objects constituting as little as a few per cent of the dark matter. Given the typical surface density of intracluster stars, we expect this phenomenon to be relevant for other extragalactic star clusters lensed by galaxy clusters.

Context. To a first approximation, the microlensing phenomenon is achromatic and great advancements have been achieved with regard to the interpretation of the achromatic signals, leading to the discovery and characterization of well above 100 new exoplanets. At a higher order accuracy in the observations, microlensing has a chromatic component (a color term) that has thus far been explored to a much lesser extent.Aims. Here, we analyze the chromatic microlensing effect of four different physical phenomena, which have the potential to contribute key knowledge of the stellar properties that is not easily achievable with other methods of observation. Our simulation is limited to the case of main-sequence source stars.Methods. Microlensing is particularly sensitive to giant and sub-giant stars near the Galactic center. While this population can be studied in short snapshots by the largest telescopes in the world, a general monitoring and characterization of the population can be achieved by use of more accessible medium-sized telescopes with specialized equipment via dual-color monitoring from observatories at sites with excellent seeing. We limit the results of this study to what will be achievable from the Danish 1.54 m telescope at La Silla observatory based on the use of the existing dual-color lucky imaging camera. Such potential monitoring programs of the bulge population from medium-sized telescopes include the characterization of starspots, limb-darkening, the frequency of close-in giant planet companions, and gravity darkening for blended source stars.Results. We conclude our simulations with quantifying the likelihood of detecting these different phenomena per object where they are present to be similar to 60 and similar to 30% for the above-mentioned phenomena when monitored during both high-magnification and caustic crossings, respectively.

The community may be on the verge of detecting low-frequency gravitational waves from massive black hole binaries (MBHBs), but no examples of binary active galactic nuclei (AGN) have been confirmed. Because MBHBs are intrinsically rare, the most promising detection methods utilize photometric data from all-sky surveys. Gravitational self-lensing has recently been proposed as a method of detecting AGN in close separation binaries. In this study, we calculate the detectability of lensing signatures in realistic populations of simulated MBHBs. Within our model assumptions, we find that VRO's LSST should be able to detect tens to hundreds of self-lensing binaries, with the rate uncertainty depending primarily on the orientation of AGN discs relative to their binary orbits. Roughly a quarter of lensing detectable systems should also show detectable Doppler boosting signatures. If AGN discs tend to be aligned with the orbit, lensing signatures are very nearly achromatic, while in misaligned configurations, the bluer optical bands are lensed more than redder ones. Whether substantial obscuring material (e.g. a dusty torus) will be present in close binaries remains uncertain, but our estimates suggest that a substantial fraction of systems would still be observable in this case.

Context. To a first approximation, the microlensing phenomenon is achromatic and great advancements have been achieved with regard to the interpretation of the achromatic signals, leading to the discovery and characterization of well above 100 new exoplanets. At a higher order accuracy in the observations, microlensing has a chromatic component (a color term) that has thus far been explored to a much lesser extent.Aims. Here, we analyze the chromatic microlensing effect of four different physical phenomena, which have the potential to contribute key knowledge of the stellar properties that is not easily achievable with other methods of observation. Our simulation is limited to the case of main-sequence source stars.Methods. Microlensing is particularly sensitive to giant and sub-giant stars near the Galactic center. While this population can be studied in short snapshots by the largest telescopes in the world, a general monitoring and characterization of the population can be achieved by use of more accessible medium-sized telescopes with specialized equipment via dual-color monitoring from observatories at sites with excellent seeing. We limit the results of this study to what will be achievable from the Danish 1.54 m telescope at La Silla observatory based on the use of the existing dual-color lucky imaging camera. Such potential monitoring programs of the bulge population from medium-sized telescopes include the characterization of starspots, limb-darkening, the frequency of close-in giant planet companions, and gravity darkening for blended source stars.Results. We conclude our simulations with quantifying the likelihood of detecting these different phenomena per object where they are present to be similar to 60 and similar to 30% for the above-mentioned phenomena when monitored during both high-magnification and caustic crossings, respectively.

The community may be on the verge of detecting low-frequency gravitational waves from massive black hole binaries (MBHBs), but no examples of binary active galactic nuclei (AGN) have been confirmed. Because MBHBs are intrinsically rare, the most promising detection methods utilize photometric data from all-sky surveys. Gravitational self-lensing has recently been proposed as a method of detecting AGN in close separation binaries. In this study, we calculate the detectability of lensing signatures in realistic populations of simulated MBHBs. Within our model assumptions, we find that VRO's LSST should be able to detect tens to hundreds of self-lensing binaries, with the rate uncertainty depending primarily on the orientation of AGN discs relative to their binary orbits. Roughly a quarter of lensing detectable systems should also show detectable Doppler boosting signatures. If AGN discs tend to be aligned with the orbit, lensing signatures are very nearly achromatic, while in misaligned configurations, the bluer optical bands are lensed more than redder ones. Whether substantial obscuring material (e.g. a dusty torus) will be present in close binaries remains uncertain, but our estimates suggest that a substantial fraction of systems would still be observable in this case.

Advanced LIGO and Advanced Virgo might be able to observe the first lensed gravitational waves in the coming years. With the addition of the KAGRA and LIGO India detectors to the detector network and with the future construction of the Einstein Telescope we might be able to observe hundreds of lensed events. Ground-based gravitational-wave detectors can resolve arrival-time differences on the order of the inverse of the observed frequencies. The LIGO and Virgo frequency band spans from a few Hz to a few kHz, therefore the typical time resolution of current interferometers is on the order of milliseconds. When microlenses are embedded in galaxies or galaxy clusters, lensing can become more prominent and result in observable time delays at LIGO and Virgo frequencies. Therefore, gravitational waves might offer an exciting alternative probe of microlensing. However, only a few lensing configurations have currently been worked out in the context of gravitational-wave lensing. In this paper, we present lensingGW, a Python package designed to handle both strong lensing and microlensing of compact binaries and the related gravitational-wave signals in the geometrical optics limit. This synergy paves the way for systematic parameter space investigations and for the detection of arbitrary lens configurations and compact sources. Here we focus on the LIGO and Virgo frequencies. We demonstrate the working mechanism of lensingGW and its use in studying microlenses that are embedded in galaxies.

In 2016, the first strongly lensed Type Ia supernova (SN Ia), iPTF16geu, at redshift z = 0.409 with four resolved images arranged symmetrically around the lens galaxy at z = 0.2163, was discovered. Here, refined observations of iPTF16geu, including the time delay between images, are used to decrease uncertainties in the lens model, including the the slope of the projected surface density of the lens galaxy, Sigma alpha r(1-eta), and to constrain the universal expansion rate H-0. Imaging with Hubble Space Telescope provides an upper limit on the slope., in slight tension with the steeper density profiles indicated by imaging with Keck after iPTF16geu had faded, potentially due to dust extinction not corrected for in host galaxy imaging. Since smaller. implies larger magnifications, we take advantage of the standard candle nature of SNe Ia constraining the image magnifications, to obtain an independent constraint of the slope. We find that a smooth lens density fails to explain the iPTF16geu fluxes, regardless of the slope, and additional substructure lensing is needed. The total probability for the smooth halo model combined with star microlensing to explain the iPTF16geu image fluxes is maximized at 12 per cent for eta similar to 1.8, in excellent agreement with Keck high-spatial-resolution data, and flatter than an isothermal halo. It also agrees perfectly with independent constraints on the slope from lens velocity dispersion measurements. Combining with the observed time delays between the images, we infer a lower bound on the Hubble constant, H-0 greater than or similar to 40 km s(-1) Mpc(-1), at 68.3 per cent confidence level.

In 2016, the first strongly lensed Type Ia supernova (SN Ia), iPTF16geu, at redshift z = 0.409 with four resolved images arranged symmetrically around the lens galaxy at z = 0.2163, was discovered. Here, refined observations of iPTF16geu, including the time delay between images, are used to decrease uncertainties in the lens model, including the the slope of the projected surface density of the lens galaxy, Sigma alpha r(1-eta), and to constrain the universal expansion rate H-0. Imaging with Hubble Space Telescope provides an upper limit on the slope., in slight tension with the steeper density profiles indicated by imaging with Keck after iPTF16geu had faded, potentially due to dust extinction not corrected for in host galaxy imaging. Since smaller. implies larger magnifications, we take advantage of the standard candle nature of SNe Ia constraining the image magnifications, to obtain an independent constraint of the slope. We find that a smooth lens density fails to explain the iPTF16geu fluxes, regardless of the slope, and additional substructure lensing is needed. The total probability for the smooth halo model combined with star microlensing to explain the iPTF16geu image fluxes is maximized at 12 per cent for eta similar to 1.8, in excellent agreement with Keck high-spatial-resolution data, and flatter than an isothermal halo. It also agrees perfectly with independent constraints on the slope from lens velocity dispersion measurements. Combining with the observed time delays between the images, we infer a lower bound on the Hubble constant, H-0 greater than or similar to 40 km s(-1) Mpc(-1), at 68.3 per cent confidence level.

In 2016, the first strongly lensed Type Ia supernova (SN Ia), iPTF16geu, at redshift z = 0.409 with four resolved images arranged symmetrically around the lens galaxy at z = 0.2163, was discovered. Here, refined observations of iPTF16geu, including the time delay between images, are used to decrease uncertainties in the lens model, including the the slope of the projected surface density of the lens galaxy, Sigma alpha r(1-eta), and to constrain the universal expansion rate H-0. Imaging with Hubble Space Telescope provides an upper limit on the slope., in slight tension with the steeper density profiles indicated by imaging with Keck after iPTF16geu had faded, potentially due to dust extinction not corrected for in host galaxy imaging. Since smaller. implies larger magnifications, we take advantage of the standard candle nature of SNe Ia constraining the image magnifications, to obtain an independent constraint of the slope. We find that a smooth lens density fails to explain the iPTF16geu fluxes, regardless of the slope, and additional substructure lensing is needed. The total probability for the smooth halo model combined with star microlensing to explain the iPTF16geu image fluxes is maximized at 12 per cent for eta similar to 1.8, in excellent agreement with Keck high-spatial-resolution data, and flatter than an isothermal halo. It also agrees perfectly with independent constraints on the slope from lens velocity dispersion measurements. Combining with the observed time delays between the images, we infer a lower bound on the Hubble constant, H-0 greater than or similar to 40 km s(-1) Mpc(-1), at 68.3 per cent confidence level.

In 2016, the first strongly lensed Type Ia supernova (SN Ia), iPTF16geu, at redshift z = 0.409 with four resolved images arranged symmetrically around the lens galaxy at z = 0.2163, was discovered. Here, refined observations of iPTF16geu, including the time delay between images, are used to decrease uncertainties in the lens model, including the the slope of the projected surface density of the lens galaxy, Sigma alpha r(1-eta), and to constrain the universal expansion rate H-0. Imaging with Hubble Space Telescope provides an upper limit on the slope., in slight tension with the steeper density profiles indicated by imaging with Keck after iPTF16geu had faded, potentially due to dust extinction not corrected for in host galaxy imaging. Since smaller. implies larger magnifications, we take advantage of the standard candle nature of SNe Ia constraining the image magnifications, to obtain an independent constraint of the slope. We find that a smooth lens density fails to explain the iPTF16geu fluxes, regardless of the slope, and additional substructure lensing is needed. The total probability for the smooth halo model combined with star microlensing to explain the iPTF16geu image fluxes is maximized at 12 per cent for eta similar to 1.8, in excellent agreement with Keck high-spatial-resolution data, and flatter than an isothermal halo. It also agrees perfectly with independent constraints on the slope from lens velocity dispersion measurements. Combining with the observed time delays between the images, we infer a lower bound on the Hubble constant, H-0 greater than or similar to 40 km s(-1) Mpc(-1), at 68.3 per cent confidence level.

The existence of cosmic superstrings may be probed by astronomical time domain surveys. When crossing the line of sight to point-like sources, strings produce a distinctivemicrolensing signature. We consider two avenues to hunt for a relic population of superstring loops: frequent monitoring of (1) stars in Andromeda, lensed by loops in the haloes of the Milky-Way and Andromeda and (2) supernovae at cosmological distances, lensed by loops in the intergalactic medium. We assess the potential of such experiments to detect and/or constrain strings with a range of tensions, 10(-15) less than or similar to G mu/c(2) less than or similar to 10(-6). The practical sensitivity is tied to cadence of observations which we explore in detail. We forecast that high-cadence monitoring of similar to 10(5) stars on the far side of Andromeda over a year-long period will detect microlensing events if G mu/c(2) similar to 10(-13), while similar to 10(6) stars will detect events if 10(-13.5) < G mu/c(2) < 10(-11.5); the upper and lower bounds of the accessible tension range continue to expand as the number of stars rises. We also analyse the ability to reject models in the absence of fluctuations. While challenging, these studies are within reach of forthcoming time-domain surveys. Supernova observations can hypothetically constrain models with 10(-12) < G mu/c(2) < 10(-6) without any optimization of the survey cadence. However, the event rate forecast suggests it will be difficult to reject models of interest. As a demonstration, we use observations from the Pantheon Type Ia supernova cosmology data set to place modest constraints on the number density of cosmic superstrings in a poorly tested region of the parameter space.

We study the highly magnified arc SGAS J122651.3+215220 caused by a star-forming galaxy at zs = 2.93 crossing the lensing caustic cast by the galaxy cluster SDSS J1226+2152 (zl = 0.43), using Hubble Space Telescope observations. We report in the arc several asymmetric surface brightness features whose angular separations are a fraction of an arcsecond from the lensing critical curve and appear to be highly but unequally magnified image pairs of underlying compact sources, with one brightest pair having clear asymmetry consistently across four filters. One explanation of unequal magnification is microlensing by intracluster stars, which induces independent flux variations in the images of individual or groups of source stars in the lensed galaxy. For a second possibility, intracluster dark matter subhaloes invisible to telescopes effectively perturb lensing magnifications near the critical curve and give rise to persistently unequal image pairs. Our modelling suggests, at least for the most prominent identified image pair, that the microlensing hypothesis is in tension with the absence of notable asymmetry variation over a six-year baseline, while subhaloes of ∼106-$10^8\, \mathrm{ M}_\odot$ anticipated from structure formation with cold dark matter typically produce stationary and sizable asymmetries. We judge that observations at additional times and more precise lens models are necessary to stringently constrain temporal variability and robustly distinguish between the two explanations. The arc under this study is a scheduled target of a Director's Discretionary Early Release Science program of the James Webb Space Telescope, which will provide deep images and a high-resolution view with integral field spectroscopy.

In 2016, the first strongly lensed Type Ia supernova (SN Ia), iPTF16geu, at redshift z = 0.409 with four resolved images arranged symmetrically around the lens galaxy at z = 0.2163, was discovered. Here, refined observations of iPTF16geu, including the time delay between images, are used to decrease uncertainties in the lens model, including the the slope of the projected surface density of the lens galaxy, Sigma alpha r(1-eta), and to constrain the universal expansion rate H-0. Imaging with Hubble Space Telescope provides an upper limit on the slope., in slight tension with the steeper density profiles indicated by imaging with Keck after iPTF16geu had faded, potentially due to dust extinction not corrected for in host galaxy imaging. Since smaller. implies larger magnifications, we take advantage of the standard candle nature of SNe Ia constraining the image magnifications, to obtain an independent constraint of the slope. We find that a smooth lens density fails to explain the iPTF16geu fluxes, regardless of the slope, and additional substructure lensing is needed. The total probability for the smooth halo model combined with star microlensing to explain the iPTF16geu image fluxes is maximized at 12 per cent for eta similar to 1.8, in excellent agreement with Keck high-spatial-resolution data, and flatter than an isothermal halo. It also agrees perfectly with independent constraints on the slope from lens velocity dispersion measurements. Combining with the observed time delays between the images, we infer a lower bound on the Hubble constant, H-0 greater than or similar to 40 km s(-1) Mpc(-1), at 68.3 per cent confidence level.

Gaia16aye was a binary microlensing event discovered in the direction towards the northern Galactic disc and was one of the first microlensing events detected and alerted to by the Gaia space mission. Its light curve exhibited five distinct brightening episodes, reaching up to I? =? 12 mag, and it was covered in great detail with almost 25 000 data points gathered by a network of telescopes. We present the photometric and spectroscopic follow-up covering 500 days of the event evolution. We employed a full Keplerian binary orbit microlensing model combined with the motion of Earth and Gaia around the Sun to reproduce the complex light curve. The photometric data allowed us to solve the microlensing event entirely and to derive the complete and unique set of orbital parameters of the binary lensing system. We also report on the detection of the first-ever microlensing space-parallax between the Earth and Gaia located at L2. The properties of the binary system were derived from microlensing parameters, and we found that the system is composed of two main-sequence stars with masses 0.57 ± 0.05 M? and 0.36 ± 0.03 M? at 780 pc, with an orbital period of 2.88 years and an eccentricity of 0.30. We also predict the astrometric microlensing signal for this binary lens as it will be seen by Gaia as well as the radial velocity curve for the binary system. Events such as Gaia16aye indicate the potential for the microlensing method of probing the mass function of dark objects, including black holes, in directions other than that of the Galactic bulge. This case also emphasises the importance of long-term time-domain coordinated observations that can be made with a network of heterogeneous telescopes.

In 2016, the first strongly lensed Type Ia supernova (SN Ia), iPTF16geu, at redshift z = 0.409 with four resolved images arranged symmetrically around the lens galaxy at z = 0.2163, was discovered. Here, refined observations of iPTF16geu, including the time delay between images, are used to decrease uncertainties in the lens model, including the the slope of the projected surface density of the lens galaxy, Sigma alpha r(1-eta), and to constrain the universal expansion rate H-0. Imaging with Hubble Space Telescope provides an upper limit on the slope., in slight tension with the steeper density profiles indicated by imaging with Keck after iPTF16geu had faded, potentially due to dust extinction not corrected for in host galaxy imaging. Since smaller. implies larger magnifications, we take advantage of the standard candle nature of SNe Ia constraining the image magnifications, to obtain an independent constraint of the slope. We find that a smooth lens density fails to explain the iPTF16geu fluxes, regardless of the slope, and additional substructure lensing is needed. The total probability for the smooth halo model combined with star microlensing to explain the iPTF16geu image fluxes is maximized at 12 per cent for eta similar to 1.8, in excellent agreement with Keck high-spatial-resolution data, and flatter than an isothermal halo. It also agrees perfectly with independent constraints on the slope from lens velocity dispersion measurements. Combining with the observed time delays between the images, we infer a lower bound on the Hubble constant, H-0 greater than or similar to 40 km s(-1) Mpc(-1), at 68.3 per cent confidence level.

The kinematics of isolated brown dwarfs in the Galaxy, beyond the solar neighborhood, is virtually unknown. Microlensing has the potential to probe this hidden population, as it can measure both the mass and five of the six phase-space coordinates (all except the radial velocity) even of a dark isolated lens. However, the measurements of both the microlens-parallax and finite-source effects are needed in order to recover the full information. Here, we combine the Spitzer satellite parallax measurement with the ground-based light curve, which exhibits strong finite-source effects, of event OGLE-2017-BLG-0896. We find two degenerate solutions for the lens (due to the known satellite-parallax degeneracy), which are consistent with each other except for their proper motion. The lens is an isolated brown dwarf with a mass of either 18 +/- 1 M-J or 20 +/- 1 M-J. This is the lowest isolated-object mass measurement to date, only similar to 45% more massive than the theoretical deuterium-fusion boundary at solar metallicity, which is the common definition of a free-floating planet. The brown dwarf is located at either 3.9 +/- 0.1 kpc or 4.1 +/- 0.1 kpc toward the Galactic bulge, but with proper motion in the opposite direction of disk stars, with one solution suggesting it is moving within the Galactic plane. While it is possibly a halo brown dwarf, it might also represent a different, unknown population.

KOI-3278 is a self-lensing stellar binary consisting of a white dwarf secondary orbiting a Sun-like primary star. Kruse & Agol noticed small periodic brightenings every 88.18 days in the Kepler photometry and interpreted these as the result of microlensing by a white dwarf with about 63% of the mass of the Sun. We obtained two sets of spectra for the primary that allowed us to derive three sets of spectroscopic estimates for its effective temperature, surface gravity, and metallicity for the first time. We used these values to update the Kruse & Agol Einsteinian microlensing model, resulting in a revised mass for the white dwarf of 0.539-0.020+0.022 M o. The spectra also allowed us to determine radial velocities and derive orbital solutions, with good agreement between the two independent data sets. An independent Newtonian dynamical MCMC model of the combined velocities yielded a mass for the white dwarf of 0.5122-0.0058+0.0057 M o. The nominal uncertainty for the Newtonian mass is about four times better than for the Einsteinian, ± 1.1% versus ± 4.1%, and the difference between the two mass determinations is 5.2%. We then present a joint Einsteinian microlensing and Newtonian radial velocity model for KOI-3278, which yielded a mass for the white dwarf of 0.5250-0.0089+0.0082M o. This joint model does not rely on any white dwarf evolutionary models or assumptions on the white dwarf mass-radius relation. We discuss the benefits of a joint model of self-lensing binaries, and how future studies of these systems can provide insight into the mass-radius relation of white dwarfs.

Extreme magnifications of distant objects by factors of several thousand have recently become a reality. Small, very luminous compact objects, such as supernovae (SNe), giant stars at z = 1 - 2, Pop III stars at z > 7, and even gravitational waves (GWs) from merging binary black holes near caustics of gravitational lenses can be magnified many thousands or even tens of thousands of times thanks to their small size. We explore the probability of such extreme magnifications in a cosmological context and include the effect of microlenses near critical curves. We show how the presence of microlenses near the critical curve sets a limit on the maximum magnification. We use a combination of state of the art halo mass functions, high-resolution analytical models for the density profiles, and inverse ray tracing to estimate the probability of magnification near caustics. We estimate the rate of highly magnified events in the case of SNe, GWs, and very luminous stars including Pop III stars. Our findings reveal that future observations will increase the number of events at extreme magnifications, and will open the door not only to studying individual sources at cosmic distances, but also to constraining compact dark matter candidates.

KOI-3278 is a self-lensing stellar binary consisting of a white dwarf secondary orbiting a Sun-like primary star. Kruse & Agol noticed small periodic brightenings every 88.18 days in the Kepler photometry and interpreted these as the result of microlensing by a white dwarf with about 63% of the mass of the Sun. We obtained two sets of spectra for the primary that allowed us to derive three sets of spectroscopic estimates for its effective temperature, surface gravity, and metallicity for the first time. We used these values to update the Kruse & Agol Einsteinian microlensing model, resulting in a revised mass for the white dwarf of 0.539(-0.020)(+0.022) M-circle dot. The spectra also allowed us to determine radial velocities and derive orbital solutions, with good agreement between the two independent data sets. An independent Newtonian dynamical MCMC model of the combined velocities yielded a mass for the white dwarf of 0.5122(-0.0058)(+0.0057) M-circle dot. The nominal uncertainty for the Newtonian mass is about four times better than for the Einsteinian, +/- 1.1% versus +/- 4.1%, and the difference between the two mass determinations is 5.2%. We then present a joint Einsteinian microlensing and Newtonian radial velocity model for KOI-3278, which yielded a mass for the white dwarf of 0.5250(-0.0089)(+0.0082) M-circle dot. This joint model does not rely on any white dwarf evolutionary models or assumptions on the white dwarf mass-radius relation. We discuss the benefits of a joint model of self-lensing binaries, and how future studies of these systems can provide insight into the mass-radius relation of white dwarfs.

Time delays between the multiple images of strongly gravitationally lensed Type Ia supernovae (glSNe Ia) have the potential to deliver precise cosmological constraints, but the effects of microlensing on time delay extraction have not been studied in detail. Here we quantify the effect of microlensing on the glSN Ia yield of the Large Synoptic Survey Telescope (LSST) and the effect of microlensing on the precision and accuracy of time delays that can be extracted from LSST glSNe Ia. Microlensing has a negligible effect on the LSST glSN Ia yield, but it can be increased by a factor of ∼2 over previous predictions to 930 systems using a novel photometric identification technique based on spectral template fitting. Crucially, the microlensing of glSNe Ia is achromatic until three rest-frame weeks after the explosion, making the early-time color curves microlensing-insensitive time delay indicators. By fitting simulated flux and color observations of microlensed glSNe Ia with their underlying, unlensed spectral templates, we forecast the distribution of absolute time delay error due to microlensing for LSST, which is unbiased at the sub-percent level and peaked at 1% for color curve observations in the achromatic phase, while for light-curve observations it is comparable to state-of-the-art mass modeling uncertainties (4%). About 70% of LSST glSN Ia images should be discovered during the achromatic phase, indicating that microlensing time delay uncertainties can be minimized if prompt multicolor follow-up observations are obtained. Accounting for microlensing, the 1-2 day time delay on the recently discovered glSN Ia iPTF16geu can be measured to 40% precision, limiting its cosmological utility.

We report the discovery of a giant planet in event UKIRT-2017-BLG-001, detected by the United Kingdom Infrared Telescope (UKIRT) microlensing survey. The mass ratio between the planet and its host is =-q 1.50+0.170-0.14 0.17 3, about 1.5 times the Jupiter/Sun mass ratio. The event lies 0 .35 from the Galactic center and suffers from high extinction of AK=1.68. Therefore, it could be detected only by a near-infrared (NIR) survey. The field also suffers from large spatial differential extinction, which makes it difficult to estimate the source properties required to derive the angular Einstein radius. Nevertheless, we find evidence suggesting that the source is located in the far disk. If correct, this would be the first source star of a microlensing event to be identified as belonging to the far disk. We estimate the lens mass and distance using a Bayesian analysis to find that the planet's mass is 1.28+ M0.44 J 0.37 , and it orbits a-+ 0.81 +0.21-0.27 Ṁ 0.21 star at an instantaneous projected separation of 4.18+0.96-0.88au. The system is at a distance of-6.3+16-2.1kpc, and so likely resides in the Galactic bulge. In addition, we find a non-standard extinction curve in this field, in agreement with previous results toward high-extinction fields near the Galactic center.

We report the discovery of a cold Super-Earth planet (m(p) = 4.4 +/- 0.5 M-circle plus) orbiting a low-mass (M = 0.23 +/- 0.03 M-circle dot) M dwarf at projected separation a(perpendicular to) l = 1.18 +/- 0.10 a.u., i.e., about 1.9 times the distance the snow line. The system is quite nearby for a microlensing planet, D-L = 0.86 +/- 0.09 kpc. Indeed, it was the large lens-source relative parallax pi(rel) = 1.0 mas (combined with the low mass M) that gave rise to the large, and thus well-measured, microlens parallax pi(E) proportional to (pi(rel)/M)(1)(/2) that enabled these precise measurements. OGLE-2017-BLG-1434Lb is the eighth microlensing planet with planet-host mass ratio q < 1 x 10(-4). We apply a new planet-detection sensitivity method, which is a variant of V/V-max, to seven of these eight planets to derive the mass-ratio function in this regime. We find dN/ d lnq proportional to q(P) , with p =1.05(-0.68)(+0.78), which confirms the turnover in the mass function found by Suzuki et al. relative to the power law of opposite sign n = -0.93 +/- 0.13 at higher mass ratios q greater than or similar to 2 x 10(-4). We combine our result with that of Suzuki et al. to obtain p = 0.73(-0.34)(+0.42.)

Proxima Centauri, our closest stellar neighbour, is a low-mass M5 dwarf orbiting in a triple system. An Earth-mass planet with an 11 d period has been discovered around this star. The star's mass has been estimated only indirectly using a mass-luminosity relation, meaning that large uncertainties affect our knowledge of its properties. To refine the mass estimate, an independent method has been proposed: gravitational microlensing. By taking advantage of the close passage of Proxima Cen in front of two background stars, it is possible to measure the astrometric shift caused by the microlensing effect due to these close encounters and estimate the gravitational mass of the lens (Proxima Cen). Microlensing events occurred in 2014 and 2016 with impact parameters, the closest approach of Proxima Cen to the background star, of 1.6 +/- 0.1 and 0.5 +/- 0.1 arcsec, respectively. Accurate measurements of the positions of the background stars during the last 2 yr have been obtained with Hubble Space Telescope/Wide Field Camera 3, and with Very Large Telescope/Spectro-Polarimetric High-contrast Exoplanet REsearch (SPHERE) from the ground. The SPHERE campaign started on 2015 March, and continued for more than 2 yr, covering nine epochs. The parameters of Proxima Centauri's motion on the sky, along with the pixel scale, true North, and centring of the instrument detector were readjusted for each epoch using the background stars visible in the IRDIS field of view. The experiment has been successful and the astrometric shift caused by themicrolensing effect has been measured for the second event in 2016. We used this measurement to derive a mass of 0.150(-0.051)(+0.062) (an error of similar to 40 per cent) M-circle dot for Proxima Centauri acting as a lens. This is the first and the only currently possible measurement of the gravitational mass of Proxima Centauri.

Mass measurements of gravitational microlenses require one to determine the microlens parallax pE, but precise pE measurement, in many cases, is hampered due to the subtlety of the microlens-parallax signal combined with the difficulty of distinguishing the signal from those induced by other higher-order effects. In this work, we present the analysis of the binary-lens event OGLE-2017-BLG-0329, for which pi(E) is measured with a dramatically improved precision using additional data from space-based Spitzer observations. We find that while the parallax model based on the ground-based data cannot be distinguished from a zero-pi(E) model at the 2 sigma level, the addition of the Spitzer data enables us to identify two classes of solutions, each composed of a pair of solutions according to the well-known ecliptic degeneracy. It is found that the space-based data reduce the measurement uncertainties of the north and east components of the microlens-parallax vector pE by factors similar to 18 and similar to 4, respectively. With the measured microlens parallax combined with the angular Einstein radius measured from the resolved caustic crossings, we find that the lens is composed of a binary with component masses of either (M-1, M-2) similar to (1.1, 0.8) M-circle dot or similar to(0.4, 0.3) M-circle dot according to the two solution classes. The first solution is significantly favored but the second cannot be securely ruled out based on the microlensing data alone. However, the degeneracy can be resolved from adaptive optics observations taken similar to 10 years after the event.

We report the discovery of OGLE-2016-BLG-1190Lb, which is likely to be the first Spitzer microlensing planet in the Galactic bulge/ bar, an assignation that can be confirmed by two epochs of high-resolution imaging of the combined source-lens baseline object. The planet's mass, M-p = 13.4 +/- 0.9 M-J, places it right at the deuteriumburning limit, i. e., the conventional boundary between planets and brown dwarfs. Its existence raises the question of whether such objects are really planets (formed within the disks of their hosts) or failed stars (lowmass objects formed by gas fragmentation). This question may ultimately be addressed by comparing disk and bulge/bar planets, which is a goal of the Spitzer microlens program. The host is a G dwarf, M-host = 0.89. +/- 0.07 M-circle dot, and the planet has a semimajor axis a similar to 2.0 au. We use Kepler K2 Campaign 9 microlensing data to break the lens-mass degeneracy that generically impacts parallax solutions from Earth-Spitzer observations alone, which is the first successful application of this approach. The microlensing data, derived primarily from near-continuous, ultradense survey observations from OGLE, MOA, and three KMTNet telescopes, contain more orbital information than for any previous microlensing planet, but not quite enough to accurately specify the full orbit. However, these data do permit the first rigorous test of microlensing orbital-motion measurements, which are typically derived from data taken over < 1% of an orbital period.

著者人数: 61名ほか (所属. 宇宙航空研究開発機構宇宙科学研究所(JAXA)(ISAS): 鈴木, 大介), Accepted: 2018-05-02