arXiv subjects

Tom Broadhurst

Publications and source records attributed to Tom Broadhurst.

At least 55 records · Page 3Linked to original sources

arXiv2023

A Magnified Compact Galaxy at Redshift 9.51 with Strong Nebular Emission Lines

Ultraviolet light from early galaxies is thought to have ionized gas in the intergalactic medium. However, there are few observational constraints on this epoch because of the faintness of those galaxies and the redshift of their optical light into the infrared. We report the observation, in JWST imaging, of a distant galaxy that is magnified by gravitational lensing. JWST spectroscopy of the galaxy, at rest-frame optical wavelengths, detects strong nebular emission lines that are attributable to oxygen and hydrogen. The measured redshift is z = 9.51 +- 0.01, corresponding to 510 million years after the Big Bang. The galaxy has a radius of 16.2+4.6-7.2 parsecs, which is substantially more compact than galaxies with equivalent luminosity at z = 6 to 8, leading to a high star formation rate surface density.

astro-ph.GA↗

arXiv2023

The Magnificent Five Images of Supernova Refsdal: Time Delay and Magnification Measurements

In late 2014, four images of Supernova (SN) "Refsdal," the first known example of a strongly lensed SN with multiple resolved images, were detected in the MACS J1149 galaxy-cluster field. Following the images' discovery, the SN was predicted to reappear within hundreds of days at a new position ~8 arcseconds away in the field. The observed reappearance in late 2015 makes it possible to carry out Refsdal's (1964) original proposal to use a multiply imaged SN to measure the Hubble constant H0, since the time delay between appearances should vary inversely with H0. Moreover, the position, brightness, and timing of the reappearance enable a novel test of the blind predictions of galaxy-cluster models, which are typically constrained only by the positions of multiply imaged galaxies. We have developed a new photometry pipeline that uses DOLPHOT to measure the fluxes of the five images of SN Refsdal from difference images. We apply four separate techniques to perform a blind measurement of the relative time delays and magnification ratios (mu_i/mu_1) between the last image SX and the earlier images S1-S4. We measure the relative time delay of SX-S1 to be 376.0+5.6-5.5 days and the relative magnification to be 0.30+0.05-0.03. This corresponds to a 1.5% precision on the time delay and 17% precision for the magnification ratios, and includes uncertainties due to millilensing and microlensing. In an accompanying paper, we place initial and blind constraints on the value of the Hubble constant.

astro-ph.CO↗

arXiv2023

Early Results from GLASS-JWST. XIX: A High Density of Bright Galaxies at $z\approx10$ in the Abell 2744 Region

We report the detection of a high density of redshift $z\approx 10$ galaxies behind the foreground cluster Abell 2744, selected from imaging data obtained recently with NIRCam onboard {\it JWST} by three programs -- GLASS-JWST, UNCOVER, and DDT\#2756. To ensure robust estimates of the lensing magnification $μ$, we use an improved version of our model that exploits the first epoch of NIRCam images and newly obtained MUSE spectra, and avoids regions with $μ>5$ where the uncertainty may be higher. We detect seven bright $z\approx 10$ galaxies with demagnified rest-frame $-22 \lesssim M_{\rm UV}\lesssim -19$ mag, over an area of $\sim37$ sq. arcmin. Taking into account photometric incompleteness and the effects of lensing on luminosity and cosmological volume, we find that the density of $z\approx 10$ galaxies in the field is about $10\times$ ($3\times$) larger than the average at $M_{UV}\approx -21~ (-20)$ mag reported so far. The density is even higher when considering only the GLASS-JWST data, which are the deepest and the least affected by magnification and incompleteness. The GLASS-JWST field contains 5 out of 7 galaxies, distributed along an apparent filamentary structure of 2 Mpc in projected length, and includes a close pair of candidates with $M_{\rm UV}< -20$ mag having a projected separation of only 16 kpc. These findings suggest the presence of a $z\approx 10$ overdensity in the field. In addition to providing excellent targets for efficient spectroscopic follow-up observations, our study confirms the high density of bright galaxies observed in early {\it JWST} observations, but calls for multiple surveys along independent lines of sight to achieve an unbiased estimate of their average density and a first estimate of their clustering.

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arXiv2023

Flashlights: An Off-Caustic Lensed Star at Redshift $z$ = 1.26 in Abell 370

We report the discovery of a transient seen in a strongly lensed arc at redshift $z_{\rm s}=1.2567$ in \emph{Hubble Space Telescope} imaging of the Abell 370 galaxy cluster. The transient is detected at $29.51\pm0.14$ AB mag in a WFC3/UVIS F200LP difference image made using observations from two different epochs, obtained in the framework of the \emph{Flashlights} program, and is also visible in the F350LP band ($m_{\rm F350LP} \approx 30.53\pm0.76$ AB mag). The transient is observed on the negative-parity side of the critical curve at a distance of $\sim 0.6"$ 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 $\sim+0.8$ days 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 ($m_{\rm F200LP} - m_{\rm F350LP} \approx [-0.3,-1.6]$ AB), rules out most other transient candidates such as (kilo)novae, for example, and makes a lensed star the prime candidate. Assuming 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 \emph{Hubble Space Telescope} and \emph{James Webb Space Telescope}.

astro-ph.CO↗

arXiv2023

Unscrambling the lensed galaxies in JWST images behind SMACS0723

The first deep field images from the James Webb Space Telescope (JWST) of the galaxy cluster SMACS~J0723.3-7327 reveal a wealth of new lensed images at uncharted infrared wavelengths, with unprecedented depth and resolution. Here we securely identify 14 new sets of multiply imaged galaxies totalling 42 images, adding to the five sets of bright and multiply-imaged galaxies already known from Hubble Space Telescope data. We find examples of arcs crossing critical curves, allowing detailed community follow-up, such as JWST spectroscopy for precise redshift determinations, and measurements of the chemical abundances and of the detailed internal gas dynamics of very distant, young galaxies. One such arc contains a pair of compact knots that are magnified by a factor of hundreds, and features a microlensed transient. We also detect an Einstein cross candidate only visible thanks to JWST's superb resolution. Our parametric lens model is available through the following link: https://www.dropbox.com/sh/gwup2lvks0jsqe5/AAC2RRSKce0aX-lIFCc9vhBXa?dl=0, and will be regularly updated using additional spectroscopic redshifts. The model is constrained by 16 of these sets of multiply imaged galaxies, three of which have spectroscopic redshifts, and reproduces the multiple images to better than an rms of $0.5^{\prime \prime}$, allowing for accurate magnification estimates of high-redshift galaxies. The intracluster light extends beyond the cluster members, exhibiting large-scale features that suggest a significant past dynamical disturbance. This work represents a first taste of the enhanced power JWST will have for lensing-related science.

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arXiv2022

JWST's PEARLS: A JWST/NIRCam view of ALMA sources

We report the results of James Webb Space Telescope/NIRCam observations of 19 (sub)millimeter (submm/mm) sources detected by the Atacama Large Millimeter Array (ALMA). The accurate ALMA positions allowed unambiguous identifications of their NIRCam counterparts. Taking gravitational lensing into account, these represent 16 distinct galaxies in three fields and constitute the largest sample of its kind to date. The counterparts' spectral energy distributions from rest-frame ultraviolet to near infrared provide photometric redshifts ($1 10^{10.5}$ Msol), which are similar to sub-millimeter galaxy (SMG) hosts studied previously. However, our sample is fainter in submm/mm than the classic SMG samples are, and our sources exhibit a wider range of properties. They have dust-embedded star-formation rates as low as 10 Msol yr$^{-1}$, and the sources populate both the star-forming main sequence and the quiescent categories. The deep NIRCam data allow us to study the rest-frame near-IR morphologies. Excluding two multiply imaged systems and one quasar, the majority of the remaining sources are disk-like and show either little or no disturbance. This suggests that secular growth is a potential route for the assembly of high-mass disk galaxies. While a few hosts have large disks, the majority have small disks (median half-mass radius of 1.6 kpc). At this time, it is unclear whether this is due to the prevalence of small disks at these redshifts or some unknown selection effects of deep ALMA observations. A larger sample of ALMA sources with NIRCam observations will be able to address this question.

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arXiv2022

JWST Imaging of Earendel, the Extremely Magnified Star at Redshift $z=6.2$

The gravitationally lensed star WHL0137-LS, nicknamed Earendel, was identified with a photometric redshift $z_{phot} = 6.2 \pm 0.1$ based on images taken with the Hubble Space Telescope. Here we present James Webb Space Telescope (JWST) Near Infrared Camera (NIRCam) images of Earendel in 8 filters spanning 0.8--5.0$μ$m. In these higher resolution images, Earendel remains a single unresolved point source on the lensing critical curve, increasing the lower limit on the lensing magnification to $μ> 4000$ and restricting the source plane radius further to $r < 0.02$ pc, or $\sim 4000$ AU. These new observations strengthen the conclusion that Earendel is best explained by an individual star or multiple star system, and support the previous photometric redshift estimate. Fitting grids of stellar spectra to our photometry yields a stellar temperature of $T_{\mathrm{eff}} \simeq 13000$--16000 K assuming the light is dominated by a single star. The delensed bolometric luminosity in this case ranges from $\log(L) = 5.8$--6.6 $L_{\odot}$, which is in the range where one expects luminous blue variable stars. Follow-up observations, including JWST NIRSpec scheduled for late 2022, are needed to further unravel the nature of this object, which presents a unique opportunity to study massive stars in the first billion years of the universe.

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arXiv2022

The miniJPAS Survey: Detection of double-core Lyα morphology of two high-redshift (z>3) QSOs

The Ly$α$ emission is an important tracer of neutral gas in a circum-galactic medium (CGM) around high-z QSOs. The origin of Lya emission around QSOs is still under debate which has significant implications for galaxy formation and evolution. In this paper, we study Ly$α$ nebulae around two high redshift QSOs, SDSS J141935.58+525710.7 at $z=3.218$ (hereafter QSO1) and SDSS J141813.40+525240.4 at $z=3.287$ (hereafter QSO2), from the miniJPAS survey within the AEGIS field. Using the contiguous narrow-band (NB) images from the miniJPAS survey and SDSS spectra, we analyzed their morphology, nature, and origin. We report the serendipitous detection of double-core Ly\al\ morphology around two QSOs which is rarely seen among other QSOs. The separations of the two Ly\al~cores are 11.07 $\pm$ 2.26 kpcs (1.47 $\pm$ 0.3$^{\prime\prime}$) and 9.73 $\pm$ 1.55 kpcs (1.31 $\pm$ 0.21$^{\prime\prime}$) with Ly$α$~line luminosities of $\sim$ 3.35 $\times 10^{44}$ erg s $^{-1} $ and $\sim$ 6.99 $\times$ 10$^{44}$ erg s $^{-1}$ for QSO1 and QSO2, respectively. The miniJPAS NB images show evidence of extended Ly$α$ and CIV morphology for both QSOs and extended HeII morphology for QSO1. These two QSOs may be potential candidates for the new enormous Lyman alpha nebula (ELAN) found from the miniJPAS survey due to their extended morphology in the shallow depth and relatively high Ly$α$ luminosities. We suggest that galactic outflows are the major powering mechanism for the double-core Ly$α$ morphology. Considering the relatively shallow exposures of miniJPAS, the objects found here could be the tip of the iceberg of a promising number of such objects that will be uncovered in the upcoming full J-PAS survey and deep IFU observations with 8-10m telescopes will be essential for constraining the underlying physical mechanism that is responsible for the double-cored morphology.

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arXiv2022

JWST's PEARLS: a new lens model for ACT-CL J0102$-$4915, "EL Gordo'', and the first red supergiant star at cosmological distances discovered by JWST

The first JWST data on the massive colliding cluster El Gordo confirm 23 known families of multiply lensed images and identify 8 new members of these families. Based on these families, which have been confirmed spectroscopically by MUSE, we derived an initial lens model. This model guided the identification of 37 additional families of multiply lensed galaxies, among which 28 are entirely new systems, and 9 were previously known. The initial lens model determined geometric redshifts for the 37 new systems. The geometric redshifts agree reasonably well with spectroscopic or photometric redshifts when those are available. The geometric redshifts enable two additional models that include all 60 families of multiply lensed galaxies spanning a redshift range $2 0.8$ and has an estimated virial mass close the maximum mass allowed by standard cosmological models. The JWST images also reveal the presence of small-mass perturbers that produce small lensing distortions. The smallest of these is consistent with being a dwarf galaxy at $z=0.87$ and has an estimated mass of $3.8\times10^9$~\Msol, making it the smallest substructure found at $z>0.5$. The JWST images also show several candidate caustic-crossing events. One of them is detected at high significance at the expected position of the critical curve and is likely a red supergiant star at $z=2.1878$. This would be the first red supergiant found at cosmological distances. The cluster lensing should magnify background objects at $z>6$, making more of them visible than in blank fields of similar size, but there appears to be a deficiency of such objects.

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arXiv2022

A Highly Magnified Star at Redshift 6.2

Galaxy clusters magnify background objects through strong gravitational lensing. Typical magnifications for lensed galaxies are factors of a few but can also be as high as tens or hundreds, stretching galaxies into giant arcs. Individual stars can attain even higher magnifications given fortuitous alignment with the lensing cluster. Recently, several individual stars at redshift $z \sim 1 - 1.5$ have been discovered, magnified by factors of thousands, temporarily boosted by microlensing. Here we report observations of a more distant and persistent magnified star at redshift $z_{\rm phot} = 6.2 \pm 0.1$, 900 Myr after the Big Bang. This star is magnified by a factor of thousands by the foreground galaxy cluster lens WHL0137--08 ($z = 0.566$), as estimated by four independent lens models. Unlike previous lensed stars, the magnification and observed brightness (AB mag 27.2) have remained roughly constant over 3.5 years of imaging and follow-up. The delensed absolute UV magnitude $M_{UV} = -10 \pm 2$ is consistent with a star of mass $M > 50 M_{\odot}$. Confirmation and spectral classification are forthcoming from approved observations with the James Webb Space Telescope

astro-ph.GA↗

arXiv2022

Panic! At the Disks: First Rest-frame Optical Observations of Galaxy Structure at $z > 3$ with JWST in the SMACS 0723 Field

We present early results regarding the morphological and structural properties of galaxies seen with the James Webb Space Telescope at $z > 3$ in the Early Release Observations of SMACS 0723, a galaxy cluster at $z=0.39$. We investigate, for the first time, the optical morphologies of a significant number of $z > 3$ galaxies with accurate photometric redshifts in this field to determine the form of galaxy structure in the relatively early universe. We use visual morphologies and \textsc{Morfometryka} measures to perform quantitative morphology measurements, both parametric with light profile fitting (Sérsic indices) and non-parametric (CAS values). Using these, we measure the relative fraction of disk, spheroidal, and peculiar galaxies at $3 < z < 8$. We discover the surprising result that at $z > 1.5$ disk galaxies dominate the overall fraction of morphologies, with a factor of $\sim 10$ relative higher number of disk galaxies than seen by the Hubble Space Telescope at these redshifts. Our visual morphological estimates of galaxies align closely with their locations in CAS parameter space and their Sérsic indices.

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arXiv2021

An analytic model for the sub-galactic matter power spectrum in fuzzy dark matter halos

Fuzzy dark matter (FDM), a scalar particle coupled to the gravitational field without self-interaction whose mass range is $m \sim 10^{-24} - 10^{-20}\ \rm{eV}$, is one of the promising alternative dark matter candidates to cold dark matter. The quantum interference pattern, which is a unique structure of FDM, can be seen in halos in cosmological FDM simulations. In this paper, we first provide an analytic model of the sub-galactic matter power spectrum originating from quantum clumps in FDM halos, in which the density distribution of the FDM is expressed by a superposition of quantum clumps whose size corresponds to the de Broglie wavelength of the FDM. These clumps are assumed to be distributed randomly such that the ensemble averaged density follows the halo profile such as the Navarro-Frenk-White profile. We then compare the convergence power spectrum projected along the line of sight around the Einstein radius, which is converted from the sub-galactic matter power spectrum, to that measured in the strong lens system SDSS J0252+0039. While we find that the current observation provides no useful constraint on the FDM mass, we show that future deep, high spatial resolution observations of strong lens systems can tightly constrain FDM with the mass around $10^{-22}\ \rm{eV}$.

astro-ph.CO↗

arXiv2021

Evidence for lensing of gravitational waves from LIGO-Virgo

Recently, the LIGO-Virgo Collaboration (LVC) concluded that there is no evidence for lensed gravitational waves (GW) in the first half of the O3 run, claiming "We find the observation of lensed events to be unlikely, with the fractional rate at $μ>2$ being $3.3\times 10^{-4}$". While we agree that the chance of an individual GW event being lensed at $μ>2$ is smaller than $10^{-3}$, the number of observed events depends on the product of this small probability times the rate of mergers at high redshift. Observational constraints from the stochastic GW background indicate that the rate of conventional mass BBH mergers (8 < M (M$_{\odot}$) < 15) in the redshift range 1<z< 2 could be as high as O($10^7$) events per year, more than sufficient to compensate for the intrinsically low probability of lensing. To reach the LVC trigger threshold these events require high magnification, but would still produce up to 10 to 30 LVC observable events per year. Thus, all the LVC observed ordinary stellar mass BBH mergers from this epoch must be strongly lensed. By adopting low-rates at high redshift, LVC assumes that lensed events can not be taking place, thus incorrectly assigning them a closer distance and higher masses by a factor of a few (typically 2 to 5). The LVC adopted priors on time delay are in tension with the distribution of observed time delays in lensed quasars. Pairs of events like GW190421-GW190910 and GW190424-GW190910, which are directly assigned a probability of zero by LVC, should be instead considered as prime candidates to be strongly lensed GW pairs, since their separation in time is consistent with observations of time delays in lensed quasars. Correcting for the LVC wrong Bayesian priors, maximum merger rate of conventional mass BBH in 1<z<2, and gravitational lensing time-delay model, reverses the LVC conclusions and supports the strong gravitational lensing hypothesis.

gr-qc↗

arXiv2021

On the Random Motion of Nuclear Objects in a Fuzzy Dark Matter Halo

Fuzzy Dark Matter (FDM), consisting of ultralight bosons ($m_{\rm b} \sim 10^{-22}\ \rm eV$), is an intriguing alternative to Cold Dark Matter. Numerical simulations that solve the Schrödinger-Poisson (SP) equation show that FDM halos consist of a central solitonic core, which is the ground state of the SP equation, surrounded by an envelope of interfering excited states. These excited states also interfere with the soliton, causing it to oscillate and execute a confined random walk with respect to the halo center of mass. Using high-resolution numerical simulations of a $6.6 \times 10^9 M_{\odot}$ FDM halo with $m_{\rm b} = 8 \times 10^{-23}\ \rm eV$ in isolation, we demonstrate that the wobbling, oscillating soliton gravitationally perturbs nuclear objects, such as supermassive black holes or dense star clusters, causing them to diffuse outwards. In particular, we show that, on average, objects with mass $\lesssim 0.3 \%$ of the soliton mass ($M_{\rm sol}$) are expelled from the soliton in $\sim 3\ \rm Gyr$, after which they continue their outward diffusion due to gravitational interactions with the soliton and the halo granules. More massive objects ($\gtrsim 1 \% M_{\rm sol}$), while executing a random walk, remain largely confined to the soliton due to dynamical friction. We also present an effective treatment of the diffusion, based on kinetic theory, that accurately reproduces the outward motion of low mass objects and briefly discuss how the observed displacements of star clusters and active galactic nuclei from the centers of their host galaxies can be used to constrain FDM.

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arXiv2021

Impact of astrophysical binary coalescence timescales on the rate of lensed gravitational wave events

The expected event rate of lensed gravitational wave sources scales with the merger rate at redshift $z\geq 1$, where the optical depth for lensing is high. It is commonly assumed that the merger rate of the astrophysical compact objects is closely connected with the star formation rate, which peaks around redshift $z\sim 2$. However, a major source of uncertainty is the delay time between the formation and merger of compact objects. We explore the impact of delay time on the lensing event rate. We show that as the delay time increases, the peak of the merger rate of gravitational wave sources gets deferred to a lower redshift. This leads to a reduction in the event rate of the lensed events which are detectable by the gravitational wave detectors. We show that for a delay time of around $10$ Gyr or larger, the lensed event rate can be less than one per year for the design sensitivity of LIGO/Virgo. We also estimate the merger rate for lensed sub-threshold for different delay time scenarios, finding that for larger delay times the number of lensed sub-threshold events is reduced, whereas for small-delay time models they are significantly more frequent. This analysis shows for the first time that lensing is a complementary probe to explore different formation channels of binary systems by exploiting the lensing event rate from the well-detected events and sub-threshold events which are measurable using the network of gravitational wave detectors.

gr-qc↗

arXiv2021

Resolved galactic superwinds reconstructed around their host galaxies at z>3

This paper presents a detailed analysis of two giant Lyman-alpha (Lya) arcs detected near known galaxies at z=3.038 and z=3.754 lensed by the massive cluster MACS 1206 (z=0.44). The Lya nebulae revealed in deep MUSE observations exhibit a double-peak profile with a dominant red peak that indicates expansion/outflowing motions. One of the arcs stretches over 1' around the Einstein radius of the cluster, resolving the velocity field of the line-emitting gas on kpc scales around a group of three star-forming galaxies of 0.3-1.6L* at z=3.038. The second arc spans 15'' in size, roughly centered around a pair of low-mass Lya emitters of ~0.03L* at z=3.754. All three galaxies in the z=3.038 group exhibit prominent damped Lya absorption (DLA) and several metal absorption lines, in addition to nebular emission lines such as HeII1640 and CIII]1906,1908. Extended Lya emission appears to emerge from star-forming regions to larger distances with suppressed surface brightness at the center of each galaxy, suggesting the presence of dusty outflowing cones of size 1-5 kpc across. There are significant spatial variations in the Lya line profile, consistent with the presence of a steep negative velocity gradient in a continuous flow of high column density gas from star-forming regions into a low-density halo environment. While the observed UV nebular line ratios show no evidence of AGN activity in the galaxies, the observed Lya signals can be explained by a combination of resonant scattering and recombination radiation due to photoionization by ionizing photons escaping from the nearby star-forming regions. These observations provide the most detailed insights yet into the kinematics of galactic superwinds associated with star-forming galaxies thought to be responsible for the chemical enrichment in the intergalactic medium.

astro-ph.GA↗

arXiv2021

Wave Dark Matter and Ultra Diffuse Galaxies

Dark matter as a Bose-Einstein condensate, such as the axionic scalar field particles of String Theory, can explain the coldness of dark matter on large scales. Pioneering simulations in this context predict a rich wave-like structure, with a ground state soliton core in every galaxy surrounded by a halo of excited states that interfere on the de Broglie scale. This de Broglie scale is largest for low mass galaxies as momentum is lower, providing a simple explanation for the wide cores of dwarf spheroidal galaxies. Here we extend these "wave dark matter" ($ψ$DM) predictions to the newly discovered class of "Ultra Diffuse Galaxies" (UDG) that resemble dwarf spheroidal galaxies but with more extended stellar profiles. Currently the best studied example, DF44, has a uniform velocity dispersion of $\simeq 33$km/s, extending to at least 3 kpc, that we show is reproduced by our $ψ$DM simulations with a soliton radius of $\simeq 0.5$ kpc. In the $ψ$DM context, we show the relatively flat dispersion profile of DF44 lies between massive galaxies with compact dense solitons, as may be present in the Milky Way on a scale of 100pc and lower mass galaxies where the velocity dispersion declines centrally within a wide, low density soliton, like Antlia II, of radius 3 kpc.

astro-ph.GA↗

arXiv2020

Inferring the lensing rate of LIGO-Virgo sources from the stochastic gravitational wave background

Strong lensing of gravitational waves is more likely for distant sources but predicted event rates are highly uncertain with many astrophysical origins proposed. Here we open a new avenue to estimate the event rate of strongly lensed systems by exploring the amplitude of the stochastic gravitational wave background (SGWB). This method can provide a direct upper bound on the high redshift binary coalescing rates, which can be translated into an upper bound on the expected rate of strongly lensed systems. We show that from the ongoing analysis of the Laser Interferometer Gravitational-wave Observatory (LIGO)-Virgo and in the future from the LIGO-Virgo design sensitivity stringent bounds on the lensing event rate can be imposed using the SGWB signal. Combining measurements of loud gravitational wave events with an unresolved stochastic background detection will improve estimates of the numbers of lensed events at high redshift. The proposed method is going to play a crucial in understanding the population of lensed and unlensed systems from gravitational wave observations.

astro-ph.CO↗