Singular Isothermal Sphere Model Research Articles

Determination of Lens Mass Density Profile from Strongly Lensed Gravitational-wave Signals

As the interferometers detecting gravitational waves are upgraded, improving their sensitivity, the probability of observing strong lensing increases. Once a detection is made, it will be critical to gain as much information as possible about the lensing object from these observations. In this work, we present a methodology to rapidly perform model selection between differing mass density profiles for strongly lensed gravitational-wave signals, using the results of the fast strong-lensing analysis pipeline GOLUM. We demonstrate the validity of this methodology using some illustrative examples adopting the idealized singular isothermal sphere and point-mass lens models. We take several simulated lensed signals, analyze them with GOLUM, and subject them to our methodology to recover both the model and its parameters. To demonstrate the methodology’s stability, we show how the result varies with the number of samples used for a subset of these injections. In addition to the analysis of simulations, we also apply our methodology to the gravitational-wave event pair GW191230–LGW200104, two events with similar frequency evolutions and sky locations, which was analyzed in detail as a potential lensing candidate but ultimately discarded when considering the full population and the uncertain nature of the second event. We find a preference for the singular isothermal sphere model over the point mass, though our posteriors are much wider than for the lensed injections, in line with the expectations for a nonlensed event. The methodology developed in this work is made available as part of the Gravelamps software package.

Constraining the Spatial Curvature of the Local Universe with Deep Learning

We use the distance sum rule method to constrain the spatial curvature of the Universe with a large sample of 161 strong gravitational lensing systems, whose distances are calibrated from the Pantheon compilation of type Ia supernovae using deep learning. To investigate the possible influence of mass model of the lens galaxy on constraining the curvature parameter Ω k , we consider three different lens models. Results show that a flat Universe is supported in the singular isothermal sphere (SIS) model with the parameter . While in the power-law (PL) model, a closed Universe is preferred at the ∼3σ confidence level, with the parameter . In the extended PL model, the 95% confidence level upper limit of Ω k is <0.011. As for the parameters of the lens models, constraints on the three models indicate that the mass profile of the lens galaxy could not be simply described by the standard SIS model.

General polytropic spheres as gravitational lenses

We propose hydrostatic polytropic spheres governed by the Lane-Emden equation (LEE) of index n as a novel set of physical models for axially averaged gravitational lenses anywhere in the Universe, alternative to the familiar singular isothermal sphere (SIS) and the Navarro–Frenk–White (NFW) profile, as such general polytropic spheres are conceptually simple, versatile in representing a series of equations of state, and able to address both the inner core and cusp features. As LEE is nonlinear, there exist several distinct classes of LEE solutions to serve as physical lens models. With a few scaling parameters, the complete problem can be readily reconstructed with full physical dimensions. A given mass density profile satisfying LEE produces lensing effects that are solely determined by a dimensionless parameter q which contains geometric and kinematic information about the source-lens-observer system. The lens mapping and tangential shear or distortion profile are derived, first analytically for special cases and then asymptotically at the outskirts or near the edge of the lens. Numerical procedures for calculating full lensing profiles of a general lens are developed. Our results include the analytical “singular polytropic sphere” (SPS) profile which generalizes the SIS model and may outperform the latter in modeling dark matter halos among others. We further point out that dynamic models of general polytropic spheres in self-similar evolution can serve as several broad classes of gravitational lenses and produce time-dependent lensing effects slow or fast depending on the pertinent time scales. Astrophysical sources that can be lensed include electromagnetic wave sources in the entire frequency band, gravitational wave sources in the entire frequency band, gravitons even possibly with finite masses, neutrino sources of three different types, neutron sources, and ultra high energy cosmic rays (UHECRs) of electrically charged particles which can also interact with magnetic fields. We discuss and elabrate applications to dark matter halos, hypermassive black holes and supermassive black holes in the entire Universe including the early Universe, magnetized supermassive stars, static and dynamically evolving spherical and cylindrical lenses in contexts of astrophysics and cosmology.

Investigating Gravitationally Lensed Quasars Observable by Nancy Grace Roman Space Telescope

In this work, we investigate the possibility of observing quasars, particularly lensed quasars, by the Nancy Grace Roman Space Telescope (Roman). To this aim, based on the capabilities of the Roman Space Telescope and the results from the quasar luminosity function (QLF) in the infrared band of the Spitzer Space Telescope imaging survey, we calculated the number of quasars expected to be in its field of view. In order to estimate the number of lensed quasars, we develop a Monte Carlo simulation to estimate the probability that a quasar is lensed once or more times by foreground galaxies. Using the mass–luminosity distribution function of galaxies and the redshift distributions of galaxies and quasars, we find that 1 per 180 observed quasars will be lensed by foreground galaxies. Further on, adopting a singular isothermal sphere (SIS) model for lens galaxies, we calculate the time delay between lensed images for single and multiple lensing systems and present their distributions. We emphasize that detailed studies of these lensing systems will provide a powerful probe of the physical properties of quasars and may allow testing the mass distribution models of galaxies in addition to being extremely helpful for constraining the cosmological parameters.

Light Curves and Polarizations of Gravitationally Lensed Kilonovae

Kilonovae are generally believed to originate from the ejecta of binary neutron stars (NSs) or black hole–NS mergers. Free neutrons might be retained in the outermost layer of the ejecta to produce a precursor via β decay. During the propagation of kilonovae to observers, a small percentage of them might be gravitationally lensed by foreground objects. In this paper, three lens models, i.e., the point-mass model, the singular isothermal sphere (SIS) model, and the Chang–Refsdal model, were taken into consideration to explore the light curves and polarizations of gravitationally lensed kilonovae. We found that, if the time delay between two images exceeds the ejecta-heating timescale for the lens mass ∼1010 M ⊙ in the SIS model, a tiny bump-like signal will be generated in the light curve, and the total luminosity will be magnified in all cases. The polarization of lensed kilonovae is significantly enhanced in most cases. Future detections of lensed kilonovae will impose constraints on the morphology of the ejecta and aid in the determination of the nature of compact object mergers and the search for strong gravitational lenses.

Gravitationally lensed orphan afterglows of gamma-ray bursts

ABSTRACT The cosmological nature of gamma-ray bursts (GRBs) implies that a small portion of them could be gravitationally lensed by foreground objects during their propagation. The gravitational lensing effect on the GRB prompt emission and on-axis afterglows has been discussed, and some candidates have been found in the literature. In this work, considering the high detection rate of GRB orphan afterglows in future wide-field survey era, we investigate the gravitationally lensed orphan afterglows in view of three lens models, i.e. the point-mass model, the singular isothermal sphere model, and the Chang–Refsdal model. The structure of the GRB jet itself is also incorporated in calculating the lensed afterglow light curves. It is found that lensed optical/X-ray orphan afterglows in principle could be diagnosed through their temporal characteristics, and the optical band is the best band to observe the galaxy-lensed orphan afterglows. Moreover, the event rate for galaxy-lensed orphan afterglows is estimated to be ≲ 1.8 yr−1 for the whole sky. If most orphan afterglows could be identified (from other transients in the survey data), the optimistic detection rates of the 2.5 m Wide Field Survey Telescope of China and 8.4 m Vera Rubin Observatory Legacy Survey of Space and Time for galaxy-lensed orphan afterglows in the optical band are ≲ 0.01–0.02 and ≲ 0.04–0.08 yr−1, respectively.

Searching for Gravitationally Lensed Gamma-Ray Bursts with Their Afterglows

Abstract Gamma-ray bursts (GRBs) at high redshifts are expected to be gravitationally lensed by objects of different mass scales. Other than a single recent claim, no lensed GRB has been detected so far by using gamma-ray data only. In this paper, we suggest that multiband afterglow data might be an efficient way to search for lensed GRB events. Using the standard afterglow model, we calculate the characteristics of the lensed afterglow lightcurves under the assumption of two popular analytic lens models: the point-mass and singular isothermal sphere models. In particular, when different lensed images cannot be resolved, their signals would be superimposed together with a given time delay. In this case, the X-ray afterglows are likely to contain several X-ray flares of similar width in linear scale and similar spectrum, and the optical afterglow lightcurve will show re-brightening signatures. Since the lightcurves from the image arriving later would be compressed and deformed in the logarithmic timescale, the larger time delay (i.e., the larger mass of the lens), the easier it is to identify the lensing effect. We analyzed the archival data of optical afterglows and found one potential candidate of the lensed GRB (130831A) with time delay ∼500 s; however, observations of this event in gamma-ray and X-ray bands seem not to support the lensing hypothesis. In the future, with the cooperation of the all-sky monitoring gamma-ray detectors and multiband sky survey projects, the method proposed in this paper would be more efficient in searching for strongly lensed GRBs.

Mapping the H2D+ and N2H+ emission toward prestellar cores. Testing dynamical models of the collapse using gas tracers

Context. The study of prestellar cores is critical as they set the initial conditions in star formation and determine the final mass of the stellar object. To date, several hypotheses have described their gravitational collapse. Deriving the dynamical model that fits both the observed dust and the gas emission from such cores is therefore of great importance. Aims. We perform detailed line analysis and modeling of H2D+ 110–111 and N2H+ 4–3 emission at 372 GHz, using 2′ × 2′ maps (James Clerk Maxwell Telescope; JCMT). Our goal is to test the most prominent dynamical models by comparing the modeled gas kinematics and spatial distribution (H2D+ and N2H+) with observations toward four prestellar (L1544, L183, L694-2, L1517B) and one protostellar core (L1521f). Methods. We fit the line profiles at all offsets showing emission using single Gaussian distributions. We investigate how the line parameters (VLSR, FWHM and TA*) change with offset to examine the velocity field, the degree of nonthermal contributions to the line broadening, and the distribution of the material in these cores. To assess the thermal broadening, we derive the average gas kinetic temperature toward all cores using the non-LTE radiative transfer code RADEX. We perform a more detailed non-LTE radiative transfer modeling using RATRAN, where we compare the predicted spatial distribution and line profiles of H2D+ and N2H+ with observations toward all cores. To do so, we adopt the physical structure for each core predicted by three different dynamical models taken from literature: quasi-equilibrium Bonnor–Ebert sphere (QE-BES), singular isothermal sphere (SIS), and Larson–Penston (LP) flow. In addition, we compare these results to those of a static sphere, whose density and temperature profiles are based on the observed dust continuum. Lastly, we constrain the abundance profiles of H2D+ and N2H+ toward each core. Results. We find that variable nonthermal contributions (variations by a factor of 2.5) are required to explain the observed line width of both H2D+ and N2H+, while the nonthermal contributions are found to be 50% higher for N2H+. The RADEX modeling results in average core column densities of ~9 × 1012 cm−2 for H2D+ and N2H+. The LP flow seems to be the dynamical model that can reproduce the observed spatial distribution and line profiles of H2D+ on a global scale of prestellar cores, while the SIS model systematically and significantly overestimates the width of the line profiles and underestimates the line peak intensity. We find similar abundance profiles for the prestellar cores and the protostellar core. The typical abundances of H2D+ vary between 10−9 and 10−10 for the inner 5000 au and drop by about an order of magnitude for the outer regions of the core (2 × 10−10–6 × 10−11). In addition, a higher N2H+ abundance by about a factor of 4 compared to H2D+ is found toward the two cores with detected emission. The presence of N2H+ 4–3 toward the protostellar core and toward one of the prestellar cores reflects the increasing densities as the core evolves. Conclusions. Our analysis provides an updated picture of the physical structure of prestellar cores. Although the dynamical models account for mass differences by up to a factor of 7, the velocity structure drives the shape of the line profiles, allowing for a robust comparison between the models. We find that the SIS model can be clearly excluded in explaining the gas emission toward the cores, but a larger sample is required to differentiate clearly between the LP flow, the QE-BES, and the static models. All models of collapse underestimate the intensity of the gas emission by up to several factors toward the only protostellar core in our sample, indicating that different dynamics take place in different evolutionary core stages. If the LP model is confirmed toward a larger sample of prestellar cores, it would indicate that they may form by compression or accretion of gas from larger scales. If the QE-BES model is confirmed, it means that quasi-hydrostatic cores can exist within turbulent ISM.

Testing the Cosmic Distance Duality Relation with the Latest Strong Gravitational Lensing and Type Ia Supernovae

Abstract We perform a model-independent and comprehensive test on the cosmic distance duality relation (CDDR) by combining the latest observations of strong gravitational lensing (SGL) including a total of 161 well-measured systems from several surveys and observations of Type Ia supernovae (SNe Ia), i.e., the joint light-curve analysis of SNe Ia and the Pantheon SNe Ia. We parameterize the CDDR in the form of , and also consider general lens mass models including the dependence on the lens redshift and surface mass density. First, we update tests using the new SGL and the two SNe Ia data sets for the singular isothermal sphere model. The constraint results suggest a moderate tension with the CDDR using the Pantheon SN Ia with a slightly negative η 0. We find that η 0 deviates significantly from the CDDR at more than the 3σ level if the lens mass model depends on redshift. Supplementary tests show that the error from aperture correction and the parameterization method of the CDDR can hardly justify the deviation. Several of the models investigated show some evidence for deviations from the CDDR. However, there is a significant scatter in the inferred level of the CDDR violation, depending on the model describing the population of strong lenses. This variance is too large for us to conclude yet that the CDDR is violated and needs further investigation and future measurements to be verified.

ALMA observations of lensed Herschel sources: testing the dark matter halo paradigm

With the advent of wide-area submillimetre surveys, a large number of high-redshift gravitationally lensed dusty star-forming galaxies have been revealed. Because of the simplicity of the selection criteria for candidate lensed sources in such surveys, identified as those with S500 μm > 100 mJy, uncertainties associated with the modelling of the selection function are expunged. The combination of these attributes makes submillimetre surveys ideal for the study of strong lens statistics. We carried out a pilot study of the lensing statistics of submillimetre-selected sources by making observations with the Atacama Large Millimeter Array (ALMA) of a sample of strongly lensed sources selected from surveys carried out with the Herschel Space Observatory. We attempted to reproduce the distribution of image separations for the lensed sources using a halo mass function taken from a numerical simulation that contains both dark matter and baryons. We used three different density distributions, one based on analytical fits to the haloes formed in the EAGLE simulation and two density distributions [Singular Isothermal Sphere (SIS) and SISSA] that have been used before in lensing studies. We found that we could reproduce the observed distribution with all three density distributions, as long as we imposed an upper mass transition of ∼1013 M⊙ for the SIS and SISSA models, above which we assumed that the density distribution could be represented by a Navarro–Frenk–White profile. We show that we would need a sample of ∼500 lensed sources to distinguish between the density distributions, which is practical given the predicted number of lensed sources in the Herschel surveys.

Constraints on a possible evolution of mass density power-law index in strong gravitational lensing from cosmological data

In this work, by using strong gravitational lensing (SGL) observations along with Type Ia Supernovae (Union2.1) and gamma ray burst data (GRBs), we propose a new method to study a possible redshift evolution of $\gamma(z)$, the mass density power-law index of strong gravitational lensing systems. In this analysis, we assume the validity of cosmic distance duality relation and the flat universe. In order to explore the $\gamma(z)$ behavior, three different parametrizations are considered, namely: (P1) $\gamma(z_l)=\gamma_0+\gamma_1 z_l$, (P2) $\gamma(z_l)=\gamma_0+\gamma_1 z_l/(1+z_l)$ and (P3) $\gamma(z_l)=\gamma_0+\gamma_1 \ln(1+z_l)$, where $z_l$ corresponds to lens redshift. If $\gamma_0=2$ and $\gamma_1=0$ the singular isothermal sphere model is recovered. Our method is performed on SGL sub-samples defined by different lens redshifts and velocity dispersions. For the former case, the results are in full agreement with each other, while a 1$\sigma$ tension between the sub-samples with low ($\leq 250$ km/s) and high ($>250$ km/s) velocity dispersions was obtained on the ($\gamma_0$-$\gamma_1$) plane. By considering the complete SGL sample, we obtain $\gamma_0 \approx 2$ and $ \gamma_1 \approx 0$ within 1$\sigma$ c.l. for all $\gamma(z)$ parametrizations. However, we find the following best fit values of $\gamma_1$: $-0.085$, $-0.16$ and $-0.12$ for P1, P2 and P3 parametrizations, respectively, suggesting a mild evolution for $\gamma(z)$. By repeating the analysis with Type Ia Supernovae from JLA compilation, GRBs and SGL systems this mild evolution is reinforced.

Gravitational lens models for cosmological black holes

If really such objects like cosmological black holes exist they may be studied with a standard technique like strong and weak gravitational lensing. Cosmological voids can be explained as the result the collapse of large perturbations into black hole with masses of the order of 1014 M ⊙ and the expansion of the universe. The resulting image of the universe is that it is more homogeneous than expected from present observations. In this paper we discuss some lensing properties related to the cosmological black holes (CBHs), namely we consider differences in gravitational lensing for point like mass and extended mass distributions. We consider the singular isothermal sphere model as a toy (illustrative) model for an extended distribution of dark matter and a slightly more complicated isothermal sphere with a core.

REVISITING STUDIES OF THE STATISTICAL PROPERTY OF A STRONG GRAVITATIONAL LENS SYSTEM AND MODEL-INDEPENDENT CONSTRAINT ON THE CURVATURE OF THE UNIVERSE

ABSTRACT In this paper, we use a recently compiled data set, which comprises 118 galactic-scale strong gravitational lensing (SGL) systems to constrain the statistical property of the SGL system as well as the curvature of the universe without assuming any fiducial cosmological model. Based on the singular isothermal ellipsoid (SIE) model of the SGL system, we obtain that the constrained curvature parameter is close to zero from the SGL data, which is consistent with the latest result of Planck measurement. More interestingly, we find that the parameter f in the SIE model is strongly correlated with the curvature . Neglecting this correlation in the analysis will significantly overestimate the constraining power of SGL data on the curvature. Furthermore, the obtained constraint on f is different from previous results: (68% confidence level [C.L.]), which means that the standard singular isothermal sphere (SIS) model (f = 1) is disfavored by the current SGL data at more than a C.L. We also divide all of the SGL data into two parts according to the centric stellar velocity dispersion and find that the larger the value of for the subsample, the more favored the standard SIS model is. Finally, we extend the SIE model by assuming the power-law density profiles for the total mass density, , and luminosity density, , and obtain the constraints on the power-law indices: and at a 68% C.L. When assuming the power-law index , this scenario is totally disfavored by the current SGL data, .

Cosmic Constraints to the wCDM Model from Strong Gravitational Lensing**Supported by the National Natural Science Foundation of China under Grant No 11275035.

We study the cosmic constraint to the wCDM (cold dark matter with a constant equation of state w) model via 118 strong gravitational lensing systems which are compiled from SLACS, BELLS, LSD and SL2S surveys, where the ratio between two angular diameter distances Dobs = DA(zl, zs)/DA(0, zs) is taken as a cosmic observable. To obtain this ratio, we adopt two strong lensing models: one is the singular isothermal sphere model (SIS) and the other one is the power-law density profile (PLP) model. Via the Markov chain Monte Carlo method, the posterior distribution of the cosmological model parameters space is obtained. The results show that the cosmological model parameters are not sensitive to the parameterized forms of the power-law index γ. Furthermore, the PLP model gives a relatively tighter constraint to the cosmological parameters than that of the SIS model. The predicted value of Ωm = 0.31−0.24+0.44 by the SIS model is compatible with that obtained by Planck2015: Ωm = 0.313 ± 0.013. However, the value of Ωm = 0.15−0.11+0.13 based on the PLP model is smaller and has 1.25σ tension with that obtained by Planck2015.

Weak lensing mass map and peak statistics in Canada–France–Hawaii Telescope Stripe 82 survey

We present a weak lensing mass map covering ~124 square degrees of the Canada-France-Hawaii Telescope Stripe 82 Survey (CS82). We study the statistics of rare peaks in the map, including peak abundance, the peak-peak correlation functions and the tangential-shear profiles around peaks. We find that the abundance of peaks detected in CS82 is consistent with predictions from a Lambda-CDM cosmological model, once noise effects are properly included. The correlation functions of peaks with different signal-to-noise ratio (SNR) are well described by power laws, and there is a clear cross-correlation between the Sloan Digital Sky Survey III/Constant Mass galaxies and high SNR peaks. The tangential-shear profiles around peaks increase with peak SNR. We fit analytical models to the tangential-shear profiles, including a projected singular isothermal sphere (SIS) model and a projected Navarro, Frenk & White (NFW) model, plus a two-halo term. For the high SNR peaks, the SIS model is rejected at ~3-sigma. The NFW model plus a two-halo term gives more acceptable fits to the data. Some peaks match the positions of optically detected clusters, while others are relatively dark. Comparing dark and matched peaks, we find a difference in lensing signal of a factor of 2, suggesting that about half of the dark peaks are false detections.

First gravitational lensing mass estimate of a damped Lyman α galaxy at z = 2.2

Abstract We present the first lensing total mass estimate of a galaxy, at redshift 2.207, that acts as a gravitational deflector and damped Lyman α absorber on the background QSO SDSS J1135−0010, at redshift 2.888. The remarkably small projected distance, or impact parameter, between the lens and the source has been estimated to be 0.8 ± 0.1 kpc in a recent work. By exploiting the Sloan Digital Sky Survey data base, we establish a likely lensing magnification signal in the photometry of the QSO. This is determined to be 2.2 mag brighter (or eight times more luminous) than the median QSO at comparable redshifts. We describe the total mass distribution of the lens galaxy with a one-component singular isothermal sphere model and contrast the values of the observed and model-predicted magnification factors. For the former, we use conservatively the photometric data of the 95 per cent of the available distant QSO population. We estimate that the values of the lens effective velocity dispersion and two-dimensional total mass, projected within a cylinder with radius equal to the impact parameter, are included between 60 and 170 km s−1 and 2.1 × 109 and 1.8 × 1010 M⊙, respectively. We conclude by remarking that analyses of this kind are crucial to exploring the relation between the luminous and dark-matter components of galaxies in the high-redshift Universe.

Gravitational lenses in the dark Universe

We discuss how different cosmological models of the Universe affect the probability that a background source has multiple images related by an angular distance, i.e., the optical depth of gravitational lensing. We examine some cosmological models for different values of the density parameter Ω i : (i) the cold dark matter model, (ii) the ΛCDM model, (iii) the Bose-Einstein condensate dark matter model, (iv) the Chaplygin gas model, (v) the viscous fluid cosmological model and (vi) the holographic dark energy model by using the singular isothermal sphere (SIS) model for the halos of dark matter. We note that the dependence of the energy-matter content of the universe profoundly modifies the frequency of multiple quasar images.

Bayesian constraints on dark matter halo properties using gravitationally lensed supernovae

A hierarchical Bayesian method is applied to the analysis of Type-Ia supernovae (SNIa) observations to constrain the properties of the dark matter haloes of galaxies along the SNIa lines-of-sight via their gravitational lensing effect. The full joint posterior distribution of the dark matter halo parameters is explored using the nested sampling algorithm {\sc MultiNest}, which also efficiently calculates the Bayesian evidence, thereby facilitating robust model comparison. We first demonstrate the capabilities of the method by applying it to realistic simulated SNIa data, based on the real 3-year data release from the Supernova Legacy Survey (SNLS3). Assuming typical values for the halo parameters in our simulations, we find that a catalogue analogous to the existing SNLS3 data set is incapable of detecting the lensing signal, but a catalogue containing approximately three times as many SNIa does produce robust and accurate parameter constraints and model selection results for two halo models: a truncated singular isothermal sphere (SIS) and a Navarro--Frenk--White (NFW) profile, thereby validating our analysis methodology. In the analysis of the real SNLS3 data, contrary to previous studies, we obtain only a very marginal detection of a lensing signal and weak constraints on the halo parameters for the truncated SIS model, although these constraints are tighter than those obtained from the equivalent simulated SNIa data set. This difference is driven by a preferred value of $\eta \approx 1$ in the assumed scaling-law $\sigma \propto L^\eta$ between velocity dispersion and luminosity, which is somewhat higher than the canonical values of $\eta = \tfrac{1}{4}$ and $\eta = \tfrac{1}{3}$ for early and late-type galaxies, respectively, and leads to a stronger lensing effect by the halo. No detection of a lensing signal is made for the NFW model.

Gravitational lensing properties of an isothermal universal halo profile

N-body simulations predict that dark matter halos with different mass scales are described by a universal model, the Navarro-Frenk-White (NFW) density profiles. As a consequence of baryonic cooling effects, these halos will become more concentrated, and similar to an isothermal sphere over a large range in radii (∼ 300 h−1 kpc). The singular isothermal sphere (SIS) model however has to be truncated artificially at large radii since it extends to infinity. We model a massive galaxy halo as a combination of an isothermal sphere and an NFW density profile. We give an approximation for the mass concentration at different baryon fractions and present exact expressions for the weak lensing shear and flexion for such a halo. We compare the lensing properties with the SIS and NFW profiles. We find that the combined profile can generate higher order lensing signals at small radii and is more efficient in generating strong lensing events. In order to distinguish such a halo profile from the SIS or NFW profiles, one needs to combine strong and weak lensing constraints for small and large radii.

A GRAVITATIONAL LENS MODEL FOR THE Lyα EMITTER LAE 221724+001716 ATz= 3.1 IN THE SSA 22 FIELD,

During the course of our Lyman continuum imaging survey, we found that the spectroscopically confirmed Lya emitter LAE 221724+001716 at z = 3.10 in the SSA 22 field shows strong Lyman continuum emission (lambda_rest ~ 900 A) that escapes from this galaxy. However, another recent spectroscopic survey revealed that the supposed Lyman continuum emission could arise from a foreground galaxy at z = 1.76 if the emission line newly detected from the galaxy at lambda_obs ~ 3360 A is Lya. If this is the case, as the angular separation between these two galaxies is very small (~ 0.6"), LAE 221724+001716 at z = 3.10 could be amplified by the gravitational lensing caused by this intervening galaxy. Here we present a possible gravitational lens model for the system of LAE 221724+001716. First, we estimate the stellar mass of the intervening galaxy as Mstar ~ 3.5x10^9 Msun from its UV luminosity and ~ 3.0x10^7--2.4x10^9 Msun through the SED fitting. Then, we find that the gravitational magnification factor ranges from 1.01 to 1.16 using the so-called singular isothermal sphere model for strong lensing. While LAE 221724+001716 is the first system of an LAE-LAE lensing reported so far, the estimated magnification factor is not so significant because the stellar mass of the intervening galaxy is small.