Intrinsic Luminosity Function Research Articles

An X-Ray Census of Active Galactic Nuclei in the Virgo and Fornax Clusters of Galaxies with SRG/eROSITA

We present a uniform and sensitive X-ray census of active galactic nuclei (AGNs) in the two nearest galaxy clusters, Virgo and Fornax, utilizing the newly released X-ray source catalogs from the first all-sky scan of Spectrum-Roentgen-Gamma/eROSITA. A total of 50 and 10 X-ray sources are found positionally coincident with the nuclei of member galaxies in Virgo and Fornax, respectively, down to a 0.2–2.3 keV luminosity of ∼1039 erg s−1 and reaching out to a projected distance well beyond the virial radius of both clusters. The majority of the nuclear X-ray sources are newly identified. There is weak evidence that the nuclear X-ray sources are preferentially found in late-type hosts. Several hosts are dwarf galaxies with a stellar mass below ∼109 M ⊙. We find that contamination by nonnuclear X-ray emission can be neglected in most cases, indicating the dominance of a genuine AGN. In the meantime, no nuclear X-ray source exhibits a luminosity higher than a few times 1041 erg s−1, which might be owing to a steep intrinsic luminosity function. The X-ray AGN occupation rate is only ∼3% in both clusters, apparently much lower than that in field galaxies inferred from previous X-ray studies. Both aspects suggest that the cluster environment effectively suppresses AGN activity. The findings of this census have important implications for the interplay between galaxies and their central massive black holes in cluster environments.

Strong lensing of high-energy neutrinos

We consider the effects of strong gravitational lensing by galaxy-scale deflectors on the observations of high-energy ($\mathrm{E}\ensuremath{\gg}\mathrm{GeV}$) neutrinos (HENs). For HENs at cosmological distances, the optical depth for multiple imaging is $\ensuremath{\sim}{10}^{\ensuremath{-}3}$, implying that while we do not expect any multiply imaged HENs with present samples, next-generation experiments should be able to detect the first such event. We then present the distribution of expected time delays to aid in the identification of such events, in combination with directional and energy information. In order to assist in the evaluation of HEN production mechanisms, we illustrate how lensing affects the observed number counts for a variety of intrinsic luminosity functions of the source population. Finally, we see that the lensing effects on the cosmic neutrino background flux calculation would be negligible by taking kiloparsec-scale jets as an example.

A measurement of Hubble’s Constant using Fast Radio Bursts

ABSTRACT We constrain the Hubble constant H0 using Fast Radio Burst (FRB) observations from the Australian Square Kilometre Array Pathfinder (ASKAP) and Murriyang (Parkes) radio telescopes. We use the redshift-dispersion measure (‘Macquart’) relationship, accounting for the intrinsic luminosity function, cosmological gas distribution, population evolution, host galaxy contributions to the dispersion measure (DMhost), and observational biases due to burst duration and telescope beamshape. Using an updated sample of 16 ASKAP FRBs detected by the Commensal Real-time ASKAP Fast Transients (CRAFT) Survey and localized to their host galaxies, and 60 unlocalized FRBs from Parkes and ASKAP, our best-fitting value of H0 is calculated to be $73_{-8}^{+12}$ km s−1 Mpc−1. Uncertainties in FRB energetics and DMhost produce larger uncertainties in the inferred value of H0 compared to previous FRB-based estimates. Using a prior on H0 covering the 67–74 km s−1 Mpc−1 range, we estimate a median ${\rm DM}_{\rm host}= 186_{-48}^{+59}\,{\rm pc \, cm^{-3}}$, exceeding previous estimates. We confirm that the FRB population evolves with redshift similarly to the star-formation rate. We use a Schechter luminosity function to constrain the maximum FRB energy to be log10Emax$=41.26_{-0.22}^{+0.27}$ erg assuming a characteristic FRB emission bandwidth of 1 GHz at 1.3 GHz, and the cumulative luminosity index to be $\gamma =-0.95_{-0.15}^{+0.18}$. We demonstrate with a sample of 100 mock FRBs that H0 can be measured with an uncertainty of ±2.5 km s−1 Mpc−1, demonstrating the potential for clarifying the Hubble tension with an upgraded ASKAP FRB search system. Last, we explore a range of sample and selection biases that affect FRB analyses.

Lensing in the darkness: a Bayesian analysis of 22 Chandra sources at z ≳ 6 shows no evidence of lensing

ABSTRACT More than 200 quasars have been detected so far at z > 6, with only one showing clear signs of strong gravitational lensing. Some studies call for a missing population of lensed high-z quasars, but their existence is still in doubt. A large fraction of high-z quasars being lensed would have a significant effect on the shape of the intrinsic quasar luminosity function (QLF). Here, we perform the first systematic search for lensed X-ray-detected quasars at z ≳ 6 employing a Bayesian analysis, with the code baymax, to look for morphological evidence of multiple images that may escape a visual inspection. We analysed a sample of 22 quasars at z > 5.8 imaged by the Chandra X-ray observatory and found none with statistically significant multiple images. In the sub-sample of the eight sources with photon counts >20, we exclude multiple images with separations r > 1 arcsec and count ratios f > 0.4, or with separations as small as 0.7 arcsec and f > 0.7 at $95{{\ \rm per\ cent}}$ confidence level. Comparing this non-detection with predictions from theoretical models suggesting a high- and a low-lensed fraction, we placed upper limits on the bright-end slope, β, of the QLF. Using only the sub-sample with eight sources, we obtain, in the high-lensing model, a limit β < 3.38. Assuming no multiple source is present in the full sample of 22 sources, we obtain β < 2.89 and β < 3.53 in the high- and low-lensing models, respectively. These constraints strongly disfavour steep QLF shapes previously proposed in the literature.

Luminosity selection for gamma-ray bursts

Aims.There exists inevitable scatter in the intrinsic luminosity of gamma-ray bursts (GRBs). If there is relativistic beaming in the source, viewing angle variation necessarily introduces variation in the intrinsic luminosity function (ILF). Scatter in the ILF can cause selection bias where sources detected at distance have a greater median luminosity than those detected close by. Median luminosity divides any given population into equal halves. When the functional form of a distribution is unknown, it can be a more robust diagnostic than those that use trial functional forms.Method.In this work, we employ a statistical test based on median luminosity and use it to test a class of models for GRBs. We assume that the GRB jet has a finite opening angle and that the orientation of the GRB jet is random relative to the observer. We calculateLmedianas a function of redshift by simulating GRBs empirically and theoretically, and use the luminosity-vs.-redshiftSwiftdata in order to compare the theoretical results with the observed ones. The method accounts for the fact that there may be GRBs that go undetected at some redshifts.Results.We find thatLmedianis extremely insensitive to the on-axis (i.e., maximal) luminosity of the jet.

The ZTF-BTS Type Ia supernovae luminosity function is consistent with a single progenitor channel for the explosions

ABSTRACT We construct the Type Ia supernovae (SNe Ia) luminosity function (LF) using the Zwicky Transient Facility Bright Transient Survey (BTS) catalogue. While this magnitude-limited survey has an unprecedented number of objects, it suffers from large distance uncertainties and lacks an estimation of host extinction. We bypass these issues by calculating the intrinsic luminosities from the shape parameters of the light curve’s g and r bands, with the luminosities calibrated from the well observed SNe Ia sample of the Carnegie Supernova Project, allowing us to construct, for the first time, the intrinsic LF of SNe Ia. We then use a novel tight relation between the colour stretch and the synthesized 56Ni mass, MNi56, to determine the MNi56 distribution of SNe Ia. We find that the LFs are unimodal, with their peaks in line with previous results, but have a much lower rate of dim events and luminous events. We show that the features on top of the unimodal LF-derived distributions are all compatible with statistical noise, consistent with a single progenitor channel for the explosions. We further derive, for the first time, the SNe Ia distribution of host galaxy extinction, and find a mean selective extinction of E(B − V) ≈ 0.1 and a non-negligible fraction with large, $\gt 1\, \text{mag}$, extinction in the optical bands. The high extinction is typical for luminous SNe, supporting their young population origin.

CRAFTS for Fast Radio Bursts: Extending the Dispersion–Fluence Relation with New FRBs Detected by FAST

Abstract We report three new FRBs discovered by the Five-hundred-meter Aperture Spherical radio Telescope (FAST), namely FRB 181017.J0036+11, FRB 181118, and FRB 181130, through the Commensal Radio Astronomy FAST Survey (CRAFTS). Together with FRB 181123, which was reported earlier, all four FAST-discovered FRBs share the same characteristics of low fluence (≤0.2 Jy ms) and high dispersion measure (DM, >1000 pc cm−3), consistent with the anticorrelation between DM and fluence of the entire FRB population. FRB 181118 and FRB 181130 exhibit band-limited features. FRB 181130 is prominently scattered (τ s ≃ 8 ms) at 1.25 GHz. FRB 181017.J0036+11 has full-bandwidth emission with a fluence of 0.042 Jy ms, which is one of the faintest FRB sources detected so far. CRAFTS has started to build a new sample of FRBs that fills the region for more distant and fainter FRBs in the fluence–DME diagram, previously out of reach of other surveys. The implied all-sky event rate of FRBs is 1.24 − 0.90 + 1.94 × 10 5 sky−1 day−1 at the 95% confidence interval above 0.0146 Jy ms. We also demonstrate here that the probability density function of CRAFTS FRB detections is sensitive to the assumed intrinsic FRB luminosity function and cosmological evolution, which may be further constrained with more discoveries.

Constraining the Gravitational Lensing of z ≳ 6 Quasars from Their Proximity Zones

Abstract Since their discovery 20 years ago, the observed luminosity function of z ≳ 6 quasars has been suspected to be biased by gravitational lensing. Apart from the recent discovery of UHS J0439+1634 at z ≈ 6.52, no other strongly lensed z ≳ 6 quasar has been conclusively identified. The hyperluminous z ≈ 6.33 quasar SDSS J0100+2802, believed to host a supermassive black hole of ∼1010 M ⊙, has recently been claimed to be lensed by a factor of ∼450, which would negate both its extreme luminosity and black hole mass. However, its Lyα-transparent proximity zone is the largest known at z > 6, suggesting an intrinsically extreme ionizing luminosity. Here we show that the lensing hypothesis of z ≳ 6 quasars can be quantitatively constrained by their proximity zones. We first show that our proximity zone analysis can recover the strongly lensed nature of UHS J0439+1634, with an estimated magnification at 68% (95%) credibility that is consistent with previously published lensing models. We then show that the large proximity zone of SDSS J0100+2802 rules out lensing magnifications of μ > 4.9 at 95% probability, and conclusively rule out the proposed μ > 100 scenario. Future proximity zone analyses of existing z ≳ 6 quasar samples have the potential to identify promising strongly lensed candidates, constrain the distribution of z ≳ 6 quasar lensing, and improve our knowledge of the shape of the intrinsic quasar luminosity function.

The Jet Structure and the Intrinsic Luminosity Function of Short Gamma-Ray Bursts

Abstract The joint observation of GW170817 and GRB 170817A indicated that short gamma-ray bursts (SGRBs) can originate from binary neutron star mergers. Moreover, some SGRBs could be detected off axis, while the SGRB jets are highly structured. Then, by assuming a universal angular distribution of the jet emission for all SGRBs, we reproduce the flux and redshift distributions of the cosmological SGRBs detected by Swift and Fermi. For self-consistency, this angular distribution is simultaneously constrained by the luminosity and event rate of GRB 170817A. As a result, it is found that the universal jet structure of SGRBs could approximately have a two-Gaussian profile. Meanwhile, the intrinsic luminosity function (LF) of the on-axis emission of the jets can be simply described by a single power law with a low-luminosity exponential cutoff. The usually discovered broken-power-law apparent LF for relatively high luminosities can naturally result from the coupling of the intrinsic LF with the angular distribution of the jet emission, as the viewing angles to the SGRBs are arbitrarily distributed.

Maximum entropy estimation of the Galactic bulge morphology via the VVV Red Clump

ABSTRACT The abundance and narrow magnitude dispersion of Red Clump (RC) stars make them a popular candidate for mapping the morphology of the bulge region of the Milky Way. Using an estimate of the RC’s intrinsic luminosity function, we extracted the three-dimensional density distribution of the RC from deep photometric catalogues of the VISTA Variables in the Via Lactea (VVV) survey. We used maximum entropy-based deconvolution to extract the spatial distribution of the bulge from Ks-band star counts. We obtained our extrapolated non-parametric model of the bulge over the inner 40° × 40° region of the Galactic centre. Our reconstruction also naturally matches on to a parametric fit to the bulge outside the VVV region and inpaints overcrowded and high extinction regions. We found a range of bulge properties consistent with other recent investigations based on the VVV data. In particular, we estimated the bulge mass to be in the range $[1.3,1.7]\times 10^{10} \, \mathrm{M}_\odot$, the X-component to be between 18 per cent and 25 per cent of the bulge mass, and the bulge angle with respect to the Sun–Galactic centre line to be between 18° and 32°. Studies of the FermiLarge Area Telescope (LAT) gamma-ray Galactic centre excess suggest that the excess may be traced by Galactic bulge distributed sources. We applied our deconvolved density in a template fitting analysis of this Fermi–LAT GeV excess and found an improvement in the fit compared to previous parametric-based templates.

Reality or Mirage? Observational Test and Implications for the Claimed Extremely Magnified Quasar at z = 6.3

Abstract In the last two decades, approximately 200 quasars have been discovered at , hosting active supermassive black holes with masses . While these sources reflect only the tip of the iceberg of the black hole mass distribution, their detection challenges standard growth models. The most massive black hole that was inferred thus far (J0100+2802, ) was recently claimed to be lensed, with a magnification factor . Here, we perform a consistency check of this claim, finding that the detection of such a source requires a bright-end slope for the intrinsic quasar luminosity function (LF), . Commonly used values of are rejected at . If the claim is confirmed, it is very unlikely that all the remaining 51 sources in the Sloan Digital Sky Survey sample are not magnified. Furthermore, it suffices that of the remaining sources are lensed for the intrinsic LF to differ significantly (i.e., ) from the observed one. The presence of additional extremely magnified sources in the sample would lower the requirement to . Our results urge the community to perform more extended multiwavelength searches targeting lensed quasars, also among known samples. This effort could vitally contribute to solving the open problem of the growth of the brightest quasars.

Properties of reionization-era galaxies from JWST luminosity functions and 21-cm interferometry

ABSTRACT Upcoming observations will probe the first billion years of our Universe in unprecedented detail. Foremost among these are 21-cm interferometry with the Hydrogen Epoch of Reionization Arrays (HERA) and the Square Kilometre Array (SKA), and high-z galaxy observations with the James Webb Space Telescope (JWST). Here, we quantify how observations from these instruments can be used to constrain the astrophysics of high-z galaxies. We generate several mock JWST luminosity functions (LFs) and SKA1 21-cm power spectra, which are consistent with current observations, but assume different properties for the unseen, ultrafaint galaxies driving the epoch of reionization (EoR). Using only JWST data, we predict up to a factor of 2–3 improvement (compared with Hubble Space Telescope, HST) in the fractional uncertainty of the star formation rate to halo mass relation and the turnover magnitude. Most parameters regulating the ultraviolet (UV) galaxy properties can be constrained at the level of ∼10 per cent or better, if either (i) we are able to better characterize systematic lensing uncertainties than currently possible; or (ii) the intrinsic LFs peak at magnitudes brighter than MUV ≲ −13. Otherwise, improvement over HST-based inference is modest. When combining with upcoming 21-cm observations, we are able to significantly mitigate degeneracies, and constrain all of our astrophysical parameters, even for our most pessimistic assumptions about upcoming JWST LFs. The 21-cm observations also result in an order of magnitude improvement in constraints on the EoR history.

Empirical Modeling of the Redshift Evolution of the [ N II ] /Hα Ratio for Galaxy Redshift Surveys

Abstract We present an empirical parameterization of the [N ii]/Hα flux ratio as a function of stellar mass and redshift valid at 0 < z < 2.7 and 8.5 < log ( M / M ⊙ ) < 11.0 . This description can (i) easily be applied to simulations for modeling [N ii]λ6584 line emission, (ii) deblend [N ii] and Hα in current low-resolution grism and narrow-band observations to derive intrinsic Hα fluxes, and (iii) reliably forecast the number counts of Hα emission-line galaxies for future surveys, such as those planned for Euclid and the Wide Field Infrared Survey Telescope (WFIRST). Our model combines the evolution of the locus on the Baldwin, Phillips & Terlevich (BPT) diagram measured in spectroscopic data out to z ∼ 2.5 with the strong dependence of [N ii]/Hα on stellar mass and [O iii]/Hβ observed in local galaxy samples. We find large variations in the [N ii]/Hα flux ratio at a fixed redshift due to its dependency on stellar mass; hence, the assumption of a constant [N ii] flux contamination fraction can lead to a significant under- or overestimate of Hα luminosities. Specifically, measurements of the intrinsic Hα luminosity function derived from current low-resolution grism spectroscopy assuming a constant 29% contamination of [N ii] can be overestimated by factors of ∼8 at log ( L ) > 43.0 for galaxies at redshifts z ∼ 1.5. This has implications for the prediction of Hα emitters for Euclid and WFIRST. We also study the impact of blended Hα and [N ii] on the accuracy of measured spectroscopic redshifts.

A parametric description of the 3D structure of the Galactic bar/bulge using the VVV survey

We study the structure of the inner Milky Way using the latest data release of the Vista Variables in Via Lactea (VVV) survey. The VVV is a deep near-infrared, multi-colour photometric survey with a coverage of 300 square degrees towards the Bulge/Bar. We use Red Clump (RC) stars to produce a high-resolution dust map of the VVV's field of view. From de-reddened colour-magnitude diagrams we select Red Giant Branch stars to investigate their 3D density distribution within the central 4 kpc. We demonstrate that our best-fit parametric model of the Bulge density provides a good description of the VVV data, with a median percentage residual of 5$\%$ over the fitted region. The strongest of the otherwise low-level residuals are overdensities associated with a low-latitude structure as well as the so-called X-shape previously identified using the split RC. These additional components contribute only $\sim5\%$ and $\sim7\%$ respectively to the Bulge mass budget. The best-fit Bulge is `boxy' with an axis ratio of [1:0.44:0.31] and is rotated with respect to the Sun-Galactic Centre line by at least $20^{\circ}$. We provide an estimate of the total, full sky, mass of the Bulge of $M_\mathrm{Bulge}^{\mathrm{Chabrier}} = 2.36 \times 10^{10} M_{\odot}$ for a Chabrier initial mass function. We show there exists a strong degeneracy between the viewing angle and the dispersion of the Red Clump absolute magnitude distribution. The value of the latter is strongly dependent on the assumptions made about the intrinsic luminosity function of the Bulge.

Preheating of the early universe by radiation from high-mass X-ray binaries

Using a reliably measured intrinsic (i.e. corrected for absorption effects) present-day luminosity function of high-mass X-ray binaries (HMXBs) in the 0.25-2 keV energy band per unit star-formation rate, we estimate the preheating of the early Universe by soft X-rays from such systems. We find that X-ray irradiation, mainly executed by ultraluminous and supersoft ultraluminous X-ray sources with luminosity L> 10^39 erg/s, could significantly heat (T>T_cmb, where T_cmb is the temperature of the cosmic microwave background) the intergalactic medium by z~10 if the specific X-ray emissivity of the young stellar population in the early Universe was an order of magnitude higher than at the present epoch (which is possible due to the low metallicity of the first galaxies) and the soft X-ray emission from HMXBs did not suffer strong absorption within their galaxies. This makes it possible to observe the 21 cm line of neutral hydrogen in emission from redshifts z<10.

Bright end of the luminosity function of high-mass X-ray binaries: contributions of hard, soft and supersoft sources

Using a spectral analysis of bright Chandra X-ray sources located in 27 nearby galaxies and maps of star-formation rate (SFR) and ISM surface densities for these galaxies, we constructed the intrinsic X-ray luminosity function (XLF) of luminous high-mass X-ray binaries (HMXBs), taking into account absorption effects and the diversity of HMXB spectra. The XLF per unit SFR can be described by a power law dN/d log L=2.0(L/10^39 erg/s)^(-0.6) (M_Sun/yr)^(-1) from L=10^38 to 10^40.5 erg/s, where L is the unabsorbed luminosity at 0.25-8 keV. The intrinsic number of luminous HMXBs per unit SFR is a factor of ~2.3 larger than the observed number reported before. The intrinsic XLF is composed of hard, soft and supersoft sources (defined here as those with the 0.25-2 keV to 0.25-8 keV flux ratio of <0.6, 0.6-0.95 and >0.95, respectively) in ~2:1:1 proportion. We also constructed the intrinsic HMXB XLF in the soft X-ray band (0.25-2 keV). Here, the numbers of hard, soft and supersoft sources prove to be nearly equal. The cumulative present-day 0.25-2 keV emissivity of HMXBs with luminosities between 10^38 and 10^40.5 erg/s is ~5 10^39 erg/s (M_Sun/yr)^(-1), which may be relevant for studying the X-ray preheating of the early Universe.

The XXL Survey

X-ray extragalactic surveys are ideal laboratories for the study of the evolution and clustering of active galactic nuclei (AGN). The XXL Survey spans two fields of a combined 50 $deg^2$ observed for more than 6Ms with XMM-Newton, occupying the parameter space between deep surveys and very wide area surveys; at the same time it benefits from a wealth of ancillary data. This paper marks the first release of the XXL point source catalogue selected in the 2-10 keV energy band with limiting flux $F_{2-10keV}=4.8\cdot10^{-14}\rm{erg\,s^{-1}\,cm^{-2}}$. We use both public and proprietary data sets to identify the counterparts of the X-ray point-like sources and improved upon the photometric redshift determination for AGN by applying a Random Forest classification trained to identify for each object the optimal photometric redshift model library. We also assign a probability to each source to be a star or an outlier. We model with Bayesian analysis the X-ray spectra assuming a power-law model with the presence of an absorbing medium. We find an average unabsorbed photon index of $\Gamma=1.85$ and average hydrogen column density $\log{N_{H}}=21.07 cm^{-2}$. We find no trend of $\Gamma$ or $N_H$ with redshift and a fraction of 26% absorbed sources ($\log N_{H}>22$). We show that the XXL-1000-AGN number counts extended the number counts of the COSMOS survey to higher fluxes and are fully consistent with the Euclidean expectation. We constrain the intrinsic luminosity function of AGN in the 2-10 keV energy band where the unabsorbed X-ray flux is estimated from the X-ray spectral fit up to z=3. Finally, we demonstrate the presence of a supercluster size structure at redshift 0.14, identified by means of percolation analysis of the XXL-1000-AGN sample. The XXL survey, reaching a medium flux limit and covering a wide area is a stepping stone between current deep fields and planned wide area surveys.

DETAILED SHAPE AND EVOLUTIONARY BEHAVIOR OF THE X-RAY LUMINOSITY FUNCTION OF ACTIVE GALACTIC NUCLEI

We construct the rest-frame 2--10 keV intrinsic X-ray luminosity function of Active Galactic Nuclei (AGNs) from a combination of X-ray surveys from the all-sky Swift BAT survey to the Chandra Deep Field-South. We use ~3200 AGNs in our analysis, which covers six orders of magnitude in flux. The inclusion of the XMM and Chandra COSMOS data has allowed us to investigate the detailed behavior of the XLF and evolution. In deriving our XLF, we take into account realistic AGN spectrum templates, absorption corrections, and probability density distributions in photometric redshift. We present an analytical expression for the overall behavior of the XLF in terms of the luminosity-dependent density evolution, smoothed two power-law expressions in 11 redshift shells, three-segment power-law expression of the number density evolution in four luminosity classes, and binned XLF. We observe a sudden flattening of the low luminosity end slope of the XLF slope at z>~0.6. Detailed structures of the AGN downsizing have been also revealed, where the number density curves have two clear breaks at all luminosity classes above log LX>43. The two break structure is suggestive of two-phase AGN evolution, consisting of major merger triggering and secular processes.

Constraining the rate and luminosity function of Swift gamma-ray bursts

We compute the intrinsic isotropic peak luminosity function (LF) and formation rate of long gamma-ray bursts (LGRBs) using a novel approach. We complement a standard log N-log P brightness distribution and Vmax estimations with two observation–time relations: a redshift–observation-time relation (log z-log T) and a new luminosity–observation-time relation (log L-log T). We show that this approach reduces degeneracies that exist between the rate and LF of a brightness distribution. To account for the complex triggering algorithm employed by Swift, we use recent results of Lien et al. (2014) to produce a suite of efficiency functions. Using these functions with the above methods, we show that a log L-log T method can provide good constraints on the form of the LF, particularly the high end. Using a sample of 175 peak luminosities determined from redshifts with well-defined selection criteria, our results suggest that LGRBs occur at a local rate (without beaming corrections) of [0.7 < ρ0 < 0.8] Gpc−3 yr−1. Within this range, assuming a broken power-law LF, we find best estimates for the low- and high-energy indices of −0.95 ± 0.09 and −2.59 ± 0.93, respectively, separated by a break luminosity 0.80 ± 0.43 × 1052 erg s−1.

Search for strong gravitational lensing effect in the current GRB data of BATSE

Because gamma-ray bursts (GRBs) trace the high-z Universe, there is an appreciable probability for a GRB to be gravitational lensed by galaxies in the universe. Herein we consider the gravitational lensing effect of GRBs contributed by the dark matter halos in galaxies. Assuming that all halos have the singular isothermal sphere (SIS) mass profile in the mass range $10^{10} h^{-1} M_\odot < M < 2\times 10^{13} h^{-1}M_\odot $ and all GRB samples follow the intrinsic redshift distribution and luminosity function derived from the Swift LGRBs sample, we calculated the gravitational lensing probability in BATSE, Swift/BAT and Fermi/GBM GRBs, respectively. With an derived probability result in BATSE GRBs, we searched for lensed GRB pairs in the BATSE 5B GRB Spectral catalog. The search did not find any convincing gravitationally lensed events. We discuss our result and future observations for GRB lensing observation.