Broken Power-law Model Research Articles

Probing broadband spectral energy distribution and variability of Mrk 501 in the low flux state

We conducted a multi-wavelength analysis of the blazar Mrk501, utilizing observations from AstroSat (SXT, LAXPC), Swift-UVOT, and Fermi-LAT during the period August 15, 2016 to March 27, 2022. The resulting multi-wavelength light curve revealed relatively low activity of the source across the electromagnetic spectrum. Notably, logparabola and broken power-law models provided a better fit to the joint X-ray spectra from AstroSat-SXT/LAXPC instruments compared to the power-law model. During the low activity state, the source showed the characteristic “harder when brighter” trend at the X-ray energies. To gain insights into underlying physical processes responsible for the broadband emission, we performed a detailed broadband spectral analysis using the convolved one-zone leptonic model with different forms of particle distributions such as logparabola (LP), broken power-law (BPL), power-law model with maximum energy (ξmax), and energy-dependent acceleration (EDA) models. Our analysis revealed similar reduced-χ2 values for the four particle distributions. The LP and EDA models exhibited the lowest jet powers. The correlation analyses conducted for the LP and BPL models revealed that there is a positive correlation between jet power and bulk Lorentz factor. Specifically, in the LP model, jet power proved independent of γmin, whereas in the broken power-law model, jet power decreased with an increase in γmin. The jet power in the LP/EDA particle distribution is nearly 10 percent of the Eddington luminosity of a 107 M⊙ black hole. This result suggests that the jet could potentially be fueled by accretion processes.

The Formation Rate and Luminosity Function of Fast Radio Bursts

Fast radio bursts (FRBs) are millisecond-duration flashes with unknown origins. Their formation rate is crucial for unveiling physical origins. However, the luminosity and formation rate are degenerate when directly fitting the redshift distribution of FRBs. In contrast to previous forward-fitting methods, we use Lynden-Bell’s c − method to derive the luminosity function and formation rate of FRBs without any assumptions. Using the nonrepeating FRBs from the first Canadian Hydrogen Intensity Mapping Experiment FRB catalog, we find a relatively strong luminosity evolution, and luminosity function can be fitted by a broken power-law model with a break at 1.33 × 1041 erg s−1. The formation rate declines rapidly as (1 + z)−4.9±0.3 with a local rate of 1.13 × 104 Gpc−3 yr−1. This monotonic decrease is similar to the rate of short gamma-ray bursts. After comparing this function with the star formation rate and stellar mass density, we conclude that the old populations, including neutron stars and black holes, are closely related to the origins of FRBs.

Efficiency of Nonthermal Pulsed Emission from Eight MeV Pulsars

We report on the properties of pulsed X-ray emission from eight MeV pulsars using XMM-Newton, NICER, NuSTAR, and HXMT data. For five of the eight MeV pulsars, the X-ray spectra can be fit by a broken power-law model with a break energy of ∼5–10 keV. The photon indices below and above the break energy are ∼1 and ∼1.5, respectively. In comparison with the X-ray emission of the Fermi-LAT pulsars, the MeV pulsars have a harder spectrum and a higher radiation efficiency in the 0.3–10 keV energy bands. When isotropic emission is assumed, the emission efficiency in the keV–MeV bands is estimated to be η MeV ∼ 0.01–0.1, and this is similar to the efficiency of the GeV emission of the Fermi-LAT pulsars with a similar spin-down power. To explain the observed efficiency of the MeV pulsars, we estimate the required pair multiplicity as 104–7, which depends on the emission process (curvature radiation or synchrotron radiation) and on the location in the magnetosphere. The high multiplicity indicates that the secondary pairs that are created by a pair-creation process of the GeV photons produce the X-ray/soft gamma-ray emission of the MeV pulsars. We speculate that the difference between MeV pulsars and Fermi-LAT pulsars can be attributed to the difference in viewing angle measured from the spin axis if the emission originates from a region inside the light cylinder (canonical gap model) or to the difference in the inclination angle of the magnetic axis if the emission is produced in the equatorial current sheet outside the light cylinder.

Constraints on primordial curvature power spectrum with pulsar timing arrays

The stochastic signal detected by NANOGrav, PPTA, EPTA, and CPTA can be explained by the scalar-induced gravitational waves. In order to determine the scalar-induced gravitational waves model that best fits the stochastic signal, we employ both single- and double-peak parameterizations for the power spectrum of the primordial curvature perturbations, where the single-peak scenarios include the δ-function, box, lognormal, and broken power law model, and the double-peak scenario is described by the double lognormal form.Using Bayesian inference, we find that there is no significant evidence for or against the single-peak scenario over the double-peak model, with log (Bayes factors) among these models ln ℬ < 1.Therefore, we cannot distinguish the different shapes of the power spectrum of the primordial curvature perturbation with the current sensitivity of pulsar timing arrays.

Mass Reconstruction of Galaxy-scale Strong Gravitational Lenses Using a Broken Power-law Model

With mock strong gravitational lensing images, we investigate the performance of the broken power-law (BPL) model proposed by Du et al. () on the mass reconstruction of galaxy-scale lenses. An end-to-end test is carried out, including the creation of mock strong lensing images, the subtraction of lens light, and the reconstruction of lensed images, where the lenses are selected from the galaxies in the Illustris-1 simulation. We notice that, regardless of the adopted mass models (the BPL model or its special cases), the Einstein radius can be robustly determined from imaging data alone, and the median bias is typically less than 1%. Away from the Einstein radius, the lens mass distribution tends to be harder to measure, especially at radii where there are no lensed images detected. We find that, with rigid priors, the BPL model can clearly outperform the single power-law models by achieving <5% median bias on the radial convergence profile within the Einstein radius. As for the source light reconstructions, they are found to be sensitive to both lens light contamination and lens mass models, where the BPL model with rigid priors still performs best when there is no lens light contamination. We show that, by correcting for the projection effect, the BPL model can estimate the aperture and luminosity weighted line-of-sight velocity dispersions to an accuracy of ∼6% scatter. These results highlight the great potential of the BPL model in strong lensing related studies.

Mapping the milky way’s stellar halo with 2D data

ABSTRACT We propose a new method for measuring the spatial density distribution of the stellar halo of the Milky Way. Our method is based on a pairwise statistic of the distribution of stars in the sky, the angular two-point correlation function (ATPCF). The ATPCF utilizes two-dimensional data of stars only and is therefore immune to the large uncertainties in the determination of distances to stars. We test our method using mock stellar data coming from various models including the single power-law (SPL) and the broken power-law (BPL) density profiles. We also test the influence of axisymmetric flattening factors using both constant and varying values. We find that the ATPCF is a powerful tool for recovering the spatial distributions of the stellar haloes in our models. We apply our method to observational data from the type ab RR Lyrae catalogue in the Catalina Survey Data Release 1. In the 3-parameter BPL model, we find that $s_{1}=2.46_{-0.20}^{+0.18}, s_{2}=3.99_{-1.33}^{+0.75}$, and $r_{0}=31.11_{-5.88}^{+7.61}$, which are in good agreement with previous results. We also find that introducing an extra parameter, the radially varying flattening factor, greatly improves our ability to model accurately the observed data distribution. This implies perhaps that the stellar halo of the Milky Way should be regarded as oblate.

Detection of spectral hardenings in cosmic-ray boron-to-carbon and boron-to-oxygen flux ratios with DAMPE

Boron nuclei in cosmic rays (CRs) are believed to be mainly produced by the fragmentation of heavier nuclei, such as carbon and oxygen, via collisions with the interstellar matter. Therefore, the boron-to-carbon flux ratio (B/C) and the boron-to-oxygen flux ratio (B/O) are very essential probes of the CR propagation. The energy dependence of the B/C ratio from previous balloon-borne and space-based experiments can be well described by a single power-law up to about 1 TeV/n within uncertainties. This work reports direct measurements of B/C and B/O in the energy range from 10 GeV/n to 5.6 TeV/n with 6 years of data collected by the Dark Matter Particle Explorer, with high statistics and well controlled systematic uncertainties. The energy dependence of both the B/C and B/O ratios can be well fitted by a broken power-law model rather than a single power-law model, suggesting the existence in both flux ratios of a spectral hardening at about 100 GeV/n. The significance of the break is about 5.6σ and 6.9σ for the GEANT4 simulation, and 4.4σ and 6.9σ for the alternative FLUKA simulation, for B/C and B/O, respectively. These results deviate from the predictions of conventional turbulence theories of the interstellar medium (ISM), which point toward a change of turbulence properties of the ISM at different scales or novel propagation effects of CRs, and should be properly incorporated in the indirect detection of dark matter via anti-matter particles.

Testing strong lensing subhalo detection with a cosmological simulation

ABSTRACT Strong gravitational lensing offers a compelling test of the cold dark matter paradigm, as it allows for subhaloes with masses of ∼109 M⊙ and below to be detected. We test commonly used techniques for detecting subhaloes superposed in images of strongly lensed galaxies. For the lens we take a simulated galaxy in a ∼1013 M⊙ halo grown in a high-resolution cosmological hydrodynamical simulation, which we view from two different directions. Though the resolution is high, we note the simulated galaxy still has an artificial core which adds additional complexity to the baryon dominated region. To remove particle noise, we represent the projected galaxy mass distribution by a series of Gaussian profiles which precisely capture the features of the projected galaxy. We first model the lens mass as a (broken) power-law density profile and then search for small haloes. Of the two projections, one has a regular elliptical shape, while the other has distinct deviations from an elliptical shape. For the former, the broken power-law model gives no false positives and correctly recovers the mass of the superposed small halo; however, for the latter we find false positives and the inferred halo mass is overestimated by ∼4–5 times. We then use a more complex model in which the lens mass is decomposed into stellar and dark matter components. In this case, we show that we can capture the simulated galaxy’s complex projected structures and correctly infer the input small halo.

Searching for an additional high-energy component in Fermi-LAT GRB afterglows

Context. The very high-energy (VHE; ≥100 GeV) component from at least two gamma-ray bursts (GRBs), that is, GRB 180720B and GRB 190114C, has been detected in the afterglow phase. It is widely discussed that the GeV to TeV emission originated from a synchrotron self-Compton (SSC) process. The VHE component may cause an upturn at the high-energy spectral ends in the Fermi-Large Area Telescope (Fermi-LAT) observing band. Aims. We aim to find out whether an additional high-energy component commonly exists in the afterglows of Fermi-LAT GRBs. This study will help us to better understand how common it is for a GRB afterglow detected by Fermi-LAT to involve a VHE component. Methods. First, we selected the GRBs that emit ≥10 GeV photons. The ≥10 GeV photons can be considered as a plausible proxy for a VHE component. We systematically analyzed 199 GRBs detected by Fermi-LAT from 2008–2019. If an additional high-energy component exists in the afterglows of Fermi-LAT GRBs, the best-fit spectral model could be a broken power law (BPL) model with an upturn above a break energy. We compared the afterglow spectra using power-law (PL) and BPL representations. Results. Out of the 30 GRBs with ≥10 GeV photons that arrived after T90 (the time duration when 90% of the prompt emission was detected), 25 GRBs are tentatively or significantly detected at 0.1–200 GeV after 2 × T90. The spectrum of GRB 131231A shows an upturn above an energy break of 1.6 ± 0.8 GeV, supporting the BPL model. For GRB 131231A, we performed a modeling of its X-ray and γ-ray spectra and found that the SSC model can explain the upturn with acceptable parameter values. In the cases of GRB 190114C, GRB 171210A, GRB 150902A, GRB 130907A, GRB 130427A, and GRB 090902B, the improvement of the BPL fit compared to the PL fit is tentative or marginal. Conclusions. There is no conclusive evidence that an additional higher energy component commonly exists in Fermi-LAT GRB afterglows, except for the group of Fermi-LAT GRBs mentioned above. Such an additional high-energy component may be explained by the SSC mechanism. Current and future VHE observations will provide important constraints on the issue.

Examining Two-dimensional Luminosity–Time Correlations for Gamma-Ray Burst Radio Afterglows with VLA and ALMA

Abstract Gamma-ray burst (GRB) afterglow emission can be observed from sub-TeV to radio wavelengths, though only 6.6% of observed GRBs present radio afterglows. We examine GRB radio light curves (LCs) to look for the presence of radio plateaus resembling the plateaus observed at X-ray and optical wavelengths. We analyze 404 GRBs from the literature with observed radio afterglow and fit 82 GRBs with at least five data points with a broken power-law model, requiring four parameters. From these, we find 18 GRBs that present a break feature resembling a plateau. We conduct the first multiwavelength study of the Dainotti correlation between the luminosity L a and the rest-frame time of break T a * for those 18 GRBs, concluding that the correlation exists and resembles the corresponding correlation at X-ray and optical wavelengths after correction for evolutionary effects. We compare T a * for the radio sample with T a * values in X-ray and optical data, finding significantly later break times in the radio. We propose that this late break time and the compatibility in slope suggest either a long-lasting plateau or the passage of a spectral break in the radio band. We also correct the distribution of the isotropic energy E iso versus the rest-frame burst duration T * 90 for evolutionary effects and conclude that there is no significant difference between the T*90 distributions for the radio LCs with a break and for those without.

Ain’t No Mountain High Enough: Semiparametric Modeling of LIGO–Virgo’s Binary Black Hole Mass Distribution

Abstract We introduce a semiparametric model for the primary mass distribution of binary black holes (BBHs) observed with gravitational waves (GWs) that applies a cubic-spline perturbation to a power law. We apply this model to the 46 BBHs included in the second gravitational-wave transient catalog (GWTC-2). The spline perturbation model recovers a consistent primary mass distribution with previous results, corroborating the existence of a peak at 35 M ⊙ (&gt;97% credibility) found with the Powerlaw+Peak model. The peak could be the result of pulsational pair-instability supernovae. The spline perturbation model finds potential signs of additional features in the primary mass distribution at lower masses similar to those previously reported by Tiwari and Fairhurst. However, with fluctuations due to small-number statistics, the simpler Powerlaw+Peak and BrokenPowerlaw models are both still perfectly consistent with observations. Our semiparametric approach serves as a way to bridge the gap between parametric and nonparametric models to more accurately measure the BBH mass distribution. With larger catalogs we will be able to use this model to resolve possible additional features that could be used to perform cosmological measurements and will build on our understanding of BBH formation, stellar evolution, and nuclear astrophysics.

Constraining Type Ia Supernova Delay Time with Spatially Resolved Star Formation Histories

Abstract We present the delay time distribution (DTD) estimates of Type Ia supernovae (SNe Ia) using spatially resolved SN Ia host galaxy spectra from MUSE and MaNGA. By employing a grouping algorithm based on k-means and earth mover’s distances (EMDs), we separated the host galaxy stellar population age distributions (SPADs) into spatially distinct regions and used maximum likelihood method to constrain the DTD of SN Ia progenitors. When a power-law model of the form DTD(t) ∝ t s (t &gt; τ) is used, we find an SN rate decay slope s = − 1.41 − 0.33 + 0.32 and a delay time τ = 120 − 83 + 142 Myr . Moreover, we tested other DTD models, such as a broken power-law model and a two-component power-law model, and found no statistically significant support for these alternative models.

The dynamical structure of broken power-law and double power-law models for dark matter haloes

ABSTRACT Galaxy kinematics and gravitational lensing are two complementary ways to constrain the distribution of dark matter on galaxy scales. The typical dark matter density profiles adopted in dynamical studies cannot easily be adopted in lensing studies. Ideally, a mass model should be used that has the global characteristics of realistic dark matter distributions, and that allows for an analytical calculation of the magnifications and deflection angles. A simple model with these properties, the broken power-law (BPL) model, has very recently been introduced. We examine the dynamical structure of the family of BPL models. We derive simple closed expressions for basic dynamical properties, and study the distribution function under the assumption of velocity isotropy. We find that none of the BPL models with realistic parameters has an isotropic distribution function that is positive over the entire phase space, implying that the BPL models cannot be supported by an isotropic velocity distribution, or models with a more radially anisotropic orbital structure. This result limits the attractiveness of the BPL family as a tool for lensing studies to some degree. More generally, we find that not all members of the general family of double power-law or Zhao models, often used to model dark matter haloes, can be supported by an isotropic or radially anisotropic distribution function. In other words, the distribution function may become negative even for spherically symmetric models with a well-behaved density profile.

The VLA-COSMOS 3 GHz Large Project: Average radio spectral energy distribution of active galactic nuclei

Context.As the Square Kilometer Array (SKA) is expected to be operational in the next decade, investigations of the radio sky in the range of 100 MHz–10 GHz have become important for simulating SKA observations. In determining physical properties of galaxies from radio data, the radio spectral energy distribution (SED) is often assumed to be described by a simple power law, usually with a spectral index of 0.7 for all sources. Even though radio SEDs have been shown to exhibit deviations from this assumption, both in differing spectral indices and complex spectral shapes, it is often presumed that their individual differences can be canceled out in large samples.Aims.Since the average spectral index around 1 GHz (observed-frame) is important for determining physical properties of large samples of galaxies, we aim to test whether individual differences in the spectra of radio-identified active galactic nuclei align with the simple assumption ofα = 0.7 and test the evolution of the parameters of the synchrotron aging model with redshift and radio luminosity.Methods.We use a sample of 744 radio-excess active galactic nuclei (RxAGN), defined as those that exhibit more than a 3σradio luminosity excess with respect to the value expected only from the contribution from star formation, out toz ∼ 4. We constructed their average radio SED by combining Very Large Array (VLA) observations of the COSMOS field at 1.4 GHz and 3 GHz with Giant Meterwave Radio Telescope (GMRT) observations at 325 MHz and 610 MHz. To account for nondetections in the GMRT maps, we employed the survival analysis technique. We binned the RxAGN sample into luminosity- and redshift-complete subsamples. In each bin, we constrained the shape of the average radio SED by fitting a broken power-law model.Results.We find that the RxAGN sample can be described by a spectral index ofα1 = 0.28 ± 0.03 below the break frequencyνb = (4.1 ± 0.2) GHz andα2 = 1.16 ± 0.04 above it, while a simple power-law model, capturing fewer spectral features, yields a single spectral index of 0.64 ± 0.07. By binning in 1.4 GHz of radio luminosity and redshift, we find that the power-law spectral index is positively correlated with redshift and that the broken power-law spectral index above 4 GHz is positively correlated with both the redshift and source size. By selecting sources with sizes less than 1 kpc, we find a subsample of flat-spectrum sources, which can be described by a spectral index ofα = 0.41 ± 0.07 and a broken power-law spectral index ofα1 = 0.1 ± 0.1 (α2 = 0.55 ± 0.09) below (above) a break frequency ofνb = (2.7 ± 0.5) GHz.Conclusions.We have constrained the radio SED for a sample of RxAGN in the COSMOS field using available VLA and GMRT data, corresponding to the rest-frame frequency range from ∼0.3 GHz to ∼10 GHz. We describe our derived average radio SED of RxAGN using power-law and broken power-law models, yielding a radio SED that steepens above ∼4 GHz.

Spatial power spectra of dust across the Local Group: No constraint on disc scale height

ABSTRACT We analyse the 1D spatial power spectra of dust surface density and mid to far-infrared emission at $24\!-\!500\, \mu$m in the LMC, SMC, M31, and M33. By forward-modelling the point spread function (PSF) on the power spectrum, we find that nearly all power spectra have a single power-law and point source component. A broken power-law model is only favoured for the LMC 24 μm MIPS power spectrum and is due to intense dust heating in 30 Doradus. We also test for local power spectrum variations by splitting the LMC and SMC maps into 820 pc boxes. We find significant variations in the power-law index with no strong evidence for breaks. The lack of a ubiquitous break suggests that the spatial power spectrum does not constrain the disc scale height. This contradicts claims of a break where the turbulent motion changes from 3D to 2D. The power spectrum indices in the LMC, SMC, and M31 are similar (2.0–2.5). M33 has a flatter power spectrum (1.3), similar to more distant spiral galaxies with a centrally-concentrated H2 distribution. We compare the power spectra of H i, CO, and dust in M31 and M33, and find that H i power spectra are consistently flatter than CO power spectra. These results cast doubt on the idea that the spatial power spectrum traces large scale turbulent motion in nearby galaxies. Instead, we find that the spatial power spectrum is influenced by (1) the PSF on scales below ∼3 times the FWHM, (2) bright compact regions (30 Doradus), and (3) the global morphology of the tracer (an exponential CO disc).

X-Ray Spectral Evolution of PSR J2032+4127 during the 2017 Periastron Passage

Abstract We report X-ray data analysis results obtained from Chandra, XMM-Newton, Nuclear Spectroscopic Telescope Array Mission (NuSTAR), and Swift observations of PSR J2032+4127 taken before, during, and after the periastron on 2017 November 13. We found the first clear evidence of a change in the X-ray spectral index over the passage period, thanks to a broad and sensitive spectral coverage by XMM-Newton and NuSTAR. We analyzed the joint XMM-Newton and NuSTAR observation epochs with power-law and broken power-law models. We have obtained changes in spectral parameters before and after the periastron passage for both models. The spectra get softened after the passage. The evolution of the spectral index and break energy before and after the periastron may indicate a change in the physical state of shock-accelerated electrons.

Signature of Stochastic Acceleration and Cooling Processes in an Outburst Phase of the TeV Blazar ON 231

Abstract We present a detailed spectral and temporal study of the intermediate-type blazar ON 231 during the TeV outburst phase in 2008 June with observations performed by Swift and XMM-Newton. The X-ray flux of the source, which was significantly dominated by the soft photons (below 3–4 keV), varies between 27% and 38% on day timescales, while mild variations were observed in the optical/UV emissions. We found a maximum soft lag of ∼1 hr between the UV and soft X-ray band, which can be understood if the magnetic field of the emitting region is ∼5.6 δ −1/3 G. The 0.6–10 keV spectra can be well represented by a broken power-law model, which indicates the presence of both synchrotron and inverse Compton components in the studied X-ray regime. The synchrotron part of the spectral energy distributions (SEDs) constructed with simultaneous optical/UV and X-ray data follows a log-parabolic shape. A time-resolved spectral analysis shows that the break energy varies significantly between 2.4 and 7.3 keV with the changing flux state of the source, and the similar variations of the spectral slopes of the two components support the synchrotron self-Compton scenario. The synchrotron tail, following a log-parabolic function, shows that the peak frequency (ν p ) varies by two orders of magnitude (∼1014–1016 Hz) during the event. A significantly positive E p –β relation is observed from both SED and time-resolved spectral analyses. The most feasible scenario for the observed trend during the flaring event could be associated with a magnetic-field-driven stochastic process evolving toward an equilibrium energy level.

A Catalog of X-Ray Point Sources in the Abell 133 Region

As an evolutionary phase of galaxies, active galactic nuclei (AGN) over a large range of redshift have been utilized for understanding cosmic evolution. In particular, the population and evolution of AGNs have been investigated through the study of the cosmic X-ray background in various fields. As one of the deep fields observed by Chandra with a total of 2.8 Msec exposures, Abell 133 is a special region to investigate AGNs, providing a testbed for probing the environmental effect on AGN trigger, since cluster environments can be different from field environments. The achieved flux limit of data at 50% completeness level of 6.95x10^(-16), 1.43x10^(-16), and 1.57x10^(-15) ergs cm^(-2) in 0.5-8, 0.5-2, and 2-8 keV. Using the wavdetect and no-source binomial probability (i.e., p<0.007), we analyze the combined \textit{Chandra} image, detecting 1617 (in 0.5-8 keV), 1324 (in 0.5-2 keV), and 1028 (in 2-8 keV), X-ray point sources in the Abell 133 region. Here, we present the X-ray point source catalogue with the source fluxes, which can be combined with multiwavelength data for future works. We find that the number count distribution of the X-ray point sources is well reproduced with a broken power-law model while the best-fit model parameters are sensitive to the fitting range of the number count distribution. Finally, we find an excess of the number density (decrease of AGN fraction) at the central region of the cluster, which reflects the effect of dense environments on AGN trigger, as similarly found in studies of other galaxy clusters.

Binary neutron star merger rate via the luminosity function of short gamma-ray bursts

The luminosity function of short Gamma Ray Bursts (GRBs) is modelled by using the available catalogue data of all short GRBs (sGRBs) detected till October, 2017. The luminosities are estimated via the `pseudo-redshifts' obtained from the `Yonetoku correlation', assuming a standard delay distribution between the cosmic star formation rate and the production rate of their progenitors. While the simple powerlaw is ruled out to high confidence, the data is fit well both by exponential cutoff powerlaw and broken powerlaw models. Using the derived parameters of these models along with conservative values in the jet opening angles seen from afterglow observations, the true rate of short GRBs are derived. Assuming a short GRB is produced from each binary neutron star merger (BNSM), the rate of gravitational wave (GW) detections from these mergers are derived for the past, present and future configurations of the GW detector networks. Stringent lower limits of $1.87 \pyr$ for the aLIGO-VIRGO, and $3.11 \pyr$ for the upcoming aLIGO-VIRGO-KAGRA-LIGO/India configurations are thus derived for the BNSM rate at $68 \%$ confidence. The BNSM rates calculated from this work and that independently inferred from the observation of the only confirmed BNSM observed till date, are shown to have a mild tension; however the scenario that all BNSMs produce sGRBs cannot be ruled out.

LOFAR/H-ATLAS: the low-frequency radio luminosity–star formation rate relation

Radio emission is a key indicator of star-formation activity in galaxies, but the radio luminosity-star formation relation has to date been studied almost exclusively at frequencies of 1.4 GHz or above. At lower radio frequencies the effects of thermal radio emission are greatly reduced, and so we would expect the radio emission observed to be completely dominated by synchrotron radiation from supernova-generated cosmic rays. As part of the LOFAR Surveys Key Science project, the Herschel-ATLAS NGP field has been surveyed with LOFAR at an effective frequency of 150 MHz. We select a sample from the MPA-JHU catalogue of SDSS galaxies in this area: the combination of Herschel, optical and mid-infrared data enable us to derive star-formation rates (SFRs) for our sources using spectral energy distribution fitting, allowing a detailed study of the low-frequency radio luminosity--star-formation relation in the nearby Universe. For those objects selected as star-forming galaxies (SFGs) using optical emission line diagnostics, we find a tight relationship between the 150 MHz radio luminosity ($L_{150}$) and SFR. Interestingly, we find that a single power-law relationship between $L_{150}$ and SFR is not a good description of all SFGs: a broken power law model provides a better fit. This may indicate an additional mechanism for the generation of radio-emitting cosmic rays. Also, at given SFR, the radio luminosity depends on the stellar mass of the galaxy. Objects which were not classified as SFGs have higher 150-MHz radio luminosity than would be expected given their SFR, implying an important role for low-level active galactic nucleus activity.