Source Count Distribution Research Articles

Source Count Distribution of Fermi LAT Gamma-Ray Blazars Using Novel Nonparametric Methods

We utilized a sample from the Fermi-LAT 14-year Source Catalog by adjusting the flux detection threshold, enabling us to derive the intrinsic source count distribution dN/dF25 of extragalactic blazars using nonparametric, unbinned methods developed by Efron and Petrosian and Lynden-Bell. Subsequently, we evaluated the contribution of blazars to the extragalactic gamma-ray background. Our findings are summarized as follows: (1) There is no significant correlation between flux and spectral index values among blazars and their subclasses FSRQs and BL Lacs. (2) The intrinsic differential distributions of flux values exhibit a broken-power-law form, with parameters that closely match previous findings. The intrinsic photon index distributions are well described by a Gaussian form for FSRQs and BL Lacs individually, while a dual-Gaussian model provides a more appropriate fit for blazars as a whole. (3) Blazars contribute 34.5% to the extragalactic gamma-ray background and 16.8% to the extragalactic diffuse gamma-ray background. When examined separately, FSRQs and BL Lacs contribute 19.6% and 13% to the extragalactic gamma-ray background, respectively.

Deepening gamma-ray point-source catalogues with sub-threshold information

We propose a novel statistical method to extend Fermi-LAT catalogues of high-latitude γ-ray sources below their nominal threshold. To do so, we rely on the determination of the differential source-count distribution of sub-threshold sources which only provides the statistical flux distribution of faint sources. By simulating ensembles of synthetic skies, we assess quantitatively the likelihood for pixels in the sky with relatively low-test statistics to be due to sources, therefore complementing the source-count distribution with spatial information. Besides being useful to orient efforts towards multi-messenger and multi-wavelength identification of new γ-ray sources, we expect the results to be especially advantageous for statistical applications such as cross-correlation analyses.

Extracting the gamma-ray source-count distribution below the Fermi-LAT detection limit with deep learning

We reconstruct the extra-galactic gamma-ray source-count distribution, or dN/dS, of resolved and unresolved sources by adopting machine learning techniques. Specifically, we train a convolutional neural network on synthetic 2-dimensional sky-maps, which are built by varying parameters of underlying source-counts models and incorporate the Fermi-LAT instrumental response functions. The trained neural network is then applied to the Fermi-LAT data, from which we estimate the source count distribution down to flux levels a factor of 50 below the Fermi-LAT threshold. We perform our analysis using 14 years of data collected in the (1,10) GeV energy range. The results we obtain show a source count distribution which, in the resolved regime, is in excellent agreement with the one derived from cataloged sources, and then extends as dN/dS ∼ S -2 in the unresolved regime, down to fluxes of 5 · 10-12 cm-2 s-1. The neural network architecture and the devised methodology have the flexibility to enable future analyses to study the energy dependence of the source-count distribution.

Exploring the High-redshift PBH-ΛCDM Universe: Early Black Hole Seeding, the First Stars and Cosmic Radiation Backgrounds

Abstract We explore the observational implications of a model in which primordial black holes (PBHs) with a broad birth mass function ranging in mass from a fraction of a solar mass to ∼106 M ⊙, consistent with current observational limits, constitute the dark matter (DM) component in the universe. The formation and evolution of dark matter and baryonic matter in this PBH-Λ cold dark matter (ΛCDM) universe are presented. In this picture, PBH-DM mini-halos collapse earlier than in standard ΛCDM, baryons cool to form stars at z ∼ 15–20, and growing PBHs at these early epochs start to accrete through Bondi capture. The volume emissivity of these sources peaks at z ∼ 20 and rapidly fades at lower redshifts. As a consequence, PBH DM could also provide a channel to make early black hole seeds and naturally account for the origin of an underlying DM halo–host galaxy and central black hole connection that manifests as the M bh–σ correlation. To estimate the luminosity function and contribution to integrated emission power spectrum from these high-redshift PBH-DM halos, we develop a halo occupation distribution model. In addition to tracing the star formation and reionization history, it permits us to evaluate the cosmic infrared and X-ray backgrounds. We find that accretion onto PBHs/active galactic nuclei successfully accounts for the detected backgrounds and their cross-correlation, with the inclusion of an additional IR stellar emission component. Detection of the deep IR source count distribution by the James Webb Space Telescope could reveal the existence of this population of high-redshift star-forming and accreting PBH DM.

Extracting the Galactic Center excess’ source-count distribution with neural nets

The two leading hypotheses for the Galactic Center Excess (GCE) in the $\textit{Fermi}$ data are an unresolved population of faint millisecond pulsars (MSPs) and dark-matter (DM) annihilation. The dichotomy between these explanations is typically reflected by modeling them as two separate emission components. However, point-sources (PSs) such as MSPs become statistically degenerate with smooth Poisson emission in the ultra-faint limit (formally where each source is expected to contribute much less than one photon on average), leading to an ambiguity that can render questions such as whether the emission is PS-like or Poissonian in nature ill-defined. We present a conceptually new approach that describes the PS and Poisson emission in a unified manner and only afterwards derives constraints on the Poissonian component from the so obtained results. For the implementation of this approach, we leverage deep learning techniques, centered around a neural network-based method for histogram regression that expresses uncertainties in terms of quantiles. We demonstrate that our method is robust against a number of systematics that have plagued previous approaches, in particular DM / PS misattribution. In the $\textit{Fermi}$ data, we find a faint GCE described by a median source-count distribution (SCD) peaked at a flux of $\sim4 \times 10^{-11} \ \text{counts} \ \text{cm}^{-2} \ \text{s}^{-1}$ (corresponding to $\sim3 - 4$ expected counts per PS), which would require $N \sim \mathcal{O}(10^4)$ sources to explain the entire excess (median value $N = \text{29,300}$ across the sky). Although faint, this SCD allows us to derive the constraint $\eta_P \leq 66\%$ for the Poissonian fraction of the GCE flux $\eta_P$ at 95% confidence, suggesting that a substantial amount of the GCE flux is due to PSs.

The z–DM distribution of fast radio bursts

ABSTRACT We develop a sophisticated model of fast radio burst (FRB) observations, accounting for the intrinsic cosmological gas distribution and host galaxy contributions, and give the most detailed account yet of observational biases due to burst width, dispersion measure, and the exact telescope beamshape. Our results offer a significant increase in both accuracy and precision beyond those previously obtained. Using results from ASKAP and Parkes, we present our best-fitting FRB population parameters in a companion paper. Here, we consider in detail the expected and fitted distributions in redshift, dispersion measure, and signal to noise. We estimate that the unlocalized ASKAP FRBs arise from z < 0.5, with between a third and a half within z < 0.1. Our predicted source-counts (‘logN–logS’) distribution confirms previous indications of a steepening index near the Parkes detection threshold of 1 Jy ms. We find no evidence for a minimum FRB energy, and rule out Emin > 1039.0 erg at 90 per cent C.L. Importantly, we find that above a certain DM, observational biases cause the Macquart (DM–z) relation to become inverted, implying that the highest-DM events detected in the unlocalized Parkes and ASKAP samples are unlikely to be the most distant. More localized FRBs will be required to quantitatively estimate this effect, though its cause is a well-understood observational bias. Works assuming a 1–1 DM–z relation may therefore derive erroneous results. Our analysis of errors suggests that limiting factors in our analysis are understanding of FRB spectral behaviour, sensitivity response of search experiments, and the treatment of the repeating population and luminosity function.

Initial results from a real-time FRB search with the GBT

ABSTRACT We present the data analysis pipeline, commissioning observations, and initial results from the greenburst fast radio burst (FRB) detection system on the Robert C. Byrd Green Bank Telescope (GBT) previously described by Surnis et al., which uses the 21-cm receiver observing commensally with other projects. The pipeline makes use of a state-of-the-art deep learning classifier to winnow down the very large number of false-positive single-pulse candidates that mostly result from radio frequency interference. In our observations, totalling 156.5 d so far, we have detected individual pulses from 20 known radio pulsars that provide an excellent verification of the system performance. We also demonstrate, through blind injection analyses, that our pipeline is complete down to a signal-to-noise threshold of 12. Depending on the observing mode, this translates into peak flux sensitivities in the range 0.14–0.89 Jy. Although no FRBs have been detected to date, we have used our results to update the analysis of Lawrence et al. to constrain the FRB all-sky rate to be $1150^{+200}_{-180}$ per day above a peak flux density of 1 Jy. We also constrain the source count index α = 0.84 ± 0.06, which indicates that the source count distribution is substantially flatter than expected from a Euclidean distribution of standard candles (where α = 1.5). We discuss this result in the context of the FRB redshift and luminosity distributions. Finally, we make predictions for detection rates with greenburst, as well as other ongoing and planned FRB experiments.

Source-count Distribution of Gamma-Ray Blazars

Abstract With 10 years of operation and an exceptional data set, the Fermi-Large Area Telescope allows us to unveil the detailed composition of the extragalactic γ-ray sky above 100 MeV. In this paper, we derive the intrinsic source-count distribution (logN–logS) of extragalactic sources (i.e., blazars) at via the efficiency correction method. With this approach, we are able to measure the distribution down to a photon flux of and to an energy flux of ∼10−12 . In both cases, the logN–logS becomes flatter at low fluxes. Moreover, we show that this logN–logS is representative of the blazar population (assuming the majority of unassociated sources are blazars) and allows us to constrain its evolution quite effectively. Among recently proposed evolutionary models, we find that the Pure Density Evolution model best describes the evolutionary properties of the blazar population and that their integrated emission accounts for of the total extragalactic γ-ray background.

Testing gamma-ray models of blazars in the extragalactic sky

The global contribution of unresolved gamma-ray point sources to the extragalactic gamma-ray background has been recently measured down to gamma-ray fluxes lower than those reached with standard source detection techniques, and by employing the statistical properties of the observed gamma-ray counts. We investigate and exploit the complementarity of the information brought by the one-point statistics of photon counts (using more than 10 years of Fermi-LAT data) and by the recent measurement of the angular power spectrum of the unresolved gamma-ray background (based on 8 years of Fermi-LAT data). We determine, under the assumption that the source-count distribution of the brightest unresolved objects is dominated by blazars, their gamma-ray luminosity function and spectral energy distribution down to fluxes almost two orders of magnitude smaller than the threshold for detecting resolved sources. The different approaches provide consistent predictions for the gamma-ray luminosity function of blazars, and they show a significant complementarity.

A Search for Neutrino Point-source Populations in 7 yr of IceCube Data with Neutrino-count Statistics

Abstract The presence of a population of point sources in a data set modifies the underlying neutrino-count statistics from the Poisson distribution. This deviation can be exactly quantified using the non-Poissonian template fitting technique, and in this work we present the first application of this approach to the IceCube high-energy neutrino data set. Using this method, we search in 7 yr of IceCube data for point-source populations correlated with the disk of the Milky Way, the Fermi bubbles, the Schlegel, Finkbeiner, and Davis dust map, or with the isotropic extragalactic sky. No evidence for such a population is found in the data using this technique, and in the absence of a signal, we establish constraints on population models with source-count distribution functions that can be described by a power law with a single break. The derived limits can be interpreted in the context of many possible source classes. In order to enhance the flexibility of the results, we publish the full posterior from our analysis, which can be used to establish limits on specific population models that would contribute to the observed IceCube neutrino flux.

Gamma-ray luminosity function of BL Lac objects and contribution to the extragalactic gamma-ray background

ABSTRACT Using a significantly enlarged Fermi-LAT BL Lac objects (BL Lacs) sample, we construct the gamma-ray luminosity function (GLF) of BL Lacs, by the joint use of the space density distribution and source counts distribution. We use three well-studied forms of the GLF, i.e. the forms of pure density evolution (PDE), pure luminosity evolution (PLE), and luminosity-dependent density evolution (LDDE). The Markov Chain Monte Carlo (MCMC) technique is used to constrain model parameters. Our results suggest that LDDE model can give the best description for the BL Lac GLF. And the model shows that the BL Lacs with a harder GeV spectrum and a less luminosity evolve as strongly as flat spectrum radio quasars, and the evolution decreases as increasing luminosity. We also model the average photon spectra of BL Lacs with a double power-laws model. Using this modelled spectra, BL Lacs contribute $\sim \!20{{\ \rm per\ cent}}$ of the total extragalactic gamma-ray background (EGB) at E > 100 MeV, $\sim \!100{{\ \rm per\ cent}}$ of the EGB at E > 50 GeV, and the unresolved BL Lacs contribute $\sim\! 20 {{\ \rm per\ cent}}$ of the isotropic diffuse gamma-ray background at E > 100 MeV. A prediction of the TeV EGB spectra are given, which may be tested by the future detectors.

The performance and calibration of the CRAFT fly’s eye fast radio burst survey

AbstractThe Commensal Real-time Australian Square Kilometre Array Pathfinder Fast Transients survey is the first extensive astronomical survey using phased array feeds. Since January 2017, it has been searching for fast radio bursts in fly’s eye mode. Here, we present a calculation of the sensitivity and total exposure of the survey that detected the first 20 of these bursts, using the pulsars B1641-45 and B0833-45 as calibrators. The beamshape, antenna-dependent system noise, and the effects of radio-frequency interference and fluctuations during commissioning are quantified. Effective survey exposures and sensitivities are calculated as a function of the source counts distribution. Statistical ‘stat’ and systematics ‘sys’ effects are treated separately. The implied fast radio burst rate is significantly lower than the 37 sky−1 day−1 calculated using nominal exposures and sensitivities for this same sample by Shannon et al. (2018). At the Euclidean (best-fit) power-law index of −1.5 (−2.2), the rate is $12.7_{-2.2}^{+3.3}$ (sys) ± 3.6 (stat) sky−1 day−1 ( $20.7_{-1.7}^{+2.1}$ (sys) ± 2.8 (stat) sky−1 day−1) above a threshold of 56.6 ± 6.6(sys) Jy ms (40.4 ± 1.2(sys) Jy ms). This strongly suggests that these calculations be performed for other FRB-hunting experiments, allowing meaningful comparisons to be made between them.

The slope of the source-count distribution for fast radio bursts

The slope of the source-count distribution of fast radio burst (FRB) fluences, $\alpha$, has been estimated using a variety of methods. Hampering all attempts have been the low number of detected FRBs, and the difficulty of defining a completeness threshold for FRB surveys. In this work, we extend maximum-likelihood methods for estimating $\alpha$, using detected and threshold signal-to-noise ratios applied to all FRBs in a sample without regard to a completeness threshold. Using this method with FRBs detected by the Parkes radio telescope, we find $\alpha=-1.18 \pm 0.24$ (68\% confidence interval, C.I.), i.e.\ consistent with a non-evolving Euclidean distribution ($\alpha=-1.5$). Applying these methods to the Australian Square Kilometre Array Pathfinder (ASKAP) Commensal Real-time ASKAP Fast Transients (CRAFT) FRB survey finds $\alpha=-2.2 \pm 0.47$ (68\% C.I.). A full maximum-likelihood estimate finds an inconsistency with the Parkes rate with a p-value of 0.86\% ($2.6\, \sigma$). If not due to statistical fluctuations or biases in Parkes data, this is the first evidence for deviations from a pure power law in the integral source-count distribution of FRBs. It is consistent with a steepening of the integral source-count distribution in the fluence range 5--40\,Jy\,ms, for instance due to a cosmological population of FRB progenitors evolving more rapidly than the star-formation rate, and peaking in the redshift range 1--3.

Deriving the Contribution of Blazars to the Fermi-LAT Extragalactic γ-ray Background at E > 10 GeV with Efficiency Corrections and Photon Statistics

Abstract The Fermi Large Area Telescope (LAT) Collaboration has recently released the Third Catalog of Hard Fermi-LAT Sources (3FHL), which contains 1556 sources detected above 10 GeV with seven years of Pass 8 data. Building upon the 3FHL results, we investigate the flux distribution of sources at high Galactic latitudes ( ), which are mostly blazars. We use two complementary techniques: (1) a source-detection efficiency correction method and (2) an analysis of pixel photon count statistics with the one-point probability distribution function (1pPDF). With the first method, using realistic Monte Carlo simulations of the γ-ray sky, we calculate the efficiency of the LAT to detect point sources. This enables us to find the intrinsic source-count distribution at photon fluxes down to 7.5 × 10−12 ph cm−2 s−1. With this method, we detect a flux break at (3.5 ± 0.4) × 10−11 ph cm−2 s−1 with a significance of at least 5.4σ. The power-law indexes of the source-count distribution above and below the break are 2.09 ± 0.04 and 1.07 ± 0.27, respectively. This result is confirmed with the 1pPDF method, which has a sensitivity reach of ∼10−11 ph cm−2 s−1. Integrating the derived source-count distribution above the sensitivity of our analysis, we find that (42 ± 8)% of the extragalactic γ-ray background originates from blazars.

The SUrvey for Pulsars and Extragalactic Radio Bursts – II. New FRB discoveries and their follow-up

We report the discovery of four Fast Radio Bursts (FRBs) in the ongoing SUrvey for Pulsars and Extragalactic Radio Bursts (SUPERB) at the Parkes Radio Telescope: FRBs 150610, 151206, 151230 and 160102. Our real-time discoveries have enabled us to conduct extensive, rapid multi-messenger follow-up at 12 major facilities sensitive to radio, optical, X-ray, gamma-ray photons and neutrinos on time scales ranging from an hour to a few months post-burst. No counterparts to the FRBs were found and we provide upper limits on afterglow luminosities. None of the FRBs were seen to repeat. Formal fits to all FRBs show hints of scattering while their intrinsic widths are unresolved in time. FRB 151206 is at low Galactic latitude, FRB 151230 shows a sharp spectral cutoff, and FRB 160102 has the highest dispersion measure (DM = $2596.1\pm0.3$ pc cm$^{-3}$) detected to date. Three of the FRBs have high dispersion measures (DM >$1500$ pc cm$^{-3}$), favouring a scenario where the DM is dominated by contributions from the Intergalactic Medium. The slope of the Parkes FRB source counts distribution with fluences $>2$ Jyms is $\alpha=-2.2^{+0.6}_{-1.2}$ and still consistent with a Euclidean distribution ($\alpha=-3/2$). We also find that the all-sky rate is $1.7^{+1.5}_{-0.9}\times10^3$FRBs/($4\pi$ sr)/day above $\sim2$ Jyms and there is currently no strong evidence for a latitude-dependent FRB sky-rate.

Fast radio burst event rate counts – I. Interpreting the observations

The fluence distribution of the Fast Radio Burst (FRB) population (the "source counts" distribution, $N(>F) \propto F^\alpha$), is a crucial diagnostic of its distance distribution, and hence the progenitor evolutionary history. We critically reanalyse current estimates of the FRB source counts distribution. We demonstrate that the Lorimer burst (FRB 010724) is subject to discovery bias, and should be excluded from all statistical studies of the population. We re-examine the evidence for flat, $\alpha >-1$, source counts estimates based on the ratio of single-beam to multiple-beam detections with the Parkes multi-beam receiver, and show that current data implies only a very weak constraint of $\alpha \lesssim -1.3$. A maximum likelihood analysis applied to the portion of the Parkes FRB population detected above the observational completeness fluence of 2 Jy ms yields $\alpha = -2.6_{-1.3}^{+0.7}$. Uncertainties in the location of each FRB within the Parkes beam render estimates of the Parkes event rate uncertain in both normalising survey area and the estimated post-beam-corrected completeness fluence; this uncertainty needs to be accounted for when comparing the event rate against event rates measured at other telescopes.

Cherenkov telescope array extragalactic survey discovery potential and the impact of axion-like particles and secondary gamma rays

The Cherenkov Telescope Array (CTA) is about to enter construction phase and one of its main key science projects is to perform an unbiased survey in search of extragalactic sources. We make use of both the latest blazar gamma–ray luminosity function and spectral energy distribution to derive the expected number of detectable sources for both the planned Northern and Southern arrays of the CTA observatory. We find that a shallow, wide survey of about 0.5 hour per field of view would lead to the highest number of blazar detections. Furthermore, we investigate the effect of axion-like particles and secondary gamma rays from propagating cosmic rays on the source count distribution, since these processes predict different spectral shape from standard extragalactic background light attenuation. We can generally expect more distant objects in the secondary gamma-ray scenario, while axion-like particles do not significantly alter the expected distribution. Yet, we find that, these results strongly depend on the assumed magnetic field strength during the propagation. We also provide source count predictions for the High Altitude Water Cherenkov observatory (HAWC), the Large High Altitude Air Shower Observatory (LHAASO) and a novel proposal of a hybrid detector.

THE CONTRIBUTION OF FERMI-2LAC BLAZARS TO DIFFUSE TEV–PEV NEUTRINO FLUX

ABSTRACT The recent discovery of a diffuse cosmic neutrino flux extending up to PeV energies raises the question of which astrophysical sources generate this signal. Blazars are one class of extragalactic sources which may produce such high-energy neutrinos. We present a likelihood analysis searching for cumulative neutrino emission from blazars in the 2nd Fermi-LAT AGN catalog (2LAC) using IceCube neutrino data set 2009-12, which was optimized for the detection of individual sources. In contrast to those in previous searches with IceCube, the populations investigated contain up to hundreds of sources, the largest one being the entire blazar sample in the 2LAC catalog. No significant excess is observed, and upper limits for the cumulative flux from these populations are obtained. These constrain the maximum contribution of 2LAC blazars to the observed astrophysical neutrino flux to 27% or less between around 10 TeV and 2 PeV, assuming the equipartition of flavors on Earth and a single power-law spectrum with a spectral index of −2.5. We can still exclude the fact that 2LAC blazars (and their subpopulations) emit more than 50% of the observed neutrinos up to a spectral index as hard as −2.2 in the same energy range. Our result takes into account the fact that the neutrino source count distribution is unknown, and it does not assume strict proportionality of the neutrino flux to the measured 2LAC γ-ray signal for each source. Additionally, we constrain recent models for neutrino emission by blazars.

STATISTICAL MEASUREMENT OF THE GAMMA-RAY SOURCE-COUNT DISTRIBUTION AS A FUNCTION OF ENERGY

ABSTRACT Statistical properties of photon count maps have recently been proven as a new tool to study the composition of the gamma-ray sky with high precision. We employ the 1-point probability distribution function of six years of Fermi-LAT data to measure the source-count distribution dN/dS and the diffuse components of the high-latitude gamma-ray sky as a function of energy. To that aim, we analyze the gamma-ray emission in five adjacent energy bands between 1 and 171 GeV. It is demonstrated that the source-count distribution as a function of flux is compatible with a broken power law up to energies of ∼50 GeV. The index below the break is between 1.95 and 2.0. For higher energies, a simple power-law fits the data, with an index of 2.2 − 0.3 + 0.7 in the energy band between 50 and 171 GeV. Upper limits on further possible breaks as well as the angular power of unresolved sources are derived. We find that point-source populations probed by this method can explain 83 − 13 + 7 % ( 81 − 19 + 52 %) of the extragalactic gamma-ray background between 1.04 and 1.99 GeV (50 and 171 GeV). The method has excellent capabilities for constraining the gamma-ray luminosity function and the spectra of unresolved blazars.

UNVEILING THE GAMMA-RAY SOURCE COUNT DISTRIBUTION BELOW THE FERMI DETECTION LIMIT WITH PHOTON STATISTICS

ABSTRACT The source-count distribution as a function of their flux, , is one of the main quantities characterizing gamma-ray source populations. We employ statistical properties of the Fermi Large Area Telescope (LAT) photon counts map to measure the composition of the extragalactic gamma-ray sky at high latitudes ( °) between 1 and 10 GeV. We present a new method, generalizing the use of standard pixel-count statistics, to decompose the total observed gamma-ray emission into (a) point-source contributions, (b) the Galactic foreground contribution, and (c) a truly diffuse isotropic background contribution. Using the 6 yr Fermi-LAT data set (P7REP), we show that the distribution in the regime of so far undetected point sources can be consistently described with a power law with an index between 1.9 and 2.0. We measure down to an integral flux of improving beyond the 3FGL catalog detection limit by about one order of magnitude. The overall distribution is consistent with a broken power law, with a break at The power-law index for bright sources above the break hardens to for fainter sources below the break. A possible second break of the distribution is constrained to be at fluxes below at 95% confidence level. The high-latitude gamma-ray sky between 1 and 10 GeV is shown to be composed of ∼25% point sources, ∼69.3% diffuse Galactic foreground emission, and ∼6% isotropic diffuse background.