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Differential source-count distribution dN/dS obtained from 6-year Fermi-LAT data for high Galactic latitudes greater than 30 •. The fit was carried out by employing the hybrid approach with two free breaks and a node at the faint end of the distribution. Notations as in Figure 5. The shape of the dN/dS distribution for very faint sources can be further constrained by the fact that the sum of the integral point-source flux and the Galactic foreground contribution must not exceed the total map flux Ftot. Corresponding constraints have been derived from the dN/dS distribution obtained from the Bayesian posterior down to the best-fit position of the last free break. Below that value, dN/dS has been extrapolated with power-law components of varying index. At the boundary of the gray-shaded region the total point-source flux equals Ftot − F gal , requiring a break.
Source publication
The source-count distribution as a function of their flux, dN/dS, is one of
the main quantities characterizing gamma-ray source populations. We employ
statistical properties of the Fermi-LAT photon counts map to measure the
composition of the extragalactic gamma-ray sky at high latitudes (|b|>30 deg)
between 1 GeV and 10 GeV. We present a new metho...
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Citations
... For all those sources which are too faint to be resolved, their cumulative distribution of photons in the sky defines an almost isotropic cosmic field, conventionally called the isotropic diffuse gamma-ray background (IGRB) or, more precisely, the unresolved gamma-ray background (UGRB). Even though individual sources below the detector flux-threshold cannot be individually seen, it has been shown [7][8][9][10] nevertheless, that it is possible to infer their source-count distribution even in this regime, looking at the collective effects of these unresolved sources. This technique, called pixel-count distribution (or 1-point PDF) and pioneered for gammarays in [7], has been improved in [8][9][10] by employing a pixel-dependent approach, in order to fully explore all the available information and to incorporate the morphological variation of the gamma-ray emission components. ...
... Even though individual sources below the detector flux-threshold cannot be individually seen, it has been shown [7][8][9][10] nevertheless, that it is possible to infer their source-count distribution even in this regime, looking at the collective effects of these unresolved sources. This technique, called pixel-count distribution (or 1-point PDF) and pioneered for gammarays in [7], has been improved in [8][9][10] by employing a pixel-dependent approach, in order to fully explore all the available information and to incorporate the morphological variation of the gamma-ray emission components. Ref. [8] used the first 6 years of Fermi-LAT [11] data to measure the dN/dS for photons in the energy range (1,10) GeV down to fluxes about one order of magnitude below the Fermi-LAT detection threshold. ...
... This technique, called pixel-count distribution (or 1-point PDF) and pioneered for gammarays in [7], has been improved in [8][9][10] by employing a pixel-dependent approach, in order to fully explore all the available information and to incorporate the morphological variation of the gamma-ray emission components. Ref. [8] used the first 6 years of Fermi-LAT [11] data to measure the dN/dS for photons in the energy range (1,10) GeV down to fluxes about one order of magnitude below the Fermi-LAT detection threshold. In [9,10] the same technique was used to extend the measurement of the dN/dS to several energy bands between 1 and 171 GeV, thus providing information on the energy dependence of the source-count distribution. ...
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.
... Roughly 7 , Fermi-LAT starts to loose sensitivity to sources below 2×10 −10 cm −2 s −1 [8,14,29,30], Counts TS=10 TS=36 TS=78 Figure 3. Analogous to figure 2, but for differential flux; i.e. number of pixels for a given flux bin. White histograms correspond to the whole catalogue map K, while colored histograms are only those pixels in K coinciding (within the 68% PSF containment angle) with the firing pixels of our dN/dS model map. ...
We propose a novel statistical method to extend Fermi-LAT catalogues of high-latitude $\gamma$-ray sources below their nominal threshold. To do so, we rely on a recent determination of the differential source-count distribution of sub-threshold sources via the application of deep learning methods to the $\gamma$-ray sky. 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. Besides being useful to orient efforts towards multi-messenger and multi-wavelength identification of new $\gamma$-ray sources, we expect the results to be especially advantageous for statistical applications such as cross-correlation analyses.
... For all those sources which are too faint to be resolved, their cumulative distribution of photons in the sky defines an almost isotropic cosmic field, conventionally called the isotropic diffuse gamma-ray background (IGRB) or, more precisely, the unresolved gamma-ray background (UGRB). Even though individual sources below the detector flux-threshold cannot be individually seen, it has been shown [7][8][9][10] nevertheless, that it is possible to infer their source-count distribution even in this regime, looking at the collective effects of these unresolved sources. This technique, called pixel-count distribution (or 1-point PDF) and pioneered for gamma-rays in [7], has been improved in [8][9][10] by employing a pixel-dependent approach, in order to fully explore all the available information and to incorporate the morphological variation of the gamma-ray emission components. ...
... Even though individual sources below the detector flux-threshold cannot be individually seen, it has been shown [7][8][9][10] nevertheless, that it is possible to infer their source-count distribution even in this regime, looking at the collective effects of these unresolved sources. This technique, called pixel-count distribution (or 1-point PDF) and pioneered for gamma-rays in [7], has been improved in [8][9][10] by employing a pixel-dependent approach, in order to fully explore all the available information and to incorporate the morphological variation of the gamma-ray emission components. Ref. [8] used the first 6 years of Fermi-LAT [11] data to measure the dN/dS for photons in the energy range (1,10) GeV down to fluxes about one order of magnitude below the Fermi-LAT detection threshold. ...
... This technique, called pixel-count distribution (or 1-point PDF) and pioneered for gamma-rays in [7], has been improved in [8][9][10] by employing a pixel-dependent approach, in order to fully explore all the available information and to incorporate the morphological variation of the gamma-ray emission components. Ref. [8] used the first 6 years of Fermi-LAT [11] data to measure the dN/dS for photons in the energy range (1,10) GeV down to fluxes about one order of magnitude below the Fermi-LAT detection threshold. In [9,10] the same technique was used to extend the measurement of the dN/dS to several energy bands between 1 and 171 GeV, thus providing information on the energy dependence of the source-count distribution. ...
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 catalogued sources, and then extends as $dN/dS \sim S^{-2}$ in the unresolved regime, down to fluxes of $5 \cdot 10^{-12}$ 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.
... Moreover, the extragalactic γ-ray luminosity (EGB) is relatively equally divided into emission between a handful of extremely bright point sources [1][2][3][4][5], and an underlying sea of dim sources, known collectively as the isotropic γ-ray background (IGRB) [6][7][8][9][10][11][12][13][14]. The observed normalization of the IGRB depends on the sensitivity of the instrument (in this case the Fermi-LAT), population models and statistical studies [6,[15][16][17][18][19] indicate that the distinction is also physically meaningful, with significant and distinct contributions from very bright and very dim sources. ...
The total extragalactic γ -ray flux provides a powerful probe into the origin and evolution of the highest energy processes in our universe. An important component of this emission is the isotropic γ -ray background (IGRB), composed of sources that cannot be individually resolved by current experiments. Previous studies have determined that the IGRB can be dominated by either misaligned active galactic nuclei (mAGN) or star-forming galaxies (SFGs). However, these analyses are limited, because they have utilized binary source classifications and examined only one source class at a time. We perform the first combined joint-likelihood analysis that simultaneously correlates the γ -ray luminosity of extragalactic objects with both star-formation and mAGN activity. We find that SFGs produce 48 ⁺³³ -20 % of the total IGRB at 1 GeV and 56 ⁺⁴⁰ -23 % of the total IGRB at 10 GeV. The contribution of mAGN is more uncertain, but can also be significant. Future work to quantify the radio and infrared properties of nearby galaxies could significantly improve these constraints.
... Guaranteed contributors to the UGRB emission are sub-detection-threshold blazars (Cuoco et al. 2012;Di Mauro et al. 2018), misaligned AGNs (mAGNs; Di Mauro et al. 2013), and star-forming galaxies (SFGs; Roth et al. 2021;Tamborra et al. 2014). Additionally, we cannot exclude contributions from more exotic components, such as dark matter (DM; Ando 2009;Bringmann et al. 2014;Ajello et al. 2015;Fornasa et al. 2016;Zechlin et al. 2018) The UGRB emission has been studied through three main observables: its energy spectrum (Abdo et al. 2011;, its 1-point probability distribution function (1pPDF), through photon count statistics (Lisanti et al. 2016;Zechlin et al. 2016bZechlin et al. , 2016aDi Mauro et al. 2018), and its angular power spectrum (APS; Ackermann et al. 2012;Fornasa et al. 2016;Ackermann et al. 2018). The latter two observables investigate fluctuations over the UGRB isotropic emission to infer the properties of the underlying sources at the subthreshold level. ...
We analyze the angular power spectrum (APS) of the unresolved gamma-ray background (UGRB) emission and combine it with the measured properties of the resolved gamma-ray sources of the Fermi-LAT 4FGL catalog. Our goals are to dissect the composition of the gamma-ray sky and to establish the relevance of different classes of source populations of active galactic nuclei in determining the observed size of the UGRB anisotropy, especially at low energies. We find that, under physical assumptions for the spectral energy distribution, i.e., by using the 4FGL catalog data as a prior, two populations are required to fit the APS data, namely flat-spectrum radio quasars at low energies and BL Lacs at higher energies. The inferred luminosity functions agree well with the extrapolation of the flat-spectrum radio quasar and BL Lac ones obtained from the 4FLG catalog. We use these luminosity functions to calculate the UGRB intensity from blazars, finding a contribution of 20% at 1 GeV and 30% above 10 GeV. Finally, bounds on an additional gamma-ray emission due to annihilating dark matter are also derived.
... The NPTF was primarily developed to analyze the excess of Galactic Center (GCE) gamma-rays observed by the Fermi telescope (Goodenough & Hooper 2009;Hooper & Goodenough 2011;Hooper & Linden 2011;Abazajian & Kaplinghat 2012;Hooper & Slatyer 2013;Gordon & Macias 2013;Abazajian et al. 2014Abazajian et al. , 2015Daylan et al. 2016;Calore et al. 2015;Ajello et al. 2016;Linden et al. 2016;Macias et al. 2018;Clark et al. 2018), and concluded that the observed excess was better described by a population of point sources, in comparison to a dark matter annihilation origin (Lee et al. , 2016; see also Bartels et al. 2016). 9 An approach similar to the NPTF that has also been widely used is the onepoint fluctuation analysis or one-point PDF method; see, for example, Lee et al. (2009), Feyereisen et al. (2015, 2017, Zechlin et al. (2016aZechlin et al. ( , 2016bZechlin et al. ( , 2018, Manconi et al. (2020), and Calore et al. (2021). In the present work, we will focus on comparisons between the CPG and the NPTF, but many of our conclusions would be similar if we compared to these alternative approaches. ...
The identification and description of point sources is one of the oldest problems in astronomy, yet even today the correct statistical treatment for point sources remains one of the field’s hardest problems. For dim or crowded sources, likelihood-based inference methods are required to estimate the uncertainty on the characteristics of the source population. In this work, a new parametric likelihood is constructed for this problem using compound Poisson generator (CPG) functionals that incorporate instrumental effects from first principles. We demonstrate that the CPG approach exhibits a number of advantages over non-Poissonian template fitting (NPTF)—an existing method—in a series of test scenarios in the context of X-ray astronomy. These demonstrations show that the effect of the point-spread function, effective area, and choice of point-source spatial distribution cannot, generally, be factorized as they are in NPTF, while the new CPG construction is validated in these scenarios. Separately, an examination of the diffuse-flux emission limit is used to show that most simple choices of priors on the standard parameterization of the population model can result in unexpected biases: when a model comprising both a point-source population and diffuse component is applied to this limit, nearly all observed flux will be assigned to either the population or to the diffuse component. A new parameterization is presented for these priors that properly estimates the uncertainties in this limit. In this choice of priors, CPG correctly identifies that the fraction of flux assigned to the population model cannot be constrained by the data.
... The NPTF has the advantage of being available as a public software package NPTFit [242], with worked examples. Similar photon statistics (or neutrino statistics) techniques have been used in other contexts in DM indirect detection and particle astrophysics, e.g. to search for point sources in IceCube neutrino data [243], and to determine the composition of the extragalactic gamma-ray background [244][245][246]. ...
These lectures, presented at the 2021 Les Houches Summer School on Dark Matter, provide an introduction to key methods and tools of indirect dark matter searches, as well as a status report on the field circa summer 2021. Topics covered include the possible effects of energy injection from dark matter on the early universe, methods to calculate both the expected energy distribution and spatial distribution of particles produced by dark matter interactions, an outline of theoretical models that predict diverse signals in indirect detection, and a discussion of current constraints and some claimed anomalies. These notes are intended as an introduction to indirect dark matter searches for graduate students, focusing primarily on intuition-building estimates and useful concepts and tools.
... Other works considered the photon count statistics and the one-point probability distribution functions of the expected UGRB components to constrain their contribution [604][605][606][607][608][609][610]. These works set constraints on the unresolved blazar population which are compatible to those resulting from the anisotropy study. ...
The last decade has brought about a profound transformation in multimessenger science. Ten years ago, facilities had been built or were under construction that would eventually discover the nature of objects in our universe could be detected through multiple messengers. Nonetheless, multimessenger science was hardly more than a dream. The rewards for our foresight were finally realized through IceCube's discovery of the diffuse astrophysical neutrino flux, the first observation of gravitational waves by LIGO, and the first joint detections in gravitational waves and photons and in neutrinos and photons. Today we live in the dawn of the multimessenger era. The successes of the multimessenger campaigns of the last decade have pushed multimessenger science to the forefront of priority science areas in both the particle physics and the astrophysics communities. Multimessenger science provides new methods of testing fundamental theories about the nature of matter and energy, particularly in conditions that are not reproducible on Earth. This white paper will present the science and facilities that will provide opportunities for the particle physics community renew its commitment and maintain its leadership in multimessenger science.
... The qualitative matching of the energy densities of photons and neutrinos, discussed in the previous section, may suggest that the unidentified neutrino sources contributing to the diffuse flux might have already been observed as strong gammaray emitters. Theoretical modeling 127,128 and recent data analyses [129][130][131] show that Fermi's extragalactic gamma-ray flux is dominated by blazars. However, a dedicated IceCube study 132 of Fermi-observed blazars shows no evidence of neutrino emission from these source candidates. ...
The IceCube experiment discovered PeV-energy neutrinos originating beyond our Galaxy with an energy flux that is comparable to that of TeV-energy gamma rays and EeV-energy cosmic rays. Neutrinos provide the only unobstructed view of the cosmic accelerators that power the highest energy radiation reaching us from the universe. We will review the rationale for building kilometer-scale neutrino detectors that led to the IceCube project, which transformed a cubic kilometer of deep transparent natural Antarctic ice into a neutrino telescope of such a scale. We will summarize the results from the first decade of operations: the status of the observations of cosmic neutrinos and of their first identified source, the supermassive black hole TXS 0506+056. Subsequently, we will introduce the phenomenology associated with cosmic accelerators in some detail. Besides the search for the sources of Galactic and extragalactic cosmic rays, the scientific missions of IceCube and similar instruments under construction in the Mediterranean Sea and Lake Baikal include the observation of Galactic supernova explosions, the search for dark matter, and the study of neutrinos themselves. This review resulted from notes created for summer school lectures and should be accessible to nonexperts.
... Photon-count statistical methods can discriminate photons from -ray sources based on their statistical properties. In particular, the 1-point probability distribution function method [16] (1pPDF) fits the contribution of diffuse and PS components to the -ray 1-point fluctuations histogram. Employing 1pPDF on Fermi-LAT data, it was possible to measure the PS count distribution per unit flux, / , below the LAT detection threshold at high latitudes [16][17][18], and to set competitive bounds on DM [19]. ...
... In particular, the 1-point probability distribution function method [16] (1pPDF) fits the contribution of diffuse and PS components to the -ray 1-point fluctuations histogram. Employing 1pPDF on Fermi-LAT data, it was possible to measure the PS count distribution per unit flux, / , below the LAT detection threshold at high latitudes [16][17][18], and to set competitive bounds on DM [19]. ...
... The 1pPDF-fit model components are: An IGRB template (free normalization), a diffuse emission template (free normalization), and an isotropic PS (IPS) population with / defined by a multiple broken power law with free parameters being the overall normalization S , the flux break positions, and the broken power-law indices, [20]. The IPS / measured by the 1pPDF fit should recover the / of Fermi-LAT detected PS in the bright regime while pushing the PS detection threshold down to lower fluxes [16,17]. Our goal being to quantify the role of PS to the GCE within the 1pPDF, we add a GCE smooth template with free normalization in the 1pPDF fit. ...
