Resolving the Extragalactic γ -Ray Background above 50 GeV with the Fermi Large Area Telescope

Abstract

The Fermi Large Area Telescope (LAT) Collaboration has recently released a catalog of 360 sources detected above 50 GeV (2FHL). This catalog was obtained using 80 months of data re-processed with Pass 8, the newest event-level analysis, which significantly improves the acceptance and angular resolution of the instrument. Most of the 2FHL sources at high Galactic latitude are blazars. Using detailed Monte Carlo simulations, we measure, for the first time, the source count distribution, dN/dS, of extragalactic γ-ray sources at E>50 GeV and find that it is compatible with a Euclidean distribution down to the lowest measured source flux in the 2FHL (∼8×10-12 ph cm-2 s-1). We employ a one-point photon fluctuation analysis to constrain the behavior of dN/dS below the source detection threshold. Overall, the source count distribution is constrained over three decades in flux and found compatible with a broken power law with a break flux, Sb, in the range [8×10-12,1.5×10-11] ph cm-2 s-1 and power-law indices below and above the break of α2[1.60,1.75] and α1=2.49±0.12, respectively. Integration of dN/dS shows that point sources account for at least 86-14+16% of the total extragalactic γ-ray background. The simple form of the derived source count distribution is consistent with a single population (i.e., blazars) dominating the source counts to the minimum flux explored by this analysis. We estimate the density of sources detectable in blind surveys that will be performed in the coming years by the Cherenkov Telescope Array.

Full text

Version 00 as of November 4, 2015
To be submitted to PRL
Resolving the Extragalactic γ-ray Background above 50 GeV with Fermi-LAT
M. Ackermann,1M. Ajello,2, ∗A. Albert,3W. B. Atwood,4L. Baldini,5, 3 J. Ballet,6G. Barbiellini,7, 8 D. Bastieri,9, 10
K. Bechtol,11 R. Bellazzini,12 E. Bissaldi,13 R. D. Blandford,3E. D. Bloom,3R. Bonino,14, 15 J. Bregeon,16
R. J. Britto,17 P. Bruel,18 R. Buehler,1G. A. Caliandro,3, 19 R. A. Cameron,3M. Caragiulo,20, 13 P. A. Caraveo,21
E. Cavazzuti,22 C. Cecchi,23, 24 E. Charles,3A. Chekhtman,25 J. Chiang,3G. Chiaro,10 S. Ciprini,22, 23
J. Cohen-Tanugi,16 L. R. Cominsky,26 F. Costanza,13 S. Cutini,22, 27, 23 F. D’Ammando,28, 29 A. de Angelis,30
F. de Palma,13, 31 R. Desiante,32, 14 S. W. Digel,3M. Di Mauro,3 , †L. Di Venere,20, 13 A. Dom´ınguez,2P. S. Drell,3
C. Favuzzi,20, 13 S. J. Fegan,18 E. C. Ferrara,33 A. Franckowiak,3Y. Fukazawa,34 S. Funk,35 P. Fusco,20, 13
F. Gargano,13 D. Gasparrini,22, 23 N. Giglietto,20, 13 P. Giommi,22 F. Giordano,20, 13 M. Giroletti,28 G. Godfrey,3
D. Green,36, 33 I. A. Grenier,6S. Guiriec,33, 37 E. Hays,33 D. Horan,18 G. Iafrate,7, 38 T. Jogler,3G. J´ohannesson,39
M. Kuss,12 G. La Mura,10, 40 S. Larsson,41, 42 L. Latronico,14 J. Li,43 L. Li,41, 42 F. Longo,7, 8 F. Loparco,20, 13
B. Lott,44 M. N. Lovellette,45 P. Lubrano,23, 24 G. M. Madejski,3J. Magill,36 S. Maldera,14 A. Manfreda,12
M. Mayer,1M. N. Mazziotta,13 P. F. Michelson,3W. Mitthumsiri,46 T. Mizuno,47 A. A. Moiseev,48, 36
M. E. Monzani,3A. Morselli,49 I. V. Moskalenko,3S. Murgia,50 M. Negro,14, 15 E. Nuss,16 T. Ohsugi,47 C. Okada,34
N. Omodei,3E. Orlando,3J. F. Ormes,51 D. Paneque,52, 3 J. S. Perkins,33 M. Pesce-Rollins,12, 3 V. Petrosian,3
F. Piron,16 G. Pivato,12 T. A. Porter,3S. Rain`o,20, 13 R. Rando,9, 10 M. Razzano,12, 53 S. Razzaque,17 A. Reimer,40, 3
O. Reimer,40, 3 T. Reposeur,44 R. W. Romani,3M. S´anchez-Conde,42, 54 J. Schmid,6A. Schulz,1C. Sgr`o,12
D. Simone,13 E. J. Siskind,55 F. Spada,12 G. Spandre,12 P. Spinelli,20, 13 D. J. Suson,56 H. Takahashi,34
J. B. Thayer,3L. Tibaldo,57 D. F. Torres,43, 58 E. Troja,33, 36 G. Vianello,3M. Yassine,16 and S. Zimmer54, 42
1Deutsches Elektronen Synchrotron DESY, D-15738 Zeuthen, Germany
2Department of Physics and Astronomy, Clemson University,
Kinard Lab of Physics, Clemson, SC 29634-0978, USA
3W. W. Hansen Experimental Physics Laboratory,
Kavli Institute for Particle Astrophysics and Cosmology,
Department of Physics and SLAC National Accelerator Laboratory, Stanford University, Stanford, CA 94305, USA
4Santa Cruz Institute for Particle Physics, Department of Physics and Department of Astronomy and Astrophysics,
University of California at Santa Cruz, Santa Cruz, CA 95064, USA
5Universit`a di Pisa and Istituto Nazionale di Fisica Nucleare, Sezione di Pisa I-56127 Pisa, Italy
6Laboratoire AIM, CEA-IRFU/CNRS/Universit´e Paris Diderot,
Service d’Astrophysique, CEA Saclay, F-91191 Gif sur Yvette, France
7Istituto Nazionale di Fisica Nucleare, Sezione di Trieste, I-34127 Trieste, Italy
8Dipartimento di Fisica, Universit`a di Trieste, I-34127 Trieste, Italy
9Istituto Nazionale di Fisica Nucleare, Sezione di Padova, I-35131 Padova, Italy
10Dipartimento di Fisica e Astronomia “G. Galilei”, Universit`a di Padova, I-35131 Padova, Italy
11Dept. of Physics and Wisconsin IceCube Particle Astrophysics Center,
University of Wisconsin, Madison, WI 53706, USA
12Istituto Nazionale di Fisica Nucleare, Sezione di Pisa, I-56127 Pisa, Italy
13Istituto Nazionale di Fisica Nucleare, Sezione di Bari, I-70126 Bari, Italy
14Istituto Nazionale di Fisica Nucleare, Sezione di Torino, I-10125 Torino, Italy
15Dipartimento di Fisica Generale “Amadeo Avogadro” ,
Universit`a degli Studi di Torino, I-10125 Torino, Italy
16Laboratoire Univers et Particules de Montpellier,
Universit´e Montpellier, CNRS/IN2P3, Montpellier, France
17Department of Physics, University of Johannesburg,
PO Box 524, Auckland Park 2006, South Africa
18Laboratoire Leprince-Ringuet, ´
Ecole polytechnique, CNRS/IN2P3, Palaiseau, France
19Consorzio Interuniversitario per la Fisica Spaziale (CIFS), I-10133 Torino, Italy
20Dipartimento di Fisica “M. Merlin” dell’Universit`a e del Politecnico di Bari, I-70126 Bari, Italy
21INAF-Istituto di Astrofisica Spaziale e Fisica Cosmica, I-20133 Milano, Italy
22Agenzia Spaziale Italiana (ASI) Science Data Center, I-00133 Roma, Italy
23Istituto Nazionale di Fisica Nucleare, Sezione di Perugia, I-06123 Perugia, Italy
24Dipartimento di Fisica, Universit`a degli Studi di Perugia, I-06123 Perugia, Italy
25College of Science, George Mason University, Fairfax, VA 22030,
resident at Naval Research Laboratory, Washington, DC 20375, USA
26Department of Physics and Astronomy, Sonoma State University, Rohnert Park, CA 94928-3609, USA
arXiv:1511.00693v1 [astro-ph.CO] 2 Nov 2015

27INAF Osservatorio Astronomico di Roma, I-00040 Monte Porzio Catone (Roma), Italy
28INAF Istituto di Radioastronomia, I-40129 Bologna, Italy
29Dipartimento di Astronomia, Universit`a di Bologna, I-40127 Bologna, Italy
30Dipartimento di Fisica, Universit`a di Udine and Istituto Nazionale di Fisica Nucleare,
Sezione di Trieste, Gruppo Col legato di Udine, I-33100 Udine
31Universit`a Telematica Pegaso, Piazza Trieste e Trento, 48, I-80132 Napoli, Italy
32Universit`a di Udine, I-33100 Udine, Italy
33NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA
34Department of Physical Sciences, Hiroshima University, Higashi-Hiroshima, Hiroshima 739-8526, Japan
35Erlangen Centre for Astroparticle Physics, D-91058 Erlangen, Germany
36Department of Physics and Department of Astronomy,
University of Maryland, College Park, MD 20742, USA
37NASA Postdoctoral Program Fellow, USA
38Osservatorio Astronomico di Trieste, Istituto Nazionale di Astrofisica, I-34143 Trieste, Italy
39Science Institute, University of Iceland, IS-107 Reykjavik, Iceland
40Institut f¨ur Astro- und Teilchenphysik and Institut f¨ur Theoretische Physik,
Leopold-Franzens-Universit¨at Innsbruck, A-6020 Innsbruck, Austria
41Department of Physics, KTH Royal Institute of Technology, AlbaNova, SE-106 91 Stockholm, Sweden
42The Oskar Klein Centre for Cosmoparticle Physics, AlbaNova, SE-106 91 Stockholm, Sweden
43Institute of Space Sciences (IEEC-CSIC), Campus UAB, E-08193 Barcelona, Spain
44Centre d’ ´
Etudes Nucl´eaires de Bordeaux Gradignan, IN2P3/CNRS,
Universit´e Bordeaux 1, BP120, F-33175 Gradignan Cedex, France
45Space Science Division, Naval Research Laboratory, Washington, DC 20375-5352, USA
46Department of Physics, Faculty of Science, Mahidol University, Bangkok 10400, Thailand
47Hiroshima Astrophysical Science Center, Hiroshima University, Higashi-Hiroshima, Hiroshima 739-8526, Japan
48Center for Research and Exploration in Space Science and Technology
(CRESST) and NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA
49Istituto Nazionale di Fisica Nucleare, Sezione di Roma “Tor Vergata”, I-00133 Roma, Italy
50Center for Cosmology, Physics and Astronomy Department,
University of California, Irvine, CA 92697-2575, USA
51Department of Physics and Astronomy, University of Denver, Denver, CO 80208, USA
52Max-Planck-Institut f¨ur Physik, D-80805 M¨unchen, Germany
53Funded by contract FIRB-2012-RBFR12PM1F from the Italian Ministry of Education, University and Research (MIUR)
54Department of Physics, Stockholm University, AlbaNova, SE-106 91 Stockholm, Sweden
55NYCB Real-Time Computing Inc., Lattingtown, NY 11560-1025, USA
56Department of Chemistry and Physics, Purdue University Calumet, Hammond, IN 46323-2094, USA
57Max-Planck-Institut f¨ur Kernphysik, D-69029 Heidelberg, Germany
58Instituci´o Catalana de Recerca i Estudis Avan¸cats (ICREA), Barcelona, Spain
(Dated: November 4, 2015)
The Fermi Large Area Telescope (LAT) Collaboration has recently released a catalog of 360
sources detected above 50 GeV (2FHL). This catalog was obtained using 80 months of data re-
processed with Pass 8, the newest event-level analysis, which significantly improves the acceptance
and angular resolution of the instrument. Most of the 2FHL sources at high Galactic latitude are
blazars. Using detailed Monte Carlo simulations, we measure, for the first time, the source count
distribution, dN/dS, of extragalactic γ-ray sources at E > 50 GeV and find that it is compatible
with a Euclidean distribution down to the lowest measured source flux in the 2FHL (∼8×10−12 ph
cm−2s−1). We employ a one-point photon fluctuation analysis to constrain the behavior of dN/dS
below the source detection threshold. Overall the source count distribution is constrained over
three decades in flux and found compatible with a broken power law with a break flux, Sb, in the
range [8 ×10−12 ,1.5×10−11] ph cm−2s−1and power-law indices below and above the break of
α2∈[1.60,1.75] and α1= 2.49 ±0.12 respectively. Integration of dN/dS shows that point sources
account for at least 86+16
−14% of the total extragalactic γ-ray background. The simple form of the
derived source count distribution is consistent with a single population (i.e. blazars) dominating the
source counts to the minimum flux explored by this analysis. We estimate the density of sources
detectable in blind surveys that will be performed in the coming years by the Cherenkov Telescope
Array.
PACS numbers:
The origin of the extragalactic γ-ray background
(EGB), the Universe’s glow in γrays, has been debated
since the first measurement with the SAS-2 satellite [1].
The EGB spectrum has been accurately measured, from
100 MeV to 820 GeV, by the Large Area Telescope (LAT)
on board the Fermi Gamma-Ray Space Telescope mission

[2]. Part of the EGB arises from the emission of resolved
and unresolved point sources like blazars, star-forming
and radio galaxies [e.g. 3, 4, 5], which are routinely de-
tected in γrays. A possible contribution to the EGB
may also come from diffuse processes such as annihilat-
ing/decaying dark matter particles (see [6] for a review).
Here we show for the first time that Fermi-LAT is able
to resolve the high-energy EGB into point-like sources.
Indeed, thanks to the accrual of 80 months of data (see
right panel of Fig. 1) and the increased acceptance and
improved point-spread function delivered by the new
event-level analysis dubbed Pass 8 [7], the LAT has re-
cently performed an all-sky survey at >50 GeV resulting
in the detection of 360 γ-ray sources that constitute the
second catalog of hard Fermi-LAT sources [2FHL, 8]
Blazars, mostly belonging to the BL Lacertae (BL Lac)
population, are the majority (74 %) of the sources in the
2FHL catalog. At Galactic latitudes (b) larger than 10◦
about 70% of the detected sources are associated with
BL Lacs. Only 7 % of the high-latitude (|b|>10◦)
sources are classified as something other than BL Lacs,
4% of them being Flat Spectrum Radio Quasars (FS-
RQs), while blazars of uncertain type and unassociated
sources constitute the remaining 23 % of the sample. The
median of the synchrotron peak frequencies for blazars
of uncertain type is very similar to that of BL Lacs
(log10(νS
peak/Hz) = 15.7 vs. 15.6). The same holds
for the median spectral index of unassociated sources
(Γ =3.0 vs. 3.1). This is supporting the fact that blazars
of uncertain type and unassociated sources are almost en-
tirely BL Lacs. Therefore, the fraction of likely blazars
in the high-latitude 2FHL sample is 97 % (93% BL Lacs
and 4% FSRQs).
In this paper, we derive the source detection efficiency
of the 2FHL catalog analysis using accurate Monte Carlo
simulations of the γ-ray sky. We then infer the intrinsic
flux distribution dN/dS of sources located at a latitude
|b|>10◦, where Sis the photon flux (ph cm−2s−1) mea-
sured in the 50 GeV–2 TeV energy band.
The simulations were performed using the gtobssim
tool, which is part of the Fermi ScienceTools distribu-
tion, and using the same pointing and live time his-
tory and event selection as used in the 2FHL cata-
log. We have employed the P8R2 SOURCE V6 in-
strument response function for the simulations and
analysis and the Galactic and isotropic diffuse emis-
sion were simulated using the gll iem v06.fits and
iso P8R2 SOURCE V6 v06.txt templates 1. The last in-
gredient of the simulations is an isotropic population
of point sources that has the characteristics of blazars
(fluxes and spectra) as detected in 2FHL. The simula-
tions described here were produced iteratively and ul-
1See http://fermi.gsfc.nasa.gov/ssc/
timately rely on the source count distribution dN/dS ∝
S−αas determined at the end of photon fluctuation anal-
ysis (see later), which is, a broken power law with a break
flux Sb= 1 ×10−11 ph cm−2s−1and a Euclidean slope
above the break, α1= 5/2, while below Sbthe slope is
α2= 1.65. Sources were generated with fluxes in the
range [Smin, Smax ] = [10−14,10−9] ph cm−2s−1and with
power-law spectra of the form dN/dE ∝E−Γ. For each
source the photon index Γ is drawn from a Gaussian dis-
tribution with average value 3.2 and standard deviation
0.7 (this reproduces the observed distribution as shown
on the right panel of Fig. 2). Galactic sources are not
considered in the simulations since we are interested in
the flux distribution of blazars at |b|>10◦. We pro-
duced 10 simulations of the γ-ray sky following these
prescriptions and in Fig. 1 the sky map of one simula-
tion is shown together with the real one. Clearly visible
in both maps are the diffuse emission along the Galac-
tic plane, the Fermi bubbles [9], the emission from point
sources and the isotropic diffuse emission.
The energy spectrum of the simulations is consistent
within 10 %, at all energies of interest and for photons
detected at |b|>10◦, with that of the LAT observations.
As clearly visible in Fig. 1, the spatial distribution of
gamma rays of the real map is also correctly reproduced.
The 10 simulations are analyzed exactly as the real data
were for the 2FHL catalog. This starts from detecting
source candidates using a sliding-cell algorithm and a
wavelet analysis [10] then analyzing each with the stan-
dard Fermi Science Tools, in order to derive the γ-ray
properties of detectable sources (see [8] for more details).
As in the 2FHL catalog, detected sources are those with
a test statistic (TS)>25 and at least 3 associated photons
predicted by the likelihood fit. This leads to the detec-
tion, in the simulations, of 271 ±18 sources at |b|>10◦,
which is in good agreement with the 253 sources detected
in the 2FHL. Moreover, the simulations show that the
2FHL catalog contains at most 1% of false detections.
In order to further validate our analysis we have per-
formed two consistency checks on the simulations. The
first compares the input source fluxes Strue with the
fluxes Smeas measured with the Fermi Science Tools in
the simulations. The result displayed in the left panel of
Fig. 2 shows that for bright sources this ratio converges
to 1 as expected in the absence of biases or errors. On
the other hand Smeas/Strue for faint sources deviates sys-
tematically from 1. This effect is readily understood as
caused by the Eddington bias, which is the statistical
fluctuations of sources with a simulated flux below the
threshold to a flux above the detection threshold [11].
Our second check compares of the average photon index
distribution (dN/dΓ), as derived from the simulations,
with the same distribution as derived from the 2FHL
catalog. This is reported in the right panel of Fig. 2 and
it shows that our description of the γ-ray sky and of the
blazar population is faithful to the real one.

FIG. 1: In the left (right) panel the adaptively smoothed count map of one simulation (real sky) in the energy range 50 GeV-2
TeV is represented in Galactic coordinates and Hammer-Aitoff projection. The two maps contain about 60000 γ-ray events.
The results from analyzing the sources in the simu-
lated data can be used to measure the detection effi-
ciency ω(S), which is a weighting factor that takes into
account the probability to detect a source as a function
of flux. The detection efficiency is simply derived from
the simulations measuring the ratio between the number
of detected sources and the number of simulated ones
as a function of measured source flux. The result re-
ported in Fig. 3 shows that the LAT detects any source
in the |b|>10◦sky for fluxes larger than ≈2×10−11 ph
cm−2s−1, but misses 80–90 % of the sources with fluxes
of ≈1×10−11 ph cm−2s−1and many more below this
flux. The peak (ω(S)>1) clearly visible at a flux of
≈2×10−11 ph cm−2s−1is due to the Eddington bias.
A reliable estimate of the detection efficiency is funda-
mental in order to correct the observed flux distribution
of the 2FHL catalog and in turn to derive the intrinsic
source count distribution, which is obtained as:
dN
dS (Si) = 1
Ω∆Si
Ni
ω(Si)[cm2s deg−2],(1)
where Ω is the solid angle of the |b|>10◦sky, ∆Siis
the width of the flux bin, Niis the number of sources in
each flux bin and Siis the flux at the center of a given
bin i. We verified through simulations that this method
allows us to retrieve the correct source count distribution
as long as the distribution used in the simulations is a
faithful representation of the real one.
This is found to be consistent, down to the sensitivity
of the 2FHL catalog (≈8×10−12 ph cm−2s−1), with a
power-law function with slope α1= 2.49 ±0.12 (see right
panel of Fig. 3). This best-fit value is consistent with
the Euclidean expectation and motivated us to choose
α1= 2.5 in the simulations.
Fig. 4 shows the cumulative source count distribution
that is defined as:
N(> S) = ZSmax
S
dN
dS0dS0[deg−2],(2)
where Smax is fixed to be 10−8ph cm−2s−1.
In order to infer the shape of the dN/dS below the flux
threshold for detecting point sources we have performed
a photon fluctuation analysis. This helps us to probe the
source count distribution to the level where sources con-
tribute on average 0.5photons each. The analysis is per-
formed by comparing the histogram of the pixel counts
of the real sky with the ones obtained via Monte Carlo
simulations and allows us to constrain the slope of the
differential flux distribution below the threshold of the
survey [15, 16]. We consider a differential flux distribu-
tion described as a broken power law where the slope
above the break is α1= 2.5 as determined in this work
while below the break the slope varies in different sim-
ulations between α2∈[1.3,2.7]. For each value of the
slope we derive the model pixel count distribution av-
eraging over the pixel count distributions obtained from
20 simulations. The simulated and real maps have been
pixelized using the HEALPix tool 2[17]. We have used a
resolution of order 9, which translates into 3145728 pixels
and an pixel size of about 0.11◦. Consistent results are
obtained when using a resolution of order 8. We consider
a single energy bin from 50 GeV to 2 TeV.
The model (averaged) pixel count distributions are
compared to the real data using a χ2analysis to deter-
mine the most likely scenario. As expected, there is a
degeneracy between the best-fit value of the slope α2and
the choice of the break flux, Sb. The result of the analy-
sis is that the break flux is limited to the range between
Sb∈[8 ×10−12,1.5×10−11 ] ph cm−2s−1while the index
below the break is in the range α2∈[1.60,1.75]. The
best configuration, which we refer to as our benchmark
model, has a break flux at 1 ×10−11 ph cm−2s−1and
a slope α2= 1.65 with a χ2= 12.4 (for 12 degrees of
freedom). This implies that the source count distribu-
tion must display a hard break |α1−α2| ≈ 0.9 from the
Euclidean behavior measured at bright fluxes. We show
in Fig. 5, for the best-fit configuration, the comparison
2See http://healpix.sourceforge.net

FIG. 2: Left Panel: ratio of the measured-to-simulated source
flux (as derived from the analysis of the simulations described
in the text) as a function of simulated source flux. Right
Panel: comparison between the photon index distributions of
sources detected in 2FHL (blue points) and the average of the
simulations (red points).
between the pixel count distribution evaluated for the av-
erage of 20 simulations, and the same quantity as derived
from the real data. The figure also shows the differences
between these two distributions.
The lowest flux that the photon fluctuation analysis
is sensitive to can be estimated by adding to the source
count distribution one more break flux below that of the
benchmark model. We fixed the slope below this second
break to α3=1.80, which is at the edge of the derived
range for α2, while the break flux is varied in the range
Slim ∈[5 ×10−13,5×10−12 ] ph cm−2s−1to register
when a worsening of the χ2(with respect to the best-fit
one) is observed. The result of this analysis is that the fit
worsened by more than 3σfor Slim &1.3×10−12 ph cm−2
s−1. The results of the photon fluctuation analysis are
reported in Figs. 3 and 4, which show that this technique
FIG. 3: Left Panel: detection efficiency ω(S) (blue points) as
a function of source flux and normalized distribution of source
fluxes detected in 2FHL (grey shaded histogram). Right
Panel: intrinsic S2dN/dS distribution (black points). The
black solid line shows our best-fit model, while the grey and
cyan bands show the 1σand 3σuncertainty bands from the
photon fluctuation analysis. The vertical brown dotted line
represents the sensitivity of the photon fluctuation analysis.
The orange and red curves indicate where 85% and 100% of
the EGB intensity above 50 GeV [2] would be produced when
extrapolating the flux distribution below the break with dif-
ferent values of faint-end slope, α2.
allows us to measure the source count distribution over
almost three decades in flux.
We have tested also the possibility that a new source
population could emerge in the flux distribution with a
Euclidean distribution, as might be expected, for exam-
ple, from star-forming galaxies [18]. In this test we set
α3= 2.50 and follow the method described above to de-
rive the maximum flux at which a possible re-steepening
of the source counts might occur. This is found to be
Slim ≈7×10−13 ph cm−2s−1and the integrated emission
of such a population would exceed at fluxes of ∼7×10−14
ph cm−2s−1the totality of the EGB intensity.

FIG. 4: Cumulative source count distribution N(> S) with
the uncertainty bands as in Fig. 3 together with the theo-
retical predictions from Ref. [12] (blue dashed line), [4] (red
dashed line) and [13] (green band). The vertical dotted brown
line shows the 5 mCrab flux reachable by CTA in 240 hrs of
exposure [14].
Our best-fit model for the flux distribution dN/dS is
therefore, for S&10−12 ph cm−2s−1, a broken power-
law with break flux in the range Sb∈[0.8,1.5] ×10−11,
slopes above and below the break of α1= 2.49 ±0.12
and α2∈[1.60,1.75], respectively and a normalization
K= (4.60 ±0.35) ×10−19 deg−2ph−1cm2s. We believe
this describes the source counts of a single population
(blazars), because no re-steepening of the source count
distribution is observed and because the large majority
(97 %) of the detected sources are likely blazars.
Fig. 4 reports the theoretical expectations for the
source count distribution given by blazars [4, 13] and BL
Lacs [12]. These models are consistent with the obser-
vations at bright fluxes, but are above the experimental
N(> S) by about a factor of 2 at S= 10−12 ph cm−2
s−1. We include in the same figure also the predicted
5 mCrab sensitivity reachable by CTA in 240 hours in
the most sensitive pointing strategy [14]. At these fluxes
the source density is 0.0194 ±0.0044 deg−2, which trans-
lates to the serendipitous detection of 200 ±45 blazars in
one quarter of the full sky. It is also interesting to note
that our analysis constrains the source count distribution
to fluxes that are much fainter than those reachable by
CTA in short exposures.
Once known, the source count distribution can be used
to estimate the contribution of point sources to the EGB.
This is performed by integrating the flux distribution
dN/dS as follows:
I=ZSmax
0
S0dN
dS0dS0[ph cm−2s−1sr−1].(3)
Choosing Smax = 10−8ph cm−2s−1we find that the
FIG. 5: Comparison between the pixel count distribu-
tion from the average of 20 simulations (blue points), and
the distribution from the real sky (red points). The
green points show the difference between the two distribu-
tions. In each number of photon bin Nphotons ranging be-
tween [Nphoton,1, Nphoton,2] we display Npixel with Nphotons ∈
[Nphoton,1, Nphoton,2).
total integrated flux from point sources is 2.07+0.40
−0.34 ×
10−9ph cm−2s−1sr−1which constitutes 86+16
−14% of the
EGB above 50 GeV estimated in [2]. This validates the
predictions of models [3, 4, 12]. Point sources with fluxes
S > 1.3×10−12 ph cm−2s−1produce 1.47+0.20
−0.24 ×10−9ph
cm−2s−1sr−1, while 6.0+2.0
−1.0×10−10 ph cm−2s−1sr−1
is produced by sources below that flux.
The Fermi-LAT has measured the angular power spec-
trum of the diffuse γ-ray background at |b|>30◦and in
four energy bins spanning the 1-50 GeV energy range [19].
For multipoles l≥155 the angular power CPis found to
be almost constant, suggesting that the anisotropy is pro-
duced by an unclustered population of unresolved point
sources. Indeed, Refs. [20, 21, 22] argue that most of
the angular power measured by the Fermi-LAT is due to
unresolved emission of radio-loud active galactic nuclei.
The angular power due to unresolved sources at
>50 GeV can be readily predicted from the source count
distribution as:
CP=ZSmax
0
(1 −ω(S0)) S02dN
dS0dS0[(ph cm−2s−1)2sr−1],
(4)
The angular power evaluates to CP(E > 50 GeV) =
9.4+1.0
−1.6×10−22 (ph/cm2/s)2sr−1. This is the first
observationally-based prediction of the angular power at
>50 GeV. Our estimation for CP(E > 50GeV ) is in good
agreement with the extrapolation of the Fermi-LAT an-
gular power measurements [19] above 50 GeV and is con-
sistent with the calculated anisotropy due to radio loud

active galactic nuclei made in Refs. [20, 21].
In conclusion, the Fermi-LAT collaboration has used
the new event-level analysis Pass 8 to conduct an all-sky
survey above 50 GeV. The resulting 2FHL catalog con-
tains 253 sources at |b|>10◦and closes the energy gap
between the LAT and Cherenkov telescopes. We have
thoroughly studied the properties of both resolved and
unresolved sources in the 50 GeV–2 TeV band using de-
tailed Monte Carlo simulations and a photon fluctuation
analysis. This allowed us to characterize, for the first
time, the source count distribution above 50GeV, which
is found to be compatible at &10−12 ph cm−2s−1with
a broken power-law model with a break flux in the range
Sb∈[0.8,1.5] ×10−11 ph cm−2s−1, and slopes above
and below the break of, respectively, α1= 2.49 ±0.12
and α2∈[1.60,1.75]. A photon fluctuation analysis con-
strains a possible re-steepening of the flux distribution
to a Euclidean behavior (α3= 2.50) to occur at fluxes
lower than ∼7×10−13 ph cm−2s−1. Our analysis per-
mits us to estimate that point sources, and in particu-
lar blazars, explain almost the totality (86+16
−14 %) of the
>50 GeV EGB.
This might have a number of important consequences,
since any other contribution, exotic or not, must nec-
essarily be small. This bound might imply strong con-
straints for the annihilation cross section or decay time of
high-mass dark matter particles producing γ-rays [3, 4].
Tight constraints could also be inferred on other γ-ray
emission mechanisms due to other diffusive processes
such as UHECRs [23, 24]. Finally, if the neutrinos
detected by IceCube have been generated in hadronic
cosmic-ray interactions, then the same sources producing
the neutrino background will produce part of the sub-
TeV γ-ray background [25]. Because blazars were found
not to be responsible for the majority of the neutrino flux
[26], the fact that the 50 GeV–2 TeV γ-ray background is
almost all due to blazars constrains the contribution of
other source classes to the neutrino background. Such
constraints will be presented in a dedicated paper.
The Fermi -LAT Collaboration acknowledges support
for LAT development, operation and data analysis
from NASA and DOE (United States), CEA/Irfu and
IN2P3/CNRS (France), ASI and INFN (Italy), MEXT,
KEK, and JAXA (Japan), and the K.A. Wallenberg
Foundation, the Swedish Research Council and the Na-
tional Space Board (Sweden). Science analysis support
in the operations phase from INAF (Italy) and CNES
(France) is also gratefully acknowledged.
∗Electronic address: ma jello@slac.stanford.edu
†Electronic address: mattia.dimauro@to.infn.it
[1] C. E. Fichtel, R. C. Hartman, D. A. Kniffen, D. J.
Thompson, H. Ogelman, M. E. Ozel, T. Tumer, and G. F.
Bignami, ApJ 198, 163 (1975).
[2] M. Ackermann et al. (Fermi-LAT), Astrophys.J. 799, 86
(2015), 1410.3696.
[3] M. Di Mauro and F. Donato, Phys.Rev. D91, 123001
(2015), 1501.05316.
[4] M. Ajello, D. Gasparrini, M. S´anchez-Conde, G. Zahari-
jas, M. Gustafsson, et al., Astrophys.J. 800, L27 (2015),
1501.05301.
[5] C. D. Dermer, ApJ 659, 958 (2007), arXiv:astro-
ph/0605402.
[6] M. Fornasa and M. A. S´anchez-Conde (2015),
1502.02866.
[7] W. Atwood, L. Baldini, J. Bregeon, P. Bruel, A. Chekht-
man, et al., Astrophys.J. 774, 76 (2013), 1307.3037.
[8] The Fermi-LAT Collaboration, ArXiv e-prints (2015),
1508.04449.
[9] M. Ackermann et al. (Fermi-LAT), Astrophys. J. 793, 64
(2014), 1407.7905.
[10] S. Ciprini, G. Tosti, F. Marcucci, C. Cecchi, G. Discepoli,
E. Bonamente, S. Germani, D. Impiombato, P. Lubrano,
and M. Pepe, in The First GLAST Symposium, edited
by S. Ritz, P. Michelson, and C. A. Meegan (2007), vol.
921 of American Institute of Physics Conference Series,
pp. 546–547.
[11] A. S. Eddington, MNRAS 73, 359 (1913).
[12] M. Di Mauro, F. Donato, G. Lamanna, D. Sanchez, and
P. Serpico, Astrophys.J. 786, 129 (2014), 1311.5708.
[13] P. Giommi and P. Padovani, MNRAS 450, 2404 (2015),
1504.01978.
[14] G. Dubus, J. L. Contreras, S. Funk, Y. Gallant, T. Has-
san, J. Hinton, Y. Inoue, J. Kn¨odlseder, P. Martin,
N. Mirabal, et al., Astroparticle Physics 43, 317 (2013),
1208.5686.
[15] G. Hasinger, R. Burg, R. Giacconi, G. Hartner,
M. Schmidt, J. Trumper, and G. Zamorani, A&A 275, 1
(1993).
[16] D. Malyshev and D. W. Hogg, ApJ 738, 181 (2011),
1104.0010.
[17] K. M. G´orski, E. Hivon, A. J. Banday, B. D. Wandelt,
F. K. Hansen, M. Reinecke, and M. Bartelmann, ApJ
622, 759 (2005), astro-ph/0409513.
[18] M. B´ethermin, E. Daddi, G. Magdis, M. T. Sargent,
Y. Hezaveh, D. Elbaz, D. Le Borgne, J. Mullaney,
M. Pannella, V. Buat, et al., ApJL 757, L23 (2012),
1208.6512.
[19] M. Ackermann, M. Ajello, A. Albert, et al., Phy. Rev. D
85, 083007 (2012), 1202.2856.
[20] A. Cuoco, E. Komatsu, and J. Siegal-Gaskins, Phys.Rev.
D86, 063004 (2012), 1202.5309.
[21] M. Di Mauro, A. Cuoco, F. Donato, and J. M. Siegal-
Gaskins, JCAP 1411, 021 (2014), 1407.3275.
[22] A. E. Broderick, C. Pfrommer, E. Puchwein, K. M.
Smith, and P. Chang (Heidelberg Institute for Theoreti-
cal Studies, Perimeter Institute for Theoretical Physics),
Astrophys. J. 796, 12 (2014), 1308.0015.
[23] M. Ahlers and J. Salvado, Phy. Rev. D 84, 085019 (2011),
1105.5113.
[24] G. B. Gelmini, O. Kalashev, and D. V. Semikoz, JCAP
1, 044 (2012), 1107.1672.
[25] M. Aartsen et al. (IceCube), Phys.Rev.Lett. 113, 101101
(2014), 1405.5303.
[26] T. Gl¨usenkamp and for the IceCube Collaboration
(2015), 1502.03104.