[a,b]Saqib Hussain

# High-Energy Neutrino and Gamma Ray Production in Clusters of Galaxies

Giulia Pagliaroli  Elisabete M. de Gouveia Dal Pino

###### Abstract

We compute the contribution from clusters of galaxies to the diffuse neutrino
and $\gamma-$ray background. Due to their unique magnetic-field configuration,
cosmic rays (CRs) with energy $\leq 10^{17}$ eV can be confined within these
structures over cosmological time scales, and generate secondary particles,
including neutrinos and gamma-rays, through interactions with the background
gas and photons. We employ three-dimensional (3D) cosmological
magnetohydrodynamical (MHD) simulations of structure formation to model the
turbulent intergalactic and intracluster media. We propagate CRs in these
environments using multi-dimensional Monte Carlo simulations across different
redshifts (from $z\sim 5$ to $z=0$), considering all relevant photohadronic,
photonuclear, and hadronuclear interactions. We also include the cosmological
evolution of the CR sources. We find that for CRs injected with a spectral
index $1.5-2.7$ and cutoff energy $E_{\text{max}}=10^{16}-10^{17}$ eV,
clusters contribute to a substantial fraction to the diffuse fluxes observed
by the IceCube and Fermi-LAT, and most of the contribution comes from clusters
with $M>10^{14}\,M_{\odot}$ and redshift $z<0.3$. We also estimated the
multimessenger contributions from the local galaxy cluster.

##  1 Introdcution

The diffuse neutrino and $\gamma-$ray background provide a very unique view of
the high-energy Universe. The origin of these messengers is unknown. They may
originate from various astrophysical sources such as galaxy clusters [1, 2],
active galactic nuclei (AGNs) [3, see also references therein], star-forming
galaxies (SFGs) [see e.g., 4], supernova remnants [e.g., 5], gamma-ray bursts
[see e.g., 6]. These high-energy messengers can be produced by a single class
of sources i.e., clusters of galaxies [1].

Galaxy Clusters are the largest astrophysical objects of sizes $\sim$ Mpc and
magnetic field strength of about $1\,\mu$ G [7, 8] They can accelerate CRs up
to very high-energies $\sim 10^{18}$ eV [8, 9] through shock and large-scale
turbulence acceleration potentially involving magnetic reconnection. Due to
the large size and magnetic field strength, these structures can confine CRs
of energy $\lesssim 10^{17}$ eV up to a few $\sim$ Gyrs [7, 10]. While
confined, CRs have the ability to interact with gas present within the
intercluster medium (ICM) and photon fields, including the cosmic microwave
background (CMB) and extragalactic background light (EBL). This interaction
leads to the production of high-energy secondary particles such as neutrinos
and gamma-rays. Consequently, clusters of galaxies emerge as potential sources
for generating high-energy multi-messenger signals [1, 7]. Previous analytical
and semi-analytical investigations [e.g., 11, 1] have estimated the
contribution of galaxy clusters to the diffuse neutrino background, revealing
their potential to contribute up to $100\%$ of the diffuse neutrino
background. Additionally, their impact on the diffuse $\gamma-$ray background
is also pronounced, particularly for energies exceeding 10 GeV [2].

In this work, we summarize our calculations of diffuse backgrounds originating
from galaxy clusters, employing the most advanced numerical methods available
to date [36, 37]. In Section 2, we present our assessment of the contribution
of galaxy clusters to the production of neutrinos and $\gamma$-rays, taking
into account the entire population of galaxy clusters. Following that, in
Section 3, we specifically focus on a cluster with properties like the local
one, the Perseus cluster. Finally, in Section 4, we discuss our results and
draw our conclusions.

##  2 Neutrinos and gamma rays from galaxy clusters

To study the diffuse neutrino and $\gamma-$ray backgrounds we used the most
detailed numerical method i.e., combining 3D-MHD simulations with the multi-
dimensional Monte-Carlo simulations of test particle propagation using CRPropa
code [39] The background of ICM is probed by 3D-MHD simulations performed by
[12]. Our assumptions are the following: (i) CRs consist of only protons; (ii)
neutrinos and $\gamma-$rays are initially produced by purely hadronic
interactions inside the clusters; and (iii) the extragalactic magnetic field
is not considered during the propagation of CRs and $\gamma-$rays because it
is highly uncertain, and most likely, it will not produce any significant
change in the results, especially above $10$ GeV energy.

Our simulation setup has two steps: the first one is to propagate CRs inside
clusters considering the background magnetic field and density distribution
directly from the MHD simulations. We considered all the relevant CR
interactions namely: photopion production, Bethe-Heitler pair production, pair
production (single, double, triplet), inverse Compton scattering (ICS), and
proton-proton (pp) interactions. We also take into account the adiabatic
energy losses due to the expansion of the Universe and the synchrotron losses.
Since the energy of synchrotron photons is most likely $<$ Gev, it is beyond
of the scope of this work. At the end of the first step, we collect the CRs
escaped as well as their byproducts $\gamma-$rays and neutrinos, at the edge
of the cluster. In the second step, we propagate those escaped CRs and the
$\gamma-$rays from the edge of the cluster to the Earth. During CR propagation
in the intergalactic medium, we implemented the photopion and Bethe-Heitler
pair production due to interactions with CMB and EBL photon fields.
Furthermore, through the propagation of $\gamma-$rays, we accounted for the
electromagnetic cascade processes (single, double, triplet pair production, as
well as inverse Compton scattering (ICS), which take place both within the
clusters and in the intergalactic medium due to CMB and EBL.

We summarize our results in Fig. 1, comparing them with the IceCube [13] and
Fermi-LAT data [14]. It shows the fluxes of neutrinos and $\gamma-$rays from
the entire population of clusters, considering the CR sources embedded in the
center. These fluxes are obtained by injecting CRs in the center of clusters
with spectral indices $\alpha=1.5-2.5$ and maximum energy in the range
$10^{16}-10^{17}$ eV. The mass range of clusters considered in our simulations
is $10^{12}<M/M_{\odot}\lesssim 5\times 10^{15}$ and the redshift interval is
$z\leq 5.0$. Furthermore, we have assumed that $1\%$ of the cluster luminosity
goes into CRs to be consistent with the prediction of Fermi-LAT [15]. Results
obtained from our simulations are quite comparable with observed diffuse
fluxes of neutrinos and $\gamma-$rays. Fig. 1 shows the connection between
neutrinos and $\gamma-$rays, but it depends on the adopted assumptions such as
spectral indices, maximum energy, and the luminosity of CRs [36, 37].

Figure 1: Multi-messenger emission from clusters of galaxies. Neutrino [36]
and $\gamma-$ray [37] from the entire population of galaxy clusters are
represented by blue and gray bands, respectively. The neutrino flux is
compared with the IceCube data (error bars correspond to the $68\%$ confidence
intervals) [16]. The $\gamma-$ray flux is compared with the DGRB observed by
Fermi-LAT (error bars denote the total uncertainties, statistical and
systematic) [17], and upper limits from HAWC ($95\%$ confidence level) [18]
and CASA-MIA ($90\%$ confidence level) [19]. The lower panel compares our
$\gamma-$ray flux (pink band) with the sensitivity curves (gray lines)
obtained for point sources from LHAASO [23], HAWC [22], and the forthcoming
CTA observatories [24] only for reference purposes. The contribution from
individual sources, namely, blazars [21], AGNs [20], and SFGs [4] is also
shown. Extracted from [36] and [37].

In the lower panel of Fig. 1, we show the contribution from misaligned AGN
[20], blazars [21], and SFGs [4] to diffuse $\gamma-$ray background. The
contribution of individual sources is dominant up to energy $100$ GeV while
the cluster contribution starts to dominate above this energy. More
importantly, our results are comparable with the sensitivity curves of the
High Altitude Water Cherenkov (HAWC) [22], the Large High Altitude Air Shower
Observatory (LHAASO) [23] and the upcoming Cherenkov Telescope Array (CTA)
[24].

##  3 Multi-messenger from Perseus-like clusters

Recently, the Telescope Array (TA) collaboration has observed an excess of CR
events of energy $\gtrsim 10^{19.4}$ eV with $\sim 3.5\;\sigma$ standard
deviations toward the center of the Perseus-Pisces supercluster (PPSC), which
is about $75$ Mpc away from the Earth [25]. In this section, we focus on the
multi-messenger emission including high-energy neutrinos and $\gamma-$rays
from an individual cluster with properties similar to Perseus cluster where
there is a high probability of existence of UHECR sources.

We have extracted a single cluster from the global MHD simulation described in
the previous section [36, 37] to probe the background of a cluster like
Perseus with mass $\sim 10^{14.5}\,M_{\odot}$, and studied the propagation of
CRs in that medium. We injected CRs at the center of the cluster with spectral
index $\alpha=2.3$, $E_{\mathrm{max}}=10^{17}$ eV, and considered that $1\%$
cluster luminosity goes to CRs. Initially, neutrinos and $\gamma-$rays are
produced by CRs interactions in the ICM. We have considered all the relevant
CR interactions during their propagation both in the cluster and in the
intergalactic medium and also taken into account the $\gamma-$ray cascade
inside and outside the cluster, as described above.

In Fig.2, we present the multi-messenger picture of a Perseus-like cluster.
The Fermi-LAT [15] collaboration estimated the upper limit for $\gamma-$rays
from individual clusters (Fig. 2) and our results are consistent with their
predictions. Nevertheless, the $\gamma-$ray flux from the central source of
Perseus cluster (NGC-$1275$) observed by the SHALON experiment ($1996-2012$)
[27] is much larger than our results.

Figure 2: Multi-messenger flux of Perseus-like cluster at $75$ Mpc. Red arrows
represent the upper limit from Fermi-LAT [26] for five clusters (top to
bottom: A400, A3112, A1367, Coma, EXO0422). We also show the high-energy
$\gamma-$ray emission from the active galaxy NGC-$1275$ in the center of
Perseus cluster, observed by SHALON experiment (1996-2012) [27].

In Fig. 3, we show the total fluxes of CRs, $\gamma-$rays, and neutrinos from
an entire sample of Perseus-like sources in the local Universe. The number
density of clusters with mass $\gtrsim 2\times 10^{14}\,M_{\odot}$ is obtained
from our MHD simulation [12, 36, 37], which is around $N\simeq 10^{-5}\log
M\,\text{Mpc}^{-3}$ and also comparable with [38]. Overall, Fig. 3 indicates
that Perseus-like clusters can significantly contribute to the emissions of
UHECRs if their composition consists of protons only. However, the CR flux is
much smaller than the observed UHECR flux from Auger data [see e.g., 28, also
references therein]. It is worth noting that the acceleration of CRs depends
on rigidity, which suggests that heavier nuclei may not be dominant.
Nevertheless, it is also important to acknowledge that individual sources
within clusters, such as starburst galaxies and compact objects like
magnetars, possess the capability to accelerate heavier nuclei to extremely
high energies. Their inclusion in our analysis could potentially enhance the
results for CRs, though the production of neutrinos and $\gamma-$rays is more
efficient for protons compared to heavier nuclei. This is primarily because
these particles are predominantly produced through pion decay processes. In
the case of heavier nuclei, photodisintegration becomes more prominent than
pion production. Therefore, the assumption of considering only protons in our
study seems to be reliable [see e.g., 29]. Still, the contribution of
individual sources should be further explored. In Fig. 3 we also showed the
flux of secondary particles produced by the interaction of CRs during their
propagation in the ICM and intergalactic medium. The neutrino flux we obtained
for Perseus-like sources is comparable with upper limits recently estimated by
the IceCube [34]. On the other hand, the $\gamma-$ray flux is smaller by an
order of magnitude from the diffuse flux observed by the Fermi-LAT [17].

Figure 3: Multi-messenger fluxes from an entire population of Perseus-like
sources located at a distance of about $75$ Mpc. The total $\gamma-$ray flux
from the entire population is presented by black curves. The DGRB from Fermi-
LAT [17] and the upper limits for DGRB from HAWC-collaboration [18] are also
depicted. The total neutrino flux from the Perseus-like clusters is presented
with blue curves, the IceCube diffuse flux (blue circle)[13, 16], and the
upper limits for clusters (blue diamonds) [34] is also shown. The red curve
shows the spectrum of CRs arrived from Perseus-like sources within a distance
$\sim 75$ Mpc and the red marker shows the CR spectrum observed by the
telescope array and telescope array low energy extension (TALE ($E\times
0.91$))[30], pink marker represents the Auger data ($E\times 1.05$) [31, 32].

##  4 Discussion and Conclusion

Our results predict that clusters of galaxies can contribute up to a sizeable
percentage to diffuse neutrinos and $\gamma-$rays. Our results on neutrinos
[36] match with the previous studies [33, 11, 1, 7, 34] and the $\gamma-$rays
flux we obtained [37] roughly agree with the predictions of [2, 33].

The contribution to diffuse $\gamma-$rays by individual sources such as active
galactic nuclei (AGN) [3], star forming galaxis (SFGs) [4], and blazars [21]
is dominant over clusters below $100$ GeV energy. However, above energy $100$
GeV, we showed that the total $\gamma-$ray flux from the entire population of
clusters is dominant over individual source contribution. Therefore, our
estimation is extremely important provided that high-energy CRs are present in
the clusters.

Our results are comparable with the diffuse fluxes of neutrinos and
$\gamma-$rays observed by IceCube [16] and Fermi-LAT [17], respectively.
Moreover, the $\gamma-$ray flux we obtained from the cluster population up to
redshift $z\leq 5.0$ is comparable with the sensitivity curves of the HAWC
[35, 18], the LHAASO [23], and even the CTA [24] which indicates possible
observations of $\gamma-$rays from these sources [36, 37].

Further, we have calculated the multi-messenger emission from Perseus-like
sources within a distance of about $75$ Mpc, in our local Universe. Our
evaluation suggests that the CR flux from these sources (calculated for
protons only) can account for a sizeable percentage of UHECR detected through
the Telescope Array (TA). The current prediction by the TA collaboration of a
probable source of UHECRs in the direction of the Perseus cluster provides
significance to our findings. However, our results are not consistent with the
Auger data which indicate that the composition of UHECRs mainly consists of
heavier nuclei. In the forthcoming work we will account for this contribution.
Nevertheless, the production of neutrinos and $\gamma-$rays calculated from
this population of local clusters shows that the flux of neutrino is
comparable with the estimated upper limits of IceCube for clusters [34], while
the $\gamma-$ray flux is about one order of magnitude less than the Fermi-LAT
[17] observations. This indicates that lower mass clusters should also be
contributing to this emission, as found in [37] (see also Fig. 1.

We acknowledge that our estimations may be subject to changes if certain
parameters are modified, such as the luminosity of the CRs and the spatial
distribution of CR sources within clusters. It is important to recognize that
the presence of the intergalactic magnetic field can also have minor effects
on our results. However, it is worth noting that the parameters we have chosen
for our calculations are in general well-established and similar to those used
in previous research. Any modifications to these parameters are expected to
have only minor impacts on our overall conclusions. Moreover, our results
establish a clear connection between the three messengers (neutrinos, gamma-
rays, and cosmic rays), enabling us to indirectly investigate the properties
of CRs within clusters. This connection provides valuable insights into the
nature and behavior of CRs in these environments.

### Acknowledgments

This work is partially supported by the Brazilian agencies FAPESP (grant
$2013/10559-5\,\&\,17/12828-4)$ and CNPq (grant $308643/2017-8$). The work of
SH and GP is partially supported by the research grant number $2017$W$4$HA$7$S
”NAT-NET:Neutrino and Astroparticle Theory Network” under the program PRIN
$2017$ funded by the Italian Ministero dell’Istruzione, dell’Universita’ e
della Ricerca (MIUR).

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