Galaxy Clusters in Dark Matter Window: The Case of the Shapley Supercluster

Abstract

Dark matter dominates the matter content of the Universe, yet its particle nature remains elusive. Among the promising multi-messenger astronomy dark matter candidates are weakly interacting massive particles and superheavy dark matter, both of which may manifest themselves in cosmic ray, $\gamma$-ray, and neutrino signatures through annihilation or decay. Here, we explore potential multi-messenger signals from these candidates in galaxy clusters of the Shapley Supercluster—one of the most massive known structures in the local Universe (located at a distance of ∼200 Mpc and containing over ${10}^{16}{M}_{\odot }$ of dark matter). Using the CLUMPY code, we model $\gamma$-ray and neutrino fluxes for weakly interacting massive particle masses between 0.1 and 100 TeV across various final states, comparing the predictions with the sensitivities of current and forthcoming observatories, including CTAO, IceCube, and KM3NeT. For superheavy dark matter scenarios with masses from ${10}^{19}$ to ${10}^{28}$ eV, we employ HDMSpectra code to compute ultra-high-energy cosmic ray proton and neutrino fluxes in the ranges available for observations using present (Pierre Auger Observatory, IceCube, KM3NeT) and future (GRAND, GCOS, etc.) instruments.

1. Introduction

The modern cosmological model rooted in the Big Bang theory incorporates three components of matter—baryonic matter, dark matter (DM), and dark energy—as described by the $\Lambda$CDM framework. Among these, DM and dark energy overwhelmingly dominate the total matter–energy content of the Universe, while baryonic matter contributes only about 4% of the critical density [1,2]. Notably, the Standard Model (SM) of particle physics accounts solely for the baryonic component. In contrast, DM is composed of particles beyond the SM and interacts primarily through gravity. Efforts to detect DM via non-gravitational signatures follow three main approaches [3,4,5]:

–

Direct detection through collisions between DM and SM particles in terrestrial detectors;

–

Indirect detection via the observation of SM particles produced in DM annihilation or decay in space;

–

Production of DM particles in high-energy collisions using particle colliders.

For indirect detection, the expected fluxes in SM particles produced as a result of DM particle annihilation or decay are sought using astronomical observations. In astrophysical sources, DM would manifest itself in the fluxes of cosmic rays (CRs) (primarily electrons and positrons, protons and antiprotons, and neutrinos) and electromagnetic radiation with SM messenger energies on the order of 0.001–1 times the DM particle mass $m_{\chi }$.

Weakly interacting massive particles (WIMPs) remain the benchmark candidates. Chemical freeze-out in the early Universe fixes their comoving density, giving the relation ${\Omega }_{\mathrm{DM}}\simeq 0.1\mathrm{pb}/\langle {\sigma }_{\mathrm{ann}}v\rangle$, where $\langle {\sigma }_{\mathrm{ann}}v\rangle$ is the velocity-averaged WIMP self-annihilation cross-section. The observed ${\Omega }_{\mathrm{DM}}\approx 0.3$ implies the “WIMP-miracle’’ value $\langle {\sigma }_{\mathrm{ann}}v\rangle \approx 3\times {10}^{-26}{\mathrm{cm}}^3{\mathrm{s}}^{-1}$ [6,7]. Viable WIMPs arise in supersymmetry (lightest neutralino), universal extra dimensions (the first excited state—Kaluza–Klein mode—of the B boson), and Higgs-portal singlet-scalar models [8,9]. Direct searches now probe spin-independent cross-sections below ${10}^{-48}{\mathrm{cm}}^2$, yet multi-TeV masses and annihilation channels suppressed at colliders remain open. Data from space-based experiments such as Fermi-LAT [10] and Planck [2] have reached a level of sensitivity sufficient to probe thermal WIMP candidates with masses near 100 GeV.

DM annihilation or decay yields stable SM messengers that are observable in cosmic-ray and $\gamma$-ray fluxes, including photons [11,12], neutrinos [13,14], positrons, antiprotons, antideuterons, and potentially exotic antinuclei such as antihelium. Electrons and protons are also produced but are less informative due to strong astrophysical backgrounds.

$\gamma$-rays, which traverse the Galactic medium with minimal absorption [15], offer valuable spectral and angular information for identifying DM structures [16], though their production is typically suppressed and model-dependent due to secondary mechanisms such as internal bremsstrahlung [17]. Moreover, for extragalactic sources, absorption due to interaction with the extragalactic background light (EBL) becomes significant. For $\gamma$-ray sources at redshift $z>0.05$ optical depth ${\tau }_{\gamma }>1$ for $\gamma$-photons with energy $E_{\gamma }>10$ TeV [18,19]. Despite this, the prompt gamma-ray signal remains a crucial observable, directly tracing the DM annihilation or decay site.

Neutrino detection offers a complementary method to $\gamma$-ray-based DM searches, as many SM annihilation/decay channels produce both neutrinos and $\gamma$-rays [20,21,22,23]. For very massive DMs, where $\gamma$-ray signals may cascade and weaken constraints, neutrinos can yield stronger upper limits on the annihilation cross-section [24,25].

Imaging Atmospheric Cherenkov Telescopes (IACTs)— the High-Energy Stereoscopic System (H.E.S.S.), the Major Atmospheric Gamma Imaging Cherenkov Telescopes (MAGIC), and the Very Energetic Radiation Imaging Telescope Array System (VERITAS)—cover the 50 GeV to 50 TeV range, with point-source sensitivities of ≲${10}^{-13}{\mathrm{cm}}^{-2}{\mathrm{s}}^{-1}$ for 100 h observations. The upcoming Cherenkov Telescope Array Observatory (CTAO) will improve sensitivity by an order of magnitude and extend coverage beyond 100 TeV. Wide-field water–Cherenkov arrays—the High-Altitude Water Cherenkov Observatory (HAWC) and the Large High-Altitude Air Shower Observatory (LHAASO)—continuously monitor the 300 GeV to 1 PeV energy range. In the neutrino sector, the IceCube Neutrino Observatory (IceCube) observes events above 100 GeV across the whole sky, while the Cubic Kilometer Neutrino Telescope (KM3NeT) is expected to deliver comparable sensitivity in the Northern Hemisphere [13]. Several studies have been motivated by the detection of ultra-high-energy (UHE) neutrinos, most notably the KM3-230213A event detected by KM3NeT at  220 PeV. Borah et al. [26] interpret this event as possibly originating from the decay of a 440 PeV right-handed neutrino (RHN) DM candidate. Jho et al. [27] offer an alternative explanation involving a multicomponent supersymmetric DM model with nearly degenerate masses. The heavier DM component decays into the lighter one, emitting a highly boosted neutrino. This setup naturally explains the isotropic nature of the KM3NeT signal and avoids the expected Galactic center excess of conventional decaying DM models. Murase et al. [28] propose a unified framework in which the inflaton of natural inflation also acts as superheavy scalar dark matter. This scenario is capable of producing neutrinos and UHE cosmic rays (CRs), potentially linking together the KM3NeT event, AMATERASU cosmic-ray detection, and inflationary physics.

Dwarf galaxies are promising targets for DM searches due to their low astrophysical backgrounds. The Galactic center is another key target, though the backgrounds there are complex [20,22]. Galaxy clusters (GCs)—having the largest DM masses ($M_{\mathrm{DM}}\sim {10}^{15}{M}_{\odot }$) —offer higher $\gamma$-ray and neutrino luminosities.

Song, Murase, and Kheirandish [29] analyze 14 years of Fermi-LAT data from seven GCs. They simulate $\gamma$-ray signals from decaying very heavy DM (VHDM), including both prompt emissions and secondary cascades from electromagnetic interactions in the cluster medium. Their results yield lower bounds on DM lifetimes up to ${\tau }_{dec}\sim {10}^{28}$ s for $m_{\chi }={10}^3$–${10}^{16}$ GeV, providing strong, complementary limits to neutrino observatories.

Shifting from decay to annihilation, Lisanti et al. [30] analyze 413 weeks of Fermi-LAT data across hundreds of galaxy groups within $z\lesssim 0.03$. By calculating J-factors and considering conservative substructure boost models, they search for diffuse $\gamma$-ray signals from DM annihilation. Although no signal was found, they set constraints comparable to those from dwarf spheroidal galaxies. Importantly, their results challenge the DM interpretation of the Galactic Center excess and refine the extragalactic $\gamma$-ray search methodology.

Cosmic-ray measurements by the Payload for Antimatter Matter Exploration and Light-nuclei Astrophysics (PAMELA), the Alpha Magnetic Spectrometer–02 (AMS-02), and the DArk Matter Particle Explorer (DAMPE) reveal an unexplained rise in the positron fraction above 10 GeV. While pulsars may account for the excess, leptophilic WIMPs with $m_{\chi }\sim$ 1–3 TeV remain viable [31]. Antiproton data constrain hadronic channels, and the forthcoming GAPS experiment will test low-mass scenarios via antideuterons [32].

The UHE CR and neutrino detectors (Pierre Auger Observatory (PAO), Telescope Array, ANITA) register events with energies of the order of ${10}^{20}$ eV [33,34,35]. In addition to the aforementioned superheavy dark matter (SHDM) candidates—including Planck-scale Planckian-Interacting Massive Particles (PIMPs)—the set of still-unidentified sources and acceleration mechanisms of such CRs includes topological defects. In particular, cusps of cosmic strings are hypothesized as sources of rapidly decaying supermassive particles with energies on the order of the grand unified theory (GUT) scale (∼${10}^{25}$ eV), which decay into lower-energy SM particles (protons, neutrinos, photons) via a top-down mechanism [36,37,38]. The characteristic features of the spectra of high-energy SM particles in such a mechanism (although we have not yet received reliable confirmation from observations [39]) allow us to establish restrictions on particle parameters beyond the SM. However, the volume of high-quality observational data is growing rapidly, which makes it possible to deepen our understanding of the physics beyond the SM and offers the chance to discover new particles [36,38]. Future detectors—the next-generation IceCube Neutrino Observatory (IceCube-Gen2), the Giant Radio Array for Neutrino Detection (GRAND), the Global Cosmic-ray Observatory (GCOS), and others—aim to probe new limits in SHDM cross-sections and lifetimes [12,40,41,42,43], exploring physics near the Planck scale.

While SHDM probes the physics close to the Planck scale, another class of candidates arises at the opposite end of the mass spectrum. Beyond WIMPs and SHDM, other dark matter candidates—very light, feebly interacting particles such as axion-like particles (ALPs)—may also produce distinctive multi-messenger signatures in galaxy clusters and active galactic nuclei [44,45,46].

In our work, we investigate multimessenger DM signatures of GCs in the Shapley Supercluster (SSC), the most massive large-scale structure in the nearby Universe ($M_{\mathrm{tot}}\approx {10}^{16}{M}_{\odot }$, $d\approx 200$ Mpc) [47,48,49,50,51].

Using the open-source code CLUMPY (available at https://clumpy.gitlab.io/CLUMPY/v3.1.1/ (accessed on 30 July 2025)) [52,53,54], we compute $J_{\mathrm{ann}}$- and $J_{\mathrm{dec}}$-factors for its four richest clusters and predict $\gamma$-ray and neutrino spectra for benchmark WIMP annihilation/decay channels ($b\overline{b}$, $W^{+}{W}^{-}$, ${\tau }^{+}{\tau }^{-}$ etc.) over $m_{\chi }=0.1$–100 TeV [4,5]. We further model the annihilation/decay channels of SHDM (${10}^{19}$–${10}^{28}$ eV) in these GCs using the open-source code HDMSpectra (available at https://github.com/nickrodd/HDMSpectra (accessed on 30 July 2025)) [55]. A comparison with PAO, IceCube and projected CTAO, KM3NeT, etc. detector sensitivities allows for new limits to be set on DM parameters $\langle {\sigma }_{\mathrm{ann}}v\rangle$ and ${\tau }_{dec}$.

These results position the SSC as a prime multi-messenger target for the next generation of indirect DM searches (see [51] and references therein). Future observations by PAO, IceCube-Gen2, CTAO, and KM3NeT, combined with theoretical innovations, will be essential in refining these models and potentially identifying the elusive dark sector.

The text is organized as follows. In Section 2, we outline the structure and main parameters of the GCs in the SSC and present the theoretical foundations for calculating $\gamma$-ray and neutrino emissions from DM annihilation and decay. In Section 3, we present the calculation of $\gamma$-ray emissions from WIMP annihilation and decay. Section 4 presents the calculation of neutrino emissions from WIMP annihilation and decay. In Section 5, we present the spectral fluxes of neutrinos from the annihilation and decay of super-heavy (${10}^3$–${10}^{10}$ TeV) DM in the SSC region. Finally, in Section 6, we discuss the obtained results.

Throughout the paper, we assume a flat $\Lambda$CDM cosmology with a Hubble constant $h=H_0/100$ km ${\mathrm{s}}^{-1}$ Mp${\mathrm{c}}^{-1}=0.7$, matter density ${\Omega }_m=0.3$, and dark energy density ${\Omega }_{\Lambda }=0.7$. At the mean redshift of the SSC, $z=0.05$, this corresponds to a luminosity distance of $d_L=222$ Mpc, angular distance of $d_A=d_L/{(1+z)}^2=201$ Mpc and an angular scale of 3.52 Mpc/$1°$.

2. GCs in SSC: Structure and DM Parameters

GCs are the most massive gravitationally bound systems in the Universe, with total masses ranging from ${10}^{14}$ to ${10}^{15}{M}_{\odot }$, dominated by DM, comprising 80–90% of their mass [56]. Their deep gravitational potential wells and extended DM halos make them excellent targets for indirect detection via $\gamma$-rays and neutrinos, observable with instruments such as Fermi-LAT and CTAO.

The $\gamma$-ray flux from DM annihilation scales with the square of the DM density favors the densest central regions. In contrast, fluxes from DM decay scale linearly with density, making the full cluster volume relevant [57]. While substructures within DM halos can enhance the annihilation signal, large uncertainties in the associated boost factors limit predictive power [58,59,60]. Consequently, GCs are currently robust targets for probing DM decay [61].

This work considers two representative targets: the SSC, among the densest large-scale structures in the local Universe, with a high DM content [62], and the Perseus cluster (Abell 426), the most X-ray-luminous cluster [63], featuring a relaxed, cool-core morphology and favorable visibility from the CTAO-North Array.

2.1. GCs: Structure and DM Distribution

The spherically averaged DM density profile in GCs is modeled using the Zhao profile [64]:

$${\rho }_{\mathrm{tot}}\left(r\right)={\displaystyle \frac{2^{(\beta -\gamma )/\alpha }{\rho }_s}{{(r/r_s)}^{\gamma }{\left[1+{(r/r_s)}^{\alpha }\right]}^{(\beta -\gamma )/\alpha }}},$$

(1)

where $\gamma$, $\alpha$, and $\beta$ determine the inner, transition, and outer slopes, and ${\rho }_s$, $r_s$ are scale parameters.

In this study, we adopt the Navarro–Frenk–White (NFW) profile [65], corresponding to $(\gamma , \alpha , \beta )=(1, 1, 3)$:

$$\rho \left(r\right)={\displaystyle \frac{4{\rho }_s}{(r/r_s){(1+r/r_s)}^2}}.$$

(2)

Key structural parameters are defined with respect to the critical density ${\rho }_{\mathrm{crit}}\left(z\right)=3H^2\left(z\right)/\left(8\pi G\right)$ at redshift z, where $H\left(z\right)$ is the Hubble parameter and G is the gravitational constant [66]. A radius $R_{\Delta }$ is the radius within which the mean total matter density (dark matter plus baryons) is $\Delta$ times the critical density of the Universe at that redshift. For example, $R_{200}$ denotes the case $\Delta =200$:

$$R_{200}={\left({\displaystyle \frac{3M_{200}}{800\pi {\rho }_{\mathrm{crit}}\left(z\right)}}\right)}^{1/3},$$

(3)

while $R_{500}$ corresponds to $\Delta =500$. The associated angular size is ${\theta }_{200}=arctan(R_{200}/d_A\left(z\right))$.

The concentration parameter $c_{200}$ is defined as the ratio of the virial radius to the scale radius of the DM halo, $c_{200}\equiv R_{200}/r_s$, and can be estimated from numerical fits as

$$c_{200}=7.85{(1+z)}^{-0.71}{\left({\displaystyle \frac{M_{200}}{2\times {10}^{12}{h}^{-1}{M}_{\odot }}}\right)}^{-0.081}.$$

(4)

The characteristic density ${\rho }_s$ then follows from mass conservation within $R_{200}$:

$${\rho }_s\left(z\right)={\displaystyle \frac{50}{3}}{\displaystyle \frac{c_{200}^3{\rho }_{\mathrm{crit}}\left(z\right)}{ln(1+c_{200})-c_{200}{(1+c_{200})}^{-1}}}.$$

(5)

Given the diffuse outskirts of GCs, we define their spatial extent using a truncation radius of $R_{\mathrm{tr}}\approx 2R_{200}$ (or equivalently, $3R_{500}$), motivated by density and pressure discontinuities typically observed near the GC accretion shock. The corresponding angular size is ${\theta }_{\mathrm{tr}}\approx 2{\theta }_{200}\approx 3{\theta }_{500}$.

2.2. $\gamma$-Ray and Neutrino Emission from DM Annihilation and Decay

The $\gamma$-ray and neutrino fluxes from DM annihilation or decay can be factorized into particle physics and astrophysical components [67,68,69]. For a GC with angular radius ${\theta }_{\mathrm{tr}}$ (corresponding to solid angle $\Delta \Omega =2\pi (1-cos{\theta }_{\mathrm{tr}})$), the differential flux at energy $E_{\gamma ,\nu }$ is given by the following:

$$\begin{array}{c}\hfill {\displaystyle \frac{d{\Phi }_{\gamma ,\nu }}{d{E}_{\gamma ,\nu }}}(E_{\gamma ,\nu },l.o.s.,\Delta \Omega )={\displaystyle \frac{d{\Phi }_{\gamma ,\nu }^{PP}}{d{E}_{\gamma ,\nu }}}\left(E_{\gamma ,\nu }\right)\times J(l.o.s.,\Delta \Omega ).\end{array}$$

(6)

where the astrophysical factor J encodes the line-of-sight (l.o.s.) integration of the DM density distribution. For annihilation and decay, respectively, the expressions for J are

$$\begin{array}{ccc}\hfill J_{\mathrm{ann}}(\Delta \Omega )& =& {\int }_{\Delta \Omega }d\Omega {\int }_{l_{\min }}^{l_{\max }}{\rho }^2(r,l)dl,\hfill \end{array}$$

(7)

$$\begin{array}{ccc}\hfill J_{\mathrm{dec}}(\Delta \Omega )& =& {\int }_{\Delta \Omega }d\Omega {\int }_{l_{\min }}^{l_{\max }}\rho (r,l)dl,\hfill \end{array}$$

(8)

with the solid angle defined as

$$\begin{array}{c}\hfill \Delta \Omega =2\pi (1-cos{\theta }_{tr}),\end{array}$$

(9)

and the radial distance is related to the line-of-sight distance l through

$$\begin{array}{ccc}\hfill r& =& \sqrt{l^2+D^2-2Dlcos\theta },\hfill \end{array}$$

(10)

where D is the distance to the target.

The particle physics term for annihilation is given by

$$\begin{array}{c}\hfill {\displaystyle \frac{d{\Phi }_{\gamma ,\nu }}{d{E}_{\gamma ,\nu }}}\left(E_{\gamma ,\nu }\right)={\displaystyle \frac{1}{4\pi }}{\displaystyle \frac{\langle {\sigma }_{\mathrm{ann}}v\rangle }{2m_{\chi }^2}}\times {\displaystyle \frac{d{N}_{\gamma ,\nu }}{d{E}_{\gamma ,\nu }}},\end{array}$$

(11)

where $d{N}_{\gamma ,\nu }/d{E}_{\gamma ,\nu }$ is the photon or neutrino yield per annihilation.

For decay, the corresponding expression is

$$\begin{array}{c}\hfill {\displaystyle \frac{d{\Phi }_{\gamma ,\nu }}{d{E}_{\gamma ,\nu }}}\left(E_{\gamma ,\nu }\right)={\displaystyle \frac{1}{4\pi }}{\displaystyle \frac{1}{m_{\chi }{\tau }_{dec}}}\times {\displaystyle \frac{d{N}_{\gamma ,\nu }}{d{E}_{\gamma ,\nu }}}.\end{array}$$

(12)

where $d{N}_{\gamma ,\nu }/d{E}_{\gamma ,\nu }$ is the photon or neutrino yield per decay.

We consider the case of Majorana WIMPs; for Dirac WIMPs, the predicted fluxes would be reduced by an additional factor of 1/2 due to the absence of identical particle symmetry in the initial state [6]. The fluxes are computed using the differential photon and neutrino yields $\mathrm{d}{N}_{\gamma ,\nu }/\mathrm{d}{E}_{\gamma ,\nu }$ provided in [70], which include electroweak corrections relevant at high energies.

2.3. CLUMPY and HDMSpectra Software for DM Annihilation/Decay Calculation

For our analysis, we use the CLUMPY v3.1.1 code [54], a C++ package developed as a publicly available tool for estimating DM-induced $\gamma$-ray and neutrino fluxes in a wide variety of objects and custom configurations. It computes signals based on different DM distribution parameterizations derived from cosmological modeling and supports indirect DM searches at Galactic and extragalactic scales.

For DM particle masses exceeding 1 PeV, we additionally use the HDMSpectra code [55], designed to compute the energy spectra of secondary particles produced in DM annihilation or decay into SM final states. It covers a mass range from 500 GeV up to ${10}^{19}$ GeV and includes electroweak corrections, hadronization, and decay chains based on particle physics models and Monte Carlo simulations. The code supports various final states and enables spectrum generation for both annihilation and decay scenarios in indirect detection studies.

In the following, we use the case of well-studied DM signatures in the Perseus cluster [71,72] as a test case for comparison with the expected manifestations of DM in GCs of SSC. We compute the J-factors for the Perseus cluster using parameters listed in

Table 1. Astrophysical parameters of selected GCs.

Cluster	l	b	z	${\mathit{R}}_{200}$	${\mathit{R}}_{\mathbf{tr}}$	${\mathit{M}}_{200}$	${\mathit{c}}_{200}$	${\mathit{r}}_{\mathit{s}}$	${\mathit{\rho }}_{\mathit{s}}$*
Perseus	150.57	$-13.26$	0.0179	1870	3730	7.5	5.0	373.0	3.09
A3556	312.37	30.72	0.049	1258	2517	2.2	5.3	236.1	3.58
A3558	311.98	31.31	0.048	1974	3948	8.6	4.8	412.9	2.79
A3560	310.90	29.55	0.0495	1515	3031	3.9	5.1	297.6	3.22
A3562	311.63	31.32	0.049	1732	3465	5.9	4.9	351.3	2.99

  * Units: l, b in degrees; $R_{200}$, $R_{\mathrm{tr}}$, $r_s$ in kpc; $M_{200}$ in ${10}^{14}$ $M_{\odot }$; ${\rho }_s$ in ${10}^5$ $M_{\odot }$ kp${\mathrm{c}}^{-3}$.

. For an integration angle of $\theta =1.4°$, we obtain $J_{\mathrm{ann}}=2.54\times {10}^{17}$ Ge${\mathrm{V}}^2$ c${\mathrm{m}}^{-5}$ and $J_{\mathrm{dec}}=1.46\times {10}^{19}$ GeV c${\mathrm{m}}^{-2}$, in agreement with the values reported in Ref. [72], $J_{\mathrm{ann}}=2.63\times {10}^{17}$ Ge${\mathrm{V}}^2$ c${\mathrm{m}}^{-5}$ and $J_{\mathrm{dec}}=1.59\times {10}^{19}$ GeV c${\mathrm{m}}^{-2}$.

Having validated our implementation, we apply the same procedure to clusters in the SSC (A3558, A3562, A3560, A3556), using the parameters listed in Table 1. The results are summarized in

Table 2. Integrated J-factors for DM annihilation and decay in selected GCs.

Cluster	${\mathit{\theta }}_{\mathbf{tr}}$ [deg]	${\mathit{J}}_{\mathbf{ann}}$ [${10}^{16}$ Ge${\mathrm{V}}^2$c${\mathrm{m}}^{-5}$]	${\mathit{J}}_{\mathbf{dec}}$ [${10}^{18}$ GeV c${\mathrm{m}}^{-2}$]
Perseus	2.73	25.0	22.4
A3556	0.66	1.26	0.93
A3558	1.06	4.23	3.78
A3560	0.78	2.01	1.60
A3562	0.91	2.92	2.45

and shown in Figure 1.

Figure 1 shows the dependence of $J_{\mathrm{ann}}$ and $J_{\mathrm{dec}}$ on the integration angle ${\alpha }_{\mathrm{int}}$. All clusters exhibit a rapid initial increase followed by saturation at angles ${\alpha }_{\mathrm{int}}>{\theta }_{\mathrm{tr}}$.

Figure 2 shows how strongly the observed manifestations of DM decay/annihilation depend on the DM distribution profile within the same cluster using the example of three distributions—the NFW profile with $(\alpha ,\beta ,\gamma )=(1, 3, 1)$, the Moore profile with $(\alpha ,\beta ,\gamma ,)=(1.5, 3, 1.5)$, and the modified isothermal profile with $(\alpha ,\beta ,\gamma ,)=(2, 2, 0)$ [54] for the Perseus cluster.

It is worth noting that expected DM manifestations of GCs are scaled by their J-factors, and the J-factors of GCs in SSC are about ten times smaller than those of the Perseus cluster, but the total multi-TeV fluxes of four GCs of SSC in over $8°$ CTAO field of view are only 2–3 times smaller. Given that the Perseus cluster contains two $\gamma$-ray-dominated AGNs (NGC 1275 and IC 310) and is located at a lower Galactic latitude (b = −13.3° vs. b = 30.7° for SSC), we expect similar detection chances for the Perseus cluster and the GCs of SSC.

3. $\mathbf{\gamma }$-Ray and Neutrino Spectral Fluxes from the Annihilation/Decay of WIMP DM in GCs

3.1. Expected $\gamma$-Ray Spectral Fluxes from the Annihilation/Decay of WIMP DM

We compute the expected $\gamma$-ray flux spectra from WIMP DM annihilation for the Perseus cluster and four members of the SSC (A3558, A3560, A3562, and A3556). Calculations are performed for two benchmark DM masses, $m_{\chi }=1$ TeV and 10 TeV, and for a representative set of annihilation channels: $b\overline{b}$, $t\overline{t}$, $HH$, $ZZ$, and $W^{+}{W}^{-}$. Each scenario is evaluated for two values of the thermally averaged annihilation cross-section: the canonical thermal relic value $\langle {\sigma }_{\mathrm{ann}}v\rangle =3\times {10}^{-26}$ c${\mathrm{m}}^3$ ${\mathrm{s}}^{-1}$ and a higher reference value of $3\times {10}^{-22}$ c${\mathrm{m}}^3$ ${\mathrm{s}}^{-1}$ close to IACT sensitivity for $m_{\chi }\ge 1$ TeV [71,72]. The resulting fluxes are compared with the expected CTAO sensitivity (northern and southern arrays) for 50 h of observation.

As shown in Figure 3 and Appendix A, Figure A1, the fluxes predicted for $\langle {\sigma }_{\mathrm{ann}}v\rangle =3\times {10}^{-22}{\mathrm{cm}}^3{\mathrm{s}}^{-1}$ approach the sensitivity threshold of CTAO-South.

In this regime, CTAO observations have the potential to place strong constraints on the DM annihilation signal. In contrast, for the thermal relic cross-section, the predicted flux lies well below the CTAO sensitivity in all channels and targets, unless amplified by additional astrophysical effects (e.g., substructure boosts) or particle-physics mechanisms (e.g., Sommerfeld enhancement) [73,74,75,76,77].

The spectral shapes across different channels follow expected trends, all displaying a sharp cutoff at photon energies near the DM mass, $E_{\gamma }\sim m_{\chi }$. Quark channels ($b\overline{b}$, see Figure 3; $t\overline{t}$, see Appendix A, Figure A1) yield relatively soft spectra. In contrast, bosonic channels ($W^{+}{W}^{-}$, Figure 3; $HH$ and $ZZ$, Figure A1) produce harder spectra with extended high-energy tails, slightly enhancing detectability at higher energies.

As expected from the scaling $\Phi \propto \langle {\sigma }_{\mathrm{ann}}v\rangle /m_{\chi }$, increasing the DM mass to 10 TeV results in a reduced flux amplitude and a shift of the spectral peak to lower relative energies (in units of $E/m_{\chi }$), further challenging detectability.

In addition to annihilation, we compute the expected $\gamma$-ray flux spectra from DM decay for particle lifetimes of ${\tau }_{\mathrm{dec}}={10}^{25}$ s and ${10}^{27}$ s. The corresponding results are shown in Figure 4 and in Figure A2 in Appendix A. For shorter lifetimes, the predicted flux in some channels exceeds the CTAO sensitivity, particularly for the Perseus cluster. At ${\tau }_{\mathrm{dec}}={10}^{27}$ s, the signal is suppressed and remains below the detection threshold across all targets.

Although the flux is lower for $m_{\chi }=1$ TeV than for 10 TeV, the spectral features and channel-dependent trends are preserved. The decay flux scales as $\Phi \propto 1/{\tau }_{\mathrm{dec}}$. This makes GCs suitable targets for decay searches even in the absence of strong central overdensities.

3.2. Expected Neutrino Fluxes and Detection Prospects with IceCube and KM3NeT

We evaluated the neutrino flux spectra from WIMP DM annihilation in the Perseus Cluster and four members of the SSC: A3558, A3562, A3560, and A3556. The analysis included five representative annihilation channels—$b\overline{b}$, $t\overline{t}$, $HH$, $ZZ$, and $W^{+}{W}^{-}$—for two benchmark DM masses: $m_{\chi }=10\mathrm{TeV}$ and $100\mathrm{TeV}$, consistent with the $\gamma$-ray analysis in the previous section. Predicted fluxes were compared to the sensitivities of the IceCube and KM3NeT neutrino observatories, assuming a 10-year exposure.

We explored two values of the thermally averaged annihilation cross-section: the standard relic value $\langle {\sigma }_{\mathrm{ann}}v\rangle =3\times {10}^{-26}{\mathrm{cm}}^3{\mathrm{s}}^{-1}$ and an enhanced value $\langle {\sigma }_{\mathrm{ann}}v\rangle =3\times {10}^{-18}{\mathrm{cm}}^3{\mathrm{s}}^{-1}$ due to a range of enhancements beyond the standard production scenario [73,77,78,79,80].

As illustrated in Figure 5 and in Appendix A Figure A3, the predicted neutrino fluxes for the thermal relic cross-section lie well below the sensitivity limits of both observatories. The spectral shapes vary by the annihilation channel: bosonic final states ($W^{+}{W}^{-}$, $ZZ$, $HH$) yield harder spectra than hadronic ones ($b\overline{b}$, $t\overline{t}$), enhancing the flux at higher energies where neutrino detectors have greater sensitivity.

We now extend the analysis to neutrino fluxes from DM decay in the same set of GCs and final-state channels, considering the same benchmark DM masses as in the annihilation case.

As shown in Figure 6 and in Appendix A, Figure A4, shorter DM lifetimes result in significantly enhanced neutrino fluxes, in some cases reaching or exceeding the KM3NeT sensitivity depending on the decay channel and cluster parameters. As in the annihilation scenario, decays into bosonic final states ($W^{+}{W}^{-}$, $ZZ$, $HH$) produce harder spectra than into hadronic channels ($b\overline{b}$, $t\overline{t}$), enhancing the flux at high energies where neutrino observatories are most sensitive.

The subhalo structure plays an insignificant role in comparison with the annihilation scenario, while the total DM content and proximity of the cluster become the dominant factors for detectability.

4. Annihilation and Decay Neutrino Spectral Fluxes for Superheavy (1–100 PeV) DM

To extend the analysis beyond the WIMP mass range considered earlier, we explored the regime of ultra-high-energy neutrinos. We computed the corresponding fluxes from DM with superheavy masses, $m_{\chi }={10}^3\mathrm{TeV}$ and $m_{\chi }={10}^5\mathrm{TeV}$, using the HDMSpectra package. This mass range aligns with the optimal sensitivity of KM3NeT and IceCube, which peaks at energies above ∼100 $\mathrm{TeV}$, where atmospheric neutrino backgrounds are strongly suppressed.

We computed neutrino fluxes from both annihilation and decay of DM in the same set of GCs and for five main representative final-state channels. For annihilation, the resulting spectra are shown in Figure 7 and in Appendix B, Figure A5. For decay, the corresponding spectra are presented in Figure 8 and in Appendix B, Figure A6.

In both cases, the DM mass controls the energy range of the emission. For $m_{\chi }={10}^3\mathrm{TeV}$, most of the neutrino flux lies in the ${10}^1$–${10}^3\mathrm{TeV}$ range, matching the peak sensitivity of IceCube and partially overlapping with KM3NeT capabilities. At $m_{\chi }={10}^5\mathrm{TeV}$, the emission shifts to higher energies ($>{10}^4$ $\mathrm{TeV}$), where the KM3NeT detector is sensitive.

The spectral shape depends on the final state. Decays or annihilations into heavy bosons ($ZZ$, $W^{+}{W}^{-}$, $HH$) produce harder spectra with enhanced flux at the highest energies, improving the prospects for detection. In contrast, quark channels ($b\overline{b}$, $t\overline{t}$) yield softer and broader spectra, less favorable for ultra-high-energy neutrino detection.

Overall, KM3NeT demonstrates strong potential for detecting neutrinos from DM annihilation/decay for intermediate masses and bosonic final states, within the 10–1000 TeV range for ${\tau }_{\mathrm{dec}}={10}^{25}$ s. IceCube offers complementary coverage at higher energies and northern sky declinations.

5. GC Neutrino and Cosmic Ray Proton Spectra for the Annihilation/Decay of 10 ZeV SHDM

GCs are one of the potential sources of UHE CRs and astrophysical neutrino due to SHDM annihilation or decay ([29] and references therein). Modern CR detectors (PAO, Telescope Array) register energy frontier events with energies over ${10}^{20}$ eV [33,34,35], and the upper limit is determined by detector’s surface and the observational time. GC SHDM in the form of PIMPs with masses up to the Planck mass ${10}^{28}$ eV, particularly SHDM particles with GUT scale energy (∼${10}^{25}$ eV), decay into lower-energy ($E<m_{\chi }$) SM particles including protons, neutrinos, and photons—extreme energy cosmic rays (EECRs, $E>{10}^{20}$ eV), created by a “top-down” mechanism [36,37,38].

Due to the large optical depth of extremely energetic $\gamma$-rays from SSC, only EE neutrinos and CRs can be detected from SHDM annihilation or decay in the GCs of SSC. EE neutrino spectral fluxes do not suffer from interaction with EBL, whereas EECR proton/antiproton-generated spectra ${\Phi }_{gen}(E,z)$ are subject to considerable modification due to energy losses in photo-pion production for CR energies higher than the GZK cut-off energy $E\approx 50$ EeV ${\Phi }_{obs}(E,z=0)={\eta }_{mod}(E,z){\Phi }_{gen}(E,z)$ [82].

We computed neutrino and CR proton fluxes from both the annihilation and decay of SHDM with $m_{\chi }=10$ ZeV in the same set of GCs and for five main representative final-state channels. Since, at such extremely high energies, we only have the observational upper limits of the isotropic intensity of extragalactic neutrinos (PAO and IceCube data) and the detected isotropic cosmic ray intensity (PAO data), we calculated a mean intensity of neutrino and CR proton emissions from inside the truncated radius of the considered GCs, i.e., we compared the mean background spectral brightness of the sky with the spectral brightness of the corresponding GC “hot spots”. These hot spots will appear as extended sources with angular radii equal to the truncated radii ${\theta }_{tr}$ and with corresponding solid angles $\Delta \Omega \approx \pi {\theta }_{tr}^2$. The mean intensity (surface brightness) of the hot spot is calculated as follows:

$$\begin{array}{c}\hfill {\displaystyle \frac{d{I}_{p,\nu }}{d{E}_{p,\nu }}}\left(E_{p,\nu }\right)={\displaystyle \frac{d{\Phi }_{p,\nu }}{d{E}_{p,\nu }}}(E_{p,\nu },\Delta \Omega )/\Delta \Omega .\end{array}$$

(13)

The calculated neutrino spectra are shown in Figure 9 and in Appendix C, Figure A7. The possibility of detecting such neutrino signatures appears only at a high cross-section value $\langle {\sigma }_{\mathrm{ann}}v\rangle \sim {10}^{-10}{\mathrm{cm}}^3{\mathrm{s}}^{-1}$ or short decay time ${\tau }_{\chi }\sim {10}^{20}$ s.

The calculated CR proton spectra are shown in Figure 10 and in Appendix C, Figure A8. Both the observable and calculated spectra show the signatures of the GZK cut-off. The prospects of detecting CR proton signatures are somewhat better than in the case of neutrinos, but still require a high enough cross-section value $\langle {\sigma }_{\mathrm{ann}}v\rangle \sim {10}^{-12}{\mathrm{cm}}^3{\mathrm{s}}^{-1}$ or small decay time ${\tau }_{\chi }\sim {10}^{21}$ s.

6. Discussion and Conclusions

Massive superclusters such as the SSC offer attractive targets for indirect DM searches. SSC is one of the most massive structures in the local Universe. Unlike individual systems such as the Perseus cluster, the SSC contains a concentration of numerous massive subclusters—currently known to comprise at least 45 members [85]—within a relatively compact angular extent. This enables stacking analyses that combine the expected fluxes from several clusters, significantly improving the signal-to-noise ratio.

Furthermore, the potential contamination from astrophysical backgrounds may be lower in SSC compared to the Perseus cluster, which hosts two bright active galactic nuclei (NGC 1275 and IC 310) known to emit strong $\gamma$-ray and X-ray emission. The southern sky position of SSC provides favorable visibility for neutrino and $\gamma$-ray observatories such as KM3NeT and CTA-South, enhancing the observational prospects.

In this work, we explore the prospects for detecting signatures of DM via $\gamma$-ray and neutrino observations of GCs, focusing on both annihilation and decay scenarios. We considered heavy DM candidates,  particularly WIMPs with masses of up to a few TeVs, and modeled the expected fluxes from nearby and massive Perseus clusters and the central core of the SSC, which includes four GCs. These environments, due to their high DM content and gravitational coupling, are promising targets for indirect DM detection.

We used two additional tools to model the expected multi-messenger signals: open code CLUMPY to compute the $\gamma$-ray and neutrino spectral fluxes produced by the annihilation/decay of DM particles, WIMPs with masses up to 100 TeV, and open code HDMSpectra to compute the final-state particle energy spectra from the annihilation/decay of SHDM with masses 1 PeV–10 ZeV. We considered a wide range of particle masses, annihilation cross-sections, and decay times.

Our analysis suggests that the $\gamma$-ray signals from DM annihilation in the GCs of SSC may be comparable with the case of the well-studied Perseus cluster and are close to the CTAO–South detection levels, especially in scenarios where the cross-section of DM annihilation exceeds the canonical WIMP value and reaches $\langle {\sigma }_{\mathrm{ann}}v\rangle \sim {10}^{-22}{\mathrm{cm}}^3{\mathrm{s}}^{-1}$. Similarly, constraints on DM decay times can be improved by $\gamma$-ray observations of massive clusters. For decay channels to gauge bosons and for lifetimes shorter than ${\tau }_{\chi }\sim {10}^{26}$ s, CTAO observations are particularly sensitive.

On the other hand, the neutrino signals from DM annihilation/decay in SSC are more difficult to detect. For annihilation, detectable neutrino fluxes require extremely high cross-sections (e.g., $\langle {\sigma }_{ann}v\rangle \sim {10}^{-18}$ c${\mathrm{m}}^3$ ${\mathrm{s}}^{-1}$).

For decays, lifetimes around ${\tau }_{\chi }\sim {10}^{25}$ s may yield minimally detectable signals from nearby clusters such as the Perseus cluster, and even from SSC, especially for heavy boson decay channels.

Since DM particles can have masses ranging up to the Planck scale, we also computed the neutrino and CR proton fluxes from both the annihilation and decay of SHDM in the SSC with $m_{\chi }$ = 1 PeV–10 ZeV. The possibility of detecting extremely energetic neutrino and CR proton signatures created by such SHDMs occurs only at high cross-section values $\langle {\sigma }_{\mathrm{ann}}v\rangle \sim {10}^{-10}{\mathrm{cm}}^3{\mathrm{s}}^{-1}$ or short decay times ${\tau }_{\chi }\sim {10}^{20}$ s.

It is worth noting that the results presented above are based on a simplified benchmark scenario, which assumes thermal WIMP DM with a self-annihilation cross-section of $3\times {10}^{-26}{\mathrm{cm}}^3{\mathrm{s}}^{-1}$ and an NFW-type dark matter density profile in GCs. There are at least two factors that improve our predictions. First, the Sommerfeld enhancement [73] results in a ∼100 times increase in the cross-section at low relative DM particle velocities [86]. Second, subhalos exhibit significantly higher DM densities than the smooth components of the main halo, and can enhance the annihilation rate—and thus the associated $\gamma$-ray and neutrino production in GCs—by a factor of approximately 50 [72]. Even if subhalos are absent, the expected fluxes from DM annihilation are significantly dependent on the DM density profiles. As shown in Figure 2, in the case of the more cuspy Moore profile (compared to the NFW profile) with $\rho \propto {(r/r_s)}^{-1.5}$ for $r<<r_s$ the value of $J_{\mathrm{ann}}$ is 18 times greater than that obtained in the NFW case. In the case of the modified isothermal profile with a flat core, $\rho \propto {(1+{(r/r_s)}^2)}^{-1}$$J_{\mathrm{ann}}$ is 13 times less than in the NFW case. At the same time, DM decay fluxes are proportional to the total mass of GCs, and only the intensity maps depend on the DM profiles.

The expected signatures of DM annihilation/decay in astrophysical sources at cosmological distances depend on the parameters of the cosmological model, particularly the value of dark energy density ${\Omega }_{\Lambda }$ and the Hubble constant $H\left(z\right)=H\left(0\right){({\Omega }_m{(1+z)}^3+{\Omega }_{\Lambda })}^{1/2}$ in the most popular flat $\Lambda$CDM cosmology. As mentioned above, we adopted a flat $\Lambda$CDM cosmology with parameters $h=0.7$, ${\Omega }_m=0.3$, and ${\Omega }_{\Lambda }=0.7$. The influence of dark energy (cosmological constant) entered our analysis primarily through its impact on the expansion history of the Universe, and thus on the critical density ${\rho }_{\mathrm{crit}}\left(z\right)=3H^2\left(z\right)/\left(8\pi G\right)$, luminosity distance $d_L\left(z\right)$, etc. Since all structural parameters of galaxy clusters ($R_{200}$, $M_{200}$, $c_{200}$) and the associated $J_{\mathrm{ann}}$- and $J_{\mathrm{dec}}$-factors were defined relative to ${\rho }_{\mathrm{crit}}\left(z\right)$, the value of ${\Omega }_{\Lambda }$ directly affects the derived quantities. However, at the relatively low redshift of the Shapley Supercluster ($z\simeq 0.05$), the impact of dark energy is small—the difference in luminosity distances of the ${\Omega }_m=1.0$ model $d_L\left(z\right)=(cz/H_0)(1+0.25z)$ and the ${\Omega }_m=0.3$ model $d_L\left(z\right)=(cz/H_0)(1+0.775z)$ is negligible.

Extragalactic and intracluster (inside GCs) magnetic fields play an important role in the formation and evolution of large-scale structures in the Universe, including GCs. Our analysis focuses on the prompt $\gamma$-ray and neutrino emissions from DM annihilation and decay, which are insensitive to the presence of intracluster magnetic fields. Although magnetic fields influence secondary processes such as synchrotron radiation from DM-induced electron–positron pairs, inverse-Compton scattering, and the propagation of UHECRs, these effects do not affect the primary fluxes considered in this work. A detailed treatment of such secondary contributions is beyond the present scope of this paper and will be addressed in future studies.

In addition to the dark matter-induced high-energy gamma-ray and neutrino emission signatures of the SSC, we expected similar multimessenger signatures of GCs due to the presence in their intracluster medium of leptonic and hadronic CRs and magnetic fields. A complementary study [51] shows that the high-energy astrophysical processes of CR hadrons—plasma particle collisions and the interaction of CR leptons with magnetic fields—result in multiwavelength nonthermal emissions (from synchrotron radio emissions to very-high-energy $\gamma$-rays and neutrino). The different spectral characteristics of the radiation in the intracluster plasma and DM cases will allow us to separate their contributions to the observed fluxes.

In summary, our study confirms that GCs are among the most promising targets for indirect DM detection through combined $\gamma$-ray and neutrino observations. Although current instruments are limited to probing only the most extreme regions of the parameter space, future observations with present and next-generation facilities, such as CTAO, LHAASO, KM3NeT, IceCube-Gen2, PAO, GCOS, etc. may prove crucial in either revealing or ruling out viable DM scenarios, as well as in placing stringent upper limits on DM particle properties. In particular, observations of the SSC, despite its larger distance compared to the Perseus cluster, are expected to yield comparable $\gamma$-ray and neutrino fluxes due to its significantly larger total mass. This makes the SSC a compelling target for future multi-messenger searches and motivates deeper observational efforts in upcoming campaigns.