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This is an index of the contributions by the Giant Radio Array for Neutrino Detection (GRAND) Collaboration to the 10th International Workshop on Acoustic and Radio EeV Neutrino Detection Activities (ARENA 2024, University of Chicago, June 11-14, 2024). The contributions include an overview of GRAND in its present and future incarnations, methods of radio-detection that are being developed for them, and ongoing joint work between the GRAND and BEACON experiments., Comment: Note: To access the list of contributions, please follow the "HTML" link that can be found on the arXiv page

High energy photons originating from the Galactic Center (GC) region have the potential to undergo significant photon-axion-like particle (ALP) oscillation effects, primarily induced by the the presence of intense magnetic fields in this region. Observations conducted by imaging atmospheric Cherenkov telescopes have detected very high energy gamma-rays originating from a point source known as HESS J1745-290, situated in close proximity to the GC. This source is conjectured to be associated with the supermassive black hole Sagittarius A$^*$. The GC region contains diverse structures, including molecular clouds and non-thermal filaments, which collectively contribute to the intricate magnetic field configurations in this region. By utilizing a magnetic field model specific in the GC region, we explore the phenomenon of photon-ALP oscillations in the gamma-ray spectrum of HESS J1745-290. Our analysis does not reveal any discernible signature of photon-ALP oscillations, yielding significant constraints that serve as a complement to gamma-ray observations of extragalactic sources across a broad parameter region. The uncertainties arising from the outer Galactic magnetic field models have minor impacts on our results, except for ALP masses around 10$^{-7}$ eV, as the dominant influence originates from the intense magnetic field strength in the inner GC region., Comment: 10 pages, 8 figures

The operation of upcoming ultra-high-energy cosmic-ray, gamma-ray, and neutrino radio-detection experiments, like the Giant Radio Array for Neutrino Detection (GRAND), poses significant computational challenges involving the production of numerous simulations of particle showers and their detection, and a high data throughput. GRANDlib is an open-source software tool designed to meet these challenges. Its primary goal is to perform end-to-end simulations of the detector operation, from the interaction of ultra-high-energy particles, through -- by interfacing with external air-shower simulations -- the ensuing particle shower development and its radio emission, to its detection by antenna arrays and its processing by data-acquisition systems. Additionally, GRANDlib manages the visualization, storage, and retrieval of experimental and simulated data. We present an overview of GRANDlib to serve as the basis of future GRAND analyses., Comment: 11 pages, 9 figures, plus appendices

Axions and axion-like particles (ALPs) appear in many extensions of the Standard Model and are being investigated as promising dark matter (DM) candidates. One viable methodology for their detection involves the investigation of the line-like radio emissions from the dwarf spheroidal galaxy, potentially originating from the radiative decay of ALPs or the conversion of ALPs in the magnetic field. In this work, we constrain the properties of ALPs using the 2-hour radio observation of Coma Berenices through the Five-hundred-meter Aperture Spherical radio Telescope (FAST). The $\rm 95\%$ upper limits of the ALP-photon coupling are calculated for the ALP decay and conversion scenarios, respectively. Note that the sensitive ALP masses for FAST range from $\sim \mu \rm eV$ to tens of $\mu \rm eV$, where ALP can explain the DM abundance naturally. However, our limits are weaker than those of the CAST helioscope, which can provide an independent and complementary check on the ALP non-detection for ground experiments. Furthermore, we evaluate the expected sensitivity on the ALP of FAST with its full designed bandwidth (70 $\rm MHz$ - 3 $\rm GHz$) for 100 hours of observation time. Our results indicate that, even with the exceptional sensitivity of the FAST, it is challenging to surpass the existing experimental constraints on ALP DM using radio observation of dSphs, unless the possible enhancements of ALP signals by compact stars in dSphs are considered., Comment: 8 pages, 3 figures, accepted for publication in PLB

High-energy photons may oscillate with axion-like particles (ALPs) when they propagate through the Milky Way's magnetic field, resulting in an alteration in the observed photon energy spectrum. The ultra-high energy gamma-ray spectra, measured by the Large High Altitude Air Shower Observatory (LHAASO) up to $\mathcal{O}(1)~\mathrm{PeV}$, provide a promising opportunity to investigate the ALP-photon oscillation effect. In this study, we utilize the gamma-ray spectra of four Galactic sources measured by LHAASO, including the Crab Nebula, LHAASO J2226+6057, LHAASO J1908+0621, and LHAASO J1825-1326, to explore this effect. We employ the $\rm CL_s$ method to set constraints on the ALP parameters. Combing the observations of the four sources, our analysis reveals that the ALP-photon coupling $g_{a\gamma}$ is constrained to be smaller than $1.4\times10^{-10}$ ${\rm GeV}^{-1}$ for the ALP mass of $\sim 4\times10^{-7} ~\mathrm{eV}$ at the 95\% C.L. By combing the observations of the Crab Nebula from LHAASO and other experiments, we find that the ALP-photon coupling could be set to be about $7.2\times10^{-11}$ ${\rm GeV}^{-1}$ for the ALP mass $\sim 4 \times10^{-7}~\mathrm{eV}$ , which is in close proximity to the CAST constraint.

The Giant Radio Array for Neutrino Detection (GRAND) is an envisioned observatory of ultra-high-energy particles of cosmic origin, with energies in excess of 100 PeV. GRAND uses large surface arrays of autonomous radio-detection units to look for the radio emission from extensive air showers that are triggered by the interaction of ultra-high-energy cosmic rays, gamma rays, and neutrinos in the atmosphere or underground. In particular, for ultra-high-energy neutrinos, the future final phase of GRAND aims to be sensitive enough to discover them in spite of their plausibly tiny flux. Presently, three prototype GRAND radio arrays are in operation: GRANDProto300, in China, GRAND@Auger, in Argentina, and GRAND@Nancay, in France. Their goals are to field-test the design of the radio-detection units, understand the radio background to which they are exposed, and develop tools for diagnostic, data gathering, and data analysis. This list of contributions to the 38th International Cosmic Ray Conference (ICRC 2023) presents an overview of GRAND, in its present and future incarnations, and a look at the first data collected by GRANDProto13, the first phase of GRANDProto300., Comment: Note: To access the list of contributions, please follow the "HTML" link that can be found on the arXiv page (v2: fixed name spelling of one author)

The diffuse gamma-ray emission between 10 and 1000 TeV from the Galactic plane was recently measured by the Large High Altitude Air Shower Observatory (LHAASO). These observations will help tremendously in constraining the propagation and interaction of cosmic rays in the Milky Way. Additionally, new measurements of CR spectra reach a very high precision up to 100 TeV energies, revealing multiple spectral structures of various species. In this work, we confront the model prediction of the diffuse gamma-ray emission, based on up-to-date measurements of the local cosmic ray spectra and simplified propagation setup, with the measurements of diffuse gamma-rays. To better constrain the low-energy part of the model, we analyze the 14.6 years of Fermi-LAT data to extract the Galactic diffuse emission between 1 and 500 GeV from the same sky regions of LHAASO, after subtracting the contribution from known sources and the isotropic diffuse gamma-ray background. The joint Fermi-LAT and LHAASO spectra thus cover a very wide energy range from 1 GeV to 1 PeV with small gaps from 0.5 to 10 TeV. Compared with the prediction, we find that clear excesses between several GeV and ~60 TeV of the diffuse emission exist. Possible reasons to explain the excesses may include unresolved sources or more complicated propagation models. We illustrate that an exponential-cutoff-power-law component with an index of -2.40 and cutoff energy of ~30 TeV is able to account for such excesses.

Ultralight dark matter (ULDM) is proposed as a theoretical candidate of dark matter particles with masses of approximately $10^{-22}$ eV. The interactions between ULDM particles and standard model particles would cause variations in pulse arrival times of millisecond pulsars, which means that the pulsar timing array (PTA) can be used to indirectly detect ULDM. In this letter, we use the gamma-ray PTA composed of 29 millisecond pulsars observed by the Fermi Large Area Telescope (Fermi-LAT) to test four ULDM effects, including gravitational effects for generalized ULDM with different Spin-0/1, the fifth-force coupling effect of dark photon, and the modified gravitational effect of the Spin-2 ULDM. The gamma-ray pulsar timing is not affected by the ionized interstellar medium and suffers relatively simple noises, unlike that of the radio band. Our work is the first time that the gamma-ray PTA has been used to search for the ULDM. No significant signals of ULDM are found based on the Fermi-LAT PTA for all four kinds of ULDM models. Constraints on ULDM parameters are set with the 95% confidence level, which provides a complementary check of the nondetection of ULDM for radio PTAs and direct detection experiments., Comment: 11 pages, 4 figures, 2 tables; publish as a Letter in Phys. Rev. D

The Galactic center $\gamma$-ray excess, detected by the Fermi-LAT, is a very attractive tentative signal from dark matter annihilation. Searching for associated synchrotron emissions can test the dark matter interpretation for this excess. We geared the Five-hundred-meter Aperture Spherical radio Telescope (FAST) towards Coma Berenices (a dwarf Spheroidal galaxy) for 2-hours of observation, and found no significant continuum radio emission, which could { put constraints on the dark matter annihilation cross section}, from our target. We set very stringent annihilation cross-section constraints, with roughly an order of magnitude improvement over a large range of masses compared with previous radio searches. The dark matter scenario for the Galactic center $\gamma$-ray excess is in tension with the FAST observation for reasonable choices of astrophysical factors. But considering the large uncertainty on astrophysical parameters, such as the magnetic field, the diffusion coefficient, and the diffusion radius, and on DM halo parameters, the dark matter interpretation for the excess could still survive. Further radio observations by the FAST and other radio telescopes may reveal more about the dark matter properties., Comment: 10 pages, 5 figures, 1 table

Axions provide a natural and well-motivated dark matter candidate, with the capability to convert directly to photons in the presence of an electromagnetic field. A particularly compelling observational target is the conversion of dark matter axions into photons in the magnetospheres of highly magnetised neutron stars, which is expected to produce a narrow spectral peak centred at the frequency of the axion mass. We point the MeerKAT radio telescope towards the isolated neutron star J0806.4$-$4123 for $10$-hours of observation and obtain the radio spectra in the frequency range $769$-$1051$ MHz. By modelling the conversion process of infalling axion dark matter (DM), we then compare these spectra to theoretical expectations for a given choice of axion parameters. Whilst finding no signal above $5\sigma$ in the data, we provide a unique constraint on the Primakoff coupling of axion DM, $g_{{\rm a}\gamma\gamma}\lesssim 9.3 \times 10^{-12}\,{\rm GeV}^{-1}$ at the $95\%$ confidence level, in the mass range $3.18$-$4.35\,\mu$eV. This result serves the strongest constraint in the axion mass range $4.20$-$4.35\,\mu$eV., Comment: 6 pages, 3 figures, accepted by Physical Review D

Dark photons can be the ultralight dark matter candidate, interacting with Standard Model particles via kinetic mixing. We propose to search for ultralight dark photon dark matter (DPDM) through the local absorption at different radio telescopes. The local DPDM can induce harmonic oscillations of electrons inside the antenna of radio telescopes. It leads to a monochromatic radio signal and can be recorded by telescope receivers. Using the observation data from the FAST telescope, the upper limit on the kinetic mixing can already reach $10^{-12}$ for DPDM oscillation frequencies at $1-1.5$ GHz, which is stronger than the cosmic microwave background constraint by about one order of magnitude. Furthermore, large-scale interferometric arrays like LOFAR and SKA1 telescopes can achieve extraordinary sensitivities for direct DPDM search from 10 MHz to 10 GHz., Comment: 5 pages, 3 figures + appendix. Match the accepted version (PRL)

For the newly discovered $W$-boson mass anomaly, one of the simplest dark matter (DM) models that can account for the anomaly without violating other astrophysical/experimental constraints is the inert two Higgs doublet model, in which the DM mass ($m_{S}$) is found to be within $\sim 54-74$ GeV. In this model, the annihilation of DM via $SS\to b\bar{b}$ and $SS\to WW^{*}$ would produce antiprotons and gamma rays, and may account for the excesses identified previously in both particles. Motivated by this, we re-analyze the AMS-02 antiproton and Fermi-LAT Galactic center gamma-ray data. For the antiproton analysis, the novel treatment is the inclusion of the charge-sign-dependent three-dimensional solar modulation model as constrained by the time-dependent proton data. We find that the excess of antiprotons is more distinct than previous results based on the force-field solar modulation model. The interpretation of this excess as the annihilation of $SS\to WW^{*}$ ($SS\to b\bar{b}$) requires a DM mass of $\sim 40-80$ ($40-60$) GeV and a velocity-averaged cross section of $O(10^{-26})~{\rm cm^3~s^{-1}}$. As for the $\gamma$-ray data analysis, besides adopting the widely-used spatial template fitting, we employ an orthogonal approach with a data-driven spectral template analysis. The fitting to the GeV $\gamma$-ray excess yields DM model parameters overlapped with those to fit the antiproton excess via the $WW^{*}$ channel. The consistency of the DM particle properties required to account for the $W$-boson mass anomaly, the GeV antiproton excess, and the GeV $\gamma$-ray excess suggest a common origin of them., Comment: 10 pages, 10 figures, accepted by PRL

We present a chatbot implementing a novel dialogue management approach based on logical inference. Instead of framing conversation a sequence of response generation tasks, we model conversation as a collaborative inference process in which speakers share information to synthesize new knowledge in real time. Our chatbot pipeline accomplishes this modelling in three broad stages. The first stage translates user utterances into a symbolic predicate representation. The second stage then uses this structured representation in conjunction with a larger knowledge base to synthesize new predicates using efficient graph matching. In the third and final stage, our bot selects a small subset of predicates and translates them into an English response. This approach lends itself to understanding latent semantics of user inputs, flexible initiative taking, and responses that are novel and coherent with the dialogue context., Comment: Published in 4th Proceedings of Alexa Prize (Alexa Prize 2020)

The Forbush Decrease (FD) represents the rapid decrease of the intensities of charged particles accompanied with the coronal mass ejections (CMEs) or high-speed streams from coronal holes. It has been mainly explored with ground-based neutron monitors network which indirectly measure the integrated intensities of all species of cosmic rays by counting secondary neutrons produced from interaction between atmosphere atoms and cosmic rays. The space-based experiments can resolve the species of particles but the energy ranges are limited by the relative small acceptances except for the most abundant particles like protons and helium. Therefore, the FD of cosmic ray electrons and positrons have just been investigated by the PAMELA experiment in the low energy range ($<5$ GeV) with limited statistics. In this paper, we study the FD event occurred in September, 2017, with the electron and positron data recorded by the Dark Matter Particle Explorer. The evolution of the FDs from 2 GeV to 20 GeV with a time resolution of 6 hours are given. We observe two solar energetic particle events in the time profile of the intensity of cosmic rays, the earlier and weak one has not been shown in the neutron monitor data. Furthermore, both the amplitude and recovery time of fluxes of electrons and positrons show clear energy-dependence, which is important in probing the disturbances of the interplanetary environment by the coronal mass ejections., Comment: This article is dedicated to the 72nd anniversary of People's Republic of China

The fast developments of radio astronomy open a new window to explore the properties of Dark Matter (DM). The recent direct imaging of the supermassive black hole (SMBH) at the center of M87 radio galaxy by the Event Horizon Telescope (EHT) collaboration is expected to be very useful to search for possible new physics. In this work, we illustrate that such results can be used to detect the possible synchrotron radiation signature produced by DM annihilation from the innermost region of the SMBH. Assuming the existence of a spike DM density profile, we obtain the flux density due to DM annihilation induced electrons and positrons, and derive new limits on the DM annihilation cross section via the comparison with the EHT integral flux density at 230 GHz. Our results show that the parameter space can be probed by the EHT observations is largely complementary to other experiments. For DM with typical mass regions of being weakly interacting massive particles, the annihilation cross section several orders of magnitude below the thermal production level can be excluded by the EHT observations under the density spike assumption. Future EHT observations may further improve the sensitivity on the DM searches, and may also provide a unique opportunity to test the interplay between DM and the SMBH., Comment: 15 pages, 4 figures, one appendix. Match the JHEP version

Cosmic rays are important probe of a number of fundamental physical problems such as the acceleration of high and very high energy particles in extreme astrophysical environments. The Galactic center is widely anticipated to be an important cosmic-ray source and the observations of some Imaging Atmospheric Cherenkov Telescopes did successfully reveal a component of TeV-PeV cosmic rays in the vicinity of the Galactic center. Here we report the identification of GeV-TeV cosmic rays in the central molecular zone with the $\gamma$-ray observations of the Fermi Large Area Telescope, whose spectrum and spatial gradient are consistent with that measured by the Imaging Atmospheric Cherenkov Telescopes but the corresponding cosmic-ray energy density is substantially lower than the so-called cosmic-ray sea component, suggesting the presence of a high energy particle accelerator at the Galactic center and the existence of a barrier that can effectively suppress the penetration of the particles from the cosmic-ray sea to the central molecular zone., Comment: 11 pages, 5 figures, matches version published in Nature Communications

Significant flares of GeV $\gamma$-ray emission from the Crab Nebula have been found by AGILE and Fermi-LAT years ago, indicating that extreme particle acceleration and radiation occurs in young pulsar wind nebulae. To enlarge the flare sample and to investigate their statistical properties will be very useful in understanding the nature of the $\gamma$-ray flares. In this paper, we investigate the flaring emission from the Crab Nebula with eleven year observations of the Fermi-LAT. We identify 17 significant flares in the light curve of the low-energy (synchrotron) component of the $\gamma$-ray emission. The flare rate is about 1.5 per year, without any significant change or clustering during the 11 years of the observation. We detect a special flare with an extremely long duration of nearly one month, occurred in October, 2018, with synchrotron photons up to energies of about 1GeV. The synchrotron component could be fitted by a steady power-law background and a variable flare component with an expotentially cutoff power-law spectrum, not only for individual flare but also for the combined data, which may favor a similar emission mechanism for all flares. However, we do not find a universal relation between the cutoff energy and the energy fluxes of the flares, which may reflect the complicated acceleration and/or cooling processes of the involved particles., Comment: 12 pages, 11 figures, 1 table

Precise measurements of the energy spectra of cosmic rays (CRs) show various kinds of features deviating from single power-laws, which give very interesting and important implications on their origin and propagation. Previous measurements from a few balloon and space experiments indicate the existence of spectral softenings around 10 TV for protons (and probably also for Helium nuclei). Very recently, the DArk Matter Particle Explorer (DAMPE) measurement about the proton spectrum clearly reveals such a softening with a high significance. Here we study the implications of these new measurements, as well as the groundbased indirect measurements, on the origin of CRs. We find that a single component of CRs fails to fit the spectral softening and the air shower experiment data simultaneously. In the framework of multiple components, we discuss two possible scenarios, the multiple source population scenario and the background plus nearby source scenario. Both scenarios give reasonable fits to the wide-band data from TeV to 100 PeV energies. Considering the anisotropy observations, the nearby source model is favored., Comment: 8 pages, 3 figures and 3 tables; accepted for publication in Frontiers of Physics

The $\gamma$-ray observation of interstellar gas provides a unique way to probe the cosmic rays (CRs) outside the solar system. In this work, we use an updated version of Fermi-LAT data and recent multi-wavelength tracers of interstellar gas to re-analyze a mid-latitude region in the third Galactic quadrant and estimate the local CR proton spectrum. Two $\gamma$-ray production cross section models for $pp$ interaction, the commonly used one from Kamae et al. (2006) and the up-to-date one from Kafexhiu et al. (2014), are adopted separately in the analysis. Both of them can well fit the emissivity and the derived proton spectra roughly resemble the direct measurements from AMS-02 and Voyager 1, but rather different spectral parameters are indicated. A break at $4\pm1~{\rm GeV}\;c^{-1}$ is shown if the cross section model by Kamae et al. (2006) is adopted. The resulting spectrum is $\lesssim 20\%$ larger than the AMS-02 observation above $15~\rm GeV$ and consistent with the de-modulated spectrum within $2\%$. The proton spectrum based on the cross section model of Kafexhiu et al. (2014) is about $1.4-1.8$ times that of AMS-02 at $2-100~\rm GeV$, however the difference decreases to $20\%$ below $10~\rm GeV$ with respect to the de-modulated spectrum. A spectral break at $20\pm11~{\rm GeV}\;c^{-1}$ is required in this model. An extrapolation down to $300~\rm MeV$ is performed to compare with the observation of Voyager 1, and we find a deviation of $\lesssim 2.5\sigma$ for both the models. In general, an approximately consistent CR spectrum can be obtained using $\gamma$-ray observation nowadays, but we still need a better $\gamma$-ray production cross section model to derive the parameters accurately., Comment: 10 pages, 6 figures. Accepted for publication in PRD

The DArk Matter Particle Explorer (DAMPE), a high energy cosmic ray and $\gamma$-ray detector in space, has recently reported the new measurement of the total electron plus positron flux between 25 GeV and 4.6 TeV. A spectral softening at $\sim0.9$ TeV and a tentative peak at $\sim1.4$ TeV have been reported. We study the physical implications of the DAMPE data in this work. The presence of the spectral break significantly tightens the constraints on the model parameters to explain the electron/positron excesses. The spectral softening can either be explained by the maximum acceleration limits of electrons by astrophysical sources, or a breakdown of the common assumption of continuous distribution of electron sources at TeV energies in space and time. The tentive peak at $\sim1.4$ TeV implies local sources of electrons/positrons with quasi-monochromatic injection spectrum. We find that the cold, ultra-relativistic $e^+e^-$ winds from pulsars may give rise to such a structure. The pulsar is requird to be middle-aged, relatively slowly-rotated, mildly magnetized, and isolated in a density cavity. The annihilation of DM particles ($m_{\chi}\sim1.5$ TeV) into $e^+e^-$ pairs in a nearby clump or an over-density region may also explain the data. In the DM scenario, the inferred clump mass (or density enhancement) is about $10^7-10^8$ M$_\odot$ (or $17-35$ times of the canonical local density) assuming a thermal production cross section, which is relatively extreme compared with the expectation from numerical simulations. A moderate enhancement of the annihilation cross section via, e.g., the Sommerfeld mechanism or non-thermal production, is thus needed., Comment: 16 pages, 11 figures, and 3 tables

We consider indirect detection of meta-stable dark matter particles decaying into a stable neutral particle and a pair of standard model fermions. Due to the softer energy spectra from the three-body decay, such models could potentially explain the AMS-02 positron excess without being constrained by the Fermi-LAT gamma-ray data and the cosmic ray anti-proton measurements. We scrutinize over different final state fermions, paying special attention to handling of the cosmic ray background and including various contributions from cosmic ray propagation with the help of the \textsc{LikeDM} package. It is found that primary decays into an electron-positron pair and a stable neutral particle could give rise to the AMS-02 positron excess and, at the same time, stay unscathed against the gamma-ray and anti-proton constraints. Decays to a muon pair or a mixed flavor electron-muon pair may also be viable depending on the propagation models. Decays to all other standard model fermions are severely disfavored., Comment: 22 pages, 7 figures and 2 tables; updated to AMS-02 antiproton data; added the comparison with the newest AMS-02 positron fluxes; accepted for publication in JCAP

With the large progress in searches for dark matter (DM) particles with indirect and direct methods, we develop a numerical tool that enables fast calculations of the likelihoods of specified DM particle models given a number of observational data, such as charged cosmic rays from space-borne experiments (e.g., PAMELA, AMS-02), gamma-rays from the Fermi space telescope, and underground direct detection experiments. The purpose of this tool --- LikeDM, likelihood calculator for dark matter detection --- is to bridge the gap between a particle model of DM and the observational data. The intermediate steps between these two, including the astrophysical backgrounds, the propagation of charged particles, the analysis of Fermi gamma-ray data, as well as the DM velocity distribution and the nuclear form factor, have been dealt with in the code. We release the first version (v1.0) focusing on the constraints from indirect detection of DM with charged cosmic and gamma rays. Direct detection will be implemented in the next version. This manual describes the framework, usage, and related physics of the code. The code LikeDM can be download from https://likedm.hepforge.org/, Comment: v2, published in Computer Physics Communications, "LikeDM can be download from https://likedm.hepforge.org/"

Galaxy clusters are the largest gravitationally bound objects in the universe and may be suitable targets for indirect dark matter searches. With 85 months of Fermi-LAT Pass 8 publicly available data, we analyze the gamma-ray emission in the directions of 16 nearby Galaxy Clusters with an unbinned likelihood analysis. No globally statistically-significant $\gamma-$ray line feature is identified and a tentative line signal may be present at $\sim 43$ GeV. The 95\% confidence level upper limits on the velocity-averaged cross section of dark matter particles annihilating into double $\gamma-$rays (i.e., $\langle \sigma v \rangle_{\chi\chi\rightarrow \gamma\gamma}$) are derived. Unless very optimistic boost factors of dark matter annihilation in these Galaxy Clusters have been assumed, such constraints are much weaker than the bounds set by the Galactic $\gamma-$ray data., Comment: The version published in Phys. Rev. D, minor revision (10 pages including 4 eps figures)