# Gamma-rays from dark matter annihilations strongly constrain the substructure in halos

###### Abstract

Recently, it has been shown that electrons and positrons from dark matter (DM) annihilations provide an excellent fit to the Fermi, PAMELA, and HESS data. Using this DM model, which requires an enhancement of the annihilation cross section over its standard value to match the observations, we show that it immediately implies an observable level of -ray emission for the Fermi telescope from nearby galaxy clusters such as Virgo and Fornax. We show that this DM model implies a peculiar feature from final state radiation that is a distinctive signature of DM. Using the EGRET upper limit on the -ray emission from Virgo, we constrain the minimum mass of substructures within DM halos to be – about four orders of magnitudes larger than the expectation for cold dark matter. This limits the cutoff scale in the linear matter power spectrum to which can be explained by e.g., warm dark matter. Very near future Fermi observations will strongly constrain the minimum mass to be : if the true substructure cutoff is much smaller than this, the DM interpretation of the Fermi/PAMELA/HESS data must be wrong. To address the problem of astrophysical foregrounds, we performed high-resolution, cosmological simulations of galaxy clusters that include realistic cosmic ray (CR) physics. We compute the dominating -ray emission signal resulting from hadronic CR interactions and find that it follows a universal spectrum and spatial distribution. If we neglect the anomalous enhancement factor and assume standard values for the cross section and minimum subhalo mass, the same model of DM predicts comparable levels of the -ray emission from DM annihilations and CR interactions. This suggests that spectral subtraction techniques could be applied to detect the annihilation signal.

###### pacs:

95.35.+d, 95.85.Pw, 98.62.Gq, 98.65.-r, 98.70.SaThe identity of the DM in the Universe has been the subject of intense speculation. In particular, the hierarchical formation of structure, as indicated from numerical simulations of Cold DM (CDM), agrees very well with observations on scales of galaxy clusters and larger, whereas the small scale behaviour on galactic and subgalactic scales is more unsecure. If dark matter particles have weak interactions, one would expect possible signals from annihilations (or decays).

Data from a new generation of cosmic ray detectors have indeed been tentatively interpreted in terms of such signatures of DM. In particular, the positron fraction measured by the PAMELA satellite pamela_positrons () and the sum of electrons and positrons by ATIC atic () have shown an unexpected excess. Very recent data from Fermi-LAT fermi (); fermicre () and H.E.S.S. hess () on the sum of electrons and positrons do not confirm the peak claimed by ATIC, but still indicate an excess compared to the expected background in conventional models. A number of attempts have been made trying to explain the excess due to DM annihilation (for recent reviews, see hooper (); lberev ()) but also other astrophysical sources such as pulsars have been investigated (e.g., pulsars (), and references therein).

One class of DM models that fits the new data has halo annihilation primarily into muon pairs, which then decay to electrons and positrons. In bez () examples of fits with remarkable quality (which also fit PAMELA pamela_positrons () and new H.E.S.S. data) were obtained by such DM models. It was pointed out that if the annihilation goes directly into a pair, a striking signature may be present. This is caused by the direct emission of -rays from the final state (final state radiation, FSR), which gives a peculiar energy spectrum, with almost linearly rising with energy. The same, but weaker, feature may in fact exist also for the theoretically perhaps more easily motivated models with intermediate spin-0 boson decay, but in this Letter we only treat the somewhat simpler direct annihilation case. In this Letter we show that such DM models face considerable tension with existing -ray limits from clusters of galaxies, systems which will be very interesting to detect and study with coming -ray detectors (Fermi, H.E.S.S., MAGIC, VERITAS, and eventually CTA).

Galaxy clusters constitute the most massive objects in our Universe that are forming today. This causes their DM subhalo mass function to be less affected by tidal stripping compared to galaxy sized halos that formed long ago. The annihilation luminosity of the smooth DM halo component scales as

(1) |

where the virial mass and the concentration (see Eqn. 3) are the two characteristic parameters of the universal Navarro-Frenk-White (NFW) density profile of DM halos NFW (). Hence, the flux ratio of a nearby cluster (Virgo) to a prominent dwarf spheroidal (Draco) is given by

(2) |

assuming an early formation epoch of the dwarf galaxy before the end of reionization Draco (). Once a satellite galaxy is accreted by our Galaxy, the outer regions are severely affected by tidal stripping. The longer a satellite has been part of our Galaxy, and the closer it comes to the center during its pericentral passage, the more material is removed subhalo (). In contrast, the substructure in clusters is not affected in the outer regions and may enhance the DM annihilation signal over its smooth contribution considerably as we will see in the following. The FSR feature of DM annihilation may in addition be more easily visible in clusters, as the average intensity of starlight, which may give a masking signal due to inverse Compton scattering of the copiously produced electrons and positrons, is lower than in the Milky Way MW. For previous work related to dark matter in clusters, see, e.g., colafrancesco (); previous (). All halo masses and length scales are scaled to the currently favored value of Hubble’s constant, . We define the virial mass and virial radius as the mass and radius of a sphere enclosing a mean density that is 200 times the critical density of the Universe .

Method. As our default model for dark matter annihilation, we take
the Sommerfeld-enhanced (see, e.g., sommerfeld (); resonance ()) direct muon
annihilation mode of bez (), i.e., mass GeV and effective
enhancement factor 1100 relative to the standard annihilation cross section
. It is
non-trivial to rescale this boost to the corresponding value for the cluster
environment. This may either give a smaller or larger value, depending, e.g., on
the velocity dispersion of bound substructure in the cluster, and whether the
Sommerfeld enhancement (SFE) increases down to very small velocities, or if it
saturates at some minimum velocity SFEformula (). We choose a simple and
generic model for the SFE factor and saturate at ^{1}^{1}1This velocity scale is a conservative choice for our DM
model under consideration. We note that local anisotropy in the dark matter
distribution, resonance effects of the cross section, and velocity
uncertainties at freeze-out bring the best-fit enhancement factor of 1100
resonance () easily into agreement with conventional models.. For a given
cluster, we assume a constant velocity dispersion of Voit (). This scaling
would result in a boost factor of for a cluster with
.

Using cluster masses from the complete sample of the X-ray brightest clusters (the extended HIFLUGCS catalogue, HIFLUGCS ()) we identify the brightest clusters for DM annihilation. In models with SFE, the DM flux to leading order scales as a power-law . The first factor accounts for the SFE and the second one is derived from Eqn. 1, using a power-law fit to the mass dependence of the NFW halo concentration derived from cosmological simulations with maccio_cfit (),

(3) |

Note that Eqn. 3 agrees well with zhao_cfit () for cluster-mass halos after converting the concentration definitions according to c_conv (). This yields Fornax () and Virgo (, M_Virgo ()) as the prime targets for DM observations and we additionally decide in favor of the well studied cluster Coma () for comparison.

The differential photon flux from DM annihilation within a given solid angle along a line-of-sight (los) is given by

(4) |

where is the source function from the smooth halo with contributions from two main processes: DM annihilating to which decay to pairs that Compton up-scatter CMB photons (IC) and FSR. The source function of FSR is given by

(5) |

where the annihilation rate density . The runs over all -ray producing channels each with the spectrum and annihilation cross-section . We use the standard photon distribution for the final state radiation from our DM model annihilating directly to charged leptons assuming Cholis:2008wq (). For the remaining part of this work, the Einasto density profile for DM halos Einasto () is used, normalized with relying on the assumption that of the flux from a NFW density profile and an Einasto density profile originate from within the scale radius .

The product of enhancement factors from SFE and from substructure enhancement over the smooth halo contribution is denoted by . High-resolution DM simulations of the MW suggest an enhancement from substructures of approximately 220 inside assuming that the subhalos extrapolate smoothly down from the simulation resolution limit to smallest scales Aquarius (), with most of the substructure residing in the outer part of the MW halo. We fit the luminosity from substructures inside a radius following subboost (),

(6) |

where is the smooth cluster halo luminosity within . The normalization , where is the minimum subhalo mass in the simulation and the free streaming mass. While its conventional value is Mlim (), we will constrain this quantity by requiring consistency with the non-detection of -ray emission from clusters by EGRET: the smaller , the more substructure is present and the larger is the expected -ray signal. This approach of fitting the scaling behaviour of directly from numerical simulations self-consistently accounts for the radial dependence of the substructure concentration Aquarius (). We note that this might result in a slight overestimate of the substructure luminosity if the assumed power-law scaling flattens towards smaller scales although current simulations show no sign of such a behavior which is also not expected since we are approaching the asymptotic behavior in the power spectrum on these scales.

The source function of inverse Compton emission resulting from DM annihilating is given by

(7) |

where is derived by convolving the IC cross-section with the differential target photon number density colafrancesco (). Assuming that the spatial diffusion time scale is much larger than the energy loss time scale, the total equilibrium distribution of the electrons plus positrons is given by

(8) | |||||

(9) |

where denote the differential number of electrons plus positrons resulting from an annihilation event, denotes the equivalent field strength of the CMB, and we parametrize the magnetic field of the galaxy cluster by , which follows from flux frozen magnetic fields.

To address the problem of source confusion by astrophysical backgrounds,
we perform high-resolution, cosmological simulations Springel:2005mi () of a
sample of 14 galaxy clusters paperII (). They span over one and a half
decades in mass and follow radiative gas physics, star formation, supernova
feedback. In particular, we use an updated version of the cosmic ray physics
that is capable of following the spectral evolution of the cosmic ray (CR)
distribution function by tracking multiple CR populations – each being
described by its characteristic power-law distribution with a distinctive slope
that is determined by the acceleration process TeVpap (). We compute the
dominating -ray emission signal from decaying neutral pions that result
from hadronic CR interactions with the ambient gas following piondecay ().
We find that it obeys a universal spectrum and spatial distribution (details
will be presented in TeVpap ()). This allows us to reliably model the cosmic
ray signal from nearby galaxy clusters using their true density profiles as
obtained by X-ray measurements electdens () that we map onto our simulated
density profiles. We compute -ray luminosity-mass scaling relations of
our sample paperIII () and use these to normalize the CR induced emission of
all clusters in HIFLUGCS HIFLUGCS (). In our optimistic CR model, we
calculate the cluster’s total -ray flux within a given solid angle while
we cut the emission from our individual galaxies and compact galactic-sized
objects in our more conservative baseline model
^{2}^{2}2These dense gas clumps are being stripped off their galaxies due to
ram pressure and dissociate incompletely in the intra-cluster medium due to
insufficient numerical resolution as well as so far incompletely understood
physical properties of the cluster plasma..

Results and Discussion. In Fig. 1, we find that, given our assumptions, the DM annihilation signal in Fornax and Virgo should be clearly visible by Fermi. It dominates over the CR induced signal for both of our CR models. The annihilation signal within is similar for Fornax and Virgo – these are clusters with a comparable distance but the latter being twice as heavy: the larger signal of Virgo due to its larger mass is counteracted by the larger substructure boost of Fornax for the same angular extent. Using the standard assumptions for the limiting mass of substructures within DM halos of , we show that the resulting annihilation flux from Virgo is already in conflict with the EGRET upper limit. This allows us to place a lower bound on the limiting mass and hence to constrain the free streaming scale in the linear matter power spectrum to

(10) |

The Fermi sensitivity will allow us to place an even more stringent limit of which is approaching the upper limit derived from Ly- power spectrum measurements wdmconstraints (). The contribution of the smooth DM halo component towards high galactic latitudes within 3.5 degree amounts to which should be easily detectable by Fermi, especially considering an enhancement factor of a few from substructure in the MW halo. This allows us to finally scrutinize the DM models motivated by the recent Fermi, H.E.S.S., and PAMELA data. Assuming SFE, the next generation of imaging air Čerenkov telescopes have good prospects of detecting the DM annihilation signal while it will be very difficult without an enhancement. We show in Fig. 2, that the DM annihilation flux is substantially boosted due to substructures in clusters as well as in the MW’s halo that has a smooth angular emission characteristic but is expected to have the same spectral behavior. This provides hope that even in the absence of SFE, the DM annihilation flux is of the same order of magnitude as our conservative model of CR induced -ray emission. The very distinctive spectral properties of the DM-induced -rays and the universality of the CR spectra suggest that spectral subtraction techniques could be applied to detect the annihilation signal and characterize the properties of DM.

Conclusions. The DM models motivated by the recent Fermi, H.E.S.S., and PAMELA measurements require an anomalous boost factor of 1100. Assuming that SFE entierly accounts for this boost, this necessarily predicts large annihilation fluxes from nearby galaxy clusters even in the case of somewhat reduced SFE due to the larger velocity dispersion of clusters. Using standard assumptions for the limiting mass of substructures within DM halos, we find a violation of the EGRET upper limit in Virgo. The lighter a DM particle, the larger the induced free-streaming scale in the power spectrum and the higher the mass cutoff for the smallest structures: since the DM interpretation fixes the DM particle mass this locks in a minimum substructure mass. Hence, a non-detection of -rays at the predicted level by Fermi would provide a serious challenge for the standard assumptions of the CDM power spectrum, or call for a new dynamical effect during non-linear structure formation that wipes out the smallest structures. The resolution may of course also be that the rising positron ratio measured by PAMELA and the electron plus positron excess seen by H.E.S.S. and Fermi is caused by local astrophysical sources, e.g. pulsars, and is unrelated to dark matter.

Acknowledgements. L.B. and A.P. are grateful to the Swedish Research Council (VR) for financial support and the Swedish National Allocations Committee (SNAC) for the resources granted at HPC2N. C.P. thanks P. McDonald for valuable comments.

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