Constraints on dark matter annihilation from M87: Signatures of prompt and inverse-Compton gamma rays
Sheetal Saxena, Alexander Summa, Dominik Elsässer, Michael Rüger, Karl Mannheim
EEur. Phys. J. C manuscript No. (will be inserted by the editor)
Constraints on dark matter annihilation from M87
Signatures of prompt and inverse-Compton gamma rays
Sheetal Saxena a,1 , Alexander Summa , Dominik Els¨asser , Michael R ¨uger , KarlMannheim Institute for Theoretical Physics and Astrophysics, University of W¨urzburg, Campus Hubland Nord, Emil-Fischer-Str. 31, 97074 W¨urzburg,GermanyReceived: date / Accepted: date
Abstract
As the largest mass concentrations in the localUniverse, nearby clusters of galaxies and their central galax-ies are prime targets in searching for indirect signatures ofdark matter annihilation (DMA). We seek to constrain thedark matter annihilation emission component from multi-frequency observations of the central galaxy of the Virgocluster. The annihilation emission component is modeledby the prompt and inverse-Compton gamma rays from thehadronization of annihilation products from generic weaklyinteracting dark matter particles. This component is fittedto the excess of the observed data above the spectral en-ergy distribution (SED) of the jet in M87, described witha best-fit synchrotron-self-Compton (SSC) spectrum. Whilethis result is not su ffi ciently significant to claim a detection,we emphasize that a dark matter “double hump signature”can be used to unambiguously discriminate the dark matteremission component from the variable jet-related emissionof M87 in future, more extended observation campaigns. Keywords dark matter · clusters of galaxies · high-energyemission · extragalactic jets · M87
The thermal freeze-out of weakly interacting particles (so-called ’WIMPs’) with masses at the electroweak symme-try breaking scale E ew = / (cid:112) / G F ≈
246 GeV leadsto a relic density agreeing with the observed one Ω dm h = . ± . a e-mail: [email protected] dark matter annihilation emission. Annihilation gives rise topairs of heavy quarks, leptons or vector bosons, which decayleading to the emission of gamma rays, electrons, positrons,and neutrinos. The secondary radiation shows a peak at E ew / ≈
10 GeV reflecting the high multiplicity of secondary par-ticles in a typical annihilation event. The canonical peakenergy lies at the high end of the bandwidth of the Fermi-LAT detector, and at the low end of the accessible energyrange for ground-based Cherenkov telescopes. A very wellmotivated WIMP candidate is the Lightest Supersymmet-ric Particle (LSP): the neutralino [12]. Annihilating neutrali-nos produce vector bosons, leptons or quarks. The di ff eren-tial gamma-ray flux [13] produced through their subsequenthadronization and decay from a source at distance D andvolume V is given by: (cid:32) d Φ d E (cid:33) π = π f (cid:104) σ A ν (cid:105) m χ d N γ d E D (cid:90) M87 d V ρ (1)where f is the boost factor that accounts for enhancementdue to sub-halo clumping of dark matter in the M87 halo, (cid:104) σ A ν (cid:105) is the thermally averaged annihilation cross section, m χ is the mass of the dark matter particle, and d N γ / d E is thegamma photon spectrum coming from the decay of neutralpions from hadronization in the annihilation process (promptpion emission) [14]. ρ is taken to be ρ NFW = ρ NFW ( r ) theNavarro-Frenk-White dark matter density profile [15] of thedark matter halo obtained from numerical simulations.A minimum mass scale of 10 − M (cid:12) for the sub-halo clum-ping has been inferred from the transfer function of densityperturbations in the early Universe for weakly interactingdark matter particles [16]. However, tidal interactions withthe baryon-dominated cores of dark matter halos and super-nova feedback could destroy these structures to a large ex-tent. Therefore, the boost factor f = (cid:82) ρ dV / (cid:82) ρ dV is a r X i v : . [ a s t r o - ph . H E ] N ov introduced as a free parameter to account for the unknownenhancement due to sub-halo clumping.The inverse-Compton interaction is the up-scattering ofphotons by high-energy charged particles. The di ff erentialgamma-ray flux given by Eq. (2) describes inverse-Comptonscattering o ff the cosmic microwave background by rela-tivistic electrons and positrons. b ( E (cid:48) ) is the total rate ofelectron / positron energy loss due to inverse-Compton scat-tering as in [17], P ( E , E (cid:48) ) is the di ff erential power emittedinto photons of energy E by an electron / positron with en-ergy E (cid:48) , and d N e / d (cid:101) E is the spectrum of secondary electronsand positrons [14]: (cid:32) d Φ d E (cid:33) IC = E f (cid:104) σ A ν (cid:105) π m χ D (cid:90) M87 d V ρ ( r ) × m χ (cid:90) m e d E (cid:48) P ( E , E (cid:48) ) b ( E (cid:48) ) m χ (cid:90) E (cid:48) d (cid:101) E d N e d (cid:101) E (2)The main challenge in constraining the putative dark mat-ter annihilation component is to discriminate it against gam-ma rays from astrophysical sources and cosmic ray interac-tions. Here, we show as an exemplary case study how recentmulti-frequency data of the center of the Virgo cluster, har-boring the giant cD galaxy M87 with its gamma-ray emittingradio jet, can be used to constrain dark matter particles. Notethat we do not refer to the inverse-Compton scattering in so-called leptophilic dark matter annihilation scenarios, but in-clude the inverse-Compton emission component due to theelectrons and positrons from the decay of isospin-symmetricannihilation products.We adopt a distance of (16 . ±
1) Mpc [18] to M87 andtherefore omit redshift corrections to the energy through-out the paper. Section 2 describes the data sets chosen forthe study. The radiation code employed to model the spec-tral energy distribution of M87 is explained in Section 3,and physical parameters inferred from the fit of the data arebriefly discussed to show that the model is a viable interpre-tation of the nonthermal particle content in the jet of M87.The generic model for the weakly interacting massive parti-cles and their radiative signatures is described in Section 4,and a fit of a component from dark matter annihilation to theexcess above the astrophysical model is presented. Finally,we discuss the results and draw conclusions regarding futuresearch strategies.
The dataset used here is comprised of observations of M87by the Chandra X-ray Observatory, Fermi-LAT, MAGIC,and the H.E.S.S. system of Cherenkov telescopes [19,20,21,22]. As presented in [20], additional observational dataexist for the radio-to-optical regime. However, we do not use these to constrain the fit, but rather only require the pro-jected emission to not exceed these observations, since inthis wavelength regime the unavoidable contamination dueto starlight and dust from the central region of M87 is verydi ffi cult to assess. There may also be hidden nonthermalcomponents in this energy region unrelated to the emissionregion where the high-energy emission originates from.The data sample was not taken contemporaneously, butwe carefully checked to avoid inclusion of an observationcontaining a significant flare. All the data used here can thusbe considered a representative long-term average, reason-ably well describing the steady and low-state spectral energydistribution of the high-energy emission component in M87. The nonthermal emission from the relativistic jet emergingfrom the nucleus of M87 follows a spectral energy distribu-tion across almost 20 orders of magnitude which can be de-scribed by the synchrotron and self-Compton radiation pro-duced by electrons (and positrons) accelerated in the jet, pre-sumably by shock waves. Whereas the high amplitude flarestrack single shock waves or magnetic reconnection eventsin the expanding flow, guided by the helical structure of themagnetic field, the steady-state (long-term average) emis-sion which dominates the energy output from the jet of M87corresponds to the superposition of a large number of shockwaves [23], a strong stationary shock such as the reconfine-ment shock [24] or the emission from a sheath surroundingthe spine of the jet [25].To obtain a fit for the broad-band spectral energy dis-tribution of M87, we used an implementation of the SSCmodel [26] in which the cooling break in the electron spec-trum is self-consistently determined, and the cross sectionfor Compton scattering in the Klein-Nishina regime is ac-curately treated. We also took into account the inhomoge-neous nature of the emission zone, by considering only theemission from the inner jet for the fit, i.e. we considered theradio to optical emission, related to the emission from largerscales in the jet, as an upper bound for the model.Adopting for the Doppler factor δ = . Γ = .
3) as in the model fitted to the data by [20]we obtain a fit with χ /ν = .
5. Physical parameters of theemission zone are the source radius R b = . × cmand the magnetic field strength B = ff , weobtain a di ff erential slope of s = .
2, maximum Lorentz fac-tor Γ max = and normalization factor K = cm − s − (cf. [26]). This results in an injection luminosity of L in j = × erg s − consistent with the energetics of the jet in-ferred from its large scale radio structure [27]. Model fitsincluding the low-energy continuum [20] yield di ff erent re- Fig. 1
Result of the combined fit including the spectral energy distri-butions due to the SSC mechanism in the jet of M87 and the annihila-tion of dark matter particles. The boost factor f accounts for sub-haloclumping, and m denotes the generic WIMP mass. sults, but fail to produce an acceptable fit including the veryhigh energy observations.For the black hole mass of M87 M BH = . × M (cid:12) ,the Eddington luminosity is given by L E = . × erg s − . Thus, the nonthermal power release amounts to only ∼ − L E . Although a sub-Eddington state of the black holeis generally expected for high-peaked blazars, the extremelylow power is peculiar. In fact, it is not possible to model thedata by simply adjusting the Doppler factor of an SSC fitobtained for high-peaked blazars, i.e. by changing the incli-nation of the jet axis with respect to the observer. The ideaof treating M87 as a misaligned blazar [28] does not seemto be su ffi cient. Furthermore the large di ff erence betweenbreak energy and cut-o ff is not typical for blazar spectra.This might be related to the extremely low accretion rate,indicating that the AGN is fading out due to a lack of acc-retable matter, or to the fact that the observed emission isdominated by the emission from a low-bulk-Lorentz-factorsheath surrounding the jet.The SSC fit of the data obtained in this way provides anaccurate and practically unique model for the SED, and thesmall size of the emission region is in line with observationsof short-time variability. To now fit an additional component due to dark matter an-nihilation, and study whether the statistical agreement be-tween model and observations can thereby be further im- proved, we assume a generic species of annihilating WIMPswith rest mass in the GeV-TeV range and a thermally aver-aged annihilation cross section of (cid:104) σ A ν (cid:105) = × − cm s − .It has been shown that many models with multi-TeV massesprovide large pair annihilation cross sections which are stillin agreement with the thermal freeze-out of these particles inthe early Universe [29]. The choice of the annihilation crosssection also reflects the possible existence of boost factorsin the particle physics sector and should be considered asmoderate upper limit (cf. [30]). For the dark matter distribu-tion of M87, we use the analysis of [31], resulting in a de-scription of the halo according to the Navarro-Frenk-White[15] model. The normalization of the intensity of the result-ing emission is furthermore fixed by choosing the boost fac-tor from unresolved substructure in the halo of M87, whichfrom recent numerical experiments [32] is expected to be oforder f = − . The spectra for the emission due to thedecay of charged and neutral pions from hadronization inthe annihilation process are generated using the DarkSUSYcode [33]. A total of 10 realizations of neutralinos are pro-duced to obtain the average secondary spectra for genericWIMPs motivated by supersymmetric theories.Here we also include a treatment of the inevitable con-tribution of inverse-Compton emission from energetic elec-trons / positrons from the decay of the charged pions up-scat-tering cosmic microwave background photons. By using theknown number density of these 2.7 K background photons(413 cm − ), the respective contribution from inverse-Comp-ton emission can be of the same order as the prompt pion de-cay emission. This results in a telltale “double hump struc-ture” of the dark matter related emission. Employing a χ -test, we search for the best-fit model of the active galacticnucleus (AGN) as discussed in the previous section, and thecomplete dark matter related model. The results of the fit areshown in Fig. 1.A minimal χ value of 1.6 is achieved for a particle massof 4.7 TeV and a boost factor of 812, both well within therange of values accessible in state-of-the-art particle physicsand numerical models, as discussed in the previous section.Assuming that the main multi-wavelength features of sucha generic dark matter model can be described by two addi-tional parameters (neutralino mass and boost factor) com-pared to the SSC model alone, it can be shown by nonlinearregression analysis that the deviation of the data points withrespect to the SSC model amounts to 2 σ . We note that thisresult is not significant enough to claim the realization of acertain dark matter model, but even our simplified assump-tions show the capability of multi-wavelength methods forunvealing the characteristics of the constituents of dark mat-ter. In Fig. 2, we show the resulting spectral energy distribu-tion from the combined SSC-DMA model. CHANDRA FERMI MAGICHESS m Χ (cid:61) f (cid:61)
812 IC Π (cid:45) (cid:45) (cid:45) (cid:45) Ν (cid:64) Hz (cid:68) Ν F Ν (cid:64) e r g s (cid:45) c m (cid:45) (cid:68) Fig. 2
Spectral energy distribution of the best-fit combined SSC model for M87 and dark matter model, including all data points used in thisanalysis [19,20,21,22]. The inset legend provides the mass and boost factor for the generic WIMP with cross section (cid:104) σ A ν (cid:105) = × − cm s − . We show that while synchrotron-self-Compton emission canfit the observations reasonably well, the introduction of acomponent due to annihilating dark matter particles margi-nally improves the agreement between theoretical modelingand multi-frequency observations of the long-term averageSED of the radio galaxy M87. It is essential to include theinverse-Compton emission component in the dark matter an-nihilation model. The method thus shows great sensitivityin ruling out dark matter models at the TeV scale which isinnate to some supersymmetric extensions of the StandardModel, while annihilation cross section and additional boostfrom substructures are concordant with the paradigm of ther-mal freeze-out of such a particle at the onset of hierarchicalstructure formation. Although the significance of this resultis not su ffi cient to claim evidence of a specific particle, it isencouraging further studies.Since the SSC component generally shows variabilitywhile the DMA component remains steady, we emphasizethat the significance of the marginal excess reported herewould increase during low states of the SSC emission. There-fore we encourage to extend the temporal coverage of multi-wavelength observations of M87. Measuring the putativedark matter “double hump structure“ in the spectrum with a high significance would open up the possibility to extractthe dark matter properties (WIMP mass, annihilation crosssection and boosting due to substructure) more accurately.The high mass scale of the generic WIMP favored inour model here is in-line with recent findings at the LHC[34]. A high mass scale may also help in explaining themeasured extragalactic gamma-ray background (EGB) [35],after a careful reassessment of the Fermi-measured EGB[36]. Detection of high-mass WIMPs by elastic scatteringexperiments [37] will be di ffi cult due to the suppression ofthe event rate by the low number density of WIMPs in theGalactic halo. References
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