Dark Matter Annihilation around Intermediate Mass Black Holes: an update

20 Pages·2009·1.34 MB·English

New Jou rnal of Ph ys ics
The open– access jour nal for physics
Dark matter annihilation around intermediate mass
black holes: an update
Gianfranco Bertone1, Mattia Fornasa2, Marco Taoso2
and Andrew R Zentner3,4
1Institutd’AstrophysiquedeParis,UMR7095-CNRS,UniversitéPierreet
MarieCurie,BdArago98bis,75014,Paris
2UniversityofPadovaandINFNsezionediPadova,viaMarzolo8,
35131Padova,Italy
3DepartmentofPhysicsandAstronomy,UniversityofPittsburgh,Pittsburgh,
PA15260,USA
E-mail:[email protected]@pd.infn.it
NewJournalofPhysics11(2009)105016(20pp)
Received29May2009
Published16October 2009
Onlineathttp://www.njp.org/
doi:10.1088/1367-2630/11/10/105016
Abstract. The formationand evolutionof blackholes (BHs)inevitably affects
the distribution of dark and baryonic matter in the neighborhood of the BH.
TheseeffectsmaybeparticularlyrelevantaroundSupermassiveandIntermediate
MassBlackHoles(IMBHs),theformationofwhichcanleadtolargedarkmatter
(DM) overdensities, called spikes and mini-spikes, respectively. Despite being
larger and more dense, spikes evolve at the very centers of galactic halos, in
regions where numerous dynamical effects tend to destroy them. Mini-spikes
may be more likely to survive, and they have been proposed as worthwhile
targets for indirect DM searches. We review here the formation scenarios and
the prospects for detection of mini-spikes, and we present new estimates for
the abundances of mini-spikes to illustrate the sensitivity of such predictions
to cosmological parameters and uncertainties regarding the astrophysics of BH
formation at high redshift. We also connect the IMBHs scenario to the recent
measurements of cosmic-ray electron and positron spectra by the PAMELA,
ATIC,H.E.S.S.andFermicollaborations.
4Authortowhomanycorrespondenceshouldbeaddressed.
NewJournalofPhysics11(2009)105016
1367-2630/09/105016+20$30.00 ©IOPPublishingLtdandDeutschePhysikalischeGesellschaft
2
Contents
1. Introduction 2
2. IMBHs 3
2.1. HintsfordetectionofIMBHs . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2. Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
3. Adiabaticcontraction 5
4. DetectionofDMaroundIMBHs 7
4.1. NeutrinosfromIMBHs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
4.2. AntimatterfromIMBHs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
5. ContributionofIMBHstotheEGBandtheirangularspectrum 13
6. Discussionandconclusions 16
References 18
1. Introduction
The distribution of matter around a black hole (BH) is inevitably affected by its formation
and evolution, both in the case of baryons [1, 2] and dark matter (DM) [3]. The physics is
relatively simple: when a compact object forms, the surrounding matter reacts to the increased
gravitational potential, and if the growth proceeds on a timescale much longer than the
dynamicaltimeofthesystem,largeoverdensitiescanbeachieved.Thisisparticularlyimportant
for the DM distribution, because the DM annihilation rate is proportional to the square of the
number density of DM particles. This means that if BH formation increases the DM density
locally,italsobooststheannihilationrateandimprovestheprospectsfordetectingDMthrough
theobservationofsecondaryparticlessuchasgammarays,antimatterandneutrinos.
Gondolo and Silk have applied this argument to the distribution of DM at the center of
the Galaxy [3], where a supermassive BH (SMBH) of 2–4×106M is known to dominate the
(cid:12)
gravitational potential within a sphere of radius r ∼1pc. The consequent enhancement in the
h
DM density around the central SMBH (dubbed a spike) was subsequently shown likely to be
reduced by major merger events, off-center formation of the seed BH, gravitational scattering
off stars and DM annihilations [4]–[7]. Zhao and Silk have subsequently suggested that mild
overdensities of DM could also be present around intermediate mass black holes (IMBHs),
remnantsofPopIIIstars,andprovidedthefirstroughestimatesofthepropertiesofmini-spikes
surroundingIMBHsintheMilkyWay[8].
Bertone, Zentner and Silk (hereafter BZS) built a consistent formation and evolution
scenarioforIMBHsandassociatedmini-spikes,fortwodifferentclassesofmodels:‘mild’mini-
spikesaroundIMBHsremnantsofPopIIIstars,and‘strong’mini-spikes,aroundmoremassive
compactobjects[9].Forbothscenarios,BZStrackedthemergerhistoryofeachindividualBH,
and selected precisely those IMBHs which never experienced mergers, to ensure at a minimum
that major mergers have not destroyed any spike that may have existed around the original BH.
This has allowed a detailed quantitative description of the mini-spikes scenario, and practically
allsubsequentstudiespublishedintheliteraturehavemadeusedirectlyorindirectlyoftheBZS
IMBH models. Moreover, BZS were able to predict some of the demographics of wandering
IMBHs,thatmaynotbedirectlyassociatedwiththeMilkyWaybulgeordisc,andtheyproposed
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tosearchforaclassofgammaraysobjectssharingthesameenergyspectrumasasmoking-gun
signatureofDMannihilations.
Here, we review the formation scenarios and the physics behind the BZS IMBH models,
and explore how the population of IMBHs, thus of mini-spikes, depends on cosmological,
astrophysical and particle physics parameters. To this aim, we update the original BZS
catalogs, including the most recent determination of cosmological parameters, and explore the
dependenceonastrophysicalquantities.
We also review here the experimental strategies that may allow the detection of mini-
spikes,includingtheobservationofmultiplegamma-rayandneutrinosourcesintheMilkyWay,
a collection of gamma-ray sources around M31, and the possible contribution to the absolute
fluxandtheangularpowerspectrumoftheextra-galacticgamma-raybackground(EGB).
The paperis organizedas follows:in section2, wereview theIMBHs formation scenarios
and discuss the current population of IMBHs in the Milky Way. In section 3, we discuss
adiabatic contraction and the formation of mini-spikes. Section 4 is dedicated to the prospects
fordetectingDMthroughgammaraysandneutrinosfromIMBHsinourGalaxyandinM31.In
section 5, we discuss the impact of the mini-spikes population on the EGB. In the final section
(section6),wediscussourresultsandpresentourconclusions.
2. IMBHs
2.1. HintsfordetectionofIMBHs
WerefertoBHswithmasseswithinarelativelylargerange,100M . M .106M asIMBHs.
(cid:12) (cid:12)
The lower limit is roughly the mass of the largest BH that can be produced by stellar
collapse [11], and the upper limit corresponds to the minimum mass for an SMBH. There is
not a clear experimental evidence for this class of objects, but they are often invoked as an
explanation of ultra luminous x-ray sources, i.e. sources that emit at a luminosity larger than
1039ergs−1,thusexceedingtheEddingtonluminosityofstellarBHs[12].
IMBHs may also be hosted inside globular clusters [13]. A hint in favor of this possibility
comes from the fact that the predicted mass of an IMBH and the velocity dispersion typical of
a globular cluster follow exactly the extrapolation at lower values of the M −σ relation valid
•
forSMBHs[14].
Fromatheoreticalpointofview,IMBHsmayprovidemassiveenoughseedsforthegrowth
of high-redshift SMBHs, as observed by the Sloan Digital Sky Survey in the form of quasars
at redshifts as high as z ∼6 [15]–[19]. Conclusive evidence for IMBHs may come in the near
future from the detection (e.g. by LISA [20]) of the gravitational waves emitted in the mergers
ofIMBHs[21]–[25].
2.2. Formation
In BZS, two formation scenarios for IMBHs have been studied, and we refer to that paper for
a detailed discussion. In the first scenario (scenario A), IMBHs are remnants of the collapse
of population III stars [26]. Since the Jeans mass scales with the temperature as T3/2, the
mass of pop III stars (which form early in a hot environment) is expected to be higher than
other stars, around 150–200M [27, 28]. Newtonian simulations suggest that the evolution of
(cid:12)
pop III stars is very different from stars in the local Universe. Zero metallicity pop III stars
NewJournalofPhysics11(2009)105016(http://www.njp.org/)
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evolve on a timescale of order t ∼1–10Myr. If their masses are in the range M ∼60–140M
∗ (cid:12)
and M &260M , they collapse directly to BHs, whereas if 140. M/M .260M , they
(cid:12) (cid:12) (cid:12)
are completely disrupted due to the pulsation-pair-production instability, leaving behind no
remnant[29].
The second formation scenario (scenario B) considered by BZS was based on [30], as an
example of models in which the collapse of primordial gas in early forming halos leads to the
‘direct’ formation of very massive objects [31]–[36]. In this specific scenario, the baryons in
the low tail of the angular momentum distribution form a pressure-supported disc at the center
of the halo. Gravitational instabilities then turn on an effective viscosity that make baryons
lose their angular momentum, causing an inward mass flow. The process comes to an end after
1–30Myr, when the first stars form or when the halo experiences a major merger [30]. The
centralobjectwillthenundergogravitationalcollapseproducingthefinalBH.
Therequirementthatlossofangularmomentumviaviscosityiseffective,fixesamassscale
of 107–108M for the initial halos, and leads to a mass scale for the final IMBHs of the order
(cid:12)
of 105M . In fact, the mass distribution for scenario B turns out to be a log-normal Gaussian
(cid:12)
(σ =0.9)withameanvalue M :
• •
(cid:16) κ (cid:17)(cid:18) f (cid:19)3/2(cid:18) M (cid:19)(cid:18)1+z (cid:19)(cid:18) t (cid:19)
M =3.8×104M vir f , (1)
• • 0.5 0.03 107M 18 10Myr
(cid:12)
where M is the virial mass of the halo, z the redshift of formation, f the fraction of the
vir f
baryonic mass of the halo that goes into the central pressure-supported disc, κ the fraction of
the mass of the disc that ends up in the final IMBH and t is the timescale available for angular
momentumtransferduetotheeffectiveviscosity.
BZS have estimated the population of IMBHs in the MW in scenario A as follows: they
populated all the halos at z =18 that constitute a 3σ peak (with respect to the average density)
with a pristine IMBH of mass 100M . The evolution of the halos is then simulated as in [21],
(cid:12)
[37]–[39], a procedure that tracks the growth and mergers of the structures down to redshift
zero. The IMBHs in the halos that never experience mergers survive until the present epoch
and constitute the current population of scenario A IMBHs. Their mass is assumed to remain
unchangedwithrespecttotheinitialvalue∼100M ,andthenumberofunmergedIMBHswas
(cid:12)
foundtobe N =(1027±84).
A
In the case of scenario B, BZS have followed a similar approach for the evolution of
IMBHs, with the difference that only those halos with a mass larger than the mass threshold
M fortheonsetoftheeffectiveviscosity(seethediscussionabove)arepopulatedwithIMBHs,
thr
with a mass function as in equation (1) (see also figure 1). The predicted number of IMBHs in
theMWforscenarioBwas N =(101±22)[9].
B
Each of these models of high-redshift seed BH formation is reasonable, but both of these
scenariosremainuncertainintheirdetail.Inparticular,thesemodelsexhibitparametersthatmay
reasonably take on a wide range of values leading to markedly different predictions for IMBH
demographicsatz =0.TheformationofseedBHsinbothscenariosiscutoffatredshiftswhen
significant small-scale fragmentation of baryonic discs sets in and BH formation in scenario B
terminates absolutely when the Universe becomes significantly reionized. In what follows we
exhibitthesignificantparameterfreedomwithinthesemodelsbyvaryingtheformationredshift
inscenarioA,andthereionizationredshiftinscenarioBamongviableandillustrativevalues.In
scenarioA,loweringtheformationredshiftrequiresthattheseedBHsgenerallyforminhalosof
highermass,leadingtoreducedabundanceofIMBHs,whileinscenarioBloweringtheredshift
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1
0.1
1 10 100
Distance to Galactic Center [Kpc]
Figure 1. Left: mass function of unmerged IMBHs in the scenario B for a MW
halo at z =0. The distribution is based on the average of 200 Monte Carlo
realizations of a halo of virial mass M =1012.1h−1M , roughly the size of
vir (cid:12)
the halo of the MW. Taken from [9]. Right: radial distribution of the IMBH
population in the MW from the numerical simulation of [9]. The points refers
to the average among 200 Monte Carlo realizations of the MW halo and the
error bars show the scatter among realizations. The solid line is the analytical fit
andthedottedlineisaNFWprofile.Takenfrom[10].
ofreionizationallowsangularmomentumlosstobeeffectiveforalongerperiod,increasingthe
numberofseedBHs.PredictionsforIMBHpropertiesaresensitivetocosmologicalparameters
as well as the parameters that describe BH coalescence, and we discuss this issue in section 4.
Wenoteherethattherangeofparameterswechoosearecurrentlyviableandreferthereaderto
BZSformodelingdetails.
The radial distribution of IMBHs was found to be steeper than a Navarro–Frenk–White
(NFW) profile [40] (see the right panel of figure 1), and it is well fitted by the following
analyticalfunction[10]:
" (cid:18) r (cid:19)0.51#−10.8
N(r)=5.96×10−2 1+ kpc−3. (2)
9.1kpc
3. Adiabaticcontraction
As mentioned in the introduction, IMBHs and SMBHs are particularly interesting for indirect
DM searches, because they may act as annihilation boosters, as their growth can lead to large
DM overdensities that enhance annihilation fluxes (see e.g. [41] for a review). In particular, if
the crossing timescale t (the time needed for a DM particle to cross the central part of the
cr
halo)ismuchsmallerthantheBHgrowthtimescalet ,DMparticlesconservetheirangular
growth
momenta and their radial actions (the integral of the radial velocity over one closed orbit), and
NewJournalofPhysics11(2009)105016(http://www.njp.org/)
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movetoorbitswhichareclosertotheBH,thusenhancingtheirnumberdensityandannihilation
rate.
ThefirststudyofadiabaticcontractionwasperformedbyYoungin1980[2]inthecontext
of stellar systems. In subsequent studies also DM has been taken into account [42]–[44] and
twodifferentsituationshaveusuallybeenconsidered:
• ‘analytical cores’, in which case the initial DM profile can be Taylor-expanded around the
BHas:ρ (r)≈ρ +1/2ρ00 r2+O(r3);
χ χ,0 χ,0
• γ-models,inwhichtheinnerinitialDMprofileisapowerlaw,ρ (r)∝r−γ.
χ
The result of adiabatic contraction is different in the two cases. A strong density
enhancement, or spike, is produced in both cases, but the final slope is steeper for γ-models.
The difference isdue to the different behavior ofthe phase-space distribution function f(E,t).
In the case of γ-models, f diverges in the limit E →8(0), meaning that cold orbits (those
orbits populated by particles with very low velocities) have a large occupation number. The
final DM profile for a γ-model is a new power law ρχ ∝r−γsp with a steeper slope. The value
ofγ dependsontheinitialslopeasinthefollowingequation:
sp
9−2γ
γ = . (3)
sp 4−γ
The effect of SMBH growth at the Galactic center on DM density profiles is shown in figure 2
foraninitialNFWprofile(γ =1).Thefinalprofileinthiscaseisapowerlawofindexγ =7/3
sp
within a region of radius r ∼0.2r , where r is the radius that encloses a DM mass equal to
sp h h
twicethemassofthecentralBH.
There is an upper limit to the DM density that can be achieved around the SMBH (see
figure 2). In fact, the power law solution is valid only down to a radius equal to the last stable
orbitaroundtheSMBHand,furthermore,DMannihilationitselfsetsanupperlimitontheDM
densityoforderm /σv(t −t ),sothatthedensityissaturatedatacut-offradiusof
χ f
r =Max[4R ,r ], (4)
cut Schw lim
where R istheSchwarzschildradiusoftheIMBH R =2.95km(M /M ).
Schw Schw bh (cid:12)
Any spike forming at the center of a galactic halo would inevitably be affected by
dynamical processes that tend to deplete the DM density [4]–[6]. For instance, a merger
between two halos, the interaction with a globular cluster or the presence of a bar are all able
to disrupt the distribution of the cold particles that constitute the spike, efficiently damping
the enhancement [4, 5]. Furthermore, the BH may not form exactly at the center of the DM
distribution [4], in which case the orbits that the BH crosses in its spiraling in will be depleted
and the final enhancement will be much shallower than what depicted in figure 2. Finally, one
shouldalsotakeintoaccounttheinteractionsoftheDMparticleswithbaryons[5]:transferring
energy to the DM particles, the effect is, as before, of heating the DM so that the particles
in the spike will be able to leave the central region. When also including the effect of DM
annihilations, it is possible to show that any DM overdensity around a BH at the center of a
galactic halo can hardly survive until today [6], although interactions of baryons can actually
leadtotheregrowthofmildoverdensitiesknownasDMcrests[45].Ourapproachistoaccount
forsomeofthesemitigatingfactorsbyconsideringonlythoseBHsthatformedathighredshift
and were found never to interact with any other BH during the hierarchical merging process,
as discussed in [9]. Moreover, at least for scenario B, off-center formation is not possible for
IMBHs and interactions of DM with baryons have only minor effects, so that, in contrast to
SMBHs,IMBHscaneffectivelyretaintheirmini-spike.
NewJournalofPhysics11(2009)105016(http://www.njp.org/)
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Figure 2. Possible models for the DM distribution in the Galaxy. The thin curve
shows the standard halo model, and the thick curve is the same model after
‘adiabaticcompression’bytheGalacticbaryons(starsandgas).Bothcurvesare
normalized to a DM density of 0.3GeVcm−3 at the solar circle. Curves labeled
‘spike’ show the increase in density that would result from growth of a Galactic
SMBH at a fixed location. The annihilation plateau, ρ =ρ =m/hσvit, was
a
computedassumingm =200GeV,hσvi=10−28cm3s−1andt =1010yr.Dotted
vertical lines indicate the SMBH Schwarzschild radius (r ≈2.9×10−7pc,
Sch
assuming a mass of 3.0×106M and zero rotation), the SMBH gravitational
(cid:12)
influence radius (r ≈1.7pc), and the radius of the Solar circle (R ≈8.0kpc).
h (cid:12)
Effects of the dynamical processes (scattering of DM off stars, loss of DM into
theSMBH,etc)areexcludedfromthisplot;theseprocesseswouldgenerallyact
todecreasetheDMdensitybelowwhatisshownhere,particularlyinthemodels
witha‘spike’.Takenfrom[7].
4. DetectionofDMaroundIMBHs
ThefluxofsecondaryparticlesproducedbyDMannihilationaroundanIMBHcanbewrittenas
d8 hσvi dN Z
(E)= (E) ρ2(r)dV, (5)
dE 8πm2 dE sp
χ
where hσvi is the thermally averaged annihilation cross section, m is the mass of the DM
χ
particleanddN/dE istheenergyspectrumofthesecondaryparticlesproducedperannihilation.
Gamma-ray photons come from the decay and possible hadronization of the final states of DM
annihilations, the resulting photon yield depending therefore on the particular DM candidate
¯
under consideration. For the rest of the paper we focus on annihilations into bb, characterized
by a typical soft photon spectrum, representative of a larger class of annihilation channels. We
discardDMintotwophotonssincethebranchingratioishighlymodeldependentandingeneral
it is predicted to be very small. The integral in equation (5) extends from the cut radius r
cut
NewJournalofPhysics11(2009)105016(http://www.njp.org/)
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Figure 3. IMBHs integrated luminosity function, i.e. number of IMBHs
producing a gamma-ray flux larger than a given flux 8 (above 1GeV), as a
functionof8,forscenarioA.Foreachcurvewealsoshowthe1σ scatteramong
the different realization of the Milky Way-size host DM halo. The blue (red)
curvereferstoaDMparticlewithamassof100GeV(1TeV)andacrosssection
of hσvi=3×10−26cm−3s−1 (hσvi=3×10−29cm−3s−1). The upper (lower)
set of lines corresponds to a redshift of formation z =18 (15). The figure can
f
be interpreted as the number of IMBHs detectable by experiments with a point
sourcesensitivity8(above1GeV)asafunctionof8.
(i.e. the radius where the DM density reaches the annihilation plateau in figure 2) to the spike
radiusr .
sp
Insertingappropriatereferencevalues,equation(5)canberecastas
d8(E)=8 dNγ (cid:18) hσvi (cid:19)(cid:16) mχ (cid:17)−2(cid:18) d (cid:19)−2(cid:18) ρsp(rsp) (cid:19)2
dE 0 dE 10−26cm3s−1 100GeV kpc 102GeVcm−3
(cid:18)r (cid:19)14/3(cid:18) r (cid:19)−5/3
× sp cut , (6)
pc 10−3pc
with 8 =9×10−10cm−2s−1, a normalization factor that makes it evident that IMBHs can be
0
brightDMannihilationsources,possiblyasbrightastheentireMW.
The fact that the cut radius itself depends on the mass and the cross section of the DM
candidate alters the naïve dependence of the annihilation flux from these quantities, and it is
easy to show that in this case d8/dE ∝hσvi2/7m−9/7. The weak dependence of the predicted
χ
annihilationfluxontheparticlephysicsparametersisoneoftheintriguingfeaturesofthemini-
spikesscenario.
In figures 3 and 4, the number of IMBHs associated with a gamma-ray flux (integrated
above1GeV)largerthan8isplottedasafunctionof8itself.Withrespecttothesimilarfigures
4 and 5 in [9], we consider here the most recent cosmological parameters from WMAP5, and
find a significant decrease of the number of IMBHs [46]. In the present work, we have taken
ω =0.136,ω =0.0227,(cid:127) =0.73,afluctuationspectrumnormalizedto12 =2.45×10−9
M B 3 R
at a pivot scale of k =0.002Mpc−1, and a scalar spectral index of n =0.96. These parameters
s
NewJournalofPhysics11(2009)105016(http://www.njp.org/)
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Figure 4. IMBHs integrated luminosity function, i.e. number of IMBHs
producing a gamma-ray flux larger than a given flux 8 (above 1GeV), as a
functionof8,forscenarioB.Foreachcurvewealsoshowthe1σ scatteramong
the different realization of the Milky Way-size host DM halo. The blue (red)
curvereferstoaDMparticlewithamassof100GeV(1TeV)andacrosssection
of hσvi=3×10−26cm−3s−1 (hσvi=3×10−29cm−3s−1) . The middle (upper,
lower) set of lines corresponds to a redshift of reionization z =12 (7, 17). The
r
figure can be interpreted as the number of IMBHs detectable by experiments
withapointsourcesensitivity8(above1GeV)asafunctionof8.
imply a power spectrum with an rms fluctuation amplitude on 8Mpch−1 scales of σ =0.81
8
(BZS worked in a cosmology where σ =0.9, roughly ∼3.5σ from the value inferred from
8
the most restrictive of the WMAP5 analyses in [46]). The fluctuation amplitude σ is a
8
degenerate combination of the primary parameters used in the WMAP5 analysis. However, of
thecosmologicalparametersincommonuse,itisthemostdirectlyrelevanttoIMBHformation
because it fixes the amplitude of density fluctuations (and thus, halo abundances and formation
epochs)onscalesclosertothoserelevantforIMBHformation.
In order to show the effect of changing the cosmological parameters we have considered
two representative values of the redshift of formation z for the scenario A and we have
f
varied the reionization redshift z for the scenario B in the WMAP5 3σ range [46]. The total
r
number of IMBHs for the different choices of astrophysical parameters is shown in table 1.
In the context of the standard 3CDM cosmological model specified by the parameters of
the previous paragraph and our IMBH models, current 1σ constraints on σ fix the low-
8
redshift abundance of IMBHs to within ∼50%. This is still a considerable uncertainty, but
astrophysical parameters introduce larger uncertainties at present. Moreover, it must be stated
thatIMBHformationissensitivetoprimordialdensityfluctuationsonscalesof.50kpch−1and
this scale is not constrained directly by well-established cosmological probes. Non-standard
cosmological models, particularly those with large spectral index running or features in the
primordial power spectrum of density fluctuations, can alter density fluctuations on such scales
significantly without violating prevailing cosmological constraints. As a result, halo formation
and abundances in non-standard cosmological models can be altered appreciably [37], with the
NewJournalofPhysics11(2009)105016(http://www.njp.org/)
10
Table 1. Number of unmerged IMBHs in a Milky Way-like halo at z =0.
The four columns indicate the formation scenario, the formation (reionization)
redshift in the case of scenario A (B), the number of IMBHs and the 1σ scatter
amongrealizations.
Scenario z N 1σ scatter
BH
A 18 319 49
A 15 54 13
B 7 278 37
B 12 62 14
B 17 8.4 3.7
consequence that the demographics of IMBHs may be very different from our predictions in
viable, non-standard cosmologies. This type of limitation due to cosmological uncertainties is
commontomanyindirectDMprobes(e.g.[39]).
Figures3and4canalsobelooselyinterpretedasthenumberofobjectsthatcanbedetected
withanexperimentofsensitivity8.ForEGRET,8 ≈3×10−8cm−2s−1 andthefactthat
EGRET
theIMBHsscenarioiswithinthereachofEGRET,meansthatsomeoftheunidentifiedEGRET
sources could be interpreted as IMBHs. If this interpretation was confirmed by Fermi, which
is expected to see many more sources, the identification of a population of point-like sources
with the same energy spectrum would provide strong evidence for a DM annihilation signal.
We stress that the number of detectable sources depend on the formation scenario but also
on other poorly constrained processes, such as the merger history of IMBHs in the Galaxy
and the initial distribution and dynamical evolution of the surrounding DM. Furthermore,
from a particle physics point of view, we recall that the DM annihilation cross section can
largely differ from the thermal value in presence of efficient coannihilations [47], significant
Sommerfeld enhancements [48]–[51], in cases where DM particles are not thermal relics, or in
non-standardcosmologicalscenarios[52]–[54].Infigures3and4,weconsideredthereference
valueofhσvi=3×10−26cm−3s−1 comingfromaback-of-the-envelopeimplementationofthe
constraint for a thermal GeV DM candidate to provide the relic density measured by WMAP,
but also a much more conservative value of hσvi=3×10−29cm−3s−1 that emphasizes the
potentiality of the IMBHs scenario even with pessimistic, low values for the annihilation cross
section.
Ontheotherhand,intheconservativecasewherenoneoftheEGRETsourcesisassociated
with a mini-spike, this can be used to put constraints on the IMBHs model, excluding, for
scenario A, the hσvi=3×10−26cm−3s−1 and m =100GeV case for both values of the
χ
formation redshift z . While, for scenario B, the constraints are even stronger and only models
f
withahighreionizationredshift z andalowannihilationcrosssectionarestillviable.
r
SimilarlimitshavebeenputalsobytheH.E.S.S.arrayofCherenkovtelescopes,asproved
by the survey of the inner Galactic plane at photon energies above 100GeV performed from
2004to2007[55].About400hofdatahavebeenaccumulatedintheregionbetween−30◦ and
+60◦ inGalacticlongitude,andbetween−3◦ and+3◦ inGalacticlatitude,aH.E.S.S.sensitivity
map was computed for DM annihilations. The data exclude scenario B at a 90% confidence
level for DM particles with velocity-weighted annihilation cross section σv &10−28cm3s−1
andmassbetween800GeVand10TeV.
NewJournalofPhysics11(2009)105016(http://www.njp.org/)