Difficulty of detecting minihalos via $γ$-rays from dark matter annihilation

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by  Lidia Pieri

PRL/V0
Difficulty of detecting minihalos via γ-rays from dark matter annihilation
Lidia Pieri1, Enzo Branchini2 and Stefan Hofmann3
1 Department of Physics, Stockholm University,
AlbaNova University Center,
SE-10691 Stockholm, Sweden
2 Department of Physics, Universit`a di Roma Tre,
Via della Vasca Navale 84, I-00146 Rome, Italy
3 Perimeter Institute for Theoretical Physics,
Waterloo, Ontario, N2L 2Y5, Canada
(Dated: February 2, 2008)
Analytical calculations and recent numerical experiments have shown that a sizable of the mass
in ourGalaxy is in a form of clumpy,virialized substructuresthat,according to [1], can beas light
6 as10−6M⊙. Inthisworkweestimate thegamma-raysfluxexpectedfrom darkmatterannihilation
0
occurringwithintheseminihalos,underthehypothesisthatthebulkofdarkmatteriscomposedby
0
neutralinos. Wegeneratemock skymapsshowingtheangular distributionoftheexpectedgamma-
2
ray signal. We compare them with the sensitivities of satellite-borne experiments such as GLAST

n and find that a possible detection of minihalos is indeed verychallenging.
a
J PACSnumbers: 95.35.+d,98.35.Gi,98.35.Jk,98.62.Gq,11.30.Pb,12.60.Jv,95.30.Cq

6
1
Analyses of the anisotropies in the cosmic microwave produced within our Galaxy under the hypothesis, sup-

3 background radiation [2] find that the matter density portedbyseveralhighresolutionnumericalexperiments,
v content of the universe is approximately six times larger that part of its mass is in the form of subhalos.
6 than the baryonic one, in agreement with the observed
5 CDM models are characterized by their excess power
abundance of light elements [3] and the matter power
3 on small scales that leads to a logarithmic divergence of
spectruminferredfromgalaxyredshiftsurveys[4]. These
5 the linear density contrast at large wavenumbers ∆
0 observations involve very different physics, but unam- δρ/ρ ln(k). Recentanalyticalcalculationshaveprove≡d
5 biguously indicate that the Universe contains a signifi- ∝
that ∆ shows exponential damping for k > k =
0 cant amount of non-baryonic cold dark matter (CDM). cut
(1)/pc. The cut-offscalek isgivenby viscous(colli-
h/ The nature of CDM is presently unknown. However, Osional)processesbeforeandfcruete(collisionless)streaming
p weakly interacting massive particles (WIMPs) are re-
after kinetic decoupling at T = (10)MeV, both lead-
- garded as generic particle candidates for CDM, as they kd O
o ing to exponential damping of the linear CDM density
naturallyariseinextensionsofthestandardmodelofpar-
r contrast [9, 10, 11]. During the linear regime most of
t ticle physics. WIMPs are a particularly attractive CDM
s the statistical power typically goes in density contrasts
candidate,sincetheaveragemassdensityofastablerelic
a ∆withk k . Sok setsalsothetypicalscaleforthe
: fromthe electroweakscaleisexpectedtobeclosetocrit- ∼ cut cut
v ical[5]. AfurtherexcitingfeatureofWIMPsisthatthey firsthalos. that typically format a redshift zn =60±10
i (for the best fit WMAP matter density) [10, 11], when
X can be investigated in ongoing and future astrophysical
the mass variance σ = 1 on a comoving length scale
r direct [6] and indirect searches [7] and in upcoming lab-
a oratory experiments. R=O(1)pc.
The fate of these early minihalos in the non linear
Indirect CDM searches focus on measuring the dif- regime when they typically merge into larger halos, rep-
fuse flux of CDM annihilation products Φ ΦSUSY resenting higher levels in the hierarchy, can only be
γ
Φcosmo [8]. The particle physics dependence≡embedde×d followed through numerical experiments. The limited
inΦSUSY involvesthe WIMP’sannihilationcross-section dynamical range explored with currently available N-
and branching ratios as well as the final photon en- body codes makes it very challenging to perform nu-
ergyspectrumandcanbecalculatedfromtheunderlying merical experiments with a resolution as high as k−1 on
cut
WIMP field theory. In this work we assume the nearly a computational box large enough to guarantee statis-
mass independent best value for the annihilation cross tical significance. Yet, [1] have recently simulated hi-
section of 2 10−26cm3s−1, which represents an upper erarchical clustering in CDM cosmologies up to a dy-
×
bound still allowing the neutralinos to be the dominant namical resolution k k in a small high resolution
res cut
∼
CDM component. The geometry dependence of the flux patch which is nested within a hierarchy of larger low
is contained in Φcosmo that is found by integrating the resolution regions. They find a steep halo mass func-
square of the neutralino mass density along the line–of– tion dn(M)/dln(M) M−1exp[ (M/Mcut)−32], with
sviigrhiatliazenddstthruecretuforreesrisepvreersyensteinngsimtivaexitmoatohfethpereDseMncdeeno-f M[10c−ut6,=10−54.7]M×⊙10w−h6ohs−e∝1Mex⊙tra∝polkact−u−it3oninfittshewmelalssthraatngoef
sityfield. Inthisworkwefocusontheannihilationsignal Galactic halos [12].
2
Since [1] stopped their experiment at z = 26 and We set A such that 10% of the MW mass (M =
MW
probed a small volume with a limited dynamical range, 1012M⊙) is distributed in subhalos with masses greater
nogeneralconsensusexistsonwhethertheseearlystruc- than 107M⊙ to match the results of [12]. As a result
tures survived within massive galactic halos until today about 53% of the dark mass within our galaxy is not
and what their mass function and distribution is. In- smoothly distributed but contained within 1.5 1016
deed,althoughtheirmassconcentrationisprobablylarge subhalos with masses larger than 10−6M⊙,∼corres×pond-
enough for them to survive the gravitational tides expe- ing to 100pc−3 halos in the solar neighborhood.
∼
rienced in the external region of the massive host halo The θ term in Eq. 1 takes into account the effect of
(see, however [13]), they could be torn into tidal stream gravitational tides which, according to the Roche crite-
by close encounters with individual stars in the galaxy rion, disrupt all halos within r (M) from the GC [27]
min
[14]. These issues could only be settled by simulating in an orbital period. At z = 0 r is an increasing
min
the gravitational clustering out to z = 0 on a volume function of the subhalo mass implying that no subhalos
large enough to overlap the results with those of other, survive within rmin(10−6M⊙) 200pc.
∼
highresolutionnumericalexperimentsofGalaxysizeha- In this work we wish to predict the annihilation sig-
los ([15, 16]), which is beyond current numerical limita- nal expected in a 100o 100o field of view (f.o.v.) with
tions. Yet, [1, 17] have suggested that these minihalos an angular resolution o×f ∆Ω = 10−5sr, matching those
might significantly contribute to the total annihilation plannedforthe GLASTexperiment,inboththeGCand
flux in our Galaxy. the anticenter(AC) directions. This requiresto evaluate
In this work we compute the expected γ-ray flux pro- the line–of–sight integral:
duced by a population of sub-Galactic halos under the
optimistic hypotheses of [1] that all minihalos of masses Φcosmo(ψ,θ)= dΩ′ ρ2(r(λ,ψ′))dλ(r,ψ′),
10−6M⊙ thatsurvivedgravitationaltidespopulatethe Z∆Ω(ψ,θ) Zl.o.s χ
≥
Galactic halo at z = 0, trace its mass, share the same (2)
self-similar cuspy density profile and have a steep mass where ψ is the angle–of–view from the GC, θ is
function M−1 up to 1010M⊙. It is worth stressing the angular resolution of the detector, ρχ(r) is the
∝ ≥
that our predictions represent an upper limit to the ex- mass density. The distance from the GC r is r =
pected photon flux and to its experimental detectability λ2+R⊙2 2λR⊙cosψ,λisthe distancefromthe ob-
that we will investigate for the case of a satellite-borne q −
experiment like GLAST [18]. serverand R⊙ =8.5kpcis thatof the Sun fromthe GC.
We evaluate of Eq. 2 in two steps. First, we nu-
Our analysis extends those of [15, 19, 20, 21, 22] since
merically integrate Eq. 2 in which ρ (r) is the sum of
weconsidersubhalosmuchlighterthan106M⊙ andsince χ
NFW profiles corresponding to all subhalos distributed
we use Monte Carlo techniques to explicitly account for
according to Eq. 1 along the l.o.s.. This gives the
thecontributionofverynearbyminihalostothetotalan-
average subhalo contribution to the Galactic annihila-
nihilation flux. The relevant properties of our minihalo
tion flux within 10−5sr along the direction (ψ,θ). We
population are: a steep mass function dn(M)/dln(M)
Mtha−t1tirnactehethraensgmeo[1o0th−6m,1a0s1s0]cMom⊙,paonsepnattiianl doiusrtrGibaultaiox∝ny fGouenVd2tchma−t6thkepcavsre,raogfescuobnhtarilbosutiinonthtoe Φracnosgmeo,10in−6uMnit⊙so<f
aanndd aforNaFlWl thmeassusbdheanlosist:yρpχro=fileρs[(2r3/]rfso)r−1b(o1th+trh/ersM)−W2, Mcarnesgahlsee<ss. t1oF06o1Mr0−⊙φ5i>sat42ψ×5o=10it−505dooamtanitndhaetteoGs4Co,×vetrh10etn−h6eslaoGtwalllyaarcdgteeicr-
where both the scale radius r and the scale density ρ
s s foreground accounting for neutralino annihilation in the
dependontheconcentrationparametercwhichisafunc-
tion of mass, redshift and the cosmologicalmodel. Since smooth Galactic halo of 4.7×1011M⊙.
To estimate the variance to the average flux we use
weaimatexploringthemostoptimisticscenarioforneu-
Eq. 2 to generate severalindependent Monte Carloreal-
tralinoannihilationwedonotconsiderheretheresultsof
izations of the closest and brightest minihalos. For each
some recent high resolution N-body experiments [25, 26]
subhalo mass, we only consider objects which are close
which suggest that halo density profiles near the center
enoughtoguaranteeΦcosmo >10−6GeV2cm−6kpcsr. If
have a continuously varying logarithmic slope, and thus
nosuchhaloexiststhenwestillMonteCarlogeneratethe
are significantly shallower than the cuspy NFW profile.
100 closest objects in that mass range, since we expect
In this work we assume the flat, ΛCDM “concordance”
the bigger fluxes to come from the closer halos.
modelandusethenumericalroutinesprovidedby[24]to
computec. Thesmallesthalosofmass10−6M⊙ turnout The contribution of nearby structures to the annihila-
tion flux can be appreciated from Fig.1 which shows the
to have c (40) at z =0.
∼O sky distribution of the annihilation signal in one of our
The previous assumption allows one to specify the
Monte Carlo realization in the direction of the GC.
number density of subhalos per unit mass at a distance
To compute the total annihilation signal from all sub-
r from the Galactic Center (GC):
Galactic halos we have followed the same procedure as
ρsh(M,r)=AM−2(r/rθsM(rW−)(r1m+inr(/MrsM))W)2M⊙−1kpc−3 [o2f0s]uabnhdalhoasvweigtehne1r0a6tMed⊙se<veMraslhM<on1te01C0Mar⊙lotroeacliozmatpiountes
(1) their contribution to the total flux.
3
FIG. 1: Sky map of the annihilation signal from nearby FIG. 3: Same as Fig.2 in thedirection of theAC.
subhalos of masses [10−6,106M⊙] contributing more than
Φcosmo =10−6GeV2cm−6kpcsr in a 100o×100o f.o.v. cen-
tered on theGC in one of ourMonte Carlo realization. MonteCarlorealizationswehavefoundthatthesubhalos
contribution to Φcosmo exceed the value of (10−3).
O
To make this statement more quantitative and to
also account for the possibility of detecting the γ-ray
annihilation line we have evaluated the sensitivity of
GLAST to the differentialspectrumofphotonsexpected
from DM annihilation, convolved with its energy reso-
lution ∆E=10%. We define the sensitivity σ(∆E) as
n (∆E)/ n (∆E) =
DM bkg
p
√T ǫ Aeff(E,θ)[dφDM/dEdΩ]dEdΩ
= δ ∆Ω ∆E γ γ .
√∆Ω R Aeff (E,θ)[dφ /dEdΩ]dEdΩ
qR∆EPbkg bkg bkg
whereT definestheeffectiveobservationtime,ǫ =0.7
δ ∆Ω
isthefractionofsignaleventswithintheoptimalsolidan-
gle ∆Ω corresponding to the angular resolution of 0.1◦,
and Aeff = 104cm2 is the effective detection area. We
optimistically assume that the photon and charged par-
FIG. 2: 3D view of the total Φcosmo contributed by subhalos ticles’ detection efficiencies ǫγ and ǫch are 100%, thus
and theGalactic foreground, in a 100o×100o f.o.v. centered we only consider galactic and extragalactic γ-ray back-
on the GC. The Galactic foreground is cut at the subhalos’ ground as it is extrapolated by EGRET data at lower
level. energies [28]. We simulated a continuous 5 years obser-
vationofapixelofourgridlocatedatψ =55o,assuming
that in that pixel the value of Φcosmo is the largestvalue
Figs. 2and3showtheexpectedcontributiontoΦcosmo found among all our Monte Carlo realizations.
accounting for both subhalos and Galactic foregroundin Wechoseaneutralinomassof100and300GeV,whose
the direction of the GC and the AC, respectively. As γ-lines would in principle be observable with GLAST.
expected, the Galactic foregroundis negligible in Fig. 3, The results are shown in Fig.4. The black curves, corre-
while it is dominating around the GC in Fig. 2. Note sponding to the left y-axis, show the sensitivity σ(∆E)
that the very prominent peak due to the Galactic fore- of GLAST as a function of E, for two different values of
groundattheGCpositionhasbeenartificiallytruncated the neutralino mass. The red curves, to be read on the
to appreciate the subhalos contribution. We estimate righty-axis,showthe expectedflux fromthe samepixel.
that Φcosmo =0.04GeV2cm−6kpcsr at the GC. It is evident that GLAST would hardly detect neither
Figs. 2and3alsoshowthateventhebiggestcontribu- continuum flux nor γ-lines from Galactic subhalos.
tiontoΦcosmo fromasubhaloiswellbelowthe (1)level Since it seems implausible to significantly increase
which, givenour best value of ΦSUSY, would beOrequired ΦSUSY,ourresultsconfirmsthoseof[17,19,20,21]show
for detection in the GLAST experiment. In fact, in no that currently planned, satellite-borne experiments such
4
the various dynamical disturbances that reduce the sub-
halosurvivalprobability,thepossibleexistenceofacutoff
scale 0.1k found [29] in the CDM power spectrum,
cut
∼
generated by acoustic oscillations with wavelength com-
parable to the size of the horizon at kinetic decoupling,
would decrease the expected annihilation signal, making
it our conclusions for subhalos more pessimistic. Unless,
of course, one adopts steeper density profiles that, how-
ever,arenotsupportedbyrecentnumericalexperiments.
Note that the γ-ray luminosity of our minihalos, which
is designed to match the predictionof [1], is significantly
smallerthan that of[17]; a difference thattraces backto
the large internal density of their minihalos.
Thepresenceofaminihalopopulationlikethatconsid-
eredinthisworkalsoenhancetheγ-rayfluxfromnearby
objects like M31. We estimate that, for a NFW profile,
thetotalΦcosmo duetoboththesmoothandthesubhalo
contributionwillnotexceedthevalueof5 10−4,making
×
FIG. 4: Left y axis (black): Experimental sensitivity of it impossible to detect.
GLASTtothephotonfluxfromDMannihilationcomingfrom
Recently, the HESS telescope has announced the
a subhalo at ψ ∼ 55o, with Φcosmo = 10−3GeV2cm−6kpcsr
serendipitous discovery of an unidentified extended TeV
for mχ = 100GeV (solid line) and 300 GeV (dashed-line). γ-ray source, with a total flux above 380 GeV of
Right y axis (red): Expected flux from the same subhalo as 10−11cm−2s−1 [30]. If explained in terms of the annih∼i-
observed by GLAST with an energy resolution of 10%.
lation of (10TeV) neutralinos, such a large flux could
O
only be accounted for by advocating a central density
asGLASTwillnotbeabletodetecttheannihilationsig- r−1.5, steeper than the NFW model. A prominent cen-
nal produced by Galactic subhalos. This is due to the tral spike might form around a supermassive black hole
fact that, as pointed out by [15], the total annihilation [31, 32] that, according to hierarchical models of galaxy
flux is dominated by massive Galactic subhalos rather formation[33],couldresideatthecenterofbothmassive
than by minihalos. A result which makes our conclusion Galactic and sub-Galactic halos.
insensitive to variations in the low-mass density cut-off, We acknowledge fruitful discussions with L.
in agreement with [22]. Bergstr¨om, D. Els¨asser, P. Faccioli, A.M. Green,
Allplausiblecosmologicalandastrophysicaleffectslike A. Lionetto, K. Mannheim, B. Moore, A. Morselli and
the existence ofa centralcorein the halo density profile, D.J. Schwarz.
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