Neutrino Constraints on the Dark Matter Total Annihilation Cross Section

0.24 MB·English

by  Hasan Yuksel

Neutrino Constraints on the Dark Matter Total Annihilation Cross Section
Hasan Yu¨ksel,1,2 Shunsaku Horiuchi,3 John F. Beacom,1,4,2 and Shin’ichiro Ando5
1Department of Physics, Ohio State University, Columbus, Ohio 43210
2Center for Cosmology and Astro-Particle Physics, Ohio State University, Columbus, Ohio 43210
3Department of Physics, School of Science, University of Tokyo, Tokyo 113-0033, Japan
4Department of Astronomy, Ohio State University, Columbus, Ohio 43210
5California Institute of Technology, Mail Code 130-33, Pasadena, CA 91125
(Dated: 17 December 2007)
In theindirect detection of dark matterthrough itsannihilation products, thesignals dependon
thesquareof thedark matterdensity,makingprecise knowledge of thedistribution of dark matter
intheUniversecriticalforrobustpredictions. Manystudieshavefocusedonregionswherethedark
matterdensityisgreatest, e.g., theGalactic Center,as well ason thecosmic signal arising from all
8
halos in the Universe. We focus on the signal arising from the whole Milky Way halo; this is less
0
0 sensitivetouncertaintiesinthedarkmatterdistribution,andespeciallyforflatterprofiles,thishalo
2 signalislargerthanthecosmicsignal. Weillustratethisbyconsideringadarkmattermodelinwhich
theprincipalannihilationproductsareneutrinos. SinceneutrinosaretheleastdetectableStandard
n
Model particles, a limit on their flux conservatively bounds the dark matter total self-annihilation
a
cross section from above. By using the Milky Way halo signal, we show that previous constraints
J
using the cosmic signal can be improved on by 1–2 orders of magnitude; dedicated experimental
1
analyses should beable toimprove both by an additional 1–2 orders of magnitude.
2

PACSnumbers: 95.35.+d,98.62.Gq,98.70.Vc,95.85.Ry
]
h
p
- I. INTRODUCTION In the Milky Way (MW), an attractive site for con-
o sideration is the GC, due to an expected increase in the
r
DM density towards the centers of gravitational poten-
st Dark matter, an invisible substance originally pro- tials [37, 38, 39], and possibly a spike aroundthe central
a posed by Zwicky in the 1930s to explain the mass-to-
[ blackhole[14,15,16]. However,theinnergradientofthe
light ratio of the Coma galaxy cluster [1], still evades
halo profile is the most uncertain part. Although simu-
3 revealing its true identity after many decades. Subse-
lations generally suggest a steep cusp towards the halo
v quent works have confirmed its pervasive existence, and
center, some observations, such as the high microlensing
6 its contribution to the critical energy density has been
optical depth, support much flatter profiles [40]. In fact,
9 measured to be Ω ≃ 0.3. The distribution of dark
1 χ thereisnodirectobservationalevidencethatanynearby
matter (DM) in the universe has also been thoroughly
0 galaxyhasacuspedDMprofile. Thesmallspatialresolu-
studied on a wide range of scales. Many DM candidates
. tionneededtosettlethedebatehasnotyetbeenreached
7 have been proposed, from axions to sterile neutrinos to
0 in simulations. Another problem is astrophysical back-
weakly interacting massive particles (WIMPs); see re-
7 grounds. For example, astrophysical gamma-ray sources
cent reviews [2, 3, 4]. WIMPs are especially popular
0 in the GC may limit the DM parameter space that can
since they are among the best theoretically motivated
: beprobedwithgammarays[41]. Soitmaybepreferable
v non-baryonicDMcandidatesandalsocapableofproduc-
i to study other regionsof the Milky Way, where both the
X ing the correct relic density. They can be detected indi-
signal and backgrounds are more certain.
rectly through the astrophysical signatures of their an-
r
a nihilation products, detected directly in low background Inthis study, DM annihilationin the whole MW halo,
experiments underground, and produced at particle ac- as opposed to just the GC, is our primary focus. While
celerators. the GC signal strongly depends on the uncertain cuspi-
ness of the underlying halo profile, the signal averaged
Forindirectdetection,theDMdistributionisessential
overlargerregionsof the halo is much less dependent on
for predicting the detectability of the signals, as the an-
the details aslongasthe density normalizationis chosen
nihilation rate depends on the annihilation cross section
consistentlywithobserveddata,e.g.,rotationcurves[42].
andthesquareoftheDMnumberdensity(the DMmass
This has been emphasized by e.g., Refs. [43, 44, 45].
density divided by the DM mass). The Galactic Center
(GC) [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18], Using the annihilation signal arising from the halo
intermediate mass black holes [19, 20, 21, 22, 23], dwarf means accepting a lower signal intensity, but the in-
satellitegalaxies[24,25,26],andnearbygalaxies[12,27], tensity of the astrophysical backgrounds is also lower.
i.e., places where the dark matter is strongly concen- The halo signal is less subject to theoretical uncertain-
trated, have been considered in the search for DM sig- ties compared to the GC or the cosmic signal, and can
nals. Additionally, the diffuse cosmic signal due to provide more robust results. Moreover, regardless of
all distant concentrations of DM has been utilized as the parametrization,the halo alwaysprovides a minimal
well [21, 28, 29, 30, 31, 32, 33, 34, 35, 36]. isotropic contribution that cannot be distinguished from
2
any truly diffuse cosmic signal. The halo isotropic com- 104
ponent is increasingly dominant over the cosmic signal
for flatter halo profiles. 3
10
In indirect detection, regardless of the identity of the
DM particle, one would expect the most stringent con- 102
straint on the annihilation cross section from the most 3 ]
detectable annihilation products, and such gamma rays -m 1
c 10
havelong been sought. However,the branchingratios to V
produce gamma rays are small and uncertain, making it Ge 0
impossibleto setacertainlimitonthe totalannihilation [ 10
cross section. Since neutrinos are much harder to de- ρ
tect, one may naively expect that they cannot yield any 10-1
meaningful constraints. However, this is not the case.
-2
While both the gamma ray and neutrino flux predic- 10
tions are very much dependent on WIMP model param-
eters, one can avoid these complications by adopting a 10-3
-2 -1 0 1 2
more conservative perspective, following Beacom, Bell 10 10 10 10 10
and Mack (BBM) [46]. If we assume that only Standard r [ kpc ]
Model(SM) finalstates areproduced,e.g.,purely sterile
neutrinosarenotconsidered,thenneutrinosandantineu- FIG. 1: The dark matter density versus radius for the three
trinos arethe leastdetectable finalstates. Anything else profiles considered (Moore, NFW and Kravtsov in order of
will inevitably produce the much more visible gamma dotted, dashed and solid lines), based on Eq. (1). The nor-
malizations are chosen to match the large scale properties of
rays,leading to a stronger cross section limit. Thus, one
theMilkyWay. Theverticalgraylineindicatesthesolarcircle
can obtain a stringent upper limit on the total annihi-
lation cross section by assuming that only neutrinos are distance,Rsc ≃8.5kpc. SeeTableIfortheotherparameters.
producedasfinalstates,andcomparingtheexpectedsig-
naltothewell-measuredandmodeledfluxofatmospheric
neutrinos, which is the dominant background. II. ANNIHILATING DARK MATTER MODEL
We focus on the importance of the annihilation sig-
nal arising from the halo in the context of obtaining Cold dark matter simulations show that DM assem-
model-independentboundsontheDMannihilationcross bles hierarchically in halos and successfully predicts the
section, as described above. For very large annihilation formation of large scale structure. The general form
crosssections,asinRef.[47],haloswouldbesignificantly of the halo is expected to be independent of the total
modified. BBMhaveshownthatsuchlargecrosssections mass enclosed over many orders of magnitude. A useful
are not possible [46], since then the cosmic signal, which parametrizationthat fits the results ofthe simulationsis
depends on the time-integrated annihilation rate of all
ρ
0
halos,cannotbeaccommodatedincomparisontotheat- ρ(r)= , (1)
(r/r )γ[1+(r/r )α](β−γ)/α
mospheric neutrino spectrum. In this study, we instead s s
use the MW halo signal, which is generally larger and
where among the variables (α,β,γ,r ), γ is the inner
s
more certain, as we show below, to set an even stronger
cusp index and r the scale radius. In Fig. 1, we plot
s
limit on total annihilation cross section.
some commonly used profiles, the Navarro-Frenk-White
We firstsummarizethehaloprofilesandthe modelfor (NFW) [38], Moore[37], andKravtsov[39] profiles,with
annihilating DM in the halo and in cosmic sources. We the corresponding parameterslisted in Table I. The nor-
also identify the various components of the annihilation malizationsarechosensothatthemasscontainedwithin
signalarisingfromthehalo. Toprovidethemostgeneral the solar circle (R = 8.5kpc) provides the appropriate
sc
results, we consider various profile shapes for the halo DM contribution to the local rotational curves (see [8]
together with a dark matter model in which neutrinos for details of a similar analysis). This yields the local
are the only annihilation products. Next, we compare DM density ρ (R ) = 0.3 GeVcm−3 for the NFW
NFW sc
the neutrino spectrum arising from annihilations to the profile; for the others, see Table I.
atmospheric neutrino spectrum, and arrive at our con- Ingeneral,theprofilesagreeonlargerscales. However,
straintsonthetotalannihilationcrosssection. Ourstudy the profiles in the inner regions are more uncertain, due
showsthateventhefull-skyhalosignalwouldleadtoover to the spatial resolution limit of the simulations. Physi-
an order of magnitude improvement on the cosmic sig- cally,baryonstypicallydominatetheseregions,andtheir
nal limit on the cross section. If the broad enhancement impact has not yet been fully taken into account in the
towards the GC direction is taken into account, further simulations. Theeffectofbaryonsiscomplicatedandcan
improvement is possible while remaining secure with re- increasetheinnercuspstrength[48,49]aswellasprovide
spect to the halo profile uncertainties. a mechanism for momentum transfer to DM particles,
3
∆Ω / 4π
which works to flatten cusps [50]. With these points in
-7 -6 -5 -4 -3 -2
mind,wechoosethehaloprofilesshowninFig.1toillus- 10 10 10 10 10 10 0.1 0.3 0.5 0.7 0.9 1
tratetheimpactofvariationsinthehaloparametrization 6
10
on the signal predictions.
5
10
A. Annihilations in the Halo
4
10
The calculation of the spectrum of DM annihilation
Ω
products fromthe halois wellestablished(e.g., Ref.[8]). J∆ 103
For annihilations, the intensity (number flux per solid ),
ψ
angle) at an angle ψ with respect to the GC direction is
( 2
proportional to the line of sight integration of the DM J 10
density squared, or,
1
10
1 ℓmax
J(ψ)= ρ2( R2 −2lR cosψ+l2)dℓ,
Rscρ2sc Z0 p sc sc 100
(2)
which we choose to normalize at the solar circle (R =
sc -1
8.5kpc) with ρsc = 0.3 GeV cm−3. Note that the pref- 100.03o0.1o0.3o 1o 3o 10o 30ψo 60o 90o 120o 180o
actor 1/(R ρ2 ) is an arbitrary scaling that is used to
sc sc
make J dimensionless regardless of the underlying DM
density profile. The upper limit of the integration, FIG. 2: Line of sight integration J(ψ) as a function of the
pointing angle ψ (bottom axis) with respect to the Galac-
ticCenter direction for thethreedifferent profiles considered
ℓ = (R2 −sin2ψR2 )+R cosψ, (3)
max q MW sc sc (Moore, NFW and Kravtsov in order of dotted, dashed and
solid thin lines). Its average, J∆Ω, inside a cone with half
dependsontheadoptedsizeofthehalo,R . However,
MW angle ψ around the GC as a function of the visible fraction
contributions beyond the scale radius, typically about of the whole sky, ∆Ω/4π = (1−cosψ)/2 (top axis), is also
20–30 kpc, are negligible. It is also useful to define the presented (thick lines). Note that the left (right) side of the
averageof J in a cone with half-angle ψ around the GC graph is presented in log (linear) scale in ∆Ω/4π.
that spans a field of view of ∆Ω=2π(1−cosψ):
1 1
J = J(ψ′)2πd(cosψ′). (4) However, while this takes advantage of the higher DM
∆Ω ∆ΩZcosψ densities aroundthe GC, it alsostrongly depends onthe
chosen profile. As shown in Fig. 2, the differences in the
Then the average intensity of DM annihilation products
intensity due to different choices of profile can be orders
from the field of view can be cast as
of magnitude at small angles. We therefore focus on the
◦
dΦ hσ vi R ρ2 dN signal arising within angles ψ ≃ 30 or larger around
dE∆Ω = A2 J∆Ω 4πscms2c dE, (5) the GC. This is motivated for three reasons. First, the
χ enhancement J is much less sensitive to the chosen
∆Ω
where dN/dE is the spectrum of annihilation products profile for larger ψ. Second, the viewing angle ψ to con-
and m is the assumed mass of the DM particle. The sider depends on the particle considered, and for neutri-
χ
factor1/2accountsforDMbeingitsownantiparticleand nos,theangularresolutionislimitedbythekinematicsof
◦
1/4πisforisotropicemission. Thethermalaverageofthe the detection reactions to be δθ(E)≃30 × [GeV]/E.
annihilationrateisproportionaltohσ vi,theproductof Thus,itisimpracticaltoconsiderthearrivaldpirectionfor
A
the annihilation cross section and the relative velocity. neutrinos less energetic than several GeV. Third, choos-
In Fig. 2, we show the behavior of J(ψ) (thin lines) ing a large field of view ensures that there are adequate
and J (thick lines), as functions of ψ and ∆Ω/4π, re- statistics for the detection of the signaland background.
∆Ω
spectively,forthethreerepresentativehaloprofiles. Note We now define three signals correspondingto different
that J diverges for very cuspy profiles. This cusp may components of the halo:
be an artifact of simulations, which cannot resolve small
spatial scales. To avoid such numerical divergences, we • Halo Angular: We consider a 30◦ half-angle cone
put in a flat core for all the profiles in at the innermost for neutrinos more energetic than 10 GeV and a
◦
0.1 , which corresponds to ≃ 0.015 kpc; our results are larger half-angle of ≃3×δθ(E) for lower energies.
not sensitive to how the inner profile is regulated. A conservativevalue for this Halo Angular compo-
◦
One can expect very large enhancements for small an- nent inside ψ ≃ 30 is J ≃ 25 (below 10 GeV,
Ang
gles ψ around the GC. Many studies have therefore fo- whenlargerangularregionsareused,thiswouldbe
cused on emission from the few degrees around the GC. smaller).
4
• Halo Average: When a large field of view ∆Ω is
TABLE I: The parameters of Eq. (1) for the three profiles
considered, the average J is much less sensitive
tJotheinchFoigse.n2.pWroefildee,fiansesht∆hoΩweHnablyotAhveedraiffgeer,eJncesi≃n caotnssoildaerrceidr.clSe,caρl(eRrsacd),iuiss,inrsu,nisitisno[fk[pGce]Vancdmt−h3e].noErsmtiamliaztaetsioonf
∆Ω Ave the various enhancement factors, J, for the halo (as defined
◦
5,asacanonicalvalueforthewholesky(ψ =180 ).
in the text) and the normalization of the cosmic intensity
Note that the differences due to different choices multiplier,f0,inunitsof[105]arealso summarized. Thelast
of profiles from this canonical value are small, less rowlistscanonicalvaluesthatweusetoderiveourconstraints
than a factor of 2. on the DMtotal annihilation cross section.
• Halo Isotropic: Another key point is that J(ψ)
never vanishes, even in the anti-GC direction(ψ = α β γ rs ρ(Rsc) JAng JAve JIso f0
180◦),duetoaminimalisotropiccomponentofthe Moore 1.5 3 1.5 28 0.27 102 8 0.3 5
halosignalthatariseswithinourimmediate neigh- NFW 1 3 1 20 0.3 26 3 0.4 0.5
borhood. Thisispresentforallprofilesandcannot Kravtsov 2 3 0.4 10 0.37 13 2.6 0.55 0.2
be differentiated from the truly cosmic signal, ex-
Canonical 25 5 0.5 1
cept by its spectrum. We define this minimal com-
ponent as Halo Isotropic, J ≃ 0.5, which yields
Iso
the most robust constraints.
where f sets the overallnormalization. This normaliza-
0
The values for these three components are summarized
tion is determined by the underlying halo profile, con-
in Table I. Finally, halos may have substructure which
centration parameter, and inclusion/exclusion of either
can contribute an additional boost to DM annihilation
smallerhalosorsubhalos,anditsdependenceonthehalo
signals, e.g., Refs. [45, 51, 52]. To be conservative, we
profile alone can be seen in Table I when the other pa-
donotattempttomodelanysubstructure,butnotethat
rameters are fixed. The uncertainties of the halo signal
it would only enhance all of the annihilation signals and
(including the inner cusp profile, whether a spike orcore
hence improve the constraints that we present below.
hasformed,andsubstructure),areimportantforthecos-
mic signal predictions as well. The cosmological cluster-
ingofhalos,halomassfunctionandlowermasscutoffare
B. Cosmic Annihilations
additional uncertainties associated with the cosmic sig-
nal. Thus, the halo signal is overall less uncertain, only
The calculation of the diffuse cosmic DM annihilation
factors of a few, compared to the cosmic signal, which
signal has been thoroughly discussed in the literature
varies by more than an order of magnitude for different
(e.g.,Ref.[29]). Theintensityofthecosmicdiffusesignal
profiles; compare the entries in Table I.
is
The ratio of the DM annihilation halo signal to the
dΦ hσ vi Ω2ρ2 c dN(E′)(1+z)3f(z) cosmic signal can be approximated as
A χ c
= dz, (6)
dE 2 4πm2 H Z dE′ h(z)
χ 0 ΦH J R ρ2 J
swithye,rHe ρc==705k.m3 s×−11M0−p6c−G1eVisctmhe−H3 uisbbtlheecocnristtiacanlt,daennd- Φ∆CΩ ∼ cH∆0−Ω1Ωs2χcρ2csfc0 ∼105 f∆0Ω, (8)
0
h(z)=[(1+z)3Ω +Ω ]1/2 with Ω =0.3 (ignoring the
χ Λ χ which is independent of hσ vi and m . Now, using the
small baryoniccontribution) and Ω =0.7. The original A χ
Λ HaloIsotropic signal(J ≃0.5)forillustration,thisra-
spectrum of annihilation products is redshifted through Iso
tio will be close to unity for f ≃5×104 (coincidentally,
E′ = (1+z)E, yielding dN(E′)/dE′. For gamma rays 0
equal to the NFW value as reported in Table I). There-
abovea few TeV, pair production with the diffuse extra-
fore, even the Halo Isotropic enhancement is significant.
galactic infrared and optical photon backgrounds is an
Itscontributiontotheapparentlydiffuse signalobserved
important loss mechanism. With neutrinos, such atten-
atEarthis comparableto thatofthe truly cosmic signal
uation considerations are unnecessary. (Attenuation in
for profiles as flat as NFW, and it exceeds the cosmic
Earthwouldbeimportantforneutrinosaboveabout100
signal for profiles flatter than the NFW. This was also
TeV,e.g.,Ref.[54],mostlybeyondourrangeofinterest.)
pointed out in Ref. [34], specifically for the NFW profile
Themostrelevantfactoristhe cosmicsourceintensity
with substructures.
multiplier, f(z), that reflects the formation history of
The flatter profiles are well-motivated both theoreti-
halos. Thisisadecreasingfunctionofincreasingredshift,
cally and observationally, and hence the Halo Isotropic
and although the redshift dependence is fairly universal,
canbeanimportantcomponent. Whilesimulationstend
thenormalizationvariesquiteconsiderably,bymorethan
toshowthe presenceofamildcusp,therearealsoobser-
an order of magnitude for different profiles [33]. The
vations indicating otherwise, motivating a flatter, cored
impact of its evolution on the predicted cosmic signal
profile [53]. It is not known whether a core is a gen-
is milder once the overall normalization is determined.
eral feature of the halo structure. In contrast to flatter
Thus we parametrize it with a simple fitting form
profiles, more cuspy profiles like the Moore profile yield
f(z)=f ×100.9(exp[−0.9z]−1)−0.16z, (7) much larger fluxes for both the Halo Average and the
0
5
cosmic signal, and then the Halo Isotropic will be rela- 10-3
tively insignificant. In our calculations below, we use a
fairly large value of f ≃ 105 to be conservative in com-
0
paringconstraints thatcanbe obtainedfrom the haloor
cosmic annihilations. It is unlikely that f0 can be any ]
liasrsgiegrn,ifiucnalnests, wcohnitcrhibwutililonbsoofrsotmthtehehahloalosigsnuablstarsucwtuerlle, -1-1ssr10-4 MW Halo + Atm.
not significantly modifying their relative strength. Con- -2m Cos
sstmraailnletrsff0rovmalutehse.halo will be even more important for E [ c mic + Atm.
Whileweuseneutrinosforconstrainingthetotalanni- Φ/d -5
hilation crosssection, the gamma-rayflux has been used d10
in many past studies. In this regard, a recent study by E
Ando[33],whichcomparedtheDMannihilationgamma-
raysignalfromtheGCtothecosmicsignalisofinterest.
Atmospheric Neutrinos
It concluded that under the assumptions that annihila-
tions account for the gamma ray flux from the GC and -6
10
that halo profiles are universal, then annihilations can- 20 50 100 200
E [ GeV ]
not be the dominant component of the isotropic extra-
galactic gamma ray background. That study dealt with
halos at least as steep as NFW; the Halo Isotropic, on FIG. 3: The atmospheric neutrino spectrum (νµ +ν¯µ) and
theexpectedincrease in thetotal received intensityfrom the
the other hand, is most interesting for flatter profiles, as
annihilationsofa100GeVDMparticle. Whilethehalosignal
we have shown. The Halo Isotropic would increase the
issharplypeakedinanarrowbandofenergy,thecosmicsignal
‘apparently’ (the cosmic signal plus the isotropic halo
spreadsover awider energy range. To defineupperlimits on
component) extragalactic gamma ray background, with-
thecross section, in each case we use a (different, see Fig. 4)
out violating the constraints placed using the GC data. cross section such that the annihilation signal would double
thetotal received intensity in thedisplayed energy ranges.
III. NEUTRINO CONSTRAINTS
bound on the total annihilation cross section using neu-
To obtain the most robust limits on the total annihi- trinos. The atmospheric neutrino spectrum (specifically,
lation cross section for dark matter, we assume that an- νµ + ν¯µ) is derived from measurements by the Fr´ejus,
nihilations produce only neutrinos (the least detectable Super-Kamiokande and AMANDA detectors, for which
known particles) and compare the resultant neutrino data are available up to 105 GeV [57]. The primary
signal to the atmospheric neutrino measurements. We source is the decay of pions and kaons produced by cos-
adopted a simple model in which dark matter particles mic ray collisions with the atmosphere. While the in-
annihilateintopairsofneutrinos,χ+χ→ν¯+ν,andthe tensities depend on zenith angle, we adopted an average
spectrum of the neutrinos per flavoris a monochromatic valuewhichwillsufficeforourpurposes(seeRef.[46]for
line with dN /dE = 2δ(E−m ), where m is the mass details). In the full energy range considered, and in fact
ν 3 χ χ
of the dark matter particle. The prefactor 2/3arisesun- to higher energies, all of the data are reported as being
der the assumption that 2 neutrinos are produced per consistent with the theoretically expected flux and en-
annihilated DM pair and that all neutrino flavors are ergyspectrumshapeforatmosphericneutrinos. Thereis
equally populated (either in production or through neu- no evidence of any other signals,e.g., from astrophysical
trino mixing). This delta function is regularized by the sources.
redshift integration for the cosmic signal. For the sake The DM annihilation signals are calculated using a
of a simple graphical representation in Fig. 3, we used fiducial DM mass of m = 100 GeV (f ≃ 105 for the
χ 0
a narrow Gaussian (width ǫ = mχ/20) to represent the cosmic signal and JIso ≃ 0.5 for the Halo Isotropic sig-
line signal. nal) and are superimposed on the atmospheric neutrino
Strictlyspeaking,itisnotpossibletohaveonlyneutri- spectrum (per flavor, using ν +ν¯ ). Since the halo sig-
µ µ
nosinthefinalstate,duetoelectroweakradiativecorrec- nal is sharply peaked, we chose an energy bin width of
tions that lead to Z and W bremsstrahlung [55]. While ∆log E = 0.3 around E = m to compare it to the
10 χ
these corrections do not significantly affect our neutrino atmospheric neutrinos, require it to double the total re-
flux calculations, the vector-boson decay chains do lead ceived intensity in this energy bin, and adjust the cross
to gamma-ray fluxes. In turn, these provide a new way sectionaccordingly. The additionalsmearingdue to red-
to model-independently limit the DM total annihilation shiftingnecessitatesalargerbinwidthof∆log E =0.5
10
cross section with results comparable to those obtained below E = m for the cosmic signal. These choices are
χ
with the cosmic neutrino fluxes [56]. withinthe energyresolutionlimits ofthe neutrinodetec-
In Fig. 3, we illustrate how we set our conservative tors [46, 57].
6
The crosssectionlimits obtainedfromthe aboveanal- 10-16
ysisarepresentedinFig.4asafunctionoftheDMmass.
Weshowresultsderivedusingthreedifferentcomponents
of the halo: the Halo Angular, the Halo Average and 10-18
the Halo Isotropic (shaded regions in order from lighter
to darker, with each also excluding all larger cross sec- ]
1
tion values), and also the cosmic diffuse signal (dotted 3 -s 10-20
m MW Halo Isotropic
line). The enhancement factors used in each case are
c
[
listed in Table I. Any larger cross section would pro- > MW Halo Average
duce too much intensity and cannot be accommodated v -22
A10 MW Halo Angular
by the data. We also show the unitarity bound (dot- σ
<
dashed line) [46, 58, 59], and the range of cross sections
for which DM annihilation may flatten cusps (dashed
-24
10
line) [46, 47]; crosssectionsabovethe lines areexcluded.
The natural scale of the DM annihilation cross section
(hatched region at the bottom) is shown for a thermal Natural Scale
-26
relic. However, larger cross sections (not exceeding the 10 -1 0 1 2 3 4 5
10 10 10 10 10 10 10
present limits) are possible, e.g., Ref. [47], if dark mat-
m [GeV]
ter is produced non-thermally or acquires mass only in χ
the late universe. (For such nonstandard dark matter
scenarios, it is also possible for the DM to have a large FIG. 4: Constraints on the DM total self-annihilation cross
section from various components of the Milky Way halo
scatteringcrosssection with baryons,thoughthis is now
(shaded regions excluded). The constraints from the cos-
strongly constrained, e.g., Refs. [60].)
mic signal (dotted line) can be compared to that of theHalo
TheHaloIsotropic component,whichappearsinalldi-
Isotropic (dark shaded) component. The successive improve-
rections,isnotdistinguishable(apartfromitsspectrum) ments of the Halo Average (medium shaded) and Halo An-
from the cosmic signal, and provides the most robust gular (light shaded) components can improve on the cosmic
constraint. We also consider the Halo Average and Halo constraint by 1–2 orders of magnitude. The unitarity bound
Angular componentsthatarerelativelymoredirectional, (dot-dashed line) and the cross sections for which annihila-
yettheycanimproveonthe cosmicconstraintby1–2or- tions flatten the cusps of DM halos (dashed-line) are also
ders of magnitude due to their larger signal intensities. shown; see the text.
If the inner density profile were assumed to be known,
a greater enhancement in the neutrino signal could be
tectable”maynotbealwaysfullyapplicableforthe
possible by restricting to a smaller angular region, as in
cosmic signal (the halo signal will still be present).
Ref. [18]. The actual neutrino experiments have differ-
entexposurestodifferentpartsofthehalo,whichshould
The neutrino limits derived from the halo signal in this
be takenintoaccountinamorethoroughanalysis. Thus
studynotonlyimproveonthepreviouslimitderivedfrom
ouractualconstraintthatisindicatedbythedataismost
the cosmic signal, but also extend their applicability.
faithfully represented by the Halo Average.
Several advantages of the halo signal over the cosmic
signal can be summarized as follows:
IV. CONCLUSIONS
• While both suffer from uncertainties such as the
Canneutrinostrulybetheonlyfinalstate? Regardless
concentrationparameterandtheshapeofthehalo,
ofthe answer,they canyield the mostconservativelimit
the halo signal on large scales is overall more cer-
ontheDMtotalself-annihilationcrosssection[46]. Neu-
tain, as noted, and shown in Table I.
trinos are the least detectable particles of the Standard
• The isotropic component of the halo signal is es- Modelandallotherfinalstatesproducemorevisiblesig-
pecially important for flatter profiles, for which it natures. Thus a limit on their flux (assuming DM only
dominates over any truly cosmic signal. For cuspy annihilates into neutrinos)conservativelybounds the to-
profiles,theHaloAngular wouldbeevenmorecon- tal annihilation cross section of dark matter. We focus
straining than displayed in our Fig. 4. on the importance of the DM annihilation signal aris-
ing from the halo, while BBM used the truly cosmic
• The cosmic signal is broadened in energy by red- DM annihilation signal (for decaying DM scenarios see
shifting, making it harder to identify over the Ref. [61] and references therein). We compare the ex-
smoothly varying atmospheric neutrino spectrum. pectedspectra ofthe neutrinosfromannihilationsto the
well-measuredatmosphericneutrinospectrumandarrive
• GammaraysfromcosmicDMannihilationsareat- at our constraints on the DM self annihilation cross-
tenuated at high energies, thus the statement that section. We show that, by using the halo signal, the
“anything other than neutrinos will be more de- previous bounds from the cosmic signal are improvedon
7
by 1–2 orders of magnitude. vative. The atmospheric neutrino background has been
This illustratesthe pointthatourintermediateresults measured with high statistics over six orders of magni-
are more generally applicable than just for neutrinos. tude in energy, and generally, only much smaller per-
Thehalosignalshaveonlyminormodeldependencecom- turbations would be allowed. Together with the other
paredtotheGCandcosmicsignals,andalsotheycanbe strategiesforimprovingsensitivity notedin Ref. [46], we
significantly larger than the cosmic signals, particularly expect that dedicated analyses will lead to much more
for flatter profiles. These results will also be useful for stringent limits than estimated here.
studies with gamma rays. In the coming age of near-term and proposed super-
An additional enhancement due to possible sub- sized detectors, like GLAST, IceCube, LHC and Hyper-
structureofthe darkmatter ordedicatedanalysesofthe Kamiokande,togetherwithlowbackgroundunderground
data[46]maybringthisimprovementupto2–4ordersof facilitieswithunprecedentedprecision,thedaysofDMas
magnitude. Thismayturnneutrinosintosurprisinglyef- anelusiveandhiddensubstancemayfinallybecomingto
fective toolsforexploringthe fullparameterspaceofthe a conclusion. Neutrinos may play a key role in unveiling
totalannihilationcrosssectionandmassoftheDM,per- the true identity of the dark matter. We have demon-
hapseventestingthecross-sectionscaleofthermalrelics. strated the excellent prospects of neutrino detectors as
We emphasize that in the most interesting mass range the largest but most conservative tools to constrain the
(for lower masses, see Ref. [62]), the cosmic and halo DM total annihilation cross section and mass.
neutrino constraints are already significantly improving
on the unitarity bound [58, 59]. Our bounds are espe-
cially useful at energies > 100 GeV in which there are
Acknowledgments
no gamma-ray data on large angular scales, whereas the
neutrino data go to >100 TeV.
In the short term, we strongly encourage dedicated We thank N. Bell, M. Kamionkowski, M. Kistler,
analyses of these halo signals by the Super-Kamiokande G. Mack, E. Rozo, W. Wada, and C. Watson for help-
and AMANDA/IceCube collaborations. Our require- ful comments. HY and JFB are supported by NSF CA-
ment that the DM neutrino signal be 100% as large as REERGrantNo.PHY-0547102toJFB,andbyCCAPP
the atmospheric neutrino background in specified and at the Ohio State University. SA is supported by the
relatively large energy and angular ranges is too conser- Sherman Fairchild Foundation.
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