Astrophysical inputs on the SUSY dark matter annihilation detectability

0.18 MB·English

by  Francisco Prada

APS/123-QED
Astrophysical inputs on the SUSY dark matter annihilation detectability
F. Prada1, A. Klypin2, J. Flix3, M. Mart´ınez3 and E. Simonneau4
1 Ram´on y Cajal Fellow, Instituto de Astrof´ısica de Andaluc´ıa (CSIC), E-18008 Granada, Spain
2 Department of Astronomy, New Mexico State University, Las Cruces NM 88003-8001, USA
3 Institut de F´ısica D’Altes Energies, Universitat Autonoma, E-08193 Barcelona, Spain
4 Institut d’Astrophysique de Paris, CNRS, 75014 Paris, France
(Dated: January 8, 2004)
If dark matter (DM), which is considered to constitute most of the mass of galaxies, is made of
supersymmetric(SUSY)particles,thecentersofgalaxies shouldemitγ-raysproducedbytheirself-
4 annihilation. Wepresentaccurateestimatesofcontinuumγ-rayfluxesduetoneutralinoannihilation
0 inthecentralregionsoftheMilkyWay. WeusedetailedmodelsofourGalaxy,whichsatisfyavailable
0 observationaldata,andincludesomeimportantphysicalprocesses,whichwerepreviouslyneglected.
2 Ourmodelspredictthatspatiallyextendedannihilationsignalshouldbedetectedathighconfidence
levelsbyincomingexperimentsassumingthatneutralinosmakeupmostoftheDMintheUniverse
n
and that they annihilate according to current SUSYmodels.
a
J
PACSnumbers: 98.80.-k,98.35.Ce,98.35Gi,95.35.+d,14.80.Ly
3
2
1 ofTImheargeinisgaAntminocsrpeahseirnicg ChˇoepreentkhoavtTtheleesnceowpesge(nIeArCatTiosn) YSUS= N2γmhσ2vi, U(Ψ0)=Z J(Ψ)B(Ω)dΩ,
v χ
would detect in the very near future the γ-ray signal
2
1 coming from the annihilation products of the SUSY DM where the factor YSUS (back-spelled SUSY) depends
5 in galaxy halos (e.g., [1, 2, 3, 4]). The success of such only on the physics of annihilating particles and all
1 a detection in competition with other indirect or direct the astrophysical properties (such as the DM distri-
0 experiments including accelerators will solve one of the bution and geometry considerations) appear only in
4
most fundamental questions in Astrophysics and Parti- the factor U(Ψ ). This factor also accounts for the
0
0
cle Physics: the nature of the dark matter. The light- beam smearing, where J(Ψ) = ρ2 (r)dl, dl =
/ l.o.s dm
h est supersymmetric particle (LSP) has been proposed to rdr/ r2 d2 sin2Ψ,isthe integRraloftheline-of-sight
p be a suitable candidate for the non-baryonic cold DM ± q − ⊙
- of the square of the DM density along the direction Ψ,
([5, 6], see also [7, 8] for a review). The LSP is stable
o
and B(Ω)dΩ is the Gaussian beam of the telescope:
r in SUSY models where R-parity is conserved [9, 10, 11]
t
s and its annihilation cross section and mass has the ap-
a propriate relic densities [8, 12] in the range allowed by B(Ω)dΩ=exp θ2 sinθdθdϕ. (2)
v: WMAP, i.e. 0.095 < ΩCDMh2 < 0.129 [13]. We focus (cid:20)−2σt2(cid:21)
i in the Minimal Supersymmetric extension of the Stan-
X The angles θ and ϕ are related with the direction of ob-
dard Model of particle physics (MSSM) where the LSP
r istheneutralino(χ). Newupperlimitsontheneutralino servation Ψ0 and the line-of-sight angle Ψ by cosΨ =
a
cosΨ cosθ+sinΨ sinθcosϕ. We have assumed spher-
mass (m ) havebeen estimateddue to the constrainson 0 0
χ
the neutralino relic densities Ω h2 provided by WMAP; ical symmetry for the DM particles around the Galactic
χ
Center and that the observer is located in the Calactic
m < 1500GeV based on the MSSM including mini-
χ
mal supergravity (mSUGRA) [12, 14]. A lower limit of equatorial plane at a distance d⊙ (here 8.0 kpc).
m 100GeV has been set by the accelerators[15]. The factor YSUS/4π represents the isotropic proba-
χ
∼ bility of γ-ray production per unit of DM density. It
The number of neutralino annihilations in galaxy ha-
can be determined for any SUSY model given the neu-
los and therefore the expected gamma signal arriving at
tralino mass m , the number of continuum γ-ray pho-
χ
the Earthdepends notonlyonthe adoptedSUSYmodel
tons N emitted per annihilation, with energyabove the
γ
but also strongly depends on the DM density ρ (r).
dm IACT energy threshold (E ), and the thermally aver-
th
This is why the central region r < 200pc of the Milky
age cross section σv of the DM particles. We can
Way, where the density is the largest, is the favorite site h i
then estimate a YSUS parameter range, given a neu-
to search for this signal. The expected total number of
tralino mass interval of 100 1500GeV, and a cross
continuum γ-ray photons receivedper unit time and per section σv interval of 5 1−0−27 3 10−26 cm3s−1
unit area, from a circular aperture on the sky of width h i × − ×
obtained for a sample of MSSM models computed in
σ (the resolution of the telescope) observing at a given
t [4, 21]with relic densities inagreementwiththe WMAP
direction Ψ relative to the center of the Milky Way can
0 constrains. The number of continuum gamma photons
be written as:
produced per annihilation N is obtained by integrat-
γ
ing the continuum spectrum given by the decay of π0
1 mesons produced in the fragmentation of quarks. It
F(E >Eth)= YSUS U(Ψ0), (1) can be well approximated by the eq.(18) in [3], i.e.
4π ·
2
N =5/6x3/2 10/3x+5√x+5/(6√x) 10/3,where
γ
− − TABLEI:Models and constraintsfor theMilky WayGalaxy
x E /m . This gives values of the YSUS parameter
th χ
in≡therangeof10−34to10−30photonsGeV−2cm3s−1 for Model A Model B Constr.
E from 1 to 400GeV. NFW Moore et al.
th
A cuspy DM halo ρ (r) r−α predicted by the sim- Virial mass, 1012M⊙ 1.07 1.14 –
dm
∝ Virial radius, kpc 264 270 –
ulations of the Cold Dark Matter with the cosmological
Halo concentration C 11 12 10.3-21.5
constant (ΛCDM ) is often assumed for the calculations
(1.5σ)
of U(Ψ0) (e.g., [1, 2, 3, 4, 16, 17, 18, 19, 20, 21, 22]). Disk mass, 1010M⊙ 3.7 4.0 –
CosmologicalN body simulationsindicate thatthe dis-
Disk scale length, kpc 3.2 3.5 2.5-3.5
−
tribution of DM in relaxed halos varies between two Bulge mass, 109M⊙ 8.0 8.0 –
shapes: theNFW[23]densityprofileρ(r)=ρ0/x(1+x)2, Black Hole mass, 106M⊙ 2.6 2.6 2.6
x r/rs with asymptotic slope α = 1 and the steeper M(<100kpc), 1011M⊙ 6.25 5.8 7.5±2.5
Mo≡oreetal. [24]profileρ(r)=ρ /x1.5(1+x)1.5,α=1.5. Σ , |z|<1.1 kpc 65 70 71±6
0 total
ThedensityofDMalsodependsontwoparametersofthe at R⊙, M⊙pc−2
approximations: the virialmass Mvir and the concentra- Σbaryon at R⊙,M⊙pc−2 47 53 48±8
tion C rvir/rs, where rs is the characteristic radius Vcirc at 3 kpc,km/s 203 205 200±5
≡
of assumed approximation. For Milky Way-size halos
the average concentration C = 15 and the 1σ-variance
is ∆log(C) = 0.11. For Moore et al profile we define radii x 1.72x0.82/(1+5x)0.085, x r/r . This ap-
s
concentration as Cmoore =CNFW 1.72. proximhaiti≈on predicts smaller contracti≡on in the central
∗
Milky Way mass models with adiabatic compression.— regions,whereindividualtrajectoriesareveryelongated.
Thepredictionsforthe DMhalosarevalidonlyforhalos Itgivesbetterfitsthanthestandardapproximationwhen
without baryons. Whennormalgas(“baryons”)losesits compared with realistic cosmologicalsimulations [30].
energy throughradiativeprocesses,it falls to the central In order to make realistic predictions for annihilation
region of forming galaxy. As the result of this redistri- rates,weconstructtwodetailedmodelsoftheMilkyWay
bution of mass, the gravitational potential in the center Galaxybyredoingthe fullanalysisofnumerousobserva-
changes substantially. The dark matter must react to tional data collected in [31]. The models are compatible
this deeper potential by moving closer to the center and with the available observational data for the Milky Way
increasingits density. This increaseinthe DMdensity is and their main parameters are given in Table I. More
often treated using adiabatic invariants. This is justified details on the model ingredients and the existing obser-
becausethereisalimittothetime-scaleofchangesinthe vational constrains can be found in [31]. Fig. 1 presents
massdistribution: changesofthepotentialatagivenra- thedistributionofmassanddensityinthemodels. While
diuscannothappenfasterthanthedynamicaltime-scale allobservationswereincluded,someofthemaremoreim-
definedbythemassinsidetheradius. Adiabaticcontrac- portantthanothers. Thesolarneighborhoodisrelatively
tion of dark matter in a collapsingprotogalaxywas used well studied and, thus, provides important observational
already in 1962 [25]. In 1980, Zeldovich et al. [26] used constraints. In Table I we present two local parameters:
it to set constraints of properties of elementary particles thetotaldensityofmatterinside1.1kpcΣ (obtained
total
(annihilatingmassiveneutrinos). Theywerealsothefirst from kinematics of stars) and the surface density of gas
topresentanalyticalexpressionforadiabaticcompression andstellarcomponentsΣ . CircularvelocityV at
baryon circ
(for pure radial orbits) and to make numerical tests to 3 kpc distance from the center provides another crucial
confirm that the mechanism works. The present form of constraintonmodelsasemphasizedin[32]. Itisdifficult
analyticalapproximation(circularorbits)wasintroduced toestimate errorsofthis parameterbecauseofuncertain
in [27]. If M (r ) is the initialdistribution ofmass (the contribution of the galactic bar. We use 5km/s error,
in in
±
one predicted by cosmological simulations), then the fi- whichisrealistic,butitcanbe eventwicelarger. Proba-
nal (after compression and formation of galaxy) mass blythemostdebatedconstraintiscomingfromcountsof
distribution is given by M (r)r = M (r )r , where microlensingeventsinthedirectionofthegalacticbulge.
fin in in in
M = M + M . This approximation was tested Our models are expected to have the optical depth of
fin DM bar
innumericalsimulations[28,29]. Theapproximationas- microlensing events τ =1.2 1.6 10−6 and, thus, they
− ×
sumesthatorbitsarecircularand,thusM(r)isthemass are compatible with the values of τ determined recently
inside the orbit. This is not true for elongated orbits: from the observations τ = 1 1.5 10−6 [33], but are
massM(r)issmallerthantherealmass,whichaparticle excludedifτ >2 10−6(see[3−1]for×adetaileddiscussion
×
“feels” when it travels along elongated trajectory. This on the bulge optical depth in our models).
differenceinmassesrequiresarelativelysmallcorrection: Gamma-ray annihilation observability in the Milky
mass M should be replaced by the mass inside time- Way.— The expected neutralino annihilation gamma
averagedradius of trajectories passing through given ra- flux,inunits ofYSUS/10−32,canbe computedfromEq.
dius r: M ( r )r = M ( r )r . We find the cor- 1 forthe compressedDM density profile providedby our
fin in in in
h i h i
rection using Monte Carlo realizations of trajectories in Milky Way models as a function of the angular distance
theNFWequilibriumhaloandfindingthetime-averaged Ψ from the Galactic Center. In Fig. 2 we show the pre-
0
3
-32YSUS/10110023
10
1
10-1
10-2
50 100 150 200 250 300 350 400
Eth (GeV)
FIG.1: DensityandmassprofilesfortheMilkyWayGalaxy. FIG. 2: Predicted continuum gamma flux as a function of
Symbols on right panel show observational constraints as distance Ψ0 from the Galactic Center for Models A and B.
taken from Klypin et al. [31]. The full and dashed curves The thick line shows the flux for the compressed NFW DM
labeled”Total”aretotalmassinNFWandMooreetal. mod- density profile of the Model A and the thin line for the com-
elswithadiabaticcompression. DMmassintheNFWmodel pressed Moore et al. profile of the Model B. The flux profile
is shown by the thick curve. In the central region most of for the uncompressed NFW profile is also shown for com-
the mass is in baryons. Left panel shows the density. The parison (dotted line). The dashed line give the minimum
top full curve is the density of baryons. The dashed and full detectable gamma flux Fmin at 5σ level for exposure of 250
curveslabeled”DM”arefortheMooreetal. andNFWmod- hoursandE =100GeVforatypicalIACT.Theinsertedpan-
th
elswith adiabatic compression. Thelong-dashed curveisthe nel shows the YSUS/10−32 dependence with the IACT E .
th
uncompressed NFW profile for comparison. ForagivenEth,theshadowregionscansallthemχ,hσviand
Nγ intervals (see text).
dictedfluxes. Wealsoshowasacomparisontheexpected
fluxfortheuncompressedNFWdensityprofile. Theflux rejected at lower E . The diffuse galactic and extra-
th
profilesweredeterminedforatypicalIACTofresolution galactic gamma radiation are negligible compare to this
σt =0.1◦ and solid angle ∆Ω=10−5sr. We have multi- background. Gamma point-like sources within the f.o.v
pliedthe flux profilesbyafactorof1.7quotedby Stoehr canberesolvedandtakenoutaposteriori. TheE ofan
th
et al. [4] to account for the presence of substructure in- IACT depends on the zenith angle of observation. The
side the Milky Way halo [34, 35]. GalacticCenteris visibleatdifferentzenith anglesbyall
The success of a detection requires that the mini- presentIACTs(e.g. CANGAROO-III,H.E.S.S.,MAGIC,
mum detectable gamma flux Fmin for an exposure of t VERITAS),butinthebestcaseanEth ofabout100GeV
seconds, given an IACT of effective area A , angular canbeachieved. Nevertheless,futureplanedinstallations
eff
resolution σt and threshold energy Eth exceeds a sig- may reduce the Eth below 10GeV. The Aeff is also sen-
nificant number M of standard deviations (M σ) the sible to the zenithangle ofobservation,here we choosea
s s
background noise √N , i.e. F A t/√N M (see, value of 1 109 cm2. This detectability condition will
b min eff b ≥ s ×
e.g., [1, 3]). The background counts (N ) due to elec- allow us to compute the 5σ minimum detectable flux
b
tronic and hadronic (cosmic protons and helium nucle- Fmin in 250 hours of integration with a typical IACT
ids) cosmic ray showers have been estimated using the of Aeff = 1 109 cm2 and Eth = 100GeV (dashed line
following expressions [1]: N = 3 10−2E−2.3tA ∆Ω, in Fig. 2). A×t a given distance from the Galactic Center
N = 6.1 10−3E−1.7tA e∆Ω. ×As an adtdhitionaleffback- only the flux values, for a particular model of the Milky
grhound, o×ne has tothconsideeffr also the contamination due Way, greater than Fmin will be detected. The detection
to isolated muons which depending on the f.o.v. and al- willbemuchharderandmayresultonlyinacentralspot
titude location of the telescope may be even the dom- inthecaseofanIACTwithhigherEth,astheYSUSpa-
inant background at some energy range (the “muon rameter declines with Eth (see Fig. 2).
wall”). Preliminary studies [36] show that the muon The Milky Way models presented here include adia-
background could be as relevant as the hadronic back- batic compression and likely will result in a detection of
ground at E & 100GeV while it can be effectively the annihilation signal no matter what was the initial
th
4
(uncompressed) DM density profile. For current experi- Transferoftheangularmomentumtothedarkmatteras
ments this detection will be successful only for the very suggested in [31] is an option. Yet, recent simulations of
centralregions,lessthan 0.4◦ inthe caseof the Model formationof barsindicate that itis difficult to arrangea
A and close to 1◦ in ∼the case of the Model B. The significanttransferoftheangularmomentumtothedark
∼
compressed Moore et al. DM profile will provide a more matter. TheDMdensityinthecentralfewparseccanbe
extended gamma flux profile. The uncompressed NFW reducedif the centralblackhole formedby spiralingand
DM profile of the Model A will not be detected even in merging of two black holes [37]. It can also be changed
the directionof the Galactic Center. Onthe other hand, (probablyreduced)byscatteringofDMparticlesbystars
eventhe uncompressedMooreet al. profileof the Model inthecentral2pc[38]. Ifthishappens,thefluxfromthe
B will give a positive detection in the very inner regions central2pccanbesignificantlyreduced. Yet,itwillonly
of the Milky Way. decrease the amplitude of the central spike. The signal
Theeffectoftheadiabaticcompressionincludedinour from0.4◦ stillcouldbe detectedbecauseitmostlycomes
Milky Way mass models, which was previously ignored, from distances 30-50pc, which are much less affected by
is a crucial factor. It should be emphasized that for the the uncertain physics around the black hole.
central 3kpc of the Milky Way, where the baryons
∼
dominate, it does not make sense to use the dark mat-
terprofilesprovidedbycosmologicalN-bodysimulations: Acknowledgments
the DM must fall into the deep potential well createdby
the collapsed baryons. Thus, the models presented here We acknowledge support of NASA and NSF grants to
are not extreme: they are the starting point for realistic NMSU. We thank J. Primack, O. Gnedin, J. Betancort,
predictions of the annihilation fluxes. One can envision A. Tasitsiomi and W. Wittek for discussions.
few mechanisms to reduce the effect of the compression.
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