Uncertainties of the antiproton flux from Dark Matter annihilation in comparison to the EGRET excess of diffuse gamma rays

0.12 MB·English

by  Iris Gebauer

Uncertainties of the antiproton flux from Dark Matter
annihilation in comparison to the EGRET excess of diffuse
gamma rays
8
0 Iris Gebauer1 a
0
2
Institut fu¨r Experimentelle Kernphysik,Universit¨at Karlsruhe(TH), P.O Box 6980, 76128 Karlsruhe, Germany

n
a
J
Abstract. TheEGRETexcessofdiffuseGalacticgammaraysshowsallthefeaturesexpectedfrom
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dark matter annihilation (DMA): a spectral shape given by the fragmentation of mono-energetic

quarks,whichisthesameinallskydirectionsandanintensitydistribution oftheexcessexpected
]
h from a standard dark matter halo, predicted by the rotation curve. From the EGRET excess
p one can predict the flux of antiprotons from DMA. However, how many antiprotons arrive at
- the detector strongly depends on the propagation model. The conventional isotropic propagation
o
modelstraptheantiprotonsintheGalaxyleadingtoalocalantiprotonfluxfarabovetheobserved
r
t flux. According to Bergstr¨om et. al. this excludes the DMA interpretation of the EGRET excess.
s Here it is shown that more realistic anisotropic propagation models, in which most antiprotons
a
escape by fast transport in the z-direction, are consistent with the B/C ratio, the antiproton flux
[
and the EGRET excess from DMA.

2
v
6 1 Introduction chargedcosmicraysisintroducedinsection3.Section
6
4 summarizes the results.
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4
The interpretation of the observed EGRET excess of
.
0 diffuse Galactic gammaraysasDark Matter annihila- 2 Antiproton flux in an isotropic
1 tion (DMA) (see [1] or contributions by W. de Boer,
propagation model
7 C.SanderandM.Weber,thisvolume)couldbe afirst
0
hint at the nature of dark matter. The excess was ob-
: In order to explain the observed isotropy of Cosmic
v servedinallskydirections.Fromthespectralshapeof
Ray (CR) fluxes one assumes the CRs to perform a
i the excess the WIMP mass was constrained to be be-
X random walk in all directions by scattering on ran-
tween50and100GeVandfromthedistributionofthe
domly oriented turbulent magnetic fields inside the
r excess in the sky the Dark Matter (DM) halo profile
a plasma. In this case the propagation is governed by
was obtained. One of the most important criticisms
adiffusionequation,whichcanbesolvedforthesteady
of this analysis was a paper by Bergstr¨om et. al. [2]
statecasenumerically.Fromtheratioofunstable/stable
claimingthattheantiprotonfluxfromDMAwouldbe nuclei (like 10Be/9Be) one obtains the average resi-
an order of magnitude higher than the observed an-
dence time of CRs in the Galaxy to be of the order
tiproton flux. They used a conventional propagation of 107 yrs. Particles can be lost either by fragmenta-
model assuming the propagation of charged particles
tion, decay or just leaving the Galaxy to outer space.
to be the same in the halo and the disk. However,the
Since they travel with relativistic speed the long res-
propagationinthehalo(perpendiculartothedisk)can
idence time requires that they cannot move rectilin-
be much faster than the propagationin the disk [3].
eartoouterspace,butmustbe scatteringmanytimes
Inthispaperweshowthatthelocalantiprotonflux withoutloosingtoomuchenergy.Duringtheirjourney
from DMA can be strongly reduced in an anisotropic CRsmayinteractwiththe gasinthe Galaxyandpro-
propagation model and that the DMA interpretation duce secondary particles. The ratio of secondary/pri-
of the EGRET excess can by no means be excluded mary particles, like the B/C ratio is a measure for
by Galactic antiprotons. In section 2 we discuss the the amount of traversed matter (grammage) by CRs
problems of the isotropic model for cosmic ray trans- during their lifetime tCR. The grammage is given by
port leading to the fact that our galaxycan work as a ρctCR, where ctCR is the path length for a particle
large storage box for antiprotons. An anisotropic pro- traveling with the speed of light c. It was found to
pagation model, which simultaneously describes the be of the order of 10g/cm2 [4,5], which corresponds
EGRET excess and and the observed local fluxes of to a density of about 0.2 atoms/cm3. This is signifi-
cantly lower than the averaged density of the disk of
a Email: [email protected] 1 atom/cm3, which suggests that CRs travel a large
Cosmology and Astrophysics Contributed Talk
Cosmic Rays +DM Cosmic Rays+DM
Cosmic Rays Cosmic Rays
1
-1]V10-1 -1]V10-1
e e
G G
-1 s -1 s
-1 sr10-2 -1 sr10-2
-2 m -2 m
x [ x [
Flu10-3 Flu10-3
10-4
10-4
10-3 10-2 10-1 1 10 102 103 10-3 10-2 10-1 1 10 102 103
Energy [GeV] Energy [GeV]
Fig.1. ComparisonoftheantiprotonproductionincludingDMAinamodelwithisotropicpropagation(a)andamodel
with anisotropic propagation and trapping between molecular clouds (b).
7
time in low density regions. In an isotropic propaga- residencetimeofchargedparticles(10 yrs),whichre-
tion model this would be the thin halo. However, as quires all particles to spend most of their lifetime in
we will see in section 3 this interpretation is strongly the thin galactic halo and enter and exit the dense
model dependent. galacticdiskmultiple times thus acquiringgrammage.
An excellent program providing a numerical solution In this caseantiprotonsfromDMA aretrappedin the
to the diffusion equationfor CRs is the publicly avail- Galactic halo, just like conventional CRs, and DMA
able GALPROP code [6,7]. The standard model for increases the averaged density of antiprotons by or-
isotropic CR transport in GALPROP does not ex- ders of magnitude, so the flux of antiprotons becomes
plain the EGRET excess of diffuse gamma rays. This ofthesameorderofmagnitudeastheEGRETexcess.
couldbe remediedpartiallyby applyingstrongbreaks Notethattheproductionratioofantiprotons/gammas
to the injection spectra of protons and electrons in fromDMAisonlyatthepercentlevel,asiswellknown
order to obtain a higher intensity of protons and elec- from acceleratorexperiments for the fragmentationof
trons above a few GeV, but the intensity below this mono-energeticquarks,sotheenhancementofantipro-
breakhadto staythe same inordernotto modify the tons comes from the propagationmodel, not from the
gamma ray spectrum below 1 GeV [8]. These breaks production.
are only applied for the electrons and protons,not for
the other nuclei in order not to upset the B/C ratio.
Different breaks in the injection spectra for different 3 Antiproton fluxes in an anisotropic
nucleiimpliesdifferentaccelerationhistoriesfordiffer-
propagation model
ent nuclei. In addition, assuming the locally observed
spectrumtobe differentfromthe spectraelsewherein
The propagation picture with isotropic propagation
the Galaxy is unexpected, since diffusion is fast com-
is based on hydromagnetic wave theories, in which
pared to the energy loss time, so diffusion equalizes
the random (small-scale) component of the magnetic
the spectrum everywhere in agreement with the ob-
fields dominates overor are of the same orderof mag-
servationthat the gamma ray spectra in all directions
can be described by the same CR spectrum. If one nitude as the regular large scale components. From
the isotropy of the CRs one assumes that the regular
attributes the EGRET excess to a new source, like
components of the magnetic fields can be neglected,
DMA, one runs into the problem of a too large flux
so there is no preferred direction for Alfv´en waves.
of antiprotons, as discussed in detail in [2]. We have
The turbulent component is locally as large as 10 µG,
implemented the DMA as a sourceterm into the pub-
while the regularfieldisonly about3µG[9,10].How-
liclyavailableGALPROPcode[6,7]andfindasimilar
ever,eveniftheturbulentsmallscaleandregularlarge
result,asshowninFig.1a.Thisisnotsurprising,since
scale components are of the same order of magnitude
GALPROP uses the same priors as the program used
the ratio of perpendicular/parallel diffusion is about
by[2]:(i)thepropagationisdominatedbydiffusescat-
0.1 (see [3]andreferencestherein), whichimplies that
tering,whichisassumedtobethesameinthehaloand
theCRsstillpreferentiallyfollowtheregularmagnetic
thedisk(ii)thegasinthediskissmoothlydistributed
field lines, as demonstrated by following the trajecto-
(iii)theinfluenceoftheobservedstaticmagneticfields
ries of CRs in models of the Galactic magnetic fields
can be neglected. The main reason for the large flux
[11,12].Theregularcomponenthasstronglypreferred
of antiprotons from DMA in such a model is the long
directions: in the disk it is toroidal with a maximum
Iris Gebauer Uncertainties of the cosmic antiproton flux
Anisotropic Propagation Anisotropic Propagation
Isotropic Propagation Isotropic Propagation
0.35
0.3
9
C0.25 Be
B/ 10/
e
B
0.2
10-1
0.15
0.1
10-3 10-2 10-1 1 10 102 103 10-3 10-2 10-1 1 10 102 103
Energy [GeV/nucleon] Energy [GeV/nucleon]
Fig.2.TheB/Cration(a)andtheberyllium-fraction(b)forananisotropicdiffusionmodelwithtrappingbetweenMCs
(red) and for a model with isotropic diffusion (green).
Name Symbol value the MCc and the MCs will form a network of inter-
Diffusion in x, y Dxx,Dyy 5.8·1028cm2/s connectedclouds,focussingthemagneticfieldlinesto-
Diffusion in z Dzz 3.0·1030cm2/s wardsthem.CRsinthe ISMfollowingthese fieldlines
break rigidity ρ0 4.0·105MV willbe reflectedbytheconcentrationofthe fieldlines.
energy dependence α for ρ<ρ0 0.33 As worked out by Chandran [14], the MCs can act as
α for ρ>ρ0 0.6 magnetic mirrors for CRs, just like the concentration
Convection V0 250km/s of magnetic field lines near the poles from the earth
Convection slope dV 37km/s/kpc
dz trapthe CRs inthe famousVan Allenradiationbelts.
grammage paramater c 12
Thelargedistances(pcscale)betweentheMCsallows
to trap particles up to the TeV scale, thus increasing
Table 1. Parameters of an anisotropic propagation
the grammageandthe residencetime. Insucha setup
model.The components off the diffusion tensor are given
particlesacquiregrammageandageinthelowdensity
by dii(ρ) = β ·Dii(ρρ0)α, convection is given by V(z) = regionsinthe disk (betweenMCs)andnotinthe halo
V0·θ(z−0.1kpc)+ ddVzz. Note that this set of parameters as in the isotropic propagation model. Thus, the halo
is not unique,since theyare all correlated.
size is not a sensitive parameter anymore and parti-
cles,onceinthehalo,willbepreferentiallytransported
away from the disk by a combination of convection
and fast diffusion along the regular poloidalfield lines
at about 150 pc above and below the disk and with
in the halo. We have implemented this propagation
an additional poloidal field with its maximum in the
picture in the publicly available source code of GAL-
centre of the Galaxy. For fast parallel diffusion this
PROPby(i)allowingforadiffusiontensorinsteadofa
implies that CRs preferentially move along the spiral
diffusionconstant;(ii)allowinganinhomogeneousgrid
fields just above or below the disk or they follow the
inorderto havestepsizesbelow 100pc inthe disk re-
polodialcomponentintothehalo.Anadditionaleffect
gionandlargestepsizesinthehalo;(iii)implementing
concerning charged particles may be related to mole-
the dark matter annihilation as a source term of sta-
cular clouds: the gas density in the disk varies from
bleprimaryparticles,especiallyantiprotons,positrons
10−3/cm3 in the warm ionized medium to 102/cm3-
and gamma rays, in the diffusion equation. The dark
3 3
10 /cm in clumps of cold gas with a size of a few pc.
matter distribution was taken to be the one obtained
In the center the density may be as high as 107/cm3
from the EGRET excess [1]. The grammage and es-
in dense molecular clouds (MCs), where star forma-
cape time were adjusted for charged particles to ac-
tionoccurs.Onaveragethegasdensityis1/cm3inthe
count for the fact that secondary particles are now
disk.InsideMCsmagneticfieldsfarabovetherandom
produced largely locally, since particles produced far
components have been observed(see [9] for a review).
away from the solar system are likely to diffuse into
What is more important, these fields seem to be cor-
the halo, thus escaping to outer space. If the trapping
related with the observed static magnetic fields out-
in MCs is effective, one would expect it to increase
side the MCs [13]. This canonly be understood,if the
the grammage and residence time by the same fac-
MCs remember the large scale magnetic fields in the
tor, called grammage parameter c. Since the trapping
interstellar medium, i.e. if during the contraction flux
mechanismisindependentofenergyandonlydepends
freezing occurs. In this case the magnetic field lines
on the pitch angle the trapping can be modeled by a
from the ISM will become highly concentrated near
Cosmology and Astrophysics Contributed Talk
constant c. The most important GALPROP parame- ratios of secondary/primary and unstable/stable nu-
ters have been summarized in Table 1. The transport clei. Clearly the DMA searchfor light DM particles is
from the disk to the halo is quite uncertain, since the propagation model dependend.
magnetic field lines have to be continuous, which im- Takingtheseuncertaintiesintoaccountshowsthat
plies they must connect from the toroidal field to the DMA is a viable explanation of the EGRET excess of
halo. It should be noted that the average scale height diffuse Galactic gamma rays, as shown in [1] and and
ofSNIaisexpectedtobeabout350pc(thickdisk)and can by no means be excluded by the antiproton flux
the ejecta connect to the halo in chimney like struc- predicted by a specific model.
tures (see e.g. [15] and references therein), which can
drive magnetic field lines towards high altitudes ( ≈
1 kpc), thus facilitating the transport to the halo by
the fast parallel diffusion. This was simulated as an
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4 Conclusion
Tracing of charged particles in realistic models of the
regularGalacticmagneticfieldswithaturbulent(small-
scale) component has shown that CRs remember the
regular field lines, even if the irregular component is
of the same order of magnitude as the regular, thus
leading to enhanced diffusion in φ and z (see Fig. A1
in [11]). With such an anisotropic propagation model
the amount of antiprotons expected from DMA can
be reducedby one to twoorders ofmagnitude. There-
fore the claim by [2] that the DMA interpretation of
the EGRET excess of diffuse Galactic gamma rays is
excluded is strongly propagation model dependent. It
onlyappliestoapropagationmodelwithisotropicdif-
fusion. An anisotropic propagation model with differ-
ent propagationin the halo and the disk canreconcile
the EGRET excess with the antiproton flux and the