Constraining Supersymmetric Dark Matter With Synchrotron Measurements

0.16 MB·English

by  Dan Hooper

Constraining Supersymmetric Dark Matter With Synchrotron Measurements
Dan Hooper
Fermi National Accelerator Laboratory, Theoretical Astrophysics, Batavia, IL 60510
(Dated: February 3, 2008)
The annihilations of neutralino dark matter (or other dark matter candidate) generate, among
otherStandardModelstates,electronsandpositrons. Theseparticlesemitsynchrotronphotonsasa
resultoftheirinteractionwiththeGalacticMagneticField. Inthisletter,weusethemeasurements
of the WMAP satellite to constrain the intensity of this synchrotron emission and, in turn, the
annihilation cross section of the lightest neutralino. We find this constraint to be more stringent
than that provided by any other current indirect detection channel. In particular, the neutralino
annihilationcrosssectionmustbelessthan≈3×10−26cm3/s(1×1025cm3/s)for100GeV(500GeV)
neutralinosdistributedwith anNFWhaloprofile. Fortheconservativecaseofan entirelyflatdark
8 matterdistributionwithintheinner8kiloparsecsoftheMilkyWay,theconstraintisapproximately
0 a factor of 30 less stringent. Even in this conservative case, synchrotron measurements strongly
0
constrain, for example, the possibility of wino or higgsino neutralino dark matter produced non-
2
thermally in theearly universe.

n
a PACSnumbers: 95.35.+d;95.30.Cq,95.55.Ka;FERMILAB-PUB-08-019-A
J

8
2 If dark matter consists of particles with a weak-scale inatedbyacombinationofheavyfermions(b¯b,tt¯,τ+τ−)
massandcouplings,thentheirannihilationsareexpected and gauge and/or Higgs bosons [12]. When produced,

] to produce a variety of potentially observable particles, these particles fragment and decay, leading to a com-
h
including gamma rays [1], neutrinos [2], positrons [3], bination of photons, electrons, protons, neutrinos and
p
antiprotons [4], antideuterons [5], X-rays [6] and syn- their antiparticles. The electrons and positrons which
-
p chrotron radiation [7, 8]. The synchrotron emission re- are produced then proceed to travel under the influence
e sulting from dark matter annihilations naturally falls of the Galactic Magnetic Field, losing energy via inverse
h
in the frequency range studied by cosmic microwave Compton and synchrotron processes. The resulting flux
[
background (CMB) missions, such as the Wilkinson Mi- of synchrotron emission is given by:

1 crowave Anisotropy Probe (WMAP) [9]. Data from
v WMAP and other CMB experiments can, therefore, be FeFcontRχ UB
F = , (2)
8 syn
7 used to potentially constrain or detect the presence of mχ UB+Urad
dark matter annihilations in our galaxy.
3
4 It has been previously argued that microwave emis- where Fe denotes the fraction of the annihilation power
. sionobservedfromthe inner Milky Way by WMAP (the that goes into electrons and positrons and Fcont is the
1 “WMAP Haze”) is likely the product of dark matter an- averagefractionoftheelectron’senergywhichisradiated
0
nihilations [8, 10] (see also Ref. [11]). In this letter, we (viasynchrotronorinverseCompton)beforeitleavesthe
8
0 do not take this conclusion for granted, but instead sim- regionofinterest. In the caseofWMAP’s observationof
: ply use the WMAP data to place an upper limit on the theinnerMilkyWay,thisquantityisexpectedtobenear
v
rate of dark matter annihilation taking place in the in- unity.
i
X nerkiloparsecsoftheMilky Way. Inparticular,wefocus UB andUrad aretheenergydensitiesofmagneticfields
r on supersymmetric neutralinos as our dark matter can- and radiation (starlight, emission from dust, and the
a didate. As we will show, the properties of such particles CMB) in the inner Galaxy, respectively. Their role in
can be meaningfully constrained by the degree of syn- Eq.2istoaccountforthefractionoftheelectrons’energy
chrotron emission observed by WMAP. which is emitted as synchrotron, as opposed to inverse
Assuming that neutralinos constitute a large fraction Compton scattering. These two processes yield similar
of the galactic dark matter, the rate of neutralino anni- energy loss rates. For example, in the local region of
hilations taking place within a distance, Rmax, from the our galaxy, Brms ∼ 3µG and Urad ≈ 0.9 eV/cm3 (0.3
center of the Milky Way is given by: and 0.6 eV/cm3 from the cosmic microwave background
andstarlight,respectively),leadingtoU /(U −U )≈
B B rad
rmax ρ2(r)hσvi 0.18. U andU arelargerintheinnerGalaxy,butthe
R =2π r2dr, (1) B rad
χ Z m2 ratioisnotexpectedtochangedramatically. At2-3kilo-
0 χ
parsecsfromtheGalacticCenter,forexample,reasonable
where ρ(r) is the density ofdark matter ata distance, r, estimates of B ∼ 10µG and U ∼ 5 eV/cm3 [13]
rms rad
fromthe Galactic Center,hσvi is the thermallyaveraged yield U /(U −U )≈0.26.
B B rad
neutralino annihilation cross section (multiplied by the The angular distribution of synchrotron emission pro-
relative velocity) and m is the neutralino’s mass. De- duced through neutralino annihilations depends on both
χ
pendingonthedetailsofthesupersymmetricmodel,neu- the spatial distribution of dark matter and on the prop-
tralinoannihilationsleadtoavarietyoffinalstates,dom- agation of electrons in the halo (ie., the geometry of
2
FIG. 2: Top: The upper limit on the neutralino annihilation
FIG. 1: The specific intensity (in kilo-Janskysper steradian) crosssectionfromthesynchrotronconstraintasafunctionof
observedbyWMAPinits22and33GHzbands,asafunction mass,forthecaseofanNFWhaloprofile(dashed)andaflat
of the angle from the Galactic Center. In each frame, the (homogeneous) distribution of dark matter within the solar
dashedlinedenotesthefluxofsynchrotronemissionfromthe circle (dot-dashed). These limits were arrived at considering
annihilationproductsofa200GeVneutralinoannihilatingto neutralinoswhichannihilatelargelytoW+W− (asisthecase
W+W− with an annihilation cross section of σv=5×10−26 forwinoorhiggsino-likeneutralinos),UB/(UB+Urad)=0.26
cm3/s and distributed with an NFW halo profile. We have and the diffusion parameters described in the text. Shown
used UB/(UB +Urad) = 0.26 and the diffusion parameters for comparison are the annihilation cross sections for a pure-
described in the text. wino (red solid) and a pure-higgsino (green solid). Bottom:
The upper limit found with an NFW profile, and for several
dominantannihilationmodes,b¯b(dotted),ZZ (bluedashed),
W+W− (black dashed) and τ+τ− (solid).
the Galactic Magnetic Field). Following Ref. [10], we
startbyconsideringanNavarro-Frenk-White(NFW)[14]
halo profile as a benchmark, and adopt a diffusion
constant of K(E ) ≈ 1028(E /1GeV)0.33cm2s−1 and other (higher) frequency bands are somewhat larger [10,
e e
an average electron energy loss time of b(E ) = 5 × 11] and thus are less useful in placing constraints on the
e
10−16(E /1GeV)2 s−1. For calculating the synchrotron contribution from dark matter annihilations.
e
spectrum, we use a 10 µG magnetic field. We arrive at In the upper frame of Fig.2, we show as a dashed line
the results shown in Fig. 1. Here, we have considered a the upper limit from synchrotron emission in the inner
200 GeV neutralino which annihilates to W+W− with a Galaxy on the neutralino annihilation cross section as a
crosssectionofσv =5×10−26 cm3/s. Thiscrosssection functionofmassforthecaseofannihilationstoW+W−.
waschosenbecauseitleadstoasynchrotronfluxthatsat- In the lower frame of Fig. 2, we show the constraint for
◦ ◦
uratesthe WMAP observationsoveranglesof10 to15 other common neutralino annihilation modes. The con-
from the Galactic Center. If the cross section were sig- straints shown here are quite stringent, especially in the
nificantly larger, the model would predict a synchrotron case of light neutralinos. The strength of this constraint
flux inconsistent with WMAP. depends strongly,however,onthe wayinwhichthe dark
Results are shown in Fig. 1 for two of the five WMAP matter is distributed in the Inner Galaxy.
frequency bands, 22 and 33 GHz. The error bars in the As the gravitational potential in inner kiloparsecs of
3
theMilkyWayisdominatedbybaryonsratherthandark
matter, it is difficult to place significant observational
constraints on the distribution of dark matter in this re-
gion. Although numerical simulations indicate that high
densitycusps(suchasthatfoundintheNFWprofile)are
expected to be present, we do not take this for granted
here. Observations of the rotation curves of our Galaxy
do, however,constrain the total mass of dark matter in-
side ofthe solarcircle (within ≈8 kpc) [15]. As a highly
conservative example, we will consider the scenario in
which the dark matter inside of the solar circle is dis-
tributed homogeneously. With such a flat distribution,
the annihilation rate is reduced considerably, leading to
a synchrotron constraint a factor of ∼ 30 less stringent
comparedtotheNFWcase. IntheupperframeofFig.2,
the dot-dashed line denotes the upper limit for the case
of a flat dark matter distribution within the solar circle.
Tobethermallyproducedintheearlyuniversewithan
abundance consistent with the observed density of dark
matter, a neutralino must annihilate with a cross sec-
tion of hσvi ∼ 3×10−26 cm3/s at the temperature of
freeze-out (typically about 1/20of the neutralino mass).
Theannihilationcrosssectionofthermallyproducedneu- FIG. 3: A comparison of the limits placed on the dark
tralinos in the galactic halo (ie. in the low velocity matter’s annihilation cross section from several astrophysi-
limit) is, therefore, expected to be not much larger than cal channels. The black dashed and dot-dashed lines repre-
hσvi∼3×10−26cm3/s,andpossiblysmaller. Thelimits sent thesynchrotron constraints(see Fig. 2) for thecase of a
shown in Fig. 2 for the conservative case of a flat profile NFWhaloprofileandtheconservativecaseofaflatdarkmat-
thusdonotstronglyconstrainscenariosinwhichthedark terdistribution,respectively. Thedottedbluelinerepresents
theconstraintwhich canbearrivedatfrom measurementsof
matter is produced thermally.
the cosmic positron spectrum by the HEAT experiment [3].
Neutralino dark matter could also be produced via
The red dashed line is the limit from the EGRET gamma-
non-thermal mechanisms, however. For example, late-
ray satellite for the case of an NFW halo profile [18]. The
time decays of gravitinos, Q-balls or other such states
upperdot-dashedcurveistheconservativelimitfromthedif-
could populate the universe with neutralino dark matter fuse neutrino flux, assuming dark matter annihilates only to
well after thermal freeze-out has occurred [16]. Further- neutrinos[19]. Withtheexceptionoftheneutrinoconstraint,
more,asthethermalhistoryofouruniversehasnotbeen each of these limits were arrived at considering neutralinos
observationally confirmed back to the time of dark mat- which annihilate largely to W+W− (as is the case for wino
ter’s chemical decoupling, one could also imagine a sce- or higgsino-like neutralinos).
nario in which neutralinos with a very large annihilation
crosssectionwereproducedwiththemeasureddarkmat-
ter abundance due to a faster than expected expansion sulting in both W+W− and ZZ final states through the
rate at freeze-out,or other non-standardcosmology[17].
t-channel exchange of a chargino or neutralino, respec-
Neutralinos whose composition is dominantly wino or
tively. In the upper frame of Fig. 2, we compare the
higgsino have particularly large annihilation cross sec-
limitspresentedheretothepredictedcrosssectionsfora
tions. The lightest neutralino in the Anomaly Mediated
wino or higgsino neutralino. Even with the very conser-
Supersymmetry Breaking (AMSB) scenario, for exam-
vativechoiceofa flatdarkmatter distribution,wino-like
ple, is a nearlypure wino. Neutral winos annihilate very
neutralino dark matter exceeds the synchrotron limit if
efficientlythroughthet-channelexchangeofanearlyde- mχ <∼210 GeV.
generate chargino. The cross section for the process, in
In Fig. 3, we compare the constraint presented here
the low velocity limit, is given by:
with those obtained using other astrophysical observa-
g4(m2 −m2 ) tions. In particular, we show the upper limit on the
σv(χχ→W+W−) ≈ χ W (3) dark matter annihilation cross section from the absence
2πm2(2m2 −m2 )2
χ χ W of gamma-rays observed from the Galactic Center by
200GeV 2 EGRET (for the case of an NFW halo profile) [18],
∼ 1.7×10−24cm3/s × ,
(cid:18) m (cid:19) and the from observations of the cosmic positron spec-
χ
trum[3]. Eachoftheseconstraintsareshownforthecase
which is much larger than the cross section required of WIMPs annihilating to W+W−. We also include, for
of a thermally produced dark matter candidate. Pure- comparison, the bound from the lack of observed diffuse
higgsino neutralinos also annihilate very efficiently, re- neutrinos, as found in Ref. [19], which corresponds to
4
theconservativecaseinwhichWIMPsannihilateonlyto constraintpresentedhere to that foundfromgamma-ray
neutrinos. From this figure, we conclude that the syn- and positron observations, and find the limit from syn-
chrotronconstraintcalculated here is the more stringent chrotron emission to be the most stringent, even for the
than is found with any other channel. conservativecaseofaflatdarkmatterdistributionwithin
To summarize, we have presentedhere a constrainton the solar circle. This constraint can be used to exclude
the annihilation cross section of neutralino dark matter darkmattercandidateswithlargeannihilationcrosssec-
derived from the observation of the inner Milky Way by tions, suchas wino or higgsino-likeneutralinosproduced
WMAP. Dark matter annihilations produce relativistic through non-thermal mechanisms in the early universe.
electronsandpositronswhichgeneratesynchrotronemis-
sion through their interactions with the Galactic Mag-
netic Field. By studying the intensity of radiation at We would like to thank Doug Finkbeiner and Greg
synchrotron frequencies, an upper limit can be placed Doblerforvaluablediscussions. Thisworkhasbeensup-
on the dark matter annihilation rate and correspond- ported by the US Department of Energy and by NASA
ing annihilation cross section. We have compared the grant NAG5-10842.
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