Table Of ContentMon.Not.R.Astron.Soc.000,1–4(XXXX) Printed12January2015 (MNLATEXstylefilev2.2)
Indirect evidence of GeV Dark Matter
Man Ho Chan ⋆
5 Department of Physics, The Chinese University of Hong Kong
1 Shatin, New Territories, Hong Kong, China
0
2
n Accepted XXXX,ReceivedXXXX
a
J
9 ABSTRACT
Recently, an excess of GeV gamma ray near the Galactic Centre has been reported.
] The spectrum obtained can be best fitted with the annihilation of 30−40 GeV dark
E matterparticlesthroughb¯bchannel.Inthisletter,Ishowthatthisannihilationmodel
H
can also solve the mysteries of heating source in x-ray plasma and the unexpected
. high gamma-ray luminosity. The cross section constrained by these observations give
h
excellentagreementswith boththe predictedrangeby usingFermi-LAT dataandthe
p
canonical thermal relic abundance cross section.
-
o
Key words: Dark matter
r
t
s
a
[
1 1 INTRODUCTION GalacticCentre.Thisevidencecanfurthersupportthedark
v matter annihilation model and constrain the cross section
Recently, high energy gamma ray observations reveal some
3 and rest mass of thedark matterparticles.
4 excess emissions near the Galactic Centre. These excess
0 emissions cannot be easily explained by standard phys-
2 ical processes. One potential origin of such emissions
0 is due to an unusual population of millisecond pulsars
1. (Gordon and Macias 2013; Abazajian et al. 2014). How- 2 X-RAY EMISSION AT GALACTIC CENTRE
0 ever, Daylan et al. (2014) point out that the large diffuse
5 signalofgammaraydisfavoursthepossibilityofpulsaremis- In the past decade, a large amount of diffuse x-ray
1 sions. Even including both known sources and unidenti- data had been obtained by Chandra, BeppoSAX, Suzaku
: fied sources, the millisecond pulsars can only account no and XMM-Newton (Sidoli et al. 1999; Muno et al. 2004;
v
more than 10 percent of the GeV excess (Hooper et al. Sakanoet al. 2004; Uchiyamaet al. 2013). In particular,
i
X 2013). In fact, the majority of discussions of the GeV ex- Munoet al. (2004) use the data from Chandra to model
r cess is now focused on the annihilation of dark matter thetemperatureof thetwo componentswithin 20 pcas 0.8
a particles(Gordon and Macias 2013;Abazajian et al. 2014; keV(softcomponent)and8keV(hardcomponent).Theen-
Daylan et al. 2014; Izaguirre et al. 2014; Calore et al. ergyrequired tosustain the0.8keVand8keVcomponents
2014). It is also because the gamma ray spectrum obtained are3 1036 erg/s and1040 erg/s respectively(Muno et al.
×
from Fermi-LAT data can be well fitted with b¯b annihi- 2004).Later,Belmont et al. (2005)pointoutthatthecool-
lation channel of dark matter particles (Abazajian et al. ingbyadiabaticexpansionmaynotbeimportantifthehard
2014; Daylan et al. 2014). The required cross section and component could actually be a gravitationally confined he-
rest mass of dark matter particle are < σv >= (1.4 lium plasma. Therefore, the actual energy required for the
7.5) 10−26 cm3 s−1 and m 30 40 GeV respectivel−y hard component to balance the radiative cooling would be
χ
(Aba×zajian et al. 2014;Daylan∼et al.−2014).Thiscrosssec- (1.4 2.6) 1036 erg/swithin20pc(Munoet al. 2004),but
tion is consistent with the expected canonical thermal relic not−1040 e×rg/s. Although supernova explosions are able to
abundance cross section (< σv > 3 10−26 cm3 s−1) providesuchahigh energy,it isnotpossible forsupernovae
≈ ×
in cosmology. Furthermore, the inner slope of the radial- toheatthehardcomponentplasmatosuchahightempera-
depedenceof thegamma rayemissions isγ 1.1 1.3 (the ture (Uchiyama et al. 2013). Also, the correlation between
≈ −
bestfitisγ =1.26)(Daylan et al. 2014),whichisconsistent thehard and soft emission suggests that they are produced
withthenumericalsimulationofdarkmatterhalostructure byrelatedphysicalprocesses(Munoet al. 2004).Therefore,
γ =1 1.5 (Navarro et al. 1997; Moore et al. 1999). therequiredenergytobalancetheradiativecoolingsofboth
In−this letter, I show that the b¯b annihilation channel soft andhardcomponentmightbegivenbysomeotherori-
canalsoexplaintheenergyrequiredinx-rayemissionsinthe gins. However, there is no widely accepted mechanism to
heat and sustain the plasma to such a high temperautre
(Munoet al. 2004; Uchiyama et al. 2013). One potential
⋆ [email protected] explanation is that the heating might result from the vis-
2 Chan
cousfriction on molecular clouds flowingtoward theGalac- 100
tic Centre (Belmont et al. 2005).
Here, I propose that the energy given out by annihila-
tionofdarkmatterparticlescanexplaintheenergyrequire- 10
ment of both soft and hard components ((4.4 5.6) 1036
− ×
erg/s)within20pc.Althoughalargeamountofenergyfrom -1V)
annihilation is givenout intheform ofgamma raywhich is Ge
E ( 1
nearlytransparenttotheplasma,alargeamountofhighen- N/de
ergy electrons and positrons can also be produced through d
the b¯b annihilation channel. The spectrum of positron (or
0.1
electron) energy dN /dE per one annihilation is shown in
e
Fig. 1 (Borriello et al. 2009; Crocker et al. 2010). These
high energy electrons and positrons would lose their energy
andgivetheirenergytotheplasmamainlybythreedifferent 0.001.01 0.1 1 10
processes: ionization loss E˙ , synchrotron loss E˙ and E (GeV)
ion syn
inverseComptonscatteringE˙IC.Thecorrespondingenergy Figure 1. The energy spectrum of positron produced per one
loss rates are (Longair 1994): annihilation(Borrielloetal. 2009).
n E
E˙ =7.64 10−9 e 3ln +19.8 eV/s,(1)
ion × 1 cm−3 mec2
(cid:16) (cid:17)(cid:16) (cid:17)
E˙ =6.6 10−10 E 2 B 2 eV/s, (2) icant reduction of the diffusion coefficient in the inner 10
syn × mec2 10−3 G pcregion is found.They applytwo models, namelyKraich-
(cid:16) (cid:17) (cid:16) (cid:17) nan and Kolmogorov, to obtain the characteristic diffusion
and
length d . They get d 10 pc and d 30 pc by using
E 2 U f f ∼ f ∼
E˙ =1.6 10−9 rad eV/s, (3) the Kraichnan model and Kolmogorov model respectively.
IC × mec2 6 104 eV/cm3 Therefore, not all of the energy of positrons or electrons is
(cid:16) (cid:17) (cid:18) × (cid:19)
lost due to the cooling process during the diffusion within
whereU istheradiationenergydensity,n andBarethe
rad e
number density of electrons and magnetic field strength in df. The diffusion length for an electron with initial energy
theplasma respectively.Thetotalnumberandtotal energy Ei is given by (Fornengo et al. 2012)
of positrons or electrons produced per one annihilation are 1/2
N6−e =8 GRe(VdNree/spdeEc)tdivEely≈fo1r2maχnd=E¯30=−R40EG(deNVe./TdEhe)rdeEfor≈e, df ="4ZEEfi K0E˙EδdE# , (4)
the average energy for one positron or electron produced
is E 0.5 0.7 GeV, which gives E/m c2 103. Since where Ef is theenergy of theelectron after thediffusion of
n ≈0.1 cm−−3 (Munoet al. 2004), U e ∼104 eV/cm3 lengthdf.Let’sconsiderthelowerboundsoftheparameters
(We o∼lfire et al. 1990;Fritz et al. 2014)anraddB∼ 10−4 10−3 from large scale diffusion K0 = 1027 cm2 s−1 and δ = 0.3.
∼ − For E = 0.6 GeV and d = 20 pc, we get E = 0.2 GeV,
G in the plasma near the Galactic centre (Crocker et al. i f f
2010),thetotalenergylossrateisE˙ =E˙ +E˙ +E˙ which means over 65% of the energy would be lost during
10−7 10−3eV/s.ThecoolingratewouldiofinrstbesydnominIaCte∼d thediffusion process.
− In the following discussion, we first neglect the effect
byinverseComptonScatteringandsynchrotronloss. When
of diffusion. The result would not be affected if the simple
thepositronorelectroniscooleddowntoabout1MeV,the
randomwalkmodelisthecorrectdiffusionmodel.However,
cooling rate would be dominated by ionization loss. As a
result, the required cooling time is t 1013 1014 s (see if either of the other two turbulence models is the correct
c ∼ − diffusion model, the calculated cross section would be at
Fig. 2).
most increased by a factor of 1.5.
For the diffusion process of the positrons or electrons,
The total annihilation rate within R = 20 pc is given
let’s first consider the simple random walk model. The
by
stopping distance of a high energy positron or electron is
d √r ct (Boehm et al. 2004), where r = E/eB R
isst∼he LaLrm×or cradius. For B 10−3 G, we haLve d < 1 Ψ(R)= ρ2 <σv>m−χ24πr2dr, (5)
s
pc,which isverysmall compar∼ed with thesizeof ourinter- Z0
Here,ρisthedarkmatterdensityprofile,whichisassumed
estedregion (20pc).Therefore, therequiredcooling timeis
to bethegeneralized NFW profile (Cirelli et al. 2014):
short enough such that the diffusion process is not impor-
tant.Nevertheless,Regis and Ullio (2008) suggest that the −γ −3+γ
r 1+(r/r )
amplitudeof therandom magnetic field and theturbulence ρ=ρ⊙ s , (6)
r⊙ 1+(r⊙/rs)
effect are also important to thediffusion process. This kind (cid:18) (cid:19) (cid:20) (cid:21)
ofdiffusioncanbedescribedbyadiffusioncoefficientK0and where ρ⊙ = 0.3 GeV/cm3, r⊙ = 8.5 kpc and rs = 20
anindexδ.Foralargescale(greaterthan100pc),theranges kpc. In our calculations, we assume γ = 1.26, which is the
ofthevaluesareK0 =1027 1030 cm2 s−1 andδ=0.3 0.6 bestfitoftheobservedgammarayspectrumbyFermi-LAT
− −
(Delahayeet al. 2008;Regis and Ullio 2008;Lacroix et al. (Daylan et al. 2014).Thetotalenergylossduetoelectron-
2014). For the innermost region near the Galactic Centre, positronpairsis 2Ψ(R) E¯.Sincetheenergyrequiredto
thepictureismuchmoreuncertain.Regis and Ullio (2008) sustain the soft a≈nd hard×components is (4.4 5.6) 1036
− ×
reveal from the analysis of γ-ray observations that a signif- erg/s, we can constrain the parameter space of m and
χ
Indirect evidence of GeV Dark Matter 3
1e+010 8
7
V)
Energy of positron/electron (e11ee++000068 -263-1σ<v> (10 cm s)4635
2
1e+004
1e+006 1e+008 1e+010 1e+012 1e+014 1e+016
Cooling time (s) 1
30 32 34 36 38 40
Figure 2. The energy of a positron or electron as a function of mχ (GeV)
timeduringcoolingprocessforB=10−3 GandUrad=6×104 Figure 3.Theparameterspaceconstrainedbytheenergyemit-
eV/cm3. We have assumed ne = 0.1 cm−3 and E = 0.6 GeV ted from x-ray plasma is bounded by the solid lines (simple
initially.
random walk diffusion model) and the dashed lines (turbulence
model,assumedonly65%oftheenergyislostduringthediffusion
process).Thedottedlinesarethelowerandupperlimitsofcross
< σv > by using Eq. (5) (see Fig. 3). In the plot, we
sections obtained from the GeV excess spectrum by using the
see that the allowed parameter space falls within the range
Fermi-LATdata(Abazajianetal. 2014;Daylanetal. 2014).
predicted by the annihilation model from Fermi-LAT data
<σv>=(1.4 7.5) 10−26 cm3 s−1 form =30 40GeV.
χ
− × −
For consistency checking, the above result also agrees energypositronswouldannihilatewithelectronstoproduce
with the total luminosity of gamma ray with en- 511 keV emission line). Therefore, the number density of
ethrgeyGgarleaactteicr Ctheanntre50d0eteMcteeVd bwyiththine ERG′ R=ET3t0elepsccopine chmig−h3e.nSeirngcyepthoesiterleocntsrownitnhuinmb20erpdcenissitnye+is∼ne10−08.1−c1m0−−73
∼
(Mayer-Hasselwander et al. 1998; Cheng et al. 2006). The (Munoet al. 2004), the positron to electron ratio becomes
total energy released perone annihilation is given by: 10−7 10−6,which general agrees with therecent analy-
∼ −
sis in interstellar medium (Vecchio et al. 2013). Further-
′
R
E˙ =2m−1c2 ρ2<σv>4πr2dr. (7) more, this range of ratio can produce the observed 511
χ keV luminosity by the accretion of intergalactic material
Z0
(Vecchioet al. 2013).
Since the energy carried by neutrinos is negligible
Toconclude,wecannoticethatalltheaboveevidences
(Bergstrom et al. 2005), by using the predicted range of
give a self-consistent picture in the Galactic Centre and
<σv> (2 4) 10−26 cm3 s−1 from x-ray emission and
≈ − × strongly support the annihilation dark matter model. The
m = 30 40 GeV, the total luminosity of gamma ray is
E˙χ E˙ −2Ψ(R′)E¯ (2.0 2.7) 1037 erg/s, which agrees rest mass and the cross section could probably be verified
wiγth≈the−detected lu≈minosi−ty L =×(2.2 0.2) 1037 erg/s bythe Large Hadron Collider Experiment in thefuture.
± ×
(Mayer-Hasselwander et al. 1998).
4 ACKNOWLEDGEMENTS
3 DISCUSSION I am grateful to the referee for helpful comments on the
manuscript.
In this letter, we show that the annihilation of dark matter
particles can satisfactorily explain the energy source of soft
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