Is a co-rotating Dark Disk a threat to Dark Matter Directional Detection ?

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by  J. Billard

Is a co-rotating Dark Disk a threat to Dark Matter Directional Detection ?
J. Billard,∗ Q. Riffard, F. Mayet, and D. Santos
Laboratoire de Physique Subatomique et de Cosmologie,
Universit´e Joseph Fourier Grenoble 1, CNRS/IN2P3,
Institut Polytechnique de Grenoble, Grenoble, France
(Dated: July 5, 2012)
Recent N-Body simulations are in favor of the presence of a co-rotating Dark Disk that might
contributesignificantly (10%-50%) to thelocal Dark Matter density. Such substructurecould have
dramatic effect on directional detection. Indeed, in the case of a null lag velocity, one expects an
isotropicWIMPvelocitydistributionarising from theDarkDiskcontribution,whichmightweaken
the strong angular signature expected in directional detection. For a wide range of Dark Disk
2
parameters, weevaluateinthisLettertheeffectofsuchdarkcomponenton thediscoverypotential
1
ofupcomingdirectionaldetectors. Asaconclusion ofourstudy,usingonlytheangulardistribution
0
ofnuclearrecoils,weshowthatDarkDiskmodelsassuggestedbyrecentN-Bodysimulationswillnot
2
affect significantly theDark Matter reach of directional detection, even in extreme configurations.

l
u
PACSnumbers: 95.35.+d,14.80.-j
J

4
I. INTRODUCTION DependingontheunknownWIMP-nucleoncrosssection,

]
directionaldetectionmaybeusedto: excludeDarkMat-
O
ter [15, 16], reject the isotropy hypothesis [17–23], dis-
C
Within the standard Dark Matter halo paradigm, cover galactic Dark Matter with a high significance [24–
h. the local Dark Matter distribution is assumed to be 26] or constrain WIMP and halo properties [27–29]. For
p smoothly spatially distributed and to be well-described neutralino Dark Matter, a large fraction MSSM configu-
- by a Maxwellian velocity distribution. However, the hi- rationswitha neutralinolighter than200GeV/c2 would
o
erarchical structure formation model indicates that the lead to a significance greater than 3σ (90% CL) in a 30
r
t Galactic Dark Matter halo results from sucessive small kg.year CF directional detector [30].
s 4
a halo accretions, thus directly linking its structure to its In the following, we focus on the effect of a co-rotating
[ merging history. The presence of substructures in the Dark Disk on the potential of forthcoming directional

MilkyWayhaloisinferredfromrecentresultsofN-body detectors to discover Dark Matter [26]. The paper is
1
v simulation [1–6]. Such substructures may be classified organized as follows. Section II presents the current
0 as follows : Dark Matter tidal streams (spatially local- knowledge on the Dark Disk. In particular, we define
5 ized), debris flows (spatially homogenized but with ve- its parametrization used throughout. The directional
0 locity substructures) and a Dark Disk. The latter has framework is recalled in sec. III, with emphasize on the
1 received much interest since late sub-halo merging is ex- directionalstatistic methodsusedtoexploitforthcoming
.
7 pectedtoleadtotheformationofaco-rotatingDarkDisk data. Then, for a wide range of Dark Disk parameters,
0 [6–9] that may affect the expected WIMP signal both in we evaluate in IV the effect of such substructure on the
2 direct and directional detection. While the influence of discovery potential of upcoming directional detectors.
1 the dark disk on Dark Matter signals has been exhaus-
:
v tively investigated for direct [6, 10–12] and indirect [13]
i detection, it is still unclear how it may affect directional
X II. A DARK DISK IN THE MILKY WAY
detection. Following a previous work from A. M. Green
r [12], we aim at evaluating the influence of the presence
a
of a co-rotating Dark Disk on the discovery potential of Recent results from N-body simulation of Milky Way
a forthcoming directional detector. In particular, we are type galaxies have shown that merging satellite galax-
interested in determining the values of the Dark Disk ies may get dragged into the plane of their host galaxy
parameters for it to significantly affect the Dark Mat- [6–9]. This leads to a Dark Matter overdensity roughly
ter reach of directional detection. In order to be model matching the baryonic disk of the host galaxy and usu-
independent from the background energy modelling, the ally in co-rotationwith the latter [7, 8]. This Dark Mat-
studyhasbeendonebyconsideringonlytheangulardis- ter component is usually referred to as Dark Disk (DD).
tribution of nuclear recoils dR/dΩ . Hitherto, there is no observationalevidence in favor of a
r
Since the pionner paperofD. N.Spergel[14],the contri- Dark Disk in the Milky Way. In fact, a Dark Disk den-
butionofdirectionaldetectiontothefieldofDarkMatter sity greater than 50% of the halo one (ρDD/ρH > 0.5)
hasbeen adressedthrougha wealthofstudies [4,15–36]. is excluded by an estimation of the dynamical surface
mass density in the solar neighbourhood obtained from
the kinematics of a sample of 1200 red giant stars [37].
TheDarkDiskisgenerallyconsideredasacoldsubstruc-
∗Electronicaddress: [email protected] ture for whichthe velocity distributionis decribed byan
2
isotropic Maxwellian distribution [7]. In such context, obtained by integrating the double-differential spec-
the astrophysical parameters relevant to the description trumovertheenergyrangechosentobeE =[5,50]keV.
r
of the Dark Disk are the density ρ , its co-rotational
DD
velocity V and its velocity dispersion given by σ . There are several approaches to exploit the forthcom-
DD DD
Therangeofinterestoftheseparametersmustbeinferred ing directional data. Either the data analysis may aim
from the results of N-body simulations and compared to at rejecting the isotropy hypothesis [17–23] or at discov-
astrophysical constraints. For instance, F. S. Ling et al. ering galactic Dark Matter with a high significance [26]
[6] have extracted a Milky way type galaxy from the re- via a profile likelihood ratio test. In the following, we
sults of the RAMSES simulation [1]. The velocity dis- investigate the effect of a Dark Disk contribution on the
tribution of Dark Matter particles within a 7 < R < 9 expected significance of a discoveryof Dark Matter with
kpc and |Z| < 1 kpc is shown to be well fitted by a directional detection. To do so, we use a twofold ap-
double gaussian along the φ direction. The first one, proach, following [20, 26].
corresponding to the Dark Matter halo component, is First, we use a profile likelihood ratio test statistic, as
described by a null average speed and a velocity disper- presented in [26] and brielfy recalled hereafter for the
sionσ ≃180km/s. Thesecondcomponent,theDark reader’s convenience. In order to remain independent
halo
Disk, is described by a co-rotation velocity V ≃ 150 from the background energy spectrum modelling, only
DD
km/s and a velocity dispersion σ ≃ 85 km/s. Note the directional information is considered in the follow-
DD
that this description is in good agreement with [7–9]. ing, i.e. the angular distribution of the recoiling events
However, as there is no clear observational constraints dR/dΩ . Noting σ the WIMP-proton cross section and
r p
on these parameters, we allow for a wide range in order R the background rate, the likelihood function is given
b
toinvestigatetheeffectofaDarkDisk componentondi- by,
rectionaldetection. Unless otherwisestated, weconsider
(µ +µ )N
hereafter the following Dark Disk parameter ranges: L(σ ,R )= s b e−(µs+µb)
p b
N!
0< ρDD/ρh <1 N µ µ
0 km.s−1 < V <220 km.s−1 × s S(R~n)+ b B(R~n)
DD (cid:20)µ +µ µ +µ (cid:21)
7 km.s−1 < σ <155 km.s−1 (1) nY=1 s b s b
DD
(3)
where µ = R ×ξ and µ corresponds to the number
III. DIRECTIONAL DETECTION b b s
of expected background and WIMP events respectively,
FRAMEWORK
whereξ correspondstotheexposure. N isthetotalnum-
ber of observedevents,R~ refers to the directionof each
n
There is a worldwide effort toward the development
event while the functions S and B are the directional
of a large TPC (Time Projection Chamber) devoted to
event rate dR/dΩ of the WIMP and backgroundevents
r
directional detection [38–42]. In the following, we ex-
respectively. Followingrecentstudiesonthe angulardis-
emplify our Dark Disk study considering a MIMAC-like
tributionofmuoninducedneutrons[44],thebackground
detector corresponding to a low exposure (30 kg.year)
angular distribution B is assumed to be isotropic in the
CF TPC allowing three dimensional track measure-
4 galactic rest frame. Note that, contrary to a previous
ments [41].
work [26] the astrophysical uncertainties are not taken
intoaccountintheestimationofthesignificancetoallow
The two dimensional directional recoil rate
fair comparison between the two statistical approaches.
d2R/dE dΩ is given by [35] :
r r Only the background rate is taken as a nuisance param-
eter.
d2R ρ σ
= 0 0 F2(E )fˆ(v ,qˆ), (2) In a frequentist approach, the significance of a new pro-
dErdΩr 4πmχm2r r min cessiscommonlyestimatedbyusingtheprofilelikelihood
ratio test [45]. It corresponds to a hypothesis test of the
with m the WIMP mass, m the WIMP-nucleus
χ r null hypothesis H (background only) against the alter-
0
reduced mass, ρ the local Dark Matter density, σ
0 0 native H which includes both background and signal.
1
the WIMP-nucleus elastic scattering cross section,
As discussed in [45] the test statistic in the case of a
F(E ) the form factor (using the axial expression
r discovery is defined as follows:
from [43]), v the minimal WIMP velocity required
min
to produce a nuclear recoil of energy Er and qˆ the q = −2lnλ(0) σˆp >0 (4)
direction of the recoil momentum. Finally, fˆ(vmin,qˆ) is 0 (cid:26) 0 σˆp <0
the three-dimensional Radon transform of the WIMP
velocity distribution f(~v). As the Radon transform with,
is a linear application, one can simply add the host
halo and the Dark Disk contribution to the directional L(σp =0,Rˆˆb)
λ(0)= (5)
event rate. The angular distribution dR/dΩr is thus L(σˆp,Rˆb)
3
11 11
Z) Z)
E( E(
e e
c c
n n
a a 10
c c
nifi 10 nifi
g g
si si
n n
a a 9
e e
M M
9 ρρDD//ρρH == 00.25 ρσDD/ ρ=H 3 =5 0km/s
ρDD/ρH = 0.5 8 σDD = 70 km/s
ρρDDDDDD//ρρHHH == 01.75 σσDDDDDD == 110461 kkmm//ss
8 7
0 50 100 150 200 0 50 100 150 200
V [km/s] V [km/s]
DD DD
FIG. 1: Mean significance E(Z) as a function of VDD, the rotation velocity of the Dark Disk at Solar radius. Left : the result
is presented for various values relative density ρDD/ρH and a fixed velocity dispersion σDD = 85 km/s. Right : the result
is presented for various values of the velocity dispersion σDD and a fixed value of the relative density ρDD/ρH = 0.5. These
studies has been done for 50 GeV/c2 WIMP mass and a fixed valueof 100 WIMP events(from thehalo and theDark Disk).
Hence, a large value of q implies a large discrepancy configuration, the expected significance for a 30 kg.year
0
between the two hypothesis which is in favor of a dis- MIMAC-like detector. We highlight the fact that for a
covery(H ). As f(q |H ) follows a χ2 distribution, the co-rotating Dark Disk to contribute to the data, the en-
1 0 0 1
discovery significance Z is simply defined as Z = qobs, ergythresholdmustbelowand/ortheWIMPmasslarge.
in units of σ [45]. p Forconcreteness,wepresentacasestudyfora50GeV/c2
WIMP mass and a total of 100 WIMP events. Figure 1
The second approach, first introduced by B. Morgan (left) presents the mean significance E(Z) as a function
et al. [20],isbasedonagenerictestofisotropyfollowing of VDD, the rotation velocity of the Dark Disk at Solar
the mean recoil deviation hcosθi such as: radius. TheblackdashedlinecorrespondstothenoDark
Diskcase. Theresultisthenpresentedforvariousvalues
N of the relative density ρ /ρ . The general feature is
1 DD H
hcosθi= cosθi (6) that the mean significance is decreasing when increasing
N
Xi=1 the co-rotating velocity of the Dark Disk at Solar radius
as it results in a loss of directionality. This effect is even
where θi is the ith angle between the recoil and the strongerwhenincreasingtheDarkDiskcontribution,i.e.
Cygnus direction, and N is the number of measured re-
for large values of the relative velocity ρ /ρ . Inter-
DD H
coils. Note that this test is, by definition, coordinate
estingly,aco-rotatingDarkDiskcanboostthemeansig-
system dependent, such as the previous one as the main
nificanceofaDirectionalDarkMatterdetection. Indeed,
recoil direction (ℓ,b) (see [25]) is not considered here as
for a velocity dispersion σ = 85 km/s and a WIMP
DD
a fitting parameter. massof50GeV/c2,onecanseethatforrotationvelocity
Eventually, one can evaluate the significance of an ob-
V ≤ 140 km/s and for any relative density, the mean
DD
served anisotropy by computing the distributions of
significance obtained is greater than the one obtained in
hcosθi for both H corresponding to the background
0 the no Dark Disk case. This enhancement of the signifi-
(isotropic) and H the alternative. It is worth noticing
1 cance at low rotation velocities can be explained by the
thattheuseofthevariablehcosθiisparticularlyinterest-
factthattheDarkDiskisacolderstructurethanthehost
inginthe caseofdirectionaldetectionofDarkMatteras halo, i.e. has a smaller velocity dispersion, implying an
the expectedsignalshouldexhibitadipole featurehence
evenmoreanisotropicrecoilangulardistribution. Hence,
maximizing the deviation between H and H .
0 1 a co-rotating Dark Disk will not necessarily degrade the
expectedperformanceofdirectionaldetection. Ofcourse,
IV. INFLUENCE OF A CO-ROTATING DARK for a perfectly co-rotating Dark Disk (VDD = v⊙ = 220
km/s),whateverthe velocity dispersion,the recoilangu-
DISK
lar distribution induced by the Dark Disk is necessarily
isotropic. Only the contribution of the Dark Disk to the
In order to investigate the effect of a Dark Disk com-
total number of events will change.
ponent onthe expected significance ofa directionaldark
Figure1(right)presentsthemeansignificanceasafunc-
matter detection, we allow for a wide range on the Dark
tion of V . For any value of the velocity dispersion
DD
Disk parameters, see eq. 1, and we evaluate, for each
4
m/s]150 m/s]150 20
k k
D [ 5 D [
σDv σDv 10
100 0 100 0
-5 -10
50 -10 50 -20
-30
-15
0 50 100 150 200 0 50 100 150 200
V [km/s] V [km/s]
DD DD
FIG. 2: Relativeasymmetry A in theplane (VDD,σvDD) for arelative density ρDD/ρH =1/3 (left) and ρDD/ρH =1 (right).
The solid and dashed lines correspond to isocontours of a relative asymmetry equal to ±1% and ±5% respectively. These
studies havebeen done for 50 GeV/c2 WIMP mass.
σ , the mean significance is continuously decreasing GeV/c2, we found hcosθi ≃ 0.51. Figure 2 presents
DD H
with the rotation velocity of the Dark Disk. However, the relative asymmetry A in the plane (V ,σDD) for
DD v
the case σ =35 km/s (red solid line) tends to the no a relative density ρ /ρ =1/3 (left) and ρ /ρ =1
DD DD H DD H
Dark Disk limit due to the fact that the contribution to (right). Onemaynotice thatthere arethree differentre-
the total number of WIMP events from the Dark Disk gions : no effect (the 1% region), a directional discovery
falls quickly to zero for V > 140 km/s. This also ex- enhancement region (low V ) and a region for which
DD DD
plains the rapiddecrease ofthe signficance enhancement the Dark Disk weakens the directional signature (high
intherange0−100km/s. Forlargervelocitydispersions, V together with a high σ value). The relative
DD DD
the mean significance does not tend to the no Dark Disk density only affects the amplitude of A, note that the
limit as the contribution of the Dark Disk to the total latter spans the range [-18,10] for ρ /ρ = 1/3 and
DD H
number of events remains non negligible. Interestingly, [-40,23]forρ /ρ =1. Thisalsoaffectstheareaofthe
DD H
one may note that the rangeof the values of V induc- no effect region which decreases with increasing value of
DD
ing an enhancement of the significance depends strongly ρ /ρ . Interestingly, one can notice that most of the
DD H
on σ . Indeed, for large values of the velocity disper- Dark Disk models suggested by N-Body simulations lie
DD
sion, the Dark Matter signal gets closer to an isotropic in the no effect region. Only extreme, yet unrealistic,
distribution. This constatation implies that lower is the DarkDiskmodelsmayaffectsignificantlythedirectional
velocity dispersion, larger is the range in values of V signature.
DD
allowing for a boost of the directional signature. As a
conclusion, larger is the velocity dispersion of the Dark
WeevaluatetheeffectoftheDarkDiskcontributionto
Disk, weakeris the directionaldiscoverysignificance,ex-
theDarkMatterreachofupcomingdirectionaldetectors.
cept for the case of σ = 35 km/s as discussed above.
DD
Following [26], we compute the directional reach in the
However, note that the value of σ = 141 km/s is ex-
DD (m ,σ )plane,i.ethelowerboundofthe3σdiscoveryre-
tremely large with respect to the recent results from N- χ p
Body simulations. Hence, for a 50 GeV/c2 WIMP mass, gionat90%CLforthetwoapproaches: profilelikelihood
(redlines)andmeanrecoildeviation(blue lines). Figure
onecouldexpectthataco-rotatingDarkDiskcouldhave
3presentsthediscoverylimitinthe(m ,log (σ ))plane
apositive,thoughsmall(∼10%),effectonthedirectional χ 10 p
correspondingtotwoDarkMattermodels: standardhalo
detection of Dark Matter.
model only (solid lines) and and with an extreme Dark
Forcompleteness,westudiedtheevolutionofthemod-
Diskmodelcontribution{ρ /ρ =1,V =220km/s,
ifications of the angular distribution dR/dΩ for various DD h DD
r
σ =106 km/s} (dashed lines).
DarkDiskparametervalues. Forthispurpose,wedefined DD
the relative asymmetry A as: The conclusion of this study is twofold. First, we found
that for both statistical tests, the effect of an extreme
hcosθi−hcosθi Dark Disk is only mild. Indeed, the directional reach is
A = H (7)
hcosθi only degraded by a factor of 3 at high WIMP masses
H
and not affected for light WIMP. Second, we found that
where hcosθi corresponds to the mean recoil deviation the two statistical tests give similar results with a max-
H
obtainedin the no DarkDisk case(ρ =0). Note that imal deviation of a few percent. However, it is worth
DD
considering the standard halo model and a WIMP of 50 emphasizing that there intepretation differ as the profile
5
V. CONCLUSION
b])
σ [pp -3 EExxttrreemmee DDDD:: PMreoafinle r Leickoeilli hdoeovdiation A co-rotating Dark Disk, as predicted by recent N-
(g10 Halo Only: Profile Likelihood Body simulations, might contribute (10%-50%) to the
o Halo Only: Mean recoil deviation
l local Dark Matter density, with a potentially dramatic
effect on directional detection. In this letter, we have
-4 evaluatedthe effectofDark Disk modelonthe discovery
potentialofupcomingdirectionaldetectors. Weconclude
that, if a co-rotating Dark Disk is present in our Galaxy
and has the properties predicted by N-Body simulations
-5 [6],thediscoverypotentialofdirectionaldetectionwould
be strictly unchanged. Only an extreme, yet unrealis-
10 102 103 tic, Dark Disk model might affect significantly the Dark
WIMP mass [GeV/c2] Matter reach of upcoming directional detectors, by in-
creasing the discovery limit by a factor of three at high
FIG. 3: Discovery limit in the (mχ,log10(σp)) plane corre- WIMP mass (m ∼1000 GeV/c2).
χ
sponding to two Dark Matter models: standard halo model
Note that even if the impact of Dark Disk contribution
only (solid lines) and and with an extreme Dark Disk model
to the local Dark Matter distribution only mildly affects
contribution {ρDD/ρh = 1, VDD = 220 km/s, σDD = 106
the discovery potential of directional detection, it may
km/s} (dashed lines). We compute the directional reach, i.e
thelowerboundofthe3σdiscoveryregionat90%CL,forthe significantly affect the mass and cross section determi-
twoapproaches: profilelikelihood (redlines)andmeanrecoil nation [27]. Indeed, as explained in [12], WIMP events
deviation (bluelines). arising from the Dark Disk contribution will induce an
excess at low recoil energies which can lower the estima-
tionoftheWIMPmasswhenconsideringastandardhalo
model. Thishighlightsthe factthatevenifaco-rotating
likelihood method favors the background plus signal hy- Dark Disk is not a threat to the discovery potential of
pothesis (H1) whereasthe meanrecoildeviationmethod directional detection, it has to be characterized in order
rejects the isotropy hypothesis. to consistently constrain the Dark Matter properties.
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