GLAST and Dark Matter Substructure in the Milky Way
arXiv:0704.0944v1  [astro-ph]  7 Apr 2007
GLAST and Dark Matter Substructure in the Milky Way
Michael Kuhlen∗, Jürg Diemand†,∗∗ and Piero Madau†,‡
∗School of Natural Science, Institute for Advanced Study, Einstein Lane, Princeton, NJ 08540, USA
†Department of Astronomy and Astrophysics, UC Santa Cruz, 1156 High Street, Santa Cruz, CA, USA
∗∗Hubble Fellow
‡Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85740 Garching, Germany
Abstract. We discuss the possibility of GLAST detecting gamma-rays from the annihilation of neutralino dark matter in the
Galactic halo. We have used “Via Lactea”, currently the highest resolution simulation of cold dark matter substructure, to
quantify the contribution of subhalos to the annihilation signal. We present a simulated allsky map of the expected gamma-ray
counts from dark matter annihilation, assuming standard values of particle mass and cross section. In this case GLAST should
be able to detect the Galactic center and several individual subhalos.
Keywords: Gamma-rays, Dark Matter Structure, Dark Matter Annihilation
PACS: 95.55.Ka, 98.70.Rz, 95.35.+d
INTRODUCTION
One of the most exciting discoveries that the Gamma-ray Large Area Space Telescope (GLAST) could make, is the
detection of gamma-rays from the annihilation of dark matter (DM). Such a measurement would directly address one
of the major physics problems of our time: the nature of the DM particle.
Whether or not GLAST will actually detect a DM annihilation signal depends on both unknown particle physics
and unknown astrophysics theory. Particle physics uncertainties include the type of particle (axion, neutralino, Kaluza-
Klein particle, etc.), its mass, and its interaction cross section. From the astrophysical side it appears that DM is not
smoothly distributed throughout the Galaxy halo, but instead exhibits abundant clumpy substructure, in the form of
thousands of so-called subhalos. The observability of DM annihilation radiation originating in Galactic DM subhalos
depends on their abundance, distribution, and internal properties.
Numerical simulations have been used in the past to estimate the annihilation flux from DM substructure [1, 2, 3, 4],
but since the subhalo properties, especially their central density profile, which determines their annihilation luminosity,
are very sensitive to numerical resolution, it makes sense to re-examine their contribution with higher resolution
simulations.
DM ANNIHILATION IN SUBSTRUCTURE
Here we report on the substructure annihilation signal in “Via Lactea”, the currently highest resolution simulation of
an individual DM halo. Details about this simulation, including the properties of the host halo and its substructure
population, can be found in [4, 5]. To briefly summarize: The central halo is resolved with ∼ 200 million high
resolution DM particles, corresponding to a particle mass of Mp = 2× 104 M⊙. At z = 0 the host halo has a mass
of M200 = 1.8× 1012 M⊙, and it underwent its last major merger at z = 1.7. In total we resolve close to 10,000
subhalos, which make up 5.3% of the host halo mass. The subhalo mass function is well approximated by a powerlaw
dN/d lnM ∝ M−1 over three orders of magnitude down to the resolution limit of about 200 particles per subhalo
(∼ 4×106 M⊙). This power law slope corresponds to equal mass in substructure per decade, and it implies that the total
subhalo mass fraction has not yet converged. Future simulations with even lower particle masses will presumably find
an even larger subhalo mass fraction. A limitation of this present simulation is that it completely neglects the effects
of baryons. Gas cooling will likely increase the DM density in the central regions of the host halo through adiabatic
compression [6]. However, because of their shallower potential wells, the DM distribution in galactic subhalos is
unlikely to be significantly altered by baryonic effects.
http://arxiv.org/abs/0704.0944v1
FIGURE 1. Left panel: The annihilation signal of individual subhalos (crosses) in units of the total luminosity of the spherically
averaged host halo. The curves are the average (solid) and total (dotted) signal in a sliding window over one decade in mass. Right
panel: The angular size subtended by 2.0rs for a fiducial observer located 8 kpc from the halo center vs. the subhalo tidal mass. For
an NFW density profile ∼ 90% of the total luminosity originates within rs. The expected GLAST 68% angular resolution at > 10
GeV of 9 arcmin is denoted by the solid horizontal line.
We approximate the annihilation luminosity of an individual subhalo by
Ssub,i =
ρ2subdVi = ∑
jε{Pi}
ρ jmp, (1)
where ρ j is the density of the jth particle (estimated using a 32 nearest neighbor SPH kernel), and {Pi} is the set of all
particles belonging to halo i. In the left panel of Figure 1 we plot Ssub normalized by Shost, the total luminosity of the
spherically averaged host halo.
We find that the subhalo luminosity is proportional to its mass. Given our measured substructure abundance of
dN/d lnMsub ∝ M−1sub, this implies a total subhalo annihilation luminosity that is approximately constant per decade of
substructure mass, as the Figure shows (dotted line). We measure a total annihilation luminosity from the host halo that
is a factor of 2 higher than the spherically-averaged smooth signal, obtained by integrating the square of the binned
radial density profile. About half of this boost is due to resolved substructure, and we attribute the remaining half to
other deviations from spherical symmetry. Similar boost factors may apply to the luminosity of individual subhalos as
well (see next section).
The detectability of DM annihilation originating in subhalos depends not only on their luminosity, but also on
the angular size of the sources in the sky, which we can constrain by “observing” the subhalo population in our
simulation. For this purpose we have picked a fiducial observer position, located 8 kpc from the halo center along the
intermediate axis of the triaxial host halo mass distribution. In the right panel of Figure 1 we plot the angular size
∆θ of the subhalos for this observer position. For an NFW density profile with scale radius rs, about 90% of the total
annihilation luminosity originates within rs. We define ∆θ to be the angle subtended by rVmax/2.16, where rVmax is
the radius of the peak of the circular velocity curve Vc(r)
2 = GM(< r)/r, which is equal to 2.16rs for an NFW profile.
GLAST’s expected 68% containment angular resolution for photons above 10 GeV is 9 arcmin. We find that (553,
85, 20) of our subhalos have angular sizes greater than (9, 30, 60) arcmin. In the following section we consider the
brightness of these subhalos and discuss the possibility of actually detecting some of them with GLAST.
FIGURE 2. Simulated GLAST allsky map of neutralino DM annihilation in the Galactic halo, for a fiducial observer located 8
kpc from the halo center along the intermediate principle axis. We assumed Mχ = 46 GeV, 〈σv〉= 5×10−26 cm3 s−1, a pixel size
of 9 arcmin, and a 2 year exposure time. The flux from the subhalos has been boosted by a factor of 10 (see text for explanation).
Backgrounds and known astrophysical gamma-ray sources have not been included.
DM ANNIHILATION ALLSKY MAP
Using the DM distribution in our Via Lactea simulation, we have constructed allsky maps of the gamma-ray flux from
DM annihilation in our Galaxy. As an illustrative example we have elected to pick a specific set of DM particle physics
and realistic GLAST/LAT parameters. This allows us to present maps of expected photon counts.
The number of detected DM annihilation gamma-ray photons from a solid angle ∆Ω along a given line of sight (θ ,
φ ) over an integration time of τexp is given by
Nγ (θ ,φ) = ∆Ω τexp
Aeff(E)dE
ρ(l)2dl, (2)
where Mχ and 〈σv〉 are the DM particle mass and velocity-weighted cross section, Eth and Aeff(E) are the detector
threshold and energy-dependent effective area, and dNγ/dE is the annihilation spectrum.
We assume that the DM particle is a neutralino and have chosen standard values for the particle mass and annihilation
cross section: Mχ = 46 GeV and 〈σv〉= 5×10−26 cm3 s−1. These values are somewhat favorable, but well within the
range of theoretically and observationally allowed models. As a caveat we note that the allowed Mχ -〈σv〉 parameter
space is enormous (see e.g. [7]), and it is quite possible that the true values lie orders of magnitude away from the
chosen ones, or indeed that the DM particle is not a neutralino, or not even weakly interacting at all. We include only
the continuum emission due to the hadronization and decay of the annihilation products (bb̄ and uū only, for our low
Mχ ) and use the spectrum dNγ/dE given in [8].
For the detector parameters we chose an exposure time of τexp = 2 years and a pixel angular size of ∆θ = 9 arcmin,
corresponding to the 68% containment GLAST/LAT angular resolution. For the effective area we used the curve
published on the GLAST/LAT performance website [9] and adopted a threshold energy of Eth = 0.45 GeV (chosen to
maximize the significance, see below). The fiducial observer is located 8 kpc from the center along the intermediate
principle axis of the host halo’s ellipsoidal mass distribution.
Lastly, we applied a boost factor of 10 to all subhalo fluxes. The motivation for this boost factor is twofold: First, we
expect the central regions of our simulated subhalos to be artificially heated due to numerical relaxation, and hence less
dense and less luminous than in reality. Secondly, we expect the subhalo signal to be boosted by its own substructure.
We in fact observe sub-subhalos in the most massive of Via Lactea’s subhalos [4], and this sub-substructure, and
indeed sub-sub-substructure, etc., will lead to a boost in the annihilation luminosity analogous to the one for the whole
host halo, discussed in the previous section. An analytical model [10] for subhalo flux boost factors gives boosts from
a few up to ∼ 100, depending on the slope and lower mass cutoff of the subhalo mass function.
Figure 2 shows the resulting allsky map in a Mollweide projection. The coordinate system has been rotated such
that the major axis of the host halo ellipsoid is aligned with the horizontal direction, which would also correspond
to the plane of the Milky Way disk, if its angular momentum vector were aligned with the minor axis of the host
halo. The halo center (at l = 0◦, b = 0◦) is the brightest source of annihilation radiation, but the most massive subhalo
(at around l = +70◦, b = −10◦) is of comparable brightness. Additionally a large number of individual subhalos are
clearly visible, especially towards the halo center (−90◦ < l <+90◦, −60◦ < b <+60◦).
In order to quantify the detectability of individual subhalos (given our assumptions) we include diffuse Galactic and
extragalactic backgrounds, and convert our photon counts Nγ into significance S = Ns/
Nb, where Ns and Nb are the
source and background counts, respectively. For the extragalactic background we use the EGRET measurement [11]
and for the Galactic background we follow [12] and assume that it is proportional to the Galactic H I column density
[13]. Whereas the extragalactic component is uniform over the sky, the Galactic background is strongest towards the
center and in a band of b± 10◦ around the Galactic disk.
We consider all objects with S > 5 to be detectable by GLAST. With our choice of parameters the halo center
could be significantly detected, with S > 100. The number of subhalos with S > 5 depends strongly on the applied
boost factor. Without boosting the subhalo fluxes, only the most massive halo is detectable. Applying a boost factor
of 5 (10), we find that 29 (71) subhalos satisfy the S > 5 threshold for detectability. Note that subhalos below our
current resolution limit might also be detectable. Their greater abundance reduces the expected distance to the nearest
neighbor, and this may compensate for their lower intrinsic luminosities (see Koushiappas’ contribution in these
Proceedings).
In conclusion we find that with favorable particle physics parameters, GLAST may very well detect gamma-ray
photons originating from DM annihilations, either from the Galactic center or from individual subhalos. This would
be a sensational discovery of great importance, and it is worth including a search for a DM annihilation signal in the
data analysis.
ACKNOWLEDGMENTS
P.M. acknowledges support from NASA grants NAG5-11513 and NNG04GK85G, and from the Alexander von
Humboldt Foundation. J.D. acknowledges support from NASA through Hubble Fellowship grant HST-HF-01194.01.
The Via Lactea simulation was performed on NASA’s Project Columbia supercomputer system.
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