Impact of axisymmetric mass models for dwarf spheroidal galaxies on indirect dark
matter searches
Niki Klop,1, ⇤ Fabio Zandanel,1 Kohei Hayashi,2 and Shin’ichiro Ando1

arXiv:1609.03509v1 [astro-ph.CO] 12 Sep 20161

GRAPPA Institute, University of Amsterdam, 1098 XH Amsterdam, The Netherlands
2
Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU),The University of Tokyo, Chiba 277-8583, Japan(Dated: September 13, 2016)

Dwarf spheroidals are low-luminosity satellite galaxies of the Milky Way highly dominated by dark
matter. Therefore, they are prime targets to search for signals from dark matter annihilation using
gamma-ray observations. We analyse about 7 years of PASS8 Fermi data for seven classical dwarf
galaxies, including Draco, adopting both the widely used Navarro-Frenk-White (NFW) profile andobservationally motivated axisymmetric density profiles. For four of the selected dwarfs (Sextans,
Carina, Sculptor and Fornax) axisymmetric mass models suggest a cored density profile rather
than the commonly adopted cusped profile. We found that upper limits on the annihilation crosssection for some of these dwarfs are significantly higher than the ones achieved using an NFW profile.
Therefore, upper limits in the literature obtained using cusped profiles like the NFW might have been
overestimated. Our results eventually show that it is extremely important to use observationallymotivated density profiles going beyond the usually adopted NFW in order to obtain accurate
constraints on the dark matter annihilation cross section.
I.

INTRODUCTION

Most of the matter in the Universe consists of an unknown component that is commonly considered to bemade of non-baryonic cold dark matter [1, 2]. Finding theparticle nature of dark matter (DM) is one of the mostpressing goals in modern physics. While many particle
physics models have been proposed to solve this puzzle,
the most favored and extensively studied candidates fall
into the category of weakly interacting massive particles(WIMPs) [3]. These are characterised by a relic density
matching the observed DM density, and naturally arise
in many theories beyond the standard model of particle physics such as supersymmetry or universal extradimension models. The self-annihilation of WIMPs canresult in the production of standard model particles. The
goal of so-called indirect DM searches is to look for theseparticles in regions of the Universe where we know DM
is abundant [4].
High-energy gamma rays are one example of those particles expected as a result of WIMP annihilation. The
search for these gamma rays is a very active field of research fuelled in the last decade by many gamma-ray observations of Milky Way (MW) satellite galaxies [5–18]
and other promising sites such as the Galactic centre [19–25] or clusters of galaxies [26–32], both from the groundwith imaging Cherenkov telescopes and from space with
the Fermi Large Area Telescope (LAT). More recently,
novel and competitive constraints have been obtained
also from the Fermi measurements of the extragalactic
gamma-ray background [33–44].
In this paper, we focus on dwarf spheroidal galaxies(dSphs) that are low-luminosity satellite galaxies which⇤ l.b.klop@uva.nl

are known to be highly DM dominated [45–49]. Theirhigh mass-to-light ratio, proximity, and very low expected gamma-ray background from other astrophysical sources make them ideal candidates to search for
gamma rays from DM annihilation. The main astrophysical uncertainty when dealing with indirect DM searches
in dSphs is their DM density profile, which is the most
crucial ingredient needed to estimate the rate of DM annihilation we expect from a given object. The common
assumption often adopted in the literature is that dSphs
are characterised by a spherically symmetric, so-called
Navarro-Frenk-White (NFW) profile [50]. This cusped
profile originally predicted by N -body simulations of cold
dark matter might not be the best choice for all cases,
and other profiles have been extensively discussed in theliterature, including the Einasto profile [51].
On the other hand, we should consider to go beyond
simple spherical symmetric mass models. In such models there is a strong degeneracy between the velocity
anisotropy of stars and the DM density profile [52], which
can be avoided by relaxing the assumption of sphericalsymmetry. Moreover, the observed stellar componentsof all MW dSphs have indeed an axisymmetric shape on
the sky-plane with typical axial ratios of 0.6–0.8 [53].
Additionally, recent high-resolution N -body simulations
showed that DM subhalos tend to have axisymmetricshapes rather than triaxial [54]. All these considerations
prove the need to relax the assumption of spherical symmetry in the mass modeling of dSphs, which is also one of
the major systematic uncertainties for the J-factor (i.e.,line-of-sight integral of density squared) estimations thatmost of previous studies have not considered.
In this paper, we investigate the impact of axisymmetric mass models on indirect DM searches with dSphs
using gamma rays. Triaxial density profiles have been
investigated in detail in Ref. [55], where they determine
the bias on the J-factor that arises when using a spheri-2
cal Jeans analysis for halos that are likely to be triaxial
in shape. In our work, we go beyond the J-factor estimates and study the impact of the axisymmetric models
of Ref. [56] on upper limits on the annihilation cross section with respect to those obtained using the commonly
adopted NFW profile. We analyse about seven years of
PASS8 Fermi -LAT data for seven classical dSphs, namely
Draco, Leo I and II, Sextans, Carina, Sculptor, and Fornax. These dSphs are selected as the overlapping partof the samples considered by Ref. [56] and Ref. [15]. We
fit each dSph both with NFW and axisymmetric profiles,
and compare their cross section upper limits. We underline, in particular, that Sextans, Carina, Sculptor andFornax are characterised by cored axisymmetric profiles
rather than cusped, and their results can di↵er significantly from those of the NFW profiles.
This paper is organised as follows. In Sec. II, we discuss the expected flux from DM annihilation from dSphs
in the case of a NFW profile. The axisymmetric massmodel is introduced in Sec. III, where we also discuss aqualitative comparison with the NFW profile. In Sec. IV,
we discuss the Fermi -LAT data analysis for the seven selected dSphs and present our results in Sec. V. We discuss
our conclusions in Section VI.

II.

GAMMA RAYS FROM DARK MATTERANNIHILATION

The gamma-ray intensity (i.e., the number of photons
received per unit area, time, energy, and solid angle) froma direction relative to the centre of the halo, expectedfrom DM annihilation can be written as
WIMP (E,) = J( )

PP

(E),

(1)

where J( ) is the astrophysical factor, also called Jfactor, which describes the DM density distribution in
the region of interest, and PP (E) is the particle physics
factor, which encloses the properties of the DM particle.
The particle physics factor can be written as
PP

(E) =

X dNf
h vi
1
Bf ,
2
2 4⇡ mWIMP
dE

(2)

f

where mWIMP is the WIMP mass, h vi is the the annihilation cross section multiplied by the relative velocityof the annihilating particles averaged over their velocity
distribution, and dNf /dE is the photon spectrum of the
final state f with its branching ratio Bf .
The astrophysical J-factor isZ
J( ) =⇢2 (l, ) dl,(3)l.o.s.

where l is the line-of-sight parameter, and ⇢(l, ) is
the DM density profile. As mentioned in Sec. I, in
our analysis of the Fermi -LAT data we compare theobservationally-motivated axisymmetric DM density profile with the widely used spherically-symmetric NFW
profile. The current section concerns the latter.
The NFW profile is given by [50](⇢s rs3r(rs +r)2 for r < rt ,⇢(r) =(4)0
for r rtwhere ⇢s is the characteristic density, rs is the scale radius, and rt is the tidal radius beyond which all the DM
particles are stripped away due to a strong tidal force
from the host halo. We calculate the values for ⇢s andrs from the parameters vmax and rmax provided by [57]using the following relations:
rmax
,
2.163
✓
◆2
4.625 vmax
⇢s =
,
4⇡G
rs
rs =

(5)
(6)

where G is the gravitational constant. We then derive rt
from the Jacobi limit [58],rt = D

✓

MdSph
3MMW

◆ 13

,

(7)

where MdSph is the mass of the dSph and D is the distance of the dSph from the MW centre. MMW is the MW
mass enclosed within the distance D, calculated assuming an NFW profile from Ref. [59]. MdSph is calculated
integrating the dSph NFW profile up to rt , and we eventually solve equation (7) to obtain rt . Note that the tidal
radius calculated in this way is subject to various uncertainties connected to the mass estimate of the Milky Way
and to several assumptions made for simplicity, such as aperfect circular orbit of the dSph around the MW. However, later in this section we will show that variations on
the tidal radius will only have little e↵ects on the resulting J-factor. The values of ⇢s , rs , rt , the distance fromus to the dSphs, and the J-factor integrated up to rt foreach of the considered dSphs are reported in Table I.
Equation (3) yields the J-factor as a function of the angle between the line of sight and the centre of the dSph.
We project this onto a spatial map of 100 ⇥ 100 pixels
of 0.1 centred on each dSph. These will be the template input for the Fermi -LAT data analysis of each dSph
that is described in Sec. IV. We show the obtained NFW
template maps in Figs. 1 and 2, where the total flux isnormalized to unity.
Our reference works for the gamma-ray limits on dSph
are those of Refs. [12, 15]. However, while Refs. [12, 15]
limit their analysis within 0.5 of each dSph, we go out tort . Our choice is motivated by the fact that we want tocarefully compare the NFW profiles to the axisymmetricones, and therefore, we do not want to limit the emission region of our dSphs in the data analysis. However,typically about 90% of the annihilation flux comes fromwithin rs for an NFW profile (see, e.g., [48]). As an example, the J-factor of Draco is 6.60 ⇥ 1018 GeV2 cm 5 and3TABLE I: Characteristics of the analysed dwarf spheroidal galaxies. The distances are taken from Ref. [15].
NameDistance

CarinaDraco
Fornax
Leo I
Leo II
Sculptor
Sextans

[kpc]
105
76
147
254
233
86
86

⇢s

rs

rt

total integrated J-factor total integrated J-factor
NFW
axisymmetric[M kpc 3 ] [kpc] [kpc][GeV2 cm 5 sr][GeV2 cm 5 sr]
3.04 ⇥ 108 0.2065 3.39
1.50 ⇥ 1018
2.61 ⇥ 10188182.30 ⇥ 10 0.3507 0.96
8.33 ⇥ 10
9.43 ⇥ 1018
1.33 ⇥ 108 0.4731 5.30
1.83 ⇥ 1018
1.67 ⇥ 1018
8
171.59 ⇥ 10 0.4027 6.26
5.06 ⇥ 10
3.95 ⇥ 10178
171.83 ⇥ 10 0.3055 4.73
3.32 ⇥ 10
3.18 ⇥ 10178
181.67 ⇥ 10 0.3935 3.25
4.91 ⇥ 10
6.75 ⇥ 10188
183.82 ⇥ 10 0.2018 1.55
3.37 ⇥ 10
2.03 ⇥ 1018

6.52⇥1018 GeV2 cm 5 inside rt and 0.5 respectively, implying di↵erences at the percent level. We note that our
J-factors do not necessary have to coincide with those ofRefs. [12, 15] as they use the method of Ref. [57] applied
to stellar kinematics data to obtain their J-factors, while
we use directly the vmax and rmax provided by Ref. [57].
Nevertheless, our total J-factors integrated up to rt arealways within the quoted errors of the J-factors from
Refs. [12, 15], with the notable exception of Leo II where
ours is almost a factor of two smaller. With this exception in mind, we expect the limits that we calculate
for NFW profiles to be directly comparable to those ofRefs. [12, 15].
The tidal radii that we obtain from Eq. (7) do notalways correspond to values we find in the literature; inparticular, our values are usually slightly larger. Taking
Draco as an example again, Ref. [60] reports a value ofrt = 0.89 kpc while we find rt = 0.96 kpc. The total Jfactor of Draco is 6.60 ⇥ 1018 GeV2 cm 5 and 6.58 ⇥ 1018
GeV2 cm 5 within 0.96 kpc and 0.89 kpc, respectively,
implying di↵erences on the sub-percent level. Indeed,
the same reasoning of the above paragraph applies here.
Most of the annihilation flux for an NFW comes from thevery inner regions, and therefore, we do not investigate
in detail these di↵erences as it goes beyond the scope of
this work.
III.

AXISYMMETRIC MASS MODELS

Our aim is to compare the constraints obtained using
an NFW density profile to those obtained by using theobservationally-motivated axisymmetric density profile.
For the axisymmetric model, we use the non-spherical
DM halo structure estimated by Ref. [56] to compute theJ-factor maps. In this section, we briefly introduce themass models based on the axisymmetric Jeans equations,the method of exploring the best-fit DM halo parameters, and the fitting results (for more details, we refer thereader to the original papers [56, 61]).
Assuming that the stellar tracers in the dSphs are in
dynamical equilibrium with a gravitational smooth potential dominated by DM, the distribution function obeys

the steady-state collisionless Boltzmann equation [62].
Given that both the stellar and DM components are axisymmetric, the axisymmetric Jeans equations can be derived from this equation by computing its velocity moments. When the distribution functions are of the formf (E, Lz ), where E and Lz are the energy and the angular momentum along the symmetry axis z respectively,
the mixed moments vanish and the velocity dispersion of
2 and v 2 , are identical;
stars in cylindrical coordinates, vRz2i.e., the velocity anisotropy parameter z = 1 vz2 /vRis exactly zero. However, since in general these velocity second moments are not identical, Ref. [56] adopted
2 = v 2 and assumed
Cappellari’s formalism that relaxed vRzz = constant [63]. In addition, they assumed that thedSph stars did not rotate, and therefore the velocity second moment was equivalent to the velocity dispersion.
Under these assumptions, the axisymmetric Jeansequations are written as
Z 1
1
@
⌫
vz2 =
dz,
(8)
⌫(R, z) z@z"#
1R @(⌫vz2 )
@
2
2
v =
vz +
+R
,
(9)
1
⌫ @R
@R
z
where ⌫ is the three-dimensional stellar density profileandis the gravitational potential. In order to compare them with the observed velocity second moments,
the above equations should be integrated along the line ofsight. Following the method given in Ref. [64], we com2,
puted the projected velocity second moments from vRv 2 , and vz2 , taking into account the inclination of eachdSph with respect to the observer. For the stellar andDM halo density models, which are related to ⌫ and , weadopted an axisymmetric Plummer profile [65] (see Eq. 3
in [56]) and an axisymmetric double power-law form (seeEq. 4 in [56]) respectively.
Comparing the line-of-sight velocity moment profiles
from theory and observations, Ref. [56] estimated thebest-fit free parameters by using a Markov Chain Monte
Carlo fitting method. There is a total of six free parameters in this model: the axial ratio, characteristic density
and scale radius of the DM halo, the inner slope of the

4
DM profile, the velocity anisotropy parameter and theinclination angle of the dSph. Applying their models tothe available data of the seven MW dSphs (Carina, Fornax, Sculptor, Sextans, Draco, Leo I and Leo II), twoimportant outcomes were found. First, while Leo I and
Leo II have almost spherical dark halos, the other dSphs(Carina, Fornax, Sculptor, Sextans and Draco) have very
flattened and oblate DM halos, with axial ratios of ⇠0.4.
Second, not all the DM halos in the dSphs have a cusped
central density profile. Most of the dSphs indicate coreddensity profiles or shallow cusps. Exceptions are Draco
and Leo I, which show a cusped profile with inner density
slopes of 0.86 ± 0.11 and 1.40+0.06
0.08 respectively. The
best-fit parameters of each dSph are summarized in Table 2 of Ref. [56]. We use these parameters to computethe sky distribution of the J-factors for Draco, Leo I,
Leo II, Sextans, Carina, Sculptor and Fornax.
Figures 1 and 2 show both the NFW and axisymmetric density profiles projected onto the sky for the sevenadopted dSphs. These are the spatial templates that areused in the Fermi -LAT data analysis of Sec. IV. The total flux in these maps is normalised to unity, and thecolour scale of each pair NFW-axisymmetric is set to be
the same, thus showing the relative size and brightnessof the two models for a given dSph.
Figure 1 shows the dSphs with a cusped density profile. For Leo I and Leo II, there is almost no visibledi↵erence between the NFW and the axisymmetric profiles projected onto the sky. For Draco, the shape of theaxisymmetric model is oblate instead of spherical andclearly di↵ers from the classical NFW, but still shows acusped core. The di↵erences between the two profiles
are larger for the cored dSphs as can be seen in Fig. 2.
In this case, the axisymmetric profiles are much more
extended than the NFW profiles, with the total integrated J-factor being of the same order of magnitude,
but distributed over a larger area. Note also that theseaxisymmetric profiles are all oblate and characterized bydi↵erent directions of the major axis following the stellar
kinematics data for a given dSph. We will show that thecase of the cored dSphs is the most a↵ected by the simplification of adopting the NFW profile when obtaining
DM constraints.

IV.

DATA SELECTION AND ANALYSIS

We analyse 86 months (August 4th 2008 15:43:36 till
October 15th 2015 02:34:52) of Fermi -LAT PASS8 datain the direction of the selected dSphs using the v10r0p5
version of the Fermi Science Tools. We follow Ref. [15]for the selection of event class and type (evclass=128,
evtype=3) and for the data cuts, which are standard,
and use the corresponding instrumental response functions. We analyse a region of interest (ROI) of 10 ⇥ 10
around each dSph, with 0.1 pixels, and perform a binned
likelihood analysis in 24 logarithmically-spaced energy
bins from 100 MeV to 50 GeV.

(a) Draco NFW(b) Draco axisymmetric(c) Leo I NFW(d) Leo I axisymmetric(e) Leo II NFW(f) Leo II axisymmetric

FIG. 1: DM density profiles projected onto the sky forthe dSphs that have a cusped halo profile in log scale.
From top to bottom, Draco, Leo I and Leo II, where the
NFW profiles are shown on the left, and theaxisymmetric profiles are shown on the right. The total
flux of all images is normalised to unity, and the colour
scale is the same in each pair of figures for every dSph.
The maps are cropped to correspond to a 5 ⇥ 5 region
in the sky.

We perform the analysis including all the sources included in the third Fermi catalog (3FGL; [66]) withina region with a radius of 25 around the centreof our ROI for each dSph. For the di↵use background, we adopt the latest Galactic di↵use model(gll iem v06) and the extragalactic isotropic di↵use
model (iso P8R2 SOURCE V6 v06) as provided by the
Fermi collaboration. We allowed the spectral parametersof the sources to vary within a circle of radius 7.07 —theradius of our ROI—together with the normalisation of
the di↵use background components, while the remaining
sources are kept fixed to the 3FGL values.
The so-obtained model is complemented in each casewith the spatial models of Figs. 1 and 2 for the dSphs’
DM-induced emission. For each dSph, we run two sepa-

5
we adopt PYTHIA [67] for the bb̄ final state. The normalisation of our dSphs’ models is left free. In each case, we
repeat the analysis for 18 values of the DM masses from10 to 5000 GeV.

(a) Sextans NFW(b) Sextans axisymmetric(c) Carina NFW(d) Carina axisymmetric(e) Sculptor NFW(f) Sculptor axisymmetric(g) Fornax NFW(h) Fornax axisymmetricWe run the binned likelihood analysis following theabove prescriptions for each dSph, for both a NFW andan axisymmetric profile, and for each DM mass. When
convergence is not achieved, we iterate by filtering out
the faintest sources in our model with test statistic (TS)values  1, and subsequently  2, while making sure thatthe model is still a good description for the data. We
eventually calculate 95% confidence-level integrated flux
upper limits between 100 MeV and 50 GeV for all casesand derive limits on the DM annihilation cross sectionthat we discuss in detail in the next section.
Before to move on to the results, we comment on
the model used for the analysis of Sextans. The residual map for Sextans showed the presence of an unmodelled excess at about 3.5 from the centre of the ROI,
as shown in Fig. 3, for which we did not find any correspondence in the 3FGL catalog or in the literature.
The position of this excess is roughly (155.93, 0.65) incelestial coordinates. We fit this excess with a point
source described by a simple power law spectrum. We
found that this source had a TS value around 1460
and its spectrum was well described by dN/dE =2.39
12.14⇥10 9 (E/28.04 MeV)
cm 2 s 1 MeV 1 , withnormalisation and spectral index having variations below
1 percent among the various analyses we ran for the NFW
and axisymmetric profiles and di↵erent DM masses. In
Fig. 3 we show the residual map before and after including this source for one of the analyses. We do not
attempt any further modelling or interpretation for thisexcess, considering our fit just an e↵ective model for it.
We are confident that this is a good description of thedata for the purposes of our work, also because the derived upper limits on the annihilation cross section from
Sextans di↵er very little if we do or do not model thisexcess out from the data. Nevertheless, the results that
we will discuss in the following section refer to the casewhere we model this source out.

FIG. 2: DM density profiles projected onto the sky for thedSphs that have a cored halo profile in log scale. From top
to bottom, Sextans, Carina, Sculptor and Fornax, where the
NFW profiles are shown on the left, and the axisymmetricprofiles are shown on the right. The total flux of all images
is normalised to unity, and the colour scale is the same ineach pair of figures for every dSph. The maps are cropped tocorrespond to a 5 ⇥ 5 region in the sky.

rate analyses with the corresponding NFW and axisymmetric profiles. The spectral part of our dSphs’ models isconstructed using Eq. (2) adopting the corresponding Jfactor for the NFW or axisymmetric model from Table I,
and making a guess for the value of h vi—the parameterthat we will constrain. As the photon spectrum dNf /dE,

FIG. 3: Maps for Sextans, covering 10 ⇥ 10 of the sky.
From left to right: Counts map, residual map before
modelling the source, and residual map after modellingthe source. The residual maps represent subtractions of
the model map from the counts map.

6
V.

RESULTSWe find no gamma-ray excess in any of the dSphs using
both the NFW profile and the axisymmetric models. For
most of the dSphs and DM masses, we find test statistic(TS) values around zero, and no TS values were larger
than 6.06, which was the case for Fornax using the axisymmetric profile (5.6 using the NFW profile) and a DM
mass of mWIMP = 10 GeV. Therefore we calculate flux
upper limits that we then convert to limits on the annihilation cross section.
We find di↵erences between the cross section upper
limits achieved through the two di↵erent models of thehalo profile. In Figs. 4 and 5, we show the cross section upper limits for the seven analysed dSphs. Figure 4
shows that the dSphs that are expected to have a cusped
profile show small di↵erences in the upper limits for thetwo analysed halo models. Despite the di↵erence in the
shape of the two halos (spherical vs oblate), we find that
the NFW profile provides a good approximation of theactual halo of these dwarfs.
The impact of the di↵erent profiles is more significant for the four dSphs that have a cored profile assuggested by the observationally motivated profile weadopted and shown in Fig. 5. In particular, we find thelargest di↵erence of about a factor of 2.5–7, depending on
the DM-particle mass, in the case of Sextans, where we
see that the axisymmetric model is most extended compared with the corresponding NFW profile as shown in
Fig. 2. Given that Sextans was one of the most important dSphs with the spherically symmetric model, i.e.,cross section upper limits reached the canonical value
3 ⇥ 10 26 cm3 s 1 for low-mass WIMPs, it is indeed
important to use a more accurate model for its density
profile, such as the observationally-driven axisymmetricmodel discussed here.
The most stringent constraints on h vi are obtainedfor Draco, whose J-factor is the largest among the sevendSphs analyzed here. In this case, the canonical annihilation cross section h vi = 3⇥10 26 cm3 s 1 can be tested
for WIMPs lighter than ⇠80 GeV, and since the DM
density is described by the cusped profile, there is only
little di↵erence between the spherical and axisymmetricmodels. Although the results of the combined likelihood
analysis (e.g., Ref. [15]) will be dominated by the mostpromising dSphs such as Draco, others, such as Sextans
discussed above, will also give a substantial contribution.
Therefore, the inclusion on observationally-motivated axisymmetric profiles will make the joint likelihood analysis of the dSphs slightly weaker for obtaining constraints
on the DM annihilation cross section compared with theprevious analysis in the literature.
To test the impact of measurement uncertainties ofstellar kinematics data on these gamma-ray constraints,
we randomly choose ten sets of the profile parametersfrom the Monte Carlo sample of Ref. [56] for the Draco
axisymmetric profile, and obtain the cross section upper
limits for each, whose results are shown in the upper

right panel of Fig. 4 along with the best-fit case. Thisshows that the current stellar kinematics data are welldetermined, giving only uncertainties on the cross section
upper limits of about 10%, which makes dSphs a robust,and hence, attractive object to test DM annihilation.
We note that a kink around ⇠2 TeV for the axisymmetric model of Carina as well as a drop toward ⇠10 GeV
of Sculptor is likely caused by some complicated interplay
between the adopted profile, energy spectrum, and photon count distribution that we interpret as a statisticalfluctuation, also considering that the models for theseparticular cases of mdm show no substantial di↵erence,i.e., in TS significance, with respect to the others.
Finally, we note that although evaluating the integrated J-factor will capture the overall importance ofeach dSph, it is not until one performs the likelihood
analysis that we know how the cross section upper limits
behave as a function of the WIMP mass. In fact, thedi↵erence in the cross section upper limits comes froman interplay of the normalisation and shape of the Jfactor. For example, the di↵erence between the J-factors
is larger for Leo I than for Fornax, with a value of 0.78
against 0.91 for the ratio Jaxisymmetric /JNFW . The difference between the upper limits however is larger for
Fornax, where the upper limit for the axisymmetric caseis up to 1.57 times larger than the NFW case, while up
to 1.33 times larger in the case of Leo I. So the di↵erence between the shapes of the halo models has a larger
contribution to the di↵erence in the cross section upper
limits than the di↵erence between the total J-factors.
While Ref. [55] studied J-factors for comprehensive listof dSphs, our focus is on the classical seven dSphs thathave the best measurements of stellar kinematics, and we
performed the likelihood analysis for all of them. Therefore, these two approaches are complementary to eachother.
Before moving to the conclusions, we want to underline that the cross section upper limits shown here, di↵erently from Refs. [12, 15], are obtained without taking inconsideration any uncertainty, i.e., without marginalisingover the uncertainty on, e.g., the J-factor determination.
However, this has no impact on the relative comparison
that we set out to made between the NFW and axisymmetric profiles.

VI.

CONCLUSION

Dwarf spheroidal galaxies are important and well established targets for indirect DM searches. The mostcommon choice for the DM density profile in the analysisof these dSphs is an NFW profile. Recent observational
data of stellar kinematics, however, imply that DM halosaround these galaxies are better described by an axisymmetric profile, with an axis ratio of 0.6–0.8, either coredor cusped.
For this reason, we investigated the impact of observationally motivated axisymmetric models on the DM

7
Draco cross section upperlimits for distinct halo models
10-22

Draco cross section upperlimits for 10 random fits + best fit
10-22

axisymmetric
NFW

best fit

-23

-23

10
<σv> (cm3 s-1)

<σv> (cm3 s-1)

10

10-24

10-25

10-26

10-27

10-25

10-26

10

100
mdm (GeV)

10-27

1000

10

100
mdm (GeV)

1000

Leo I cross section upperlimits for distinct halo models
10-21

LeoII cross section upperlimits for distinct halo models
10-21

10-22

10-22

10-23

-24

10-23

-24

10

10-25

axisymmetric
NFW<σv> (cm3 s-1)

axisymmetric
NFW<σv> (cm3 s-1)

10-24

10

10

100
mdm (GeV)

1000

10-25

10

100
mdm (GeV)

1000

FIG. 4: Dark matter annihilation cross section upper limits in the bb̄-channel for the dSphs with a cusped profile.
The upper right frame shows the cross section upper limits obtained through the analysis of 10 axisymmetricprofiles for Draco, corresponding to 10 random sets of the profile parameters from the Monte Carlo sample ofRef. [56], along with the best-fit case.

annihilation cross section upper limits in seven classicaldSphs. We find significant di↵erences in the cross section upper limits between the two models for four of theinvestigated dSphs—the ones with a cored axisymmetricprofile, in particular Sextans. For these dSphs, an NFW
profile is not a good approximation for the DM distribution for obtaining upper limits on the annihilation crosssection. In these cases, axisymmetric models are the preferred choice.
The most promising dwarf galaxy among the sevenanalysed is Draco. Although its DM distribution is welldescribed by a cusped oblate profile, the total amount of
gamma rays yielding from the overall region will be about
the same (i.e., similar J-factors). As a result, we obtained
very similar upper limits on the annihilation cross section
for Draco using an NFW and axisymmetric model. The
same is true for Leo I and II, the other two dwarfs featuring an inner cusp. By testing ten axisymmetric profiles
randomly chosen from a Monte Carlo sample of the analyses of stellar kinematics data of Draco, we find that thecurrent uncertainty on the density profile of Draco will

give a systematic uncertainty on the cross section upper
limits by about 10%. This proves that our conclusions
are robust.
The analyses of the dSphs best described by a coredprofile result in a more substantial di↵erence between the
adopted two profiles. In particular, for Sextans, the bestfit model of its stellar kinematics data yields a much more
extended J-factor map. As the result, we found that thecross section upper limits were weaker by a factor of a few
to several compared with those obtained with an NFW
profile. This demonstrates the importance of properly
assessing dark matter density profiles from observationaldata, and also that upper limits in the literature obtained
assuming a cusped spherical model (such as an NFW)
might have been overestimated.

ACKNOWLEDGMENTS

This work was supported by the Foundation for Fundamental Research on Matter (FOM) through the FOM

8Sculptor cross section upperlimits for distinct halo models
10-22

Sextans cross section upperlimits for distinct halo models
10-21

axisymmetric
NFW

axisymmetric
NFW

-22

10
<σv> (cm3 s-1)

<σv> (cm3 s-1)

10-23

-24

10

10-25

10-26

10-24

10-25

10

100
mdm (GeV)

10-26

1000

Carina cross section upperlimits for distinct halo models
10-21

10

100
mdm (GeV)

1000

Fornax cross section upperlimits for distinct halo models
10-21

axisymmetric
NFW

axisymmetric
NFW

10-22

10-22
<σv> (cm3 s-1)

<σv> (cm3 s-1)

10-23

10-23

10-24

10-23

-24

10

10-25

10-26

10

100
mdm (GeV)

1000

10-25

10

100
mdm (GeV)

1000

FIG. 5: Dark matter annihilation cross section upper limits in the bb̄-channel for the dSphs with a cored profile.
Program (N.K. and S.A.), the Dutch Organization for
Scientific Research (NWO) through Veni (F.Z.) and Vidi
(S.A.) grants, and partly by the Japan Society for the

Promotion of Science (JSPS) KAKENHI Grant Number
16H01090 (K.H.). We also thank Stephan Zimmer for
the useful discussions.

[1] E. Komatsu et al., ApJS 192, 18 (2011), 1001.4538.
[2] Planck Collaboration, ArXiv e-prints (2015), 1502.01589.
[3] G. Bertone, D. Hooper, and J. Silk, Physics Reports 405,
279 (2005), hep-ph/0404175.
[4] J. M. Gaskins, ArXiv e-prints (2016), 1604.00014.
[5] E. Aliu et al., ApJ 697, 1299 (2009), 0810.3561.
[6] V. A. Acciari et al., ApJ 720, 1174 (2010), 1006.5955.
[7] J. Aleksić et al., JCAP 6, 035 (2011), 1103.0477.
[8] M. Ackermann et al., Physical Review Letters 107,241302 (2011), 1108.3546.
[9] E. Aliu et al., Physics Review D 85, 062001 (2012),
1202.2144.
[10] J. Aleksić et al., JCAP 2, 008 (2014), 1312.1535.
[11] A. A. Abdo et al., ApJ 712, 147 (2010), 1001.4531.
[12] M. Ackermann et al., Physics Review D 89, 042001(2014), 1310.0828.
[13] A. Abramowski et al., Physics Review D 90, 112012(2014), 1410.2589.

[14] A. Geringer-Sameth, S. M. Koushiappas, and M. G.
Walker, Phys. Rev. D91, 083535 (2015), 1410.2242.
[15] M. Ackermann et al., Physical Review Letters 115,
231301 (2015), 1503.02641.
[16] A. Geringer-Sameth et al., Phys. Rev. Lett. 115, 081101(2015), 1503.02320.
[17] A. Drlica-Wagner et al.,ApJl 809, L4 (2015),
1503.02632.
[18] MAGIC Collaboration, JCAP 2, 039 (2016), 1601.06590.
[19] A. Abramowski et al., Physical Review Letters 106,
161301 (2011), 1103.3266.
[20] D. Hooper and T. Linden, Physics Review D 84, 123005(2011), 1110.0006.
[21] A. Abramowski et al., Physical Review Letters 114,081301 (2015), 1502.03244.
[22] F. Calore, I. Cholis, and C. Weniger, JCAP 3, 038 (2015),
1409.0042.

9[23] T. Daylan et al., Physics of the Dark Universe 12, 1(2016), 1402.6703.
[24] F. Calore, I. Cholis, C. McCabe, and C. Weniger, Physics
Review D 91, 063003 (2015), 1411.4647.
[25] M. Ajello et al., ApJ 819, 44 (2016).
[26] J. Aleksić et al., ApJ 710, 634 (2010), 0909.3267.
[27] M. Ackermann et al., JCAP 5, 025 (2010), 1002.2239.
[28] A. Abramowski et al., ApJ 750, 123 (2012), 1202.5494.
[29] S. Ando and D. Nagai, JCAP 7, 017 (2012), 1201.0753.
[30] T. Arlen et al., ApJ 757, 123 (2012), 1208.0676.
[31] M. Ackermann et al., ApJ 812, 159 (2015), 1510.00004.
[32] B. Anderson et al., JCAP 2, 026 (2016), 1511.00014.
[33] M. Ackermann et al., Physics Review D 85, 083007(2012), 1202.2856.
[34] M. Fornasa et al., MNRAS 429, 1529 (2013), 1207.0502.
[35] S. Ando and E. Komatsu, Physics Review D 87, 123539(2013), 1301.5901.
[36] S. Ando, A. Benoit-Lévy, and E. Komatsu, Physics Review D 90, 023514 (2014), 1312.4403.
[37] G. A. Gómez-Vargas et al.,Nuclear Instruments
and Methods in Physics Research A 742, 149 (2014),
1303.2154.
[38] M. Fornasa and M. A. Sánchez-Conde, Physics Reports
598, 1 (2015), 1502.02866.
[39] A. Cuoco et al., ApJs 221, 29 (2015), 1506.01030.
[40] S. Camera, M. Fornasa, N. Fornengo, and M. Regis,
JCAP 6, 029 (2015), 1411.4651.
[41] N. Fornengo, L. Perotto, M. Regis, and S. Camera, ApJl
802, L1 (2015), 1410.4997.
[42] M. Regis et al., Phys. Rev. Lett. 114, 241301 (2015),
1503.05922.
[43] S. Ando and K. Ishiwata, JCAP 1606, 045 (2016),
1604.02263.
[44] M. Fornasa et al., (2016), 1608.07289.
[45] M. L. Mateo, Annual Review of Astronomy and Astrophysics 36, 435 (1998), astro-ph/9810070.

[46] L. E. Strigari, S. M. Koushiappas, J. S. Bullock, and
M. Kaplinghat, Physics Review D 75, 083526 (2007),
astro-ph/0611925.
[47] L. E. Strigari et al., ApJ 678, 614 (2008), 0709.1510.
[48] M. A. Sánchez-Conde, M. Cannoni, F. Zandanel, M. E.
Gómez, and F. Prada, JCAP 12, 011 (2011), 1104.3530.
[49] A. Chiappo et al., (2016), 1608.07111.
[50] J. F. Navarro, C. S. Frenk, and S. D. M. White, Astrophys. J. 490, 493 (1997), astro-ph/9611107.
[51] J. Einasto, Trudy Astrofizicheskogo Instituta Alma-Ata
5, 87 (1965).
[52] N. W. Evans, J. An, and M. G. Walker, MNRAS 393,
L50 (2009), 0811.1488.
[53] A. W. McConnachie, Astronomical Journal 144, 4(2012), 1204.1562.
[54] C. A. Vera-Ciro, L. V. Sales, A. Helmi, and J. F. Navarro,
MNRAS 439, 2863 (2014), 1402.0903.
[55] V. Bonnivard, C. Combet, D. Maurin, and M. G. Walker,
Mon. Not. Roy. Astron. Soc. 446, 3002 (2015), 1407.7822.
[56] K. Hayashi and M. Chiba, Astrophys. J. 810, 22 (2015),
1507.07620.
[57] G. D. Martinez, mnras 451, 2524 (2015), 1309.2641.
[58] J. Binney and S. Tremaine, Galactic dynamics , 747(1987).
[59] S. Colafrancesco, S. Profumo, and P. Ullio, Phys. Rev.
D75, 023513 (2007), astro-ph/0607073.
[60] SDSS, M. Odenkirchen et al., Astron. J. 122, 2538
(2001), astro-ph/0108100.
[61] K. Hayashi et al., Mon. Not. Roy. Astron. Soc. 461, 2914
(2016), 1603.08046.
[62] J. Binney and S. Tremaine, Galactic Dynamics: Second
Edition (Princeton University Press, 2008).
[63] M. Cappellari, mnras 390, 71 (2008), 0806.0042.
[64] E. Tempel and P. Tenjes, mnras 371, 1269 (2006), astroph/0606680.
[65] H. C. Plummer, mnras 71, 460 (1911).
[66] Fermi-LAT, F. Acero et al., (2015), 1501.02003.
[67] T. Sjostrand, S. Mrenna, and P. Z. Skands, JHEP 05,
026 (2006), hep-ph/0603175.