Dynamical Models of Dwarf Galaxies and Dark Matter

Particle Searches

Alex Geringer-SamethImperial College London

Exploring the Dark Universe — Quy Nhon, July 25, 2017

Milky Way dwarf galaxies

Nearby

Lots of dark matter

Not much else: no astrophysical background*(compare with Galactic center)

“gamma-ray flux = particle physics x astrophysics”

dJ(n)

d⌦=

Zd` [⇢DM(`n)]2

n`

⇢2DM

Jeans equation: gravitational potential

spectroscopic line of sight velocities velocity dispersion profile

6 Bonnivard, Combet, Daniel et al.

R [kpc]0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

[km

/s]

pσ

0

2

4

6

8

10

12

14

16

For DataMedian95% CIs

R [kpc]0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2

[km

/s]

pσ

0

2

4

6

8

10

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14

16

Dra

R [kpc]0.2 0.4 0.6 0.8 1 1.2

[km

/s]

pσ

0

2

4

6

8

10

12

14

16

Car

R [kpc]0.2 0.4 0.6 0.8 1

[km

/s]

pσ

0

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14

16

Leo1

R [kpc]0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

[km

/s]

pσ

0

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4

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Leo2

R [kpc]0.2 0.4 0.6 0.8 1 1.2

[km

/s]

pσ

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Scl

R [kpc]0.1 0.2 0.3 0.4 0.5

[km

/s]

pσ

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16

Sext

R [kpc]0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

[km

/s]

pσ

0

2

4

6

8

10

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14

16

Umi

Figure 1. Velocity dispersion profiles �p of the eight ‘classical’ dSphs: data (symbols) and reconstructed median and 95% CIs (blue lines). These profiles areshown for illustration; our results are based on an unbinned analysis.

and saturates beyond (see figure 4, where the J-factor obtained forFornax is plotted as a function of the integration angle ↵

int

; themedian value is seen to saturate above ⇠ 1

�).There is no clear criterion to define the size of DM halos

hence we adopt two different approaches for each dSph galaxy andfor each set of DM parameters accepted by the MCMC. The firstmethod considers the tidal radius rt to be a good estimator of thehalo size (as shown by N-body or hydrodynamical simulations —see e.g. Springel et al. 2008; Mollitor, Nezri & Teyssier 2015); thisis computed as:

rt =

M

halo

(rt)

[2� d lnMMW/d ln r(d)]⇥MMW(d)

�(1/3)

⇥ d , (18)

where MMW(d) is the mass of the MW enclosed within the galac-tocentric distance d of the dSph and M

halo

is the mass of the dSphgalaxy. A second method to estimate the size of a DM halo consistsin determining the radius r

eq

where the halo density is equal to thedensity of the MW halo, namely,

⇢haloDM

(req

) = ⇢MW

DM

(d� req

). (19)

We have used both a Navarro-Frenk-White (Navarro, Frenk &White 1997; Battaglia et al. 2005) and an Einasto profile (Navarroet al. 2004; Springel et al. 2008) for the MW density, with no im-pact on the results. We also find the above two estimates of the dSphgalaxy size to be comparable, leading to very similar astrophysi-cal factors (see Appendix B). Note that other assumptions can also

c� Xxxx RAS, MNRAS 000, 1–18

Bayesian analysis of resolved stellar spectra 5

Figure 2. Sky-subtracted Hectochelle spectra (black) for probable members of Draco (left panels) and probable foreground dwarf stars (right panels) spanning magnitudes 18<∼ g <

∼ 20.5. Overplotted withcoloured curves are best-fitting model spectra synthesized from the spectral library of de Laverny et al. (2012). Text lists equatorial coordinates, SDSS g-band magnitude, and our estimates of vlos , Teff , log g,[Fe/H], [α/Fe].

gives shape to the continuum and T (λ[1 + Qm(λ)+vlosc ]) is a

continuum-normalized template that is redshifted according to agiven 1) line-of-sight velocity, vlos, and 2) order-m polynomial,

Qm(λ) ≡ q0 + q1

!

λ− λ0

λs

"

+ q2

!

(λ− λ0)λs

"2

+...+ qm

!

(λ− λ0)λs

"m

. (4)

The latter, wavelength-dependent redshift accounts for linear andhigher-order systematic differences between wavelength solutionsof target and template spectra. Notice that the zeroth-order term,q0, is degenerate with vlos; therefore we assume in all cases thatq0 = 0, leaving our velocity estimates susceptible to a uniformerror in zero point that we can estimate using spectra from stars ofknown velocity (e.g., the solar spectra taken at twilight, see Section4.2).

3.1.1 Templates

Lacking Hectochelle spectra spanning a sufficient range of stan-dard stars, we generate template spectra using a library of syntheticspectra that has generously been provided by Young Sun Lee (pri-vate communication, 2013), and has previously been used to es-timate stellar-atmospheric parameters as part of the SEGUE Stel-lar Parameter Pipeline (Lee et al. 2008,?, ‘SSPP’ hereafter,). TheSSPP library contains rest-frame, continuum-normalized, stellarspectra computed over a grid of atmospheric parameters spanning4000 ≤ Teff/K ≤ 10000 in effective temperature (with spacing∆Teff/K = 250), 0 ≤ log10[g/(cm/s2)] ≤ 5 in surface gravity(∆ log10[g/(cm/s2)] = 0.25 dex) and −5 ≤ [Fe/H] ≤ +1 inmetallicity (∆[Fe/H] = 0.25 dex). While the library spectra arecalculated for a range in the abundance ratio of α elements to iron,this ratio is not independent of metallicity. Rather, [α/Fe] = +0.4for library spectra with [Fe/H] < −1, [α/Fe] decreases linearly as

Bayesian analysis of resolved stellar spectra 5

Figure 2. Sky-subtracted Hectochelle spectra (black) for probable members of Draco (left panels) and probable foreground dwarf stars (right panels) spanning magnitudes 18<∼ g <

∼ 20.5. Overplotted withcoloured curves are best-fitting model spectra synthesized from the spectral library of de Laverny et al. (2012). Text lists equatorial coordinates, SDSS g-band magnitude, and our estimates of vlos , Teff , log g,[Fe/H], [α/Fe].

gives shape to the continuum and T (λ[1 + Qm(λ)+vlosc ]) is a

continuum-normalized template that is redshifted according to agiven 1) line-of-sight velocity, vlos, and 2) order-m polynomial,

Qm(λ) ≡ q0 + q1

!

λ− λ0

λs

"

+ q2

!

(λ− λ0)λs

"2

+...+ qm

!

(λ− λ0)λs

"m

. (4)

The latter, wavelength-dependent redshift accounts for linear andhigher-order systematic differences between wavelength solutionsof target and template spectra. Notice that the zeroth-order term,q0, is degenerate with vlos; therefore we assume in all cases thatq0 = 0, leaving our velocity estimates susceptible to a uniformerror in zero point that we can estimate using spectra from stars ofknown velocity (e.g., the solar spectra taken at twilight, see Section4.2).

3.1.1 Templates

Lacking Hectochelle spectra spanning a sufficient range of stan-dard stars, we generate template spectra using a library of syntheticspectra that has generously been provided by Young Sun Lee (pri-vate communication, 2013), and has previously been used to es-timate stellar-atmospheric parameters as part of the SEGUE Stel-lar Parameter Pipeline (Lee et al. 2008,?, ‘SSPP’ hereafter,). TheSSPP library contains rest-frame, continuum-normalized, stellarspectra computed over a grid of atmospheric parameters spanning4000 ≤ Teff/K ≤ 10000 in effective temperature (with spacing∆Teff/K = 250), 0 ≤ log10[g/(cm/s2)] ≤ 5 in surface gravity(∆ log10[g/(cm/s2)] = 0.25 dex) and −5 ≤ [Fe/H] ≤ +1 inmetallicity (∆[Fe/H] = 0.25 dex). While the library spectra arecalculated for a range in the abundance ratio of α elements to iron,this ratio is not independent of metallicity. Rather, [α/Fe] = +0.4for library spectra with [Fe/H] < −1, [α/Fe] decreases linearly as

Walker, Olszewski, Mateo 1504.03060 (ApJ) Bonnivard+ 2015 1504.02048 (MNRAS)

stellar kinematics

Observation: stars orbiting inside the dwarf

Bayesian exploration of possible dark matter density profiles

Velocity anisotropy, light profile, truncation, priors

Dark matter annihilation and decay in dSphs 11

Leo5 Leo4 Seg1 LeoT Cvn1 Leo1 Cvn2 For Sext Leo2 Car Her Seg2 Boo1 Scl UMa1 Dra Wil1 UMi Coma UMa2

)-5

kpc

2)/M c

α (J

(10

Log

7

8

9

10

11

12

13

14Median values

68% CIs (+ triaxiality systematics [ ] )

d [kpc]180 160 23 407 218 250 160 138 86 205 101 132 35 66 79 97 82 38 66 44 30

]° [cα

0.027 0.083 0.14 0.05 0.3 0.11 0.053 0.55 0.91 0.084 0.27 0.29 0.11 0.42 0.38 0.38 0.27 0.063 0.49 0.2 0.53

ClassicalUltrafaint

J-factor

cα = intα

Leo5 Leo4 Seg1 Cvn1 LeoT Sext For Leo1 Car Leo2 Her Cvn2 Boo1 Scl UMa1 Seg2 UMi Dra Wil1 Coma UMa2

)-5

kpc

2)/M°

= 0

.5in

tα

(J(

10Lo

g

7

8

9

10

11

12

13

14

15Charbonnier et al. (2011)Ackermann et al. (2013)Geringer-Sameth et al. (2015)This work68% CIs

d [kpc]180 160 23 218 407 86 138 250 101 205 132 160 66 79 97 35 66 82 38 44 30

ClassicalUltrafaint

° = 0.5intα

J-factor

Figure 6. Top: J-factors and 68% CIs for ↵int = ↵

Jc : the ’[]’ symbols combine in quadrature the 68% statistical uncertainties and possible systematics (±0.4)

from triaxiality of the dSph galaxies (Bonnivard et al. 2015). Bottom: comparison of the J-factors to other works, with ↵

int

= 0.5

�. See also Section 5.4 for acritical discussion of the targets most favoured by our analysis.

5.3 D-factor: ranking of the dSphs and comparison to otherworks

Dark matter decay is less often considered than annihilation, how-ever recent observations of an unidentified X-ray line at 3.55 keV ingalaxy clusters has generated increasing interest in this possibility(e.g., Bulbul et al. 2014a; Boyarsky et al. 2014b).

Ranking. The blue squares in figure 7 and the three rightmostcolumns of table 2 give an overview of the D-factors computedhere. First, comparing the top panels of figures 6 and 7, we find thatthe ordering of the most promising targets changes significantlywhether focusing on DM annihilation or decay, even though UrsaMajor II remains the best candidate for ↵

int

= ↵Dc . Furthermore,

the two panels in figure 7 show that changing the integration anglefor a decaying DM signal also has a strong impact on the ranking

and on the error bars, more strongly than in the case of DM anni-hilation. In particular, for ↵

int

= 0.1� (bottom panel), most targetshave very similar D-factors and the increased error bars make theranking less obvious.

Comparison to other works. The availability of independently-derived D-factors for dSphs in the literature remains limited, mak-ing comparison less straightforward than in the case of annihilation.

• Although not published in the Charbonnier et al. (2011) studywhich focused on J-factors only, the D-factors for the eight ‘clas-sical’ dSphs were also obtained from our original analysis setup.As in the case of annihilation, these values (green dots in figure 7)are systematically lower than that obtained by the present analysisand this is connected, as for J , to the choice of the light profile.• We also compare our results to those of Geringer-Sameth,

c� Xxxx RAS, MNRAS 000, 1–18

Bonnivard+ 1504.02048 (MNRAS)

see also Charbonnier+ 1104.0412 (MNRAS), Martinez 1309.2641 (MNRAS), Geringer-Sameth+1408.0002 (ApJ), Hayashi+ 1603.08046 (MNRAS)

Cross section upper limits

Geringer-Sameth, Koushiappas, Walker 1410.2242 (PRD)

22

101 102 103

Mass [GeV]

10�27

10�26

10�25

10�24

10�23

h�vi

[cm

3

s�1

]

�+��

101 102 103

Mass [GeV]

10�27

10�26

10�25

10�24

10�23

h�vi

[cm

3

s�1

]

µ+µ�

FIG. 11: Annihilation cross section limits from the joint analysis of 20 dwarf galaxies. The shaded band is the systematic 1�

uncertainty in the limit derived from many realizations of halo J-profiles of the dwarfs consistent with kinematic data. Thesolid line depicts the median of this distribution of limits over the halo realizations. The thin dashed line corresponds to thebenchmark value of the required relic abundance cross section (3 ⇥ 10�26cm3

/s), while the solid horizontal line correspondsto the detailed calculation of this quantity derived by Steigman et al. [18]. The observed limits are below this latter curvefor masses less than [0, 26, 54] GeV (for annihilation into bb), [18, 29, 62] GeV (⌧+

⌧

�), [21, 35, 64] GeV (uu, dd, ss, cc, and gg),[87, 114, 146] GeV (��), and [5, 6, 10] GeV (e+

e

�), where the quantities in brackets are for the �1�, median, and +1� levels ofthe systematic uncertainty band. A machine-readable file tabulating these limits is available as Supplemental Material.

observed test statistic. The signal significance is shownassuming the two di↵erent background PDFs. An as-sumption of a Poisson background does not describe theactual background in many cases and can lead to a mis-takenly large detection significance.

The di�culty in fitting a multi-component Poissonbackground model is illustrated in Fig. 4 of [92]. There,“blank sky locations” are used to test whether the like-lihood ratio test statistic is accurately described by an“asymptotic” �2 distribution. This sampling of blank skylocations is analogous to the empirical background sam-pling developed in [48] and employed in the present work.Ackermann et al. [92] found that the blank sky PDF ofthe test statistic deviated from the �2 distribution at

large values of the test statistic. One of the reasons forthe deviation could be that the background model is notflexible enough to describe the true background. Carl-son et al. [56] present evidence that unresolved blazarsand radio sources are at least partly responsible for theinsu�ciency of the background treatment used in [92].

The blank sky location sampling of Ackermann et al.[92, Fig. 4] reduces the tail probability of a TS = 8.7observation to a local p-value of 0.13. This correspondsto a significance of 2.2� which can be directly comparedto the values shown in our Figs. 8, 9, and 10. Thus,when calibrating the detection significance using an em-pirical sampling of the background, the results of Acker-mann et al. [92] are closer in line with what we find. We

see also Fermi collab 1503.02641 (PRL), Fermi+DES 1611.03184 (ApJ),H.E.S.S. collab 1410.2589 (PRD), MAGIC collab 1312.1535 (JCAP)

102 103 104 105

Mass [GeV]

10�24

10�23

10�22

10�21

h�vi

[cm

3s�

1]

⌧+⌧� All

No Seg1

VERITAS collaboration 1703.04937 (PRD)

flux / h�viJ

20 dwarfs 4 dwarfs

Reticulum II

Gamma-rays 1-300 GeV Gamma-ray background model at 8 GeV

�105 �100 �95 �90 �85 �80Galactic longitude [Deg]

�60

�55

�50

�45

�40

Gal

actic

latitu

de

[Deg

]

0.9

1.0

1.1

1.2

1.3

1.4

1.5

1.6

Rel

ativ

ein

tensi

ty

Uniform backgroundFar away from known sources

very close (30 kpc)(Koposov+ 1503.02079 (ApJ), Bechtol+ 1503.02584 (ApJ))

100 101 102

Energy [GeV]

10�7

10�6

10�5

E2dF

/dE

[GeV

cm�

2s�

1sr

�1]

Fermi diffuse model

Empirical background

Fermi isotropic model

Geringer-Sameth+ 1503.02320 (PRL)

100 101 102

Energy [GeV]

10�7

10�6

10�5

E2dF

/dE

[GeV

cm�

2s�

1sr

�1]

1339051 33 22

18 11

10 6

1

1

135.496.3

59.2 33.519.911.56.5 3.9 2.3 1.3

0.6 0.30.2 0.1 0.1

Events within 0.5° of RetII

detection significance (p value) of 0.01% to 1% depending on background modeling

Geringer-Sameth+ 1503.02320 (PRL)

see also Fermi+DES 1503.02632 (ApJL), 1611.03184 (ApJ),Hooper, Linden 1503.06209 (JCAP), Baring+ 1510.00389 (PRD),Siegert+ 1608.00393 (A&A), Zhao+ 1702.05266,Regis, Richter, Colafrancesco 1703.09921

101 102 103

Mass [GeV]

10�1

100

101

102

103

J19

h�vi �

26

bb

⌧+⌧�hh

µ+µ�

Jh�vi

<σv> upper limits from other dwarfs gives a prediction for RetII’s J value22

101 102 103

Mass [GeV]

10�27

10�26

10�25

10�24

10�23

h�vi

[cm

3

s�1

]

�+��

FIG. 11: Annihilation cross section limits from the joint analysis of 20 dwarf galaxies. The shaded band is the systematic 1�

uncertainty in the limit derived from many realizations of halo J-profiles of the dwarfs consistent with kinematic data. Thesolid line depicts the median of this distribution of limits over the halo realizations. The thin dashed line corresponds to thebenchmark value of the required relic abundance cross section (3 ⇥ 10�26cm3

/s), while the solid horizontal line correspondsto the detailed calculation of this quantity derived by Steigman et al. [18]. The observed limits are below this latter curvefor masses less than [0, 26, 54] GeV (for annihilation into bb), [18, 29, 62] GeV (⌧+

⌧

�), [21, 35, 64] GeV (uu, dd, ss, cc, and gg),[87, 114, 146] GeV (��), and [5, 6, 10] GeV (e+

e

�), where the quantities in brackets are for the �1�, median, and +1� levels ofthe systematic uncertainty band. A machine-readable file tabulating these limits is available as Supplemental Material.

observed test statistic. The signal significance is shownassuming the two di↵erent background PDFs. An as-sumption of a Poisson background does not describe theactual background in many cases and can lead to a mis-takenly large detection significance.

The di�culty in fitting a multi-component Poissonbackground model is illustrated in Fig. 4 of [92]. There,“blank sky locations” are used to test whether the like-lihood ratio test statistic is accurately described by an“asymptotic” �2 distribution. This sampling of blank skylocations is analogous to the empirical background sam-pling developed in [48] and employed in the present work.Ackermann et al. [92] found that the blank sky PDF ofthe test statistic deviated from the �2 distribution at

large values of the test statistic. One of the reasons forthe deviation could be that the background model is notflexible enough to describe the true background. Carl-son et al. [56] present evidence that unresolved blazarsand radio sources are at least partly responsible for theinsu�ciency of the background treatment used in [92].

The blank sky location sampling of Ackermann et al.[92, Fig. 4] reduces the tail probability of a TS = 8.7observation to a local p-value of 0.13. This correspondsto a significance of 2.2� which can be directly comparedto the values shown in our Figs. 8, 9, and 10. Thus,when calibrating the detection significance using an em-pirical sampling of the background, the results of Acker-mann et al. [92] are closer in line with what we find. We

h�vi

allowed

ruled out

Reticulum II Other dwarfs

log10 J & 19.6± 0.3

AGS, Koushiappas, Walker 1410.2242 (PRD) AGS et. al. 1503.02320 (PRL)

Bonnivard+ 1504.03309 (ApJL)

Measured J values

4 Bonnivard et al.

[deg]intα-210 -110 1 10

]-5

cm

2) [

GeV

int

αJ(

1710

1910

2110

2310

Median68% CIs95% CIs

Reticulum II

J-factor

[deg]intα-210 -110 1 10

]-2

) [G

eV c

min

tα

D(

1610

1710

1810

1910

2010

2110

2210

Median68% CIs95% CIs

Reticulum II

D-factor

Figure 3. Median (solid), 68 % (dashed), and 95% (dash-dot) CIsof the J- (top) and D-factors (bottom) of Ret II, as a function ofintegration angle, reconstructed from our Jeans/MCMC analysis.

0.1 < Pi < 0.95, we obtain very similar results. Thesetwo tests confirm that the reconstruction of the astro-physical factors of Ret II is not significantly a↵ected byoutliers. This is not always the case, notably for Segue I(Bonnivard, Maurin & Walker, in prep.).We note that Simon et al. (2015) independently per-

formed an analysis of the M2FS Ret II spectroscopic dataand found a slightly smaller J-factor. This can be tracedto their choice of priors and light profile (L. Strigari,private communication). A detailed comparison will bepresented in Geringer-Sameth at al. (in prep.).

4. COMPARISON TO OTHER DSPHS

The same Jeans analysis has been applied to twenty-one other dSphs in Bonnivard et al. (2015b). In Figure 4,we compare the J-factors (for ↵

int

= 0.5�) of Ret II to thebrightest objects identified in Bonnivard et al. (2015b)11.Ret II is comparable to Wilman I in terms of its medianJ-factor, but slightly below Coma Berenices and UrsaMajor II. Its CIs are typical of an ‘ultrafaint’ dSph, andsignificantly larger than the uncertainties of ‘classical’dSphs.Interpreting the possible �-ray signal in Ret II in

terms of DM annihilation (Geringer-Sameth et al. 2015b;Hooper & Linden 2015), one would expect similar emis-sions from the dSphs with comparable J-factors, such asUMa II, Coma, and Wil I. However, no excess was re-ported from these latter objects (Geringer-Sameth et al.2014; Fermi-LAT Collaboration 2015). This could beexplained by the large statistical and systematic12 un-

11 Segue I may have a highly uncertain J-factor (Bonnivard,Maurin & Walker, in prep.). We show it only for illustration pur-poses.

12 The latter comes from a possible triaxiality of the dSph (0.4and 0.3 dex for annihilation and decay respectively, see Bonnivardet al. 2015a), and depends on the l.o.s. orientation with respect to

Ret II UMa II Coma Wil I Dra UMi Seg I

)-5

cm

2)/G

eV°

= 0

.5in

tα

(J(

10Lo

g

15

16

17

18

19

20

21

Ret II:Optimised setupPi-weightedBinned analysisBootstrap68% CIs (+ triaxiality systematics [ ] )

d [kpc]30 30 44 38 82 66 23

Bonnivard et al. (2015b)ClassicalUltrafaint

Figure 4. Comparison of the J-factors at ↵int = 0.5� obtainedfor Ret II (red circle) and for the potentially brightest objectsfrom Bonnivard et al. (2015b) (blue squares), with the sameJeans/MCMC analysis. Ret II is comparable to Wil I in termsof J-factors, but slightly below Coma and UMa II. A 0.4 dex sys-tematic uncertainty was added in quadrature to the 68% CIs toaccount for possible triaxiality of the DM halo (Bonnivard et al.2015a). Also shown are the J-factors obtained for Ret II by varyingdi↵erent ingredients of the analysis - see Section 3.

certainties in the J-factors. Moreover, the Jeans analysisassumes all of these objects to be in dynamical equilib-rium, but tidal interactions with the Milky Way couldartificially inflate the velocity dispersion and thereforethe astrophysical factors. UMa II, and to a lesser extentComa, appear to be experiencing tidal disturbance (Si-mon & Geha 2007; Fellhauer et al. 2007; Munoz et al.2010; Smith et al. 2013), while Wil I may show non-equilibrium kinematics (Willman et al. 2011). Cautionis therefore always advised when interpreting the astro-physical factors of these objects. The dynamical statusof Ret II is not yet clear. Its flattened morphology maysignal ongoing tidal disruption. However, the availablekinematic data do not exhibit a significant velocity gra-dient that might be associated with tidal streaming mo-tions (Walker et al. 2015).

5. CONCLUSION

We have applied a spherical Jeans analysis to the newlydiscovered dSph Ret II, using sixteen likely membersfrom the kinematic data set of Walker et al. (2015).We employed the optimized setup of Bonnivard et al.(2015a,b), which was found to mitigate several biasesof the analysis, and checked that our results are robustagainst several of its ingredients. We find that Ret IIpresents one of the largest annihilation J-factors amongthe Milky Way’s dSphs, possibly making it one of thebest targets to constrain DM particle properties. How-ever, it is important to obtain follow-up photometric andspectroscopic data in order to test the assumptions of dy-namical equilibrium as well as to constrain the fraction ofbinary stars in the kinematic sample. Nevertheless, theproximity of Ret II and its apparently large dark mattercontent place it among the most attractive targets fordark matter particle searches.

This work has been supported by the “Investissementsd’avenir, Labex ENIGMASS”, and by the French ANR,Project DMAstro-LHC, ANR-12-BS05-0006. MGW

the principle axes of the halo.

19.6

Use line of sight velocities + Jeans equation to infer dark matter density profile

Unmodeled systematics and statistics issues:

Ultrafaint dwarf galaxies: need to measure small from 10s of stars

Tidal stripping, not in equilibrium

Contamination

(and many more!) e.g. non-sphericity: Bonnivard+ 1407.7822 (MNRAS), Hayashi+ 1603.08046 (MNRAS) binary stars: Minor+ 1001.1160 (ApJ)

�2

Other large J contenders

Tucana III

Triangulum II

30 kpcReticulum II

Segue 1 23 kpc

30 kpc

Ursa Major II 32 kpc

Willman 1 38 kpc

25 kpc

Cetus II 30 kpc

Simon et. al. 1610.05301 (ApJ)� < 1.5 km/s

Kirby et. al. 1510.03856 (ApJ)� = 5.1 km/s� < 3.4 km/s Kirby et. al. 1703.02978 (ApJ)

star cluster or tidally stripped dwarf

no follow-up yet (too small, extremely low luminosity)

� = 3.6 km/s Walker et. al. 1504.03060 (ApJ)

suffers contamination -> giant error bar on J

irregular kinematics

tidal disturbance? e.g. Munoz et. al. 0910.3946 (AJ)

Coma Berenices 44 kpc

revised to

Draco and Ursa Minor classical dwarfs — good handle on J76 kpcEffect of contamination on J not studied except for Ret2 and Seg1

Contamination

4 Bonnivard et al.

[deg]intα-210 -110 1 10

]-5

cm

2) [

GeV

int

αJ(

1710

1910

2110

2310

Median68% CIs95% CIs

Reticulum II

J-factor

[deg]intα-210 -110 1 10

]-2

) [G

eV c

min

tα

D(

1610

1710

1810

1910

2010

2110

2210

Median68% CIs95% CIs

Reticulum II

D-factor

Figure 3. Median (solid), 68 % (dashed), and 95% (dash-dot) CIsof the J- (top) and D-factors (bottom) of Ret II, as a function ofintegration angle, reconstructed from our Jeans/MCMC analysis.

0.1 < Pi < 0.95, we obtain very similar results. Thesetwo tests confirm that the reconstruction of the astro-physical factors of Ret II is not significantly a↵ected byoutliers. This is not always the case, notably for Segue I(Bonnivard, Maurin & Walker, in prep.).We note that Simon et al. (2015) independently per-

formed an analysis of the M2FS Ret II spectroscopic dataand found a slightly smaller J-factor. This can be tracedto their choice of priors and light profile (L. Strigari,private communication). A detailed comparison will bepresented in Geringer-Sameth at al. (in prep.).

4. COMPARISON TO OTHER DSPHS

The same Jeans analysis has been applied to twenty-one other dSphs in Bonnivard et al. (2015b). In Figure 4,we compare the J-factors (for ↵

int

= 0.5�) of Ret II to thebrightest objects identified in Bonnivard et al. (2015b)11.Ret II is comparable to Wilman I in terms of its medianJ-factor, but slightly below Coma Berenices and UrsaMajor II. Its CIs are typical of an ‘ultrafaint’ dSph, andsignificantly larger than the uncertainties of ‘classical’dSphs.Interpreting the possible �-ray signal in Ret II in

terms of DM annihilation (Geringer-Sameth et al. 2015b;Hooper & Linden 2015), one would expect similar emis-sions from the dSphs with comparable J-factors, such asUMa II, Coma, and Wil I. However, no excess was re-ported from these latter objects (Geringer-Sameth et al.2014; Fermi-LAT Collaboration 2015). This could beexplained by the large statistical and systematic12 un-

11 Segue I may have a highly uncertain J-factor (Bonnivard,Maurin & Walker, in prep.). We show it only for illustration pur-poses.

12 The latter comes from a possible triaxiality of the dSph (0.4and 0.3 dex for annihilation and decay respectively, see Bonnivardet al. 2015a), and depends on the l.o.s. orientation with respect to

Ret II UMa II Coma Wil I Dra UMi Seg I

)-5

cm

2)/G

eV°

= 0

.5in

tα

(J(

10Lo

g

15

16

17

18

19

20

21

Ret II:Optimised setupPi-weightedBinned analysisBootstrap68% CIs (+ triaxiality systematics [ ] )

d [kpc]30 30 44 38 82 66 23

Bonnivard et al. (2015b)ClassicalUltrafaint

Figure 4. Comparison of the J-factors at ↵int = 0.5� obtainedfor Ret II (red circle) and for the potentially brightest objectsfrom Bonnivard et al. (2015b) (blue squares), with the sameJeans/MCMC analysis. Ret II is comparable to Wil I in termsof J-factors, but slightly below Coma and UMa II. A 0.4 dex sys-tematic uncertainty was added in quadrature to the 68% CIs toaccount for possible triaxiality of the DM halo (Bonnivard et al.2015a). Also shown are the J-factors obtained for Ret II by varyingdi↵erent ingredients of the analysis - see Section 3.

certainties in the J-factors. Moreover, the Jeans analysisassumes all of these objects to be in dynamical equilib-rium, but tidal interactions with the Milky Way couldartificially inflate the velocity dispersion and thereforethe astrophysical factors. UMa II, and to a lesser extentComa, appear to be experiencing tidal disturbance (Si-mon & Geha 2007; Fellhauer et al. 2007; Munoz et al.2010; Smith et al. 2013), while Wil I may show non-equilibrium kinematics (Willman et al. 2011). Cautionis therefore always advised when interpreting the astro-physical factors of these objects. The dynamical statusof Ret II is not yet clear. Its flattened morphology maysignal ongoing tidal disruption. However, the availablekinematic data do not exhibit a significant velocity gra-dient that might be associated with tidal streaming mo-tions (Walker et al. 2015).

5. CONCLUSION

We have applied a spherical Jeans analysis to the newlydiscovered dSph Ret II, using sixteen likely membersfrom the kinematic data set of Walker et al. (2015).We employed the optimized setup of Bonnivard et al.(2015a,b), which was found to mitigate several biasesof the analysis, and checked that our results are robustagainst several of its ingredients. We find that Ret IIpresents one of the largest annihilation J-factors amongthe Milky Way’s dSphs, possibly making it one of thebest targets to constrain DM particle properties. How-ever, it is important to obtain follow-up photometric andspectroscopic data in order to test the assumptions of dy-namical equilibrium as well as to constrain the fraction ofbinary stars in the kinematic sample. Nevertheless, theproximity of Ret II and its apparently large dark mattercontent place it among the most attractive targets fordark matter particle searches.

This work has been supported by the “Investissementsd’avenir, Labex ENIGMASS”, and by the French ANR,Project DMAstro-LHC, ANR-12-BS05-0006. MGW

the principle axes of the halo.

19.6

10 Bonnivard, Maurin, Walker

Seg I UMa II Ret II Wil I Coma UMi Dra

)-5

cm

2)

/ G

eV

° =

0.5

int

α (

J(

10

Log

12

14

16

18

20

22

Membership prob. (P)

EM P-weighted MCMC

Bayesian Cut-95% Bootstrap

d [kpc]23 30 30 38 44 66 82

Bootstrapσ68% CIs/

No P available

P analysis Stat. analysis

Figure 8. Comparison of the J-factors of Seg I, obtained with the severaltests of this paper, to the values for the closest dSphs galaxies from Bon-nivard et al. (2015a,b). The J-factor can vary from ⇠ 10

16 to ⇠ 10

21

GeV2 cm�5 from one analysis to another. On the other hand, Ret II’s J-factor was found to be robust against the different tests.

for other dSph galaxies10. Depending on choice of procedure, forSeg I we can recover estimates of J-factors spanning ⇠ 3 orders ofmagnitude, covering the range of previously published values. Weconclude that estimates of J-factors for Seg I should be regardedwith extreme caution when planning and interpreting indirect de-tection experiments.

ACKNOWLEDGEMENTS

We thank Celine Combet and Alex Geringer-Sameth for useful dis-cussions, and Manoj Kaplinghat for comments that have helpedus improve the paper. This work has been supported by the “In-vestissements d’avenir, Labex ENIGMASS” and by the FrenchANR, Project DMAstro-LHC, ANR-12-BS05-0006. MGW is sup-ported by National Science Foundation grants AST-1313045, AST-1412999. This study used the CC-IN2P3 computation center ofLyon.

REFERENCES

Aaronson M., 1983, ApJ, 266, L11Ackermann, Fermi-LAT Collaboration, 2011, Physical Review

Letters, 107, 241302Ackermann M. et al., 2014, Phys. Rev. D, 89, 042001Aleksic J. et al., 2014, J. Cosmology Astropart. Phys., 2, 8Aliu E. et al., 2012, Phys. Rev. D, 85, 062001Baes M., van Hese E., 2007, A&A, 471, 419Belokurov V. et al., 2009, MNRAS, 397, 1748Belokurov V., et al., 2007, ApJ, 654, 897Binney J., Tremaine S., 2008, Galactic Dynamics: Second Edi-

tion. Princeton University PressBonnivard V. et al., 2015a, ArXiv e-printsBonnivard V. et al., 2015b, ArXiv e-printsBonnivard V., Combet C., Maurin D., Walker M. G., 2015c, MN-

RAS, 446, 3002

10 For Ursa Major II (UMa II), Willman I (Wil I) and Coma, we could notrepeat our tests for sensitivity to choice of procedure for handling member-ship probabilities, as the relevant stellar-kinematic samples are not publiclyavailable.

Bonnivard V., Hutten M., Nezri E., Charbonnier A., Combet C.,Maurin D., 2015d, ArXiv e-prints

Brooks A. M., Zolotov A., 2014, ApJ, 786, 87Charbonnier A. et al., 2011, MNRAS, 418, 1526Charbonnier A., Combet C., Maurin D., 2012, Computer Physics

Communications, 183, 656Cholis I., Salucci P., 2012, Phys. Rev. D, 86, 023528Efron B., 1982, The Jackknife, the Bootstrap and other resampling

plansEssig R., Sehgal N., Strigari L. E., Geha M., Simon J. D., 2010,

Phys. Rev. D, 82, 123503Evans N. W., Ferrer F., Sarkar S., 2004, Phys. Rev. D, 69, 123501Fermi-LAT Collaboration et al., 2015, ArXiv e-printsGeringer-Sameth A., Koushiappas S. M., 2011, Physical Review

Letters, 107, 241303Geringer-Sameth A., Koushiappas S. M., Walker M., 2015, ApJ,

801, 74Geringer-Sameth A., Koushiappas S. M., Walker M. G., 2014,

ArXiv e-printsGeringer-Sameth A., Walker M. G., Koushiappas S. M., Koposov

S. E., Belokurov V., Torrealba G., Wyn Evans N., 2015, ArXive-prints, 1503.02320

Hooper D., Linden T., 2015, ArXiv e-prints, 1503.06209Kirby E. N. et al., 2010, ApJS, 191, 352Klimentowski J., Łokas E. L., Kazantzidis S., Prada F., Mayer L.,

Mamon G. A., 2007, MNRAS, 378, 353Koposov S. E., Belokurov V., Torrealba G., Wyn Evans N., 2015a,

ArXiv e-prints, 1503.02079Koposov S. E. et al., 2015b, ArXiv e-printsLake G., 1990, Nature, 346, 39Martin N. F., Ibata R. A., Chapman S. C., Irwin M., Lewis G. F.,

2007, MNRAS, 380, 281Martinez G. D., Bullock J. S., Kaplinghat M., Strigari L. E., Trotta

R., 2009, Journal of Cosmology and Astro-Particle Physics, 6, 14Martinez G. D., Minor Q. E., Bullock J., Kaplinghat M., Simon

J. D., Geha M., 2011, ApJ, 738, 55Mateo M. L., 1998, ARA&A, 36, 435McConnachie A. W., 2012, AJ, 144, 4Putze A., Derome L., 2014, Physics of the Dark Universe, 5, 29Robin A. C., Reyle C., Derriere S., Picaud S., 2003, A&A, 409,

523Simon J. D. et al., 2015, ArXiv e-printsSimon J. D., Geha M., 2007, ApJ, 670, 313Simon J. D. et al., 2011, ApJ, 733, 46Springel V. et al., 2008, MNRAS, 391, 1685Strigari L. E., 2013, Phys. Rep., 531, 1Strigari L. E., Bullock J. S., Kaplinghat M., Simon J. D., Geha M.,

Willman B., Walker M. G., 2008a, Nature, 454, 1096Strigari L. E., Koushiappas S. M., Bullock J. S., Kaplinghat M.,

2007, Phys. Rev. D, 75, 083526Strigari L. E., Koushiappas S. M., Bullock J. S., Kaplinghat M.,

Simon J. D., Geha M., Willman B., 2008b, ApJ, 678, 614The DES Collaboration et al., 2015, ArXiv e-printsWalker M. G., Combet C., Hinton J. A., Maurin D., Wilkinson

M. I., 2011, ApJ, 733, L46Walker M. G., Mateo M., Olszewski E. W., 2009, AJ, 137, 3100Walker M. G., Mateo M., Olszewski E. W., Bailey, III

J. I., Koposov S. E., Belokurov V., Wyn Evans N., 2015,ArXiv:1504.03060

Walker M. G., Mateo M., Olszewski E. W., Penarrubia J., WynEvans N., Gilmore G., 2009a, ApJ, 704, 1274

c� Xxxx RAS, MNRAS 000, 1–10

Use line of sight velocities + Jeans equation to infer dark matter density profile

Bonnivard+ 1506.08209 (MNRAS)

Seg1

Bonnivard+ 1504.03309 (ApJL)

see also Simon+ 1504.02889 (ApJ), Ichikawa+ 1608.01749 (MNRAS), 1706.05481

Everything* in these plots requires a J value and dynamical modeling is always involved

the bb and τþτ− channels with expectation bands derivedfrom the analysis of 300 randomly selected sets of blankfields. Sets of blank fields are generated by choosingrandom sky positions with jbj > 30° that are centered atleast 0.5° from 3FGL catalog sources. We additionallyrequire fields within each set to be separated by at least7°. Our expected limit bands are evaluated with the 3FGL

source catalog based on four years of PASS7 REPROCESSED

data and account for the influence of new sources present inthe six-year PASS8 data set.Comparing with the results of Ackermann et al. [13], we

find a factor of 3–5 improvement in the limits for allchannels using six years of PASS8 data and the same sampleof 15 dSphs. The larger data set as well as the gains in the

LAT instrument performance enabled by PASS8 bothcontribute to the increased sensitivity of the presentanalysis. An additional 30%–40% improvement in thelimit can be attributed to the modified functional formchosen for the J factor likelihood (3). Statistical fluctua-tions in the PASS8 data set also play a substantial role.Because the PASS8 six-year and PASS7 REPROCESSED

four-year event samples have a shared fraction of only20%–40%, the two analyses are nearly statistically inde-pendent. For masses below 100 GeV, the upper limits ofAckermann et al. [13] were near the 95% upper bound ofthe expected sensitivity band while the limits in the presentanalysis are within 1 standard deviation of the medianexpectation value.

FIG. 1 (color). Constraints on the DM annihilation cross section at the 95% CL for the bb (left) and τþτ− (right) channels derived froma combined analysis of 15 dSphs. Bands for the expected sensitivity are calculated by repeating the same analysis on 300 randomlyselected sets of high-Galactic-latitude blank fields in the LAT data. The dashed line shows the median expected sensitivity while thebands represent the 68% and 95% quantiles. For each set of random locations, nominal J factors are randomized in accord with theirmeasurement uncertainties. The solid blue curve shows the limits derived from a previous analysis of four years of PASS7 REPROCESSED

data and the same sample of 15 dSphs [13]. The dashed gray curve in this and subsequent figures corresponds to the thermal relic crosssection from Steigman et al. [5].

FIG. 2 (color). Comparison of constraints on the DM annihilation cross section for the bb (left) and τþτ− (right) channels from thiswork with previously published constraints from LAT analysis of the Milky Way halo (3σ limit) [57], 112 hours of observations of theGalactic center with H.E.S.S. [58], and 157.9 hours of observations of Segue 1 with MAGIC [59]. Pure annihilation channel limits forthe Galactic center H.E.S.S. observations are taken from Abazajian and Harding [60] and assume an Einasto Milky Way density profilewith ρ⊙ ¼ 0.389 GeV cm−3. Closed contours and the marker with error bars show the best-fit cross section and mass from severalinterpretations of the Galactic center excess [16–19].

PRL 115, 231301 (2015) P HY S I CA L R EV I EW LE T T ER Sweek ending

4 DECEMBER 2015

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