SPATIAL UNIFORMITY OF THE GALACTIC GAMMA-RAY EXCESS

Manoj Kaplinghat, UC Irvine

THE GALACTIC CENTER EXCESS 4

0.69 0.95 GeV 0.95 1.29 GeV 1.29 1.76 GeV 1.76 2.40 GeVObserved

Cou

nts

BaselineModel

Residuals

Extended

Sou

rceModel

Extended

Sou

rceCou

nts

FullModel

Residuals

FIG. 1. Shown in the top row are photon counts in four energy bins that have significant evidence for an extended sourcewith a spectrum, morphology, and rate consistent with a 30 GeV mass WIMP annihilating to bb-quarks in the 7 7 regionabout the GC. This row shows the 17 2FGL point sources in the ROI as circles. The second row shows the residuals for thefit to the region varying all the sources in the 2FGL catalog as well as the amplitudes of Galactic di↵use and isotropic di↵usemodels. The presence of an extended source and oversubraction of the central point sources are visible here. The third rowshows the best fit model counts for 30 GeV WIMP annihilating to bb-quarks. The fourth row is the residual emission for thismodel without subtracting the extended component. The fifth row contains the residuals when the extended component is alsosubtracted. The maps have been filtered with a Gaussian of width = 0.3.

* GC excess: Goodenough and Hooper (2009), Hooper and Goodenough (2010), Boyarsky, Malyshev, Ruchayskiy (2010), Hooper and Linden (2011), Abazajian and Kaplinghat (2012), Yusef-Zadeh et al (2012), Gordon and Macias (2013).

* Hooper and Slatyer (2013), Daylan et al (2014) and Calore et al (2014) argued that this signal is extended, at least to 10 degrees.

4

0.69 0.95 GeV 0.95 1.29 GeV 1.29 1.76 GeV 1.76 2.40 GeV

Observed

Cou

nts

BaselineModel

Residuals

Extended

Sou

rceModel

Extended

Sou

rceCou

nts

FullModel

Residuals

FIG. 1. Shown in the top row are photon counts in four energy bins that have significant evidence for an extended sourcewith a spectrum, morphology, and rate consistent with a 30 GeV mass WIMP annihilating to bb-quarks in the 7 7 regionabout the GC. This row shows the 17 2FGL point sources in the ROI as circles. The second row shows the residuals for thefit to the region varying all the sources in the 2FGL catalog as well as the amplitudes of Galactic di↵use and isotropic di↵usemodels. The presence of an extended source and oversubraction of the central point sources are visible here. The third rowshows the best fit model counts for 30 GeV WIMP annihilating to bb-quarks. The fourth row is the residual emission for thismodel without subtracting the extended component. The fifth row contains the residuals when the extended component is alsosubtracted. The maps have been filtered with a Gaussian of width = 0.3.

Characterizing the Fermi excess in the inner galaxy

Galactic Center: Innermost 7x7 deg

Inner galaxy: innermost ~20x20 deg, without the Galactic Center

ASTROPHYSICAL GAMMA-RAY BACKGROUND MODEL

Supermassive black hole Sag A*Point sources Stellar remnants

Blazars ...

Extended sources: Cosmic rays impinging on gas in disk

Upscattered starlight Extragalactic background

Fermi bubbles

EXTRACTING THE GALACTIC CENTER EXCESS

356358024

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0

2

4

GLON

GLATJIMAGE_G12_35x35x0_1_norm.fits_0

– 40 –

Grey scale flux range= 1.000 7.000 JY/BEAM

GAL

ACTI

C LA

T.

GALACTIC LONG.02 01 00 -01 -02

02 30

00

01 30

00

00 30

00

-00 30

-01 00

30

-02 00

30

2 4 6

Fig. 1.— (a - Top) Contours of background-subtracted continuum emission at 2, 4, 6, 8,

10, 12.5, 15, 20, 30, 40, 50, 75, 100, 150, 200 Jy beam−1 are superimposed on a grayscaleimage at 1.415 GHz with a spatial resolution of 539′′. The greyscale ranges between 1 and

7 Jy beam−1. (b - Bottom) The same as (a) except that only the greyscale image is shown.

+ Free isotropic component.

+Galactic diffuse +1.4 GHz +Excess model

+ Use Fermi tools for analyzing data.+ Point sources refit simultaneously within the ROI

Yusef-Zadeh et al 2012

Method based on Abazajian and Kaplinghat 2012 and Abazajian, Canac, Horiuchi and Kaplinghat 2014

EXTRACTING THE INNER GALAXY EXCESS

356358024

-4

-2

0

2

4

GLON

GLATJIMAGE_G12_35x35x0_1_norm.fits_0

+ Free isotropic component.+ Each energy bin analyzed separately, i.e., only use spatial information.

+Galactic diffuse +Excess model

+ Use Fermi tool Complike2. + Bright point sources refit simultaneously.

Horiuchi, Kaplinghat, Kwa, in prep

6

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Fig. 3.— Template decomposition of the Fermi-LAT 1.6 year 1 − 5 GeV map (see §3.1.2). Top left: Point source subtracted 1 − 5GeV map, and large sources, including the inner disk (−2 < b < 2,−60 < ℓ < 60), have been masked. Top middle: The 1 − 5GeV map minus SFD dust map (top right panel) which is used as a template of π0 gammas. Middle row: The left panel is the same asthe top middle panel but stretched 2× harder. The middle panel subtracts a simple geometric disk template (shown in the right panel),representing mostly inverse Compton emission, to reveal features close to the Galactic center. Two large bubbles are apparent (spanning−50 < b < 50). Bottom row: The left panel is the same as the middle panel of the second row. Finally we subtract a simple bubbletemplate (right panel), with a shape derived from the edges visible in the maps, and uniform projected intensity. After subtracting thebubble template, the two bubbles features have nearly vanished (bottom middle panel), indicating a nearly flat intensity for the Fermi

bubbles.

+Bubble

26 deg

20 deg

Use Fermi tool Complike2 to tie astrophysical background model templates across inner galaxy subregions, separately for IC and π0+Bremsstrahlung. NFW-like template normalization allowed to vary between regions.

GAMMA RAYS FROM DARK MATTER ANNIHILATION

4

TABLE I. Models’ renormalized log likelihood values, asreported by the Fermi Science Tools, ln[L (

Pi ki!))],

where ki is the photon count in bin i, for the various mod-els and the ln(L) as compared to the 2FGL-only modelfor the analysis where photons in the energy range 0.2to 300 GeV were included. The model in the last row,2FGL+2PS+I+MG+ND+GCE, defines our full model.

Model ln[L(P

i ki!)] lnL

2FGLa -1080408.3 –2FGL+2PSb -1080510.3 102.02FGL+2PS+Ic -1080685.7 277.42FGL+2PS+I+MGd -1080931.1 522.82FGL+2PS+I+MG+NDe =0.5 -1081012.9 604.72FGL+2PS+I+MG+GCEf =1.1 -1081061.5 653.22FGL+2PS+I+MG+GCE =1.1

+ ND =0.5 -1081098.3 690.0

a Point sources in the 2FGL catalog, together withgal 2yearp7v6 v0 and iso p7v6source di↵use models

b The two additional point sources (PS) found in the ROIc The new isotropic component (I) with free power-law spectrum;note iso p7v6source is kept fixed when this is added.

d The 20 cm radio map template (MG)e The new di↵use model (ND) with its respective f The Galactic Center Excess (GCE) with its respective

The di↵erential flux for a dark matter candidate withcross-section h

A

vi toward Galactic coordinates (b, `) is

d(b, `)

dE

=h

A

vi2

J(b, `)

J

0

1

4m2

dN

dE

, (2.3)

where dN/dE is the gamma-ray spectrum per annihi-lation and m is the dark matter particle mass. Thequantity J is the integrated mass density squared alongline-of-sight, x,

J(b, `) = J

0

Zd x

2(rgal

(b, `, x)) , (2.4)

where distance from the GC is given by

r

gal

(b, `, x) =q

R

2

2xR

cos(`) cos(b) + x

2

. (2.5)

Here, J0

1/[8.5 kpc(0.3 GeV cm3)2] is a normaliza-tion that makes J unitless and cancels in final expressionsfor observables. The value for the solar distance is takento be R

= 8.25 kpc [23]. The density s for the ↵

profile is a normalization constant determined uniquelyby the local dark matter density,

.

C. Method

In order to find the best fit models, and quantify thesystematic error inherent in the model-choice dependencein the analyses, we found fits to a very large number ofdi↵use and extended source model combinations. Our

FIG. 2. Shown are two cases of our determination of the SgrA source spectrum. The 2FGL+2PS+I binned spectrum isin pink circles, with best fit binned log-parabola spectrum inpink. The full model 2FGL+2PS+I+MG+ND+GCE spec-trum is in blue squares, with best fit binned log-parabolaspectrum in blue. The presence of GCE associated photonsat 1 to 3 GeV in the Sgr A spectrum is evident in the caseof the 2FGL+2PS+I modeling. The errors shown are solelythe Poisson errors within the energy band and do not reflectcovariances or systematic uncertainties.

2FGL+2PS+I model consists of all the 2FGL sourcesplus the two additional point sources, 1FGL J1744.0-2931c and bkgA, and the new isotropic component. Weadd to this the MG template and the GCE template indi-vidually and then together to test the significance of theirdetection. Then, we include the ND model and simulta-neously vary the density squared and 2D projected to find the best fit morphologies for these sources.For each of the model combination cases, we scan

the dark matter particle mass for WIMPs annihilatinginto bb, +, and a mixture of both channels to findthe best fit particle masses. To do this, we add toeach model a dark matter source with a

2 spatial tem-plate, Eq. (2.2), and spectrum generated via PYTHIAas in Refs. [24, 25]. For finer mass binning, we usegamma-ray spectra generated with DarkSUSY [26] andmicrOmegas [27]. Due to the finite intervals betweenparticle masses, we determine the best fit masses anderrors for the various mass cases with a fourth orderspline interpolation. As can be seen in Fig. 7, this ismethod is suciently accurate. For each particle mass,we vary all of the parameters in the region of interest.We repeat this procedure for several di↵erent models:for 2FGL+2PS+I+GCE (only point sources and di↵usebackgrounds), 2FGL+2PS+I+MG+GCE (with the MGtemplate included), and 2FGL+2PS+I+MG+ND+GCE(the full model, adding both the MG and new di↵usecomponents).Note that the prompt spectrum produced by the par-

ticle annihilation into both b quarks and leptons can

4

TABLE I. Models’ renormalized log likelihood values, asreported by the Fermi Science Tools, ln[L (

Pi ki!))],

where ki is the photon count in bin i, for the various mod-els and the ln(L) as compared to the 2FGL-only modelfor the analysis where photons in the energy range 0.2to 300 GeV were included. The model in the last row,2FGL+2PS+I+MG+ND+GCE, defines our full model.

Model ln[L(P

i ki!)] lnL

2FGLa -1080408.3 –2FGL+2PSb -1080510.3 102.02FGL+2PS+Ic -1080685.7 277.42FGL+2PS+I+MGd -1080931.1 522.82FGL+2PS+I+MG+NDe =0.5 -1081012.9 604.72FGL+2PS+I+MG+GCEf =1.1 -1081061.5 653.22FGL+2PS+I+MG+GCE =1.1

+ ND =0.5 -1081098.3 690.0

a Point sources in the 2FGL catalog, together withgal 2yearp7v6 v0 and iso p7v6source di↵use models

b The two additional point sources (PS) found in the ROIc The new isotropic component (I) with free power-law spectrum;note iso p7v6source is kept fixed when this is added.

d The 20 cm radio map template (MG)e The new di↵use model (ND) with its respective f The Galactic Center Excess (GCE) with its respective

The di↵erential flux for a dark matter candidate withcross-section h

A

vi toward Galactic coordinates (b, `) is

d(b, `)

dE

=h

A

vi2

J(b, `)

J

0

1

4m2

dN

dE

, (2.3)

where dN/dE is the gamma-ray spectrum per annihi-lation and m is the dark matter particle mass. Thequantity J is the integrated mass density squared alongline-of-sight, x,

J(b, `) = J

0

Zd x

2(rgal

(b, `, x)) , (2.4)

where distance from the GC is given by

r

gal

(b, `, x) =q

R

2

2xR

cos(`) cos(b) + x

2

. (2.5)

Here, J0

1/[8.5 kpc(0.3 GeV cm3)2] is a normaliza-tion that makes J unitless and cancels in final expressionsfor observables. The value for the solar distance is takento be R

= 8.25 kpc [23]. The density s for the ↵

profile is a normalization constant determined uniquelyby the local dark matter density,

.

C. Method

In order to find the best fit models, and quantify thesystematic error inherent in the model-choice dependencein the analyses, we found fits to a very large number ofdi↵use and extended source model combinations. Our

FIG. 2. Shown are two cases of our determination of the SgrA source spectrum. The 2FGL+2PS+I binned spectrum isin pink circles, with best fit binned log-parabola spectrum inpink. The full model 2FGL+2PS+I+MG+ND+GCE spec-trum is in blue squares, with best fit binned log-parabolaspectrum in blue. The presence of GCE associated photonsat 1 to 3 GeV in the Sgr A spectrum is evident in the caseof the 2FGL+2PS+I modeling. The errors shown are solelythe Poisson errors within the energy band and do not reflectcovariances or systematic uncertainties.

2FGL+2PS+I model consists of all the 2FGL sourcesplus the two additional point sources, 1FGL J1744.0-2931c and bkgA, and the new isotropic component. Weadd to this the MG template and the GCE template indi-vidually and then together to test the significance of theirdetection. Then, we include the ND model and simulta-neously vary the density squared and 2D projected to find the best fit morphologies for these sources.For each of the model combination cases, we scan

the dark matter particle mass for WIMPs annihilatinginto bb, +, and a mixture of both channels to findthe best fit particle masses. To do this, we add toeach model a dark matter source with a

2 spatial tem-plate, Eq. (2.2), and spectrum generated via PYTHIAas in Refs. [24, 25]. For finer mass binning, we usegamma-ray spectra generated with DarkSUSY [26] andmicrOmegas [27]. Due to the finite intervals betweenparticle masses, we determine the best fit masses anderrors for the various mass cases with a fourth orderspline interpolation. As can be seen in Fig. 7, this ismethod is suciently accurate. For each particle mass,we vary all of the parameters in the region of interest.We repeat this procedure for several di↵erent models:for 2FGL+2PS+I+GCE (only point sources and di↵usebackgrounds), 2FGL+2PS+I+MG+GCE (with the MGtemplate included), and 2FGL+2PS+I+MG+ND+GCE(the full model, adding both the MG and new di↵usecomponents).Note that the prompt spectrum produced by the par-

ticle annihilation into both b quarks and leptons can

fluxcross section

mass

spectrum

dark matter density profile

COMPARING THE CENTRAL AND MORE EXTENDED REGIONS

107

106

GCGCGC NNN SSS

107

106

(JT

ot/J

RO

I)

E

2dN

/dE

[GeV

cm

2s

1]

NENENE SESESE NWNWNW

107

106

SWSWSW

100 101 102

E [GeV]

N2N2N2 S2S2S2

Good agreement between different regions at the factor of 2 level.

Horiuchi, Kaplinghat, Kwa, in prep

COMPARING THE CENTRAL AND MORE EXTENDED REGIONS

High energy tail of GC vs Inner galaxy spectra !GC prefers γ=1.1 but inner galaxy shows no preference.

108

107

106

Model A Model E

=

0.9

Model F

108

107

106

(JT

ot

/JR

OI

)

E2

dN

/dE

[GeV

cm

2s

1]

=

1.0

108

107

106

=

1.1

100 101 102

108

107

106

GC

Inner galaxy

100 101 102

E [GeV]100 101 102

=

1.2

Figure 3. Best-fit GCE spectra in the galactic center and inner galaxy regions, shown for varieddi↵use background models (rows) and NFW density profile slopes (columns). The spectrum of theGCE in the inner galaxy is shown for the sum of all inner galaxy ROIs. Normalizations are scaled toshow the expected flux for the entire GCE template (35 35). Also shown are the broken powerlaw (blue dashed line) and exponential cuto↵ (red dot-dashed line) parameterized fits to the innergalaxy spectrum.

– 9 –

Horiuchi, Kaplinghat, Kwa, in prep

Background models

Templates ~ r–2γ in the inner part.

FERMI-LAT COLLABORATION ANALYSIS

Fermi-LAT analysis in 15x15 degree region around GC led by Troy Porter and Simona Murgia (arXiv:1511.02938): preference for an extended centrally concentrated component

GeV Observations of the Galactic Centre 19

Figure 13. Differential fluxes for the 15 15

region about the GC of theNFW component with spectrum modelled with an exponential cut-off powerlaw. The envelopes include the fit uncertainties for the normalisation andspectral index. Hatch styles: Pulsars, intensity-scaled (red, vertical); Pulsars,index-scaled (black, horizontal); OBstars, intensity-scaled (blue, diagonal-right); OBstars, index-scaled (green, diagonal-left). Results from selectedother works are overlaid. Filled symbols: Hooper & Slatyer (2013), differentsymbols bracket the results obtained when different regions of the sky areconsidered in the fit; Angled crosses: Gordon & Macıas (2013); Open sym-bols: Abazajian et al. (2014), front-converting events shown with triangles,front- and back-converting events shown with squares and circles, depend-ing on the modelling of the fore-/background. Stars : Calore et al. (2015a).Note: the overlaid results are rescaled to the DM content over the 15 15

region for an NFW profile with index =1.

stant for each IEM, the interplay between the centrally peakedpositive residual template and the interstellar emission com-ponents is not surprising. Because the IC component is max-imally peaked toward the GC for all IEMs an additional tem-plate that is also peaked there will also be attributed someflux when fit. Over all IEMs the effect of including the NFWmodel for the residual results in an IC annulus 1 contributionthat is up to three times smaller and H I annulus 1 contributionthat is up to three times larger.

Note that even if a centrally peaked template is included asa model for the positive residual, it does not account for all ofthe emission. This can be seen in Fig. 14, which shows theresidual counts for the NFW template and IEM with the bestspectral residuals (Pulsars index-scaled). Qualitatively, the re-mainder does not appear distributed symmetrically about theGC below 10 GeV, and still has extended positive residualseven at higher energies along and about the plane.

5. DISCUSSION5.1. Interstellar Emission

This study is the first using the Fermi–LAT data that hasmade a separation between the large-scale interstellar emis-sion of the Galaxy and that from the inner 1 kpc about theGC. The IC emission from annulus 1 is found to dominatethe interstellar emission from the innermost region, and rep-resents the majority of the IC brightness from this componentalong and through the line-of-sight toward the GC. The con-

Pulsars index-scaled IEM was tested by also setting them to the GALPROPpredictions and refitting for the annulus 1 interstellar emission, point sources,and residual model parameters. The normalisation and cut-off energy of theresidual model did not appreciably change, indicating that the majority of anyeffect related to the structured fore-/background from the index-scaled IEMsis likely from annulus 4.

tribution by the IC from annulus 1 to the total flux depends onthe IEM and whether the residual is fitted (Sec. 4.3). For thelatter case the IC from annulus 1 is still up-scaled comparedto the GALPROP predictions, but by a factor 2 lower thanif fitted solely for the interstellar emission components andpoint sources. The remainder is distributed across the H I-related

0-decay annulus 1 component and the template usedto fit the residual centred on the GC. For either case (residualtemplate used/not-used), the fitted fluxes attributed to the ICannulus 1 component across all IEMs are within a factor 2

– the flux and its range is the important quantity, instead ofthe individual (model-dependent) scaling factors.

The Pulsars intensity-scaled IEM with the residual tem-plate gives the minimal ‘enhanced’ flux for IC annulus 1.The average CR electron intensity & 5 GeV in the Galac-tic plane is estimated for this model within 1 kpc of theGC as 2.8± 0.1 10

4 cm2 s1 sr1, where the uncer-tainty is statistical only. This energy range is used because itslower bound corresponds to the CR electron energies produc-ing 1 GeV IC -rays. This is a factor of two higher thanthe local total CR electron density for this same energy rangefor the Pulsars baseline model. On the other hand, the OB-stars intensity-scaled IEM fitted without the residual compo-nent gives the maximal ‘enhanced’ flux for IC annulus 1. Theaverage CR electron intensity & 5 GeV in the Galactic planewithin 1 kpc of the GC for this IEM is 9.4± 0.1 10

4

cm2 s1 sr1.Measurements of the interstellar emission at hard X-ray

energies to MeV -rays by INTEGRAL/SPI (Bouchet et al.2011) show that the majority is due to IC scattering by GeVenergy CR electrons off the infrared component of the ISRF21.The GALPROP calculations, which follow the same “conven-tional” model normalisation condition to local CR measure-ments as used in this paper, made to interpret the SPI measure-ments indicate that IEMs with at least factor of 2 higher CRdensities toward the inner Galaxy are a plausible explanationfor the data. Another possible explanation is a higher intensityfor the radiation field energy density in the inner Galaxy thanused in the standard ISRF model of Porter et al. (2008); thesepossibilities are not tested here because they require detailedinvestigations that are beyond the scope of the current work.The higher CR electron densities obtained from this analy-sis are plausible given the same electrons are IC scatteringdifferent components of the ISRF to produce the interstellaremission & 1 GeV and at SPI energies.

The purpose for fitting the baseline IEMs to the datawas to obtain estimates for the interstellar emission fore-/background. However, the fit results for the individual ringsfor each IEM potentially give some information on the large-scale distribution of CRs througout the Galaxy. Tables 5 and 6in Appendix A.1 give the fit coefficients and fluxes for thescaled IEMs, while Fig.15 shows the integrated fluxes for the1–10 (top) and 10–100 GeV (bottom) energy ranges, respec-tively, over the 15 15

region for the GALPROP-predictedand scaled version of each IEM for the Pulsars (left) and OB-stars (right) source distributions.

The fitting procedure generally increases the intensity ofeach annulus relative to the nominal model. The coeffi-cients for the intensity-scaled Pulsars and OBstars IEMs aremostly higher than the GALPROP predictions toward the in-ner Galaxy (annuli 2 3). Those for the OBstars IEM are

21 The majority of the IC -rays in the energy range of this study areproduced by scattering off the optical component of the ISRF.

UNRESOLVED POINT SOURCE EXPLANATION OF THE EXCESS?

The excess spectrum is similar to the milli-second pulsar (MSP) spectrum [Abazajian 2010] !Both the spectrum and the spatial distribution could be consistent with a population of unresolved MSPs [Abazajian and Kaplinghat (2012)]

* For plausibility arguments for and against all of the excess being due to pulsars see Hooper, Cholis, et al (2013), Petrovic et al (2014), Calore et al (2015) and others. They boil down to issues of the luminosity function of MSPs.

-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2-1.5

-1.0

-0.5

0.0

0.5

Log@EnergyêGeVD

Log10@E

2 dNêdEHarb

itraryunitsLD

MSP ENERGY SPECTRUM

47 Tuc M62N6440 ωCen

Μ28N6388 N6652 Terzan5

Globular cluster spectra compared to excess in the inner galaxy (out to 10 degrees) obtained by Daylan et al 2014

0.8 GeV 2 GeV 8 GeV

Voss+Gilfanov 2007

400’’ towards M31 center =1.5 kpc distance from M31 center =10 deg towards MW center

HYPOTHESIS FOR THE SPATIAL PROFILE OF UNRESOLVED MILLISECOND PULSARS

R–1.2

Orange line is same as best-fit excess template (R–1.2 in projection implies r–2.2 de-projected)

Assume MSPs trace Low Mass X-ray Binaries

steepening with respect to Bulge stellar distribution

HYPOTHESIS FOR THE SPATIAL PROFILE OF UNRESOLVED MILLISECOND PULSARS

Created from Voss+Gilfanov 2007 data

GC signal requires ~ 4000 “MSPs” if each has the same E>2 GeV luminosity as (1/30) of 47 Tucanae globular cluster. ~30 MSPs

in 47 Tuc

Assume MSPs trace LMXBs

HAVE THE UNRESOLVED POINT SOURCES BEEN DISCOVERED?2

Γ = −2.5 and a hard cutoff at radius r = 3 kpc [13, 15].As reference γ-ray energy spectrum, we adopt the stackedMSP spectrum from Ref. [35], dN

dE ∝ e−E/3.78GeVE−1.57.The γ-ray luminosity function is modeled with a power-law, dN

dL ∝ L−α, with index α = −1.5 [31, 35], and withlower and upper hard cutoffs at Lmin = 1029 erg s−1 andLmax = 1034–1036 erg s−1, respectively. Luminosities areintegrated over 0.1–100 GeV. Our results depend little onLmin. Given that only about 70 MSPs have been detectedin γ-rays up to now [32], Lmax is not well constrained.The γ-ray luminosity of the brightest observed MSP issomewhere in the range 0.5–2 · 1035 erg s−1 [32, 35], de-pending on the adopted source distance [25, 31]. Diffuseemission is modeled with the standard model for pointsource analysis, gll iem v06.fits, and the correspond-ing isotropic background.

Data. For our analysis, we use almost seven years ofultraclean Fermi-LAT P8R2 data, taken between 4 Aug2008 and 3 Jun 2015. We select both front and back con-verted events in the energy range 1–4 GeV, which coversthe peak of the GCE spectrum. The Region Of Interest(ROI) covers the inner Galaxy and spans Galactic longi-tudes |ℓ| ≤ 12 and latitudes 2 ≤ |b| ≤ 12. The data isbinned in Cartesian coordinates with a pixel size of 0.1.

Wavelet peaks. The wavelet transform of the γ-raydata is defined as the convolution of the photon countmap, C(Ω), with the wavelet kernel, W(Ω),

FW [C](Ω) ≡!

dΩW(Ω− Ω′)C(Ω′) , (1)

where Ω denotes Galactic coordinates (note that"

dΩW(Ω) = 0). However, the central observable forthe current analysis is the signal-to-noise ratio (SNR) ofthe wavelet transform, which we define as

S(Ω) ≡FW [C](Ω)

#

FW2 [C](Ω), (2)

where in the denominator the wavelet kernel is squaredbefore performing the convolution. If the γ-ray flux var-ied only on scales much larger than the extent of thewavelet kernel, and in the limit of a large number ofphotons, S(Ω) would behave like a smoothed Gaussianrandom field. Consequentially, S(Ω) can be loosely in-terpreted as the local significance for having a source atposition Ω, in units of standard deviations.As wavelet kernel, we adopt the second member of the

Mexican Hat Wavelet Family, MHWF2, which was shownto provide very good source discrimination power [36],and which was used for identification of compact sourcesin Planck data [37]. The wavelet can be obtained bya successive application of the Laplacian operator to atwo-dimensional Gaussian distribution with width σb ·R.Here, σb = 0.4 corresponds to the Fermi-LAT angu-lar resolution at 1–4 GeV, and R is a tuning parameter.We find best results when R varies linearly with latitude

−10−50510

ℓ, Gal. longitude [deg]

−10

−5

0

5

10

b,Gal.latitude[deg]

−16

−8

0

8

16

24

32

40

FIG. 1. SNR of the wavelet transform of γ-rays with energiesin the range 1–4 GeV, S(Ω). The black circles show the po-sition of wavelet peaks with S ≥ 2; the red circles show theposition of 3FGL sources. In both cases, the circle area scaleswith the significance of the source detection in that energyrange. The dashed lines indicate the regions that we use forthe binned likelihood analysis, where latitudes |b| < 2 are ex-cluded because of the strong emission from the Galactic disk.The subset of 3FGL sources that remains unmasked in ouranalysis is indicated by the green crosses.

from R = 0.53 at b = 0 to R = 0.83 at b = ±12. Thiscompensates to some degree the increasing diffuse back-grounds towards the Galactic disk, while optimizing thesource sensitivity at higher latitudes [37].

The resulting SNR of the wavelet transform, S(Ω),is shown in Fig. 1. As expected, the Galactic diffuseemission is almost completely filtered out by the wavelettransform, whereas bright sources lead to pronouncedpeaks. We adopt a simple algorithm for peak identifi-cation: We find all pixels in S(Ω) with values larger thanin the four adjacent pixels. We then clean these resultsfrom artefacts by forming clusters of peaks with cophe-netic distances less than 0.3, and only keep the mostsignificant peak in each cluster.

In Fig. 1, we show the identified wavelet peaks withpeak significance S > 2, as well as all 3FGL sources forcomparison [1]. For sources that are bright enough inthe adopted energy range, we find a good correspondencebetween wavelet peaks and the 3FGL, both in terms ofposition and significance (we compare the significance ofwavelet peaks, S, with the 1–3 GeV detection significancefor 3FGL sources).

It is worth emphasizing that for the adopted spheri-cally symmetric and centrally peaked distribution of theCSP, most of the sources would be detected not directlyat the GC, but a few degrees away from the Galactic disk.This is simply due to the much weaker diffuse emission

Lee et al 2015Bartels et al 2015

4

00 3 5

18

9

22

0

FIG. 2: (Left) Best-fit source-count functions within 10 of the GC and |b| 2, with the 3FGL sources unmasked. Themedian and 68% confidence intervals are shown for each of the following PS components: NFW (dashed, orange), thin-disk(solid, blue), and isotropic (dotted, green). The number of observed 3FGL sources in each bin is indicated. The normalizationfor the di↵use emission in the fit is consistent with that at high latitudes, as desired. (Right) Posteriors for the flux fractionwithin 10 of the GC with |b| 2 arising from the separate PS components, with 3FGL sources unmasked. The inset showsthe result of removing the NFW PS template from the fit. Dashed vertical lines indicate the 16th, 50th, and 84th percentiles.

FIG. 3: Same as Fig. 2, except with 3FGL sources masked.

sources. When the NFW PS template is omitted (inset),the fraction of flux absorbed by the disk PS population isessentially unchanged at 6.8+0.7

0.9%, and the DM template

absorbs 7.7+0.70.8% of the flux. The DM flux obtained in

absence of an NFW PS template is consistent with otherestimates in the literature [12, 14]. The model includingthe NFW PS contribution is preferred over that withoutby a Bayes factor 106.4

When the 3FGL sources are masked, the NPTF proce-dure yields a best-fit source-count function given by theorange band in the left panel of Fig. 3. Below the break,the source-count function agrees well with that found bythe unmasked fit. In this case, the contributions from theisotropic and disk-correlated PS templates are negligible.

4 For reference, this corresponds to test statistic 2 lnL 36.

The flux fraction attributed to the NFW PS componentis 5.3+1.0

1.1%, while the NFW DM template absorbs nosignificant flux.

In the masked analysis, the Bayes factor for a modelthat contains an NFW PS component, relative to onethat does not, is 102, substantially reduced relative tothe result for the unmasked case. Masking the 3FGLsources removes most of the ROI within 5 of the GC,reducing photon statistics markedly, especially for anysignal peaked at the GC. Furthermore, in the maskedROI, non-NFW PS templates can absorb a substantialfraction of the excess. For example, if only disk andisotropic PS templates are added, the flux fraction at-tributed to the disk template is 2.5+0.70

0.62%, while that

attributed to NFW DM is 2.2+1.62.2% (the flux attributed

to isotropic PSs is negligible). When no PS templatesare included in the fit, the NFW DM template absorbs4.1+1.1

1.2% of the total flux. As we will discuss later, this

Issue: are all of the detected point sources real or are they due to small-scale structure in the diffuse background? See Fermi-LAT paper for a discussion on this issue.

POSSIBLE SECONDARY EMISSION FROM ELECTRONS AND POSITRONS

Figure 3. Shown here is an example 8 GeV dark matter annihilation model with equal branchingto all charged leptons, e±, µ±, ±, with the residual spectra of the prompt GCE (blue square), IC(golden triangle), and bremsstrahlung (pink circle) sources. The blue (dashed) GCE spectrum is isdetermined by the particle mass and annihilation rate fit to the observations. The solid predicted

resultant spectra for this annihilation channel’s IC (golden) and bremsstrahlung (pink) cases are insolid lines. ULTRACLEAN class photons are used for this analysis.

The e± in the products created by dark matter annihilation lose energy through threedistinct process [28]: (1) IC, which leads to upscattering of the interstellar radiation field(ISRF) photons, (2) bremsstrahlung (Br) radiation o↵ the gas, and (3) synchrotron radiationin the Galactic magnetic field. We focus on the first two components in this letter. Thedi↵erential flux of photons for these two components may be written as,

EdNIC,Br

dE=

Z

FOV

d

4

Z

LOSd`

Z m

Emin

dEedne

dEe

dPIC,Br

dE(3.1)

where FOV and LOS indicate integration over the field-of-view and line-of-sight respec-tively, dPIC/dE and dPBr/dE are the di↵erential power emitted per electron due to IC andbremsstrahlung processes. For bremsstrahlung, we include energy losses from atomic H andHe. To get the source energy distribution of electrons, positrons and gamma rays, we usethe software PPPC4DMID [29]. The number density of electrons and positrons per unitenergy, dne/dEe, is computed after including di↵usion and energy losses according to theprescriptions in Refs. [13, 30].

To propagate the e±, we assume a spatially constant di↵usion coecient K(E) = K0E,

– 6 –

The spatial profile and spectrum consistent with IC off of starlight due to e+e– with E < 10-20 GeV. The sharp cut-off in energy required distinguishes this from the other cosmic ray components.

7

FIG. 2. Spectral energy distribution for the GCE modelled with 10 GeV WIMPs annihilating into Model I, democratic leptons( 13

e+e + 1

3

µ+µ + 1

3

+). IC and Bremss stand for inverse Compton and bremsstrahlung emission respectively. Black andred error bars refer to the LAT (1) statistical and systematic errors, respectively. The fit and plot only consider energy binswith TS 1. Left Panel: shows the results of a bin-by-bin analysis when the secondaries’ di↵erent morphologies were notaccounted for in determining the bins. Right Panel: Displays the results of the bin-by-bin analysis when the full spectral andspatial information from secondaries was considered.

10

0

10

1

E [GeV]

10

9

10

8

10

7

10

6

E2

dN/dE

[GeV

cm

2

s

1

]

Millisecond Pulsars

Spectra + SpatialTotal emission

Prompt

IC

Bremss

FIG. 3. Spectral energy distribution for the GCE modelled with Model III (MSPs). This scenario assumes monochromaticinjection of e± at 20 GeV [48]. Line and color conventions used in the panels are the same as in Fig. 2. Left Panel: Results ofa bin-by-bin analysis when the di↵erent spatial morphologies of the three-component source spectra were not considered [47].Right Panel: Shows the results of a bin-by-bin analysis when the full spectral and spatial information of the three-componentsource was used.

ondary emission.

C. Model III, MSPs

As seen from Table I, the spectral-only analysis wouldnot reveal the need for secondary component for the MSP

case (Model III ) as the p-value is well above the 103

threshold before or after adding the secondaries. This isdue to the three parameters of the prompt componentthat absorb the spectral dependence of the excess.However, the broadband analysis results in a high TS

for both the total spectrum and the secondaries as shownin Table II. Therefore, this case is distinct from Model I

Abazajian et al 2015 Lacroix et al 2015

New excess

New excess

SUMMARY• The status of a centrally concentrated extended source

that is bright in GeV photons seems secure.

• Many questions remain:

• Is it all unresolved point sources? If yes, are they dominantly MSPs?

• What is the spatial profile of the source in the inner galaxy?

• Is there a change in the spectrum as one moves away from the GC? Does the spectrum in the inner galaxy extend beyond 10 GeV?

• How does the new IC-like excess fit in the big picture?