On Dark Matter Explanations of the Gamma-Ray Excesses from the Galactic Center and M31
Anne-Katherine Burns, Max Fieg, Christopher M. Karwin, Arvind Rajaraman
UUCI-HEP-TR 2020-17
On Dark Matter Explanations of the Gamma-Ray Excesses from the Galactic Centerand M31
Anne-Katherine Burns, ∗ Max Fieg, † and Arvind Rajaraman ‡ Department of Physics and Astronomy, University of California, Irvine, CA 92697-4575 USA
Christopher M. Karwin § Department of Physics and Astronomy, Clemson University, Clemson, SC 29634-0978, USA
The presence of an excess γ -ray signal toward the Galactic center (GC) has now been well estab-lished, and is known as the GC excess. Leading explanations for the signal include mis-modeling ofthe Galactic diffuse emission along the line of sight, an unresolved population of millisecond pulsars,and/or the annihilation of dark matter (DM). Recently, evidence for another excess γ -ray signalhas been reported toward the outer halo of M31. In this work we interpret the excess signals fromboth the GC and outer halo of M31 in the framework of DM annihilation, and show that the twospectra are consistent with a DM origin once J -factors are taken into account. We further comparethe excesses to models of DM annihilation, and determine the corresponding best-fit parameters.We find good fits to the spectrum both in two body and four body annihilation modes. I. INTRODUCTION
There is now overwhelming evidence that most of thematter in the Universe is composed of dark matter (DM)[1–9]. However, despite much experimental effort formany decades now, the nature of DM still remains elu-sive. Determining the characteristics of DM is one of themost important outstanding problems in particle physics.One of the most promising approaches for detectingDM is indirect detection. DM particles can annihilate ordecay to Standard Model (SM) particles, which can bedetected in astrophysical searches. In particular, annihi-lation or decay into photons gives a striking signal, sincetheir direction of arrival is correlated with their annihila-tion location, and because photons can travel over largedistances.Simulations predict that the highest DM densityshould be near the Galactic center (GC), though modelsdiffer on the exact profile shape. Since the annihilationsignal goes as the square of the density, the GC is thusexpected to be one of the brightest sources of γ -rays fromDM annihilation, and this makes it is an important targetfor indirect searches.It has now been well established that there exists anexcess of γ -rays toward the GC (as compared to the ex-pected background) [10–24]. Intriguingly, the signal isfound to be broadly consistent with having a DM origin,in regards to the energy spectrum and morphology. How-ever, there are other plausible interpretations of the ex-cess, including mis-modeling of the foreground emissionfrom the Milky Way (MW), and an un-resolved popula-tion of point sources, such as millisecond pulsars. These ∗ [email protected] † mfi[email protected] ‡ [email protected] § [email protected] other possibilities make it very difficult to extract a DMsignal with a high degree of confidence.Determining whether or not the GC excess does in facthave a DM origin (at least in part) will likely require com-plementarity with other targets, as well as other searchmethods (e.g. direct detection). For γ -ray searches, theMW’s dwarf spheroidal (dSph) satellite galaxies offer an-other promising target, as they are expected to be domi-nated by DM, with very little astrophysical background.However, thus far there has been no global signal de-tected, a result that is in tension with the DM interpre-tation of the GC excess [25, 26]. However, it is importantto note that the limits from the dSphs are subject to sys-tematic uncertainties relating to their DM content, andthis prohibits their ability to robustly constrain the GCexcess [27–29].Looking beyond the MW, the Andromeda galaxy (alsoknown as M31) is the closest large spiral galaxy to usand is predicted to be the brightest extragalactic sourceof DM annihilation [30, 31]. Recently, observations to-wards M31’s outer halo reported evidence for an excesssignal, with a peak in the γ -ray spectrum at an energysimilar to the GC excess [32]. Moreover, the analysis isbased on the outer regions of M31 where backgroundsfrom standard astrophysical emission are less dominant.It is thus plausible that both these signals result fromDM annihilation.In this work we perform a simultaneous analysis ofthe GC and M31 to determine if these two excesses areconsistent with having a DM origin. We first examine thetwo spectra and see if they are consistent with each otheronce J -factors are taken into account. This turns out tobe the case; furthermore, the required scaling turns outto be within the allowed range from a recent analysis ofthe M31 J -factor [33].We then compare these spectra to various models ofDM annihilation, We first consider 2-body final states,such as DM annihilating to bottoms and taus. It is alsointeresting to consider four-body final states, which are a r X i v : . [ a s t r o - ph . H E ] O c t motivated in models where DM which is coupled to theSM through pseudoscalar mediators [34–37] (such mod-els avoid direct detection constraints). We therefore con-sider a few motivated examples of annihilation to fourfinal-state particles. As we shall show, both two-bodyannihilations and four-body annihilations can producegood fits to the observed spectra.The paper is organized as follows. In section II we re-view the observational data leading to the GC excess,and the more recent signal towards the outer halo ofM31. We also review the current bounds on the J -factorsof the two signal regions. In the following section, Sec-tion III, we compare the M31 and GC spectra and ex-amine whether they are consistent with the allowed J -factors. We then, in Section IV, consider the spectrafrom specific DM models, for example, annihilation tob-quarks, and find the best fit to the observations. Weend with a summary of our results. In Appendix A, wepresent results for other two-body and four-body annihi-lation channels, along with a table summarizing all ourresults. II. REVIEW OF GC AND M31 OBSERVATIONSA. GC
For the GC excess we use data from Ref. [19]. Here wesummarize a few main aspects of the analysis. The obser-vations are based on approximately 5.2 years of
Fermi -LAT data, with energies between 1–100 GeV, in 20 log-arithmically spaced energy bins.A majority of the diffuse emission in the Galaxy isdue to the interaction of cosmic rays (CRs) with the in-terstellar gas and radiation fields. Indeed, the emissiontoward the GC is dominated by standard astrophysicalprocesses, and the GC excess only amounts to a smallfraction of the total emission. To quantify the uncer-tainty in the foreground/background emission, Ref. [19]employs the CR propagation code GALPROP [38–48] tobuild four different interstellar emission models (IEMs),corresponding to two main systematic variations.First, Galactic CRs are thought to be accelerated pri-marily from supernova remnants (SNRs) via diffusiveshock acceleration (see Ref. [19] and references therein).However, the distribution of SNRs is not well determineddue to the observational bias and the limited lifetimeof their shells, and so other tracers are often employed.Ref. [19] uses two possible tracers, namely, the distribu-tion of OB stars, which are progenitors of supernovae,and pulsars, which are the end states of supernovae.The second main variation comes from the tuning ofthe IEMs to the γ -ray data. This was done outside ofthe signal region, working from the outer Galaxy inward, Available at https://galprop.stanford.edu Energy (MeV) F l u x ( M e V c m s ) OB Stars, index-scaledOB Stars, intensity-scaledPulsars, index-scaledPulsars, intensity-scaledM31 spherical halo component
FIG. 1: The colored dashed lines show the spectra ofthe GC excess for different IEMs, based on Ref. [19].The bands show the 1 σ uncertainty. Black points showthe spectrum for M31’s spherical halo component, basedon Ref. [32].with two variations in the fit. In the intensity-scaled vari-ation, only the normalizations of the IEM componentswere left free to vary. In the index-scaled variation, ad-ditional degrees of freedom were given to the gas-relatedcomponents interior to the Solar circle by also freely scal-ing the spectral index.Combining the variations in the CR density and thetuning procedure gives four possible IEMs which quan-tify the uncertainty in the foreground/background emis-sion. We shall denote these four IEMs as (a) OB Stars,index-scaled (b) OB Stars, intensity-scaled (c) Pulsars,index-scaled; and (d) Pulsars, intensity-scaled. Figure 1shows the spectra for the GC excess, corresponding to thefour IEMs. Note that the intensity-scaled models have ahigh energy tail which is not present in the index-scaledmodels. B. M31
For the M31 analysis we follow Ref. [32]. The anal-ysis employs 7.6 years of
Fermi -LAT data, with ener-gies between 1–100 GeV, in 20 logarithmically spacedenergy bins. Similar to the GC, the foreground emissionfrom the MW is the dominant component when look-ing towards M31’s outer halo, and Ref. [32] again usedGALPROP to build specialized IEMs to characterize theemission.Evidence for an excess signal was found, having a ra-dial extension of ∼ −
200 kpc from the center ofM31. To characterize the excess, three additional signalcomponents were added to the model (i.e. in additionto the IEM). For the inner galaxy a 0 . ◦ disk was used,consistent with what has previously been reported [49–51]. A second concentric ring was also added, extendingfrom 0 . ◦ to 8 . ◦ (corresponding to a projected radiusof ∼
120 kpc); this is referred to as the spherical halocomponent. Finally, a third concentric ring was added,extending from 8 . ◦ and covering the remaining extentof the field (corresponding to a projected radius of ∼ γ -ray signalthat is detected [32, 33]. This is due to an uncertainty inthe underlying H I gas maps that are used for the MilkyWay (MW) foreground. We also ignore the far outer haloregion because it begins to approach the MW disk towardthe top of the field, which significantly complicates theanalysis. If the excess γ -ray emission observed towardM31’s outer halo does in fact have a physical associationwith the M31 system, then it is particularly importantto establish this in the spherical halo region [33]. C. J-factors
The greatest uncertainty for the DM interpretation ofM31’s outer halo comes from the J -factor. This is coveredin extensive detail in Ref. [33]. Here, we use results fromthat study to quantify the full uncertainty range, andbelow we summarize the key points.The J -factor characterizes the spatial distribution ofthe DM, and is given by the integral of the mass densitysquared, over the line of sight. When describing the DMdistribution as an ensemble of disjoint DM halos, the J -factor is: J = (cid:88) i (cid:90) ∆Ω d Ω (cid:90) LoS dsρ i ( r i ( s, n )) , (1)summed over all halos in the line of sight (LoS), where ρ i ( r ) is the density distribution of halo i , and r i ( s, n ) isthe position within that halo at LoS direction n and LoSdistance s . J -factors determined from these spherically-averagedprofiles are an underestimate of the total J -factor be-cause of the effect of the non-spherical structure. Thisunderestimate is typically encoded with a boost factor.The substructure component is very important for indi-rect detection, as it enhances the overall signal, since thepredicted γ -ray flux scales as the mass density squared.This is especially true for MW-sized halos and towardthe outer regions.The main uncertainties in the boost factor include theminimum subhalo mass, the subhalo mass function, theconcentration-mass relation, the distribution of the sub-halos in the main halo, the mass distribution of the sub-halos themselves, and the number of substructure levels.In Ref. [33] these physical parameters are varied within physically motivated ranges (as representative of the cur-rent uncertainty found in the literature) in order to quan-tify the uncertainty in the substructure boost. Addition-ally, there is also an uncertainty in the halo geometry,which is quantified by calculating J -factors for the dif-ferent experimental estimates found in the literature.In addition to the substructure and halo geometry,another primary driver of the J -factor uncertainty forobervations toward M31’s outer halo is the contributionto the signal from the MW’s DM halo along the lineof sight, which is also accounted for in Ref. [33]. In-cluding all these uncertainties, the J -factor integratedover the spherical halo region, (which we will hence-forth denote as J M ) is found to range from (2 . − . × GeV cm − , with a geometric mean of 7 . × GeV cm − . We emphasize that this range accountsfor the contribution from the MW’s halo along the lineof sight.For the GC we use the J -factor from Ref. [19] thatwas used to extract the excess signal (which is consis-tent with the data that we use in this analysis). Thiscorresponds to an NFW density profile with a slope γ = 1, a scale radius r s = 20 kpc, and local DM den-sity ρ (cid:12) = 0 . − . The J -factor integrated overthe 15 ◦ × ◦ GC region (which we will henceforth denoteas J GC ) has a value of 2 . × GeV cm − . We notethat there is an uncertainty in the GC J -factor due tothe value of the local DM density, as well as the other pa-rameters in the density profile. However, in this work weconsider just the uncertainty in the M31 J -factor, sinceit is dominant.As described in more detail in the next section, a par-ticularly important quantity in our analysis will be theratio of the J -factors: J r ≡ J GC /J M (2)For the values of J M between (2 . − . × GeV cm − , and J GC = 2 . × GeV cm − wefind that J r lies between J r,low = 7 .
07 and J r,high =110 .
0. Using the geometric mean of J M = 7 . × GeV cm − , we define J r,mid = 28 . III. SPECTRAL COMPARISON OF THE GCAND M31 EXCESSESA. Best-fit J-factor ratios
The flux observed from M31 is much lower than thatof the GC excess. If the excesses are indeed from an un-derlying DM model, then the underlying cross-section forDM annihilation to photons should be the same. The dif-ference in the spectra would then be attributable mostlyto the ratio between J M and J GC . We note, however,that there may be some differences that arise from sec-ondary emission, which depends on the particular astro-physical backgrounds in each respective targets (i.e. the Energy (MeV) F l u x ( M e V c m s ) M31 scaledOB Stars, index-scaled 10 Energy (MeV) F l u x ( M e V c m s ) M31 scaledPulsars, index-scaled10 Energy (MeV) F l u x ( M e V c m s ) M31 scaledOB Stars, intensity-scaled 10 Energy (MeV) F l u x ( M e V c m s ) M31 scaledPulsars, intensity-scaled
FIG. 2: Comparison of GC spectra (colored bands) to scaled M31 spectra (black data points). The bands and errorbars give the 1 σ statistical error. The top two panels show the index-scaled IEMs, and the bottom two panels showthe intensity-scaled IEMs. In each case the M31 data is scaled by the appropriate J -factor for the IEM.gas and interstellar radiation fields) [52]. For simplicitythese effects are not considered in this analysis.To test the agreement between the two spectra we mul-tiply the M31 data by a scaling factor. This factor is thenthe ratio J r . Since the four GC background models yieldsignificantly different spectra, we fit the scaling factorindependently for each of them.The best-fit scaling factor is determined using a χ fit. We account for upper limits (ULs) in the data byincluding an error function in the χ definition [33, 53,54] χ = m (cid:88) i =1 w i − (cid:88) i = m +1 ln 1 + erf( w i / √ w i = ( y i z i − J ) σ ri (4)and erf( z ) = √ π (cid:90) z e − t d t (5)The first term on the right-hand side of Eq. (3) is theclassic definition of χ , and the second term introducesthe error function to quantify the fitting of ULs. Thenumber of good data points is given by m , and the sumis over the 20 energy bins. Here y i is the flux from theGC and z i is the flux from M31, for the ith energy bin.The error on the flux ratio J r is taken to be σ ri = σ yi z i (6) IEM J r Pulsars, intensity-scaled 48 . ± . . ± . . ± . . ± . TABLE I: J -factor ratio for each IEM.where we use just the statistical error on the GC data,which we assume to be symmetric. This allows for a rea-sonable spectral comparison, and is further justified bythe fact the uncertainty in the GC excess is dominated bythe systematics. We note that in general a more sophis-ticated treatment of the errors may be appropriate (e.g.[33, 53]). However, we have tested different prescriptionsfor handling the error and in all cases we find that theresults are qualitatively consistent.We minimize the χ with respect to J , and identify theminimum with the optimized rescaling factor. The thirdcolumn of Table I shows the best-fit results for each IEM.We note that the best-fit J -factor ratios are well withinthe bounds from section II C. There is a preference forsmaller values of J r ∼
40, corresponding to larger valuesof J M . We will refer to these as the model-independent J r values (as these are found without reference to a spe-cific DM annihilation model). Energy (MeV) F l u x ( M e V c m s ) OB Stars, intensity-scaledPulsars, intensity-scaledOB Stars, index-scaledPulsars, index-scaledM31, Adjusted Range
FIG. 3: The blue band shows the range of M31 fluxvalues scaled up by a J -factor ratio between 7.7 and110. Dashed lines show the four different GC IEMs withone sigma error bands. B. Spectral Comparisons
We further examine the agreement between the M31spectrum and the GC excess by scaling the M31 data bythe best-fit J -ratio found above, and comparing the twospectral shapes. These comparisons are shown in Fig. 2.The top panel shows the rescaled M31 data comparedto the GC excess for the index-scaled IEMs. As can beseen, the spectra show excellent agreement.The bottom panel shows the intensity-scaled IEMs. Ascan be seen, there is a strong tension between the GC andM31 spectra at high energy (above ∼
10 GeV). This is dueto the existence of the so-called ”high-energy tail” in theintensity-scaled IEMs. The nature of the high-energy tailof the GC excess has been investigated in numerous stud-ies (e.g. [19, 55–57]). It remains uncertain whether thisfeature is a true property of the signal or if it is due tomis-modeling of the background. When comparing theGC excess to the M31 excess, it is important to note thatthe two signals are extracted from very different regionsof the galaxy, and thus they may not be directly com-parable. In particular, this is the case when consideringsecondary emission, which depends on the astrophysicalbackgrounds. With that said, the M31 data does not pos-sess a high-energy tail, and so seems to be in strong ten-sion with those models. Indeed, this would be in generalagreement with previous studies which have found thatthe high-energy tail is not very compatible with havinga pure DM explanation [56, 57].One can also examine whether a different choice of J -factor could ameliorate the tension at high energies be-tween the M31 excess and the intensity scaled GC ex-cesses. To examine this, we find the range of possibil-ities for the M31 flux, by rescaling it by the maximumand minimum J -factors allowed from Ref. [33]. Figure 3 shows the scaled M31 data compared to the GC excess forthe four IEMs. As can be seen, the M31 data shows goodagreement with the index-scaled IEMs, whereas there isstill tension with the intensity-scaled IEMs. IV. DARK MATTER MODELS
In this section we perform a DM fit simultaneously toboth signals. We will take a model where DM is a realscalar field χ of mass m χ , and consider various possibili-ties for the dominant annihilation process; specifically, wewill consider both two-body and four-body final states.For the standard WIMP models the DM spectra weregenerated using PPPC [58]. For the four-body annihila-tions the spectra were produced using FeynRules [59] andMadGraph [60], and showered with Pythia 8 [61]. Thephotons were binned in 20 logarithmically-spaced binsfrom 1 −
100 GeV, just as for the GC and M31 data.The predicted γ -ray flux from DM annihilation is givenby E d Φ dE (cid:12)(cid:12)(cid:12)(cid:12) GC = N GC ( E dndE ) (7) E d Φ dE (cid:12)(cid:12)(cid:12)(cid:12) M = N GC J r ( E dndE ) (8)Here N GC = J GC (cid:104) σv (cid:105) πηm χ (9)where (cid:104) σv (cid:105) is the velocity averaged cross section, η is2 (4) for conjugate (non-self conjugate) DM, m χ is theDM mass, and dn/dE is the number of γ -ray photons perannihilation.We perform a χ fit as in Eqs. 3-5. The main differenceis the definition of w i . This quantity is defined separatelyfor the GC and M31. For the GC: w i = y i − N E dnde σ yi (10)where σ yi is the 1-sigma error on the GC flux and y i is thebest fit value of the GC flux for a given IEM. Similarlyfor M31 we have x i = z i − J − N E dnde σ zi (11)where the error σ zi is the 1-sigma error on the M31 fluxand z i is the best fit value of the M31 flux.Finally, we define the total chi-squared as χ tot = χ GC + χ M (12)We marginalize over N in order to minimize this quantitywith respect to J r and m χ . This is done separately foreach GC IEM.Figure 4 shows the results for the two-body annihila-tion to bottom quarks with the OB Stars, index-scaled
20 30 40 50 600204060 20406080100120140
FIG. 4: ∆ χ for χχ → b ¯ b , for the OB-Starsindex-scaled IEM. The red dot indicates the best fitpoint, and the contours are 1,2, and 3 σ contours. Thedashed red line shows the model independent J r value.Dash-dotted and dotted black lines show high and meanvalues of J r from section II C. Energy (MeV) F l u x ( M e V c m s ) M31 scaledOB Stars, index-scaledBest Fit Spectra: bb FIG. 5: Dashed lines show the GC excess with the OBStars, index IEM. Black points show the M31 flux datascaled up by the appropriate ratio J r taken fromTable II. The dotted line shows the correspondingbest-fit model spectra for χχ → b ¯ b .IEM. The color scale indicates the value of ∆ χ . Thebest-fit is shown with a red point, and also overlaid arethe 1 σ , 2 σ , and 3 σ confidence contours, corresponding to∆ χ = 2 . , .
61 and 9 .
21, respectively. For comparison,we also show the model-dependent J r value from Table 1and J r,low , J r,mid from Section II. As can be seen, the J r corresponding to the DM fit is in good agreement withthe range found in Ref. [32]. In Figure 5 we show thecorresponding best-fit DM spectrum compared to the GCand scaled M31 data.We have also extended our analysis to other possibleannihilation modes; these results are presented in the Ap-pendix. Specifically, we first considered other two-bodyannihilations where the DM annihilates to two tau lep-tons, and the case where the DM annihilates to two lightquarks, which we take to be down quarks for concrete-ness. Figure 6 shows the results for these annihilationchannels.As mentioned above, direct detection and collidersearches significantly constrain DM couplings. This has motivated the study of models where the DM is cou-pled to the SM quarks through a pseudoscalar mediator[34–37]. For example, one can consider a model with amediator φ and the interactions L int = χ φ + φbb (13)In this model, DM primarily annihilates to four b-quarks.The precise annihilation mode depends on the coupling,for example if the mediator coupled as φdd , there wouldbe a annihilation to four d quarks. Generically we get afour-body annihilation.Results for some possible 4-body final states are shownin Figure 7. We note that the best fit DM mass increasesfor the four body annihilation mode; this is expectedbecause each quark has less energy.The corresponding best-fit parameters for all modelsare summarized in Table II. V. CONCLUSION
The GC excess, an excess of γ -ray photons from theGC, has been a long-standing potential signal of DM an-nihilation. However, the large astrophysical backgroundand the potential existence of new sources makes it dif-ficult to make definitive statements about the origin ofthis excess. On the other hand, the M31 excess is from aregion where astrophysical backgrounds (not associatedwith the conventional interstellar emission from the MWforeground) are not expected to be large, and hence lendscredence to the possibility that the excess is indeed as-sociated with DM annihilation, rather than an unknownastrophysical background.We have further examined these two excesses, to seeif their magnitudes and spectral shapes are consistentwith DM annihilation. The two signals are expected tobe related by the ratio of the two J -factors. The recentanalysis of the M31 J -factor allows us to check this re-lation, and we have found that indeed the excesses areconsistent with the determined J -factors. The spectralshapes for the index-scaled IEMs are also in very goodagreement. On the other hand, there is tension with theintensity-scaled IEMs due to the so-called high-energytail.We also fit the excesses to a number of DM models,where the DM annihilates to either two or four SM par-ticles. We found that excellent fits can be achieved bothin two-body and four-body annihilations, as can be seenin the Appendix.In summary, we have found that the M31 excess andthe GC excess are mutually consistent with a dark matterorigin. The DM models prefer a somewhat higher valuefor the M31 J -factor, and prefer a particular IEM (theindex-scaled models) for the GC. Currently, several DMmodels are consistent with the excesses.Future prospects to confirm the excess toward theouter halo of M31, and to better understand its nature,will crucially rely on improvements in modeling the in-terstellar emission towards M31. For the GC, the excesshas been under investigation for many years now, andfurther improvements in the IEM will continue to playa significant role in better understanding the nature ofthe signal. Additionally, working towards a better un-derstanding of the possible point-like nature of the ex-cess will be key. Improved sensitivity from other indirectdetection constraints will also continue to play an im-portant role in DM interpretations of the two signals,and likewise for constraints from direct detection. Fur-ther analysis of these complementary signals would be extremely interesting, and could shed light on the natureof DM. ACKNOWLEDGEMENTS
We are especially grateful to Simona Murgia for manyinformative discussions, and for sharing several of herunpublished calculations. This work was supported inpart by NSF Grant No. PHY-1915005. [1] A. G. Riess et al. (Supernova Search Team), Astron. J. , 1009 (1998), arXiv:astro-ph/9805201 [astro-ph].[2] S. Perlmutter, G. Aldering, G. Goldhaber, R. Knop,P. Nugent, P. Castro, S. Deustua, S. Fabbro, A. Goo-bar, D. Groom, et al. , Astrophys. J. , 565 (1999).[3] D. Clowe, M. Bradac, A. H. Gonzalez, M. Markevitch,S. W. Randall, C. Jones, and D. Zaritsky, Astrophys. J. , L109 (2006), arXiv:astro-ph/0608407 [astro-ph].[4] G. Hinshaw et al. (WMAP), Astrophys. J. Suppl. Ser. , 19 (2013), arXiv:1212.5226 [astro-ph.CO].[5] P. A. R. Ade et al. (Planck), A&A , A13 (2016),arXiv:1502.01589 [astro-ph.CO].[6] D. J. Eisenstein et al. (SDSS), Astrophys. J. , 560(2005), arXiv:astro-ph/0501171 [astro-ph].[7] L. Anderson et al. (BOSS), Mon. Not. Roy. Astron. Soc. , 24 (2014), arXiv:1312.4877 [astro-ph.CO].[8] M. Tanabashi et al. (Particle Data Group), Phys. Rev.D , 030001 (2018).[9] J. A. Peacock et al. , Natur , 169 (2001), arXiv:astro-ph/0103143 [astro-ph].[10] L. Goodenough and D. Hooper, arXiv e-prints ,arXiv:0910.2998 (2009), arXiv:0910.2998 [hep-ph].[11] D. Hooper and L. Goodenough, Physics Letters B ,412 (2011), arXiv:1010.2752 [hep-ph].[12] D. Hooper and T. Linden, Phys. Rev. D , 123005(2011), arXiv:1110.0006 [astro-ph.HE].[13] K. N. Abazajian and M. Kaplinghat, Phys. Rev. D ,083511 (2012), arXiv:1207.6047 [astro-ph.HE].[14] D. Hooper and T. R. Slatyer, Physics of the Dark Uni-verse , 118 (2013), arXiv:1302.6589 [astro-ph.HE].[15] C. Gordon and O. Mac´ıas, Phys. Rev. D , 083521(2013), arXiv:1306.5725 [astro-ph.HE].[16] W.-C. Huang, A. Urbano, and W. Xue, arXiv e-prints ,arXiv:1307.6862 (2013), arXiv:1307.6862 [hep-ph].[17] T. Daylan, D. P. Finkbeiner, D. Hooper, T. Linden,S. K. N. Portillo, N. L. Rodd, and T. R. Slatyer, Physicsof the Dark Universe , 1 (2016), arXiv:1402.6703[astro-ph.HE].[18] K. N. Abazajian, N. Canac, S. Horiuchi, and M. Kapling-hat, Phys. Rev. D , 023526 (2014), arXiv:1402.4090[astro-ph.HE].[19] M. Ajello et al. (Fermi-LAT), Astrophys. J. , 44(2016), arXiv:1511.02938 [astro-ph.HE].[20] B. Zhou, Y.-F. Liang, X. Huang, X. Li, Y.-Z. Fan,L. Feng, and J. Chang, Phys. Rev. D , 123010 (2015),arXiv:1406.6948 [astro-ph.HE]. [21] F. Calore, I. Cholis, and C. Weniger, JCAP , 038(2015), arXiv:1409.0042 [astro-ph.CO].[22] K. N. Abazajian, N. Canac, S. Horiuchi, M. Kaplinghat,and A. Kwa, JCAP , 013 (2015), arXiv:1410.6168[astro-ph.HE].[23] F. Calore, I. Cholis, C. McCabe, and C. Weniger, Phys.Rev. D , 063003 (2015), arXiv:1411.4647 [hep-ph].[24] E. Carlson, T. Linden, and S. Profumo, Phys. Rev. D , 063504 (2016), arXiv:1603.06584 [astro-ph.HE].[25] M. Ackermann et al. (Fermi-LAT), Phys. Rev. Lett. ,231301 (2015), arXiv:1503.02641 [astro-ph.HE].[26] A. Albert et al. (Fermi-LAT, DES), Astrophys. J. ,110 (2017), arXiv:1611.03184 [astro-ph.HE].[27] S. Ando, A. Geringer-Sameth, N. Hiroshima, S. Hoof,R. Trotta, and M. G. Walker, arXiv e-prints, arXiv:2002.11956 (2020), arXiv:2002.11956 [astro-ph.CO].[28] V. Bonnivard, C. Combet, D. Maurin, and M. Walker,Mon. Not. Roy. Astron. Soc. , 3002 (2015),arXiv:1407.7822 [astro-ph.HE].[29] N. Klop, F. Zandanel, K. Hayashi, and S. Ando, Phys.Rev. D , 123012 (2017).[30] M. Lisanti, S. Mishra-Sharma, N. L. Rodd, and B. R.Safdi, Phys. Rev. Lett. , 101101 (2018).[31] M. Lisanti, S. Mishra-Sharma, N. L. Rodd, B. R. Safdi,and R. H. Wechsler, Phys. Rev. D , 063005 (2018).[32] C. M. Karwin, S. Murgia, S. Campbell, andI. V. Moskalenko, Astrophys. J. , 95 (2019),arXiv:1812.02958 [astro-ph.HE].[33] C. Karwin, S. Murgia, I. Moskalenko, S. Fillingham, A.-K. Burns, and M. Fieg, (2020), arXiv:2010.08563 [astro-ph.HE].[34] C. Karwin, S. Murgia, T. M. Tait, T. A. Porter, andP. Tanedo, Physical Review D , 103005 (2017).[35] M. Escudero, D. Hooper, and S. J. Witte, Journal ofCosmology and Astroparticle Physics , 038 (2017).[36] M. Abdullah, A. DiFranzo, A. Rajaraman, T. M. Tait,P. Tanedo, and A. M. Wijangco, Phys. Rev. D ,035004 (2014), arXiv:1404.6528 [hep-ph].[37] A. Rajaraman, J. Smolinsky, and P. Tanedo, (2015),arXiv:1503.05919 [hep-ph].[38] I. V. Moskalenko and A. W. Strong, Astrophys. J. ,694 (1998), arXiv:astro-ph/9710124 [astro-ph].[39] I. V. Moskalenko and A. W. Strong, Astrophys. J. ,357 (2000), arXiv:astro-ph/9811284 [astro-ph]. [40] A. W. Strong and I. V. Moskalenko, Astrophys. J. ,212 (1998), arXiv:astro-ph/9807150 [astro-ph].[41] A. W. Strong, I. V. Moskalenko, and O. Reimer, Astro-phys. J. , 763 (2000), arXiv:astro-ph/9811296 [astro-ph].[42] V. S. Ptuskin, I. V. Moskalenko, F. C. Jones, A. W.Strong, and V. N. Zirakashvili, Astrophys. J. , 902(2006), arXiv:astro-ph/0510335 [astro-ph].[43] A. W. Strong, I. V. Moskalenko, and V. S. Ptuskin,Annual Review of Nuclear and Particle Science , 285(2007), arXiv:astro-ph/0701517 [astro-ph].[44] A. E. Vladimirov, S. W. Digel, G. J´ohannesson, P. F.Michelson, I. V. Moskalenko, P. L. Nolan, E. Orland o,T. A. Porter, and A. W. Strong, Computer Physics Com-munications , 1156 (2011), arXiv:1008.3642 [astro-ph.HE].[45] G. J´ohannesson, R. Ruiz de Austri, A. C. Vincent, I. V.Moskalenko, E. Orlando, T. A. Porter, A. W. Strong,R. Trotta, F. Feroz, P. Graff, and M. P. Hobson, Astro-phys. J. , 16 (2016), arXiv:1602.02243 [astro-ph.HE].[46] G. J´ohannesson, T. A. Porter, and I. V. Moskalenko,Astrophys. J. , 45 (2018), arXiv:1802.08646 [astro-ph.HE].[47] T. A. Porter, G. J´ohannesson, and I. V. Moskalenko,Astrophys. J. , 67 (2017), arXiv:1708.00816 [astro-ph.HE].[48] Y. G´enolini, D. Maurin, I. V. Moskalenko, and M. Unger,Phys. Rev. C , 034611 (2018), arXiv:1803.04686 [astro-ph.HE].[49] A. Abdo et al. (Fermi-LAT), Astron. Astrophys. , L2(2010), arXiv:1012.1952 [astro-ph.HE].[50] M. S. Pshirkov, V. V. Vasiliev, and K. A. Post-nov, Mon. Not. Roy. Astron. Soc. , L76 (2016), arXiv:1603.07245 [astro-ph.HE].[51] M. Ackermann et al. (Fermi-LAT), Astrophys. J. ,208 (2017), arXiv:1702.08602 [astro-ph.HE].[52] M. Cirelli, P. D. Serpico, and G. Zaharijas, J. COSMOL.ASTROPART. P. , 035 (2013), arXiv:1307.7152[astro-ph.HE].[53] J. Lyu, G. H. Rieke, and S. Alberts, Astrophys. J. ,85 (2016).[54] T. Isobe, E. D. Feigelson, and P. I. Nelson, Astrophys.J. , 490 (1986).[55] F. Calore, I. Cholis, and C. Weniger, JCAP , 038(2015), arXiv:1409.0042 [astro-ph.CO].[56] S. Horiuchi, M. Kaplinghat, and A. Kwa, JCAP , 053(2016), arXiv:1604.01402 [astro-ph.HE].[57] T. Linden, N. L. Rodd, B. R. Safdi, and T. R. Slatyer,Phys. Rev. D , 103013 (2016), arXiv:1604.01026 [astro-ph.HE].[58] M. Cirelli, G. Corcella, A. Hektor, G. Hutsi, M. Kadastik,P. Panci, M. Raidal, F. Sala, and A. Strumia, JCAP , 051 (2011), [Erratum: JCAP 10, E01 (2012)],arXiv:1012.4515 [hep-ph].[59] N. D. Christensen and C. Duhr, Comput. Phys. Com-mun. , 1614 (2009), arXiv:0806.4194 [hep-ph].[60] J. Alwall, R. Frederix, S. Frixione, V. Hirschi, F. Maltoni,O. Mattelaer, H. S. Shao, T. Stelzer, P. Torrielli, andM. Zaro, JHEP , 079 (2014), arXiv:1405.0301 [hep-ph].[61] T. Sjostrand, S. Mrenna, and P. Z. Skands, Comput.Phys. Commun. , 852 (2008), arXiv:0710.3820 [hep-ph]. Appendix A: Other Annihilation Channels Energy (MeV) F l u x ( M e V c m s ) M31 scaledOB Stars, index-scaledBest Fit Spectra: 10 Energy (MeV) F l u x ( M e V c m s ) M31 scaledOB Stars, index-scaledBest Fit Spectra: dd FIG. 6: The left panels are similar to Figures 4 and 5 for χχ → τ ¯ τ , and the right panels are similar to Figures 4 and5 for χχ → d ¯ d
20 30 40 50 60 70102030405060 20406080100120140 Energy (MeV) F l u x ( M e V c m s ) M31 scaledOB Stars, index-scaledBest Fit Spectra: bbbb Energy (MeV) F l u x ( M e V c m s ) M31 scaledOB Stars, index-scaledBest Fit Spectra: dddd
FIG. 7: Similar to Fig 6, but for χχ → bb ¯ b ¯ b and χχ → dd ¯ d ¯ d respectively.0 DM Model IEM m χ [GeV] N GC × [cm − s − ] J r χ red b ¯ b Pulsars, intensity-scaled 57 . − . . +0 . − . . +8 . − . +1 . − . . +0 . − . . +6 . − . +1 . − . . +0 . − . . +8 . − . +4 . − . . +0 . − . . +7 . − . d ¯ d Pulsars, intensity-scaled 43 +3 . − . . +0 . − . . +9 . − . +1 . − . . +0 . − . . +6 . − . +3 . − . . +0 . − . . +9 . − . +6 . − . . +0 . − . . +8 . − . bb ¯ b ¯ b Pulsars, intensity-scaled 81 +0 . − . . +0 . − . . . − . +1 . − . . +0 . − . . +5 . − . +0 . − . . +0 . − . . +8 . − . +4 . − . . +0 . . . +7 . − . dd ¯ d ¯ d Pulsars, intensity-scaled 67 +3 . − . . +0 . − . . +9 . − . +1 . − . . +0 . − . . +6 . − . +4 . − . . +0 . − . . +9 . − . +3 . − . . +0 . − . . +8 . − . τ + τ − Pulsars, intensity-scaled 15 +1 . − . . +1 . − . . +9 . − . +0 . − . . +0 . − . . +9 . − . +1 . − . . +1 . − . . +9 . − . +2 . − . . +1 . − . . +12 . − . TABLE II: Best-fits for m χ , N GC , and the ratio J rr