Celestial-Body Focused Dark Matter Annihilation Throughout the Galaxy
Rebecca K.Leane, Tim Linden, Payel Mukhopadhyay, Natalia Toro
SSLAC-PUB-17586
Celestial-Body Focused Dark Matter Annihilation Throughout the Galaxy
Rebecca K. Leane, ∗ Tim Linden, † Payel Mukhopadhyay,
1, 3, ‡ and Natalia Toro § SLAC National Accelerator Laboratory, Stanford University, Stanford, CA 94039, USA Stockholm University and The Oskar Klein Centre for Cosmoparticle Physics, Alba Nova, 10691 Stockholm, Sweden Physics Department, Stanford University, Stanford, CA 94305, USA
Indirect detection experiments typically measure the flux of annihilating dark matter (DM) par-ticles propagating freely through galactic halos. We consider a new scenario where celestial bodies“focus” DM annihilation events, increasing the efficiency of halo annihilation. In this setup, DMis first captured by celestial bodies, such as neutron stars or brown dwarfs, and then annihilateswithin them. If DM annihilates to sufficiently long-lived particles, they can escape and subsequentlydecay into detectable radiation. This produces a distinctive annihilation morphology, which scalesas the product of the DM and celestial body densities, rather than as DM density squared. Weshow that this signal can dominate over the halo annihilation rate in γ -ray observations in both theMilky Way Galactic center and globular clusters. We use Fermi and H.E.S.S. data to constrain theDM-nucleon scattering cross section, setting powerful new limits down to ∼ − cm for sub-GeVDM using brown dwarfs, which is up to nine orders of magnitude stronger than existing limits. Wedemonstrate that neutron stars can set limits for TeV-scale DM down to about 10 − cm . I. INTRODUCTION
Celestial bodies provide versatile environments to dis-cover new physics. Peppered throughout the Galaxy,their large abundances can be used to collectively powera bright dark matter (DM) annihilation signal.Previous studies have examined DM particles thatscatter in celestial bodies and become gravitationallybound. The trapped DM can heat the objects that cap-ture it, with contributions from both the DM kinetic en-ergy and the absorption of DM annihilation products bythe capturing body. The latter, dominant source of heat-ing relies on the DM annihilation products either inter-acting or decaying within the celestial body. For neutronstars (NS), this DM heating signal has been studied ine.g. Refs. [1–23]. DM heating using the full BD pop-ulation was considered recently in Ref. [24]. NSs andBDs are both efficient accumulators of DM, due to beingrelatively dense, and in the case of BDs, very large.A complementary approach arises when DM annihi-lates to long-lived mediators. In this scenario, the medi-ator can escape the celestial body and decay to observ-able final states. Long-lived particles appear naturally inmany well-motivated extensions of the SM [25–30], withan extensive search program [31–33]. Dark sectors withlong-lived mediators have previously been considered inlocal searches of the Sun [29, 34–53] and Earth [41].We consider, for the first time, DM annihilation tolong-lived particles in NSs and BDs, which are advan-tageous systems due to their superior and complemen-tary scattering cross-section sensitivity. This allows usto consider a new type of annihilation signal: one “fo-cused” by the population of celestial bodies. DM is first ∗ Email : [email protected];
ORCID : 0000-0002-1287-8780 † Email : [email protected];
ORCID : 0000-0001-9888-0971 ‡ Email : [email protected];
ORCID : 0000-0002-3954-2005 § Email : [email protected];
ORCID : 0000-0002-8150-3990 efficiently captured in dense NSs or BDs. As the DM den-sity increases, DM annihilation inside the object becomesefficient. The DM annihilation proceeds through a long-lived particle which escapes the celestial body and sub-sequently decays, producing a flux detectable at Earth.Our signal exploits the fact that celestial bodies existin large quantities in the inner Galaxy [54–56], as wellas other DM-dense environments such as globular clus-ters [57–59]. Notably, while DM annihilation in the haloscales as the DM density squared, the celestial-body fo-cused annihilation rate scales as a single power in DMnumber density (assuming equilibration between the an-nihilation and capture rates in a given object) multipliedby the celestial-body number density. This distinctivescaling can potentially disentangle the origin of an ob-served DM annihilation signal. Moreover, because theDM density within the celestial body can become ex-tremely high, our scenario potentially provides a moresensitive probe than halo annihilation, especially for largeDM masses or suppressed annihilation cross sections,such as p − wave annihilation [60, 61].In this paper, we investigate the relative strength ofcelestial-body-focused annihilation compared to DM an-nihilation in the Milky Way halo. We compare our re-sults with existing γ -ray data, and produce new limits onDM annihilation to long-lived particles. We identify twoenvironments where a NS-focused or BD-focused annihi-lation signal can dominate over halo annihilation. Theseare the Galactic center, which is extremely DM dense,and globular clusters, which can have not only large DMdensities, but also low DM velocity dispersions, allowingmore DM to be captured by the celestial body.This paper is organized as follows. In Section II, wereview DM capture and annihilation in celestial bodies,and detail the long-lived mediator model. We then dis-cuss the Milky Way Galactic center signal in Section III,and the resulting constraints in Section IV. We discussthe globular cluster signal in Section V. We discuss theimplications of our results in Section VI. a r X i v : . [ a s t r o - ph . H E ] J a n II. SETUPA. Dark Matter Capture in Celestial Bodies
As in the case of standard halo annihilation, thestrength of the NS- and BD-focused signal depends onthe DM density in the object’s environment. However,for BD/NS-focused annihilation, the DM density directlydetermines the rate of DM capture onto celestial bodies,an interaction that is only linearly (rather than quadrat-ically) dependent on the DM density. Here, we use ageneralized Navarro-Frenk-White (NFW) density profile,which is defined as a function of galactic radius r , [62] ρ χ ( r ) = ρ ( r/r s ) γ (1 + ( r/r s )) − γ , (1)where r s is the scale radius, ρ is normalized to the localDM density value, and γ is the index that determines theinner slope of the DM profile.DM from the Galactic halo can fall onto a ce-lestial object, encountering the surface after beingsped up to approximately the object’s escape velocity, v esc = (cid:112) G N M /R , where G N is the gravitational con-stant, M is the mass of the object, and R is the object’sradius. As the DM particle transits through the object,it can scatter with the stellar material and lose energy.Once the kinetic energy of the DM is less than the grav-itational potential, the DM particle is captured. DMcapture can occur via single or multiple scatters with thestellar constituents [42, 63–65].The largest possible rate of capture is obtained by as-suming that all DM that passes through the effective areaof the BD/NS is captured. This “maximum capture rate”(sometimes also referred to as “geometric capture rate”)is given by [66] C max = πR n χ ( r ) v (cid:18) v v ( r ) (cid:19) ξ ( v p , v ( r )) , (2)where ¯ v is the DM velocity dispersion, n χ ( r ) is theDM number density profile, related to Eq. 1 via n χ ( r ) = ρ ( r ) /m χ , v = (cid:112) / (3 π ) v , and ξ ( v p , v ( r )) takesinto account the motion of the compact object with re-spect to the DM halo (this is ∼ N scatters is p N ( τ ) = 2 (cid:90) dy ye − yτ ( yτ ) N N ! , (3) where τ is the optical depth, τ = 32 σσ sat . (4)Here σ sat is the saturation cross section of DM captureonto nucleons, and is given by σ sat = πR /N n where N n is the number of nucleons.The total capture rate in this formalism for a singlecelestial body is then given by C = ∞ (cid:88) N =1 C N , (5)where C N , defined below, is the capture rate associatedwith particles that scatter N times. In practice, this sumcan be truncated at a maximum finite N (cid:29) τ , becausescattering more than τ times is exponentially suppressed.The rate for a particle to impinge on the body, scatter N times, and lose enough energy in the process to becometrapped in the star is given by C N = πR p N ( τ )(1 − G N M/R ) √ n χ √ π ¯ v × (6) (cid:18) (2¯ v + 3 v ) − (2¯ v + 3 v N ) exp (cid:18) − v N − v )2¯ v (cid:19)(cid:19) , where the term v N = v esc (1 − β + / − N/ with β + =4 m χ m n / ( m χ + m n ) takes into account energy lost byDM in each scattering event. For sufficiently large N , v N − v becomes much larger than ¯ v and C N in Eq. 6rapidly approaches p N × C max (neglecting the ξ factor inEq. 2). In other words, particles that undergo N scattersare efficiently captured. As τ increases above this min-imum number of scatters required for efficient capture,the capture rate C in Eq. 5 asymptotes to the maximumcapture rate given by Eq. 2.We note that DM capture will be truncated for suffi-ciently light DM masses, because DM can rapidly evap-orate out from the system. Evaporation occurs if thecore of the system has both sufficiently high tempera-tures (which impart kinetic energy to the DM), and suf-ficiently low gravitational potential. From Ref. [24], weexpect an evaporation mass of around a few MeV forBDs. For NSs, the DM evaporation mass is ∼
300 eVfor old NSs which have cooler cores [67], and we estimateup to ∼ MeV for very young NSs. As we will (arbitrar-ily) consider DM masses above 10 MeV, the evaporationmass will be lighter than our range of interest.To calculate the total expected capture rate from thefull celestial body population in a given system (e.g. theGalactic center or globular clusters), we also need to takeinto account the number density of the object in the re-gion of interest, n BD / NS . In this scenario, the total DM For NSs, blue-shifted incoming DM velocities are included byreplacing v esc → √ χ , where χ = 1 − (cid:112) − G N M/R . capture rate by a population of BDs/NSs, C BD / NS , tot ,can be written as C BD / NS , tot = 4 π (cid:90) r r r n BD / NS C dr, (7)where C is the capture rate by a single BD or NS, n BD / NS is the BD or NS number density, and r is the radial dis-tance from the center of the system. This total capturerate of the full population of celestial bodies will be com-puted in Sec. III, IV and V. In the following subsection,we compare cross sections for DM capture in a single celestial body. B. Comparing Different Celestial Targets
To determine which type of celestial body will dom-inate the results for a given mass or cross-section sen-sitivity range, we compare choices of different objects.The optimal target can be chosen based on the system’score temperatures (lower core temperatures provide lesskinetic energy for DM to escape, potentially providingmore sensitivity to lower DM masses), and the system’sdensity (which increases the probability of DM capturefor small DM/nucleon cross sections).Figure 1 shows the approximate cross sections at whichcapture becomes efficient for different celestial bodies atour local position. For definiteness, we plot contours cor-responding to 99% efficient capture (i.e. C = 0 . C max ).We emphasize, however, that significant capture ratescan also be achieved for lower cross sections. For ex-ample, scattering cross sections an order of magnitudebelow this line still yield capture rates of ∼
50% the max-imum capture rate. For the “Brown Dwarfs” and “Sun”sensitivities, we calculate an approximate sensitivity byassuming that Brown Dwarfs and the Sun are composedof 100% hydrogen. The lower end of each DM mass sen-sitivity curve is truncated by evaporation of DM out ofthe systems, which significantly curtails the annihilationsignal. For the neutron star rates, we note that nucleareffects are not taken into account for this approximation(see Ref. [68] for discussion of how this may weaken ratesfor DM interaction choices).Note that the cross sections in Fig. 1 apply to bothspin-dependent and spin-independent interactions, asthere is no coherent enhancement considered for these ob-jects (although Brown Dwarfs and the Sun contain somehelium, this is sub-dominant and has been neglected). Inthe case that only spin-dependent scattering with neu-trons is applicable, the only sensitivity would arise fromneutron stars (the other systems predominately containhydrogen, and therefore only protons), and visa versa forspin-dependent proton scattering only.It is important to note that while Fig. 1 shows thecross sections corresponding to 99% efficient capture inthe given object, the maximum capture rates themselvesalso differ between these types of objects. That is, larger m [GeV]10 N [ c m ] B r o w n D w a r f s Neutron Stars S u n FIG. 1. Comparison of the approximate cross sections pro-ducing efficient capture (at 99% of maximum capture rate) atthe local position for the Sun, Brown Dwarfs, and NeutronStars, as a function of DM mass. Cross sections above thesevalues produce comparable DM annihilation rates. We showa benchmark Brown Dwarf with radius that of Jupiter, andmass 0.0378 M (cid:12) . The neutron star benchmark has a radiusof 10 km and mass 1.4 M (cid:12) . radii generally lead to more DM passing through the ob-ject, so large objects can efficiently capture DM. On theother hand, this will also depend on the DM velocity inthe system, which when slow can be advantageous as theeffective capture radius grows in size. The translationbetween maximum capture rate, and the cross section itcorresponds to, depends on the density of the object. AsNSs are the most dense, they lead to the greatest reachin scattering cross section; weaker interactions are morelikely occur in a denser material. This means that whileNSs have a superior reach in cross section, they do notnecessarily provide the largest capture rate, and there-fore do not necessarily provide the largest annihilationrate when scattering/annihilation equilibrium is reached.The relative sizes of capture rates will be compared forthe Milky Way environment in Sec. III.At masses below a few GeV, the Sun no longer pro-vides any sensitivity to compact-body focused annihila-tion, due to the efficient evaporation of any captured DMparticle. However, NSs and BDs continue to provide sig-nificant sensitivities. While the neutron star cross sectionis smaller, if DM has sufficiently large scattering crosssections, BDs may actually provide the dominant signal,as they have (i) higher number densities in the Galaxy,and (ii) larger DM capture rates due to their larger radii.For lower DM cross sections, NSs potentially provide theonly sensitivity. For DM masses above 4 GeV with suffi-ciently large scattering cross sections, the long-lived par-ticles from solar gamma rays may also be present, de-pending on the scattering cross section. In that case,very strong limits have already been set [45, 47]. Weagain stress that the cross sections shown do not corre-spond to the maximum possible cross-section sensitivity;they instead correspond to scattering cross sections whichwill approximately provide the largest possible signal forthe given object. Therefore, cross sections smaller thanthose shown can still be probed, given sufficient telescopesensitivity to the smaller signals that would be producedfrom the lower cross sections. C. Dark Matter Annihilation in Celestial Bodies
Once a DM particle becomes trapped in a BD or NS,it has two possible fates. In the case that DM annihila-tion is forbidden (for example, in the well-studied case ofasymmetric DM) the DM density will build-up near thecore, potentially leading to eventual black hole formationand collapse. On the other hand, in cases where DM canself-annihilate, there is an interplay between the captureand annihilation in the NS or BD. DM annihilation candeplete the incoming DM density, such that the numberof DM particles inside the object N ( t ) evolves over time,governed by [42] dN ( t ) dt = C tot − C A N ( t ) (8)where C tot is the total capture rate given in Eq. 5 and C A = (cid:104) σ A v (cid:105) /V is the thermally averaged annihilationcross section over the effective volume in which the an-nihilation takes place. Eq. 8 has the well known solution N ( t ) = (cid:114) C tot C A tanh tt eq , (9)where t eq = 1 / √ C A C tot is the timescale over whichthe equilibrium between capture and annihilation of DMwithin the object is reached. Under the equilibrium con-dition, the annihilation rate (Γ ann ) is simply:Γ ann = Γ cap C tot , (10)where the factor of 2 comes from the fact that in eachannihilation event, 2 DM particles are involved. We notefrom Eqs. 6 and 10 that if equilibrium between captureand annihilation is reached, the annihilation rate is pro-portional to the local DM density i.e. Γ ann ∝ n χ . Therate will also be proportional to the number density ofneutron stars in that region, so the total annihilation ratevia BD or NS capture is Γ ann ∝ n χ n BD / NS . D. Dark Matter Annihilation to Long-LivedMediators
If DM is captured by, and subsequently annihilateswithin, celestial objects, several outcomes are possible depending on the annihilation products. If DM annihi-lates promptly into SM final states, they will be absorbedin the material of the celestial body in which they werecreated, heating it [2–24]. However, models of hidden-sector DM provide another possibility whereby DM an-nihilates into SM-neutral meta-stable particles. These“mediators” ultimately decay to SM particles, but canbe long-lived due to weak coupling and/or approximatesymmetries. In some models, they may also be producedwith a substantial Lorentz boost η . These features allowthe mediator to escape the celestial object and then de-cay in vacuum. The products of these mediator decaysare then observable through searches closely related tothe standard indirect detection searches for halo annihi-lation.In order to calculate the sensitivities for possible sig-nals, we assume that the mediator φ has a sufficientlylong lifetime τ or a sufficiently large boost factor η ≈ m χ /m φ such that the decay length L exceeds the radiusof the object R , as L = ηβτ (cid:39) ηcτ > R. (11)The differential energy flux (henceforth referred to simplyas “energy flux”) at Earth from long-lived particles incelestial bodies is given by [45] E d Φ dE = Γ ann πD × E dNdE × BR(X → SM) × P surv , (12)where D is the distance to Earth, BR(X → SM) is thebranching ratio of the mediator to a given SM final state.The probability of the signal surviving to reach the de-tector near Earth, P surv , provided the decay productsescape the object is [45] P surv = e − R/ηcτ − e − D/ηcτ , (13)where R is the object’s radius. In order to estimate thesensitivities for signals in our analysis, we further assumethat the decay of the mediator does not significantly alterthe morphology of the annihilation signal (compared todirect annihilation into standard-model particles). Thiscan be accomplished in two ways, either: (1) the medi-ator decays reasonably close to the source, (2) the masssplitting between the DM particle mass and mediatormass is much larger than the mass splitting between themediator mass and the mass of the standard model par-ticles it decays into (i.e., it is very boosted). However, aslong as the decay impact parameter is short compared tothe (Galaxy-scale) distances over which the BD/NS andDM density profiles are varying, this will not significantlyimpact the results.We also assume that the mediator escapes the objectwithout attenuation. This assumption is generally rea-sonable when the mediator particle is long-lived due toits weak coupling with SM particles – which tend to alsosuppress scattering cross sections. For example, assum-ing that the same coupling g (cid:48) controls both decays andscatters of the mediator off protons, the expected in-verse path-length for decays (in the celestial body’s restframe) scales as Γ decay ∼ g (cid:48) m φ /η , where η is a boost fac-tor. Meanwhile, the expected rate for scattering scales asΓ scatter ∼ g (cid:48) αµ /s n ∼ g (cid:48) α/ ( ηm φ ) , where α is an SMcoupling constant (cid:46) / n the number density of SMmatter, and µ is the DM-proton reduced mass. There-fore, even within dense compact objects such as NSs with n ∼ (100 MeV) , decays are the dominant means of at-tenuation so long asΓ scatter Γ decay (cid:39) αnηm φ (cid:39) αη (cid:18)
100 MeV m φ (cid:19) . (14)For mediators heavier than 1 MeV and/or produced withappreciable boost, this is typically <
1. Attenuation byscattering is even less relevant in BDs, due to their muchlower densities.
E. Dark Matter Annihilation in the Halo
Particle DM models relevant for BD/NS-focused an-nihilation can also, in general, produce the more stan-dard signal of DM particles annihilating in the halo whichhosts the BD/NS population. To facilitate future com-parisons of the two signals, we briefly review the standardhalo annihilation rate and highlight important contrastswith the BD/NS-focused annihilation rate.In particular, the standard halo annhilation rate scalesquadratically with DM density ( ∝ n χ ), while BD/NS an-nihilation rate scales linearly with n χ as seen in Eqs. 7and 10. Therefore the expected signals from BD/NS fo-cused annihilation will be different from the standardhalo annihilation signals. The annihilation rate in thehalo scales as Γ halo ∝ (cid:104) σ A v (cid:105) n χ , (15)which highlights the characteristic scaling that is propor-tional to the thermally-averaged annihilation cross sec-tion and the square of the number density of DM parti-cles. The quadratic dependence of the halo annihilationrate on the DM density implies that the brightest an-nihilation targets typically correlate with peaks in theDM density, such as the Milky Way Galactic center, thecenters of dwarf galaxies, and of distant galaxy clusters.In general, the annihilation cross section can be ex-panded in velocity ( v ) as (cid:104) σ A v (cid:105) ∝ v (cid:96) , (16)where the leading rate is found when (cid:96) = 0, i.e. an s − wave contribution is present. The next leading termin velocity is the p − wave contribution (with (cid:96) = 2).From the Boltzmann velocity distribution, (cid:104) v (cid:105) ∼ √ T so that (cid:104) σ A v (cid:105) ∝ x − n (17) where x = m χ /T and n = p/
2. Using this expansion, theWIMP relic density can be estimated as [69]Ω h = 0 . n + 1) x n +1 f (cid:114) g (cid:63) (cid:18) − GeV − (cid:104) σv (cid:105) (cid:19) , (18)where x f is the freeze-out time and g (cid:63) is the number ofdegrees of freedom at freeze-out. Given the present dayDM density, and assuming an s -wave dominant annihila-tion rate, we obtain a thermal annihilation cross sectionof (cid:104) σ ann v (cid:105) s − wave ∼ . × − cm s − [70].Importantly, we note that for a p -wave dominated an-nihilation rate, the annihilation cross section today willbe velocity suppressed (cid:104) σv (cid:105) p − wave ∝ v . This means thatthe expected cross section for typical DM velocities of ∼
200 km/s today will be about 10 − times smaller thanexpected for s-wave annihilation. Noting that cutting-edge experiments are only beginning to probe the fluxesexpected from s-wave annihilation processes, we stressthat p -wave rates are typically unobservable in the halo.By contrast, for celestial body focused annihilation,DM annihilation typically occurs deep within the fo-cusing object, when myriad captures have produced asharply peaked DM density. In this case, DM can anni-hilate efficiently even when the annihilation cross sectionis extremely low. Smaller DM cross sections simply cor-respond to a longer equilibration timescale, rather thana smaller DM signal.To summarize, halo-based annihilation is quadraticallydependent on the DM density, and linearly dependent onthe DM annihilation rate. Celestial-body focused annihi-lation that has reached equilibrium is linearly dependenton the DM density has a flux that depends on the scat-tering rate rather than the DM annihilation rate. Thesedifferences provide two stark observable signatures thatcan differentiate halo and celestial-body focused annihi-lation. III. MILKY WAY GALACTIC CENTER SIGNAL
We first investigate the detectability of our BD/NS-focused annihilation signal in the Milky Way’s Galacticcenter, where the luminosity of the signal is expected tobe high due to the large population of NSs and BDs inthe inner parsecs of the galaxy. In this section we intro-duce specific models for the (i) DM velocity distribution,(ii) NS number density, and (iii) BD number density inthe inner galaxy. These, together with the DM density(modeled as a generalized NFW profile as in Eq. 1, de-termine the GC BD/NS-focused annihilation fluxes for agiven capture rate. We will then compare the resultingBD/NS-focused annihilation fluxes to both halo annihi-lation fluxes and telescope sensitivities in this complexregion.
A. Modeling Milky Way Velocity Components
In addition to the DM density, the DM velocity disper-sion strongly affects the rate at which DM particles in thevicinity of a NS fall into its potential well and intersectthe NS surface. We calculate the DM velocity disper-sion using models for the mass distribution and velocityprofile of the Milky Way following Ref. [71]. This modelassumes five components for the total mass M ( r ): thecentral Black Hole (BH) with mass M BH = 4 × M (cid:12) ,an exponential disk ( ρ disk ), an inner and outer spheroidalbulge ( ρ inner and ρ outer ) and a DM generalized NFWhalo as per Eq. 1 ( ρ DM ). Our DM density profile is nor-malized to the local DM density of 0 .
42 GeV/cm , andthe inner slope is taken to be either γ = 1 . γ = 1 . r s = 12 kpc (these val-ues are our DM density profile choices, not adapted fromRef. [71]). The steeper choice for the inner profile slopecan be motivated by expectations from adiabatic con-traction in the inner Galaxy [72, 73].These components are combined to provide a modelfor the total mass, M ( r ) = M BH + 4 π (cid:90) r ( ρ outer + ρ inner + ρ disk + ρ DM ) dr . (19)From this mass distribution, it is straightforward to cal-culate the galactic rotation velocity, as per Ref. [71].However, it is important to note that the models for ve-locities towards the inner Galaxy are not robust. Indeed,recent work finds significantly lower Galactic velocities inthe inner ∼ v c of Ref. [71], are relatedto the velocity dispersion v d by v d = (cid:112) / v c . B. Neutron Star Population in the Galactic Center
We now investigate the properties of the NSs that arerelevant for our GC signal. There is strong evidence fora population of NSs near the Milky Way GC. In par-ticular, observations of hundreds of O/B stars currentlylocated in the central parsec indicate a high rate of insitu
NS/BH formation in this region [75, 76]. Indeed,it is expected that a dense system of compact objectsreside in the GC region, and the expected populationhas been estimated in the literature [54, 55, 77, 78] . For arguments to the contrary, we note that the observation ofradio pulsars near the galactic center has proven unexpectedlydifficult, leading some to conclude that there is a “missing pulsar
The number densities of black holes and neutron starsin the Galactic Center region have been previously ob-tained with numerical simulations of nuclear star clusterdynamics [55]. These studies utilize the Fokker-Planckequation to numerically evolve the radial distribution ofstars and compact objects over time, taking into accounttwo-body relaxation.In Ref. [55], two types of nuclear cluster models weredescribed. One is the ‘Fiducial ×
10’ model where it isassumed that compact objects which are injected nearthe present disk of massive stars at ∼ N NS = 4 × − yr − and ˙ N BH = 2 × − yr − corre-sponding to the present day formation rates of massivestars. This model also takes into account ‘Primordial’NS’s of masses 1.5 M (cid:12) which are deposited impulsivelyat t = 0. The other model is labeled the ‘Fiducial’ model,and utilizes very conservative star formation rates (SFR)of ˙ N NS = 4 × − yr − and ˙ N BH = 2 × − yr − , whichare approximately an order of magnitude lower than thepresent day star formation rate. The order of magni-tude smaller formation rates for the ‘Fiducial’ model inRef. [55] were motivated by the results of Ref. [81] whereit was found that that the SFR 1 − − (cid:46) (cid:12) ), and their results do not directly constrain therate of NS/BH formation within the star-forming discsif the top-heavy disc IMF is truncated below a few so-lar masses (for a more detailed discussion see Ref. [55]).Therefore, given the observational uncertainties, both the‘Fiducial’ and ‘Fiducial ×
10’ models outlined in Ref. [55]are potentially equally good candidates for representinga generic NS distribution in the nuclear star cluster.The NS number density for the ‘Fiducial ×
10’ modelat 10 Gyr is roughly a factor of 3 − ×
10’ model to demon-strate our idea, while noting that the signals with the‘Fiducial’ model will be roughly a factor of 3 − (cid:12) . We also note that other studies focused on modelingthe compact object distribution in the nuclear star clus-ters [54, 82] are in rough agreement with the NS numberdensity estimates of Ref. [55].For a radial distribution for NSs, we extract the NSradial number density distribution of the ‘Fiducial × problem” which may indicate an unexpected absence of pulsarsnear the Galactic center [79]. However, Ref. [80] argues that thisis merely an observational effect, and the pulsar density near theGalactic center is still likely to be large. number density, n NS = 5 . × (cid:18) r (cid:19) − . pc − ; 0 . < r < , = 2 . × (cid:18) r (cid:19) − . pc − ; r > . C. Brown Dwarf Population in the Galactic Center
A huge number of BDs are expected to be present inthe Milky Way. In Ref. [83], it was estimated that theMilky Way may contain as many as 25 −
100 billion BDs.To obtain the radial distribution of BDs, we use the BDdistribution function outlined in Refs. [84, 85]. In thistreatment, the Kroupa Initial Mass function (IMF) [84] isextended to include sub-stellar BD masses. The BD IMFis described by a broken power law of the form dN BD dm ∝ m − α , where N BD and m are the BD number and massrespectively, and α = 0 . . − .
07 M (cid:12) is given by [84, 85] n BD = 7 . × r − . pc − , (20)where r pc is the radius of the containment volume in par-secs. Unlike many NSs and BHs, BDs are not born withnatal kicks. 3-Body interactions in the dense Galacticcenter might eject some BDs from the center, but thatnumber is expected to be small.Note that for our BD calculations, we take the aver-age mass M BD = 0.0378 M (cid:12) to be representative of thepopulation mass between 0 . − .
07 M (cid:12) , with the massdistribution given by the Kroupa IMF discussed above.We have checked that the error introduced in the totalcapture rate by using the average mass compared to usingthe full mass distribution ( ∝ m − . ) is less than 10%. D. Celestial-Body Focused vs. Standard HaloAnnihilation
We first calculate the DM capture rate from a sin-gle
NS or BD located at a distance r from the GalacticCenter. To do this, we use the multi-scatter formalismoutlined in Sec. II A, taking the DM density and Galacticvelocity dispersion as defined in the previous subsection.Figure 2 shows the NS and BD capture rates as a func-tion of radius r , assuming a maximum capture rate forDM particles. These capture rates correspond to a single BD/NS that accumulates DM particles with any scat-tering cross section that is larger than the cross sectionsshown in Fig. 1. We see that BDs have a much largermaximum capture rate than NSs. This is because themaximum capture rate is determined by the total DMflux that passes through the object; the effective captureradius is larger for BDs, because their radius that is about1,000 times larger than NSs. The wiggles in the plot aredue to the interplay between the DM density and halo Distance from Galactic Center [pc]10 M a ss C a p t u r e R a t e [ G e V / s ] N e u t r o n S t a r ( = . ) N e u t r o n S t a r ( = . ) B r o w n D w a r f ( = . ) B r o w n D w a r f ( = . ) FIG. 2. Maximum DM mass capture rates for a single neutronstar or brown dwarf as a function of radius ( r ) from the Galac-tic center. Results are shown for NSs with R NS = 10 km and M NS = 1.4 M (cid:12) , and BDs with M BD = 0.0378 M (cid:12) and R BD = R J (where R J is the radius of Jupiter). We show variedresults for generalized NFW DM profiles, with γ = 1 . , . velocity. For demonstration, we show two cases of theNFW slope, γ = 1.0 (standard NFW) and γ = 1.5 (gen-eralized NFW, with a steep slope). The smaller NFWslope decreases the DM density in the GC region (wherethe BDs/NSs are present in largest numbers), which leadsto a lower total capture rate.To calculate the total capture rate from the GC popu-lation of NSs, C tot , NS , we use Eq. 7, and the number den-sity of neutron stars n NS from Eq. 20. We integrate overa volume between r = 0.1 pc to r = 100 pc. The cutoffradius of r = 0 . ∼
90 % of allNSs are ejected out [86], the signals will correspondinglydecrease. For the NFW density slope γ = 1 .
5, we obtaina total DM capture rate by all the NSs in the GC regionof C NS , GC = Γ cap , NS ∼ × GeV/s. For γ = 1 . cap , NS ∼ GeV/s.To calculate the total capture rate from the GC popu-lation of BDs, we follow the same integration procedureas NSs (but note that BDs do not receive natal kickscapable of ejecting them from the GC). We find that DM Mass [GeV] T o t a l A nn i h il a t i o n R a t e w i t h i n p c [ G e V / s ] p - w a v e - H a l o NS-focused-GC BD-focused-GC s - w a v e - H a l o = 1.5 DM Mass [GeV] T o t a l A nn i h il a t i o n R a t e w i t h i n p c [ G e V / s ] = 1.0 p - w a v e - H a l o NS-focused-GC BD-focused-GC s - w a v e - H a l o FIG. 3. NS-focused annihilation and BD-focused annihilation (solid) vs. halo annihilation in the Milky Way Galactic center,for s − wave and p − wave DM rates (dashed) for varying DM mass. This plot assumes the maximum capture rates for BD/NS.Two panels for different NFW slope γ = 1.0 and 1.5 are shown. the total capture rate from the GC population of BDs isΓ cap , BD ∼ × GeV/s for γ = 1.5. For γ = 1.0, theBD capture rate is Γ cap , BD ∼ × GeV/s.For a celestial object in equilibrium, the total annihila-tion rate from all NSs or BDs corresponds to half the to-tal capture rates (because self-annihilation removes twoDM particles), as shown in Eq. 10. If this entire fluxescapes the celestial body through annihilation into thelong-lived mediator and then decays, the total annihi-lation rate within 100 pc from BDs will be Γ ann , BD =3 . × GeV/s for γ = 1.5 and ∼ . × GeV/sfor γ = 1 .
0. For NSs, the total annihilation rate will beΓ ann , NS = 3 × GeV/s for γ = 1 . ∼ × GeV/s for γ = 1.0.Figure 3 demonstrates the relative strength of the NS-focused and BD-focused annihilation, compared to haloannihilation, as a function of DM mass for both p - and s -wave DM for γ = 1.0 and 1.5. The total halo annihi-lation rate is calculated by integrating the annihilationrate along the line of sight over the whole angular rangeof the sky. For NS-focused annihilation, when m χ (cid:46) GeV, halo annihilation dominates for both s − and p − wave DM. When m χ (cid:38) GeV, NS-focused annihila-tion becomes dominant over the p − wave halo annihila-tion rate. For BD-focused annihilation, when m χ > p − wave annihilation. For m χ (cid:46) s − wavehalo signal for BDs. For m χ (cid:38) s − and p − wave signals.This result holds for both γ = 1.0 and 1.5.In the heavy DM case, celestial- body-focused annihila-tion enhancement is particularly pronounced for both NS and BDs, as their linear dependence on the DM numberdensity means that their flux is constant with DM mass,while the halo rate becomes suppressed. IV. DARK MATTER PARAMETER SPACE
To translate these observations into constraints on theDM parameter space, we now calculate the capture ratesand corresponding cross section limits that can be con-strained via current γ -ray observations. A. Gamma-Ray Telescope Sensitivity
To set scattering cross section limits, we use the fluxesalready measured by
Fermi and H.E.S.S. at the Galacticcenter [87]. We use
Fermi data for all observations cor-responding to DM masses less than O (100) GeV. This isappropriate because the Fermi -LAT has produced sen-sitive measurements across the entire sky. At highermasses, however, our results require separate instrumen-tation. For the Sun, we utilize the solar limits derived inRef. [47] using the HAWC telescope, because atmosphericCherenkov telescopes (like H.E.S.S. and VERITAS) arenot designed to work when pointed at the Sun. For GClimits at TeV energies we utilize H.E.S.S. data, becauseHAWC and VERITAS lie in the northern hemisphere,and have poor exposures of the Galactic center region.We set limits by simply requiring that the normaliza-tion of the DM flux does not exceed 100% of the mea-sured gamma-ray flux. This is done by determining the DM Mass [GeV] M a x i m u m E d / d E [ G e V c m s ] NS, = 1.5NS, = 1.0BD, = 1.0BD, = 1.5Fermi H . E . S . S . FIG. 4. Maximum E d Φ /dE values (at E γ ≈ m χ ) for theGalactic center population of Brown Dwarfs or Neutron Stars,for DM densities described by NFW profiles with indices of1.0 or 1.5, as labelled. The Galactic center gamma-ray fluxesmeasured by Fermi and H.E.S.S. are shown for comparison,where E γ ≈ m χ is assumed (see text for details). smallest scattering cross section for which the energy fluxfound in Eq. 12 (and using Eqs. 7 and 10) exceeds themeasured flux in any energy bin. This is a very conser-vative approach.The photon energy spectrum from DM annihilation,and hence the observational constraints we consider, de-pend on the final states into which DM annihilates. Wefocus below on modes χχ → φφ , φ → γ , where themediator φ escapes the system of interest, as per Eq. 11,before it decays. This process is expected to dominateover production of only one mediator, due to phase spacesuppression. The mediator mass and its precise lifetimehave little effect on the signal, so long as the mediatorlifetime is (cid:46) parsec-scale. We will later comment brieflyon other decay modes.To generate our gamma-ray energy spectra, we use Pythia [88]. We create an effective resonance with en-ergy 2 m χ , by colliding two back-to-back neutral beams.This resonance is then decayed into two mediators, whichdecay to SM particles. These SM particles can radiatefurther particles, decay themselves, or shower. All suchpossibilities are taken into account, and we use the fullydecayed spectra in vacuum.Figure 4 shows the relative sizes of the E d Φ /dE flux(as defined in Eq. 12) values for direct decay to gammarays, for BDs and NSs in DM NFW profiles with indicesof 1.0 and 1.5. We see that compared to Fig. 3 (whichonly considers the total integrated flux), the maximumvalues of the fluxes are higher. This is because the energyspectrum for direct decay into gamma rays, E dN/dE , is peaked near the DM mass, putting a large amountof gamma rays into a particular energy bin. We haveshown the maximum flux value of the whole spectrum;as this is what will generally set the limit relative tothe measured telescope flux. For comparison, we showthe fluxes measured in the Galactic center by Fermi andH.E.S.S., where we have taken for demonstration pur-poses E γ ≈ m χ just for this plot, which is a valid ap-proximation given the sharp box spectrum expected fordirect decay to gamma rays. We see that BD fluxes arehigher than that measured by Fermi and H.E.S.S., whichleads to strong constraints. On the other hand, for NSs,only the γ = 1 . B. Cross Section Limits
Figure 5 shows our cross section constraints for me-diator decay to gamma rays, via χχ → φφ , φ → γ .We show for comparison, limits obtained for long-livedmediators in the Sun from Refs. [45, 47], as well as di-rect detection limits [89, 90]. Our analysis, based onexisting telescope data, can outperform both solar anddirect detection limits. The BD limits can outperformexisting limits in the same sub-GeV mass range by morethan nine orders of magnitude . The reasons for such newpowerful bounds are (i) direct detection sensitivities aregreatly weakened, because lighter recoils fall below thedetection threshold, and (ii) BDs have cooler cores anddo not evaporate DM with masses above a few MeV, pro-viding new sensitivity to light DM (the Sun on the otherhand, has truncated limits around 4 GeV). BDs also canoutperform spin-dependent indirect detection, althoughin this region our bounds overlap with solar constraints.Neutron stars outperform SD direct detection by ∼ − ∼ − DM mass range.In this mass range, NSs even can potentially outperformthe Sun, by ∼ − γ = 1 . γ = 1 .
5. For NSs,we only show γ = 1 .
5. This is because the maximumgamma-ray flux produced by NSs is only just detectableover the H.E.S.S. background flux. We emphasize again,however, that we have taken a very conservative approachin setting our limits. As such, it is possible that in a lessconservative analysis, the NS signal could potentially beprobed across a range of DM masses even with a pro-file index of γ = 1 . γ = 1 . m [ GeV ]10 S D N [ c m ] D i r e c t D e t e c t i o n Sun, Fermi S u n , H A W C NS, HESS (this work) = 1.5
BD, Fermi (this work)= 1.0= 1.5
FIG. 5. Scattering cross section limits for DM annihilation to long-lived mediators decaying to γγ in Brown Dwarfs (using Fermi ), the Sun (using
Fermi and HAWC [45, 47]), and Neutron Stars (using H.E.S.S.). The BD and NS limits are newcalculations in this work, calculated using the full Galactic Center population of BDs or NSs. The γ = 1 . , . for varying Lorentz interactions. As such, we only showthe NS limit range with a dashed line – in full model-dependent contexts, the limits will likely be containedsomewhere within this range.We note several ways to construct models that canchange the relative strength of these limits. First, wenote that the solar and BD limits require proton scatter-ing, while the NS limits require neutron scattering, so inthe case that only one coupling is present, the other limitswill disappear. We also note that we have assumed thatthe mediator has a sufficiently long lifetime and/or boostthat it escapes the celestial body in question. However,each of these systems shown have differing radii, and assuch, if the mediator lifetime or boost were shorter, theSun, BD or NS limits may disappear, in that order. Fur-thermore, much longer lifetimes may be probed by theGC populations of BDs/NSs compared to the Sun – a de-cay length that is much longer than an A.U. suppressesthe flux from the Sun, and depending on mediator boost,can also enlarge the angular region that the signal ap-pears to emanate from. In this sense, the BD/NS limitsare the most general; they apply to a wider range of decaylengths.While we have only shown mediator decay to gammarays χχ → φφ → γ in Fig. 5, other final states can alsobe probed. For electron final states, there is some ad-ditional sensitivity at lower DM masses with BDs thancan be probed with the Sun, however this is only a fewGeV improvement, as the electron gamma-ray spectrumis very soft, it peaks outside Fermi ’s energy range for any lower DM masses. For b -quarks or τ leptons, there is noadditional sensitivity with BDs using Fermi comparedto current constraints from the Sun. The main reasonwhy b -quarks or τ spectral types do not gain new sub-GeV sensitivity is that their softer spectral shapes peakoutside Fermi ’s sensitivity. As such, upcoming MeV tele-scopes such as AMEGO and e-ASTROGAM could pro-vide strong limits for these additional final states. Note,however, that generically, the direct decay to photons willprovide the strongest constraints.It also is possible to probe final states other than φ → φ → γ processes (motivated by light vectors)and or φ → φ (cid:48) + γ (e.g. a long-lived dipole-type transitionbetween two massive dark sector states). However due totheir spectral shape, we expect these will likely produceweaker constraints.Lastly, we comment on our expectation that the crosssections shown in Fig. 5 will lead to equilibrium beingreached. Most stars in the Galactic center nuclear starcluster are expected to be very old, potentially olderthan ∼ t eq to be lessthan O (1 Gyr). Conservatively, we consider the effectiveannihilation volume V to be the volume of the celestialbody BD/NS. For NS, and for both s − and p − wave DM, t eq will be smaller than 1 Gyr for scattering cross sectionsof O (10 − cm ) and higher, which is much lower thanthe sensitivity for NS as shown in Fig. 5. For BDs, the1volume within which annihilation takes place is larger,because BDs have larger radii than NSs. As such, t eq forBDs is generically longer. For s − wave DM, equilibriumcan be reached within O (1 Gyr) if the scattering crosssection is greater than O (10 − cm ) for all DM massesup to 10 TeV, which is approximately the testable crosssection with BDs in Fig. 5. For p -wave, DM masses up to10 GeV can reach equilibrium for scattering cross sectionsof 10 − cm and higher, while 10 GeV can equilibrateonly for cross sections higher than 10 − cm . However,we emphasize again that these equilibriation timescaleswill be much faster if the DM thermalizes within the ce-lestial body and settles into a thermal volume. Therefore,except for very high mass (more than 10 GeV) p − waveDM in BDs, the equilibration condition is justified forthe parameter space covered in Fig. 5. C. Galactic Center Excess
Our results are particularly interesting in light of ob-servations of a γ -ray excess of unknown origin emanatingfrom the Galactic center, the “Galactic Center Excess”.The origin of this excess is not yet known [91–100]. Wenote that the BD-focused annihilation signal could po-tentially explain the GCE, as the 100 GeV DM signal iswithin the normalization of the GCE (and the annihila-tion of 100 GeV DM can produce the correct gamma-rayspectrum).Such a signal would be particularly interesting as itprovides a density scaling that does not follow annihilat-ing DM, but instead follows the DM density multipliedby the local BD number density. While the morphologyof the galactic center excess is not definitively known,some recent work claims that it may be consistent withthe morphology of the stellar bulge [98] (though see e.g.Ref. [100]), a result which has been used to conclude thatastrophysics, rather than DM, powers the excess. Oursetup, on the other hand, could potentially explain sucha morphology with a DM origin.For this combination of mass and cross section param-eters, our results would also predict a bright γ -ray signalfrom the Sun, which is not observed [45, 47]. However,these constraints can be broadly evaded, depending onthe particle decay lengths. For example, the solar limitscan be decreased if the mediator has a decay length thatis shorter, and is therefore extinguished in the Sun (whichis larger) but escapes the BD. More generally, the solarlimits can be evaded with a decay length that is muchlonger than an AU, as this suppresses the flux from theSun and depending on mediator boost can also enlargethe signal’s angular region. In any case, it is also impor-tant to note that the direct detection limits overlap withthe favored GCE parameter space (and are stronger byabout an order of magnitude), so this GCE explanationwould only be valid for classes of models with slightlysuppressed DD rates, and non-suppressed annihilationrates. Finally, the NS-focused annihilation signal cannot beresponsible for the Galactic Center GeV gamma-ray Ex-cess or the overlapping anti-proton excess [101–104]. Thisis simply because the flux produced by NSs is low, andboth the GCE and anti-proton excess have substantiallylarger rates. V. SIGNALS IN GLOBULAR CLUSTERS
Globular clusters are very dense stellar systems. Theyhave the typical mass of dwarf galaxies, but their sizeis a O (10) factor smaller. They can be found in thehalo or bulge regions of galaxies. Neutron stars canexist in the center of globular clusters, while BDs maybe mostly expelled into the halo [105–107] because ofmass-segregation. As such, in this section we study theprospects of ‘NS-focused’ annihilation in globular clus-ters. We will focus on the globular cluster Tucanae 47(also called “Tuc 47”), as it is relatively close by, massive(and so contains a high number of NSs), and is expectedto be DM dense. While we expect the globular clustersignal to be weaker than that from the Galactic center,it may provide a corroborating signal in case a detec-tion is first made in the Galactic center. We also expectthat new clusters will be found, which may improve thesensitivities compared to Tuc 47 observations. A. Dark Matter in Globular Clusters
In order to study the DM capture from NS in glob-ular clusters, we first need to calculate the DM densityin globular clusters. Although it is currently impossi-ble to do this with any great accuracy, developments inobservation and simulated evolution of globular clustersembedded in Galactic halos can provide an estimate ofthe DM content. Some time ago, in Ref. [108], it was sug-gested that globular clusters might be formed in subhalosof DM before falling into Galactic halos. Observations of O (1) mass-to-light ratios and tidal stripping from starsfrom some globular clusters suggest that a significant DMcomponent cannot reside with the observed stellar distri-bution [109]. These observations set an upper limit onthe DM content of globular clusters.Simulations have suggested how the above observationscan be reconciled with a scenario of globular cluster for-mation via tidal stripping. Ref. [110] suggested a sce-nario where continuous mass-loss occurs via tidal strip-ping once a subhalo falls into a larger halo. In this pro-cess, the orbit of the subhalo decays down towards thecentre of the larger halo. The tidal stripping of DM fromold globular clusters has been studied with N -body sim-ulations [111–115]. These results render support for thescenario of globular cluster formation within DM subha-los that are tidally stripped by the host galaxy. In thismanner, it also explains how these globular clusters growwith baryon-dominated cores.2DM in the core of such globular clusters might havesurvived tidal stripping until the present time. This as-sumption is supported by the results of Ref. [111], whereit is seen that the presence of the stellar core makes thesubhalos more resilient to tidal stripping. For NFW ha-los, the innermost DM density is not modified by theexternal tidal field. Motivated by these results, DM sig-nals from globular clusters has been studied in severalworks [3, 7, 64, 116–119]. B. Mass and Velocity Distributions for Tucanae 47
Here, we utilize the well-studied globular cluster Tuc 47as a template globular cluster for our calculations, notingthat future observations may find stronger constraints foralternative systems. The baryonic properties of Tuc 47are well studied. It has a baryonic mass of ∼ M (cid:12) , acore radius of r c = 0.5 pc, a tidal radius r t = 70 pc anda half-light radius, r h = 3.7 pc [120].For the mass of the DM halo in Tuc 47 cluster, we canuse the relation between the current baryonic mass of theglobular cluster, and the mass of the initial DM subhalo, M GC = 0 . M DM, [115]. This imples that the initialmass of the DM subhalo of Tuc 47 is ∼ × M (cid:12) .To estimate the DM density in Tuc 47, we follow asimilar approach to Refs. [3, 7, 117]. The original DMhalo of Tuc 47 can be modeled using an NFW profile, asper Eq. 1. Further inclusion of baryonic feedback leadsto an adiabatic contraction of the DM halo [121, 122].However, the DM cusp created by the adiabatic contrac-tion can be shallowed by the heating of DM due to col-lision with stars [123], creating a core of constant den-sity [3, 7, 117, 123]. The size of this core can be esti-mated as the radius at which the two-body relaxationtimescale becomes greater than the age of the cluster.In Tuc 47, this radius is about ∼ ∼ ρ DM = 10 GeV/cm .If Tuc 47 hosts a central IMBH [124], there may bea spike in the DM density in the central regions of theglobular cluster [125]. This effect is most pronouncedfor radii less than 0 .
01 pc. However, according to recentsimulations, most NS will be present only beyond ∼ v ∼ −
20 km/s[126].
C. Neutron Stars in Globular Clusters
Globular clusters are known to be efficient at produc-ing millisecond pulsars (MSPs). Multiple surveys have found 157 pulsars in 30 globular clusters, including 38 inTerzan 5 and 25 in Tuc 47 (see e.g. Refs. [127, 128]).Although globular clusters make up only about 0.05% ofstars in the Milky Way, collectively, globular clusters con-tain more than one third of known MSPs in our Galaxy[129]. Globular clusters also contain many low-mass X-ray binaries (LMXBs) with NS acceretors [130].The large number of MSPs and LMXBs suggest thata typical Galactic globular cluster on average contain atleast a few 100 NSs. The high numbers of NSs seen inglobular clusters is in tension with the fact that NSs maybe born with large natal kicks [131] when the formationoccurs from core-collapse supernovae (CCSNe). How-ever, the discovery of the high-mass X-ray binaries withlong orbital periods and low eccentricities [57] suggeststhat some NSs must be born with very small natal kicks.More recent studies have suggested that electron-capturesupernovae (ECSNe) can solve the retention of NS prob-lem by producing many NS with small kicks [58, 132].These studies showed that a large number of NSs couldbe retained in globular clusters by formation through EC-SNes [58, 132, 133]. Simulations [58, 59, 134] indicatethat O (100) NSs could be retained in a typical globularcluster with mass ∼ M (cid:12) .We note that for a massive cluster like Tuc-47, thenumber of NSs that could be retained within the clusteris debated. The range in the number of NSs that couldbe retained within a Tuc-47 like cluster cited in literaturelies between ∼ − ∼ NSs retained in Tuc-47 motivated byrecent numerical simulations that takes into account EC-SNe formation of NSs with small natal kicks in a Tuc-47like cluster (model 26 of [59]). However, while interpret-ing our results, this uncertainty in NS numbers shouldbe kept in mind.
D. Neutron-Star Focused vs. Standard HaloAnnihilation
We now calculate our NS-focused signal for Tuc 47. Weintegrate over the inner 4 pc of Tuc 47 using an assumedconstant DM density of 10 GeV/cm , and ∼ NSs.The 4 pc integration boundary is chosen because we as-sume that most of the NSs are confined within this regionof Tuc-47, roughly consistent with the results of Ref. [59].Similar to the total NS numbers, the NS radial numberdistributions in the central regions of globular clusters isnot well known and is a topic of active research. We em-phasize that for this globular cluster signal, we are takinga number of well-motivated estimates (rather than defini-tively known quantities), to simply demonstrate how thepopulation of NSs in globular clusters may provide NS-focused annihilation signals.Figure 6 shows the relative strength of the NS-focusedannihilation rate for Tuc 47, compared to s - and p -wavehalo annihilation within the integration volume. We seethat the NS-focused annihilation can be orders of magni-3 DM Mass [GeV]10 T o t a l A nn i h il a t i o n R a t e w i t h i n p c [ G e V / s ] p - w a v e - H a l o NS-focused-Tuc-47 s - w a v e - H a l o FIG. 6. NS-focused annihilation vs. halo annihilation signalsin globular cluster Tuc 47, for s − wave and p − wave DM, forvaried DM masses. tude higher than the p − wave standard halo annihilationsignal. In the globular cluster case, p − wave annihilationsare even more suppressed due to the especially low ve-locity dispersions in these systems. In fact, if the DMis sufficiently massive, greater than 10 GeV, then the‘NS-focused’ signal can even dominate over the standard s − wave annihilation signal within the integration vol-ume. Fermi has seen bright γ -ray emission from Tuc 47 [137].This emission generally has been attributed to millisec-ond pulsar emission, though there is some debate whetherDM can contribute to it [125, 138, 139]. The ‘NS-focused’signal described in Fig. 6 is too low to explain this emis-sion from Tuc 47. In general, we note that the ‘NS-focused’ signal from Tuc 47 is below the reach of present Fermi -LAT sensitivity [140]. In the future, a more opti-mal signal from a different globular cluster may be found.
VI. SUMMARY AND CONCLUSIONS
Indirect DM searches have typically focused on eitherthe effects of DM-DM interactions (e.g., annihilation) orDM-SM interactions (e.g., DM scattering off compact ob-jects). In this work, we have demonstrated new detectionpossibilities which combine these interactions, and allowcelestial body populations to “focus” DM-DM interac-tions and significantly enhance their rate.The signals from such processes have several new phe-nomenological features. The signal (i) distinctively scaleslinearly with DM density, rather than with the squaredDM density like standard halo annihilation, and (ii) candominate over standard halo annihilation in some situ- ations, especially when the annihilation rate is velocitysuppressed. This is particularly valuable in the case ofsuppressed halo annihilation (e.g. p -wave annihilation),which would otherwise be undetectable. This signal re-quires that DM annihilates to a sufficiently long-livedmediator, in order to allow products to escape the ce-lestial object and be detectable with indirect detectionexperiments.We surveyed the potential celestial object targets forthis signal, and identified neutron stars and brown dwarfsas ideal targets. Neutron stars can be a particularly in-teresting laboratory, due to their extreme densities andgravitational wells. A standard scenario considered in theliterature is DM that scatters and is captured by neutronstars, and subsequently either heats the neutron star orcollapses the entire system into a black hole. In con-trast, for the first time, we have considered the indirectdetection signals that arise from neutron stars. Simi-larly, brown dwarfs are quite dense, and produce larger γ -ray fluxes (compared to neutron stars) for relatively-large DM scattering cross sections, due to their large radiiand larger number density in our Galaxy. For the firsttime, we considered DM annihilation to long-lived parti-cles within brown dwarfs.We studied this focusing signal in two different envi-ronments; the Galactic center, and in the globular clusterTuc 47. For the Galactic center, we found that for NSs,the focused rate can exceed the p-wave rate for masses m χ > GeV. For brown dwarfs, we found the focusedrate can exceed the p-wave suppressed flux from halo an-nihilation for m χ > . m χ (cid:38) GeV .We pointed out that brown-dwarf-focused annihilationmay also explain the Galactic Center Gamma-Ray Ex-cess, and can do so with a morphology partially scalingwith the stellar matter, providing a DM interpretation ofthe excess using typically non-DM morphologies.When studying globular cluster Tuc 47, we pointed outthat while the Galactic center signal could be stronger,the globular cluster signal could be used as a corroborat-ing check in the case a signal is first seen in the Galacticcenter. We also pointed out that, importantly, new glob-ular clusters may be found, and even better sensitivitieswill be possible using this framework for more optimalclusters.For the first time, we have set limits on DM annihi-lation to long-lived particles in brown dwarfs and neu-tron stars, and the resulting DM scattering cross sec-tions. In different parts of parameter space, we out-perform both existing solar limits, and direct detectionexperiments. Using
Fermi ’s measured Galactic centergamma-ray fluxes, brown dwarfs provide the strongestnew limits, with an improvement in the sub-GeV massrange up to nine orders of magnitude. This is due tocomparably poor direct detection sensitivity in the sub-GeV mass regime, and the cooler cores of brown dwarfswhich allow DM to not evaporate, unlike the Sun. Weshowed that depending on model assumptions, neutron4stars can potentially outperform spin-dependent directdetection by ∼ − ∼ − ACKNOWLEDGMENTS
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