If cold dark matter is present at the galactic center, as in current models
of the dark halo, it is accreted by the central black hole into a dense spike.
Particle dark matter then annihilates strongly inside the spike, making it a
compact source of photons, electrons, positrons, protons, antiprotons, and
neutrinos. The spike luminosity depends on the density profile of the inner
halo: halos with finite cores have unnoticeable spikes, while halos with inner
cusps may have spikes so bright that the absence of a detected neutrino signal
from the galactic center already places interesting upper limits on the density
slope of the inner halo. Future neutrino telescopes observing the galactic
center could probe the inner structure of the dark halo, or indirectly find the
nature of dark matter.Comment: 4 pages, 5 figure

A. Eckart

A. M. Ghez

A. V. Kravtsov

B. Moore

G. D. Quinlan

H. Adarkar

H. S. Zhao

J. Binney

J. Edsjö

J. F. Navarro

Joseph Silk

K. Nakamura

L. Bergström

N. W. Evans

P. Ullio

Paolo Gondolo

R. Svoboda

S. Dimopoulos

W. Dehnen

Y. Oyama

Z. Bern

English

arXiv

Crossref

Physical Review Letters

Dark Matter Annihilation at the Galactic Center

Journal ArticleCold dark matter near the galactic center is accreted by the central black hole into a dense spike. Particle dark matter annihilation makes the spike a compact source of photons, electrons, positrons, protons, antiprotons, and neutrinos. The spike luminosity depends on the halo density profile: halos with finite cores have unnoticeable spikes; halos with inner cusps may have spikes so bright that the absence of a neutrino signal from the galactic center already places upper limits on the density slope of  the inner halo. Future neutrino telescopes observing the galactic center could probe the inner structure of the dark halo or indirectly find the nature of dark matter

Gondolo, Paolo

Silk, Joseph

The University of Utah: J. Willard Marriott Digital Library

VOLUME 83, NUMBER 9 P H Y S I C A L R E V I E W L E T T E R S 30 AUGUST 1999Dark Matter Annihilation at the Galactic CenterPaolo Gondolo*Max Planck Institut für Physik, Föhringer Ring 6, 80805 Munich, GermanyJoseph Silk†Astrophysics, University of Oxford, Keble Road, Oxford, OX1 3RH, United Kingdomand Department of Astronomy and Physics, University of California, Berkeley, California 94720(Received 24 March 1999; revised manuscript received 24 June 1999)Cold dark matter near the galactic center is accreted by the central black hole into a dense spike.Particle dark matter annihilation makes the spike a compact source of photons, electrons, positrons,protons, antiprotons, and neutrinos. The spike luminosity depends on the halo density profile: haloswith finite cores have unnoticeable spikes; halos with inner cusps may have spikes so bright that theabsence of a neutrino signal from the galactic center already places upper limits on the density slope ofthe inner halo. Future neutrino telescopes observing the galactic center could probe the inner structureof the dark halo or indirectly find the nature of dark matter.PACS numbers: 95.35.+d, 98.35.GiThe evidence is mounting for a massive black holeat the galactic center. Ghez et al. [1] have confirmedand sharpened the Keplerian behavior of the star velocitydispersion in the inner 0.1 pc of the Galaxy found byEckart and Genzel [2]. These groups estimate the massof the black hole to be ✁   ✂✄☎✆ ✝ ✞☎✄✟ ✠ ✡✞☛✁☞.If cold dark matter is present at the galactic center, asin current models of the dark halo, it is redistributed bythe black hole into a cusp. We call it the central “spike,”to avoid confusion with the inner halo cusp favored bypresent ✌-body simulations of Galaxy formation [3]. Ifcold dark matter contains neutral elementary particles thatcan annihilate with each other, like the supersymmetricneutralino, the annihilation rate in the spike is stronglyincreased as it depends on the square of the matter density.The steep spike profile, with index ✍✎✏✄, then impliesthat most of the annihilations take place at the inner radiusof the spike, determined either by self-annihilation or bycapture into the black hole.Of the annihilation end products, neutrinos escape thespike and propagate to us undisturbed. Current limitson the neutrino emission from the galactic center placeupper limits on the slope of the inner halo. Futureneutrino telescopes may improve on these limits or bringinformation on the nature of dark matter.Adiabatic spike around the central black hole.—Wefind the dark matter density profile in the region wherethe black hole dominates the gravitational potential. Fromthe data in [1,2], this is the region ✑ ✒ ✓✔✕✞☎✄pc.Other masses (the central star cluster, for example) alsoinfluence the dark matter distribution, but since they makethe gravitational potential deeper, their effect is to increasethe central dark matter density and the annihilationsignals.We work under the assumption that the growth of theblack hole is adiabatic. This assumption is supported bythe collisionless behavior of particle dark matter. We canfind the final density after black hole formation from thefinal phase-space distribution ✖✗✂✘✗✙ ✚✗✟as✛✗✂✑✟  ✜✢✣✤✥✦✘✗✜✧✤✥✧✤★✦✚✗✩✪✚✗✑✫✬✭✖✗✂✘✗✙ ✚✗✟✙ (1)with✬✭ ✮✄✯✘✗✰✱✁✑✲✚✗✫✄✑✫✳✴✵✶✫✙ (2)✘✗✷ ✲✱✁✑✯✡✲✩✓✸✑✳✙ (3)✚✗✹  ✄✺✓✸✙ (4)✚✗✷ ✮✄✑✫✯✘✗✰✱✁✑✳✴✵✶✫☎(5)We have neglected the contribution from unbound orbits(✘✗ ✻ ✞). The lower limit of integration ✚✗✹and the sec-ond factor in ✘✗✷are introduced to eliminate the particleswith ✚ ✼ ✄✺✓✸, which are captured by the black hole.(✓✸  ✄✱✁✏✺✫ is the Schwarzschild radius.) We relate✖✗✂✘✗✙ ✚✗✟to the initial phase-space distribution✖✂✘✙✚✟through the relations, valid under adiabatic conditions,✖✗✂✘✗✙ ✚✗✟   ✖✂✘✙ ✚✟, ✚✗ ✚, ✽✗✂✘✗✙ ✚✗✟   ✽✂✘✙✚✟, wherethe last two equations are the conservation of the angularmomentum ✚ and of the radial action ✽✂✘✙✚✟.The density slope in the spike depends not only on theslope of the inner halo but also on the behavior of theinitial phase-space density✖✂✘✙ ✚✟as ✘ approaches the po-tential at the center ✾✂✞✟ [4]. If ✖✂✘✙ ✚✟ approaches aconstant, as in models with finite cores, the spike slopeis ✿❀❁  ✎✏✄. If ✖✂✘✙ ✚✟ diverges as ❂✘ ✲ ✾✂✞✟❃❄❅ , as inmodels with an inner cusp, the spike slope is✿❀❁✻ ✎✏✄.Models with finite cores include [5] the nonsingular and themodified isothermal sphere, the Hénon isochrone model,the Plummer model, the King models, the modified Hubbleprofile, the Evans power-law models with ✓✹❆✞, and0031-9007✏99✏83(9)✏1719(4)$15.00 © 1999 The American Physical Society 1719VOLUME 83, NUMBER 9 P H Y S I C A L R E V I E W L E T T E R S 30 AUGUST 1999the Zhao ✁✏✞ ✍✞ ✌✂ models, ✆   ✄✠☎✁✝ ✟ ✄✡☛☞✂✠✎☞ , with✌ ✑ ✒ and ✝✓✁✔✏✂ ✑ integer. Models with an inner cuspinclude [5] the models of Jaffe, Hernquist, Navarro-Frenk-White, the ✌✓✕ models of Dehnen and Tremaine et al.,and the other Zhao models.As an example of models with finite cores, weconsider the isothermal sphere. It has ✖✁✗✞ ✘✂ ✑✆✙✁✔✚✛✜✢✂✠✣☛✜ exp✁✤✗✓✛✜✢✂. Close to the black hole, wehave ✗ ✥ ✛✜✢, and ✖✁✗✞ ✘✂ ✦ ✆✙✁✔✚✛✜✢✂✠✣☛✜, a constant.Then from Eq. (1) we easily find✆✧★✩✪✁✄✂ ✑✫✆✙✬✭✚✮✯✰✄✛✜✢✱✣☛✜✮✝ ✤✫✲✳✄✱✣☛✜✞ (6)valid for ✄ ✥ ✲✴✦ ✒✵✔pc. The last factor comes fromthe capture of particles by the black hole: the densityvanishes for ✄ ✶ ✫✲✳.As an example of models with an inner cusp, weconsider a single power-law density profile, ✆✁✄✂ ✑✆✙✁✄✓✄✙✂✠☎, with✒ ✶ ✌ ✶ ✔. Its phase-space distribu-tion function is✖✁✗✞ ✘✂✑✆✙✁✔✚✷✙✂✣☛✜✸✁✍✂✸✁✍ ✤✣✜✂✷✎✙✗✎✞ (7)with ✍ ✑ ✁✹ ✤ ✌✂✓✺✔✁✔ ✤ ✌✂✻ and ✷✙✑✫✚✯✄✜✙✆✙✓✺✁✬ ✤ ✌✂ ✁✔✤ ✌✂✻. To find ✖✧✁✗✧✞ ✘✧✂, we need tosolve ✼✧✁✗✧✞ ✘✧✂ ✑ ✼✁✗✞ ✘✂ for ✗ as a function of ✗✧.In the field of a pointlike mass, we have ✼✧✁✗✧✞ ✘✧✂ ✑✔✚✺✤✘✧✟ ✯✰✓✭✤✔✗✧✻. In the field of the power-lawprofile, whose potential is proportional to ✄✜✠☎ , the actionintegral cannot be performed exactly. We have found anapproximation good to better than 8% over all of phasespace for ✒ ✶ ✌ ✶ ✔:✼✁✗✞ ✘✂✑✔✚✽✾✤✘✿✟❀✔✄✜✙✷✙✮✗✷✙✱❁❂❃❄❅❄❂❃❆❇✞ (8)where ✿✑ ✺✔✓✁✫ ✤ ✌✂✻✡☛❈✜✠☎❉✺✁✔✤ ✌✂✓✁✫ ✤ ✌✂✻✡☛✜ and✽✑✚✁✔✤ ✌✂✓❊✁✡✜✠☎✞✣✜✂. Expressing ✗ as a functionof ✗✧ and integrating Eq. (1), we obtain✆✧✁✄✂✑✆❋●☎✁✄✂✮✲✩❍✄✱☎■❏✞ (9)with ✆❋✑✆✙✁✲✩❍✓✄✙✂✠☎, ✌✩❍✑✁❑ ✤✔✌✂✓✁✫ ✤ ✌✂, and✲✩❍✑✏☎✄✙✁✰✓✆✙✄✣✙✂✡☛❈✣✠☎❉. For ✒ ▲ ✌ ▲ ✔, the den-sity slope in the spike, ✌✩❍, varies only between 2.25and 2.5.While the exponent ✌✩❍can also be obtained by scalingarguments [4], the normalization ✏☎and the factor ●☎✁✄✂accounting for capture must be obtained numerically. Wefind that ●☎✁✄✂✦✁✝ ✤ ✫✲✳✓✄✂✣ over our range of ✌, andthat ✏☎✦ ✒✵✔❑✬✌▼☛◆ for ✌✥✝, and is ✏☎✑ ✒✵✒✒❖ ✬✬,0.120, 0.140, 0.142, 0.135, 0.122, 0.103, 0.0818, 0.0177at ✌✑ ✒✵✒P✞✒✵✔✞✒✵✫✞ ✵ ✵ ✵ ✞ ✝✵✫✞✔. The density falls rapidlyto zero at ✄ ◗ ❑✵PP✲✳, vanishing for ✄ ✶ ✫✲✳.Annihilations in the inner regions of the spike set amaximal dark matter density ✆❘✪❙❚✑❯✓✛❱❲❳❨, where❲❳❨is the age of the black hole, conservatively ✝✒✡✙ yr,❯ is the mass of the dark matter particle, and ✛❱ is itsannihilation cross section times relative velocity (noticethat for nonrelativistic particles ✛❱ is independent of ❱).Using ❩✆✓❩❲ ✑ ✤✛❱✆✜✓❯, the final spike profile is✆✩❍✁✄✂ ✑✆✧✁✄✂✆❘✪❙❚✆✧✁✄✂ ✟ ✆❘✪❙❚✞ (10)which has a core of radius ✲❘✪❙❚✑ ✲✩❍✁✆❋✓✆❘✪❙❚✂✡☛☎■❏. Inthe particle models we consider, not more than the initialamount of dark matter within 300 pc is annihilated.Examples of spike density profiles are shown in Fig. 1.To conclude this section, we derive a conservativeestimate of the dark matter density near the galactic center.Assume that the halo density is constant on concentricellipsoids. Then the halo contribution ❱❬✁✄✂ to the rotationspeed at distance ✄ fixes the halo mass within ✄ . Assumefurther that the halo density decreases monotonically withdistance. Since at large radii it decreases at least as fast as✄✠✜, and at small radii only as ✄✠☎ with ✌ ✶ ✔, the densityprofile becomes steeper with distance. So to continuethe ✄✠☎ dependence to all radii keeping the same halomass interior to ✄ as given by the rotation speed, we mustdecrease the density normalization. In this way we obtainan underestimate of the density near the center. Letting✆❭✑✆✙✁❪✓✄✙✂✠☎, we have✆❭✝ ✤ ✌✓✬ ✬❱✜❬✁❪✂✫✚✯❪✜✦ ✒✵✒✒✹✔✰❫❴❵✣✦ ✒✵✔✫GeVcm✣✞(11)where we have taken ❱❬✁❪✂✑❑✒km s✠✡ at the Sundistance ❪ ✑ ❛✵P kpc, as obtained after subtracting a(somewhat overestimated) luminous matter contribution of180 km s✠✡ to the circular speed of ✔✔✒ ❜ ✔✒ km s✠✡ [6].Signals from neutralino annihilations.—Our analysisapplies in general to a self-annihilating dark matterparticle. To make it concrete, we examine a case ofsupersymmetric dark matter, the lightest neutralino. Theminimal supersymmetric standard model privides a well-defined calculational framework but contains at least 106yet-unmeasured parameters [7]. Most of them controldetails of the squark and slepton sectors and can safelyFIG. 1. Examples of spike density profiles.1720VOLUME 83, NUMBER 9 P H Y S I C A L R E V I E W L E T T E R S 30 AUGUST 1999be disregarded in dark matter studies. So we restrictthe number of parameters to 7, following Bergström andGondolo [8]. Out of the database of points in parameterspace built in Refs. [8–10], we use the 35 121 pointsin which the neutralino is a good cold dark mattercandidate, in the sense that its relic density satisfies☎ ☎✁✂ ☛ ✄✘✑✆☛ ✝. The upper limit comes from theage of the Universe, the lower one from requiring thatneutralinos are a major fraction of galactic dark halos.Gravitational interactions bring the cold neutralinosinto our galactic halo and into the central spike, whereneutralino pairs can annihilate and produce photons,electrons, positrons, protons, antiprotons, and neutrinos.While most products are subject to absorption and/ordiffusion, the neutrinos escape the spike and propagate tous undisturbed. We focus on the neutrinos and postponethe study of other signals.The expected neutrino flux from neutralino annihila-tions in the direction of the galactic center can be dividedinto two components: emission from the halo along theline of sight and emission from the central spike,✙✗✞✟✠✒✚✛☞✗✌✡✍✎ ✙✕✚✛✌✍✏ ✙✡✓☞✔✞✍  (12)The halo flux from neutralino annihilations between usand the galactic center can be estimated assuming that asingle power-law profile ✖✜✢✣ ✎ ✖✤✜✢✥✦✣✧★ extends outto the Sun position ✢ ✎ ✦. The integrated neutrino fluxwithin an angle ✩ of the galactic center is✙✕✚✛✌✍✎✖✆✤✪✍✫✬✦✄✜✩✣✭✆✮ (13)where✭is the neutralino mass, ✪✍is the number ofneutrinos produced per annihilation, either differentialor integrated in energy, ✫✬ is the neutralino-neutralinoannihilation cross section times relative velocity, and✄✜✩✣ ✎✩✆✁✜✝ ✯ ✁✰✣✯✁★✧✱✲✆✩✳✧✆★✜✴ ✯ ✁✰✣ ✜✝ ✯ ✁✰✣✯✩✳✧✆★min✴ ✯ ✁✰ (14)Here ✩ is in radians and ✩min ✎ max✵✝☎✶✷✥✦✮✜✁✰✥✴✣✱✲✸✳✧✆★✹✜✖✤✥✖✺✌✒✞✣✱✲★✻.We evaluate the neutrino yield ✪✍and the neutralinoannihilation cross sections ✫ using the DARKSUSY pack-age [11], which incorporates Pythia simulations of the✼ continuum [12] and the annihilation cross sections in[9,13].To the halo flux we need to add the contribution fromthe spike around the black hole at the galactic center. Foran isothermal distribution we find✙✡✓☞✔✞✍✎✖✆✤✪✍✫✬✦✭✆✽✶✾✦✿✳ln✽✶✾✁✂✶✷✿✮(15)the factor of 25 serving to match the exact integration.This flux is a factor of ❀✝☎✧❁ smaller than the fluxfrom dark matter annihilations between us and the galacticcenter, and so the addition of the spike does not modifythe signal. The same conclusion is reached in general forhalo models with finite cores.FIG. 2. Enhancement of annihilation signals from the galacticcenter.A strong enhancement results instead for power-lawprofiles. We find✙✡✓☞✔✞✍✎✖✆✤✪✍✫✬✦✭✆✽✶✡✓✦✿✳✧✆★✽✶✡✓✶☞✗✿✆★❂❃✧✳✮(16)where ✶✡✓is given after Eq. (9) with ✖❄replaced by✖✤and ✢❄by ✦. We fix ✶☞✗so as to match theintegration of the numerically calculated density profileincluding capture and annihilation: we find that ✶☞✗✎✝ ✂✵✜✁☎✶✷✣✆✏ ✶✆✺✌✒✞✻✱✲✆ gives a good approximation tothe flux (within 6% for our values of ✰).Contrary to the case of finite cores, for cusped halosthere is a huge increase in flux from the galactic centerwhen the spike is included, typically 5 orders of magni-tude or more, unless the inner halo slope ✰ is very smallFIG. 3. For a Moore et al. halo profile, flux of neutrino-induced muons in a neutrino telescope from neutralino darkmatter annihilations in the direction of the galactic center, with(upper panel) and without (lower panel) the central spike. Thehorizontal line is the current upper limit.1721VOLUME 83, NUMBER 9 P H Y S I C A L R E V I E W L E T T E R S 30 AUGUST 1999FIG. 4. Maximum inner slope ✌ of the dark matter halocompatible with the upper limit on the neutrino emission fromthe galactic center. (a) Current limit at 1 GeV; (b) future reachat 25 GeV.(see Fig. 2, where ✛ ✁ ✆ ✂✄). The enhancement is no-table, for example, for the profile of Moore et al. whichhas ☎ ✁ ✆ ✝ (see Fig. 3): including the spike around theblack hole dramatically changes the prospects of observ-ing a neutrino flux.The neutrino flux from the spike increases with theinner halo slope ☎. Imposing that it does not exceedthe observed upper limit of ✞✟ ✠✆✡☛ muons (☞✆GeV)km✍✎ yr✍✏ [14] leads to an upper bound on ☎. There isa separate upper bound for each model. They are plottedin Fig. 4a. (Plotted values of ☎max ☞ ✟ are unphysicalextrapolations but are shown for completeness.) Presentbounds are of the order of☎max ✞ ✆ ✂.Future neutrino telescopes situated in the NorthernHemisphere may improve on this bound or find a signal.FIG. 5. Maximal flux of neutrino-induced muons in a neutrinotelescope from neutralino annihilations at the galactic center,after imposing the current constraints on the neutrino emission.For example, with a muon energy threshold of 25 GeV,the neutrino flux from the spike after imposing the currentconstraints could still be over 3 orders of magnitudeabove the atmospheric background (Fig. 5), allowing toprobe☎as low as 0.05 (Fig. 4b).In conclusion, we have shown that if the galactic darkhalo is cusped, as favored in recent ✑-body simulations ofGalaxy formation, a bright dark matter spike would formaround the black hole at the galactic center. A search ofa neutrino signal from the spike could either set upperbounds on the density slope of the inner halo or clarifythe nature of dark matter.This research has been supported in part by grants fromNASA and DOE.*Email address: gondolo@mppmu.mpg.de†Email address: silk@astro.ox.ac.uk[1] A. M. Ghez, B. L. Klein, M. Morris, and E. E. Becklin,Astrophys. J. 509, 678 (1998).[2] A. Eckart and R. Genzel, Nature (London) 383, 415(1996); Mon. Not. R. Astron. Soc. 284, 576 (1997).[3] J. F. Navarro, C. Frenk, and S. White, Astrophys. J. 462,563 (1996); A. V. Kravtsov, A. A. Klypin, and A. M.Khokhlov, Astrophys. J. Suppl. 111, 73 (1997); B. Mooreet al., Astrophys. J. Lett. 499, 5 (1998).[4] G. D. Quinlan, L. Hernquist, and S. Sigurdsson, Astro-phys. J. 440, 554 (1995).[5] See references in [4] and in J. Binney and S. Tremaine,Galactic Dynamics (Princeton University Press, Princeton,NJ, 1987); J. F. Navarro, C. Frenk, and S. White, in [3];N. W. Evans, Mon. Not. R. Astron. Soc. 267, 333 (1994);H. S. Zhao, Mon. Not. R. Astron. Soc. 278, 488 (1996).[6] W. Dehnen and J. Binney, Mon. Not. R. Astron. Soc. 294,429 (1998), and references therein.[7] S. Dimopoulos and D. Sutter, Nucl. Phys. B465, 23(1995).[8] L. Bergström and P. Gondolo, Astropart. Phys. 5, 183(1996).[9] J. Edsjö and P. Gondolo, Phys. Rev. D 56, 1879 (1997).[10] L. Bergström, P. Ullio, and J. H. Buckley, Astropart. Phys.9, 137 (1998).[11] P. Gondolo et al. (unpublished).[12] L. Bergström, J. Edsjö, P. Gondolo, and P. Ullio, Phys.Rev. D 59, 043506 (1999).[13] L. Bergström and P. Ullio, Nucl. Phys. B504, 27 (1997);Z. Bern, P. Gondolo, and M. Perelstein, Phys. Lett. B 411,86 (1997); P. Ullio and L. Bergström, Phys. Rev. D 57,1962 (1998).[14] R. Svoboda et al., Astrophys. J. 315, 420 (1987);Y. Oyama et al., Phys. Rev. D 39, 1481 (1989);H. Adarkar et al., Astrophys. J. 380, 235 (1991); K. Naka-mura, in Proceedings of the 3rd NESTOR InternationalWorkshop, Pylos, Greece, 1993, edited by L. K. Resvanis(University Press, Athens, 1993).1722

Dark matter annihilation at the galactic center

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Dark matter annihilation at the galactic center

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