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    Indirect Detection of Dark Matter with raysStefan Funk

    Kavli Institute for Particle Astrophysics and Cosmology, Stanford University & SLAC National Accelerator Center

    Submitted to Proceedings of the National Academy of Sciences of the United States of America

    The details of what constitutes the majority of the mass that makesup dark matter in the Universe remains one of the prime puzzles ofcosmology and particle physics today - eighty years after the firstobservational indications. Today, it is widely accepted that darkmatter exists and that it is very likely composed of elementary par-ticles that are weakly interacting and massive (WIMPs for WeaklyInteracting Massive Particles). As important as dark matter is in ourunderstanding of cosmology, the detection of these particles has sofar been elusive. Their primary properties such as mass and inter-action cross sections are still unknown. Indirect detection searchesfor the products of WIMP annihilation or decay. This isq generallydone through observations of gamma-ray photons or cosmic rays.Instruments such as the Fermi-LAT, H.E.S.S., MAGIC and VERI-TAS, combined with the future Cherenkov Telescope Array (CTA)will provide important complementarity to other search techniques.Given the expected sensitivities of all search techniques, we are at astage where the WIMP scenario is facing stringent tests and it canbe expected that WIMPs will be either be detected or the scenariowill be so severely constrained that it will have to be re-thought. Inthis sense we are on the Threshold of Discovery. In this article, Iwill give a general overview over the current status and the futureexpectations for indirect searches for dark matter (WIMP) particles.

    Gamma rays | Dark Matter | Cosmology

    There is a broad consensus that dark matter is made up ofelementary particles. The most promising candidates areweakly interacting massive particles (WIMPs), particularly ifthey also form the lightest supersymmetric particle. The gen-eral assumption is that the thermal freeze-out in the earlyUniverse leaves a relic density of dark matter particles in thecurrent Universe (after the freeze-out the particles become toodiluted to annihilate in appreciable numbers and thermal en-ergies were too low to produce them. The co-moving densityis therefore roughly constant since then). The annihilationof these particles into standard-model particles controls theabundance in the Universe, there is thus a tight connectionbetween the annihilation cross section and cosmologically rel-evant quantities. For particles annihilating (in the simplestcase, i.e. annihilating through S waves [1]) the relic densityonly depends on the annihilation cross section ann weightedby the average velocity of the particle (see e.g.[2]):

    h2 = 0.11

    3 1026cm3s1

    < annv >

    As the value for the relic dark matter density from CMBobservations is h

    2 = 0.113 0.004 [3], it follows that theexpected velocity-weighted annihilation cross-section is in therange of 3 1026cm3s1. This represents a striking con-nection that for typical gauge couplings to ordinary standardmodel particles and a dark matter mass at the weak interac-tion scale WIMPs have the right relic density (using standardearly Universe conditions) to match those of the cosmolog-ically measured dark matter particles. In other words, thevalue for < Annv > corresponds to a cross section of approx-imately 1 pb, i.e. a typical weak interaction cross section.This is the so-called WIMP miracle in which particles thatare motivated by a microphysical puzzle (or better a gaugehierarchy problem) are excellent dark matter candidates. Ob-viously, this connection could be merely a coincidence but iftrue, then naturally, WIMP masses would be expected in the

    range of 10 GeV and a few TeV which is why a lot of at-tention has been devoted to exploring that mass range in thedark matter parameter space.

    Given the tight connection between the amount of WIMPdark matter in the current Universe and the annihila-tion cross-section it is natural to expect dark matter self-annihilations. To be able to self-annihilate the dark matterparticle much either be a Majorana particle or a Dirac parti-cle with no matter-antimatter asymmetry. In the annihilation(or decay) of the dark matter particles all kinds of standardmodel particles are created (quarks, bosons, leptons) and thenproduce either gamma rays or cosmic rays. In particular re-gions in the Universe with high dark matter densities (suchas the centers of galaxies, and clusters of galaxies) have en-hanced probabilities that dark matter particles encounter eachother and annihilate. With an appropriate assumption aboutthe density distribution of dark matter (e.g. from numericalsimulations) one can predict the expected annihilation signalwhen assuming a certain annihilation cross section or put lim-its on the latter in the absence of a signal.

    A more quantitative description of the expected flux ofparticles from dark matter annihilation can be drawn fromthe following relation:



    < annv >2m2WIMP




    Particle Physics



    2r(l, )dl(r, )

    Astrophysics orJ(E)

    The left-hand side contains the (measureable) gamma rayflux. The right-hand side contains two components (1) a parti-cle physics term which is given by the velocity-averaged anni-hilation cross-section (< annv >), the mass of the dark mat-ter particle (m) and the sum over the gamma-ray yields for acertain annihilation channel into channel f (dNf/dE) multi-plied by the branching ratio into that channel (Bf ), and (2)an astrophysics term J(E) (called the J-factor) given by theline-of-sight integral of the square of the dark matter density. Given that both the particle physics and the astrophysicsterm are unknown, one needs to make an assumption aboutone in order to put constraints on the other when measuringa gamma-ray flux (or an upper limit). This in turn alreadypoints to one of the major challenges in the indirect detectionof dark matter: the astrophysical uncertainties, both in thedensity profile of dark matter (which enters quadratically) andin the suppression of the astrophysical foregrounds (which af-fect the sensitivity or the minimal gamma-ray flux that can be

    Reserved for Publication Footnotes PNAS Issue Date Volume Issue Number 19

  • detected). In order to derive meaningful dark matter limits,the astrophysical foregrounds have to be understood and sub-tracted. For excellent general recent reviews on selected topicsrelated to the indirect detection of dark matter, see [4, 5, 6, 7].

    While most recent studies to detect the secondary prod-ucts of dark matter annihilations have focussed on gammarays, annihilations into cosmic rays can also be used. Giventhe large flux of cosmic rays accelerated directly in astrophys-ical sources (primary cosmic rays) and produced in the in-teraction of cosmic rays with interstellar material (secondarycosmic rays) it is beneficial to use particles that are less-frequently produced in these settings. The most commonlyused are antimatter particles, in particular anti-deuterons,anti-protons and positrons, which are not so copiously pro-duced in astrophysics accelerators. These can provide impor-tant clues towards the dark matter puzzle as e.g. seen in therise in the positron fraction recently observed by PAMELA [8]and confirmed by the Fermi-LAT and AMS [9, 10]. However,I will mention them in this article only in passing and willfocus on gamma-ray observations.

    Gamma rays can be produced by dark matter anni-hilations in two major ways: (a) continuum signals fromannihilation into other particles which eventually producesgamma rays either through pion production, or final statebremsstrahlung and inverse Compton from leptonic channelsand (b) line signals from dark matter annihilating directlyto X, where X usually is another neutral state, typically ray or Z or a Higgs boson. Given that dark matter parti-cles are essentially at rest (for cold dark matter), the pho-tons will emerge back-to-back with an energy directly relatedto the rest mass of the dark matter particle E = m orE = m(1mX/4M

    2). While the line signal can provide a

    smoking gun signal for dark matter annihilation, its flux istypically loop suppressed by a factor of 2e where e is the finestructure constant (the electrically neutral dark matter parti-cle does not couple directly to photons but has to go througha charged particle loop) . The signal is therefore expected tobe much smaller than the continuum flux. This continuumsignal has a smooth energy distribution with an exponentialcutoff at the mass of the dark matter particle E = m. Thespectral shape is universal in the sense that it takes a similarform for almost any channel and depends somewhat weakly onm. The exact annihilation channel depends on the proper-ties of the WIMP but is typically (for bino-like WIMPs) dom-inated by annihilation into bb pairs with pair production into -leptons also contributing. For more massive WIMPs witha wino or higgsino component annihilation will proceed intomassive gauge bosons. Annihilations that have a large branch-ing fraction into e+e pairs will enhance the gamma-ray signalthrough inverse Compton scattering these on starlight or theCMB (see e.g. [11, 12]).

    Gamma rays have several unique properties which makethem ideally suited to study dark matter annihilations. Pri-marily, they do not get deflected in intervening magnetic fieldsand thus point back at the site at which they are created.This allows one to search for gamma ray signatures not onlyin our vicinity in the Galaxy but also in distant objects s