Indirect Evidence For Light WIMPs

Dan Hooper Fermilab/University of Chicago

UCLA Dark Matter 2012 Symposium February 23, 2012

Dark Matter In The Galactic Center Region With Fermi § The region surrounding the Galactic Center is complex; backgrounds present are not necessarily well understood

§ This does not, however, necessarily make searches for dark matter in this region intractable

§ The signal from dark matter annihilation is large in most benchmark models (for a typical 10 GeV WIMP, comparable to total flux observed in inner 1°)

§ To separate dark matter annihilation products from backgrounds, we must focus on the distinct observational features of these components

Dark Matter In The Galactic Center Region With Fermi

The characteristics of a signal from dark matter annihilations:

1) Distinctive “bump-like” spectral feature

2) Signal highly concentrated around the Galactic Center (but not entirely point-like); precise morphology determined by dark matter distributution

The Distribution of Dark Matter in the Inner Milky Way

§ Dark matter only simulations (Via Lactea, etc.) yield halos which possess -γ inner profiles of ρ α r where γ=1.0 to 1.2 § The inner volume (~10 kpc) of the Milky Way is dominated by baryons, not dark matter – significant departures from dark matter only results should be 10 expected 2.0 0.5 v0230 km s, R08.0 kpc v0230 km s, R08.0 kpc § For years, an active debate has taken place NFW , rs 20 kpc model5 Einasto, rs20 kpc in the literature over the question of how the ⇤ 0.4 ⇤ baryons alter the profiles of dark matter halos 1.5

0.3

§ Existing microlensing and dynamical data γ ⇥ 1.0 ⇥ are not capable of determining the inner 0.2 slope, although γ~1.3 provides the best fit 0.5

0.1 model5 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 3 3 ⇤0 GeV cm ⇤0 GeV cm

FIG. 5: ConstraintsIocco, onPato, the Dark Bertone, Matter distribution Jetzer, parameters ⇥0 and for a generalised NFW (left) and an Einasto (right) profile using the baryonic model 5. The⇤ thick⇥ dot-dashed curve is the 2⇤ constraint already ⇤ shown⇥ in Figure 3, while the contours showarXiv:1107.5810 the parameter space producing a good fit to the rotation curve (⌅2 =2.30, 6.18) with the best-fit configuration indicated by the cross. The shadowed rectangle encompasses the ranges of profile slopes found in numerical simulations and the

values of ⇥0 found in the recent literature (see Section II), while the red filled circle in the left frame marks the parameter set 3 (⇥0 =0.4GeV/cm, =1.0) used to produce Figure 2. The empty up-triangle, circle and down-triangle in the left frame show the local density and shape of the DM profile upon adiabatic contraction of the initial profile indicated by the corresponding filled symbols. The adiabatic contraction was applied using model 5 to fix the baryonic distribution Mb(

5 for the baryonic component, we have contracted the VI. CONCLUSIONS initial profiles indicated in Figure 5 (left) by the filled up-triangle, circle and down-triangle with f = M (< b b We have studied the constraints that microlensing and 200 kpc)/M (< 200 kpc) = 5.2%, 4.0%, 3.0%, respec- tot dynamical observations can set on the distribution of tively. The final DM profile turns out to be well fitted by Dark Matter in the Galaxy, keeping into account all a generalised NFW function with parameters marked by experimental uncertainties. Starting from state-of-the- the empty symbols in the same Figure (the contracted art models for the galactic baryonic component, we have profile corresponding to the filled circle is indicated by rescaled them to match the observed microlensing optical the red long-dashed line in the bottom right frame of depth towards the galactic bulge, and compared the re- Figure 2). In particular, we find enhanced local DM den- sulting rotation curve with the one inferred from terminal sities and slopes 1.6 1.7, which are slightly above velocities of gas clouds and other kinematical probes. the value =1.5⇥ found elsewhere [73] (see also refer- ences therein) but note that we are using the original This allowed us to revisit the compatibility of di⇥erent adiabatic contraction model [57] and not one of its refine- observational probes with the results that emerge from ments [58, 59]. Although our analysis cannot rule out the numerical simulation in CDM cosmologies. We have presence of adiabatically compressed profiles since they followed two di⇥erent approaches. In the first one, we depend on the initial total mass distribution and on the have set conservative upper limits on the Dark Matter specific baryonic model adopted, it definitely allows us to local density and profile shape towards the centre of the claim that if the present-day DM profile is steeply rising Galaxy, working with generalised NFW and Einasto pro- towards the centre, then the local DM density must be files. The fiducial parameters usually adopted in the lit- small. For the specific case of =1.5(1.7) we find an erature for both profiles have been found to be safely 3 1⇤ range ⇥0 0.25 0.35 (0.22 0.30) GeV/cm . Some within the allowed regions set by our analysis, contrary of the extreme⇥ models discussed in the literature, e.g. in to earlier claims of inconsistency between observations the context of indirect DM searches [73, 74], are therefore and cuspy Dark Matter profiles. found to be ruled out by a combination of microlensing In our second approach, we focussed on the only bary- and dynamical observations. onic model among those discussed here that also contains The Distribution of Dark Matter in the Inner Milky Way

§ Recently, state-of-the-art hydrodynamical simulations carried out by several

different groups, running different codes, have begun to converge in favor of a moderate degree of contraction in Milky Way-like halos, typically steepening the inner slope γ from ~1.0 to ~1.2-1.5

6 § Such simulations includeGNEDIN rapid ET AL. supernova winds, cold accretion, galactic bars, 6 inspiraling of dense baryonicGNEDIN ET clumps AL. by dynamical friction, etc., but consistently find that baryonic contraction dominates over these effects HALO CONTRACTION EFFECT 7

bar-ad bar-sf

bar-sf bar-ad bar-sfbar-ad bar-sf bar-sf dm-sf bar-ad bar-ad dm-sf

dm-sf

dm-sf dm-ad dm-ad dm-sf 1 0.3 0.5 dm-ad dm-ad dm-ad

FIG.3.—Contractionofthedarkmatterprofileinasimulatedgroup of FIG.4.—Contractionofthedarkmatterprofileinasimulatedgalaxy at galaxies at z =0,fromNagai(2006).Solidlinesshowtheencloseddark z =0,fromGottloeberetal.(2010).LinenotationisthesameasinFigure3. matter mass profile, in the non-radiative (ad) run and star formation (sf) run. Black solid line is the best-fit MAC model with A0 =1.79, w =1.2. Dashed Dotted lines show the corresponding baryon mass profiles. Black solid line line in top panel shows the MAC model prediction with fixed A =1.6, and FIG.3.—ContractionofthedarkmatterprofileinasimulatedgroD. Nagai (2006) up of FIG.4.—Contractionofthedarkmatterprofileinasimulatedgal0 axy at FIG.6.—Best-fittingparametersoftheoriginalMACmodel(Equation 3) galaxiesis the at bestz =0,fromNagai(2006).Solidlinesshowtheencloseddark fit of the MAC model, with parameters A0 =1.61, w =0.86. Top z =0,fromGottloeberetal.(2010).Linenotationisthesameabest-fitting w =1.07. sinFigure3. for all simulations discussed in this paper. Asterisk marks the fiducial param- panel shows the mass residuals for the MAC model with freely adjustable A matter mass profile, in the non-radiative (ad) run and star formation (sf) run. 0 Black solid line is the best-fit MAC model with A0 =1.79, w =1.2. Dashed eters of the MAC model in Gnedin et al. (2004). Solid lines showtherelation (solid)andtheMACmodelwithfixedA =1.6(dashed). In this plot the two Gottloeber et al. (2010) Dotted lines show the corresponding baryon0 mass profiles. Black solid line line in top panel shows the MAC model prediction with fixed A0 =1.6, and FIG.5.—Contractionofthedarkmatterprofileinasimulatedgalaxy at between A and w that gives the same amount of contraction (enhancement lines almost coincide. 5 is the best fit of the MAC model, with parameters A0 =1.61, w =0.86. Top best-fittingresolutionw =1. halos07. the particle mass is 3.5 × 10 M!.Thevirialz =3,fromLevineetal.(2008).LinenotationisthesameasinFigure 3. of dark matter mass) at r =0.005rvir,forthebaryonprofilewithν =2nor- panel shows the mass residuals for the MAC model with freely adjustable A0 11 Black solid line is the best-fit MAC model with A =1.32, w =1.26. Vertical malized to equal the initial dark matter mass at re =0.05r .Thetopline (Gnedin, et al. arXiv:1108.5736)masses of the three halos at z =0are(3− 8) × 10 M!.The 0 vir (solid)andtheMACmodelwithfixedA0 =1.6(dashed). In this plot the two bars onLevine the MAC model in theet top panelal. indicate (2008) the Poisson unc ertainty of gives the same amount of contraction as the SAC model. The other two lines linesKravtsov, almost coincide. Klypin, & Hoffman 2002). The simulations have inner truncation radius is set by the condition5 that the local ∆ resolution halos the particle mass is 3.5 × 10 M!.Thevirialthe mass profile derived in the simulation. Dashed line in top panel shows the correspond to 50% and 30% of that amount. apeakspatialresolution =3.5kpcanddarkmatterparticle two-body relaxation time exceeds the age of the11 universe.MAC model prediction with fixed A0 =1.6, and best-fitting w =1.26. 8 masses of the three halos at z =0are(3− 8) × 10 M!.The mass of 3.9 × 10 M!.Thevirialmassofthesystemsranges Figure 4 shows the profile of the most massive of the three Kravtsov, Klypin, & Hoffman 2002). The simulations have 13 14 innergalaxies. truncation The radius dark matter is set by mass the is condition enhanced that by the an order local of apeakspatialresolutionfrom 2 × 10 M! to∆ 4 ×=310.5kpcanddarkmatterparticleM!.Starformationisimple- two-body relaxation time exceeds the age of the universe. mented using8 the standard Kennicutt’s law and is allowed to magnitude at the innermost radius. The MAC model with pa- mass of 3.9 × 10 M!.Thevirialmassofthesystemsranges Figure 4 shows the profile of the most massive of the three 4 rameters (A0 =1.79, w =1.2) predicts the dark matter profile 6 proceed in13 regions with temperature14 T < 10 Kandgasden- galaxies. The dark matter mass is enhanced by an order of1.3 × 10 M! and the peak force resolution at z =3is0.064 from 2 × 10 M! to−3 4 × 10 M!.Starformationisimple-∆ to better than 4% accuracy in any bin, with the rms deviation mentedsity n usingg > 0 the.1cm standard.Wetruncatetheinnerprofilesat4 Kennicutt’s law and is allowed to to magnitude at the innermost radius. The MAC model with pa-kpc for the gas and 0.1 kpc for the dark matter, a very small ensure that the gravitational dynamics is calculated correctly of only 1.4%. proceed in regions with temperature T < 104 Kandgasden- rametersWe ( considerA0 =1.79, alsow =1 the.2) simulations predicts the of dark a Milky matter Way-sized profilescale for cosmologicalsimulations. We truncate the inner pro- in the studied− region.3 ∆ to better than 4% accuracy in any bin, with the rms deviationfile such that the innermost bin contains at least 200 dark mat- sity nFigureg > 0.1cm 3 shows.Wetruncatetheinnerprofilesat4 the mass profiles for one of the groups.to The galaxy and a dwarf galaxy at z =1byCeverino&Klypin ensure that the gravitational dynamics is calculated correctly of only(2009). 1.4%. These simulations are run with the ART code withter particles. dark matter mass is significantly enhanced in the star forma- We consider also the simulations of a Milky Way-sized Figure 5 shows that the MAC model is able to describe even in thetion studied run relative region. to the non-radiative run, by a factor of 4 at averydifferentprescriptionforstellarfeedbackthaninNagai galaxy and a dwarf galaxy at z =1byCeverino&Klypin11 this case, with the rms deviation of 10%. This case is extreme Figurethe innermost 3 showsthe resolved mass profiles radius. for The one baryons of thegroups. strongly The domi- (2006). The large galaxy mass is 8 × 10 M!,thedwarf (2009). These simulations10 are run with the ART code withbecause the baryons dominate the dark matter by two orders darknate matter the totalmass mass is significantly at that point. enhanced The MAC in the model star forma- provides galaxy mass is 5 × 10 M!,bothatz =1.Thedarkmatter tion run relative to the non-radiative run, by a factor of 4 at averydifferentprescriptionforstellarfeedbackthaninN5 agaiof magnitude at the innermost radius, and the dark matter an excellent fit to the contracted dark matter profile, with the particle mass is 7.5×10 M! and the peak11 spatial resolution is the innermost resolved radius. The baryons strongly domi- (2006). The large galaxy mass is 8 × 10 M!,thedwarfmass is enhanced by a factor of 300 relative to the extrapo- parameters (A0 =1.61, w =0.86) close to the fiducial values. 100 comoving pc for10 the larger galaxy. For the smaller galaxy, nate the total mass at that point. The MAC model provides galaxy mass is 5 × 10 M!,bothatz =1.Thedarkmatter4 lation of the dissipationless profile. The maximum deviation of the mass profile predicted by the the dark matter particle5 mass is 9.4 × 10 M! and the peakWe also note that the stellar profile is contracted similarly an excellentMAC model fit to is the 6%, contracted and the rms dark deviation matter over profile, allbins with at th radiie particle mass is 7.5×10 M! and the peak spatial resolution is resolution is 50 comoving pc. Compared to the non-radiativeto the dark mater profile, because gas accretion is faster than 1 0.5 0.3 parametersr < 0.1r (A0 is=1 3%..61, w We=0 similarly.86) close analyzed to the fiducial the other values. eleven 100 comoving pc for the larger galaxy. For the smaller galaxy, vir runs, the dark matter mass is enhanced4 by a factor of 8star for formation. Thegroups maximum and present deviation their of thebest-fit mass parameters profile predicted in the discussi by the on thethe dark larger matter galaxy particle and mass by a factor is 9.4 of× 10 5 forM the! and smaller the peak galaxy, MACof Figuremodel is6. 6%, and the rms deviation over all bins at radii resolutionat the innermost is 50 comoving radius. pc. The Compared MAC model to the (with non-radiative parameters r < 0.1rvir is 3%. We similarly analyzed the other eleven runs, the dark matter mass is enhanced by a factor of 8 for 5. DISTRIBUTION OF MODEL PARAMETERS A0 =2.07, w =0.64 and A0 =2.92, w =0.85, respectively) pre- groups and present their4.2. best-fitIndividual parameters Galaxies in the discussion thedicts larger the galaxy darkmatter and by profile a factor to of better 5 for than the9% smaller accuracy, galaxy, withAll of the simulations considered here indicate some de- of Figure 6. at the innermost radius. The MAC model (with parameters We consider the simulation of three Milky Way-sized the rms deviation of about 2%. gree of enhancement of the dark matter profile. Not a single A0 =2.07, w =0.64 and A0 =2.92, w =0.85, respectively) pre-case indicates halo expansion rather than contraction. Fig- galaxies by the CLUES4.2. Individual project (http://www.clues-project.Galaxies org; dicts the dark matter profile to better than 9% accuracy, with Gottloeber et al. 2010; Knebe et al. 2010). The simulation is 4.3. Galaxy Center ure 6 combines the resulting constraints on the parameters A FIG.7.—Best-fittingparametersoftherevisedMACmodelwith r0 = the rms deviation of about 2%. 0.03r (Equation 4). Symbols and lines are as in Figure 6. Werun consider using the the SPH simulation code Gadget-2. of three This Milky code includes Way-sized stan- Finally, we consider the resimulation of the galaxy runand re-w of Equation (3). The models do not fill all the available vir galaxiesdard byradiative the CLUES cooling, project star (http://www.clues-project. formation, and supernovaorg; feed- ported in Gnedin et al. (2004) that zooms into the innermostparameter space, but instead concentrate in a fairly narrow re- Gottloeber et al. 2010; Knebe et al. 2010). The simulation is 4.3. Galaxy Center back. The force softening length ! =0.14 kpc. The halos were region of the galaxy at z =3(Levineetal.2008).Thissim-gion in which A and w are strongly correlated. The original model: run using the SPH code Gadget-2. This code includes stan- Finally, we consider the resimulation of the galaxy run re- selected from a large box and resimulated with the effective ulation follows the early evolution of a galaxy that becomesMAC model suggested by Gnedin et al. (2004) falls right in FM(r|A,w) dard radiative cooling, star3 formation, and supernova feed- ported in Gnedin et al. (2004) that zooms into the innermost fM ≡ (12) mass resolution of 4096 dark matter particles. In the highest- aMilkyWay-sizedobjectatz =0.TheDMparticlemassisthe middle of the new distribution. F (r|1,1) back. The force softening length ! =0.14 kpc. The halos were region of the galaxy at z =3(Levineetal.2008).Thissim- It is interesting to determine which combination of the pa- M selected from a large box and resimulated with the effective ulation follows the early evolution of a galaxy that becomesrameters A and w yields the same amount of contraction. and evaluating it at some inner radius where the linear ap- mass resolution of 40963 dark matter particles. In the highest- aMilkyWay-sizedobjectatz =0.TheDMparticlemassisGiven the radial dependence of the mass enhancement fac- proximation for the contraction factor y(r)isvalid.Wetake tor FM (Equation 7), the solution to this problem varies with r =0.005rvir,whichcorrespondstoabout1kpcfortheMilky radius. However, we can remove most of the radial depen- Way galaxy. The exact value of r affects the resulting value dence by defining the enhancement factor relative to the SAC of parameter w (for a given A)onlylogarithmically,aslongas A Simple (but effective) Approach To The Galactic Center 1) Start with raw map (smeared over 0.5° circles)

A Simple (but effective) Approach To The Galactic Center 1) Start with raw map (smeared over 0.5° circles) 2) Subtract known point sources (Fermi 2nd point source catalog)

A Simple (but effective) Approach To The Galactic Center 1) Start with raw map (smeared over 0.5° circles) 2) Subtract known point sources (Fermi 2nd point source catalog) 3) Subtract line-of-sight gas density template (empirical, good match to 21 cm)

A Simple (but effective) Approach To The Galactic Center

§ This method removes ~90% of emission in the inner galaxy (outside of the innermost few degrees) § Typical residuals are ~5% or less as bright as the inner residual – spatial variations in backgrounds are of only modest importance

Hooper and Linden, PRD, arXiv:1110.0006 A Simple (but effective) Approach To The Galactic Center

§ This method removes ~90% of emission in the inner galaxy (outside of the innermost few degrees) § Typical residuals are ~5% or less as bright as the inner residual – spatial variations in backgrounds are of only modest importance § Clearly isolates the emission associated with the inner source or sources (supermassive black hole? dark matter?), along with a subdominant component of “ridge” emission

Hooper and Linden, PRD, arXiv:1110.0006

Characteristics of the Observed Gamma ray Residual

1) The spectrum peaks between

~300 MeV and ~10 GeV

Characteristics of the Observed Gamma ray Residual

1) The spectrum peaks between

~300 MeV and ~10 GeV 2) Clear spatial extension - only a small fraction of the emission above ~300 MeV is point-like

Characteristics of the Observed Gamma ray Residual

1) The spectrum peaks between

~300 MeV and ~10 GeV 2) Clear spatial extension - only a small fraction of the emission above ~300 MeV is point-like

3) Good agreement is found between our analysis and those of other groups

How Much Of This Emission Could Be

Coming From Dark Matter?

§ If the inner profile is fairly steep (as is expected due to adiabatic contraction), the majority of the residual could originate from dark matter

§ Viable regions include mDM~7-12 GeV, annihilating (mostly) to leptons, with an annihilation cross section on the order of σv~10-26 cm3/s (uncertainties dominated by local density)

Parameter space in which the majority of

the 0.3-10 GeV emission originates from dark matter The Dark Matter Interpretation § The spectral shape of the excess can be well fit by a dark matter particle with a mass in the range of 7 to 12 GeV (similar to that required by CoGeNT, DAMA, and CRESST), annihilating primarily to +- (possibly among other leptons)

Hooper and Linden, PRD, arXiv:1110.0006

The Dark Matter Interpretation § The spectral shape of the excess can be well fit by a dark matter particle with a mass in the range of 7 to 12 GeV (similar to that required by CoGeNT, DAMA, and CRESST), annihilating primarily to +- (possibly among other leptons)

§ The angular distribution of the signal is well fit by a halo profile with (r) ~ r -, with  ~ 1.25 to 1.4 (in good agreement with expectations from simulations)

Hooper and Linden, PRD, arXiv:1110.0006

The Dark Matter Interpretation § The spectral shape of the excess can be well fit by a dark matter particle with a mass in the range of 7 to 12 GeV (similar to that required by CoGeNT, DAMA, and CRESST), annihilating primarily to +- (possibly among other leptons)

§ The angular distribution of the signal is well fit by a halo profile with (r) ~ r -, with  ~ 1.25 to 1.4 (in good agreement with expectations from simulations)

§ The normalization of the signal requires the dark matter to have an annihilation cross section within a factor of a few of the value predicted for a simple thermal relic (v ~ 3x10-26 cm3/s)

Hooper and Linden, PRD, arXiv:1110.0006

Astrophysical Interpretations? Unresolved Point Sources?

Perhaps a population of several/many unresolved points sources distributed throughout the inner tens of parsecs of the Milky Way could produce the observed signal - millisecond pulsars, for example

Astrophysical Interpretations? Unresolved Point Sources?

Perhaps a population of several/many unresolved points sources distributed throughout the inner tens of parsecs of the Milky Way could produce the observed signal - millisecond pulsars, for example

-Much has been made of the qualitative similarity with the spectra of gamma ray pulsars, but in actuality very few of the pulsars observed by Fermi are compatible (the average spectrum is clearly incompatible); perhaps a somewhat different population or class of pulsars could be responsible?

-Why is the signal so concentrated (why so many in the inner 20 pc, and so few at 100 pc?); the signal (F α r -2.5) is much more steeply cusped than the -1.25 observed stellar distribution (nstar α r )

-With typical pulsar kicks of 250-500 km/s, millisecond pulsars should escape the inner region of the galaxy, and be distributed no more steeply than r -2 (assuming that none are created outside of the inner tens of parsecs) Abazajian, JCAP, arXiv:1011.4275, Hooper, Goodenough PLB 2010,

Hooper, Linden PRD 2011

Astrophysical Interpretations? Pion Decay Gamma Rays From Cosmic Rays Accelerated by the Supermassive Black Hole?

§ The observed emission (above ~300 MeV) is spatially extended, and does not originate directly from the SMBH

§ But protons accelerated by or nearby the SMBH could propagate outward, leading to an extended gamma ray signal (Chernyakova et al., Ap. J, 2011)

§ The spectrum of the extended emission, however, rises very rapidly between 100 MeV and 1 GeV; Much more so than the spectrum from proton collisions (for any proton spectrum)

§ This is not what pion decay gamma rays should look like

Note: If only photons above 1 GeV are studied, much of this emission could be interpreted as pion decay gammas – sub-GeV emission is essential to distinguish between CR-gas and DM origins Boyarsky et al., arXiv:1012.5839

Other Signatures of Light WIMP Annihilation in the Inner Milky Way?

If dark matter annihilations are generating the gamma ray emission observed from the Galactic Center, where else in the sky, and in what other channels, might signals of this appear?

Other Signatures of Light WIMP Annihilation in the Inner Milky Way?

§ For years, it has been argued that the WMAP data contains an excess of synchrotron emission from the inner ~20 around the Galactic Center, and that this cannot be explained by known astrophysical mechanisms – now “unambiguously” confirmed by Planck (expect a paper soon)

§ Previous studies have shown that this emission WMAP (22 GHz) could be accounted for electrons produced in dark matter annihilations

Planck (30 and 44 GHz) Finkbeiner, astro-ph/0409027; Hooper, Finkbeiner, Dobler, PRD (2007); Dobler, Finkbeiner, ApJ (2008)

Dark Matter Annihilations and the Synchrotron Haze

§ Using the halo profile, mass, annihilation cross section and annihilation channels determined by the Fermi GC data, we proceed to calculate the corresponding synchrotron spectrum and distribution

§ Set B-field model to obtain the spectrum and angular profile observed by WMAP (almost no additional freedom) § The resulting synchrotron intensity is forced to be very close to that observed

A dark matter interpretation of the Galactic Center gamma rays

(almost) automatically generates Annihilations to e+e-, +-, +- the WMAP Haze B~10 G in haze region

D. Hooper and Tim Linden, arXiv:1011.4520

Non-Thermal Radio Filaments

§ Radio filaments are long (~40 pc) and thin (~1 pc) structures with extremely hard and polarized radio spectra, located 10-200 pc from the Galactic Center

§ Observations imply very strong (~100 µG) and highly ordered magnetic fields

§ It has been a long-standing challenge to explain the synchrotron spectra from these objects

Linden, Hooper, and Yusef-Zadeh, arXiv:1106.5493

Non-Thermal Radio Filaments

§ Radio filaments are long (~40 pc) and thin (~1 pc) structures with extremely hard and polarized radio spectra, located 10-200 pc from the Galactic Center

§ Observations imply very strong (~100 µG) and highly ordered magnetic fields

§ It has been a long-standing1988A&A...200L...9L challenge to ex p explain the synchrotron spectra from these obj objects

§ Since the late 1980’s, observations and modeling of NRFs has found that they must contain a nearly mono-energetic spectrum of electrons, with an energy of ~10 GeV

§ The highly ordered magnetic fields of these objects effectively confine the electrons they contain, and act as a magnetic mirror, preventing external electrons from entering (the ~10 GeV electrons responsible for the observed synchrotron emission must be produced within the volume of the filaments)

Linden, Hooper, and Yusef-Zadeh, arXiv:1106.5493

Non-Thermal Radio Filaments

§ The roughly mono-energetic spectrum of electrons, found in every well measured filament, is very difficult to explain with astrophysics, but is an automatic prediction for a ~10 GeV WIMP annihilating to leptons

§ The intensity from a filament is determined by the dark matter density, the annihilation cross section, the volume of the filament, and the fraction of electrons’ energy lost before escaping filament (roughly proportional to length, on the order unity for most filaments)

§ Spectrum is predictable, further depending only on the magnetic field strength (which can vary by a factor of a few from filament-to-filament)

Linden, Hooper, and Yusef-Zadeh, arXiv:1106.5493

Non-Thermal Radio Filaments § We find that the handful of best-measured NRFs have spectra that can be easily explained by annihilating dark matter

Annihilations to e+e-, +-, +- -26 3 mX=8 GeV, σv=3x10 cm /s

Linden, Hooper, and Yusef-Zadeh, arXiv:1106.5493 Non-Thermal Radio Filaments § We find that the handful of best-measured NRFs have spectra that can be easily explained by annihilating dark matter § We also observe a correlation between brightness and distance from the Galactic Center; in a dark matter interpretation, this corresponds to roughly ρ ~ r -1.25

1.4 GHz

Annihilations to e+e-, +-, +- m =8 GeV, σv=3x10-26 cm3/s X

Linden, Hooper, and Yusef-Zadeh, arXiv:1106.5493 –4–

Virgo Observation

DEC (deg) Galactic Diffuse + ExtraGal Diffuse + Point Sources Extended20:00 Gamma Ray Emission

15:00From Galaxy Clusters

§ The regions of the Virgo, Fornax, and Coma clusters were recently10:00 studied, using the first three years of Fermi data + Cosmic Ray ? + DM Annihilation? + Fluctuation § In contrast to (hadronic)5:00 cosmic ray induced backgrounds, dark matter annihilations are predicted to produce a 13h00msignificantly12h40m extended12h20m 12h00m RA (deg) pattern of emission

1 deg. Fig. 1.— Decomposition of the Fermi-LAT image in the region oftheVirgoclusterintomodel components. The observed photon count image from 100MeV to 100 GeV is shown on the left. The right panels show the integrated image over the same energy range for the various model

components: galactic diffuse emission, extragalactic diffuse emission, 2FGL point sources, cosmic- ray photons and DM annihilation emission, as labeled. The green circle in the “Point Sources” panel marks the virial radius of the cluster. The “Fluctuation” panel shows the residual image for our best-fit DM model. The images have been enhanced individually in color space for contrast.

point sources, DM annihilation and CR-induced emission. TheGALandEGdiffuse emission are Han, Frenk, Eke, Gao, White, arXiv:1201.1003 given by the most recent templates, gal 2yearp7v6 v0.fits and iso p7v6source.txt,whichcan be obtained from the Fermi-LAT data server, while the point sources are taken from the LAT 2-year point source catalogue (2FGL,The Fermi-LAT Collaboration (2011)). We now describe in detail our models for DM annihilation and CR emission.

2.1. Cluster annihilation emission

The gamma-ray intensity along the line-of-sight due to DM annihilation is given by:

1 dNf ρχ 2 I = σf v ( ) (l)dl, (1) 8π dE " Mχ !f l.o.s. dN where M is the DM particle mass, f the particle model dependent term giving the differential χ dE number of photons produced from each annihilation event as a function of energy, E,inaparticular

annihilation channel, f,andσf v is the cross-section (or annihilation rate) for that channel, which is predicted to be constant for cold dark matter. The line-of-sight integration of the density squared –14–

component with free normalization is included and is even lower when the CR level is fixed either to the fiducial or the optimal levels. There is a general trend for the significance to peak in the mass range 20 60 GeV for all three clusters. This is consistent with the conclusion of Hooper & Linden − (2011), who claim that a DM model with particle mass in the range 25 45 GeV annihilating into − b¯b final states can explain the excess extended emission observed from the direction of the Galactic center. –14– –14– 1 2 3 2 3 10 10 10 10 10 Coma –14– component20 withFornax free normalizationcomponent is included with free and normalization is even lower is20 when included the CR and level is even is fixed lower either when the CR level is fixed either Virgo to the fiducial or the optimal levels.to the fiducial There is or a the general optimal trend levels.for the There significance is a general to peak trend infor the the mass significance to peak in the mass range15 20 60 GeV for allFiducial threerange clusters. 20 60 This GeV iscomponent consistentfor all threeFree with with clusters. free the15 normalization con Thisclusion is consistent of is Hooper included with & Lindenand the con is evenclusion lower of whenHooper the & CR Linden level is fixed either − − (2011), who claim that a DM(2011), model withwho claim particleto that the mass a fiducial DM in the model or ran the withge optimal 25 particle45 levels. GeV mass There annihilating in theis a generalrange into 25 trend45for GeV the annihilating significance to into peak in the mass − − b¯bTS 10final states can explain theb excess¯b final extendedstates canrange emission explain 20 the observ60 excess GeVed for from10 extended all the three direction emission clusters. of observ This the is Galacticed consistent from the with direction the con ofclusion the Galactic of Hooper & Linden Extended Gamma Ray Emission− center. (2011), who claim that a DM model with particle mass in the range 25 45 GeV annihilating into center. − 5 b¯b final states can explain5 the excess extended emission observed from the direction of the Galactic From Galaxy1 2 Clusters13 22 33 2 3 10 10 10 center.1010 1010 10 10 0 Coma Coma 0 § The regions of the Virgo, Fornax,20 and ComaFornax 20 Fornax 1 202 3 202 3 20 Virgo Virgo 10 1020 10 10 10 clusters were recently studied, using the first Coma Fiducial 20 FiducialFreeFornax Free 20 three years of Fermi data 15 No CR15 OptimalVirgo 1515 15 15 Fiducial Free 15 TS § In contrast to (hadronic) cosmicTS ray induced TS 10 10 1010 10 backgrounds, dark matter annihilations are bb TS 10 10 predicted to produce a significantly55 extended 5 55 5 pattern of emission 5 5 00 Virgo τ +τ ,Free-CR 0 00 0 § Highest significance signal 2012 1 2 20 3 2 203 20 10 10 + - 10 100 10 0 is found from Virgo (4.4σ); 10 M /GeVτ τ M /GeV20 20 χ χ No CR Optimal 2.3 and 2.1σ for others 158 No CR15 Optimal 15 15 No CR Optimal Fig. 4.—6 TS values for a DM component annihilating15 through the b¯b channel. Different colors rep- 15

§ Can be fit by dark matter TS

TS 10 10 10TS 10 annihilations with same mass,resent 4 di ff erent clusters. Solid lines correspond to the extended model while dashed lines correspond TS 10 10 to the point source model. The four panels areMass for the range various CR models as labeled. channels, and cross section 5 2 5 5 5 favored by GC required by the Galactic Center 0 5 5 EventClass=2 To0 facilitateEventClass=3 comparison between0 1 all different model2 familiesandassessthesignificanceofa03 2 03 § Preferred over vanilla cosmic − 2 0 1 1 2 2 3 4 3 2 3 CR component,1010 10 we1010 show the10 maximum1010 likelihood10100 values for each1010 model of10 the Virgo cluster10 in 0 ray interpretation at ~3σ Mχ/GeV 1 2 3 2 3 Figure 5. As seenM in/GeV the TS curves, the likelihoodMMχ/GeV/GeV10 for the extended10 modelMχ is/GeV10 always higher10 than 10 Han,χ Frenk, Eke, Gao, White,χ arXiv:1201.1003 that for the point source model. For the most likely mass rangMχe,/GeV 20 60 GeV, the No-CRMχ/GeV and ∼ ¯ Free-CRFig. 4.— models TS values with for extended a DMFig. component DM 4.— emission TS annihilating values share for the a throughDM highest component th likelihood,e b¯b channel. annihilating with Di thefferent through No-CR colors th modele rep-bb channel. Different colors rep- Fig. 4.— TS values for a DM component annihilating through the b¯b channel. Different colors rep- beingresent superior different by clusters. having Solid oneresent linesfewer correspond di parameter.fferent clusters. to Actually the exte Solidnded ther lineseise model correspondffectively while dashedto no the contribution exte linesnded correspond model from while dashed lines correspond resent different clusters. Solid lines correspond to the extended model while dashed lines correspond CRto the when point CR source and DM model. are fitted Theto the four simultaneously point panels source are for model.for the this various The particle fourCR m panelsass models range, are as for and labeled. the the various fiducialCR and models as labeled. to the point source model. The four panels are for the various CR models as labeled. optimal CR levels are above the 95% CR upper limit predicted from the Free-CR model in the To facilitate comparison between all different model familiesandassessthesignificanceofa To facilitate comparison between all different model familiesandassessthesignificanceofa CR component, we showTo facilitate the maximum comparison likelihood between values all di forfferent each modelmodel familie of thesandassessthesignificanceofa Virgo cluster in CR component, we show the maximum likelihood values for each model of the Virgo cluster in Figure 5. As seenCR in component, the TS curves, we show the likelihood the maximum for the likelihood extended values model for is each alwaysmodel higher of the than Virgo cluster in Figure 5. As seen in the TS curves, the likelihood for the extended model is always higher than that for the pointFigure source 5. model. As seen For in the TSmost curves, likely the mass likelihood range, 20 for the60 exte GeV,nded the model No-CR is always and higher than that for the point source model. For the most likely mass range, 20 60 GeV, the No-CR and ∼ Free-CR models withthat extended for the point DM source emission∼ model. share For the the highest most l likelyikelihood, mass with range, the 20 No-CR60 GeV, model the No-CR and Free-CR models with extended DM emission share the highest likelihood, with the No-CR model ∼ being superior byFree-CR having one models fewer with parameter. extended DM Actually emission ther shareeiseff theectively highest no likelihood, contribution with from the No-CR model being superior by having one fewer parameter.being Actually superior ther byeise havingffectively one fewer no contribution parameter. Actually from thereiseffectively no contribution from CR when CR and DM are fitted simultaneously for this particle mass range, and the fiducial and CR when CR and DM are fitted simultaneouslyCR for when this CR particle and DM mass are range, fitted and simultaneously the fiducial for and this particle mass range, and the fiducial and optimal CR levels are above the 95% CR upper limit predicted from the Free-CR model in the optimal CR levels are above the 95% CR upperoptimal limit CR predicted levels are from above the the Free-CR 95% CR model upper in limit the predicted from the Free-CR model in the

Summary § An intriguing body of evidence has accumulated in support of dark matter in the form of ~10 GeV WIMPs

§ In the first three years of publicly available FGST data, we have identified a component of gamma rays concentrated around the Galactic Center, with a spectrum peaked at GeV energies

§ The spectrum and morphology of the observed emission can be easily accounted for with annihilating dark matter distributed with a halo profile similar to those inferred from simulations (  r -1.3), with a mass of 7-12 GeV, and an annihilation cross section consistent with a simple thermal relic (v ~ 10-26 cm3/s); this dark matter scenario also automatically leads to the observed WMAP Haze and to the peculiar signals from non-thermal radio

filaments

§ The mass range favored by these indirect signals is similar to that favored by the long standing claim of annual modulation from DAMA/LIBRA, and by the more recent results CoGeNT and CRESST-II IDM 2012 in Chicago!

§ The Identification of Dark Matter Conference Series is coming to the US for the first time, hosted by the Kavli Institute for Cosmological Physics at the University of Chicago

§ July 23-27th, 2012 in beautiful/exciting/glorious downtown Chicago

§ For more information, and to register: kicp-workshops.uchicago.edu/IDM2012

§ Register early! Register often! (the way of Chicago politics)

Looking Forward § The sensitivity of: -Fermi dwarfs -CMB power spectrum -LEP, mono-photon+missing energy -Super Kamiokande, neutrinos from Sun -PAMELA, low-energy positron fraction

Are each within a factor of a few needed to test this scenario

§ Planck, AMS-02, LHC, and further Fermi data will each bring much information to bear on this topic

§ Not to mention new information on the direct detection front: -CDMS modulation analysis (tomorrow?!) -Much more data from CoGeNT (C4) -Southern hemisphere experiments (DM-Ice)

5

considered in our analysis becomes:

L(D p , p )= LLAT (D p , p ) | W { }i i | W i i 2 1 log (J ) log (J ) /22 e( 10 i 10 i ) i , ⇥ ln(10) Ji 2⇥i (1)

LAT where Li denotes the binned Poisson likelihood that is commonly used in a standard single ROI analysis of the LAT data, i indexes the ROIs, D represents the binned gamma-ray data, pW represents the set of ROI-independent DM parameters ( ⇥annv ,mW , and the annihilation branching ratios b ),⌃ p ⌥ are the ROI- Constraints/Testsf { }i dependent model parameters. In this analysis, p i in- cludes the normalizations of the nearby point and{ } dif- § Gamma fuserays sources from and thedwarf J-factor, spheroidalJi. log10(Ji) and galaxies⇥i are FIG. 1. Derived 95% C.L. upper limits on WIMP annihilation the mean and standard deviation of the distribution of cross section for all selected dSphs and for the joint likelihood ¯ log (Ji), approximated to be gaussian, and their values analysis for annihilation into bb final state. The most generic 10 26 3 1 cross section ( 3 10 cm s for a purely s-wave cross -The gammaare given signal in cols. 5 from and 6 respectively the GC of Tableis dominated I. by annihilations⇥ · to taus; to The fit proceeds as follows. For given fixed values of section) is plotted as a reference. Uncertainties in the J-factor are included. -27 3 + - accommodatemW and bthef , we observed optimize ln L,with fluxL givenwe inneed eq. 1. roughly σv~3x10 cm /s to τ τ (for canonicalConfidence local intervals density) or upper limits, taking into account uncertainties in the nuisance parameters, are then com- puted using the ‘profile likelihood’ technique, which is a -Fermi’s studystandard methodof dwarf for treating galaxies nuisance parameters places in like- lihood analyses (see e.g., [30]),-26 and consists3 of calculat- a constrainting the of profile σv likelihood < 1.5x10ln L ( ⇥ cmv ) for/s several for fixed p ⌃ ann ⌥ masses mW , where for each ⇥annv , ln L is minimized a 10 GeVwith WIMP respect toannihilating all other parameters.⌃ ⌥to Thetaus intervals are

then obtained by requiring 2 ln(Lp)=2.71 for a one- -Dwarfs aresided still 95% confidence a factor level. of The a MINUIT few subroutineaway MI- NOS [31] is used as the implementation of this technique. Note that uncertainties in the background fit (di⇥use and nearby sources) are also treated in this way. The cover- age of this profile joint likelihood method for calculating confidence intervals has been verified using toy Monte Carlo for a Poisson process with known background and F ermi-LAT simulations of galactic and isotropic di⇥use gamma-ray emission. The parameter range for ⇥annv FIG. 2. Derived 95% C.L. upper limits on WIMP annihilation + + ⌃ ⌥ cross section for the bb¯ channel, the ⇥ ⇥ channel, the µ µ is restricted to have a lower bound of zero, to facilitate + channel, and the W W channel. The most generic cross convergence of the MINOS fit, resulting in slight over- 26 3 1 section ( 3 10 cm s for a purely s-wave cross section) coverage for small signals, i.e. conservative limits. is plotted⇥ as· a reference. Uncertainties in the J-factor are included. RESULTS AND CONCLUSIONS arXiv:1108.3546; see also Geringer-Sameth, limit compared to using nominal J-factors, a factor of As no significant signal is found, we report upperKoushiappas lim- 1.3. arXiv:1108.2914 its. Individual and combined upper limits on the anni- The combined upper limit curve shown in Fig. 1 in- hilation cross section for the bb¯ final state are shown in cludes Segue 1 and Ursa Major II, two ultra-faint satel- Fig. 1, see also [32]. Including the J-factor uncertainties lites with small kinematic datasets and relatively large in the fit results in increased upper limits compared to uncertainties on their J-factors. Conservatively, exclud- using the nominal J-factors. Averaged over the WIMP ing these objects from the analysis results in an increase masses, the upper limits increase by a factor up to 12 in the upper limit by a factor 1.5, which illustrates the ⇤ for Segue 1, and down to 1.2 for Draco. Combining the robustness of the combined fit. dSphs yields a much milder overall increase of the upper Finally, Fig. 2 shows the combined limits for all stud-

Constraints/Tests

§ Effects on the CMB from annihilations in the recombination epoch

-Energy injected by dark matter annihilations can heat and ionize the photon- baryon plasma at z~1000, potentially altering the CMB power spectrum 10

-WMAP does not yet constrain this one example, a 1/v enhancement which saturates at too scenario, but Planck likely will low a velocity can also cause runaway annihilations in the first DM halos at the onset of structure formation 2 5 1 [58]. Furthermore, as shown in Fig. 6, models which fit Ruled out by WMAP5 8 4 3 the recently observed cosmic-ray anomalies are already 6 7 close to being ruled out by WMAP5. If the Sommer- 10 feld enhancement in such models has not saturated by 9 11 (v/c) 10−8,thisimpliesaneffective cross section at re- 12 1 XDM µ+µ- 2500 GeV, BF = 2300 + - ∼ 13 2 µ µ 1500 GeV, BF = 1100 combination 4 5ordersofmagnitudehigherthanin 3 XDM µ+µ- 2500 GeV, BF = 1000 4 XDM e+e- 1000 GeV, BF = 300 ∼ − 5 XDM 4:4:1 1000 GeV, BF = 420 the present-day Galactic halo. Such models are therefore Planck 6 e+e- 700 GeV, BF = 220 + - strongly excluded by WMAP5. Similarly, if the WIMP forecast 7 µ µ 1500 GeV, BF = 560 CVL 8 XDM 1:1:2 1500 GeV, BF = 400 9 XDM µ+µ- 400 GeV, BF = 110 annihilates to the same particle which mediates the Som- 10 µ+µ- 250 GeV, BF = 81 11 W+W- 200 GeV, BF = 66 merfeld enhancement, then in order for the enhancement 12 XDM e+e- 150 GeV, BF = 16 13 e+e- 100 GeV, BF = 10 to evade the constraints in Fig. 6, the coupling α between the WIMP and the force carrier must be extremely small –reducingtheannihilationcrosssectionatfreeze-outto unacceptable levels for a thermal relic. Thus for a broad (f~0.45 in dem. lepton case) Slatyer, Padmanabhan, Finkbeiner, range of well motivated models, it is self-consistent to as- FIG. 6: Constraints on the annihilation cross-section !σAv" the ePRD,fficiency arXiv:0906.1197; factor f.Thedarkblueareaisexcludedby see also Finkbeiner, sume that the Sommerfeld enhancement is saturated for the redshift range of interest (z 100 4000). WMAP5Galli, data Lin, at Slatyer, 95% confidence, arXiv:1109.6322 whereas the lighter blue ∼ − area shows the region of parameter space that will be probed We can write the 95 % confidence limits from WMAP5 by Planck. The cyan area is the zone that can ultimately be in terms of constraints on the total cross section, explored by a cosmic variance limited experiment with angu- −24 3 2 lar resolution comparable to Planck. Constraints are taken 3.6 10 cm /s MDMc σ v saturated < × , (6) from [42] (Fig. 4). The data points indicate the positions of % A & f 1TeV models which fit the observed cosmic-ray excesses, as fitted in ! " [20, 55]. Squares: PAMELA only. Diamonds: PAMELA and or as constraints on the maximum saturated enhance- Fermi. Crosses: PAMELA and ATIC. Error bars indicate the ment, relative to the thermal relic cross section σAv = factor-of-4 uncertainty in the required boost factor due to un- 3 10−26 cm3/s, % & certainties in the local dark matter density (any substructure × 2 contributions are not taken into account). For models labeled 120 MDMc by “XDM” followed by a ratio, the annihilation is through an Smax < . (7) f 1TeV XDM intermediate light state to electrons, muons and pions ! "

in the given ratio (e.g. “XDM 4:4:1” corresponds to 4:4:1 In both cases values of f for the different channels are annihilation to e+e−, µ+µ− and π+π−). given in Table I. These results directly limit the maximum boost fac- tor possible from substructure, in Sommerfeld-enhanced by WMAP5 constraints, either the enhancement must models. There has recently been considerable interest be saturated over the redshift range in question (z in possible annihilation signals from dark matter sub- 100 4000), or α or f(z)mustbeextremelysmall–in∼ − halos, where the DM velocity dispersion is reduced and which case the model could not explain the cosmic-ray the Sommerfeld-enhanced cross section is boosted (e.g. anomalies described in the Introduction. For the models [59, 60, 61, 62]). However, the saturated cross section of greatest interest, the enhancement S thus provides a cannot be much larger than that required to fit the cos- constant boost factor to the annihilation cross section at mic ray anomalies, so for models which fit the cosmic ray z 1000, and our constraints apply directly. ∼ anomalies, the lower velocity dispersion in subhalos will At redshift z,theCMBtemperatureis 2.35 not result in a higher annihilation cross section. 10−4(1 + z)eV.Thisplacesanupperboundonthetem-∼ × perature of the DM: however, after kinetic decoupling the DM temperature evolves adiabatically as T z2, 2. Sommerfeld-enhanced models fitting cosmic ray excesses and thus the WIMPs can be much colder than the∝ pho- −8 ton temperature. [42] suggests v/c 10 at z 1000 In Sommerfeld-enhanced models which produce the ob- ∼ ∼ for a 100 GeV WIMP. served excesses in e+e− cosmic rays, the saturation of If the enhancement is still unsaturated at such low ve- the enhancement is even more constrained than in the locities, then the force carrier must be extremely light general case. Since the cross sections required to fit compared to the WIMP mass. For the models recently the cosmic ray anomalies are already nearly excluded by proposed in the literature [21, 23, 25, 57], the enhance- WMAP5, as shown in Fig. 6, the enhancement must al- ment has always saturated by this point as the force carri- ready be close to saturation at v 150 km/s (5 10−4c), −8 ∼ × ers are much heavier than 10 MDM.Otherconstraints the estimated local WIMP velocity dispersion. Astro- on models with very low-mass mediators also exist: as physical uncertainties – in the propagation of cosmic rays, 10

Annihilation only into e⇥e⇤ Equal coupling to all charged leptons ⇥ ⇥ s s ⌥ ⇤22 ⌥ ⇤22 3 10 3 10 ⇤23 90 C.L. ⇤23 90 C.L. cm cm

10 10 ⇤ ⇤24 ⇤ ⇤24 e 10 10 ⇥ ⇥ e 10⇤25 Thermal relic 10⇤25 Thermal relic

⇤ ⇤ 5 26 ⇧ 26 ⇧ ⌃ 10 10 ⌃ ⌥ ⌥

e ⇧ ⇧ ⌃ ⌥ ⌥ ⇧ ⌃ ⇤27 ⌥ e ⇤27 ⌃ ⇧ 5 ⇧ 10 ⌃ ⇧ ee 10 ⇧ ⇧ ⌥ ⌃

for ⌃ for ⇧ ⇧⇧ ⇧

⇤28 ⌃ ⇤28 ⌃ 5 , 10 e ⇧ ⌃ e 10

rel rel e ⌃ ⌥ ⇧

⇧ v v ⇤29 5 ⇧ e Constraints/Tests⇤29 ⇧ 10 ⌥ 10 ⌃ ⇧ ⇧ ⇧⌃ 10⇤30 10⇤30 § Constraints10⇤ 31from LEP 10⇤31 section section 10⇤32 2 10⇤32 2 vrel ⌅ 0.24 freeze⇤out vrel ⌅ 0.24 freeze⇤out ⇤33 ⇤33 -The photon10 plus0 missing1 energy2 channel 3at LEP10 0provides 1the strongest2 3 Cross Cross 10 10 10 10 10 10 10 10 collider bound on lightWIMP darkmass matterm GeV with sizeable couplingsWIMP tomass electronsm GeV ⇧ ⌃ ⇧ ⇤ ⌅ ⇧ ⌃ ⇧ ⇤ ⌅ -For heavy mediatorsEqual coupling (makingto all charged use ofleptons Equal coupling to all charged leptons ⇥ ⇥ s s

⌥ ⇤22 ⌥

3 10 3 effective field theory),90 C.L. and 1/3 of ⇥ 90 C.L. ⇥ ⇤23 ⇥ ⇤ cm ⌥ cm

10 annihilations to electrons, constraints ⌥ ⇤22 ⇤ ⇤24 ⇧⇧ ⇤ 10 10 ⌃: ⇥ -26 3 ⇥ ⇤ Draco Fermi ⇥ ⌥ are near the10 ⇤σ25v~10 cm /s level⇧ ⇤23 ⌥ 10 ⇤ ⇤ ⇧ ⇥ ⇧ 26 ⇧ ⌅ 10 ⌃ ⌥ : ⇧⇧ ⇧ ⇧ ⌃ ⌥ ⇧ ⇤24 ⇤ ⇧⇧ -Once again,⇤ 27close,⌃ but not a problem 10 ⇥ : ⇤ 10 ⇧ ⌥ 5 5 Fermi e e for ⇧⌃ ⌃ ⇧ ⌃⌥⌃ for

⌃ ⇤28 ⌃ 10 ⇤25 Fermi rel rel

10

v v Thermal relic 10⇤29 ⇧

⇧ ⇧ ⇤30 ⇧ 10⇤26 10 ⌥ Hooper Goodenough ⌃ 10⇤31 ⌥ ⇧ Fermi⇤LAT, WMAP haze 10⇤27 ⇧⌃ ⇧ section section 10⇤32 2 2 ⇧ 2 vrel ⌅ 69.3 km sec Draco Only vrel ⇤independent models ⇤33 ⇤28 ⌥ 10 0 1 2 3 10 0 1 2 3 Cross 10 10 10 10 Cross 10 10⇤ 10 ⌅10 WIMP mass m⇧ GeV WIMP mass m⇧ GeV ⇧ ⌃ ⇤ ⌥ ⌅ ⇤ ⌅ ⇧ ⌃ Fox, Harnik, Kopp, Tsai, ⇥ ⇥ Dan HooperFigure - Indirect 6: LEP Evidence upper limits For on Light the darkWIMPs matter annihilation crossPRD, section arXiv:1103.0240⇥v , assuming that dark matter production at LEP and dark matter annihilation as probed by astrophysical⌅ and⇧ cosmological observations + can be described by contact operators. In the upper left panel, we show limits on the process⇤⇤ ¯ e e ⇥ (the only one that can be constrained model-independently by LEP), while in the other panels we have made the assumption that dark matter couples equally to all charged leptons. For the average dark matter 2 velocity v we have assumed the value at freeze-out in the top panels, while the bottom left panel is for the Draco dwarf galaxy which has very small v2 . In the bottom right panel we compare the LEP limit on ⇥ the v-independent interactions, V and t, to limits from a variety of astrophysical observations [39–41]. O O ⇥ 1 In order to translate the LEP constraints on the coupling strength into limits on dark matter annihilation, we need to calculate the annihilation cross sections corresponding to the operators in equations (1)–(4). For annihilation into a single single lepton flavor of mass m⇤, they read 2 1 m⇤ 2 2 2 ⇥Svrel = 4 1 2 (m m⇤ ) vrel , (7) 8 ⇤ m