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Lacroix, Thomas and Karami, Mansour and Broderick, Avery E. and Silk, Joseph and Boehm, C�eline (2017)'Unique probe of dark matter in the core of M87 with the Event Horizon Telescope.', Physical review D., 96(6). 063008.

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Unique probe of dark matter in the core of M87 withthe Event Horizon Telescope

Thomas Lacroix,1,2* Mansour Karami,3,4 Avery E. Broderick,3,4 Joseph Silk,2,5,6 and Céline Bœhm7,81Laboratoire Univers & Particules de Montpellier (LUPM), CNRS & Université de Montpellier

(UMR 5299), Place Eugène Bataillon, F-34095 Montpellier Cedex 05, France2Institut d’Astrophysique de Paris, UMR 7095, CNRS, UPMC Université Paris 6,

Sorbonne Universités, 98 bis boulevard Arago, 75014 Paris, France3Perimeter Institute for Theoretical Physics,

31 Caroline Street North, Waterloo, Ontario N2L 2Y5, Canada4Department of Physics and Astronomy, University of Waterloo,

200 University Avenue West, Waterloo, Ontario N2L 3G1, Canada5The Johns Hopkins University, Department of Physics and Astronomy,

3400 N. Charles Street, Baltimore, Maryland 21218, USA6Beecroft Institute of Particle Astrophysics and Cosmology, Department of Physics, University of Oxford,

Denys Wilkinson Building, 1 Keble Road, Oxford OX1 3RH, United Kingdom7Institute for Particle Physics Phenomenology, Durham University, Durham DH1 3LE, United Kingdom

8LAPTH, Université de Savoie, CNRS, BP 110, 74941 Annecy-Le-Vieux, France(Received 6 November 2016; published 15 September 2017)

We demonstrate the unprecedented capabilities of the Event Horizon Telescope (EHT) to image theinnermost dark matter profile in the vicinity of the supermassive black hole at the center of the M87 radiogalaxy. We present the first model of the synchrotron emission induced by dark matter annihilations from aspiky profile in the close vicinity of a supermassive black hole, accounting for strong gravitational lensingeffects. Our results show that the EHT should readily resolve dark matter spikes if present. Moreover, thephoton ring surrounding the silhouette of the black hole is clearly visible in the spike emission, whichintroduces observable small-scale structure into the signal. We find that the dark matter-induced emissionprovides an adequate fit to the existing EHT data, implying that in addition to the jet, a dark matter spikemay account for a sizable portion of the millimeter emission from the innermost (subparsec) region of M87.Regardless, our results show that the EHT can probe very weakly annihilating dark matter. Current EHTobservations already constrain very small cross sections, typically down to a few 10−31 cm3 s−1 for a10 GeV candidate, close to characteristic values for p-wave-suppressed annihilation. Future EHTobservations will further improve constraints on the DM scenario.

DOI: 10.1103/PhysRevD.96.063008

I. INTRODUCTION

The dark matter (DM) density profile at the centers ofgalaxies is critical to indirect searches but remains poorlyconstrained. In objects such as M87, the DM profile may besignificantly enhanced on subparsec scales by the centralsupermassive black hole (SMBH), although there is nodirect evidence for such a sharp density increase, referred toas a DM spike.DM spikes however leave a very distinctive signature in

the spectral energy distribution (SED) of a galaxy if DM canannihilate [1–3]. More specifically, in the case of M87,where a spike should plausibly have formed and survivedgalaxy dynamics, an anomalous contribution to the SED isexpected when the DM annihilation cross section is largerthan∼10−30 cm3 s−1 for light (10 to 100GeV)DMparticles,and above ∼3 × 10−26 cm3 s−1 for candidates as heavy as100 TeV [2].

Here we show that it is possible to probe even fainterDM-induced radiation in M87 by using the spatial mor-phology of the DM-induced synchrotron emission near thecentral black hole (BH). Due to a lack of angular resolutionin existing observational facilities, such a study of the DM-induced signal in the inner part of M87 has not beenperformed yet—nor has it been done in similar objects.However, this is now possible with the advent of the EventHorizon Telescope (EHT).Heavy DM particles annihilating into Standard Model

particles near the central BH are expected to producesynchrotron emission in the frequency range that iscurrently being probed by the EHT. Here, we show thatthe synchrotron halo induced by DM is bright enough to beresolved by the EHT, if there is a DM spike. Moreover, thisadditional radiation enhances the photon ring around theBH shadow, thus making it a prominent feature in the EHTdata and a new probe of the DM properties.In Sec. II, we provide a description of the EHT, and then

we present our DM model in Sec. III and the EHT data we*[email protected]

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used in Sec. IV. Our results can be found in Sec. V, and weconclude in Sec. VI.

II. THE EVENT HORIZON TELESCOPE

A. General features

The EHT is a global network of millimeter andsubmillimeter facilities that employs very long baselineinterferometry (VLBI) to create an effective Earth-scale high angular resolution telescope [4,5]. The purposeof this array is to test general relativity and shed lighton physical processes taking place in the vicinity ofSMBHs at the centers of galaxies. To date, EHT data forM87 has been reported for a three-station array com-prised of the Submillimeter Telescope (SMT) in Arizona,the Combined Array for Research in Millimeter-waveAstronomy (CARMA) in California, and a network ofthree facilities in Hawaii: the James Clerk MaxwellTelescope, the Submillimeter Array, and the CaltechSubmillimeter Observatory. This configuration has alreadyachieved an impressive angular resolution of order 40 μasat 230 GHz. Presently, the Atacama Large Millimeter/submillimeter Array in Chile, the Large MillimeterTelescope in Mexico, the Institut de RadioastronomieMillimétrique 30m, the Plateau de Bure interferometer,and the South Pole Telescope (SPT)1 will be added to theEHT. Longer term, the Greenland Telescope will join thearray. Combined, the EHT will directly access angularscales as small as 26 μas at 230 GHz and 17 μas at345 GHz.The angular scale of the Schwarzschild radius of

the SMBH at the center of M87 is about 8 μas.2 Thestrong gravitational lensing near the black hole (BH)magnifies this by a factor of as much as 2.5, onlyweakly dependent on BH spin, making M87 a primarytarget for the EHT [5].

B. Imaging the shadow of a black hole

Characteristic in all images of optically thin emissionsurrounding BHs is a “shadow”—a dark central regionsurrounded by a brightened ring, the so-called “photonring.”This is a direct consequence of the strong gravitationallensing near the photon orbit, and is directly related to theprojected image of the photon orbit at infinity. The shadowinterior is the locus of null geodesics that intersect thehorizon, and thus does not contain emission from behindthe BH. The bright ring is in general sharply defined due tothe instability of the photon orbit and a consequence of thepileup of higher-order images of the surrounding emission.For a Schwarzschild BH the radius of this shadow isrshadow ¼ 3

ffiffiffi3

p=2RS ≈ 2.6RS [11,12]. For Kerr BHs, this

radius ranges from 2.25RS to 2.6RS, deviating substantiallyonly at large values of the dimensionless spin parameterand viewed from near the equatorial plane, i.e. a ≳ 0.9 andθ ≳ 60° [13].The generic appearance of the shadow, its weak depend-

ence on BH spin, and fundamentally general-relativisticorigin make it a prime feature in EHT science. Alsoimprinted on EHT images will be the high-energy astro-physics of the near-horizon region: the physics of BHaccretion and relativistic jet formation. Horizon-scale fea-tures have already been observed in early EHTobservationsof Sagittarius A* (Sgr A*) [14–16] and M87 [17,18],demonstrating that such structure exists. Here, we assessthe observability of the shadow of the SMBH at the center ofM87 in the electromagnetic signal from DM annihilation,and the limits that may be placed on DM properties givensuch a scenario.

III. PROBING A DARK MATTER SPIKEAT THE CENTER OF M87 WITH THE EVENT

HORIZON TELESCOPE

A. Ingredients and assumptions

In the context of the observational opportunities offeredby the EHT, we now discuss the potential of this instrumentin terms of DM searches. In particular, we study theobservability of a DM spike at the center of M87, sincesuch a sharply peaked morphological feature is expected toyield strong annihilation signals. At the frequencies ofinterest for the EHT, typically a few hundred GHz, themain DM signature comes from synchrotron radiation.Therefore, in order to assess the ability of the EHT to probethe inner part of the DMprofile ofM87, we need to computethe synchrotron emission of electrons and positrons pro-duced in DM annihilations in the inner region. We make thefollowing assumptions:(1) The presence of a SMBH at the center is likely to

lead to fairly strong magnetic fields, typically around10–102 G [19]. As a result of such strong magneticfields, synchrotron radiation and advection towardsthe central BH are the dominant physical processes

1Note that M87 cannot be seen by the SPT.2We use MBH ¼ ð6.4� 0.5Þ × 109 M⊙ [6] for the mass of the

central BH. This value is based on stellar dynamics measure-ments, and is consistent with other more recent similarestimates [7,8]. The corresponding Schwarzschild radius isRS ¼ 6 × 10−4 pc and the distance of M87 is dM87 ≈ 16 Mpc[9]. Throughout we adopt the higher stellar dynamical mass forM87; using the ð3.5� 0.8Þ × 109 M⊙ value found by gasdynamical studies [10] would reduce the angular scales byroughly a factor of 2 throughout. This would make it moredifficult to detect horizon-scale features with the EHT. How-ever, we believe stellar dynamics measurements to be morereliable than gas dynamical studies since the latter make ratherextreme assumptions on the kinematical properties of thegas—such as considering that it moves on circular, Keplerianorbits—or using a simplified disk model for the gas, which isunlikely to account for the high-velocity dispersions derivedfrom line measurements.

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by which DM-induced electrons and positrons loseor gain energy [20,21], whereas inverse Comptonscattering and bremsstrahlung are negligible. Addi-tionally, the time scales associated with synchrotronradiation and advection are much shorter than that ofspatial diffusion, so we disregard the latter in thefollowing. Note that even larger magnetic fields—upto ∼103 G—would arise if the equipartition scenarioproposed in Ref. [22] for the center of theMilkyWaywere realized in M87. Therefore, to account for theuncertainty on the central magnetic field strength,we consider values in the range 10–103 G.

(2) We also disregard two processes that can reducethe synchrotron intensity. On the one hand, thesynchrotron self-Compton effect, which would leadto additional energy losses for electrons and posi-trons, is only relevant for magnetic fields signifi-cantly smaller than 0.1 G [20]. For larger magneticfields, such as the ones we consider here, synchro-tron self-Compton losses are negligible with respectto synchrotron losses. On the other hand, synchro-tron self-absorption is only relevant below ∼10 GHz[20,21], so it can be neglected for the EHT frequencyof 230 GHz.

(3) We want to test the presence of a spike in the DMprofile, formed through adiabatic growth of a SMBH[1] at the center of a DM halo with power-lawdensity profile. The existence of such a strongenhancement of the DM density—correspondingto ρðrÞ ∝ r−γsp with typically γsp ¼ 7=3—is debated.An adiabatic spike can actually be weakened byvarious dynamical processes such as mergers [23]. Itturns out that M87 may contain a BH binary in thecentral region, considering current evidence for a∼10 pc displacement between the SMBH and thecenter of the galaxy [24,25], and the discovery of ahypervelocity cluster [26]. This is suggestive ofbinary scouring at ∼10 pc scales. However, herewe are actually interested in the DM spike muchcloser in, which would be unaffected. A softer cuspis also formed if the BH did not grow exactly at thecenter of the DM halo (within ∼50 pc) [27,28], or ifthe BH growth cannot be considered adiabatic [28].Moreover, dynamical heating in the central stellarcore would also soften a spike [29]. However, unlikein theMilkyWay, an adiabatic spike is more likely tohave survived in a dynamically young galaxy suchas M87, in which stellar heating is essentiallynegligible—essentially due to the large velocitydispersion caused by the very massive SMBH—asdiscussed in Refs. [2,30]. Furthermore, otherdynamical processes can have the opposite effectof making the survival of a spike more likely, such asenhanced accretion of DM to counteract the depop-ulation of chaotic orbits in triaxial halos [31]. Allthese arguments motivate the assumption that a steep

spike effectively formed at early times at the centerof M87 and has survived until today.3,4

B. Electron propagation in the presence of advection

To derive the intensity of DM-induced synchrotronradiation, we first need to compute the electron andpositron spectra from the DM annihilation rate. This isdone by solving the propagation equation of DM-inducedelectrons and positrons which, in the presence of synchro-tron radiation and advection, and assuming a steady statereads (see e.g. Refs. [20,21])

v∂fi∂r −

1

3r2∂∂r ðr

2vÞp ∂fi∂p þ1

p2∂∂p ðp

2 _pfiÞ ¼ Qi; ð1Þ

where fiðr; pÞ is the distribution function of electrons andpositrons inmomentum space, at radius r andmomentump,for annihilation channel i. The first, second and third termscorrespond to the advection current, the energy gain ofelectrons due to the adiabatic compression, and the loss termdue to radiative losses, respectively. vðrÞ ¼ −cðr=RSÞ−1=2 isthe radial infall velocity of electrons and positrons onto theBH in the accretion flow, where RS is the Schwarzschildradius. The minus sign in the expression of the inflow

3An additional caveat is related to a putative stellar spike whichmight have formed jointly with a DM spike in the adiabaticformation scenario. However, this would strongly rely on theexistence of a nuclear star cluster (NSC), which in the mostaccepted view is formed by merging globular clusters [32].Unlike the Milky Way, M87 is actually not an optimal candidatefor such mergers, due to the large velocity dispersion induced bythe very massive central BH. Moreover, no NSC has beenobserved in M87 (e.g. Ref. [33]). Therefore, stars and DMessentially decouple in this regard, and the absence of a stellarspike in observations does not preclude the existence of aDM spike.

4We note that there is significant uncertainty on the haloprofile, which can in principle affect the central density in thespike and the resulting synchrotron fluxes. Here for definitenesswe assume that the halo follows the NFW profile, although this isdebatable. In Ref. [34] the authors found the data to be consistentwith the NFW profile, while the results of Ref. [8] favored a coredgeneralized NFW-like DM distribution. The authors of Ref. [35]discussed the impact of the outer halo on the spike model—especially on the outer radius of the spike Rsp—using theprescription given in Ref. [1] (see Appendix A). They arguedthat a cored halo would lead to a lower central density due to asmaller value for Rsp. However, the prediction for Rsp should notbe taken at face value, especially when comparing different haloprofiles. It should only be interpreted as a benchmark, all themore so as it can be significantly affected by the variousdynamical processes described above. The extent of the spikeshould actually be of the order of the radius of gravitationalinfluence of the SMBH—of order 100 pc for M87 from theMBH − σ relation [36]—regardless of the halo profile. As a result,our conclusions would only be mildly affected by a differentchoice in the outer halo, provided the spike roughly spans thesphere of influence of the BH and the inner slope is γsp ≳ 2.

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velocity accounts for the direction of the flow, orientedtowards the BH.The source function Qiðr; pÞ is the DM annihilation rate

in momentum space for channel i, related to the annihi-lation rate qiðr; EÞ in energy space via

Qiðr; pÞ ¼c

4πp2qiðr; EÞ ð2Þ

in the ultrarelativistic (UR) regime where E ¼ pc. The URapproximation can be safely used for electrons and posi-trons for the energy range relevant for this study. The usualannihilation rate in energy space reads

qiðr; EÞ ¼hσviiη

�ρðrÞmDM

�2 dNe;idE

ðEÞ; ð3Þ

where η ¼ 2 for the case of self-annihilating DM that weconsider here. The injection spectrum dNe;i=dE is takenfrom Ref. [37] and the associated website.Since radiative losses are dominated by synchrotron

losses, the total radiative loss term _p ¼ dp=dt reduces tothe synchrotron loss term [38]

_pðr; pÞ ¼ _psynðr; pÞ ¼ −2σTB2p2

3μ0ðmecÞ2: ð4Þ

We assume the intensity of the magnetic field to behomogeneous, i.e.B≡ B0, over the accretion region, whichhas a size racc corresponding to the sphere of influence of theBH [21], so typically ∼60 pc (as discussed in Ref. [2]),which is also roughly the size of the spike.The resolution of the propagation equation, Eq. (1), in

the presence of synchrotron losses and advection, in the URregime, and with the method of characteristics, yields theelectron and positron spectrum in terms of the DMannihilation rate [20]

fiðr;pÞ¼1

c

�rRS

�Zracc

rQiðRinj;pinjÞ

�RinjRS

�52

�pinjp

�4

dRinj;

ð5Þ

where the injection momentum pinj ≡ pinjðRinj; r; pÞ for ahomogeneous magnetic field is given in Appendix B. Fromthere, the electron and positron energy spectrum is given by

ψ iðr; EÞ ¼4πp2

cfiðr; pÞ: ð6Þ

We then convolve ψ i with the synchrotron powerPsynðν; E; rÞ to obtain the synchrotron emissivity:

jsyn;iðν; rÞ ¼ 2Z

mDM

me

Psynðν; E; rÞψ iðr; EÞdE: ð7Þ

C. Relevance of advection

Advection shapes the inner part of the intensity profile bydisplacing electrons and positrons towards the BH, thereby

accelerating them. This effect is in competition with syn-chrotron losses. Therefore, depending on themagnetic field,electrons either lose their energy in place through synchro-tron radiation, or are first advected towards the center. Thedependence on the magnetic field of the size of the regionwhere electrons are affected by advection is obtained bycomparing the synchrotron loss term given in Eq. (4) withthe momentum gain rate due to adiabatic compression,

_pad ¼ −1

3r2∂∂r ðr

2vðrÞÞp: ð8Þ

The shape of the emissivity profile is thus governed byadvection for

r≲�3R

12

Sμ0m2ec4

4σTB20Esyn

�23

; ð9Þ

where Esyn ¼ ð4πm3ec4ν=ð3eB0ÞÞ1=2 is the peak synchro-tron energy at the frequency ν of interest [38]. In terms of theangular distance from the center θ≡ r=dM87—wheredM87 ≈ 16 Mpc is the distance between Earth and the centerof M87—this condition reads, for ν¼ 230 GHz,

θ ≲ 7�

B010 G

�−1μas: ð10Þ

It is therefore essential to include the advection process forB0 ≲ 10 G, since in that regime it has a strong impact on thesynchrotron intensity in the region of interest for the EHT.For B0 ≫ 10 G, advection is negligible since it would onlydominate for radii smaller than the Schwarzschild radius ofthe BH.

D. Dark synchrotron intensity in a curved spacetime

The DM-induced synchrotron intensity for a flat space-time is computed by integrating the emissivity over the lineof sight. However, the actual spacetime accounting for thepresence of the SMBH at the center is characterized by theSchwarzschild or Kerr metric respectively if the BH is staticor rotating. In these realistic cases, the correct spatialmorphology of the synchrotron intensity Iν is obtainedusing a ray-tracing technique that accounts for the gravi-tational lensing effect due to the BH. In our case, this isachieved via the ray-tracing and radiative transfer schemedescribed in Refs. [39–41].

IV. DATA

Here we provide a brief overview of the EHT data usedto constrain our models. Details regarding individualobserving runs, data calibration, and the uncertainty esti-mates can be found in Refs. [17,18], to which we directinterested readers.The EHT, like all interferometers, directly constructs

visibilities by cross-correlating observations at pairs ofstations. These are directly proportional to the Fourier


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transform of the image at a spatial frequency proportionalto the ratio of the projected baseline distance betweenthe two stations to the observation wavelength. Throughoutthe night the rotation of the Earth results in a rotation of theprojected baseline, changing both its orientation and length,thereby generating a moderate variation in the spatialfrequencies probed by any particular pair of sites.Importantly, like any interferometer the EHT acts as a

“high-pass” filter, sensitive primarily to structures on angularscales that lie between λ=ushort and λ=ulong, where ushort andulong are the shortest and longest baselines in the array,respectively.Within the context of the publishedEHTdata onM87 these angular scales are 75 to 450 μas, though the highsignal-to-noise ratio of the data extends these by roughly afactor of 2. Therefore, features that extend over more than amilliarcsecond are effectively invisible to the EHT.Upon measuring a sufficient number of these visibilities

an image can be produced via inverting the Fourier trans-form. In practice, this is performed via a number ofsophisticated image-inversion techniques that impose addi-tional requirements on the final image, e.g. positivity,smoothness, etc. [42]. However, because the publishedEHT observations only sparsely sample the spatial-frequency plane (often called the “u-v” plane) we comparedirectly with the measured visibilities.By construction the visibilities are complex valued, and

therefore described by an amplitude and phase. However, inpractice the amplitudes are known much better than thephases as a result of the typically large, and highly variable,atmospheric phase delays. This does not mean that phaseinformation is completely unavailable; “closure phases”constructed from triplets of sites, equal to the sum of thephases over the closed triangle of baselines, are insensitiveto site-specific phase errors. Therefore, the two data sets weemploy consist of visibility amplitudes and closure phasesobtained with the Hawaii-SMT-CARMA array, reported inRefs. [17,18]. In all cases observations were taken at230 GHz.Altogether, 160 visibility amplitudes were constructed

from data taken on April 5, 6, and 7, 2009, reported inRef. [17], and March 21, 2012, reported in Ref. [18]. Allnights showed visibility amplitudes consistent with a singlesource structure. Of these 54 visibilities were reported onthe CARMA-SMT baseline, 83 on the Hawaii-CARMAbaseline, and 23 on the Hawaii-SMT baseline. Note that inall of the reported measurements a 5% systematic calibra-tion error has been added to the uncertainties in quadrature.On the Hawaii-CARMA-SMT triangle, 17 closure

phases were constructed from data taken on March 21,2012 and reported in Ref. [18]. Where visibility amplitudesprovide a measure of the “power” in an image at a givenspatial scale, closure phases are particularly sensitive toasymmetry; e.g. a point-symmetric image has identicallyzero closure phases. These are consistent with a constantclosure phase of 0°, with typical uncertainties of 10°.

V. RESULTS

Predicted images are shown in Fig. 1, corresponding tothe synchrotron intensity at 230 GHz from DM. The upperpanels correspond to a DM spike with γsp ¼ 7=3, whereasthe maps in the lower panels are computed for the no-spikecase, for which we consider a standard Navarro-Frenk-White (NFW) DM profile with power-law index γ ¼ 1. Weassume annihilation of 10 GeVDM particles into bb̄,5 and amagnetic field of 10 G, for a static BH (left panels) and amaximally rotating BH (right panels).The photon ring, i.e. the bright ring of radius∼20 μas that

surrounds the darker shadow of the BH, is clearly visible inthe simulations for all DM models we consider, although inpractice in the absence of a spike the signal is tooweak to bedetectable with the EHT, as discussed in the following. Thepresence of a photon ring introduces small-scale structureinto the signal, readily observable with the EHT on longbaselines. For a static BH the shadow is exactly circular. Forall but the most rapidly rotating BHs it is also very nearlycircular [43,44]. For a maximally rotating Kerr BH viewedfrom the equatorial plane the photon ring is flattened in thedirection aligned with the BH spin.At scales above 25 μas the DM spike-induced emission

produces a diffuse synchrotron halo whose intensity fallswith radius as a power law with index ≈3.5. This is generic,occurring independently of the BH spin and is present evenwhen gravitational lensing is ignored. The extended natureof this component ensures that it is subdominant on Earth-sized baselines. In the absence of a spike, the profile is muchflatter, and falls with radius as a power law with index ≈1.Figure 1 also illustrates the fact that the intensity issignificantly enhanced in the presence of a DM spike withrespect to the no-spike case. To better stress this enhance-ment,we show themaps for the spike case computed for verysmall annihilation cross sections of a few 10−31 cm3 s−1—corresponding to the best fits to the EHT data, as discussedbelow—while in the absence of a spike we use the thermals-wave cross section of 3 × 10−26 cm3 s−1.6

Shown in the blue solid line in Fig. 2 is the visibilityamplitude at 230 GHz as a function of baseline length for thecurrent EHT triangle, for the simulated DM-induced syn-chrotron signal, computed with a cross section that gives thebest fit to theEHTmeasurements fromRefs. [17,18]. The left

5We focus on the standard b quark channel for simplicity.Injection of electrons through a different channel wouldprimarily result in a rescaling of the intensity at the frequencyof interest, slightly changing the best-fit cross sections we derive.

6For a light candidate (10 GeV), the spike becomes detectablewhen the cross section is greater than 10−31 cm3 s−1, while for aTeV candidate, the spike becomes visible when the cross sectionexceeds 10−27 cm3 s−1. However, in both cases, a NFW cuspwould lead to a much smaller emission and would be essentiallyinvisible unless the cross section is about 10−17 cm3 s−1 ifmDM ∼10 GeV and 10−13 cm3 s−1 ifmDM ∼ 1 TeV, which is completelyexcluded by indirect detection limits (e.g. Refs. [45,46]).


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panel corresponds to the Schwarzschild case and the rightpanel to the maximally rotating case. The DM-inducedvisibility amplitudes shown in Fig. 2 correspond to theintensity maps shown in Fig. 1. Note that no additionalastrophysical component has been included in these.A standard NFW cusp actually results in visibility

amplitudes that are about 8 orders of magnitude lowerthan the EHT data. Note that these no-spike visibilityamplitudes are not shown in Fig. 2 for clarity. Therefore,the EHT is only sensitive to spiky profiles, which makes it adedicated probe of such sharply peaked DM distributions.7

As shown in Fig. 2, a spike of annihilating DM gives agood fit to the EHT measurements of the visibilityamplitudes, with best-fit cross sections and reduced chi-squared—χ2red ¼ χ2=d:o:f:, with a number of degrees offreedom (d.o.f.) equal to 160 (data points) minus one (crosssection)—given in Tables I and II.8 While the fits appear byeye to be quite good, the reduced chi-squareds coupled with

FIG. 1. Simulated maps of the synchrotron intensity at 230 GHz from a spike of 10 GeV DM annihilating into bb̄, accounting for thestrong gravitational lensing induced by the central BH, for a Schwarzschild BH (left panel) and a maximally rotating BH (right panel), inthe presence (upper panels) and absence (lower panels) of a spike in the DM profile. Note that considering the wide range of intensities,we use different color scales, but with the same dynamic range spanning 3 orders of magnitude for comparison. The angular coordinatesξ and η correspond to the directions respectively perpendicular and parallel to the spin of the BH. For the spike cases, the slope of theDM spike is γsp ¼ 7=3, and the annihilation cross sections correspond to the best fit to EHT observations (see text for details), namely7.4 × 10−31 cm3 s−1 for the Schwarzschild case and 3.1 × 10−31 cm3 s−1 for the maximally rotating case. In the absence of a spike, theintensity is computed for the thermal s-wave cross section of 3 × 10−26 cm3 s−1. For all the simulated maps the magnetic field is 10 G.

7Moreover, the intensity profile for the no-spike case is muchflatter than for a spiky profile, leading to a larger ratio of flux onlong to short baselines, with no significant contribution on longbaselines.

8The mass dependence of the intensity—and thus of the best-fit cross section—is fairly simple, though it changes from onechannel to another. For the b − b̄ channel, the intensity goesroughly as logðmDMÞ=m2DM—the logarithm appears in the in-tegral of the injection spectrum andm2DM in the number density ofDM particles—which results in an increase of a factor ∼50 in thecross section when increasing the mass by an order of magnitude.This allows for an extrapolation of our results at higher masses(typically 100 TeV), where prompt γ-ray emission is howevermore constraining [2].


063008-6

the large number of degrees of freedom result in a p-value

because of the near degenerate nature of the projectedbaseline triangle due to the comparatively short CARMA-SMT baseline; closure phases on trivial triangles (in whichone baseline has zero length) vanish identically. However,the inclusion of a number of additional sites in the nearfuture will result in many additional, open triangles forwhich the closure phases are likely to differ substantiallyfrom zero [18]. These will be instrumental to discriminatingboth between astrophysical and DM-dominated models.

VI. CONCLUSION

In this paper, we have demonstrated the potential of theEHT for DM searches. We have presented the first model ofthe DM-induced synchrotron emission in the close vicinityof a SMBH accounting for strong gravitational lensingeffects. Our conclusions are the following.(1) The synchrotron emission from DM spikes should

be readily visible in EHT images of M87 if present.This remains true even for very small values of theannihilation cross section. The resulting emissionfollows the structure of the DM spike, resulting in asynchrotron halo extending from horizon scales toroughly 100 μas.

(2) Within the spike emission, the silhouette of the BHis clearly visible on small scales for all spins andmodels we considered. This imparts small-scalestructure on the image on scales of 50 μas, andcontributes substantially to the visibilities on longbaselines.

(3) DM spike emission provides an adequate fit to theexisting horizon-scale structural constraints fromthe EHT. This necessarily ignores astrophysicalcontributions associated with the jet launchingregion. Such an additional astrophysical componentis strongly motivated by the existence of extendedemission at wavelengths of 3 mm and longer. Even

within the 1.3 mm data, the fit quality suggests thatthe simple spike structures we present here areincomplete.

(4) Nevertheless, the limits on M87’s flux and small-scale structure place corresponding constraintson the putative DM annihilation cross sections.For a 10 GeV DM candidate this cross sectionmust be less than a few 10−31 cm3 s−1, close to thecharacteristic cross sections for p-wave-suppressedannihilation. The introduction of additional astro-physical components would decrease this limitfurther.

(5) EHT observations in the near future will includea number of additional stations, enabling thereconstruction of M87’s image with substantiallyhigher fidelity. As a result, the limits on the existenceof DM spikes and the properties of DM candidateswill similarly improve. Thus, the EHT opens a new,powerful path to probing the structure and featuresof DM in the centers of galaxies.

ACKNOWLEDGMENTS

This work has been supported by Université Pierreet Marie Curie (UPMC), Centre National de la RechercheScientifique (CNRS) and Science and TechnologyFacilities Council (STFC). This research has also receivedsupport at Institut d'Astrophysique de Paris (IAP) from theEuropean Research Council (ERC) Project No. 267117(DARK) hosted by UPMC, and has been carried out in theInstitut Lagrange de Paris (ILP) Laboratoire d'Excellence(LABEX) (ANR-10-LABX-63) and supported by Frenchstate funds managed by the Agence Nationale de laRecherche (ANR), within the Investissements d’Avenirprogramme (ANR-11-IDEX-0004-02). A. E. B. and M. K.receive financial support from the Perimeter Institutefor Theoretical Physics and the Natural Sciences andEngineering Research Council of Canada through aDiscovery Grant. Research at Perimeter Institute is sup-ported by the Government of Canada through IndustryCanada and by the Province of Ontario through theMinistry of Research and Innovation. We acknowledgesupport by the Canadian Institute for Advanced Researchfor the participation of A. E. B. and J. S. at the annualmeetings of the Canadian Institute for Advanced Research(CIFAR) cosmology program where this project wasinitiated.

APPENDIX A: NORMALIZATION OFTHE DM PROFILE

Here we describe how we normalize the profile corre-sponding to a DM spike growing adiabatically from aninitial power-law profile ρ0ðr=r0Þ−γ [1] at the center of theM87 galaxy:

FIG. 3. Closure phase as a function of universal time, for aSchwarzschild BH (solid) and a maximally rotating BH (dashed),for the current VLBI triangle between Arizona, Californiaand Hawaii.


063008-8

ρðrÞ ¼

8>>>>>><>>>>>>:

0 r < RS;

ρspðrÞρsatρspðrÞ þ ρsat

RS ≤ r < Rsp;

ρ0

�rr0

�−γ�1þ r

r0

�−2

r ≥ Rsp;

ðA1Þ

where the saturation density determined by DM annihila-tions reads

ρsat ¼mDM

hσvitBH; ðA2Þ

where mDM and hσvi are respectively the mass andannihilation cross section of the DM particle, and we taketBH ¼ 108 yr for the age of the BH.9 The spike profile reads

ρspðrÞ ¼ ρR�Rspr

�γsp; ðA3Þ

where ρR ¼ ρ0ðRsp=r0Þ−γ, Rsp ¼ αγr0ðMBH=ðρ0r30ÞÞ1

3−γ andγsp ¼ ð9 − 2γÞ=ð4 − γÞ. We use MBH ¼ 6.4 × 109 M⊙ forthe mass of the BH [6], the corresponding Schwarzschildradius is RS ¼ 6 × 10−4 pc, and we take αγ ¼ 0.1. We fixr0 ¼ 20 kpc for the halo (as for the Milky Way), and wemust then determine the normalization ρ0.We choose ρ0 in such a way that the profile is compa-

tible with both the total mass of the galaxy and the massenclosed within the radius of influence of the BH, of order105RS. We thus follow the procedure described in Ref. [48]:the DM mass within the region that is relevant for thedetermination of theBHmass, typicallywithinR0 ¼ 105RS,must be smaller than the uncertainty on the BH massΔMBH. ρ0 is thus obtained by solving the followingequation:

Z105RS

RS

4πr2ρðrÞdr ¼ ΔMBH; ðA4Þ

with ΔMBH ¼ 5 × 108 M⊙. Considering the complexdependence of ρ on ρ0, we use the fact that the mass isdominated by the contribution from r ≫ RS, i.e. typicallyr > Rmin ¼ Oð100RSÞ. In this regime we have ρ ∼ ρspðrÞ.We can also factorize the dependence on ρ0 in ρsp, ρspðrÞ¼gγðrÞρ

14−γ0 ðR0sp=r0Þ−γðR0sp=rÞγsp , withR0sp ¼ αγr0ðMBH=r30Þ

13−γ,

and we finally obtain

ρ0 ¼� ð3 − γspÞΔMBH4πR

0γsp−γsp r

γ0ðR

3−γsp0 − R

3−γspmin Þ

�4−γ

: ðA5Þ

We take γ ¼ 1, which corresponds to the NFW profile. Thecorresponding spike has a power-law index of γsp ¼ 7=3.Numerically, we get ρ0 ≈ 2.5 GeV cm−3 for γ ¼ 1. Finally,the total mass within 50 kpc is ∼4 × 1012 M⊙, compatiblewith the value derived from observations, 6 × 1012 M⊙ [49].In practice, the saturation radius rsat—for which

ρsat ¼ ρðrsatÞ—is smaller than the Schwarzschild radiusof the BH for all values of the DM mass and annihilationcross section of interest here, so that the DM profile readsmore simply

ρðrÞ ¼

8>>><>>>:

0 r < RS;

ρspðrÞ RS ≤ r < Rsp;

ρ0

�rr0

�−γ�1þ r

r0

�−2

r ≥ Rsp:ðA6Þ

Note that one usually assumes that the DM profile vanishesbelow 4RS (or 2RS from the full relativistic calculation for astatic BH [50]) due to DM particles captured by the BH.Here, for simplicity, to study the potential of the EHT forprobing very steep power-law density profiles, we considera DM spike that goes all the way down to the horizon of theBH, i.e. RS for a Schwarzschild BH and RS=2 for amaximally rotating BH. However, this simplification hasa negligible impact on our results.

APPENDIX B: SOLVING THE COSMIC-RAYEQUATION IN THE PRESENCE OFAN ADVECTION FLOW TOWARDS

THE CENTRAL BH

The propagation equation of electrons and positrons inthe presence of advection and synchrotron losses,

v∂f∂r −

1

3r2∂∂r ðr

2vÞp ∂f∂pþ1

p2∂∂p ðp

2 _pfÞ ¼ Q; ðB1Þ

can be rewritten as

∂f∂r þ

_pad þ _psynv

∂f∂p ¼ −

1

vp2∂∂p ðp

2 _psynÞf þQv; ðB2Þ

where _pad is the momentum gain rate due to adiabaticcompression in the advection process, and vðrÞ is thevelocity field of the accretion flow. The associated char-acteristic curves are obtained by solving the followingdifferential equation:

dpdr

¼ _pad þ _psynv

: ðB3Þ

Generalizing the method of Ref. [20] to an arbitrary power-law profile for the magnetic field, BðrÞ ¼ B0ðr=RSÞ−α=2,solving Eq. (B3) with the initial condition pðRinjÞ ¼ pinjleads to

9For an isotropic DM distribution function, a weak cusp goingas r−1=2 arises instead of a plateau [47].


063008-9

pðr;Rinj;pinjÞ

¼pinj�k0R

α−12

S

ðα−1Þcr32−αpinj

�1−

�rRinj

�α−1

�þ�

rRinj

�12

�−1;

ðB4Þ

where

k0 ¼2σTB20

3μ0ðmecÞ2: ðB5Þ

We consider the case α ¼ 0, corresponding to a homo-geneous magnetic field.The solution of the propagation equation in the ultra-

relativistic regime is then given by

fðr;pÞ¼ 1c

�rRS

�Zracc

rQðRinj;pinjÞ

�RinjRS

�52

�pinjp

�4

dRinj;

ðB6Þwhere pinj ≡ pinjðRinj; r; pÞ is the injection momentum ofan electron injected at Rinj (≥ r) and arriving at r with

momentum p. Using Eq. (B4) and expressing pinj as afunction of p, we obtain, for α ¼ 0

pinjðRinj; r; pÞ ¼ p�k0R

−12

S

cR

32

injp

�rRinj

− 1�þ�Rinjr

�12

�−1:

ðB7Þ

Note that the denominator of pinj can vanish and becomenegative, leading to nonphysical values of the injectionmomentum. This is related to the efficiency of the accretionflow and characterizes the region of the injection parametersðRinj; pinjÞ corresponding to a given arrival point ðr; pÞ. Inpractice, pinj remains positive for Rinj < R0inj where

R0inj ¼ rþc

k0p

�rRS

�−12

: ðB8Þ

We then use this value as an effective upper bound for theintegral of Eq. (B6).

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