Ultra Light Boson Dark Matter and Event Horizon Telescope Observations of M87* 1, 1, Hooman Davoudiasl ∗ and Peter B. Denton y 1Department of Physics, Brookhaven National Laboratory, Upton, NY 11973, USA The initial data from the Event Horizon Telescope (EHT) on M87∗, the supermassive black hole at the center of the M87 galaxy, provide direct observational information on its mass, spin, and accretion disk properties. A combination of the EHT data and other constraints provide evidence 9 that M87∗ has a mass 6:5 10 M and dimensionless spin parameter a∗ > 0:5. These deter- ∼ × 21 j j minations disfavor ultra light bosons of mass µb 10− eV, within the range considered∼ for fuzzy dark matter, invoked to explain dark matter distribution∼ on kpc scales. Future observations of ∼ M87∗ could be expected to strengthen our conclusions. INTRODUCTION its production in the early Universe. These interactions could then result in its detection in a variety of labora- Black holes (BHs) are at the same time simple and tory experiments. Nonetheless, DM has only been ob- mysterious. They are characterized by only a few pa- served through its gravitational effects in astrophysics rameters - mass, spin, and charge - and are considered and cosmology. Therefore, purely gravitational probes purely gravitational objects. Yet their essential character of DM provide the most model-independent approach to is quite enigmatic: they represent a one-way exit (up to constraining its properties. quantum effects [1]) from the causally connected Uni- It turns out that BHs, themselves purely gravitational, verse, and their internal properties are masked by an can provide a unique probe of ultra light DM states event horizon that is the point of no return. The most through the mechanism of superradiance [5{14]. That direct evidence for their existence has until very recently is, roughly speaking, a spinning BH will lose its angular been provided by the observation of gravitational waves momentum very efficiently if a boson with a particular from binary mergers ascribed to black holes [2]. This sit- mass exists in the spectrum of physical states. This is uation changed upon the release of a first ever image of only a condition on the mass of the boson and does not the M87∗ supermassive black hole (SMBH) at the center depend on whether the boson has any non-gravitational of the Messier 87 (M87) galaxy, by the Event Horizon interactions. In fact, the boson does not even need to Telescope (EHT) [3]. In some sense, this is the most have any ambient number density, since quantum fluctu- direct evidence for BHs, as it manifests their defining ations suffice to populate a boson cloud around the BH characteristic: a region of space from which no matter by depleting its spin. and light can escape. The superradiance mechanism can then provide an in- The EHT imaging of M87∗ through a worldwide net- teresting probe of DM states that would be otherwise work of radio telescopes is a historic scientific accom- practically inaccessible to experiments. These states in- plishment. Future observations of this and other SMBHs clude ultra light axions [15{17] and vector bosons [18] will usher in a new age of radio astronomy where direct that can appear in various high energy frameworks, such data on their event horizons and associated accretion dy- as string theory. For extremely small masses µb (21 22) ∼ namics become available and will get increasingly more 10− − eV such states can also address certain ob- precise. There are numerous astronomical questions that servational features of the DM distribution on scales of kpc; this class of bosons is often referred to as fuzzy could be addressed with such observations and we can ∼ expect new and interesting questions to arise as well. DM [19{21] (for a fuzzy DM model based on infrared dy- However, it is also interesting to inquire whether the im- namics, see Ref. [22]). We will show that the results of pressive new EHT data on M87∗ could also be used to the EHT collaboration on the spin of the M87∗ SMBH [23] can probe and constrain this interesting regime of arXiv:1904.09242v1 [astro-ph.CO] 19 Apr 2019 shed light on fundamental questions of particle physics and cosmology. ultralight DM masses. In this letter, we use the results of the EHT collabo- ration on the parameters of M87∗ in the context of par- ticle physics, and in particular ultra light bosons. These SUPERRADIANCE OVERVIEW states could potentially provide motivated candidates for dark matter (DM), one of the most important open fun- Black hole superradiance leads to the growth of the bo- damental questions of physics. Dark matter constitutes son population once its energy ! satisfies the condition the dominant form of matter in the Universe, making b (see, for example, Refs. [15, 16]) up 25% of its energy density [4], with at best feeble ∼ couplings to the visible world. It is generally assumed ! b < Ω ; (1) that DM has non-gravitational interactions that led to m H where m is the magnetic quantum number of the boson, to a mass estimate of (6:5 0:7) 109 M [23]. This is ± × associated with its angular momentum. Here, ΩH is the fairly consistent with previous estimates that are in the angular velocity of the BH event horizon related to the di- [3:5; 7:2] 109 M range [24{26]. 2 × mensionless spin parameter a∗ JBH=(GN MBH) [0; 1) The shortest timescale that could be relevant for a ≡ 2 7 by SMBH is the Salpeter time τSalpeter 4:5 10 years [27] which is the case for when material∼ is accreting× on 1 a∗ ΩH = ; (2) to the object at the Eddington limit. In Ref. [18] they 2 2rg 1 + p1 a∗ τ τ = − conservatively take BH Salpeter 10 to account for the possibility of super-Eddington∼ accretion. Observations where rg GN MBH, GN is Newton's constant, and MBH 5 ≡ of M87∗, however, show that M=_ M_ Edd 2:0 10− is the BH mass. In the above expression JBH is the BH ∼ × angular momentum. [23] consistent with previous measurements [28] which In addition to the condition in eq.1, there is another suggests that the relevant timescale is much longer. We τ 9 condition that must be met for superradiance to deplete conservatively take BH = 10 years as our fiducial value the spin of a BH, since the accretion time is much longer. In addition, in the last billion years there was likely only one merger Γb τBH ln Nm ; (3) event which involved a much smaller galaxy and was un- ≥ likely to significantly affect the spin of M87∗ [29]. We where τBH is the characteristic timescale of the BH, Nm also note that the dependence of the ultra light boson 1=7 is the final occupation number of the cloud after the BH limits on τBH is at most τBH− . spins down by ∆a∗, The final parameter that remains to be observation- 2 ally constrained, and perhaps the most important in this GN MBH∆a∗ Nm ; (4) context, is the spin. The EHT checked if various spin ' m configurations are consistent with the data. They found that a = 0 is inconsistent with the data, while spins and Γb is the growth rate of the field for b S; V (scalar ∗ 2 f g a∗ 0:5 up to a∗ = 0:94 (as high as their analysis or vector). The leading contribution for Γb is different for j j ≥ j j scalars and vectors and, up to a factor of 2, we have goes) are consistent with the data, although there was ∼ no analysis made of any spins 0 < a∗ < 0:5 [23]. This j j 1 8 9 leads to an approximate estimate of a∗ > 0:5 which re- ΓS = a∗rgµS ; (5) j j 24 lies strongly on the observed jet power to rule out the 6 7 ΓV = 4a∗rgµV : (6) smaller spins. The EHT collaboration takes a very con- servative estimate of the jet power [23]. A separate de- For an observation of a BH mass and spin, an upper tailed analysis was performed which finds a∗ = 0:9 0:1 ± and lower limit on µb can be placed (that is, demanding [30] which we take as our fiducial value and uncertainty. that superradiance has not depleted the spin of the BH by ∆a∗) by, RESULTS µb > ΩH ; (7) or Using eqs.7,8, and9, it is possible to constrain light bosons across a range of masses. We assume that the 1=9 24 ln Nm largest value of ∆a∗ is 1 a∗ where a∗ is the spin today. µS < 8 ; (8) − a∗rgτBH We report the 1 σ results accounting for the uncertainties 1=7 in the mass and spin as described in the previous section, ln Nm µV < 6 ; (9) as well as a factor of two in the uncertainty in the the- 4a∗rgτBH oretical calculation of Γb. Then we find that M87∗ rules where we used the fact that for the dominant mode one out light bosons in the following ranges, has m = 1 for both scalars and vectors. That is, if the 21 21 2:9 10− eV < µS < 4:6 10− eV ; (10) constraint in eq.7 applies to a larger mass than the con- × × 22 21 straint in eq.8 or9, the mass range of ultra light bosons 8:5 10− eV < µV < 4:6 10− eV ; (11) × × in between is ruled out. as shown in fig.1 which also includes the constraint from 9 the lighter Ark 120 with MBH = 0:15 10 M and EHT OBSERVATIONS OF M87 × ∗ a∗ = 0:64 [18, 31{33].