PHYSICAL REVIEW LETTERS 123, 251101 (2019) Primordial Black Holes as a Dark Matter Candidate Are Severely Constrained by the Galactic Center 511 keV γ-Ray Line Ranjan Laha * Theoretical Physics Department, CERN, 1211 Geneva 23, Switzerland (Received 25 June 2019; revised manuscript received 9 October 2019; published 16 December 2019) We derive the strongest constraint on the fraction of dark matter that can be composed of low mass primordial black holes by using the observation of the Galactic Center 511 keV γ-ray line. Primordial black holes of masses ≲1015 kg will evaporate to produce eÆ pairs. The positrons will lose energy in the Galactic Center, become nonrelativistic, then annihilate with the ambient electrons. We derive robust and conservative bounds by assuming that the rate of positron injection via primordial black hole evaporation is less than what is required to explain the SPI/INTEGRAL observation of the Galactic Center 511 keV γ-ray line. Depending on the primordial black hole mass function and other astrophysical uncertainties, these constraints are the most stringent in the literature and show that primordial black holes contribute to less than 1% of the dark matter density. Our technique also probes part of the mass range which was completely unconstrained by previous studies. DOI: 10.1103/PhysRevLett.123.251101 Introduction.—Is it possible to constrain the primordial a few hundred M⊙. PBHs are one of the oldest candidates black hole (PBH) density such that it cannot contribute to of dark matter, and their abundance has been studied in a the entire dark matter density over its viable mass range? Answering this question will have important implications 0 for the search of the identity of dark matter and inflationary 10 dynamics which can give rise to PBHs [1–6]. In this Letter, we take one step toward answering this question. We show Iso 1.5 kpc that combining the observation that light PBHs can produce Cosmic rays −rays Æ CMB e −1 pairs via evaporation [7] with the fact that an intense 10 NFW 1.5 kpc gamma Iso 3 kpc 511 keV γ-ray line has been observed in the Galactic Center NFW 3 kpc – [8 15] can efficiently constrain PBHs in a mass range which cannot yet be constrained by any other technique. DM The morphology of the 511 keV γ-ray line (it has a bulge f and a disk component) is such that primordial black 10−2 holes, acting as the dark matter, cannot explain the entire emission. We do not yet know the source of these low- energy astrophysical positrons; therefore an understanding Monochromatic of the underlying astrophysical source(s) [16–20] can −3 further improve our constraints. 10 Cosmic rays The identity of dark matter is one of the most enduring 13 14 mysteries of physics. Numerous astrophysical and cosmo- 10 10 M (kg) logical observations give an irrefutable indication of the PBH presence of dark matter, yet an absence of its microphysical FIG. 1. Upper limits on the fraction of dark matter which can be understanding drives a great deal of research. A large composed of primordial black holes for monochromatic mass number of dark matter candidates have been proposed in distribution. The black lines show the limits derived in this Letter. −22 the literature, and these range in masses from ∼10 eV to These limits depend on the dark matter density near the Galactic Center (NFW and isothermal) and the propagation of low-energy positrons. While deriving the limit for the “3 kpc” (“1.5 kpc”) Published by the American Physical Society under the terms of constraint, we assume that low-energy positrons can travel about the Creative Commons Attribution 4.0 International license. a kiloparsec (100 pc) before annihilating. The upper limits from Further distribution of this work must maintain attribution to Voyager 1 (two lines denote the propagation and background the author(s) and the published article’s title, journal citation, uncertainties) [7], Planck [80], and γ-ray observatories [21,81] and DOI. are in red dotted lines. 0031-9007=19=123(25)=251101(8) 251101-1 Published by the American Physical Society PHYSICAL REVIEW LETTERS 123, 251101 (2019) number of ways. The various constraints on PBHs arise shown in Fig. 1 by the black solid and dashed lines. Various from evaporation (and the subsequent detection of standard black lines indicate the dependence of this upper limit on model particles), capture on astronomical bodies, lensing the underlying astrophysical parameters. A part of this observations, dynamics of galaxies, gravitational wave parameter space is already probed by γ-ray observations, observations, and accretion [21–44]. The recent detection cosmic microwave background (CMB) observations, and of gravitational waves from binary black hole mergers Voyager 1 measurements. Our constraints are stronger than [45,46] have rekindled an interest in the contribution these and probe a new mass range of PBHs. Our constraints of PBHs to the dark matter energy density [47–49]. This close a part of a mass window where PBHs could have has led to a detailed reanalysis of older constraints contributed to the entire dark matter energy density of the [22,41,42,50], research into new ways to constrain PBHs Universe. Our technique introduces a new electromagnetic (for e.g., lensing of fast radio bursts [51,52] and other probe of PBHs beyond what has already been discussed in techniques [53,54]), and the study of spinning PBHs the literature [79]. [55–57]. A detailed study of older constraints has shown Formalism.—In natural units, the temperature of a black M that there are viable regions of parameter space where hole of mass BH is [82,83] primordial black holes can satisfy the entire dark matter 1 1010 kg density [22,58]. Reference [7] pointed out that PBHs with T ¼ ¼ 1.06 GeV; ð1Þ 14 Æ BH 8πG M M masses ≲10 kg can produce e pairs via Hawking N BH BH radiation, and such a process can be constrained via the where GN denotes Newton’s gravitational constant. The observations of the Voyager 1 satellite [59,60]. This temperature of the black hole also dictates the rate at which eÆ naturally leads us to wonder about the fate of pairs particles are produced via evaporation. The energy spec- produced via PBH evaporation in the Galactic Center. trum of these particles follows the distribution [84] PBHs are much more numerous in the Galactic Center than Z dN Γ 1 in the solar circle (where the Voyager 1 observations were s ¼ s dt ; ð Þ dE 2π ðE=T Þ − ð−1Þ2s 2 made), and thus a stronger bound can be expected if there is exp BH an appropriate observable. Thus, we are led to the question: is there an observable in the Galactic Center which points to where the dimensionless absorption probability is denoted Γ s E the fact that eÆ pairs are copiously present there? by s, where denotes the particle spin, and denotes the – The answer is yes. There is a smoking gun signature energy of the emitted particle [84 87]. Since the positrons which indicates that there is a huge reservoir of low-energy in our case of interest are semirelativistic to nonrelativistic, positrons near the Galactic Center. For many decades, an we use the full formula of the dimensionless absorption enduring astrophysical mystery is the observation of probability as in Eq. (6) of Ref. [84]. The values of the σ 511 keV γ-ray line at the Galactic Center (see Ref. [11] absorption cross section s is taken from Fig. 1 of Ref. [87]. for a historical account). This γ-ray line has been observed We also take into account the factor of 2 for the two by a number of observatories and a detailed study has been chiralities of the positron in the full formula of the made by the SPI/INTEGRAL observatory. Despite the dimensionless absorption probability. Since a black hole T intense scrutiny of this signal, we do not yet know the loses mass via evaporation, BH is a function of time. In our origin of this signal. Many viable astrophysical models calculation, we will use the observed positron injection (i.e., models which do not require a dark matter origin of luminosity of over one year, and the mass loss during this the 511 keV signal) have been proposed [19,61–71], time is negligible for the black hole masses that we T although none are confirmed to be the source of these consider. As such, BH will be a constant for a given low-energy positrons. A detailed morphological study of black hole mass in our Letter. this signal and its absence in the dwarf galaxies [72] The Galactic Center 511 keV γ-ray line has been indicate that this it is not produced via dark matter observed for a few decades, and its origin has remained interactions [73] (see, however, Ref. [74] for a particle unknown throughout. Recent attempts at measuring the dark matter model which can explain the signal). Earlier Doppler shifts have also not led to the identification of the studies trying to connect PBHs and the Galactic Center source [10] (note that a similar search technique has also 511 keV line can be found in Refs. [75–78]. Thus, any been proposed for the 3.5 keV line [88,89]). The observed astrophysical source (present in the Galactic Center/ flux of this γ-ray line indicates that the rate of positron Galactic bulge) which produces low-energy positrons annihilation at the Galactic Center is ∼6.3 × 1050/yr [11]. can be constrained via this observation.