Physics Letters B 808 (2020) 135624 Contents lists available at ScienceDirect Physics Letters B www.elsevier.com/locate/physletb X-ray and gamma-ray limits on the primordial black hole abundance from Hawking radiation ∗ ∗ ∗ Guillermo Ballesteros a,b, , Javier Coronado-Blázquez a,b, , Daniele Gaggero a, a Instituto de Física Teórica UAM/CSIC, Calle Nicolás Cabrera 13-15, Cantoblanco E-28049 Madrid, Spain b Departamento de Física Teórica, Universidad Autónoma de Madrid (UAM), Campus de Cantoblanco, 28049 Madrid, Spain a r t i c l e i n f o a b s t r a c t 16 Article history: The non-observation of extragalactic Hawking radiation from primordial black holes of 10 g sets a Received 28 April 2020 conservative strong bound on their cosmological abundance. We revisit this bound and show how it can Received in revised form 4 July 2020 be improved (both in mass reach and strength) by an adequate modeling of the combined AGN and blazar Accepted 13 July 2020 emission in the MeV range. We also estimate the sensitivity to the primordial black hole abundance of Available online 16 July 2020 a future X-ray experiment capable of identifying a significantly larger number of astrophysical sources Editor: M. Trodden contributing to the diffuse background in this energy range. © 2020 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license 3 (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP . 1. Introduction from the observed distribution of white dwarfs [7], as well as from the disruption of neutron stars in the PBH mass range from 19 23 The isotropic background radiation that fills the Universe and 10 g to 10 g [8] has been challenged [9], opening the possibil- 22 extends over more than 16 orders of magnitude in frequency ity that PBHs of mass below ∼ 5 × 10 g –with higher masses –from radio waves all the way up to high-energy gamma rays [1]– being constrained by microlensing [10]– could explain all the carries information on the emission mechanisms of different astro- DM. The lower end of the current PBH mass window for DM, at 17 physical and cosmological sources over the history of the Universe, ∼ 10 g, comes instead from Hawking evaporation limits. As we and can possibly shed further light on the nature of the elusive already mentioned, in this work we focus specifically on extra- dark matter (DM) that constitutes the largest fraction of its mass. galactic gamma-ray bounds from evaporation [4]. However, there We consider the hypothesis that the bulk of the DM is made up are other phenomena, related to Hawking radiation, which have of (non-rotating) black holes of primordial origin (PBHs), formed been used to constrain this low mass region: the Voyager mea- ± from the collapse of overdense Hubble patches prior to the big- surements of e [11], the 511 keV positron-electron annihiliation bang nucleosynthesis epoch [2,3]. We focus on the current PBH line from INTEGRAL [12–14], the non-detection of a neutrino flux mass window for DM ranging from approximately 1017 g to 1019 g, from PBH emission at Superkamiokande [14], distortions on the revisiting the Hawking radiation constraints on their abundance CMB anisotropies [15,16], and the Galactic emission of gamma/X- from extragalactic gamma-ray data [4] and showing how future rays [17](see also [18]). The advantage of the bounds coming from gamma- and X-ray observations1 with an increased sensitivity the possible PBH extragalatic emission is that they are free from have the potential for discovering a population of PBHs compris- Galactic propagation uncertainties. As we will see, making use of ing the totality of the DM. their full potential requires an adequate characterization of the This mass range is indeed particulary relevant for DM, given emission from other astrophysical sources, mostly active galactic that it has been found that previously claimed femtolensing nuclei (AGNs) and blazars. bounds [5]were marred by an inadequate treatment of the in- Hawking radiation [19–23]is an approximately thermal particle volved optics, leaving much of that window open [6]. In addition, emission expected to be emitted by black holes, with temper- ∼ 19 20 = −1 2 2 × −8 the 10% limit on the abundance of PBHs at 10 g – 10 g ature T (8πkB ) c mP /M 6 10 M/M K, being M the mass of the black hole, M = 3 × 1033 g the mass of the Sun and mP = hc¯ /G the Planck Mass. In Ref. [4], a conservative Corresponding authors. * (but nonetheless stringent) upper bound on the cosmological PBH E-mail addresses: [email protected] (G. Ballesteros), 17 abundance was set for M 10 g by comparing the predicted [email protected] (J. Coronado-Blázquez), [email protected] (D. Gaggero). Hawking gamma-ray emission with the isotropic gamma-ray back- 1 The frontier between gamma- and X-rays is not sharply defined. A reasonable ground in the approximate energy range 0.1 MeV — 10 GeV that distinction can be made setting it at ∼ 100 keV. was measured by EGRET [24], Fermi-LAT [25] and COMPTEL [26]. https://doi.org/10.1016/j.physletb.2020.135624 0370-2693/© 2020 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3. 2 G. Ballesteros et al. / Physics Letters B 808 (2020) 135624 This bound has recently been updated in [27](with the data from the same experiments), finding a good agreement with [4]. The main focus of our analysis is on the isotropic gamma- and X-ray background in the 10 keV – MeV domain. Using a power-law modeling of such background –motivated by the assumption that a population of unresolved extra-Galactic sources (mainly AGNs and blazars) represent the main contribution to it– we place an up- per limit on the abundance of PBHs (as a function of their mass) by considering an array of datasets acquired by a variety of in- struments over the latest decades. We also estimate the expected improvement in the bounds from a putative future experiment. We do so by assuming that such a (more sensitive) experiment will re- solve a significantly larger number of individual AGNs and blazars and will therefore provide a lower isotropic unresolved background for energies above ∼ 200 keV. We show that, under this assump- tion, a significantly better upper limit on the PBH abundance than Fig. 1. Cosmic X-ray background spectrum, as measured by various experiments. the current one may be placed in the future. This result motivates Overimposed are the Ueda+14 model (blue dashed line), the fit to a double power- the investment in future gamma- and X-ray experiments in this law (black dashed line) of Eq. (4), and the corrections to the latter due to two range, as well as in further theoretical studies geared towards a hypothetical monochromatic PBH distributions with different masses M and cos- mological abundances f = / . more precise modeling of astrophysical sources. PBH DM 2. Hawking radiation from PBHs and X-rays. The integrand in (1) decreases very rapidly with z and accurate results are obtained integrating up to z ∼ O(100). The photon emission from a population of PBHs of mass M ac- 3. The X-ray and gamma-ray AGN background counting for a fraction f = PBH/DM of the total DM density in the Universe is There has been a considerable effort dedicated to interpreting − dN c ρ e τ (z) the measurements of the X-ray and gamma-ray background from M = = f dz M [(1 + z)E] , (1) ∼ dE dt 4π M H(z) keV energies all the way up to 100 GeV in terms of a super- position of a large number of unresolved extra-Galactic sources. −30 3 where ρ = 2.17 × 10 g/cm is the current DM density of the In particular, the data in the range ∼ 5–200 keV observed by Universe [28], and H(z) is the Hubble rate of expansion as a func- Swift/BAT [30], MAXI [31], ASCA [32], XMM-Newton [33], Chandra tion of redshift. The function M [E] denotes the differential flux [34] and ROSAT [35]are well reproduced by a population syn- emitted by a single PBH, as a function of the energy E, per unit of thesis model of active galactic nuclei (AGNs) developed by Ueda 16 energy and time. For PBHs of masses above 10 g is well approx- et al. in [36](see the blue dotted line in Fig. 1). AGNs are pow- 2 imated by the primary Hawking emission: ered by gas accretion onto a supermassive black hole and are very efficient X-ray emitters. The model of [36]is based on the extrap- −1 M [E]=(2πh¯ ) s/(exp(E/kB T ) − 1), (2) olation of the luminosity functions of AGNs in different redshift ranges inferred by a sample of 4039 AGNs in soft (up to 2 keV) where the so-called grey factor s is a function of M and E. and/or hard X-ray bands (>2 keV). The objects in the sample in- In the high-energy limit E kB T , the grey factor approximately clude both Compton-thin and Compton-thick AGNs (with the latter 2 2 2 satisfies s ∝ (M/mP ) (E/mP c ) ; whereas for E kB T , s ∝ being heavily obscured by dust). As can be seen if Fig. 1, this AGN 4 2 4 (M/mP ) (E/mP c ) [22].