Physics Letters B 820 (2021) 136459 Contents lists available at ScienceDirect Physics Letters B www.elsevier.com/locate/physletb Gas heating from spinning and non-spinning evaporating primordial black holes ∗ Ranjan Laha a,b, Philip Lu c, Volodymyr Takhistov c,d, a Theoretical Physics Department, CERN, 1211 Geneva, Switzerland b Centre for High Energy Physics, Indian Institute of Science, Bangalore 560012, India c Department of Physics and Astronomy, University of California, Los Angeles, Los Angeles, CA, 90095-1547, USA d Kavli Institute for the Physics and Mathematics of the Universe (WPI), UTIAS, The University of Tokyo, Kashiwa, Chiba 277-8583, Japan a r t i c l e i n f o a b s t r a c t Article history: Primordial black holes (PBHs) from the early Universe constitute a viable dark matter (DM) candidate and 15 Received 21 October 2020 can span many orders of magnitude in mass. Light PBHs with masses around 10 g contribute to DM Received in revised form 15 June 2021 and will efficiently evaporate through Hawking radiation at present time, leading to a slew of observable Accepted 15 June 2021 signatures. The emission will deposit energy and heat in the surrounding interstellar medium. We revisit Available online 29 June 2021 the constraints from dwarf galaxy heating by evaporating non-spinning PBHs and find that conservative Editor: J. Hisano constraints from Leo T dwarf galaxy are significantly weaker than previously suggested. Furthermore, we analyze gas heating from spinning evaporating PBHs. The resulting limits on PBH DM abundance are found to be stronger for evaporating spinning PBHs than for non-spinning PBHs. © 2021 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 Usually, PBHs are assumed to be non-rotating (Schwarzschild) [57– 1 59]. However, PBHs can be formed with significant spin (Kerr Primordial black holes (PBHs), formed in the early Universe BHs) [22–26,61,62]. BH spin will affect the Hawking radiation, prior to any galaxies and stars, are a viable candidate for DM (e.g., generally increasing the emission while favoring particles with [1–31]). Depending on formation, PBHs surviving until the present larger spin [39,41,63,64]. Furthermore, the mass limit of ∼ 2.5 × ∼ 15 −19 can span many orders of magnitude in mass, from 10 g to 10 M for PBHs below which their lifetime is smaller than the 10 well over 10 M. They can account for the entirety of the DM in age of the Universe varies by a factor of ∼ 2for maximally ro- −16 −10 the mass window ∼ 10 − 10 M, where there are no obser- tating PBHs [63,65,66]. Besides mass (and electric charge), angular vational constraints [32–38]. While significant attention has been momentum constitutes a fundamental conserved parameter of a devoted to larger mass PBHs, it has been realized recently that BH. Hence, it is important to explore the implications of spin for light PBHs can result in a larger variety of observable signatures observations [35,44,65–68]. than previously thought and is thus ripe for further exploration. Recently, observations from dwarf galaxies (in particular, Leo T) −16 Light PBHs with mass 10 M existing at present time will have been used to constrain stellar and intermediate-mass PBHs by be evaporating and copiously emitting particles through Hawk- considering heating of interstellar medium (ISM) gas due to PBH × ing radiation [39]. Non-rotating PBHs with masses below 2.5 interactions [69]. This represents a new signature not previously −19 10 M have lifetimes smaller than the age of the Universe and considered for PBHs. Subsequently, Ref. [70] considered heating of thus do not contribute to DM abundance [40,41]. Particle emission ISM gas due to light evaporating non-rotating PBHs. from currently evaporating PBHs produces a variety of signatures, In this work, we revisit and provide an alternative treatment of providing insight into this region of PBH DM parameter space. gas heating due to evaporating PBHs, focusing on the dwarf galaxy Leading constraints on light PBHs have been obtained from ob- Leo T. We find that a more detailed, conservative, and proper treat- servations of photon flux [42–45], cosmic microwave background ment of energy deposition from PBH emission results in signifi- [46–49], electron and positron cosmic rays [50], 511 keV gamma- cantly weaker constraints than reported in the analysis of Ref. [70]. ray line [35,51–56], as well as neutrinos [35]. Furthermore, we study gas heating due to evaporating PBHs with significant spin. * Corresponding author. E-mail addresses: [email protected] (R. Laha), [email protected] (P. Lu), [email protected] (V. Takhistov). 1 Heavier PBHs can also efficiently acquire spin via accretion [60]. https://doi.org/10.1016/j.physletb.2021.136459 0370-2693/© 2021 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. R. Laha, P. Lu and V. Takhistov Physics Letters B 820 (2021) 136459 19 −2 This study is organized as follows. In Sec. 2, we discuss emis- 10 cm and the mass column density as mHnHrs = 1.627 × −4 −2 sion and generate the spectrum for spinning and non-spinning 10 gcm . The velocity dispersion of the HI gas in this re- PBHs. In Sec. 3, we describe properties of target system Leo T gion σv = 6.9km/s[80,82,83]suggests a gas temperature of T dwarf galaxy. In Sec. 4, we discuss the energy deposition and heat- 6000 K. In contrast to the case of PBH accretion emission analysis ing in dwarf galaxies from evaporating PBHs, focusing on Leo T. In [69], the velocity dispersion and distribution of the HI gas and DM Sec. 5, we discuss gas cooling and thermal balance with heating. are not as relevant here as long as they remain non-relativistic. Finally, we summarize in Sec. 6. 4. Gas heating by evaporating PBHs 2. Evaporating black hole emission As proposed in Ref. [69], accretion emission from heavier PBHs An un-charged2 rotating (Kerr) PBH radiates at a temperature will deposit energy and heat the gas in surrounding interstellar given by [40,41,63,73–75] medium. It was subsequently suggested that emitted particles from evaporating light PBHs can also deposit energy and heat surround- 1 1 − a∗2 ing gas [70]. Below, we revisit gas heating due to non-rotating T = , (1) PBH evaporating PBHs with an improved treatment. We also extend our 4π GMPBH 1 + 1 − a∗2 study of gas heating to emission from rotating evaporating PBHs. = where G is the gravitational constant, MPBH and a∗ JPBH/ For our PBH masses of interest, both photon as well as elec- 2 (GMPBH) are the PBH mass and reduced spin Kerr parameter, tron/positron emission channels from evaporating PBHs can con- for a PBH with angular momentum J . In the limit a∗ → 0, PBH tribute to heating. In Ref. [70], photon heating contribution has Eq. (1)reduces to the usual Hawking evaporation temperature of a − been assumed negligible due to power law scaling of photo-electric 16 1 Schwarzschild BH, T 1.1MeV M /10 g . The temper- −3.5 PBH PBH cross-section σPE ∝ E when photon energies are above keV. ature is seen to be significantly diminished for a Kerr BH in the However, for photon energies around MeV that are typical to our limit a∗ → 1. study, the cumulative photon interaction cross-section levels out, Evaporating PBHs start to emit significant quantities of a given primarily due to Compton scattering contribution (see Fig. 33.19 of particle as the BH temperature reaches the particle mass, and at Ref. [84]). The average heating rate due to photon emission of PBH high temperatures the emission spectrum resembles that of black- of mass M and spin a∗ is given by [69] body radiation [40]. For spin-1/2 particles, the emission peak oc- PBH ∞ curs at E 4.03 TPBH [75]. At lower BH masses, secondary emis- 2 d Nγ − sion channels due to quark and gluon QCD jets become relevant. τ Hγ (MPBH,a∗) = fh(E)E 1 − e dE , (3) For primary emission, the number of particles, Ni , emitted per dtdE 0 unit energy per unit time is given by [40,41,63,73–75] where fh(E) ∼ O(1) is the fraction of photon energy loss deposited 2 d Ni 1 i(E, MPBH,a∗) as heat, and τ = mHnHrs/λ is the optical depth of gas in terms of = , (2) dtdE 2π eE /TPBH ± 1 the absorption length λ. We take the cumulative photon absorp- dof tion length from Ref. [84]. We assume that the photon deposits where the graybody factor i (E, MPBH, a∗) encodes the probabil- heat similarly to electrons of the same energy. Hence, we approxi- ity that the emitted particle overcomes the gravitational well of mate the fraction of energy deposited as heat to be similar to that 0.7 the BH, E is the total energy of a particle when taking BH ro- of electrons, fh(E) = 0.367 + 0.395(11 eV/(E − me)) [70,85–87], tation into account, the ± signs are for fermions and bosons, re- where me is the electron mass. The efficiency of photon heating is spectively, and summation is over considered degrees of freedom. rather poor, with the heat deposited within Leo T from character- − Secondary emission of particles from QCD jets can be computed istic MeV photons with λ 10 g/cm2 being only ∼ 10 5 fraction numerically [76].