QUANTUM gravitational effects are usually ignored in calculations of the formation and evolution of black holes. The justification for this is that the radius of curvature of space-time outside the event horizon is very large compared to the Planck length (Għ/c3)1/2 ≈ 10−33 cm, the length scale on which quantum fluctuations of the metric are expected to be of order unity. This means that the energy density of particles created by the gravitational field is small compared to the space-time curvature. Even though quantum effects may be small locally, they may still, however, add up to produce a significant effect over the lifetime of the Universe ≈ 1017 s which is very long compared to the Planck time ≈ 10−43 s. The purpose of this letter is to show that this indeed may be the case: it seems that any black hole will create and emit particles such as neutrinos or photons at just the rate that one would expect if the black hole was a body with a temperature of (κ/2π) (ħ/2k) ≈ 10−6 (M/M)K where κ is the surface gravity of the black hole1. As a black hole emits this thermal radiation one would expect it to lose mass. This in turn would increase the surface gravity and so increase the rate of emission. The black hole would therefore have a finite life of the order of 1071 (M/M)−3 s. For a black hole of solar mass this is much longer than the age of the Universe. There might, however, be much smaller black holes which were formed by fluctuations in the early Universe2. Any such black hole of mass less than 1015 g would have evaporated by now. Near the end of its life the rate of emission would be very high and about 1030 erg would be released in the last 0.1 s. This is a fairly small explosion by astronomical standards but it is equivalent to about 1 million 1 Mton hydrogen bombs. It is often said that nothing can escape from a black hole. But in 1974, Stephen Hawking realized that, owing to quantum effects, black holes should emit particles with a thermal distribution of energies — as if the black hole had a temperature inversely proportional to its mass. In addition to putting black-hole thermodynamics on a firmer footing, this discovery led Hawking to postulate 'black hole explosions', as primordial black holes end their lives in an accelerating release of energy.

Black Hole Explosions

Monthly Notices is one of the three largest general primary astronomical research publications. It is an international journal, published by the Royal Astronomical Society. This article 1 describes its publication policy and practice.

Monthly Notices of the Royal Astronomical Society

We update the constraints on the fraction of the Universe going into primordial black holes (PBHs) over the mass range $10^{-5}$--$10^{50}$ g. Those smaller than $\sim 10^{15}$ g would have evaporated by now due to Hawking radiation, so their abundance at formation is constrained by the effects of evaporated particles on big bang nucleosynthesis, the cosmic microwave background (CMB), the Galactic and extragalactic $\gamma$-ray and cosmic ray backgrounds and the possible generation of stable Planck mass relics. PBHs larger than $\sim 10^{15}$ g are subject to a variety of constraints associated with gravitational lensing, dynamical effects, influence on large-scale structure, accretion and gravitational waves. We discuss the constraints on both the initial collapse fraction and the current fraction of the cold dark matter in PBHs at each mass scale but stress that many of the constraints are associated with observational or theoretical uncertainties and some are no longer applicable. We also consider indirect constraints associated with the amplitude of the primordial density fluctuations, such as second-order tensor perturbations and $\mu$-distortions arising from the effect of acoustic reheating on the CMB, but these only apply if PBHs are created from the high-$\sigma$ peaks of nearly Gaussian fluctuations. Finally we discuss how the constraints are modified if the PBHs have an extended mass function, this being relevant if PBHs provide some combination of the dark matter, the LIGO/Virgo coalescences and the seeds for cosmic structure.

Constraints on Primordial Black Holes

Recent measurements of the cosmic microwave background (CMB) anisotropies by Planck provide a sensitive probe of dark matter annihilation during the cosmic dark ages, and specifically constrain the annihilation parameter ${f}_{\mathrm{eff}}⟨\ensuremath{\sigma}v⟩/{m}_{\ensuremath{\chi}}$. Using new results (paper II) for the ionization produced by particles injected at arbitrary energies, we calculate and provide ${f}_{\mathrm{eff}}$ values for photons and ${e}^{+}{e}^{\ensuremath{-}}$ pairs injected at keV-TeV energies; the ${f}_{\mathrm{eff}}$ value for any dark matter model can be obtained straightforwardly by weighting these results by the spectrum of annihilation products. This result allows the sensitive and robust constraints on dark matter annihilation presented by the Planck collaboration to be applied to arbitrary dark matter models with $s$-wave annihilation. We demonstrate the validity of this approach using principal component analysis. As an example, we integrate over the spectrum of annihilation products for a range of Standard Model final states to determine the CMB bounds on these models as a function of dark matter mass, and demonstrate that the new limits generically exclude models proposed to explain the observed high-energy rise in the cosmic ray positron fraction. We make our results publicly available at http://nebel.rc.fas.harvard.edu/epsilon.

Indirect dark matter signatures in the cosmic dark ages. I. Generalizing the bound on s-wave dark matter annihilation from Planck results

INTEGRAL, (INTErnational Gamma-Ray Astrophysics Laboratory) is an astronomical satellite for observing the gamma-ray sky. It was launched in October, 2002. The use of INTEGRAL is planned for 2 years with a possible extension for up to 5 years. The INTEGRAL spacecraft features 4 instruments: a gamma ray spectrometer, a gamma ray imager, two X-ray monitors and an optical monitoring camera.

The INTEGRAL Mission

We investigate the possibilities for probing MeV dark matter (DM) particles and primordial black holes (PBHs) (for masses $\sim 10^{15}$--$10^{17}$ g) at the upcoming radio telescope SKA, using photon signals from the Inverse Compton (IC) effect within a galactic halo. Pair-annihilation or decay of MeV DM particles (into $e^+ e^-$ pairs) or Hawking radiation from a population of PBHs generates mildly relativistic $e^{\pm}$ which can lead to radio signals through the IC scattering on low energy cosmic microwave background (CMB) photons. We study the ability of SKA to detect such signals coming from nearby ultra-faint dwarf galaxies Segue I and Ursa Major II as well as the globular cluster $\omega$-cen and the Coma cluster. We find that with $\sim 100$ hours of observation, the SKA improves the Planck constraints on the DM annihilation/decay rate and the PBH abundance for masses in the range $\sim 1$ to few tens of MeV and above $10^{15}$ to $10^{17}$ g, respectively. Importantly, the SKA limits are independent of the assumed magnetic fields within the galaxies. Previously allowed regions of diffusion parameters of MeV electrons inside a dwarf galaxy that give rise to observable signals at the SKA are also excluded. For objects like dwarf galaxies, predicted SKA constraints depend on both the DM and diffusion parameters. Independent observations in different frequency bands, e.g., radio and $\gamma$-ray frequencies, may break this degeneracy and thus enable one to constrain the combined parameter space of DM and diffusion. However, the constraints are independent of diffusion parameters for galaxy clusters such as Coma.

Constraints on MeV dark matter and primordial black holes: Inverse Compton signals at the SKA

We present the first observational limits on the predicted synchrotron signals from particle dark matter annihilation models in dwarf spheroidal galaxies at radio frequencies below 1 GHz. We use a combination of survey data from the Murchison Widefield Array (MWA) and the Giant Metre-wave Radio Telescope to search for diffuse radio emission from 14 dwarf spheroidal galaxies. For in situ magnetic fields of $1\text{ }\text{ }\ensuremath{\mu}\mathrm{G}$ and any plausible value for the diffusion coefficient, our limits do not constrain any dark matter models. However, for stronger magnetic fields our data might provide constraints comparable to existing limits from gamma-ray and cosmic-ray observations. Predictions for the sensitivity of the upgraded MWA show that models with dark matter particle mass up to $\ensuremath{\sim}1.6\text{ }\text{ }\mathrm{TeV}$ (1 TeV) may be constrained for a magnetic field of $2\text{ }\text{ }\ensuremath{\mu}\mathrm{G}$ ($1\text{ }\text{ }\ensuremath{\mu}\mathrm{G}$). While much deeper limits from the future low frequency Square Kilometre Array (SKA) will challenge the LHC in searches for dark matter particles, the MWA provides a valuable first step toward the SKA at low frequencies.

Constraints on dark matter annihilation in dwarf spheroidal galaxies from low frequency radio observations

A weakly interacting dark matter candidate is difficult to detect at high-energy colliders like the LHC, if its mass is close to or higher than a TeV. On the other hand, pair annihilation of such particles may give rise to ${e}^{+}{e}^{\ensuremath{-}}$ pairs in dwarf spheroidal galaxies (dSph), which in turn can lead to radio synchrotron signals that are detectable at the upcoming Square Kilometre Array (SKA) telescope within a moderate observation time. We investigate the circumstances under which this complementarity between collider and radio signals of dark matter can be useful in probing physics beyond the standard model of elementary particles. Both particle physics issues and the roles of diffusion and electromagnetic energy loss of the ${e}^{\ifmmode\pm\else\textpm\fi{}}$ are taken into account. First, the criteria for detectability of trans-TeV dark matter are analyzed independently of the particle physics model(s) involved. We thereafter use some benchmarks based on a popular scenario, namely, the minimal supersymmetric standard model. It is thus shown that the radio flux from a dSph like Draco should be observable in about 100 h at the SKA, for dark matter masses up to 4--8 TeV. In addition, the regions in the space spanned by astrophysical parameters, for which such signals should be detectable at the SKA, are marked out.

Heavy dark matter particle annihilation in dwarf spheroidal galaxies: Radio signals at the SKA telescope

We study the potential of the Square Kilometre Array in the first phase (SKA1) in detecting dark matter annihilation signals from dwarf spheroidals in the form of diffuse radio synchrotron. Taking the minimal supersymmetric standard model as an illustration, we show that it is possible to detect such signals for dark matter masses about an order of magnitude beyond the reach of the Large Hadron Collider, with about 100 hours of observation with the SKA1.

Arpan Kar

Papers

Constraints on MeV dark matter and primordial black holes: Inverse Compton signals at the SKA

Constraints on dark matter annihilation in dwarf spheroidal galaxies from low frequency radio observations

Heavy dark matter particle annihilation in dwarf spheroidal galaxies: Radio signals at the SKA telescope

Can Square Kilometre Array phase 1 go much beyond the LHC in supersymmetry search

Constraints on MeV dark matter and primordial black holes: Inverse Compton signals at the SKA