Primordial black holes induced stochastic axion-photon oscillations in primordial magnetic field

TL;DR

This work investigates ALPs produced by ultra-light primordial black holes (PBHs) evaporating before BBN and their stochastic oscillations with photons in the primordial magnetic field (PMF). It combines Hawking-emission calculations for Schwarzschild and Kerr PBHs with a domain-like, both homogeneous and stochastic PMF, applying the latest PMF limits to compute ALP-photon conversion probabilities using a density-matrix formalism. A key finding is that a stochastic PMF can drastically enhance the conversion probability for sizable ALP-photon couplings $g_{a\gamma}$, with the low-energy behavior shaped by the ALP mass $m_a$ and the high-energy regime approaching a plateau, while redshift and recombination absorption modify present-day photon fluxes. These stochastic ALP-photon oscillations could leave imprints in the CMB, CXB, and EGB, offering guidance for current and future ALP searches and photon-ALP phenomenology (e.g., ADMX, IAXO, ALPS-II, LiteBIRD, CMB-S4, THESEUS, eXTP, LHAASO, CTA).

Abstract

Primordial black holes (PBHs) can be produced in the very early Universe due to the large density fluctuations. The cosmic background of axion-like particles (ALPs) could be non-thermally generated by PBHs. In this paper, we investigate the ALPs emitted by ultra-light PBHs with the mass range $10 \, {\rm g} \lesssim M_{\rm PBH} \lesssim 10^9 \, \rm g$, in which PBHs would have completely evaporated before the start of Big Bang Nucleosynthesis (BBN) and can therefore not be directly constrained. In this case, the minimal scenario that ALPs could interact only with photons is supposed. We study the stochastic oscillations between the ALPs and photons in the cosmic magnetic field in detail. The primordial magnetic field (PMF) can be modelled as the stochastic background field model with the completely non-homogeneous component of the cosmic plasma. Using the latest stringent limits on PMF, we show the numerical results of ALP-photon oscillation probability distributions with the homogeneous and stochastic magnetic field scenarios. The PBH-induced stochastic ALP-photon oscillations in the PMF may have the effects on some further phenomena, such as the cosmic microwave background (CMB), the cosmic X-ray background (CXB), and the extragalactic gamma-ray background (EGB).

Figures (5)

• Figure 1: The instantaneous spectra of the spin-0 particle emitted by a black hole as a function of energy. The different panels correspond to the Schwarzschild black holes and Kerr black holes (with $a_*=0.5$, $0.75$, and $0.99$). The black, blue, and red lines correspond to the PBH masses $M_{\rm PBH}=10^5\, \rm g$, $10^7\, \rm g$, and $10^9\, \rm g$, respectively.
• Figure 2: The distributions of ALP-photon oscillation probability in the $m_a-g_{a\gamma}$ plane for several typical energy values. The top, middle, and bottom panels correspond to $E=10^{-3}\, \rm GeV$, $1\, \rm GeV$, and $10^{3}\, \rm GeV$, respectively. The left and right panels represent $B_T=47\,\rm pG$ and $5\,\rm nG$, respectively.
• Figure 3: Same as figure \ref{['fig_pa_contour_1']} but for different energy values. The top, middle, and bottom panels correspond to $E=10^{4}\, \rm GeV$, $10^{5}\, \rm GeV$, and $10^{6}\, \rm GeV$, respectively. The left and right panels represent $B_T=47\,\rm pG$ and $5\,\rm nG$, respectively.
• Figure 4: Effective magnetic field strength distributions for the stochastic magnetic field scenario with 100 domains for $1\, \rm Mpc$. The blue and red lines correspond to the magnetic field strength in each domain with the two stochastic magnetic field configurations. The dot-dashed black lines represent $|B_T| = 8.9\, \rm pG$.
• Figure 5: ALP-photon oscillation probability in the stochastic magnetic field as a function of energy with the limit $B<8.9\, \rm pG$. Several typical ALP parameter sets [$m_a=10^{-10}\, \rm eV$, $g_{a\gamma}=10^{-9}\, \rm GeV^{-1}$] (a), [$m_a=10^{-8}\, \rm eV$, $g_{a\gamma}=10^{-9}\, \rm GeV^{-1}$] (b), [$m_a=10^{-10}\, \rm eV$, $g_{a\gamma}=10^{-10}\, \rm GeV^{-1}$] (c), and [$m_a=10^{-8}\, \rm eV$, $g_{a\gamma}=10^{-10}\, \rm GeV^{-1}$] (d) are selected for comparisons. The brown and orange bounds represent the $1\sigma$ and $2\sigma$ contours with 1000 random magnetic field configurations, respectively. The blue lines represent the oscillation probability with the random one configuration.