Genesis of Axion Dark Matter via Black Hole and Cosmic String Dynamics

TL;DR

This work investigates whether axion dark matter can arise from the dynamics of cosmic axion strings contracted around a Schwarzschild black hole. By deriving the loop energetics and performing numerical analyses across primordial to supermassive black holes and a wide range of axion decay constants, the authors show that central black holes substantially speed up string-loop decay and drive substantial energy release into axions, with a smaller share into gravitational waves. The total radiated energy spans $~10^{27}$ GeV to $~10^{53}$ GeV, with axion emission dominating over gravitational waves by a factor set by $P_{\rm GW}/P_{\varphi} \approx \mathcal{O}(10) (v/m_{\rm p})^2 \ll 1$, but even the upper end remains below the Galactic DM energy scale $\sim 10^{68}$ GeV, suggesting a non-negligible yet not dominant contribution to galactic dark matter. The results imply potential observational signatures via the decay-time behavior and co-emitted gravitational waves, motivating more detailed modeling of evolving BH masses and more complex string configurations to assess the mechanism's cosmological relevance.

Abstract

The global $U_{PQ}(1)$ Peccei-Quinn (PQ) symmetry, proposed to resolve the strong CP problem, predicts the existence of the axion, a pseudo Nambu-Goldstone boson and a leading dark matter candidate. The spontaneous breaking of this symmetry generates global strings that decay predominantly via the emission of massive axions and gravitational waves. In this work, we investigate the decay of cosmic axion strings in the vicinity of a Schwarzschild black hole and estimate the corresponding energy losses and decay timescales of the resulting string loops. For primordial black holes (PBHs) with masses as small as $10^{-16} M_\odot$, the total energy radiated by the contracting strings is found to be on the order of $10^{27} \, \mathrm{GeV}$, accounting for both axion and gravitational radiation. Our analysis shows that the presence of a central black hole considerably accelerates string loop decay, leading to significantly reduced lifetimes. These results constitute an initial exploration of whether axion radiation from PBH-cosmic string systems could provide a non-negligible contribution to the dark matter content of galactic halos. The study also identifies the decay time as a potentially valuable observational signature. Further detailed modeling will be necessary to assess the cosmological implications of this mechanism more precisely.

Figures (7)

• Figure 1: Depiction of the spherical cell considered for the cosmic string-black hole system
• Figure 2: $\Delta E$ for varying black hole mass $(M)$
• Figure 3: $\Delta E$ for varying decay constant ($f_a$)
• Figure 4: $\Delta E$ for varying black hole mass $(M)$ and decay constant $f_a$
• Figure 5: $\Delta E$ corresponding to the GWs (green dotted line) and particle emission (purple line) for varying mass