Astrophysical positronium and Dicke superradiance

TL;DR

This work investigates whether astrophysical Dicke superradiance can occur in spin-flip transitions, focusing on the hydrogen 21 cm line and the positronium spin-flip line. It provides a Maxwell-Bloch–based framework and derives key limits, such as the causality bound $N\le\frac{4}{3}\omega\tau_0$ and the ideal burst dynamics with a delay $T_D$ and peak scaling $I\propto N^2$, while accounting for non-ideal dephasing through $T_{dph}$ and Doppler effects. The study yields quantitative estimates for ideal and non-ideal conditions, discusses possible astrophysical pumping scenarios, and explores observational signatures, including the intriguing suggestion that the Wow! signal might be related to hydrogen SR. The results highlight a potential new radiative-coherence mechanism in space that could produce brief, powerful bursts and provide novel probes of inverted populations and positronium production near energetic astrophysical sources.

Abstract

Dicke superradiance is a fascinating phenomenon in which a large number of atoms cooperate to produce a brief and very intense burst of spontaneous emission. This phenomenon has been well studied in the laboratory, but its astrophysical aspects have only recently attracted the attention of a small number of researchers. Since the phenomenon of Dicke superradiance is relatively little known to the wider astrophysical community, we provide a fairly detailed review of its elementary theory in the appendix and speculate on the significance of superradiance for astrophysical hydrogen and positronium, given the abundant formation of the latter near the galactic center.

Figures (3)

• Figure 1: Radiance $\iota T_R$ of ideal samples of atoms of hydrogen (left) and of positronium (right) as a function of dimensionless time $t_-/T_R$. The number of atoms is maximal and corresponds to (\ref{['eq138']}). Red dashed line -- small Bloch angle approximation $\iota T_R\approx \theta_0^2 \,I_1(q)^2/q^2$.
• Figure 2: Radiance $\iota T_R$ of a non-ideal sample of positronium atoms as a function of dimensionless time $t_-/T_R$. The number of atoms is maximal and corresponds to (\ref{['eq138']}), but dephasing effects with a common time scale $T_{dph}$ are present. The solid curve corresponds to $T_{dph}=400\,T_R$, the dashed blue curve corresponds to $T_{dph}=300\,T_R$, and the dashed red curve corresponds to $T_{dph}=200\,T_R$.
• Figure 3: An illustration of a classical analogue in which Dicke superradiance can occur: $N$ identical magnets with magnetic moment $\mu$ each, precessing in a constant external magnetic field $\bf{B}$ with angular velocity $\boldsymbol{\omega}$ under the action of the radiation reaction. The inset shows the configuration of a typical magnet precessing in the magnetic field $\bf{B}$. The scale of $r_i$ as appears in the figure is used only for the purpose of a clear illustration. Both the gray horizontal circle in the $(x,y)$ plane and the vertical dotted lines between it and the magnets are imaginary objects; they were added only to help picturing the group of magnetic dipoles in the $3D$ space around the origin.