The Deep Newtonian Regime in Late-Time Blast Waves: Inevitable Transition and Distinct Flux Signatures

TL;DR

This paper develops an analytic framework for the deep Newtonian regime in late-time astrophysical blast waves, revealing its impact on synchrotron emission and flux signatures in various transient phenomena.

Contribution

It introduces a unified model for synchrotron emission in the deep Newtonian phase, applicable to different ejecta types, and quantifies its effects on observed flux and spectral evolution.

Findings

Deep Newtonian transition occurs at specific times for GRB afterglows, affecting decay rates.

Neglecting the deep Newtonian phase leads to underestimating radio flux in kilonova remnants.

The model constrains ambient density and outflow energetics from radio observations.

Abstract

In many astrophysical transients, outflows drive shocks into the ambient medium, accelerating electrons to non-thermal energy distributions that produce broadband synchrotron emission. At late times, even initially collimated relativistic jets evolve into quasi-spherical Newtonian blastwaves. As the shock decelerates, the post-shock internal energy per particle decreases; below a critical velocity $\beta_{\rm DN} \approx 0.2$, only a fraction $\xi_e < 1$ of electrons are accelerated to relativistic energies, defining the deep Newtonian (DN) regime. We develop a unified analytic framework for synchrotron emission in this phase, applicable to both single-velocity and stratified ejecta. For gamma-ray burst afterglows in a uniform medium, the DN transition occurs at $t_{\rm DN} \approx 3.7\,E_{51}^{1/3} n_0^{-1/3}$~yr, yielding a shallower decay by $\delta\alpha = 6(p-2)/5$ relative to standard Newtonian predictions. For kilonova remnants ($E_0 = 10^{50.5}$~erg, $M_{\rm ej} = 0.1\,M_\odot$), the DN phase begins prior to deceleration; neglecting it underestimates radio flux by factors of $\sim 3$--$5$ during coasting and even more thereafter. Magnetar-boosted remnants ($E \sim10^{52}$~erg) should reach $\sim$\,10\,--\,100\,$\mu$Jy at 3~GHz at $\sim$\,40\;Mpc, though limits on GW170817 already disfavor a long-lived millisecond magnetar. In core-collapse supernovae in a wind medium ($\rho\!\propto\!r^{-k}$), the peak luminosity remains constant during coasting, while $\nu_{\rm pk} \propto t^{-1}$; for SN~2023ixf, we find $k = 1.29 \pm 0.14$. The DN spectral energy distribution typically satisfies $\nu_m\!<\!\nu_{\rm sa}\!<\!\nu_c$, peaking at sub-GHz frequencies where LOFAR and SKA-low are most sensitive. Even non-detections place robust constraints on ambient density and outflow energetics.