Detecting dark objects with plasma microlensing by their gravitational wakes

TL;DR

This work investigates plasma microlensing produced by gravitational wakes of moving masses in a partially ionized interstellar medium. It develops two analytic wake models—collisionless and damped acoustic—and computes the associated electron-column-density and lensing signals within a thin-lens framework, comparing wake-induced lensing to turbulence and to gravitational microlensing. The key finding is that wakes can yield a large-area plasma lens and a characteristic magnification sequence (initial brightening followed by dimming) as the wake passes, but detectable signals from stellar-mass objects are typically limited by ISM turbulence; only much heavier objects or nonlinear wake effects are likely to be observable in typical conditions. The study highlights the potential of plasma microlensing as a complementary channel for discovering or constraining dark massive objects, while noting practical challenges and inviting further exploration of nonlinear regimes and multi-event associations.

Abstract

A moving mass makes a gravitational wake in the partially ionized interstellar medium, which acts as a lens for radio-frequency light. Consequently, plasma microlensing could complement gravitational microlensing in the search for invisible massive objects, such as stellar remnants or compact dark matter. This work explores the spatial structure of the plasma lens associated with a gravitational wake. Far away from the moving mass, the characteristic lensing signal is the steady demagnification or magnification of a radio source as the wake passes in front of it at the speed of sound. Sources can be plasma lensed at a much greater angular distance than they would be gravitationally lensed to the same degree by the same object. However, only the wakes of objects greatly exceeding stellar mass are expected to dominate over the random turbulence in the interstellar medium.

Figures (8)

• Figure 1: Gravitational wake from a supersonic point-like object of mass $M=30~\mathrm{M}_\odot$ traveling to the right at $|\bm{v}|=200~\mathrm{km}\,\mathrm{s}^{-1}$ through the interstellar medium. The pictures show a thin slice of the gas density contrast $\delta\equiv\delta n/\bar{n}$ evaluated under the collisionless approximation (upper middle panel; section \ref{['sec:collisionless']}), the damped acoustic approximation (lower middle panel; section \ref{['sec:damping']}), and an idealized acoustic description (bottom panel; appendix \ref{['sec:idealized']}). At top, we show for comparison the gravitational potential scaled to comparable units.
• Figure 2: Excess column density $N_e$ (upper panel) and approximate lensing magnification $2\kappa$ (lower panel) due to the gravitational wake of a $30$-$\mathrm{M}_\odot$ object moving to the right at $200~\mathrm{km}\,\mathrm{s}^{-1}$. More precisely, $\kappa$ is the lensing convergence, and we assume the observation distance $d=1~\mathrm{kpc}$ and wavelength $\lambda=15~\mathrm{m}$. We use the collisionless approximation (section \ref{['sec:collisionless']}), which is appropriate for the length scales depicted. An image is magnified (red) if the source is behind the outside part of the wake and demagnified (blue) if the source is behind the interior. For comparison, we also show the Einstein radius $r_\mathrm{E}$ (dotted line), which corresponds roughly to the size of the gravitational lens associated with the same object. Outside the wake, the figure contains some artifacts due to the difficulty of numerically integrating equation (\ref{['f_collisionless']}).
• Figure 3: Excess column density $N_e$ (upper panels) and approximate lensing magnification $2\kappa$ (lower panels) due to the gravitational wake of an object of mass $30~\mathrm{M}_\odot$ moving to the right at $200~\mathrm{km}\,\mathrm{s}^{-1}$ (left-hand panels) or $20~\mathrm{km}\,\mathrm{s}^{-1}$ (right-hand panels). Here $\kappa$ is the lensing convergence, and we assume an observation distance of $1~\mathrm{kpc}$ and wavelength $\lambda=15~\mathrm{m}$. We show much larger length scales than figure \ref{['fig:conv_close']} and accordingly employ the damped acoustic approximation (section \ref{['sec:damping']}). The gravitational Einstein radius $r_\mathrm{E}$ is indicated with a black dot.
• Figure 4: Definitions of $l$ and $l_\perp$ for the wake of an object moving to the right. $l$ is the distance from the object along the edge of the Mach cone, which has half-angle $\arctan w$ (see equation \ref{['w']}). $l_\perp$ is the distance from the edge, defined such that $l_\perp<0$ corresponds to positions outside the cone.
• Figure 5: Structure of the edge of the gravitational wake of a dark object of mass $30~\mathrm{M}_\odot$ moving at $200~\mathrm{km}\,\mathrm{s}^{-1}$. For a range of distances $l$ from the object (different colors), we show the excess column density $N_e$ as a function of the perpendicular distance $l_\perp$ from the edge of the Mach cone associated with the wake. $l_\perp$ is defined such that $l_\perp<0$ lies outside the cone, and we show it in units of the acoustic damping scale $\sigma_\mathrm{coll}$ (which depends on $l$). We show both the damped acoustic description (solid curves) and the collisionless description (dashed curves, only shown for $l\leq 1000~\mathrm{au}$). For comparison, the dotted line indicates the simplified description of equation (\ref{['column']}), which closely matches the damped acoustic approximation at large $l$.