Probing a minimal dark gauge sector via microlensing of compact dark objects

TL;DR

This work investigates whether a minimal Dark Standard Model with a dark $U(1)$ gauge sector can be constrained by purely gravitational observations. It develops gauged scalar solitons (gauged boson stars) for a spin-0 field with mass $μ$ and charge $q$, derives their mass–radius relations and a maximum mass $M_{\max}$, and confronts them with microlensing limits that exclude asteroid-mass lenses $M \lesssim 10^{-11} M_\odot$. It finds that asteroid-mass microlensing requires $M_{\max}(q) < 1.48×10^{-8}$ m, translating into a lower bound $μ \gtrsim 13$ eV for a given $q$ and a permitted region with $\tilde{q} < 1/\sqrt{2}$. The study shows that gravitational data can illuminate the internal parameters of the dark sector and point to future gravitational-wave probes and possible effects of self-interactions.

Abstract

We introduce a minimal Dark Standard Model (DSM) consisting of a single spin-0 particle with dark $U(1)$ gauge symmetry, and completely decoupled from the visible sector. Characterized only by the scalar mass $μ$ and the dark charge $q$, this framework naturally gives rise to a rich phenomenology, including stable solitonic configurations that behave as dark "mini-MACHOs". We numerically build and evolve these gauged scalar-field solitons, derive their mass-radius relations, and identify a critical charge beyond which no gravitationally bound configurations exist. By combining these results with microlensing surveys that exclude compact objects heavier than the asteroid-mass scale ($M\lesssim 10^{-11}M_\odot$), we obtain the constraint $μ\gtrsim 10\,\rm eV$ for viable configurations, depending on $q$. Our results represent a step forward in showing that purely gravitational observations can constrain the internal parameters of a dark gauge sector, and provide a framework for exploring broader DSM scenarios through future probes such as gravitational wave detections.

Figures (3)

• Figure 1: Gauge dark matter solitons sequence of solutions. Top panel: Mass vs. radius diagram for families of configurations with different values of $q$. Dashed-line displays the maximum mass configurations. Lower panel: Maximum mass configuration as a function of $q$ in the region where gravitationally bound, and stable configurations exist. Beyond the critical $\tilde{q}_{\rm crit}=1/\sqrt{2}\approx0.707$, no gravitationally bound solutions are found.
• Figure 2: Summary of current microlensing limits on MACHO dark matter fraction as a function of lens mass. The solid black lines mark the $95\%$ confidence level exclusion boundaries from recent surveys: Niikura et al. Niikura:2017zjd covers the sub-lunar window around $10^{-11}-10^{-6}\,M_\odot$, Smyth et al. Smyth:2019whb covers the Earth–Jupiter range $10^{-6}-10^{-3}\,M_\odot$, Wyrzykowski et al. Wyrzykowski:2011tr covers the stellar range $\sim10^{-1}-10\,M_\odot$, and Blaineau et al. Blaineau:2022nhy covers the intermediate range $10-10^3\,M_\odot$. The red-shaded regions within these curves are excluded.
• Figure 3: Constraints in the plane $(\mu,q)$ parameter space derived from the non-observation of microlensing events. The shaded region indicates the values of the scalar-field mass $\mu$ and coupling $q$ consistent with current MACHO limits. Larger masses are excluded by Eq. \ref{['eq:constraint']}.