Probing Exotic Astrophysical Dark objects through Astrometric Microlensing from Gaia

Abstract

We present the first comprehensive study of astrometric microlensing by exotic astrophysical dark objects, focusing on two theoretically motivated models -- Q-ball and boson star. We demonstrate that these extended objects generate distinctive signatures that depart markedly from point-mass lenses like primordial black holes. The smoking-gun signature for these exotic objects is the emergence of caustics, which form when the lens radius is below a critical threshold. Crossing these caustics induces discontinuous jumps in the images-centroid trajectory, a distinctive feature of these extended dark objects. We show these patterns are sensitive to the internal mass profile, with boson stars generating larger, more prominent caustic structures than Q-balls -- enabling the models to be distinguished. Using the Gaia DR3 stellar catalogue, we forecast a high-yield discovery potential, up to $\sim 6000$ detectable astrometric microlensing events for a 10-year mission, peaking for $M \sim 1-10~M_\odot$ and $R \lesssim 10~\text{AU}$. In the absence of anomalous detections, Gaia can set powerful 90% confidence level constraints on the fractional abundance of these exotic objects, reaching $f_{\mathrm{DM}} \le 10^{-3}$ in the peak region which covers masses from $10^{-1}-10^{7}~M_{\odot}$ and radii $R<10^{6}~\text{AU}$. Crucially, these projected astrometric microlensing constraints are significantly stronger than existing photometric microlensing limits in the $1-10~M_\odot$ mass range. This work establishes astrometric microlensing with Gaia as a powerful, complementary, and near-future probe with the potential to discover exotic astrophysical dark objects.

Figures (20)

• Figure 1: The plot displays a heuristic estimate of the mass and size of EADOs that can be probed by Gaia Gaia:2016zol. The blue-shaded region indicates Gaia’s sensitivity to such lenses for AML. For comparison, we also show the PML sensitivity of other surveys: EROS Croon:2018ybs, OGLE Croon:2018ybs, and HSC-Subaru Croon:2020ouk, highlighting the complementarity of these observational probes in constraining EDS populations. For Gaia, the maximum lens radius relevant for AML is approximately $\sim R_{\text{\tiny E}}^2/(\sigma_{\text{\tiny a,min}}D_{\text{\tiny L}})$. For the estimation of the maximum probe-able radius, $R_{\text{\tiny L,max}}(M_{\text{\tiny L}})$, we assume a source distance of $D_{\text{\tiny S}}=8.5$ kpc, a lens distance of $D_{\text{\tiny L}}=D_{\text{\tiny S}}/2$, and a minimum astrometric uncertainty of $\sigma_{\text{\tiny a,min}}=0.05~\text{mas}$. Furthermore, the lower bound on the lens radius for each survey is given by the Schwarzschild radius, $R_{\text{\tiny Sch}}$ corresponding to the EADO, while the upper bound for surveys probing PML signatures is of the order of the maximum Einstein radius, $R_{\text{\tiny E}}$, accessible in that survey. Below the grey dashed line (drawn at $\sim 0.01 R_{\text{\tiny E}}$ ), the AML signal of EADOs effectively behave as point-like objects. The minimum and maximum EDS masses accessible to a given survey are determined by comparing the survey cadence and total observation time with the characteristic microlensing event timescale. Refer to Sec. \ref{['sec:AML_class']} for further details.
• Figure 2: We display the density profiles of mini-boson stars (BS, solid lines) and thin-wall Q-balls (u, dashed lines) for EADO mass $M_{\text{\tiny L}} \sim 2.2\,\textup{M}_\odot$ (for which we get the most stringent constraint) with different radii. The mini-boson star profiles are obtained by solving the Schrödinger–Poisson system of equations, Eqs. \ref{['eq:app_bs_einstein_tt_final']}, \ref{['eq:app_bs_kg_weak_eq_final_sch']}, and \ref{['eq:app_bsmini_bos_star_density']}, with boson mass $m \simeq (0.28,1.59,2.8,8.9)\times 10^{-14}\,\text{eV}$ corresponding to radii $R_{\text{\tiny 99,BS}} \simeq (10^2,10,1,0.1)\,\text{AU}$ respectively. As expected, boson stars have a higher mass distribution closer to the center compared to thin-wall Q-balls (modeled as uniform-density spheres), which instead display an almost flat core profile followed by a sharp drop at the boundary.
• Figure 3: A schematic representation illustrates an extended lens, an observer (O), a point source (S), and image position (I) within a lensing scenario. The center of a spherically symmetric extended lens with total mass $M_{\text{\tiny L}}$ is taken as the origin and is located at an angular diameter distance $D_{\text{\tiny L}}$ from an observer (O). The source (S) is located at an angular diameter distance $D_{\text{\tiny S}}> D_{\text{\tiny L}}$ from the observer, and the angular diameter distance between the lens and the source is denoted as $D_{\text{\tiny LS}}$. Light rays illustrated by the solid line travel along the $z$ direction, with an impact parameter $\chi$ with the lens is deflected by an angle $\hat{\theta}_{\text{\tiny D}}$. The angular positions of the source and the image as seen by the observer are denoted by $\theta_{\text{\tiny S}},~\theta_{\text{\tiny I}}$, respectively and $\theta_{\text{\tiny D}}\equiv \theta_{\text{\tiny I}}-\theta_{\text{\tiny S}}$ . The lens plane is shown at the centre, passing through the lens.
• Figure 4: In the left panel, we present the lens equation for the UDS lens (see Eq. \ref{['eq:aml_eds_uds_lens_eq_1']}) as a function of the image position $\theta_{\text{\tiny I}}$. The right panel shows the corresponding centroid shifts, $\Delta\theta_{\text{\tiny cent}}$ (see Eq. \ref{['eq:aml_rev_cent_shift']}), as a function of the source position $\theta_{\text{\tiny S}}$. The curves are plotted for several values of the scaled radius, $R_{\text{\tiny u}}/R_{\text{\tiny E}}=(0.1,0.5,1,\sqrt{3/2},3.0)$. The kink in the centroid shift for $R_{\text{\tiny u}}/R_{\text{\tiny E}}=(0.1, 0.5, 1)$ arises when the source crosses a caustic. For comparison, the point-lens case is indicated by the black dashed line. All angular quantities are normalised with respect to $\theta_{\text{\tiny E}}$. See text for more details.
• Figure 5: Illustration for the solutions to the lens equation. Left panel: Case with $R_{\text{\tiny u}} < R_{\text{\tiny u,crit}}=\sqrt{3/2}~R_{\text{\tiny E}}$. Right panel: Case with $R_{\text{\tiny u}} > R_{\text{\tiny u,crit}}=\sqrt{3/2}~R_{\text{\tiny E}}$. The lens is located at the center. The lens equation and source position are shown by the blue and yellow curves, respectively. The sky blue, green, and red solid lines represent the three image positions. For a given source position $\theta_{\text{\tiny S}}$, we draw a horizontal line whose intersection with the lens equation identifies the image positions along the $x$-axis. The red dashed horizontal line marks the caustic, $\theta_{\text{\tiny S}} = \theta_{\text{\tiny S,caust}}$. For $R_{\text{\tiny u}} < R_{\text{\tiny u,crit}}$, when the source lies beyond the caustic ($\theta_{\text{\tiny S}} > \theta_{\text{\tiny S,caust}}$), only one image (referred to as Image I) is formed. However, for the source position near the caustic ($\theta_{\text{\tiny S}} \lesssim \theta_{\text{\tiny S,caust}}$, two additional images (referred to as Image II and Image III) appear. In contrast, for $R_{\text{\tiny u}} > R_{\text{\tiny u,crit}}$, no caustic exists, and only a single image (Image I) is present for all source positions. See text for more details