The "Little Dark Dot": Evidence for Self-interacting Dark Matter in the Strong Lens SDSS J0946+1006?

TL;DR

This work tests whether the extremely compact dark perturber in SDSS J0946+1006 can be explained by a core-collapse SIDM halo. Using an isothermal Jeans framework to build SIDM density profiles and a mirror-based evolution to model core collapse, the authors connect internal structure to lensing observables and compare against observed constraints. They find that a halo with $M_{200}\sim 10^{11}\,M_\odot$ at a specific evolutionary stage can reproduce the lensing signal, but such a mass would ordinarily host a visible galaxy, conflicting with current luminosity limits unless future observations reveal a faint counterpart. The study also shows that fitting a core-collapse SIDM halo with a CDM-based profile (tNFW) biases inferred parameters, underscoring the need for careful modeling and motivating JWST and future surveys to test SIDM predictions and the prevalence of such compact perturbers.

Abstract

Previous studies, based on precise modeling of a gravitationally lensing image, have identified what may be an extremely compact, dark perturber in the well-known lensing system SDSS J0946+1006 (the "Jackpot"). Its remarkable compactness challenges the standard cold dark matter (CDM) paradigm. In this paper, we explore whether such a compact perturber could be explained as a core-collapse halo described by the self-interacting dark matter (SIDM) model. Using the isothermal Jeans method, we compute the density profiles of core-collapse halos across a range of masses. Our comparison with observations indicates that a core-collapse halo has an inner density profile and mass enclosed within 1 kpc that fit the data well, but only if the halo has a total mass $\sim10^{11}~{\rm M_{\odot}}$. While a halo of this mass should host a detectable galaxy, the current observational upper limit on the perturber's luminosity remains uncertain. Resolving whether or not the data support the presence of a core-collapse SIDM halo therefore requires future deep observations to measure its luminosity.

Figures (10)

• Figure 1: The temporal evolution of the central density $\rho_0$ (left panel) and velocity dispersion $\nu_0$ (right panel) of an SIDM core with $M_{200}=1\times10^{11}~{\rm M_\odot}$. Considering the degeneracy between the formation time $t_{\rm age}$ and the scattering cross section $\sigma_{m}$, we choose their product as the horizontal axis, with time measured in units of the cosmic time of J0946+1006 (11.06 Gyr). The blue, orange, and magenta scatter points represent the evolution for the low-density solution, high-density solution, and mirrored high-density solution, respectively. The moments corresponding to $t_{\rm merge}$ and $t_{\rm coll}$ are marked by a green dashed line and a purple dashed-dotted line, respectively. The black dots represent the moments we chose to examine the evolution of the SIDM profile, while the red star represents the moment closest to the result of Minor2021 in the 2D observational space.
• Figure 2: The density and mass profiles of a core-collapse SIDM halo with $M_{200}=10^{11}~{\rm M_\odot}$ (corresponding to the evolutionary stage indicated by the red star in Fig. \ref{['fig:evolution']}) and its CDM counterpart. SIDM and CDM profiles are shown in blue and black, respectively. Left: 3D density profiles, with the blue vertical dashed-dotted line marking the stitching radius, $r_1$. Middle: 2D projected surface density profiles. Right: 2D enclosed mass profiles.
• Figure 3: Compare the results of constructed SIDM halos with J0946+1006 observations in the parameter space defined by $\gamma_{\rm 2D}~{\rm (1~kpc)}$ and $M_{\rm 2D, tot}~{\rm (<1~kpc)}$. The evolutionary trajectories of SIDM halos with different masses are represented by color-coded curves, where dots indicate the starting points of post-$t_{\rm merge}$ evolution. The black dashed square shows the 3$\sigma$ measurement uncertainty of Minor2021. For the SIDM halo with $M_{200} = 10^{11}~{\rm M_\odot}$, a red star marks the moment when it most closely matches the results from Minor2021. Fitting results for different models from Despali2024 are represented by markers of various shapes. Our tNFW fitting results derived from the mock lensing image are represented by a green point with $1\sigma$ error bars.
• Figure 4: The evolution of the 3D density profiles (left panel), the 2D projected surface density profiles (middle panel), and the 2D enclosed mass profiles (right panel) during the post-$t_{\rm merge}$ stage for an SIDM halo with $M_{200} = 1\times10^{11}~{\rm M_\odot}$. The black curves represent the density profiles prior to the turning point identified in Fig. \ref{['fig:compare']}, with line darkness increasing to indicate temporal evolution. The red curve corresponds to the final snapshot after the turning point. In the left panel, the values of $t_{\rm age} \cdot \sigma_m$ (in units of 11.06 ${\rm Gyr\cdot cm^2/g}$) are labeled below each line.
• Figure 5: Left: the MGE fitting result for the density profile of the input SIDM halo. The 3D density profile of the perturber is shown as a gray line, while the MGE fitting result is represented by a navy dashed line. The relative error is illustrated in the bottom subplot. Right: the mock lensing image, with the red cross representing the position of the input SIDM halo.