SHARP -- IX. The dense, low-mass perturbers in B1938+666 and J0946+1006: implications for cold and self-interacting dark matter

Abstract: We present an extended analysis of the gravitational lens systems SDSS J0946+1006 and JVAS B1938+666. We focus on the properties of two low-mass dark matter haloes previously detected in these systems and compare them with predictions from different dark matter models. In agreement with previous studies, we find that the object H detected in J0946+1006 is a dark-matter-dominated subhalo. Object A, in B1938+666, is a foreground halo at $z = 0.13\pm0.07$, contradicting previous analyses which suggested this object to be located either within or at higher redshift than the lens. Given the new redshift for this object, we update the 3$\sigma$ upper limit on its luminosity to $L_V < 6.3 \times 10^5 {(z/0.13)}^2 L_{V,\odot}$. By selecting central galaxies from the TNG50 hydrodynamical simulation, we find that analogues with projected mass density profiles around the robust radius of $\sim$ 91 pc and luminosities consistent with detection A can be found, although they lie near the edge of the halo distribution in the relevant mass and redshift ranges. We conclude, therefore, that this object is an atypical but possible event in $\Lambda$CDM. The projected mass density profile of both detections over the well-constrained range of radii may be consistent with expectations from SIDM gravothermal fluid model if the effective self-interaction cross-section $\sigma_{c,0}/m_{\rm{dm}}$ is of order $300 \ \rm{cm}^2 g^{-1}$ or larger.