Using Strong Lensing to Detect Subhalos with Steep Inner Density Profiles

TL;DR

This work probes how a subhalo's inner density slope $\beta$ shapes its strong-lensing detectability. By simulating HST-, Euclid-, and JWST-like data with a gNFW subhalo across a range of masses ($M_{200}$) and slopes, the authors show that Steep profiles ($\beta=2.2$) yield far stronger lensing signals than NFW ($\beta=1$) or Cored ($\beta=0.2$), enabling detections at masses more than an order of magnitude lower along the Einstein ring. The analysis uses Bayesian model comparison via $\Delta\ln\varepsilon$ and evaluates robustness to subhalo position, data quality, and lens-model multipoles, finding that Steep subhalos remain detectable even when macro-model flexibility is increased or a pixelized source reconstruction is used. These results imply a powerful discriminator between CDM and SIDM scenarios and motivate applying these methods to upcoming large lens samples from Euclid and JWST to constrain the diversity of subhalo inner density profiles.

Abstract

The inner region of a subhalo's density distribution is particularly sensitive to dark matter microphysics, with alternative dark matter models leading to both cored and steeply-rising inner density profiles. This work investigates how the lensing signature and detectability of dark matter subhalos in mock HST-, Euclid-, and JWST-like strong lensing observations depends on the subhalo's radial density profile, especially with regards to the inner power-law slope, $β$. We demonstrate that the minimum-mass subhalo detectable along the Einstein ring of a system is strongly dependent on $β$. In particular, we show that subhalos with $β\sim 2.2$ can be detected down to masses over an order-of-magnitude lower than their Navarro-Frenk-White (NFW) counterparts with $β\sim 1$. Importantly, we find that the detectability of subhalos with steep inner profiles is minimally affected by increasing the complexity of the main lens galaxy's mass model. This is a unique characteristic of these subhalos, as those with NFW or shallower profiles become essentially undetectable when multipole perturbations are added to the lens model. The results of this work highlight how the underlying dark matter physics can significantly impact the expected number of subhalo detections from strong gravitational lensing observations. This is important for testing Cold Dark Matter against alternatives, such as Self-Interacting Dark Matter, which predict the existence of subhalos with diverse inner density profiles.

Figures (12)

• Figure 1: Left: Dark matter density profiles as a function of three-dimensional radius, $r$, for a subhalo of mass $M_{\rm 200} = 10^9$ M$_\odot$ and a concentration ($c_{\rm gNFW}$) of 13.5, which is set based on the 2016MNRAS.460.1214L mass-concentration relation. The results are shown for the Cored ($\beta=0.2$), NFW ($\beta=1$), and Steep ($\beta=2.2$) subhalo profiles in purple, blue, and red, respectively. The black dashed line marks the $r_{200}$ radius for these subhalos. Right: Subhalo deflection-angle strength as a function of projected distance from the subhalo, $R$, for the same three subhalos as on the left. On the top axis, we use the angular diameter distance to the lens plane to convert the physical distance to angular distance. For small $R$, the subhalo's deflection strength strongly depends on its inner slope.
• Figure 2: Mock HST- (left), Euclid- (center), and JWST-like (right) observations of the macro system described in Sec. \ref{['sec:macro']}. Subhalos in the HST-like data are positioned at a projected location in the lens plane of either (0.3, 1.3) or (0.3, 2.3), labeled as On-Ring and Offset, respectively. Subhalos in the Euclid- and JWST-like data are positioned only at the On-Ring position. For each image, the color bar represents the intensity of the data normalized by the maximum intensity of each image. The images shown here are noiseless (see Sec. \ref{['sec:fitting']} for further discussion).
• Figure 3: Difference between the total marginalized Bayesian evidence of the lens model with and without a subhalo component as a function of the true mass of the subhalo in the data. Points are only shown for data sets from the HST On-Ring suite with $\Delta\ln\varepsilon> 5$, which results in no Cored subhalos being shown. Blue (red) points correspond to data sets with an NFW (Steep) subhalo. The black dashed line marks the $\Delta\ln\varepsilon=50$ threshold used for detectability. Steep subhalos become detectable at a mass of $5.4\times10^8$ M$_\odot$, while NFW subhalos remain undetectable until a mass of $6.0\times10^9$ M$_\odot$, over an order of magnitude above the minimum detectable Steep subhalo mass.
• Figure 4: Posterior probabilities for the subhalo parameters inferred for the HST On-Ring Steep (red) and NFW (blue) subhalos. The left plot is for the $10^{10}$ M$_\odot$ Steep and NFW subhalos. The right plot is for the subhalo in the HST On-Ring suite with a mass closest to the minimum value detectable for each density slope. The true value of each parameter is marked by the vertical line of the corresponding color. Since both the Steep and NFW subhalos in the left corner plot correspond to the same subhalo mass and concentration, there is only one vertical truth line shown for each. The 2D contours correspond to the 68% and 95% confidence regions. In both cases, the subhalo mass and inner slope are well-recovered, with the uncertainties decreasing at higher mass. The posterior distributions for concentration are not constrained as well, but still consistent with the true values.
• Figure 5: Minimum Cored (purple), NFW (blue), and Steep (red) subhalo mass detectable for all variations explored in this work. An upper arrow is used to indicate when subhalos remain below the detectability threshold even for the maximum subhalo mass used ($10^{10}$ M$_\odot$). Steep subhalos are significantly more detectable in all variations except for the HST Offset (Multipole) case. Remarkably, the minimum-mass detectable for Steep subhalos is barely affected by adding multipoles to the lens model.