Quantifying the Line-of-Sight Halo Contribution to the Dark Matter Convergence Power Spectrum from Strong Gravitational Lenses

Abstract

Galaxy-galaxy strong gravitational lenses have become a popular probe of dark matter (DM) by providing a window into structure formation on the smallest scales. In particular, the convergence power spectrum of subhalos within lensing galaxies has been suggested as a promising observable to study DM. However, the distances involved in strong-lensing systems are vast, and we expect the relevant volume to contain line-of-sight (LOS) halos that are not associated with the main lens. We develop a formalism to calculate the effect of LOS halos as an effective convergence power spectrum. The multi-lens plane equation couples the angular deflections of consecutive lens planes, but by assuming that the perturbations due to the LOS halos are small, we show that they can be projected onto the main-lens plane as effective subhalos. We test our formalism by simulating lensing systems using the full multi-plane lens equation and find excellent agreement. We show how the relative contribution of LOS halos and subhalos depends on the source and lens redshift, as well as the assumed halo and subhalo mass functions. For a fiducial system with fraction of DM halo mass in substructure f sub = 0.4% for subhalo masses [10 5 − 10 8 ]M , the interloper contribution to the power spectrum is at least several times greater than that of subhalos for source redshifts zs 0.5. Furthermore, it is likely that for the SLACS and BELLS lenses the interloper contribution dominates: f sub 2% (4%) is needed for subhalos to dominate in SLACS (BELLS), which is higher than current upper bounds on f sub for our mass range. Since the halo mass function is better understood from first principles, the dominance of interlopers in galaxy-galaxy lenses with high-quality imaging can be seen as a significant advantage when translating this observable into a constraint on DM.

Line-of-sight effects in strong gravitational lensing

“…Because of its practical simplicity, the tidal approach (external convergence/shear) has been widely used in the modelling of strong-lensing systems. In particular, the external convergence is known to be a key source of uncertainty in the measurement of the Hubble-Lemaître constant H 0 from time-delay cosmography [22][23][24][25][26], while the external shear is essential to explain the observed abundance of quadruply imaged quasars [27,28]. In those examples, line-of-sight perturbations are viewed as additional ingredients which improve strong-lensing models.…”

Domain Adaptation for Simulation-Based Dark Matter Searches Using Strong Gravitational Lensing

“…While we will not consider their impact in this work, it is important to also consider line of sight halos, i.e. interlopers [108][109][110][111]. In some cases their influence may dominate the signal of substructure, so it is important to take care that they are not incorrectly associated with the dark matter halo when working with real data sets (see for example [112]).…”

A forward-modelling method to infer the dark matter particle mass from strong gravitational lenses

“…Recent studies (Li et al 2016(Li et al , 2017Despali & Vegetti 2017;Çağan Şengül et al 2020) have shown that for the lens and source redshifts typical of SLACS lenses, the lensing perturbations mainly arise from line-of-sight haloes. This is fortunate because the irrelevance of uncertain baryon effects, makes line-of-sight haloes a particularly clean probe of a cutoff scale in the halo mass function.…”

“…For example, to simplify the theoretical calculations, a random Gaussian field is often assumed for the convergence, potentially omitting multiplane lensing effects (Schneider 2014;McCully et al 2014). Indeed, recent studies have shown that the expected signal in a ΛCDM universe is dominated by line-of-sight haloes at different redshifts to the lens galaxy as opposed to subhaloes within the lens galaxy itself (Li et al 2016(Li et al , 2017Despali et al 2018;Çağan Şengül et al 2020). Here, we will focus on how the line-of-sight low mass dark matter haloes contribute to perturbations on lensing images.…”

“…To form a visual impression of how the line-of-sight low-mass dark haloes perturb the images, in Fig. 1 we show the effective convergence, as derived from the deflection angles (upper panels; Gilman et al 2019;Çağan Şengül et al 2020), and the corresponding residuals obtained by fitting the smooth lensing model to the image (lower panels). As may be seen from the effective convergence map, even though all low-mass dark matter haloes are modelled as spherical profiles, some are heavily stretched into arc-like features due to multiplane lensing effects 1 , which are difficult to compute analytically.…”