Line-of-sight effects on double source plane lenses

Abstract

Weak gravitational lensing perturbations have a non-negligible impact on strong lensing observables, and several degeneracies exist between the properties of the main lens, line of sight, and cosmology. In this work, we consider the impact of the line of sight on double-source-plane lenses (DSPLs), a rare class of lens systems in which two sources at different redshifts are lensed by the same foreground galaxy, and which enable competitive constraints on the dark energy equation of state. Generating and sampling statistically representative lines of sight from N-body simulations, we show that line-of-sight perturbations add a $\sim1\%$ uncertainty to measurements of the cosmological scaling factor $η$ (a ratio of angular diameter distance ratios), which is subdominant but non-negligible compared to the measurement error. We also show that the line-of-sight shear experienced by images of the two sources can differ significantly in both magnitude and direction. Including a line-of-sight error budget, we measure $w=-1.17^{+0.19}_{-0.21}$ from the Jackpot DSPL in combination with Planck. We show that the line of sight is expected to introduce an additional scatter in the constraints possible with a larger sample of DSPLs from Euclid, but that this scatter is subdominant compared to other sources of error.

Figures (8)

• Figure 1: $\kappa_{\mathrm{os}}(z_{\mathrm{s}})$, the convergence between the observer at $z=0$ and a source at $z_{\mathrm{s}}$, for a random sample of 10 lines of sight. The datapoints taken from the RalGalGroup simulations are plotted as crosses, and the interpolated convergence between them as solid lines.
• Figure 2: On the left, the probability density function for $\eta^\mathrm{inferred}/\eta-1$, and on the right, the probability density function for $|g_{\mathrm{LOS,2}}-\eta \, g_{\mathrm{LOS,1}}|$, for the Jackpot lens. In blue, we consider values corresponding to the first and second source planes ($z_{\mathrm{s_1}} = 0.609$, $z_{\mathrm{s_2}} = 2.035$), and in orange, we consider values corresponding to the first and third source planes ($z_{\mathrm{s_1}} = 0.609$, $z_{\mathrm{s_2}} = 5.975$). The standard deviation of the bias on $\eta$ is 0.67% for the inner pair of rings, and 1.3% for the outer pair.
• Figure 3: Expected fractional error on $\eta$ arising from the line of sight as a function of $\eta$, for a sample of $\sim 1700$ forecasted Euclid DSPLs. The colour of the points shows this error as a fraction of the error on $\eta$ from measurement uncertainties.
• Figure 4: Expected differences arising from the line of sight between $g_{\mathrm{LOS,2}}$ (the true "external shear" acting on the images of s$_2$) and $\eta \, g_{\mathrm{LOS,1}}$ for a sample of $\sim1700$ forecasted Euclid lenses, as a function of the deflector redshift $z_{\mathrm{d}}$, with $\eta$ shown as the colours of the points.
• Figure 5: Constraints on $w$ and $\Omega_{\mathrm{m}}$ in a flat-$w$CDM cosmology. Shown in blue are the constraints from the Jackpot lens alone, where the uncertainty from the line of sight added in quadrature to the measurement error reported in Smith_2022. In gray are the constraints from PlanckPlanck_2020, and in red are the combined constraints from the Jackpot lens and Planck. The combined constraints give a value of $w=-1.17^{+0.19}_{-0.21}$.