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Galaxy-galaxy strong gravitational lenses have become a popular probe of darkmatter (DM) by providing a window into structure formation on the smallestscales. In particular, the convergence power spectrum of subhalos withinlensing galaxies has been suggested as a promising observable to study DM.However, the distances involved in strong-lensing systems are vast, and weexpect the relevant volume to contain line-of-sight (LOS) halos that are notassociated with the main lens. We develop a formalism to calculate the effectof LOS halos as an effective convergence power spectrum. The multi-lens planeequation couples the angular deflections of consecutive lens planes, but byassuming that the perturbations due to the LOS halos are small, we show thatthey can be projected onto the main-lens plane as effective subhalos. We testour formalism by simulating lensing systems using the full multi-plane lensequation and find excellent agreement. We show how the relative contribution ofLOS halos and subhalos depends on the source and lens redshift, as well as theassumed halo and subhalo mass functions. For a fiducial system with fraction ofDM halo mass in substructure $f_{\rm sub}=0.4\%$ for subhalo masses$[10^5-10^8]\rm{M}_{\odot}$, the interloper contribution to the power spectrumis at least several times greater than that of subhalos for source redshifts$z_s\gtrsim0.5$. Furthermore, it is likely that for the SLACS and BELLS lensesthe interloper contribution dominates: $f_{\rm sub}\gtrsim2\%$ ($4\%$) isneeded for subhalos to dominate in SLACS (BELLS), which is higher than currentupper bounds on $f_{\rm sub}$ for our mass range. Since the halo mass functionis better understood from first principles, the dominance of interlopers ingalaxy-galaxy lenses with high-quality imaging can be seen as a significantadvantage when translating this observable into a constraint on DM.

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