Measuring the Moving Lens Effect with Wide-Separation Lensed Quasars
Abstract
The transverse motion of a gravitational potential induces frequency shifts in photons propagating through it, giving rise to the moving-lens effect and providing a probe of transverse peculiar velocities. Statistical evidence for this effect has recently been reported using cross-correlations between cosmic microwave background temperature maps and large-scale-structure tracers. Here, we investigate a complementary spectroscopic approach based on wide-separation lensed quasars, for which different lensed images probe distinct deflection geometries through a moving foreground lens. We focus on SDSS J1004+4112 and assess the differential redshift that could be measured from its broad emission-line spectra. Using an estimator that combines information across the line profiles, we perform Monte Carlo forecasts for C IV and C III] under an ELT-like configuration, considering photon noise only. For an assumed lens transverse velocity of 500 km s−1 and the orientation maximizing the signal, the expected differential redshift reaches |ΔzML|≃6.7×10−7. At an integration time of 40 hr, the joint photon-noise-limited precision is σz≃2.5×10−7. C IV dominates the constraint, while C III] provides only a modest additional improvement, and integrations of tens of hours reach the 10−7 precision regime. These results show that photon statistics alone can reach the characteristic moving-lens signal scale, although practical detectability will depend on controlling astrophysical and instrumental systematics.
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BibTeX
@misc{zhang2026measuring,
title = {{Measuring the Moving Lens Effect with Wide-Separation Lensed Quasars}},
author = {Yupeng Zhang and Shuxun Tian and Zhengxiang Li},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.04865},
eprint = {2610.04865},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.04865},
}
RIS
TY - UNPB
TI - Measuring the Moving Lens Effect with Wide-Separation Lensed Quasars
AU - Yupeng Zhang
AU - Shuxun Tian
AU - Zhengxiang Li
PY - 2026
DA - 2026/10/04
PB - arXiv
DO - 10.48550/arxiv.2610.04865
UR - https://arxiv.org/abs/2610.04865
AB - The transverse motion of a gravitational potential induces frequency shifts in photons propagating through it, giving rise to the moving-lens effect and providing a probe of transverse peculiar velocities. Statistical evidence for this effect has recently been reported using cross-correlations between cosmic microwave background temperature maps and large-scale-structure tracers. Here, we investigate a complementary spectroscopic approach based on wide-separation lensed quasars, for which different lensed images probe distinct deflection geometries through a moving foreground lens. We focus on SDSS J1004+4112 and assess the differential redshift that could be measured from its broad emission-line spectra. Using an estimator that combines information across the line profiles, we perform Monte Carlo forecasts for C IV and C III] under an ELT-like configuration, considering photon noise only. For an assumed lens transverse velocity of 500 km s^−1 and the orientation maximizing the signal, the expected differential redshift reaches |Δz_ML|≃6.7×10^−7. At an integration time of 40 hr, the joint photon-noise-limited precision is σ_z≃2.5×10^−7. C IV dominates the constraint, while C III] provides only a modest additional improvement, and integrations of tens of hours reach the 10^−7 precision regime. These results show that photon statistics alone can reach the characteristic moving-lens signal scale, although practical detectability will depend on controlling astrophysical and instrumental systematics.
ER -