Proper Motions Of VLBI Lenses, Inertial Frames and The Evolution of Peculiar Velocities

Abstract

Precise determinations of the image positions in quad gravitational lenses using VLBI can be used to measure the transverse velocity of the lens galaxy and the observer. The typical proper motions are $\mu$as yr${}^{-1}$, so the time scale to measure the motion is ten years. By measuring the dipole of the proper motions in an ensemble of lenses we can set limits on the deviation of the inertial frame defined by the lenses from that defined by the CMB dipole and estimate the Hubble constant. The residual proper motions after subtracting the dipole probe the evolution of peculiar velocities with redshift and can be used to estimate the density parameter ${\Omega }_0$. For $N$ lenses, VLBI measurement accuracies of ${\sigma }_{\theta }$, and a baseline of $T$ years, we estimate that the 2$\sigma$ limit on the rms peculiar velocity of the lens galaxies is $3100 (σ_θ/10μ\{as})({yrs}/T)/N^{1/2} \kms$, and that the time required for the 2--$\sigma$ limit to reach the level of the local rms peculiar velocity $v_{0,rms}$ is approximately $10 N^{-1/2} (v_{0,rms}/600\kms)(σ_θ/10μas)$ years. For a ten year baseline and $N=10$ lenses we expect the 1$\sigma$ limit on the misalignment with the CMB dipole to be $\Delta \theta =20^{\circ }$ or equivalently to obtain an upper limit of $\Delta H_0/H_0<0.34$.

23 pages, figures included uuencoded gzipped ps-file, submitted to the ApJ. One correction made from the original version

References in corpus (1)

• Is There A Cosmological Constant?

Cited by in corpus (11)

• Constraints on Cosmological Anisotropy out to z=1 from Supernovae Ia
• Milliarcsec-scale polarisation observations of the gravitational lens B1422+231
• Cosmology with gravitationally lensed repeating Fast Radio Bursts
• The Gaia inertial reference frame and the tilting of the Milky Way disk
• Changes in the measured image separation of the gravitational lens system, PKS 1830-211
• Probing motion of fast radio burst sources by timing strongly lensed repeaters
• Proper motion in lensed radio jets at redshift 3: a possible dual super-massive black hole system in the early Universe
• Magnification Ratio of the Fluctuating Light in Gravitational Lens 0957+561
• Peculiar Transverse Velocities of Galaxies from Quasar Microlensing. Tentative Estimate of the Peculiar Velocity Dispersion at $z\sim 0.5$
• All Transverse Motion is Peculiar: Connecting the Proper Motions of Galaxies to the Matter Power Spectrum
• Probing ~100 AU Intergalactic MgII Absorbing "Cloudlets" with Quasar Microlensing