Measuring the Gravitomagnetic Distortion from Rotating Halos. I. Methods

Source galaxy images are distorted not only by a static gravitational potential, but also by frame-dragging induced by massive rotating objects like clusters of galaxies. Such an effect is well understood theoretically; it is therefore of great interest to estimate its detectability for future surveys. In this work, we analyze the lensing convergence kappa around rotating dark matter halos. The rotation of the massive objects generates a gravitomagnetic potential giving rise to an anisotropic contribution to the lensing potential. We construct an estimator delta kappa to describe the difference between the symmetric enhancement and reduction of kappa around the halo rotation axis, finding that it is well approximated by a function proportional to the halo velocity dispersion squared times a dimensionless angular momentum parameter. Using simulation mocks with realistic noise level for a survey like the Legacy Survey of Space and Time (LSST), we test our estimator, and show that the signal from frame-dragging of stacked rotating lenses is consistent with zero within 1 sigma. However, we find that the most massive cluster in SDSS DR7 spectroscopic selected group catalog has a line-of-sight rotation velocity of 195.0 km s(-1) and velocity dispersion of 667.8 km s(-1), which is at 1.2 x 10(-8) odds according to the angular momentum probability distribution inferred from N-body simulations. By studying SDSS DR7 spectroscopic selected group catalog, we show how rotating clusters can be identified, and, finding that fast rotating clusters might be more abundant than in estimates based on simulations, a detection of gravitomagnetic distortion may be at reach in future surveys.

Automated summary

The study analyzes the lensing convergence κ around rotating dark matter halos, finding that the gravitomagnetic potential generated by the rotation of massive objects contributes to an anisotropic lensing potential. Testing an estimator using simulation data for future surveys, the signal from frame-dragging of stacked rotating lenses is shown to be consistent with zero within 1 sigma, while the rotation velocity of the most massive cluster in the SDSS DR7 spectroscopic selected group catalog suggests a potential detection of gravitomagnetic distortion.