What is Kinematic Weak Lenisng?

When a galaxy is distorted via gravitational lensing, it undergoes a shear that the is usually parameterized as a rotation and elongation of the galaxy's elliptical shape. In the diagram, the dashed line represents an elliptical isophote of the galaxy pre-lensing, and the solid line is the shape of that isophote after it has been lensed. Conventional weak lensing surveys look for systematic alignments of many galaxies that can be statistically combined to characterize mass distributions.

However, the galaxy's kinematics behave differently. Since kinematic information is tied directly to the galaxy's intrinsic coordinate system, it is sheared in a way that can't just be parameterized as a rotation but must instead be understood as a shear (shown as colored contours). Kinematic weak lensing is the modeling of sheared velocity fields to recover the shear that has been applied to the galaxy.

I furthered this idea by introducing a new piece of information to the model: the mismatch between imaging and kinematics. The rotated and elongated elliptical isophote isn't actually the same as the pre-lensed isophote. It's a sheared ellipse that has different major and minor axes than before. The open white circle shows the original location of the galaxy's major axis on the isophote, and the filled black circle shows where it has moved to because of the lensing distortion. However, the kinematic information continues to be aligned with the original major axis of the galaxy, meaning that the velocity field is misaligned with the image.

If we can measure the difference between the kinematic major axis (filled white circle) and the photometric major axis (filled black circle), then we can determine how much the galaxy has been lensed.

Improvements over existing techniques

I developed a Bayesian model using on the Python package emcee that fits a sheared velocity field and also incorporates the mismatch between the photometric and kinematic axes.

I generated mock data meant to simulate measurements of disk galaxies at moderate redshifts using existing instruments, along with realistic measurements of the photometric position angle. I applied realistic PSFs to the data and degraded the spatial resolution of the velocity fields to the level that can be expected from the MUSE spectrometer.

My model was able to recover input shear values with much greater certainty than previous techniques. In the marginalized shear posterior distributions for a mock galaxy (right) we see that the model that includes the imaging information (orange) has a much more constrained and accurate posterior than the model that only uses kinematic information (blue).

Greatly increased S/N

In the expected range of errors on galaxy position angles from images of moderate redshift galaxies, my technique leads to a factor of ~6 increase in shear signal-to-noise ratio compared to existing kinematic weak lensing techniques. This increase means that the number of galaxies require to obtain a mass measurement should fall by over an order of magnitude.

Less dependence on velocity error

Because of the additional information gained from imaging, the quality of the velocity data has a significantly smaller impact on the final signal-to-noise than previous techniques. High quality spatially-resolved spectroscopy is expensive to obtain at moderate redshifts, so this technique allows kinematic weak lensing to use more easily available observations.

Future Projects

  • Can kinematic weak lensing be detected in real moderate redshift data? MUSE has taken deep spectroscopy over wide fields surrounding Abell clusters at moderate redshifts, picking up many background galaxies in the process. Can the effects of lensing be seen in those background galaxies?
  • How do kinematic irregularities affect the lensing signal? Nonaxisymmetric motions have the potential to cause shear-like signals even in the absence of lensing. With Nirvana, we can create realistic models of galaxies with and without these kinematic disturbances. How will the signal be degraded for galaxies that are not kinematically regular?