Geometric redshifts for distant faint galaxies

Abstract

The formation and evolution of galaxies is one of the major frontiers in contemporary astrophysics. Searches for and studies of distant and therefore young galaxies are necessary for testing and developing theoretical models for their assembly in the early universe. Through gravitational lensing by galaxy clusters, astronomers have been able to probe a few magnitudes deeper than blind surveys. To infer the intrinsic properties of lensed images, the most challenging aspects are to accurately derive the redshifts and magnifications of the lensed images, which require an accurate lens model for the galaxy cluster. A robust mass model is constrained by the positions and redshifts of reliable lensed images. My thesis addresses these problems by using redshifts derived purely geometrically. Given a lens model, along a given line of sight, lensed images of a more distant galaxy have larger angular separations. A ``geometric redshift" is derived by choosing the best redshift that reproduces the observed positions of the lensed images.

In my first project, I derived the geometric redshift of the triply-lensed galaxy, MACS0647-JD. This galaxy, with a probable photometric redshift of $z\simeq 10.7^{+0.6}_{-0.4}$, is claimed be one of the known earliest galaxies. One of the lensed images, however, has a somewhat higher probably redshift $z\sim2.5$. We construct a lens model using the non-parametric algorithm WSLAP+ of the lensing galaxy cluster. Our lens model convincingly excludes the low redshift regime of $z<3$, for which convoluted critical curves are generated by our method. These critical curves are unlikely to appear with the real mass model as background galaxies will be lensed to giant arcs which are not observed in the data. Instead, a best fit to all sets of lensed galaxy positions and redshifts provides a geometric redshift of $z\simeq 10.8^{+0.3}_{-0.4}$ for MACS0647-JD, strongly supporting the higher photometric redshift solution.

In my second project, I explore the possibility of using geometric redshifts to refine the lens model for a galaxy cluster, and predict the geometric redshifts of all lensed images having photometric redshifts. By removing the dependence of photometric redshifts from the mass model construction, we can potentially improve the accuracy of the mass model. We first use all 10 spectroscopically secure multiply-lensed systems to define an initial model for RXC J2248.7-4431 (Abell S1063). We then derive geometric redshifts of other multiply-lensed sets that do not have spectroscopic measurements. This allows us to incorporate iteratively, in a novel way, 6 additional new systems without spectroscopic measurements. We also demonstrate the accuracy of geometric redshifts by applying the same iterative method to know spectroscopic redshift systems, finding a close one-to-one relationship of the derived geometric redshifts and the true spectroscopic redshifts.

This thesis provides a pioneering study of geometric redshift techniques that I anticipate will be used extensively in the future, towards the launch of \textit{JWST} when photometric redshifts will be even more unreliable in the infrared regime. (472 words)