David M Goldberg

We present ARCH (Adaptive Reconstruction of Cluster Halos), a new gravitational lensing pipeline for cluster mass reconstruction that applies a joint shear-flexion analysis to JWST imaging. Previous approaches have explored joint shear+flexion reconstructions through forward modeling and Bayesian inference frameworks; in contrast, ARCH adopts a staged optimization strategy that incrementally filters and selects candidate halos rather than requiring a global likelihood model or strong priors. This design makes reconstruction computationally tractable and flexible, enabling systematic tests of multiple signal combinations within a unified framework. ARCH employs staged candidate generation, local optimization, filtering, forward selection, and global strength refinement, with a combined fit metric weighted by per-signal uncertainties. Applies to Abell 2744 and El Gordo, the pipeline recovers convergence maps and subcluster masses consistent with published weak+strong lensing results. In Abell 2744 the central core mass within 300 $h^{-1}$kpc is$2.1\times 10^{14} M_\odot h^{-1}$ , while in El Gordo the northwestern and southeastern clumps are recovered at$2.6\times 10^{14} M_\odot h^{-1}$and$2.3\times 10^{14} M_\odot h^{-1}$ . Jackknife resampling indicates typical 1 $σ$uncertainties of$10^{12}-10^{13} M_\odot h^{-1}$ , with the all signal and shear+ $\mathcal{F}$reconstructions providing the most stable results. These results demonstrate that flexion, when anchored by shear, enhances sensitivity to cluster substructure while maintaining stable cluster-scale mass recovery.

We present the first flexion-focused gravitational lensing analysis of the first of the strong-lensing "cosmic telescope" galaxy clusters, observed as part of the Hubble Frontier Fields initiative. Using HST observations of Abell 2744 (z = 0.308), we apply a modified Analytic Image Model (AIM) technique to measure source galaxy flexion and shear values at a final number density of 82 arcmin$^{-2}$. By using flexion data alone we are able to identify the primary mass structure aligned along the heart of the cluster in addition to a major substructure peak offset 1.43' from the cluster core. We generate two types of nonparametric reconstructions: a flexion aperture mass map, which identifies the central potential and substructure peak with mass signal-to-noise of 3.5$\sigma$ and 2.3$\sigma$ respectively; and a convergence map derived directly from the smoothed flexion field. For the primary peak we find a mass of $1.93\times10^{14}\,h^{-1}\,M_{\odot}$ within a 45" (145h$^{-1}$ kpc) aperture, and for the western substructure we find a mass of $7.12\times10^{13}\,h^{-1}\,M_{\odot}$ within a 25" (80h$^{-1}$ kpc) aperture. The associated peak velocity dispersions were determined to be $\sigma_v$ = 1630 km/s and $\sigma_v$ = 766 km/s, respectively, by fitting nonsingular isothermal sphere profiles to the flexion data. Additionally, we use simultaneous shear measurements to independently reconstruct the broader cluster mass structure, and find that it is unable to reproduce the small-scale structure associated with the flexion reconstructions. Finally, we perform the same analysis on the Abell 2744 parallel sky field, and find no strong phantom signals in the noise reconstructions.

Astrophys.J. 621 (2005) 643-650 We estimate the Mass Function of void galaxies in the second public data
release of the Sloan Digital Sky Survey from a sample of 1000 galaxies with
local density contrasts of delta_v < -0.6. The galaxy sample is split into
ellipticals and spirals using a color-Sersic index criteria. We estimate the
virial masses of ellipticals using the measured spectral line-widths along with
the observed size. Projection effects and uncertainties in halo properties make
mass estimates of spirals more difficult. We use an inversion of the
Tully-Fisher relation to estimate the isothermal rotational velocity, and
introduce a scaling factor to estimate the halo extent. We then fit the
measured mass function against a theoretical Press-Schechter model, and find
that the distribution of galaxies in voids appears to be nearly unbiased
compared to the mass.