Weak Gravitational Lensing in the GOODS Fields

Updates

March 2005. I have been accepted to the Harvard Physics Department for PhD studies. The term begins in mid-September and my graduate studies will likely last 4-6 years.

December 2004. I have just graduated with a AB in physics from Berkeley. From now until my presumed entry into grad school (about September) I will be a fulltime Research Assistant with Prof. Richard Ellis at Caltech. Please visit the website dedicated to that research at www.astro.caltech.edu/~fwh.

Papers

Following are a couple papers that I have written on weak gravitational lensing. Please contact me if you would like a copy.

1. Senior Honors Thesis. Completed 17 December 2004. Titled Weak Lensing in GOODS. Reviews weak gravitational lensing theory, relates it to cosmology, discusses some methods to measure it, and presents a first pass at measuring weak lensing in GOODS images.
2. 2004 Caltech Summer Undergraduate Research Fellowship report. Completed 1 October 2004. Presents the results of a pixel scale study I conducted summer 2004 as a Caltech Summer Undergraduate Research Fellow. The study pertains in particular to the proposed Supernova/Acceleration Probe satellite, or SNAP, which will measure the accelerating expansion of the Universe via type Ia supernova and dark matter concentrations using weak gravitational lensing.

Overview

Gravity stands alongside neutrino and electromagnetic radiation as an independent probe of the cosmos. Gravitational lensing, because it arises solely from spacetime curvature, allows physicists to map baryonic and dark matter in the sky. Theorists have shown that gravitational lensing's weakest regime probes structure on scales from galaxy halos to galaxy superclusters. Weak gravitational lensing allows us to directly measure, for example, the power spectrum of mass density perturbation on the scale of eight megaparsecs.

The power spectrum tells us how matter clumps together in the domain of large-scale structure (LSS). From it we can infer the interplay between matter condensation and cosmological expansion, and thus the early evolution of the universe as well as its fate. Measuring the power spectrum via weak gravitational lensing therefore yields a better understanding of our universe.

A strong gravitational lens as imaged by the Hubble Space Telescope (HST). HST is one of the telescopes responsible for the GOODS images.

Three Principal Problems

A weak lensing signal manifests as about a two to ten percent shear and convergence in an image. Our earthbound perspective prevents us from knowing directly how the image would appear without the shear. One principal problem is to extract this signal without reference to the unbiased image.

A second principal problem involves systematic error. We want to analyze small background galaxies because it is their images that foregrounding LSS biases with weak lensing. An anisotropic point-spread function (PSF), which also manifests as a small shear, can distort weak lensing signals. Pixelization also distorts smooth galaxy shapes. Identification and deconvolution of systematic error from PSF and pixelization effects are essential for measuring the weak lensing shear. We must keep systematic error below the threshold of the weak lensing shear, which requires of our images high resolution, low noise, and correctible PSF. This pushes the limits of current technology.

This animation illustrates the effect of each component of shear, denoted as gamma, on a noisy (left) and noiseless, colorized (right) simulated galaxy. These are the same simulated galaxy. One can see that the effect is barely perceptible---a reason weak lensing must be measured on a statistical basis.

A third principal problem is that we need not only deep images with a high density of small galaxies, but wide images as well, for weak lensing analysis is statistical by nature. We postulate that (1) distant galaxies appear elliptical in our images, and (2) in the absence of shear, a local ensemble has null average ellipticity. Shear manifests as a locally nonzero average. To generate a meaningful shear map, though, we need to average over multiple locales. Our images must therefore resolve many distant galaxies over a wide region of the sky.

Modern Data and Methods

These three principal problems dictate that we need wide and deep images with low systematic error to map matter with weak lensing. Fortunately, the Hubble Space Telescope (HST) fulfills these requirements. The Great Observatories Origins Deep Survey, or GOODS, which, in part, uses HST, has resolutions from 0.05 down to 0.03 arcseconds per pixel with varying but low noise. And whereas GOODS covers roughly 320 square arcminutes in two disjointed fields, another HST project currently underway, the Cosmic Evolution Survey, or COSMOS, covers solidly two square degrees at comparable resolution.

To tackle the three principal problems given modern HST data, three methods have become prominent. Kaiser, Squires, and Broadhurst (KSB, 1995) propose an elegant and simple method to measure galaxy shape and determine PSF using nearby stars. Rhodes, Refregier, and Groth (RRG, 2000) revisit the KSB algorithm, seeking to improve on it. Then, in 2003, Refregier and Bacon introduce their innovative Shapelets method, which involves mapping galaxy shapes onto the two-dimensional quantum harmonic oscillator space. Here image deconvolution reduces to simple matrix operations.

Advisers

Jodi Lamoureux, scientific staff with Professor George Smoot's observational astrophysics research group at the Lawrence Berkeley National Laboratory (LBNL), guides me on my project. She now works on gravitational lensing computer algorithms and models for the planned Supernova Acceleration Probe, and provides me with seasoned and highly relevant expertise. She also takes an interest in and has experience working with undergraduate physicists.

Resources

I first engaged in this project through the Undergraduate Research Apprentice Program at the start of the fall 2003 semester. My thesis project officially began in the spring 2004 semester.

For large computing tasks I use the Parallel Distributed Supercomputing Facility, based at LBNL.

About the Author

This was the honors senior thesis of Will High.