Methods in Gravitational Shear Measurements

1. Methods in Gravitational Shear Measurements Michael Stefferson Mentor: Elliott Cheu Arizona Space Grant Consortium Statewide Symposium Tucson, Arizona April 17, 2010

2. Outline • Research background • Research objectives • General progression and issues • PSF measurement • Bayesian method • Areas of future study • Acknowledgments

3. Research background • Gravitational shear is the distortion of galaxy due to weak gravitational lensing. • Gravity bends the fabric of space-time. Thus, the light from galaxies is bent causing a distorted or sheared image of the star. • The interest of the our research was to understand various shear measurement methods. We are interested in improving algorithms for gravitational shear measurements for the Large Synoptic Survey Telescope (LSST). • For our interests, the measurement of gravitational shear can be used to map the dark matter distribution in the universe. • Image courtesy of www.lsst.org

4. Research objectives • Gain a general idea on how shear can be measured. • Understand the factors that effect shear measurements. • Still working to optimize shear measurements. • Great08 challenge presents various methods from several different teams. • Great08 did not use real data, but provided a sample data to make shear measurements. • Run several programs to understand a logical path to results from a given set of data. • Worked through the code to understand the programming behind shear measurements.

5. General progression and issues • Main issues with measuring shear: atmospheric effects, signal is convoluted with a point spread function, pixilation. • Process begins with the deconvolution of the point spread function (PSF) from point sources, stars. • PSF causes images to appear rounder. • Once PSF is deconvoluted, this information can be used on galaxy images. • PSF can vary across an image. • Code exists to account for PSF effects, but optimizing PSF deconvolution is crucial for shear measurements. • Great care in obtaining a high ratio of signal/noise. Noise causes image to appear more elliptical. • Pixilation

6. PSF measurement • The image is convoluted with the PSF. • Signal is convoluted with a convolution kernel. • GREAT08 used a known kernel. • Can be solved using a fast Fourier transform (FFT) to get functions in frequency space. • Other methods involve stacking images. Stacking images allows to estimate the surface brightness profile. • For a varying PSF, divide the image in invariant zones. From there, FFT can done on these zones. • Various deconvolution methods exist to determine the input signal.

7. Bayesian method • One sample method was Bayesian probability method used in lensfit code by T. Kitching and L. Miller. • Bayesian method measures the shapes of galaxies through a model-fitting approach. • Bayesian probability is used to find the full posterior probability in ellipticity. • Fits galaxy individually and takes a mean average to estimate the ellipticity. • With a known ellipticity, the shear can be determined. • Strengths: lensfit code produced a quality factor nearly 10 times greater than other codes submitted. Uses realistic galaxy profiles which other codes fail to do. • Weaknesses: Has to fit each galaxy individually which results in longer computation time.

8. Areas of future study • Further analysis of software • New area of study would be to determine what galaxy sizes are ideal for shear measurements. • Along same lines, how does redshift effect which galaxies are ideal for shear measurements?

9. Thanks • Dr. Elliot Cheu • Mentor • Dr. Lance Miller • Lensfit • Questions/comments/concerns