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

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

Research background Gravitational shear is the distortion of galaxy due to weak gravitational lensing. 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. 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). 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. For our interests, the measurement of gravitational shear can be used to map the dark matter distribution in the universe. Image courtesy of Image courtesy of

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

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

PSF measurement The image is convoluted with the PSF. The image is convoluted with the PSF. Signal is convoluted with a convolution kernel. Signal is convoluted with a convolution kernel. GREAT08 used a known kernel. GREAT08 used a known kernel. Can be solved using a fast Fourier transform (FFT) to get functions in frequency space. 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. 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. 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. Various deconvolution methods exist to determine the input signal.

Bayesian method One sample method was Bayesian probability method used in lensfit code by T. Kitching and L. Miller. 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 method measures the shapes of galaxies through a model-fitting approach. Bayesian probability is used to find the full posterior probability in ellipticity. Bayesian probability is used to find the full posterior probability in ellipticity. Fits galaxy individually and takes a mean average to estimate the ellipticity. Fits galaxy individually and takes a mean average to estimate the ellipticity. With a known ellipticity, the shear can be determined. 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. 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. Weaknesses: Has to fit each galaxy individually which results in longer computation time.

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

Thanks Dr. Elliot Cheu Dr. Elliot Cheu MentorMentor Dr. Lance Miller Dr. Lance Miller LensfitLensfit Questions/comments/concerns Questions/comments/concerns