Methods in Gravitational Methods in Gravitational Shear MeasurementsShear Measurements

Michael SteffersonMichael SteffersonMentor: Elliott CheuMentor: Elliott Cheu

Arizona Space Grant ConsortiumArizona Space Grant ConsortiumStatewide Symposium Statewide Symposium

Tucson, ArizonaTucson, ArizonaApril 17, 2010April 17, 2010

OutlineOutline

Research backgroundResearch background Research objectivesResearch objectives General progression and issuesGeneral progression and issues PSF measurementPSF measurement Bayesian methodBayesian method Areas of future studyAreas of future study Acknowledgments Acknowledgments

Research backgroundResearch background Gravitational shear is the Gravitational shear is the

distortion of galaxy due to weak distortion of galaxy due to weak gravitational lensing.gravitational lensing.

Gravity bends the fabric of space-Gravity bends the fabric of space-time. Thus, the light from galaxies time. Thus, the light from galaxies is bent causing a distorted or is bent causing a distorted or sheared image of the star.sheared image of the star.

The interest of the our research The interest of the our research was to understand various shear was to understand various shear measurement methods. We are measurement methods. We are interested in improving interested in improving algorithms for gravitational shear algorithms for gravitational shear measurements for the Large measurements for the Large Synoptic Survey Telescope (LSST).Synoptic Survey Telescope (LSST).

For our interests, the For our interests, the measurement of gravitational measurement of gravitational shear can be used to map the shear can be used to map the dark matter distribution in the dark matter distribution in the universe.universe.

Image courtesy of www.lsst.orgImage courtesy of www.lsst.org

Research objectivesResearch 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 Great08 challenge presents various methods from several different teams.different teams.

Great08 did not use real data, but provided a sample data Great08 did not use real data, but provided a sample data to make shear measurements.to make shear measurements.

Run several programs to understand a logical path to Run several programs to understand a logical path to results from a given set of data.results from a given set of data.

Worked through the code to understand the programming Worked through the code to understand the programming behind shear measurements. behind shear measurements.

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General progression and issuesGeneral progression and issues Main issues with measuring shear: atmospheric effects, Main issues with measuring shear: atmospheric effects,

signal is convoluted with a point spread function, pixilation. signal is convoluted with a point spread function, pixilation. Process begins with the deconvolution of the point spread Process begins with the deconvolution of the point spread

function (PSF) from point sources, stars. 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 Once PSF is deconvoluted, this information can be used on

galaxy images.galaxy images. PSF can vary across an image.PSF can vary across an image. Code exists to account for PSF effects, but optimizing PSF Code exists to account for PSF effects, but optimizing PSF

deconvolution is crucial for shear measurements.deconvolution is crucial for shear measurements. Great care in obtaining a high ratio of signal/noise. Noise Great care in obtaining a high ratio of signal/noise. Noise

causes image to appear more elliptical. causes image to appear more elliptical. Pixilation Pixilation

PSF measurementPSF 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) Can be solved using a fast Fourier transform (FFT)

to get functions in frequency space.to get functions in frequency space. Other methods involve stacking images. Stacking Other methods involve stacking images. Stacking

images allows to estimate the surface brightness images allows to estimate the surface brightness profile.profile.

For a varying PSF, divide the image in invariant For a varying PSF, divide the image in invariant zones. From there, FFT can done on these zones. zones. From there, FFT can done on these zones.

Various deconvolution methods exist to Various deconvolution methods exist to determine the input signal.determine the input signal.

Bayesian methodBayesian method One sample method was Bayesian probability method used One sample method was Bayesian probability method used

in lensfit code by T. Kitching and L. Miller. in lensfit code by T. Kitching and L. Miller. Bayesian method measures the shapes of galaxies through Bayesian method measures the shapes of galaxies through

a model-fitting approach. a model-fitting approach. Bayesian probability is used to find the full posterior Bayesian probability is used to find the full posterior

probability in ellipticity. probability in ellipticity. Fits galaxy individually and takes a mean average to Fits galaxy individually and takes a mean average to

estimate the ellipticity.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 Strengths: lensfit code produced a quality factor nearly 10

times greater than other codes submitted. Uses realistic times greater than other codes submitted. Uses realistic galaxy profiles which other codes fail to do.galaxy profiles which other codes fail to do.

Weaknesses: Has to fit each galaxy individually which Weaknesses: Has to fit each galaxy individually which results in longer computation time. results in longer computation time.

Areas of future studyAreas of future study

Further analysis of softwareFurther analysis of software New area of study would be to New area of study would be to

determine what galaxy sizes are determine what galaxy sizes are ideal for shear measurements. ideal for shear measurements.

Along same lines, how does redshift Along same lines, how does redshift effect which galaxies are ideal for effect which galaxies are ideal for shear measurements?shear measurements?

ThanksThanks

Dr. Elliot CheuDr. Elliot Cheu• MentorMentor

Dr. Lance MillerDr. Lance Miller• LensfitLensfit

Questions/comments/concernsQuestions/comments/concerns