Weak Gravitational Lensing

Image Source: NASA, ESA, M.J. Jee and H. Ford (Johns Hopkins University)

By Patrick Kantorski & Cory Gerrity

Introduction What is Weak Gravitational Lensing?

Image Source: Astrophysicist Dr. Katherine J Mack

Why is Weak Gravitational Lensing important? What are some of the fundamental limitations and assumptions?

Methodology

Previous Presentation: Thin-Lens Approximation

Transformation: Lensed Un-lensed via Jacobian Matrix Formalism

Symmetry of Partial Derivatives -> Decomposition [Diagonal Convergence Term + Trace-Free Shear Term]

What is Convergence?

What is Shear?

Convergence by Jackson Pollock

The second term in action.

Methodology

Image Source: Schneider, P. 2005

Shear and Convergence Transformations

Scale of Weak Lensing Survey

Small Scale Limits - Intrinsic ellipticities

- Add Shot Noise - Limited by Depth of Survey

Large Scale Limits: - Large Sky Coverage

- Limited by Variance Image Source: Wikipedia.org

Observational Considerations Applying the Shear Method

Source to Image Ellipticity Minimum Lens Strength Magnication Eects

Observational Instruments Size of Telescope Size of CCD Camera

Working with Instruments Exposure Time Seeing Conditions

Apparent Size of Galaxies vs. Faintness

Image Source: Schneider, P. 2005

Observational Considerations Mean Number Density of Galaxy Images vs. Seeing

Source: Schneider, P. 2005

Observational Challenges Data Reduction

Individual Frames

Coaddition

Image Analysis The Point-Spread Function

Shape Measurements Numerical Algorithms

Shear Observations from Space Image Source: Wikipedia.org

Point-Spread Function (PSF)

Mass Reconstruction

Kaiser ~ Squires Inversion Surface Mass Density from Shear

Convolution Product: Fourier Transform Solve for Mass Density -> Transform Back

Discrete Process Requires Smoothing > Kernel Prevents Summation

[Kaiser & Squires (1993)]

Dark Matter Mass Reconstruction (k contours) for COSMOS Advanced Camera for Surveys (ACS) 2 square degree eld. The Mass Density along LOS is Proportional to k.

Dark Matter Map from Hubble Space Telescope Survey and the Cosmic Evolution Survey

Dark Matter Map from Hubble Space Telescope Survey and the Cosmic Evolution Survey

Dark Matter Map from Hubble Space Telescope Survey and the Cosmic Evolution Survey

Creation of cosmic structure in the complex galaxy cluster merger Abell 2744

Image Source: Merten, J. 2011

On the Horizon Euclid (2020), ESA

15,000 Square Degree Weak Lensing Survey in 3 NIR Filters 24.5 Magnitude Resolution, 550-900 nm

Square Kilometer Array (2022), Australia/South Africa Large RA Instrument will allow 50x higher sensitivity than any other

Large Synoptic Survey Telescope (2022), El Pen, Chile Large Field/High Z Capability Mass Map of Universe to Half Current Age

On the Horizon

The LSST is a new kind of telescope. With a light-gathering power among

the largest in the world, it can detect

faint objects with short exposures. Its

uniquely wide eld of view allows it

to observe large areas of the sky at

once; compact and nimble, it can

move quickly between images.

Taking more than 800 panoramic

images each night, it can cover the

sky twice each week. - LSST.org

Large Synoptic Survey Telescope

Image Source: news.slac.stanford.edu

Conclusion Why pursue research applying Gravitational Lensing?

Gravitational Lensing is used to produce large-eld survey maps of the Universe!

By mapping where regions of Dark Matter, we can understand more about its properties and properties of galaxy clusters!

Weak-lensing is a fairly new method due to recent technological advancements! There will also be many improvements to its

application the coming years! (Euclid, LSST, etc)

Gravitational Lensing Video