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
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