Gravitational Lensing and the Most Powerful Explosions in the Space
Talk for The Astronomy Club, IISER Mohali
March 21, 2023
Kelly et al, 2015
Bending of light due to the gravitational field of massive objects.
Different forms
Strong gravitational lensing
Weak gravitational lensing
Microlensing
JWST's First Deep Field Image
Lens Equation
The Lens Equation
Deflection Angle
where
where, lensing/deflection potential is given as,
and Fermat Potential,
The Fermat principle: The physical light rays are those for which the light travel time is stationary.
1. Magnification
2. Distortion
1. Magnification
2. Distortion
3. Time Delay
Magnification and Distortion
The magnification of each image is related to the Jacobian of the transformation equation.
where the magnification matrix is given as,
where the magnification matrix can also be written as,
combination of the symmetric magnification and the sheer
The magnification of each image is related to the Jacobian of the transformation equation.
µ = fluxes observed from image/fluxes observed from unlensed source
Magnification and Distortion
Critical Curves in image plane
Extended, elliptical lens
Joachim Wambsganss, 1998 + Narayan and Bartelmann, 1998
Caustics in source plane
curves
Based on the eigenvalues of the Jacobian A, the lensed images can be divided into three types
contours
Blandford and Narayan, 1986
Time Delay
Two components
1. Geometrical Time Delay: the individual light rays get deflected at different angles, their geometrical lengths are different giving rise to the geometrical time delay.
2. Gravitational Time Delay: light rays propagate through a gravitational potential which retards them, resulting in the gravitational time delay.
Total time delay = geometrical time delay + gravitational time delay
Cosmological parameters governing the evolution of the universe:
Parameters to be found observationally:
∵ First Friedmann Equation
∵ Equation of state
Taylor expanding a(t):
∵ Independent of cosmological
models
∵ The Deceleration parameter
The luminosity distance DL is defined as,
L: Standardized luminosity
f: Flux of the standard candle measured on earth
z: Redshift of the standard candle, found from (1+z) = 1/a(t) relation
Collaborations like High-z supernova Search Team, PI: Perlmutter;
Supernova Cosmology Project, PI: Schmidt and Riess
H0 measurement from low-z supernovae,
q0 measurement from high-z supernovae
Riess et al, 1999
Permutter et al, 1999
Collaborations like H0LiCoW, COSMOGRAIL, TDCOSMO
Source: https://www.lsst.org/about
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