How do I calculate magnification using multiple gravitational lenses?

In summary, the Jacobian matrix is a useful tool for calculating the magnification of light due to multiple gravitational lens and is defined by Ai = (∂(x1,y1)/∂(x2,y2))i, with i representing the nth 2x2 matrix. Its purpose is to determine the relationship between the coordinates of the source and image.
  • #1
xeorns
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0
Hi,
I've been working on a problem involving gravitational lens, and right now I'm trying to learn the formula to calculate magnification of light due to multiple gravitational lens. I've gotten to an equation that I've become stuck on. I've been using formulas from this paper:
http://adsabs.harvard.edu/full/1992A&A...265...1S

In particular, I'm don't understand equation 2.10, and 2.11, for the value of Ai where i is the nth 2x2 matrix.

What would the Jacobian matrix look like?
Thanks!
 
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  • #2
The Jacobian matrix is a square matrix of partial derivatives that can be used to calculate the magnification of light due to multiple gravitational lens. It is defined as: Ai = (∂(x1,y1)/∂(x2,y2))iwhere (x1,y1) and (x2,y2) are the coordinates of the source and image, respectively. The i represents the nth 2x2 matrix. So, the Jacobian matrix would look something like this: A1 = [ d(x1,y1)/d(x2,y2) ]A2 = [ d(x1,y1)/d(x3,y3) ]A3 = [ d(x1,y1)/d(x4,y4) ]...An = [ d(x1,y1)/d(xn,yn) ]
 

1. What is gravitational lensing?

Gravitational lensing is a phenomenon in which the light from a distant object, such as a star or galaxy, is bent and distorted as it passes through the gravitational field of a massive object, such as a galaxy or cluster of galaxies.

2. How does gravitational lensing occur?

Gravitational lensing occurs due to the warping of space-time by massive objects. This warping causes light to follow a curved path around the object, resulting in the object appearing distorted or magnified to an observer.

3. What are the different types of gravitational lenses?

There are two main types of gravitational lenses: strong and weak. Strong lenses produce highly distorted and magnified images, while weak lenses produce subtle distortions in the background object's shape.

4. How is gravitational lensing useful in astronomy?

Gravitational lensing allows us to study objects that would otherwise be too distant or faint to observe. It also provides a way to measure the mass of the lensing object, such as a galaxy or cluster of galaxies, which can help us understand the distribution of dark matter in the universe.

5. Can we observe gravitational lensing in our everyday lives?

No, gravitational lensing is only observable on a large scale, such as in space. The effects of gravitational lensing are too subtle to be observed in our daily lives or with the naked eye.

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