Gravitational Lensing-IV
“An expert is a person who has made all the mistakes that can be made in a very narrow field” — Neils Bohr.
To summarize a bit we have till far discussed the basic overview of gravitational lensing, how it happens, and its types- strong lensing, weak lensing, and microlensing then we discuss further obtaining the deflection angle which comes from the fundamental bending principle of a photon.
where b is the impact parameter. Then we proceeded by discussing the basics of lensing on a linear plane. (If you haven't already I suggest you just skim through or use the audio versions and go through the previous 4 parts of Gravitational Lenaing so that we are on the same page) Now we see the Multiplane Lensing.
Multiplane Lensing happens when the diffraction pattern of a multiplane lens system is sensitive to the redshifts of the lens planes. It serves a very important purpose when it comes to gravitational lensing. Often we see lensed bodies undergoing distortion due to shearing which plays in our favour helping us recognize if it's lensed or not before drawing further conclusions and statistics.
We know that for an axially symmetric lens, the deflection is along the line connecting \beta and the center of the lens, and the lensing equation for axially symmetric lenses therefore reduces to a 1D equation for the position \theta or this line (at least when \beta not equal to 0)
The derivation in the attached document is self-explanatory but in case drop me a text in my email or comment section.
We go further to replace Einstein’s angle.
Einstein’s angle is a very characteristic angle for gravitational lensing. He was the first one to detect the s faint massive object lined up in front of a bright BG source might produce a bright ring of deflected light. It is also said to be the Einstein ring radius which is basically the radius of an Einstein ring. It stands as the conventional way of ordering in Gravitational Lensing. (I am not very confident about this point, if anyone is aware of why so happens i.e why we keep the the typical lensing distances in the order of Einstein angle please let me know)
Now moving back to our lens equation. Now applying Sridhar Acharya’s formula we get equitation 12.
(We maintain that this Einstein angle is a positive value ie a modulus- we omit considering a negative value)
If we consider if beta is 0, we find | \theta |=\theta_E which satisfies the equation perfectly.
Then we get,
In the following attachment, I have shown the Einstein range in a singular isothermal sphere. Since it is isothermal, we can for the time being consider the medium to be consistent.
The following attachment comes very handy when we discuss weak lensing- which is actually a very important phenomenon and the one most sought after by cosmologists. We see a slight change in distortion due to convergence which we observe using the surface density and critical surface density which characterizes the lens system and is a very powerful tool in identifying clusters and galaxies(shape and structure analysis). It is given by the lens mass smeared over the area of the Einstein ring.
With this, I conclude the overview section of gravitational lensing. Next, I aim at diving deeper into the mathematics of weak lensing which I am currently studying to develop my niche. I am actively seeking out doctoral positions in this domain and I am quite a bit relying on my mathematical intuition on it. That is partly a reason behind my not-so-active blog posts recently as I am constantly striving to create a niche by reading but sometimes theoretical knowledge needs to reach the mark. So I am looking for projects in these domains to try my hands on some simulations- wish me luck! (and pray for me:\) That's all for today Bye!!
For reference, in addition to the books mentioned in the previous posts here are some important links one can consider:
Have a Great Day Ahead, signing off!
