Question

This problem will give you a taste of how we model gravitational lens systems to measure galaxy masses. Imagine you observe a galaxy lens system with distances Dl = 940 Mpc, Dls = 1,293 Mpc, and Ds = 1,745 Mpc. One image appears at an angular position of θ+ = 1.05" from the lens galaxy, while the other appears at an angular position θ- = -0.35" on the opposite side of the galaxy. You may assume the lens is circularly symmetric.

Assume the galaxy can be modeled as a point mass. Find the Einstein radius and mass of the lens galaxy.

Answer 1

The student's question involves using observational data from a galaxy lens system to calculate the Einstein radius and mass of the lensing galaxy by applying the principles of general relativity and gravitational lensing equations.

Step-by-step explanation:

The problem given by the student involves calculating the Einstein radius and the mass of a lensing galaxy based on its gravitational lensing effects on the light from a more distant galaxy. The gravitational lensing effect described here is a validation of general relativity, which illustrates how massive objects can cause light to bend, creating multiple lensed images of distant objects. The specific details about angular positions of the images and distances to the lensing galaxy and the source galaxy allow us to perform calculations based on the Einstein radius formula.

Steps to Find the Einstein Radius and Mass:

1. Calculate the Einstein radius θ_E using the lens equation that relates the distances Dl (distance to the lens), Ds (distance to the source), and Dls (distance between the lens and the source) with the observed angular positions θ+ and θ-.
2. With the Einstein radius, we can then find the mass of the galaxy using the critical density formula that includes the calculated θ_E and distance values.

In practical terms, to solve for the Einstein radius and mass, the student will need to apply the lensing equations using the given distances and angular positions. This involves knowledge of the general theory of relativity and the mathematics of gravitational lensing effects.