Simulating the Light Curve

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glossary of terms

The initial requirement for this project was to develop code which would simulate the light curve of a gravitational microlensing event. For a point-source-point-lens model, the magnification \(A\) can be exactly described by a quadratic in terms of \(u\), the impact parameter in units of the Einstein radius.Einstein radius. The Einstein radius is a characteristic scale in microlensing, defined as \[\theta_E = \left (\frac{4GM}{D_{rel}c^2} \right )^{1/2}\] In the case that the impact parameter \(u\) is zero, the source image is deflected to a circle with a radius equivalent to the Einstein radius. \[A(u) = \frac{u^2 + 2}{u\sqrt{u^2 + 4}}\] Add a second body to the lens system, and a fifth-order complex polynomial must be solved to describe the resulting time-series magnification. No analytical solution is possible for fifth order polynomials, and so this requires a significant degree of numerical computation.

After one week of trying to write this simulation from scratch and becoming increasingly conscious of the twelve week project timeframe, I opted to use the existing Python package MulensModel. This package utilises contour integration methods to rapidly determine the expected magnification of a given microlensing event, and for the high volume of parameters that I intended to test with efficiency was a crucial requirement. MulensModel also provides a trajectory map for your specified event which allows the user to visually determine which planetary configurations should result in a detectable perturbation.