CriticalCurvesAndCaustics.md

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Critical curves and caustics

The gravitational lensing phenomenology is strictly related to the existence of critical curves and caustics (see the recommended reviews for a full treatment).

VBMicroLensing offers the calculation of critical curves and caustics with an arbitrary number of points through the functions Caustics and CriticalCurves for binary lenses, and Multicaustics and Multicriticalcurves for multiple lenses.

The result is a list of curves, where each curve is a pair of lists containing the x and y coordinates of the points along the curve. The use of these objects is very intuitive, as illustrated by these examples:

Binary Lens

import VBMicrolensing
from matplotlib import pyplot as plt

VBM = VBMicrolensing.VBMicrolensing() # Instance to VBMicroLensing

# Parameters of our binary lens
s=0.6;  # separation between the two lenses
q=0.1;  # mass ratio

caustics = VBM.Caustics(s,q)

#plot
fig = plt.figure(figsize=(5, 5))
for cau in caustics:
        plt.plot(cau[0], cau[1], 'k')

Similarly for critical curves:

criticalcurves = VBM.Criticalcurves(s,q)

#plot
fig = plt.figure(figsize=(5, 5))
for crit in criticalcurves:
        plt.plot(crit[0], crit[1], 'k')

Multiple Lens

import VBMicrolensing
from matplotlib import pyplot as plt

VBM = VBMicrolensing.VBMicrolensing() # Instance to VBMicroLensing

parameters = [0,0,1,
              -1.2,0.5,0.5,
              -1,0.4,1.1e-1,
              0.6,0,1.1e-2]

VBM.SetLensGeometry(parameters) #Initialize the lens configuration

caustics = VBM.Multicaustics()

#plot
fig = plt.figure(figsize=(5, 5))
for cau in caustics:
        plt.plot(cau[0], cau[1], 'k')

Similarly for critical curves:

criticalcurves = VBM.Multicriticalcurves()

#plot
fig = plt.figure(figsize=(5, 3))
for crit in criticalcurves:
        plt.plot(crit[0], crit[1], 'k')

Critical curves and caustics are calculated through the resolution of a complex polynomial of order $2N$ (see reviews) by the Skowron & Gould algorithm.

The number of points calculated for the critical curves is controlled by VBM.NPcrit, which can be changed by the user according to the desired sampling. The default value is 200.

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