🍓 compote (Coefficients Of Multipoles of lensing POTEntials)

The compote package computes the coefficients of the multipolar expansion of a lensing potential.

Figure: even coefficients of the singular isothermal sphere (SIE) and the elliptical power law (EPL) lensing potential for different values of the axis ratio $f$, computed and plotted with compote. When $f\rightarrow 1$, the singular isothermal sphere is recovered.

Physics

Strong gravitational lens galaxies are typically described by elliptical mass distributions. However, an elliptical lensing potential will have contributions from higher-order multipoles beyond the monopole and the quadrupole term which describes an ellipse. To understand how relevant these higher-order modes may be, we want to compute the multipole coefficients $c_n(\theta) = \frac{1}{2\pi} \int_0^{2\pi} \mathrm{d} \varphi e^{-in\varphi} \psi(\theta, \varphi)$, where $\psi(\theta, \varphi)$ is the given potential. The compote package can perform this calculation for the EPL and SIE potentials, with trivial extensibility to other cases.

Usage

First import and instantiate the potential whose coefficients you wish to calculate:

from compote.potentials.epl import EPL

epl = EPL()

Then, import and instantiate the Calculate class, pass the number of orders to be computed along with the arguments for the potential function, and get the result:

from compote.calculate.calculate import Calculate

calc = Calculate()

theta = 1   # radial coordinate; result is independent of this
f = 7/8     # axis ratio of ellipse
theta_E = 1 # Einstein radius; result is independent of this
gamma = 2   # slope of the power law

orders = range(0, 12)

c_epl, error_epl = calc.coefficients(epl.potential, orders, theta, f, theta_E, gamma)

You can view the results as a pandas dataframe or as a LaTeX table for convenience:

dataframe = calc.results_dataframe(c_epl, error_epl, orders)

latex = calc.results_dataframe(c_epl, error_epl, orders, to_latex=True)

print(dataframe)

print(latex)

And lastly you can plot your results with the Plot class:

from compote.plots.plots import Plot

plt = Plot()

plot_kwargs = {'color': 'crimson', 'ls': ' ', 'marker': 'x', 'label': 'EPL'}

plt.coefficient_plot(c_epl, orders, plot_kwargs,  title='my amazing compote plot')

An example notebook demonstrating how to use compote can be found here.

Contribution

To contribute to the code, please fork the repository, create a branch with your modification and then open a pull request.

Name

Compôte is a stewed fruit dessert.