Figure for WIMP freeze out

freeze_out.py

"""
WIMP miracle
============
"""

import matplotlib
import numpy as np
import matplotlib.pyplot as plt

from matplotlib.ticker import MaxNLocator
from scipy.interpolate import spline
from numpy.random import normal


matplotlib.rc('text', usetex=False)
plt.xkcd()
matplotlib.rc('font', **{'size': 25})


fig, ax = plt.subplots(figsize=(8, 8))

T = np.linspace(0, 50, 10)

def equilibrium(x):
    """
    """
    k = 1
    return k * x**1.5 * np.exp(-x)
 
def freezeout(x, x_fo=500.):
    """
    """
    if x < x_fo:
      return equilibrium(x)
    else:
      return equilibrium(x_fo)

        
x = np.logspace(0, 4, 100)
eq = equilibrium(x)
fo = map(freezeout, x)

plt.loglog(x, fo, color="RoyalBlue", lw=4, label="DM abundance")
plt.loglog(x, eq, ls="--", color="Crimson", lw=4, label="Equilibrium")

plt.setp(ax, yticklabels=[], xticklabels=[])
plt.text(3, 1E-179, "Freezes-out at correct\nabundance for\nweak interaction")

plt.xlabel("1/Temperature")
plt.ylabel("Abundance")
ax.legend(loc='lower left')
plt.title("WIMP miracle")
        
plt.savefig("freeze_out.png")