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star_simulator.py
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star_simulator.py
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# -*- coding: utf-8 -*-
"""
Created on Fri Nov 7 21:55:12 2014
@author: lucio tolentino
Script for calculating the movement of stars under different amount of dark
matter.
"""
import sys
import os
import numpy as np
import numpy.random as random
from matplotlib import rcParams
import matplotlib.animation as animation
import matplotlib.pyplot as plt
import json
import scipy.constants as cons
rcParams["savefig.dpi"] = 150
rcParams["axes.facecolor"] = '#000000'
rcParams["axes.linewidth"]=2
rcParams["axes.edgecolor"]='#dddddd'
rcParams["figure.facecolor"] = '#000000'
rcParams["figure.edgecolor"] = '#000000'
rcParams["axes.labelcolor"] = '#ffffff'
rcParams["xtick.color"] = '#ffffff'
rcParams["ytick.color"] = '#ffffff'
#define movement functions -- given an x,y return x',y'
def rotate(x, y, theta):
"""
Rotate a cartesian coordinate given by *x*, *y* by an angle *theta*.
Returns the new cartesian coordinate *x'*, *y'*.
"""
return x*np.cos(theta) - y*np.sin(theta), y*np.cos(theta) + x*np.sin(theta)
def newton_angular_velocity(mass, radius):
#print radius, np.sqrt(cons.G*mass/radius/ly2m), np.sqrt(cons.G*mass/radius/ly2m)/(ly2m*radius)
return np.sqrt(cons.G*mass/radius/ly2m)
def iso_angular_velocity(Rc,Vinf, radius):
tmp=1.0-Rc/radius/ly2m*np.arctan(radius*ly2m/Rc)
#print radius, Vinf*np.sqrt(tmp), Vinf*np.sqrt(tmp) / (radius * ly2m)
return Vinf*np.sqrt(tmp)
def nfw_angular_velocity(Vv,cv,Rv,radius):
gcinv=np.log(1.0+cv)-1.0/(1.0/cv+1.0)
s=radius/Rv/kpc2ly
cvs=cv*s
vsq=Vv*Vv/s/gcinv*(np.log(1.0+cvs)-1.0/(1.0/cvs+1))
#print radius, np.sqrt(vsq), np.sqrt(vsq)/ (radius * ly2m)
return np.sqrt(vsq)
#Will be called with input as JSON
if __name__ == "__main__":
#set parameters
#parameters = sys.argv[0]
parameters = {"dark_matter":False, "model": "NFW", "amount_dark_matter": 6, "distribution": "Scenario A"}
if not parameters['dark_matter']:
pngnameroot= 'nodm'
else:
pngnameroot= parameters['model']
width = 50000
number_of_stars = 200
timesteps = 50
lambda_ = 0.2 # exponential distribution of stars
#constants
dt = 1e14
kpc2ly=3261.63344
ly2m=1.0/1.05702341e-16
H=2.1e-18
kpc2m=3e19
Msun=2e30 #kg
gal='M33'
Mv=2e11*Msun
tmp=4.0/3.0*np.pi*2e-24
Rv=np.power(Mv/tmp,0.33)*5
M={'M33':1e40, 'Vinf':105400, 'Rc':1.39*kpc2m, 'Vv':H*10*Rv, 'cv':4.0,'Rv':Rv/kpc2m}
#exponentially distribute stars from center of galaxy
stars_r = [width*random.exponential(lambda_) for i in range(number_of_stars)]
stars_theta = [random.uniform(2.0*np.pi) for i in range(number_of_stars)]
stars_x = [stars_r[i]*np.cos(stars_theta[i]) for i in range(number_of_stars)]
stars_y = [stars_r[i]*np.sin(stars_theta[i]) for i in range(number_of_stars)]
#BUILD JSON
positions = {0:{i:(stars_x[i], stars_y[i]) for i in range(number_of_stars)}} # save initial positions
for t in range(1,timesteps):
positions[t] = {}
for s in range(number_of_stars):
#rotate star's position
if not parameters["dark_matter"]:
#print "NEWTON"
new_angle = dt*newton_angular_velocity(M[gal], stars_r[s]) / (stars_r[s] * ly2m)
elif parameters["model"]=="ISO":
#print "ISO"
new_angle = dt*iso_angular_velocity(M['Rc'],M['Vinf'],stars_r[s]) / (stars_r[s] * ly2m)
elif parameters["model"]=="NFW":
#print "NFW"
new_angle = dt* nfw_angular_velocity(M['Vv'],M['cv'],M['Rv'],stars_r[s]) / (stars_r[s] * ly2m)
else:
print "ERROR!"
stars_x[s], stars_y[s] = rotate(stars_x[s], stars_y[s], new_angle)
#save position
positions[t][s] = (stars_x[s], stars_y[s])
#json.dumps(positions)
#VISUALIZE
#plt.close('all')
#orbits
colors = ['r', 'b', 'g', 'k', 'c', 'm',]
plt.figure(figsize=(6,6))
for t in range(timesteps):
for s in range(number_of_stars):
x = positions[t][s][0]
y = positions[t][s][1]
plt.plot(x,y,'.',c = colors[s%len(colors)], alpha = t/float(timesteps), linewidth=0)
plt.xlim(-30000,30000)
plt.ylim(-30000,30000)
# plt.savefig(pngnameroot+"%02d.png"%t)
#
fig = plt.figure(facecolor='k')
ax = fig.add_subplot(111, autoscale_on=False, xlim=(-30000,30000), ylim=(-20000,30000))
nodmplot, = ax.plot([], [],'.', marker='o',c = '#ffffff')#,label='NO DM')
isoplot, = ax.plot([], [],'.', marker='o',c = '#ffffff')#,label='ISO')
nfwplot, = ax.plot([], [],'.', marker='o',c = '#ffffff')#,label='NFW')
def init():
nodmplot.set_data([], [])
isoplot.set_data([], [])
nfwplot.set_data([], [])
return nodmplot,isoplot,nfwplot
def animate(t):
x=[positions[t][s][0] for s in range(number_of_stars)]
y=[positions[t][s][1] for s in range(number_of_stars)]
if not parameters['dark_matter']:
nodmplot.set_data(x,y)
elif parameters['dark_matter'] and parameters['model']=='ISO':
isoplot.set_data(x,y)
elif parameters['dark_matter'] and parameters['model']=='NFW':
nfwplot.set_data(x,y)
return nodmplot,isoplot,nfwplot
#add universe center
plt.scatter([0], [0], c = 'y', marker='o', s=60)
ani = animation.FuncAnimation(fig, animate, np.arange(1, timesteps),
interval=25, blit=False, init_func=init)
#set graph properties
plt.xlim((-width*1.1,width*1.1))
plt.ylim((-width*1.1,width*1.1))
plt.show()