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| import numpy as np
import matplotlib.pyplot as plt
import scipy.constants as cons
sun = 1.98855e30
chirp = np.power(5*sun,3/5)*np.power(20*sun,2/5)
distance = 1e8*cons.parsec
def time(t, n):
return np.linspace(-t,0,n)
def frequency(t):
return np.power(5,3/8)/(8*cons.pi)*np.power(np.power(cons.c,3)/(cons.G*chirp),5/8)*np.power((-t),-3/8)
plt.figure(figsize = (6, 6))
plt.plot(time(cons.year, 10000), frequency(time(cons.year, 10000)))
plt.xlabel('Time(s)')
plt.ylabel('Frequency(Hz)')
plt.title('Inspiral', fontsize = 14)
plt.savefig('frequency.jpg')
plt.show()
def phi(t):
return -2*np.power(np.power(cons.c,3)/(5*cons.G*chirp)*(-t),5/8)
plt.figure(figsize = (6, 6))
plt.plot(time(cons.year, 10000), phi(time(cons.year, 10000)))
plt.xlabel('Time(s)')
plt.ylabel(r'$\Phi$')
plt.title('Inspiral', fontsize = 14)
plt.savefig('phi.jpg')
plt.show()
def radius(t):
return np.power(256*np.power(cons.G,3)/(5*np.power(cons.c,5))*5*sun*np.power(10*sun,2),1/4)*np.power(-t,1/4)
def h(t):
omega = np.sqrt(cons.G*20*sun/(np.power(radius(t),3)))
return cons.G*5*sun*np.power(radius(t),2)*np.power(omega,2)/(np.power(cons.c,4)*distance)*np.cos(phi(t))
plt.figure(figsize = (6, 6))
plt.plot(time(1, 10000), h(time(1, 10000)))
plt.xlabel('Time(s)')
plt.ylabel('h')
plt.title('Inspiral', fontsize = 14)
plt.savefig('ht.jpg')
plt.show()
def hf(f):
phif = -cons.pi/4+3/4*np.power(8*cons.pi*cons.G*chirp*f/np.power(cons.c,3),-5/3)
return np.sqrt(5/384)/distance*np.power(cons.G,5/6)*np.power(cons.c,-3/2)*np.power(chirp,5/6)*np.power(np.pi,-2/3)*np.power(f,-7/6)*np.cos(phif)
freq = np.linspace(np.log(frequency(-cons.year)), np.log(frequency(-1e-3)), 5000)
freq = np.exp(freq)
plt.figure(figsize = (6, 6))
plt.loglog(freq, hf(freq))
plt.xlabel('Frequency(Hz)')
plt.ylabel('h')
plt.title('Inspiral', fontsize = 14)
plt.savefig('hf.jpg')
plt.show()
G = 6.67428e-8
def freq_dot_tau(freq, tau):
return(freq/(2*tau*cons.year))
def freq_dot_gauss(freq, gauss):
return(np.power(1e18*gauss,2)*8*cons.pi*cons.pi/(3*np.power(cons.c*100,3)*1e45*freq))
def freq_dot_ergs(freq, ergs):
return(ergs*np.power(freq,3)/(4*cons.pi*cons.pi*1e45))
freq = np.power(10, np.linspace(-3,1,1000))
fig, ax = plt.subplots()
plt.ylim((1e-22,1e-8))
plt.xlim((1e-3,10))
for i in (1e3, 1e5, 1e7, 1e9):
plt.loglog(freq, freq_dot_tau(freq, i), 'k--', linewidth=1.5)
xytext = (0, 5)
text = ax.annotate(
f'$10^{{ {int(np.log10(i)):d} }}$ yr',
xy=(1e-3, np.min(freq_dot_tau(freq, i)*1.5)),
xytext=xytext,
textcoords="offset points",
size=15,
color='k',
zorder=1,
horizontalalignment="left",
verticalalignment="center_baseline",
)
text.set_rotation_mode("anchor")
text.set_rotation(10)
for i in (1e9, 1e10, 1e11, 1e12, 1e13, 1e14):
plt.loglog(freq, freq_dot_gauss(freq, i), 'r:', linewidth=1.5)
xytext = (0, 5)
text = ax.annotate(
f'$10^{{ {int(np.log10(i)):d} }}$ G',
xy=(6, np.min(freq_dot_gauss(freq, i)*2)),
xytext=xytext,
textcoords="offset points",
size=15,
color='r',
zorder=1,
horizontalalignment="left",
verticalalignment="center_baseline",
)
text.set_rotation_mode("anchor")
text.set_rotation(-10)
for i in (1e30, 1e33, 1e36):
plt.loglog(freq, freq_dot_ergs(freq, i), 'b-.', linewidth=1.5)
xytext = (0, 5)
text = ax.annotate(
f'$10^{{ {int(np.log10(i)):d} }}$ erg/s',
xy=(1, freq_dot_ergs(1.1, i)),
xytext=xytext,
textcoords="offset points",
size=15,
color='b',
zorder=1,
horizontalalignment="left",
verticalalignment="center_baseline",
)
text.set_rotation_mode("anchor")
text.set_rotation(25)
plt.xlabel('Period(s)')
plt.ylabel('Period Derivative')
plt.show()
|
