def fitting_method_subpart_skyrme(central_pressure, surface_guess, mass_guess,
f1, f2, lst_x, lst_y, lst_z):
fitting_point = surface_guess / 2.0
small_x = 0.001
yout, zout = central_pressure, 0
xout = small_x
num_steps = 400
hsout = fitting_point / float(num_steps)
lst_x.append(0)
lst_y.append(yout)
lst_z.append(zout)
for j in range(num_steps):
if xout + hsout - fitting_point > -0.00000001:
hsout = fitting_point - xout
xout, yout, zout = rungeKetta(xout, yout, zout, f1, f2, hsout, 0)
lst_x.append(xout)
lst_y.append(yout)
lst_z.append(zout)
break
else:
xout, yout, zout = rungeKetta(xout, yout, zout, f1, f2, hsout, 0)
lst_x.append(xout)
lst_y.append(yout)
lst_z.append(zout)
to_reverse_x = []
to_reverse_y = []
to_reverse_z = []
xin = surface_guess
yin, zin = 0, mass_guess
hsin = -fitting_point / float(num_steps)
to_reverse_x.append(xin)
to_reverse_y.append(yin)
to_reverse_z.append(zin)
for i in range(num_steps):
if fitting_point - (xin + hsin) > -0.000000001:
hsin = fitting_point - xin
xin, yin, zin = rungeKetta(xin, yin, zin, f1, f2, hsin, 0)
break
else:
xin, yin, zin = rungeKetta(xin, yin, zin, f1, f2, hsin, 0)
to_reverse_x.append(xin)
to_reverse_y.append(yin)
to_reverse_z.append(zin)
to_reverse_x.reverse()
to_reverse_y.reverse()
to_reverse_z.reverse()
lst_x.extend(to_reverse_x)
lst_y.extend(to_reverse_y)
lst_z.extend(to_reverse_z)
Y = yin - yout
Z = zin - zout
return Y, Z
def fitting_method_subpart(zeta, sigma, f1, f2, lst_x, lst_y, lst_z, surface, G, total_mass): fitting_point = surface/2.0 xout = 0 yout = zeta zout = -5 * zeta num_steps = 100 hsout = fitting_point/(num_steps) lst_x.append(xout) lst_y.append(yout) lst_z.append(zout) for j in range(num_steps): if xout + hsout - fitting_point > -0.00000001: hsout = fitting_point - xout xout, yout, zout = rungeKetta(xout, yout, zout, f1, f2, hsout, 2) lst_x.append(xout) lst_y.append(yout) lst_z.append(zout) break else: xout, yout, zout = rungeKetta(xout, yout, zout, f1, f2, hsout, 2) lst_x.append(xout) lst_y.append(yout) lst_z.append(zout) to_reverse_x = [] to_reverse_y = [] to_reverse_z = [] xin = surface yin = 1 zin = -(4 + (sigma**(2) * surface**(3)/(G * total_mass))) hsin = -fitting_point/(num_steps) to_reverse_x.append(xin) to_reverse_y.append(yin) to_reverse_z.append(zin) for i in range(num_steps): if fitting_point - (xin + hsin) > -0.000000001: hsin = fitting_point - xin xin, yin, zin = rungeKetta(xin, yin, zin, f1, f2, hsin, 2) break else: xin, yin, zin = rungeKetta(xin, yin, zin, f1, f2, hsin, 2) to_reverse_x.append(xin) to_reverse_y.append(yin) to_reverse_z.append(zin) to_reverse_x.reverse() to_reverse_y.reverse() to_reverse_z.reverse() lst_x.extend(to_reverse_x) lst_y.extend(to_reverse_y) lst_z.extend(to_reverse_z) Y = yin - yout Z = zin - zout return Y, Z
def one_direction_shot_adiabatic_radial(n=2): lei= get_information_polytrope(n=n) lst_M = lei[-1] lst_P = lei[-2] lst_rho = lei[-3] lst_R = lei[-4] total_mass = lei[-5] surface = lei[-6] G = lei[-7] sigma_guess = (3.9 * G * total_mass * surface**(-3)) zeta_outside = 1 num_steps =300 hs = -surface/(num_steps) for i in range(1000): print(i) R = surface zeta = zeta_outside delP = -(((sigma_guess * surface**(3))/(G * total_mass)) * zeta + 4 * zeta) print(delP) delPdr = createDelPdr(lst_P, lst_rho, lst_R, lst_M, G, sigma_guess, surface) for j in range(num_steps): R, zeta, delP = rungeKetta(R, zeta, delP, dcdr, delPdr, hs, n) bc = 3 * zeta + 0.6 * delP print(R) print(zeta) print(delP) delta = 0.001 shiftsigma_guess = sigma_guess * (1 + delta) R = surface zeta = zeta_outside delP = -(((shiftsigma_guess * surface**(3))/(G * total_mass)) * zeta + 4 * zeta) newdelPdr = createDelPdr(lst_P, lst_rho, lst_R, lst_M, G, shiftsigma_guess, surface) for j in range(num_steps): R, zeta, delP = rungeKetta(R, zeta, delP, dcdr, newdelPdr, hs, n) sbc = 3 * zeta + 0.6 * delP print(bc) print(sbc) break
def shooting_direct(central_density, f1, f2):
small_x = 0.00001
y, z = central_density, 0
x = small_x
approximate_radius = 2 * 10**(6)
hs = approximate_radius / 1000
lst_x = [0]
lst_y = [central_density]
lst_z = [0]
for i in range(10000):
x, y, z = rungeKetta(x, y, z, f1, f2, hs, gamma)
lst_x.append(x)
lst_y.append(y)
lst_z.append(z)
if abs(y) < 3 * hs and hs > (approximate_radius / 10000000):
hs = hs / 2
if y < 0.000001:
break
print("Surface at: ", x / (10**(5)))
print("Total mass: ", z / mass_sun)
def shooting_skyrme(central_pressure):
small_x = 0.00001
y, z = central_pressure, 0.0
x = small_x
approximate_radius = 2 * 10**(6)
hs = approximate_radius / 1000
hs = 1.15988 * 10**(2)
lst_x = [0.0]
lst_y = [central_pressure]
lst_z = [0.0]
lst_logbrunt = []
lst_brunt = []
lst_x_logbrunt = []
lst_x_brunt = []
lst_speed_sound = []
lst_n = []
lst_xp = []
lst_xe = []
lst_xmu = []
lst_xn = []
for i in range(10000):
x, y, z = rungeKetta(x, y, z, dPSkyrme, dMSkyrme, hs, gamma)
print(x)
lst_x.append(x)
lst_y.append(y)
lst_z.append(z)
g = (z * G) / (x**(2))
try:
curr_n = extract_n_pressure(y)
if rho(curr_n) > 10**(14):
xp, xe, xmu, xn = get_I(curr_n, sc=True)
lst_xp.append(xp)
lst_xe.append(xe)
lst_xmu.append(xmu)
lst_xn.append(xn)
lst_n.append(curr_n)
adiabatic_speed = get_v_adiabatic(curr_n)
xdiff, ydiff, zdiff = rungeKetta(x, y, z, dPSkyrme, dMSkyrme,
0.1, gamma)
n_diff = extract_n_pressure(ydiff)
equilibrium_ratio = (ydiff - y) / (
(energy_density(n_diff) - energy_density(curr_n)))
if adiabatic_speed / c > 1:
print(adiabatic_speed / c)
print('Adiabatic speed suspicious')
elif equilibrium_ratio > 1:
print(equilibrium_ratio)
print('Equilibrium speed suspicious')
equilibrium_speed = c * equilibrium_ratio
brunt = (g**(2) * ((1 / equilibrium_speed)**(2) -
(1 / adiabatic_speed)**(2)))**(0.5)
lst_x_logbrunt.append(x)
lst_logbrunt.append(math.log(brunt, 10))
lst_speed_sound.append(adiabatic_speed)
if brunt < 10**(4.5):
lst_x_brunt.append(x)
lst_brunt.append(brunt)
except Exception as e:
value = 2
if abs(y) < 2 * hs and hs > (approximate_radius / 10, 000, 000):
hs = hs / 2
if y < 0.000001:
break
if x > 10**(4):
break
#print(y)
print("Surface at: ", x / (10**(5)))
print("Total mass: ", z / mass_sun)
#return lst_n, lst_xp, lst_xe, lst_xmu, lst_xn
#return [x/(10**(5)), z/mass_sun]
lst_xrho = []
lst_rho = []
lst_P = []
for i in range(len(lst_y)):
try:
curr_n = extract_n_pressure(lst_y[i])
curr_rho = rho(curr_n)
lst_P.append(lst_y[i])
lst_rho.append(curr_rho)
lst_xrho.append(lst_x[i])
except:
pass
print(lst_x[:5])
print(lst_y[:5])
lst_mass = [lst_z[i] / mass_sun for i in range(len(lst_z))]
print(lst_mass[:5])
return lst_x_brunt, lst_brunt, lst_x_logbrunt, lst_logbrunt, lst_xrho, lst_rho, lst_P
def shooting_skyrme(central_pressure):
small_x = 0.00001
y, z = central_pressure, 0.0
x = small_x
approximate_radius = 2 * 10**(6)
hs = approximate_radius / 1000
hs = 1.15988 * 10**(2)
lst_x = [0.0]
lst_y = [central_pressure]
lst_z = [0.0]
lst_logbrunt = []
lst_brunt = []
lst_x_logbrunt = []
lst_x_brunt = []
lst_speed_sound = []
lst_eq_speed = []
lst_n = []
lst_xp = []
lst_xe = []
lst_xmu = []
lst_xn = []
lst_g = []
lst_rho2 = []
for i in range(10000):
x, y, z = rungeKetta(x, y, z, dPSkyrme, dMSkyrme, hs, gamma)
print(x)
lst_x.append(x)
lst_y.append(y)
lst_z.append(z)
g = (z * G) / (x**(2))
lst_g.append(g**(2))
try:
curr_n = extract_n_pressure(y / conversion_pressure)
if rho(curr_n) > 1.6 * 10**(14):
xp, xe, xmu, xn = get_I(curr_n, sc=True)
lst_xp.append(xp * curr_n * 10**(39))
lst_xe.append(xe * curr_n * 10**(39))
lst_xmu.append(xmu * curr_n * 10**(39))
lst_xn.append(xn * curr_n * 10**(39))
lst_n.append(curr_n * 10**(39))
adiabatic_speed = get_v_adiabatic(curr_n)
xdiff, ydiff, zdiff = rungeKetta(x, y, z, dPSkyrme, dMSkyrme,
10, gamma)
n_diff = extract_n_pressure(ydiff / conversion_pressure)
equilibrium_ratio = (ydiff - y) / (
conversion_pressure *
(energy_density(n_diff) - energy_density(curr_n)))
if adiabatic_speed / c > 1:
print(adiabatic_speed / c)
print('Adiabatic speed suspicious')
elif equilibrium_ratio > 1:
print(equilibrium_ratio)
print('Equilibrium speed suspicious')
equilibrium_speed = c * equilibrium_ratio
lst_eq_speed.append(equilibrium_speed**(2))
brunt = (g**(2) * ((1 / equilibrium_speed)**(2) -
(1 / adiabatic_speed)**(2)))**(0.5)
lst_x_logbrunt.append(x)
lst_logbrunt.append(math.log(brunt, 10))
lst_speed_sound.append(adiabatic_speed**(2))
lst_x_brunt.append(x)
lst_brunt.append(brunt**(2))
lst_rho2.append(rho(curr_n))
except Exception as e:
value = 2
if abs(y) < 2 * hs and hs > (approximate_radius / 10, 000, 000):
hs = hs / 2
if y < 0.000001:
break
#print(y)
print("Surface at: ", x / (10**(5)))
print("Total mass: ", z / mass_sun)
#return lst_n, lst_xp, lst_xe, lst_xmu, lst_xn
#return [x/(10**(5)), z/mass_sun]
lst_mass = [lst_z[i] / mass_sun for i in range(len(lst_z))]
surface = x
total_mass = z
lst_r = lst_x
lst_m = lst_z
lst_moverM = [-29.0]
for i in range(1, len(lst_m)):
lst_moverM.append(math.log(lst_m[i] / total_mass))
lst_P = lst_y
lst_rho = []
for i in range(len(lst_P)):
try:
val = getrho(lst_P[i])
if val > 3 * 10**(14):
lst_rho.append(val)
else:
lst_rho.append(getRhoBSM(lst_P[i]))
except:
try:
val = getRhoBSM(lst_P[i])
lst_rho.append(val)
except:
val = getRhoPoly(lst_P[i])
lst_rho.append(val)
adiabatic_exp = []
adiabatic_val = 0
for i in range(len(lst_rho)):
y = lst_P[i]
try:
curr_n = extract_n_pressure(y / conversion_pressure)
adiabatic_speed = get_v_adiabatic(curr_n)
adiabatic_val = adiabatic_speed * (lst_rho[i] / y)
adiabatic_exp.append(adiabatic_val)
except:
if i != (len(lst_rho) - 1):
top = lst_P[i + 1] - lst_P[i - 1]
bot = lst_rho[i + 1] - lst_rho[i - 1]
adiabatic_val = top / bot * (lst_rho[i] / y)
adiabatic > exp.append(adiabatic_val)
else:
adiabatic_exp.append(adiabatic_val)
deriv_diff = []
diff_val = 0
for i in range(len(lst_r)):
if i != (len(lst_r) - 1):
top1 = lst_P[i + 1] - lst_P[i]
top2 = lst_rho[i + 1] - lst_rho[i]
bot = lst_r[i + 1] - lst_r[i]
term1 = (1. / adiabatic_exp[i]) * (top1 / bot) * (lst_r[i] /
lst_P[i])
term2 = (top2 / bot) * (lst_r[i] / lst_rho[i])
diff_val = term1 - term2
deriv_diff.append(diff_val)
else:
deriv_diff.append(diff_val)
lst_Rminusr = [surface - lst_x[i] for i in range(len(lst_r))]
print(len(lst_r))
print(len(lst_moverM))
print(len(lst_P))
print(len(lst_rho))
print(len(adiabatic_exp))
print(len(deriv_diff))
print(len(lst_Rminusr))
print('writing')
file = open('skyrme.fgong', 'w')
nl = "\n"
file.write("fee" + nl)
file.write("fi" + nl)
file.write("fo" + nl)
file.write("fum" + nl)
separator = " "
file.write(
str(len(lst_r)) + separator + "15" + separator + "40" + separator +
"1300" + nl)
empty_val = str(0.0) + separator
file.write(
str(total_mass) + separator + str(surface) + separator +
get_n_copies(empty_val, 12) + str(0.0) + nl)
for i in range(len(lst_r)):
print(i)
full_string = ""
full_string = full_string + str(lst_r[i]) + separator + str(
lst_moverM[i]) + separator
full_string = full_string + empty_val
full_string = full_string + str(lst_P[i]) + separator + str(
lst_rho[i]) + separator
full_string = full_string + get_n_copies(empty_val, 4)
full_string = full_string + str(adiabatic_exp[i]) + separator
full_string = full_string + get_n_copies(empty_val, 4)
full_string = full_string + str(deriv_diff[i]) + separator
full_string = full_string + get_n_copies(empty_val, 2)
full_string = full_string + str(lst_Rminusr[i]) + separator
full_string = full_string + get_n_copies(empty_val, 21)
full_string = full_string + str(0.0) + nl
file.write(full_string)
file.close()
return surface, total_mass, lst_r, lst_moverM, lst_P, lst_rho, adiabatic_exp, deriv_diff, lst_Rminusr