def dynamic_height_1d(Tb, Sb, dT, dS):
#
# INPUT: background Tb and Sb
# departure from background: dT, dS
# OUTPUT: Dynamic height departure from background
#
ogrid = ModelGrid(fname='../wrkdir/grid_spec.nc')
p = np.ones(np.shape(Sb))
h = np.ones(np.shape(Sb))
for index in range(0, np.shape(p)[0]):
p[index] = ogrid.zt[index]
if (index == 0):
h[index] = ogrid.zb[index] #-eta
else:
h[index] = abs(ogrid.zb[index] - ogrid.zb[index - 1])
print 'compute rho'
rho_b = eos.density(Sb, Tb, p)
rho_a = eos.density(Sb + dS, Tb + dT, p)
rho_a_halo = eos.density(Sb + dS, Tb, p)
rho_a_thermo = eos.density(Sb, Tb + dT, p)
dh = -np.nansum(h * (rho_a - rho_b) / rho_b, axis=0)
dh_halo = -np.nansum(h * (rho_a_halo - rho_b) / rho_b, axis=0)
dh_thermo = -np.nansum(h * (rho_a_thermo - rho_b) / rho_b, axis=0)
return dh, dh_thermo, dh_halo
def central_values(Pc, delta_m, mue):
"""
Constructs the boundary conditions at the edge of a small, constant density
core of mass delta_m with central pressure P_c
Arguments
Pc
central pressure (units = Pa)
delta_m
core mass (units = kg)
mue
nucleon/electron ratio
Returns
z = array([ r, p ])
central values of radius and pressure (units = m, Pa)
"""
z = np.zeros(2)
r_delta_m = ((3 * delta_m) / (4 * sc.pi * density(Pc, mue)))**(
1 / 3) #Radius depends on delta_m and density
p_delta_m = Pc #Pressure is equal to Pc
# compute initial values of z = [ r, p ]
z = [r_delta_m, p_delta_m]
return z
def stellar_derivatives(m, z, mue):
"""
RHS of Lagrangian differential equations for radius and pressure
Arguments
m
current value of the mass (units = kg)
z (array)
current values of (radius, pressure) (units = m, Pa)
Returns
dzdm (array)
Lagrangian derivatives dr/dm, dP/dm (units =m/kg,Pa/kg)
"""
rho = density(z[1], mue)
drdm = 1 / (4 * np.pi * z[0]**2 * rho
) #Lagrangian Derivative of r w.r.t. m
dpdm = (-sc.G * m) / (4 * z[0]**4 * np.pi
) #Lagrangian Derivative of p w.r.t. m
dzdm = np.zeros_like(z)
dzdm[0] = drdm
dzdm[1] = dpdm
return dzdm
def create_table():
"""
Creates tables of values and saves them as a .txt file
returns: nothing explicitly, function creates table
"""
outfile = 'table.txt'
with open(outfile, 'w') as fout:
fout.write(
' | {0:7} | {1:7} | {2:7} | {3:7} | {4:7} | {5:7} | \n'.format(
'M/M_sun ', 'R/R_sun', 'P_c (MKS)', 'P_c / GM^2R^-4',
'rho_c (MKS)', 'rho / [3M /4 *pi R^3] '))
# '--:' means right-align
fout.write(
' | {0:7} | {1:7} | {2:7} | {3:7} | {4:7} | {5:7} | \n'.format(
'--:', '--:', '--:', '--:', '--:', '--:'))
for i in range(len(actual_masses)):
mass = actual_masses[i]
Pc, ms, rs, ps = get_zeros(mass)
#getting actual central density and radius
central_r = rs[-1]
central_dens = density(ps[0], mue)
fout.write(
' | {0:7.1f} | {1:7e} | {2:7e} | {3:7e} | {4:7e} | {5:7f} | \n'
.format(mass / sc.Msun, central_r / sc.Rsun, Pc,
Pc * central_r**4 / (sc.G * mass**2), central_dens,
central_dens / (3 * mass /
(4 * np.pi * central_r**3))))
def rotprofile(eos, energy_center, number=100, initr=0.001, energy_0=1e7):
'''Calculate the enthalpy profile of a slowly rotating neutron star with
equation of state eos and central energy density energy_center in g/cm^3.
optional arguments:
number: number of points
initr: size of central seed
energy_0: energy density at which to stop resolving crust. This doesn't
need to be tiny (and may cause problems if it is). Integration still
goes to surface.
'''
#TODO: consolodate the profile functions; this mostly just repeats
#profile but with different initial conditions
# central enthalpy and density
enth_c = eos.enthalpy(energy_center)
dens_c = eos.density(enth_c)
# set up a core with small initial radius and mass
initm = 4.0 / 3.0 * np.pi * (initr)**3 * energy_center * Gcc
initma = 4.0 / 3.0 * np.pi * (initr)**3 * dens_c * Gcc
init_rm = np.array([initr, initm, initma, 0.0, 1.0])
# resolve core with linear spacing
linenths = np.linspace(enth_c, enth_c / 10, number)[:-1]
# resolve crust with log enth spacing
enth_0 = eos.enthalpy(energy_0) # end the crust spacing here and jump to 0
logenths = np.logspace(np.log10(linenths[-1]), np.log10(enth_0),
number / 2 + 1)
# set of enthalpies to calculate energy density, radius, and mass at
enths = np.hstack(
(np.array(linenths), np.array(logenths[1:]), np.array(0)))
# enths = np.linspace(enth_c, 0, number) # boring way for debugging
# integrate the TOV equations specified in deriv above
rms = integrate.odeint(rotderiv, init_rm, enths, args=(eos, ))
return np.vstack((enths, np.transpose(rms)))
def rotprofile(eos, energy_center , number=100, initr=0.001, energy_0=1e7):
'''Calculate the enthalpy profile of a slowly rotating neutron star with
equation of state eos and central energy density energy_center in g/cm^3.
optional arguments:
number: number of points
initr: size of central seed
energy_0: energy density at which to stop resolving crust. This doesn't
need to be tiny (and may cause problems if it is). Integration still
goes to surface.
'''
#TODO: consolodate the profile functions; this mostly just repeats
#profile but with different initial conditions
# central enthalpy and density
enth_c = eos.enthalpy(energy_center)
dens_c = eos.density(enth_c)
# set up a core with small initial radius and mass
initm = 4.0/3.0*np.pi*(initr)**3 * energy_center * Gcc
initma = 4.0/3.0*np.pi*(initr)**3 * dens_c * Gcc
init_rm = np.array([initr,initm, initma, 0.0, 1.0])
# resolve core with linear spacing
linenths = np.linspace(enth_c, enth_c/10, number)[:-1]
# resolve crust with log enth spacing
enth_0 = eos.enthalpy(energy_0) # end the crust spacing here and jump to 0
logenths = np.logspace(np.log10(linenths[-1]),np.log10(enth_0),
number/2+1)
# set of enthalpies to calculate energy density, radius, and mass at
enths = np.hstack((np.array(linenths),np.array(logenths[1:]),np.array(0)))
# enths = np.linspace(enth_c, 0, number) # boring way for debugging
# integrate the TOV equations specified in deriv above
rms = integrate.odeint(rotderiv, init_rm, enths, args=(eos,))
return np.vstack((enths,np.transpose(rms)))
def rotderiv(rm_vector, enthalpy, eos):
''' The TOV equations augmented for a linearly perturbed, slowly
rotating neutron star. Also includes rest mass of star.'''
(rad, mass, restmass, alpha, omega) = rm_vector
pr = eos.pressure(enthalpy) * Gcc
en = eos.energy(enthalpy) * Gcc
rho = eos.density(enthalpy)**Gcc
factor = rad - 2 * mass
coef = 4.0 * np.pi
drdenth = -rad * factor / (mass + coef * rad**3 * pr)
dmdenth = coef * en * rad**2 * drdenth
dmadenth = coef * rho * rad**2 * drdenth / (factor / rad)**0.5
domega = alpha * drdenth
dalpha = drdenth * (- 4.0 * alpha / rad \
+ coef * rad * (pr + en) * (4.0 * omega + rad * alpha ) / factor )
return np.array([drdenth, dmdenth, dmadenth, dalpha, domega])
def rotderiv(rm_vector, enthalpy, eos):
''' The TOV equations augmented for a linearly perturbed, slowly
rotating neutron star. Also includes rest mass of star.'''
(rad, mass, restmass, alpha, omega) = rm_vector
pr = eos.pressure(enthalpy) * Gcc
en = eos.energy(enthalpy) * Gcc
rho = eos.density(enthalpy) ** Gcc
factor = rad - 2 * mass
coef = 4.0 * np.pi
drdenth = - rad * factor / (mass + coef * rad**3 * pr)
dmdenth = coef * en * rad**2 * drdenth
dmadenth = coef * rho * rad**2 * drdenth / ( factor / rad )**0.5
domega = alpha * drdenth
dalpha = drdenth * (- 4.0 * alpha / rad \
+ coef * rad * (pr + en) * (4.0 * omega + rad * alpha ) / factor )
return np.array([drdenth,dmdenth, dmadenth, dalpha, domega])
def steric(Tb, Sb, dT, dS, deta, eta):
ogrid = ModelGrid(fname='../wrkdir/grid_spec.nc')
p = np.ones(np.shape(Sb))
h = np.ones(np.shape(Sb))
for index in range(0, np.shape(p)[0]):
p[index, :, :] = ogrid.zt[index]
if (index == 0):
h[index, :, :] = ogrid.zb[index] #-eta
else:
h[index, :, :] = abs(ogrid.zb[index] - ogrid.zb[index - 1])
rho_b = eos.density(Sb, Tb, p)
rho_a = eos.density(Sb + dS, Tb + dT, p)
rho_a_halo = eos.density(Sb + dS, Tb, p)
rho_a_thermo = eos.density(Sb, Tb + dT, p)
dsteric = -np.nansum(h * (rho_a - rho_b) / rho_b, axis=0)
dhalosteric = -np.nansum(h * (rho_a_halo - rho_b) / rho_b, axis=0)
dthermosteric = -np.nansum(h * (rho_a_thermo - rho_b) / rho_b, axis=0)
return dsteric, dhalosteric, dthermosteric
'''
print np.shape(dsteric), np.shape(Sb)
dsteric[dsteric==0.0]=np.nan
deta[deta==0.0]=np.nan
print 'deta-dsteric=',np.nansum(np.abs(deta-dsteric))
fig = plt.figure(num=1, figsize=(19,12), facecolor='w')
#grid = AxesGrid(fig, 111, nrows_ncols = (2, 3), axes_pad = 0.5,
# cbar_location="bottom",
# cbar_mode="each",
# cbar_size="7%",
# cbar_pad="2%")
vmax=0.1
vmin=-vmax
#plt.sca(grid[0])
plt.subplot(231)
ch=plt2d(ogrid.x, ogrid.y, dsteric, minval=vmin, maxval=vmax, colmap=cm.jet)
#grid.cbar_axes[0].colorbar(ch)
plt.title('Steric height infered increment [m]')
#plt.sca(grid[1])
plt.subplot(232)
incr_s=np.flipud(dhalosteric)
incr_s[incr_s==0.0]=np.nan
ch=plt2d(ogrid.x, ogrid.y, dhalosteric, minval=vmin, maxval=vmax, colmap=cm.jet)
#grid.cbar_axes[1].colorbar(ch)
plt.title('Halo Steric height infered increment [m]')
#plt.sca(grid[2])
plt.subplot(233)
incr_t=np.flipud(dthermosteric)
incr_t[incr_t==0.0]=np.nan
ch=plt2d(ogrid.x, ogrid.y, dthermosteric, minval=vmin, maxval=vmax, colmap=cm.jet)
#grid.cbar_axes[2].colorbar(ch)
plt.title('Thermo Steric height infered increment [m]')
#plt.sca(grid[3])
plt.subplot(234)
ch=plt2d(ogrid.x, ogrid.y, deta, minval=vmin, maxval=vmax, colmap=cm.jet)
#grid.cbar_axes[3].colorbar(ch)
plt.title('SSH increment [m]')
vmin=-0.1
vmax=0.1
#plt.sca(grid[4])
plt.subplot(235)
err=deta-dsteric
#err[np.abs(err)<0.05]=np.nan
#err=np.abs(deta/dsteric)
ch=plt2d(ogrid.x, ogrid.y, err, minval=vmin, maxval=vmax, colmap=cm.bwr)
#grid.cbar_axes[4].colorbar(ch)
plt.title('SSH - Steric [m]')
#plt.sca(grid[5])
plt.subplot(236)
err=deta-dthermosteric
#err=np.abs(deta/dthermosteric)
#err[np.abs(err)<0.05]=np.nan
ch=plt2d(ogrid.x, ogrid.y, err, minval=vmin, maxval=vmax, colmap=cm.bwr)
#grid.cbar_axes[5].colorbar(ch)
plt.title('SSH - Thermosteric [m]')
'''
plt.subplot(235)
incr_t = np.flipud(dthermosteric)
incr_t[incr_t == 0.0] = np.nan
plt.imshow(incr_t, vmin=vmin, vmax=vmax)
#plt.imshow(np.flipud(dthermosteric),vmin=vmin,vmax=vmax)
plt.colorbar()
plt.subplot(231)
plt.imshow(np.flipud(deta), vmin=vmin, vmax=vmax)
plt.title('SSH increment [m]')
plt.colorbar()
plt.subplot(233)
err = np.flipud(deta - dsteric)
err[np.abs(err) < 0.02] = np.nan
plt.imshow(err, vmin=vmin, vmax=vmax)
#plt.imshow(np.flipud(deta-dsteric),vmin=vmin,vmax=vmax)
plt.title('SSH - Steric height [m]')
plt.colorbar()
'''
