from xpsi.global_imports import *
from xpsi.utils import make_verbose
from xpsi.Parameter import Parameter
from xpsi.ParameterSubspace import ParameterSubspace
[docs]class Spacetime(ParameterSubspace):
""" The ambient Schwarzschild spacetime and Earth coordinates.
:param dict bounds:
Tuples of hard bounds on parameters with keys matching the names
in the initialiser body. A ``None`` bound will be interpreted as
fixed variable, in which case a value must be supplied in the
corresponding dictionary. If there is no entry for a default
parameter, it will be assumed to be fixed, but an exception
will be raised if there is no associated value.
:param dict values:
Values of fixed parameters or initial values for free parameters,
with keys matching the names in the initialiser body. If there is
no entry for a default parameter, no initial value will be specified,
but an exception will be raised if there is also no bound specified.
We define a property for parameters and combinations of parameters to
shortcut access, given that this subspace is passed to other subspaces
for model computation. We would like to access the values with fewer
characters than ``self[<name>]``.
"""
required_names = ['frequency',
'mass',
'radius',
'distance',
'cos_inclination']
def __init__(self, bounds, values):
if not isinstance(bounds, dict) or not isinstance(values, dict):
raise TypeError("Both bounds and values need to be dictionaries.")
f = Parameter('frequency',
strict_bounds = (0.0, 800.0),
bounds = bounds.get('frequency', None),
doc = 'Spin frequency [Hz]',
symbol = r'$f$',
value = values.get('frequency', None))
M = Parameter('mass',
strict_bounds = (0.001, 3.0),
bounds = bounds.get('mass', None),
doc = 'Gravitational mass [solar masses]',
symbol = r'$M$',
value = values.get('mass', None))
R = Parameter('radius',
strict_bounds = (1.0, 20.0),
bounds = bounds.get('radius', None),
doc = 'Coordinate equatorial radius [km]',
symbol = r'$R_{\rm eq}$',
value = values.get('radius', None))
D = Parameter('distance',
strict_bounds = (0.01, 30.0), # inside Milky Way
bounds = bounds.get('distance', None),
doc = 'Earth distance [kpc]',
symbol = r'$D$',
value = values.get('distance', None))
cosi = Parameter('cos_inclination',
strict_bounds = (-1.0, 1.0),
bounds = bounds.get('cos_inclination', None),
doc = 'Cosine of Earth inclination to rotation axis',
symbol = r'$\cos(i)$',
value = values.get('cos_inclination', None))
super(Spacetime, self).__init__(f, M, R, D, cosi)
@property
def M(self):
""" Get the (rotationally deformed) gravitational mass in SI. """
return self['mass'] * _GM * _csq / _G
@property
def r_g(self):
""" Get the Schwarzschild gravitational radius in SI. """
return self['mass'] * _GM
@property
def r_s(self):
""" Get the Schwarzschild radius in SI. """
return 2.0 * self.r_g
@property
def R(self):
""" Get the coordinate equatorial radius in SI. """
return self['radius'] * _km
@property
def R_r_s(self):
""" Get the ratio of the equatorial radius to the Schwarzschild radius.
"""
return self.R / self.r_s
@property
def f(self):
""" Get the coordinate rotation frequency. """
return self['frequency']
@property
def Omega(self):
""" Get the coordinate *angular* rotation frequency. """
return _2pi * self['frequency']
@property
def i(self):
""" Get the inclination of the Earth to the rotational axis. """
return _m.acos(self['cos_inclination'])
@property
def d(self):
""" Get the distance of the Earth to the star in SI. """
return self['distance'] * _kpc
@property
def d_sq(self):
""" Get the squared distance of the Earth to the star in SI. """
return self.d * self.d
@property
def zeta(self):
""" Get the derived parameter ``zeta`` for universal relations.
A dimensionless function of stellar properties.
See Morsink et al. (2007), and AlGendy & Morsink (2014).
"""
try:
return self._zeta
except AttributeError:
return self.r_g / self.R
@property
def epsilon(self):
""" Get the derived parameter ``epsilon`` for universal relations.
A dimensionless function of stellar properties.
See Morsink et al. (2007), and AlGendy & Morsink (2014).
"""
try:
return self._epsilon
except AttributeError:
return self.Omega**2.0 * self.R**3.0 / (_G * self.M)
@property
def a(self):
""" Get the spin parameter, first order in spin.
See AlGendy & Morsink (2014).
"""
try:
return self._a
except AttributeError:
zeta = self.zeta
I_dimless = _m.sqrt(zeta) * (1.136 - 2.53 * zeta + 5.6 * zeta * zeta)
a = self.R * self.R * self.Omega * I_dimless / _c
return a
@a.setter
def a(self, a):
""" Set the spin parameter. """
self._a = a
@a.deleter
def a(self):
""" Delete the spin parameter. """
try:
del self._a
except AttributeError:
pass # silently do nothing
@property
def q(self):
""" Get the dimensionless mass quadrupole, second order in spin.
See AlGendy & Morsink (2014).
"""
try:
return self._q
except AttributeError:
temp = self.epsilon * 0.11 / (self.zeta * self.zeta)
temp -= self.a * self.a / (self.r_g * self.r_g)
return temp + 0.4554 * 4.0 * self.epsilon * self.zeta / 3.0
@q.setter
def q(self, q):
""" Set the mass quadrupole moment. """
self._q = q
@q.deleter
def q(self):
""" Delete the mass quadrupole moment. """
try:
del self._q
except AttributeError:
pass # silently do nothing
Spacetime._update_doc()