def luminosity_distance(z, k=0):
''' Calculate the luminosity distance for a given redshift.
Parameters:
* z (float or array): the redshift(s)
* k = 0 (float): the curvature constant.
Returns:
The luminosity distance in Mpc
'''
if not (type(z) is np.ndarray): #Allow for passing a single z
z = np.array([z])
n = len(z)
if const.lam == 0:
denom = np.sqrt(1+2*const.q0*z) + 1 + const.q0*z
dlum = (const.c*z/const.H0)*(1 + z*(1-const.q0)/denom)
return dlum
else:
dlum = np.zeros(n)
for i in xrange(n):
if z[i] <= 0:
dlum[i] = 0.0
else:
dlum[i] = quadrature(_ldist, 0, z[i])[0]
if k > 0:
dlum = np.sinh(np.sqrt(k)*dlum)/np.sqrt(k)
elif k < 0:
dlum = np.sin(np.sqrt(-k)*dlum)/np.sqrt(-k)
return outputify(const.c*(1+z)*dlum/const.H0)
def z_to_cdist(z):
''' Calculate the comoving distance
Parameters:
z (float): redshift
Returns:
Comoving distance in Mpc
'''
Ez_func = lambda x: 1./np.sqrt(const.Omega0*(1.+x)**3+const.lam)
dist = const.c/const.H0 * quadrature(Ez_func, 0, z)[0]
return outputify(dist)
def angular_size(dl, z):
''' Calculate the angular size of an object at a given
redshift.
Parameters:
* dl (float or array): the physical size in kpc
* z (float or array): the redshift of the object
Returns:
The angluar size in arcseconds
'''
angle = 180./(3.1415)*3600.*dl*(1+z)**2/(1000*luminosity_distance(z))
return outputify(angle)
def z_to_cdist(z):
''' Calculate the comoving distance
Parameters:
z (float or array): redshift
Returns:
Comoving distance in Mpc
'''
z = np.atleast_1d(z)
dist = np.zeros_like(z)
for i in range(len(z)):
Ez_func = lambda x: 1./np.sqrt(const.Omega0*(1.+x)**3+const.lam)
dist[i] = const.c/const.H0 * quadrature(Ez_func, 0, z[i])[0]
return outputify(dist)
def cdist_to_z(dist):
''' Calculate the redshift correspoding to the given redshift.
Parameters:
* dist (float or array): the distance in comoving Mpc
Returns:
redshift corresponding to the distance.
.. note::
Uses a precalculated table for interpolation. Only valid for
0 <= z < 100
'''
dist = np.atleast_1d(dist)
z = np.zeros_like(dist)
func = interp1d(precalc_table_cdist, precalc_table_z, kind='cubic')
for i in range(len(dist)):
z[i] = func(dist[i])
return outputify(z)