def lumdist(z,
h0=None,
k=None,
lambda0=None,
omega_m=None,
q0=None,
silent=None):
'''Syntax: result = lumdist(z, H0 = ,k=, Lambda0 = ])
Returns luminosity distance in Mpc'''
scal = False
scalret = lambda x: x[0] if scal else x
if isinstance(z, list):
z = numpy.array(z)
elif isinstance(z, ndarray):
pass
else:
scal = True
z = array([z])
n = len(z)
omega_m, lambda0, k, q0 = cosmo_param(omega_m, lambda0, k, q0)
# Check keywords
c = 2.99792458e5 # speed of light in km/s
if h0 is None:
h0 = 70
if not silent:
print 'LUMDIST: H0:', h0, ' Omega_m:', omega_m, ' Lambda0', lambda0, ' q0: ', q0, ' k: ', k #, format='(A,I3,A,f5.2,A,f5.2,A,f5.2,A,F5.2)'
# For the case of Lambda = 0, we use the closed form from equation 5.238 of
# Astrophysical Formulae (Lang 1998). This avoids terms that almost cancel
# at small q0*z better than the more familiar Mattig formula.
#
if lambda0 == 0:
denom = sqrt(1 + 2 * q0 * z) + 1 + q0 * z
dlum = (c * z / h0) * (1 + z * (1 - q0) / denom)
return scalret(dlum)
# For non-zero lambda
else:
dlum = z * 0.0
for i in range(n):
if z[i] <= 0.0:
dlum[i] = 0.0
else:
lz = quad(ldist, 0, z[i], args=(q0, lambda0))
dlum[i] = lz[0]
if k > 0:
dlum = sinh(sqrt(k) * dlum) / sqrt(k)
else:
if k < 0:
dlum = maximum(sin(sqrt(-k) * dlum) / sqrt(-k), 0)
return scalret(c * (1 + z) * dlum / h0)
def lumdist(z, h0=None, k=None, lambda0=None, omega_m=None, q0=None, silent=None):
'''Syntax: result = lumdist(z, H0 = ,k=, Lambda0 = ])
Returns luminosity distance in Mpc'''
scal=False
scalret = lambda x : x[0] if scal else x
if isinstance(z, list):
z = numpy.array(z)
elif isinstance(z, ndarray):
pass
else:
scal = True
z = array([z])
n = len(z)
omega_m, lambda0, k, q0 = cosmo_param(omega_m, lambda0, k, q0)
# Check keywords
c = 2.99792458e5 # speed of light in km/s
if h0 is None:
h0 = 70
if not silent:
print 'LUMDIST: H0:', h0, ' Omega_m:', omega_m, ' Lambda0', lambda0, ' q0: ', q0, ' k: ', k#, format='(A,I3,A,f5.2,A,f5.2,A,f5.2,A,F5.2)'
# For the case of Lambda = 0, we use the closed form from equation 5.238 of
# Astrophysical Formulae (Lang 1998). This avoids terms that almost cancel
# at small q0*z better than the more familiar Mattig formula.
#
if lambda0 == 0:
denom = sqrt(1 + 2 * q0 * z) + 1 + q0 * z
dlum = (c * z / h0) * (1 + z * (1 - q0) / denom)
return scalret(dlum)
# For non-zero lambda
else:
dlum = z * 0.0
for i in range(n):
if z[i] <= 0.0:
dlum[i] = 0.0
else:
lz = quad(ldist, 0, z[i], args=(q0, lambda0))
dlum[i] = lz[0]
if k > 0:
dlum = sinh(sqrt(k) * dlum) / sqrt(k)
else:
if k < 0:
dlum = maximum(sin(sqrt(-k) * dlum) / sqrt(-k), 0)
return scalret(c * (1 + z) * dlum / h0)
def galage(z, zform, h0=None, omega_m=None, lambda0=None, k=None, q0=None, silent=None):
""" NAME:
GALAGE
PURPOSE:
Determine the age of a galaxy given its redshift and a formation redshift.
CALLING SEQUENCE:
age = galage(z, [zform, H0 =, k=, lambda0 =, Omega_m= , q0 =, /SILENT])'
INPUTS:
z - positive numeric vector or scalar of measured redshifts
zform - redshift of galaxy formation (> z), numeric positive scalar
To determine the age of the universe at a given redshift, set zform
to a large number (e.g. ~1000).
OPTIONAL KEYWORD INPUTS:
H0 - Hubble constant in km/s/Mpc, positive scalar, default is 70
/SILENT - If set, then the adopted cosmological parameters are not
displayed at the terminal.
No more than two of the following four parameters should be
specified. None of them need be specified -- the adopted defaults
are given.
k - curvature constant, normalized to the closure density. Default is
0, (indicating a flat universe)
Omega_m - Matter density, normalized to the closure density, default
is 0.3. Must be non-negative
Lambda0 - Cosmological constant, normalized to the closure density,
default is 0.7
q0 - Deceleration parameter, numeric scalar = -R*(R'')/(R')^2, default
is -0.55
OUTPUTS:
age - age of galaxy in years, will have the same number of elements
as the input Z vector
EXAMPLE:
(1) Determine the age of a galaxy observed at z = 1.5 in a cosmology with
Omega_matter = 0.3 and Lambda = 0.0. Assume the formation redshift was
at z = 25, and use the default Hubble constant (=70 km/s/Mpc)
IDL> print,galage(1.5,25,Omega_m=0.3, Lambda = 0)
===> 3.35 Gyr
(2) Plot the age of a galaxy in Gyr out to a redshift of z = 5, assuming
the default cosmology (omega_m=0.3, lambda=0.7), and zform = 100
IDL> z = findgen(50)/10.
IDL> plot,z,galage(z,100)/1e9,xtit='z',ytit = 'Age (Gyr)'
PROCEDURE:
For a given formation time zform and a measured z, integrate dt/dz from
zform to z. Analytic formula of dt/dz in Gardner, PASP 110:291-305, 1998
March (eq. 7)
COMMENTS:
(1) Integrates using the IDL Astronomy Library procedure QSIMP. (The
intrinsic IDL QSIMP() function is not called because of its ridiculous
restriction that only scalar arguments can be passed to the integrating
function.) The function 'dtdz' is defined at the beginning of the
routine (so it can compile first).
(2) Should probably be fixed to use a different integrator from QSIMP when
computing age from an "infinite" redshift of formation. But using a
large value of zform seems to work adequately.
(3) An alternative set of IDL procedures for computing cosmological
parameters is available at
http://cerebus.as.arizona.edu/~ioannis/research/red/
PROCEDURES CALLED:
COSMO_PARAM, QSIMP
HISTORY:
STIS version by P. Plait (ACC) June 1999
IDL Astro Version W. Landsman (Raytheon ITSS) April 2000
Avoid integer overflow for more than 32767 redshifts July 2001
Convert to python S. Koposov 2010
"""
if h0 is None:
h0 = 70.0
omega_m, lambda0, k, q0 = cosmo_param(omega_m, lambda0, k, q0)
if silent is not None:
print 'GALAGE: H0:', h0, ' Omega_m:', omega_m, ' Lambda0', lambda0, ' q0: ', q0, ' k: ', k#, format='(A,I3,A,f5.2,A,f5.2,A,f5.2,A,F5.2)'
scal = False
if isinstance(z, list):
z = array(z)
elif isinstance(z, ndarray):
pass
else:
z = array([z])
scal = True
nz = len(z)
age = z * 0. #Return same dimensions and data type as Z
#
# use qsimp to integrate dt/dz to get age for each z
# watch out for null case of z >= zform
#
for i in range(nz):
if (z[i] >= zform):
age_z = 0
else:
#qsimp('dtdz', z[i], zform, age_z, q0=q0, lambda0=lambda0)
age_z = quad(dtdz, z[i], zform, args=(lambda0, q0))[0]
age[i] = age_z
# convert units of age: km/s/Mpc to years, divide by H0
# 3.085678e19 km --> 1 Mpc
# 3.15567e+07 sec --> 1 year
if scal:
age = age[0]
return age * 3.085678e+19 / 3.15567e+7 / h0
def galage(z,
zform,
h0=None,
omega_m=None,
lambda0=None,
k=None,
q0=None,
silent=None):
""" NAME:
GALAGE
PURPOSE:
Determine the age of a galaxy given its redshift and a formation redshift.
CALLING SEQUENCE:
age = galage(z, [zform, H0 =, k=, lambda0 =, Omega_m= , q0 =, /SILENT])'
INPUTS:
z - positive numeric vector or scalar of measured redshifts
zform - redshift of galaxy formation (> z), numeric positive scalar
To determine the age of the universe at a given redshift, set zform
to a large number (e.g. ~1000).
OPTIONAL KEYWORD INPUTS:
H0 - Hubble constant in km/s/Mpc, positive scalar, default is 70
/SILENT - If set, then the adopted cosmological parameters are not
displayed at the terminal.
No more than two of the following four parameters should be
specified. None of them need be specified -- the adopted defaults
are given.
k - curvature constant, normalized to the closure density. Default is
0, (indicating a flat universe)
Omega_m - Matter density, normalized to the closure density, default
is 0.3. Must be non-negative
Lambda0 - Cosmological constant, normalized to the closure density,
default is 0.7
q0 - Deceleration parameter, numeric scalar = -R*(R'')/(R')^2, default
is -0.55
OUTPUTS:
age - age of galaxy in years, will have the same number of elements
as the input Z vector
EXAMPLE:
(1) Determine the age of a galaxy observed at z = 1.5 in a cosmology with
Omega_matter = 0.3 and Lambda = 0.0. Assume the formation redshift was
at z = 25, and use the default Hubble constant (=70 km/s/Mpc)
IDL> print,galage(1.5,25,Omega_m=0.3, Lambda = 0)
===> 3.35 Gyr
(2) Plot the age of a galaxy in Gyr out to a redshift of z = 5, assuming
the default cosmology (omega_m=0.3, lambda=0.7), and zform = 100
IDL> z = findgen(50)/10.
IDL> plot,z,galage(z,100)/1e9,xtit='z',ytit = 'Age (Gyr)'
PROCEDURE:
For a given formation time zform and a measured z, integrate dt/dz from
zform to z. Analytic formula of dt/dz in Gardner, PASP 110:291-305, 1998
March (eq. 7)
COMMENTS:
(1) Integrates using the IDL Astronomy Library procedure QSIMP. (The
intrinsic IDL QSIMP() function is not called because of its ridiculous
restriction that only scalar arguments can be passed to the integrating
function.) The function 'dtdz' is defined at the beginning of the
routine (so it can compile first).
(2) Should probably be fixed to use a different integrator from QSIMP when
computing age from an "infinite" redshift of formation. But using a
large value of zform seems to work adequately.
(3) An alternative set of IDL procedures for computing cosmological
parameters is available at
http://cerebus.as.arizona.edu/~ioannis/research/red/
PROCEDURES CALLED:
COSMO_PARAM, QSIMP
HISTORY:
STIS version by P. Plait (ACC) June 1999
IDL Astro Version W. Landsman (Raytheon ITSS) April 2000
Avoid integer overflow for more than 32767 redshifts July 2001
Convert to python S. Koposov 2010
"""
if h0 is None:
h0 = 70.0
omega_m, lambda0, k, q0 = cosmo_param(omega_m, lambda0, k, q0)
if silent is not None:
print 'GALAGE: H0:', h0, ' Omega_m:', omega_m, ' Lambda0', lambda0, ' q0: ', q0, ' k: ', k #, format='(A,I3,A,f5.2,A,f5.2,A,f5.2,A,F5.2)'
scal = False
if isinstance(z, list):
z = array(z)
elif isinstance(z, ndarray):
pass
else:
z = array([z])
scal = True
nz = len(z)
age = z * 0. #Return same dimensions and data type as Z
#
# use qsimp to integrate dt/dz to get age for each z
# watch out for null case of z >= zform
#
for i in range(nz):
if (z[i] >= zform):
age_z = 0
else:
#qsimp('dtdz', z[i], zform, age_z, q0=q0, lambda0=lambda0)
age_z = quad(dtdz, z[i], zform, args=(lambda0, q0))[0]
age[i] = age_z
# convert units of age: km/s/Mpc to years, divide by H0
# 3.085678e19 km --> 1 Mpc
# 3.15567e+07 sec --> 1 year
if scal:
age = age[0]
return age * 3.085678e+19 / 3.15567e+7 / h0
