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cosmocalc.py
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cosmocalc.py
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#!/usr/bin/env python
"""
This distribution of cosmocalc is for running the Illustris Virtual Observatory/sunpy module by Paul Torrey, Greg Snyder, and Tyler Metivier
Calculate useful values for a given cosmology. This module uses code adapted
from `CC.py`_ (`James Schombert`_) which is a Python version of the
`Cosmology Calculator`_ (`Ned Wright`_).
The following values are calculated:
==== =================================== ===========
Name Value Units
==== =================================== ===========
z Input redshift
H0 Hubble constant
WR Omega(radiation)
WK Omega curvaturve = 1-Omega(total)
WM Omega matter
WV Omega vacuum
DTT Time from z to now Gyr
age Age of Universe Gyr
zage Age of Universe at redshift z Gyr
DCMR Comoving radial distance Gyr Mpc cm
VCM Comoving volume within redshift Gpc3
DA Angular size distance Gyr Mpc cm
DL Luminosity distance Gyr Mpc cm
PS Plate scale - distance per arcsec kpc cm
==== =================================== ===========
.. _`James Schombert`: http://abyss.uoregon.edu/~js/
.. _`CC.py`: http://www.astro.ucla.edu/~wright/CC.python
.. _`Ned Wright`: http://www.astro.ucla.edu/~wright/intro.html
.. _`Cosmology Calculator`: http://www.astro.ucla.edu/~wright/CosmoCalc.html
:Copyright: Smithsonian Astrophysical Observatory (2009)
:Author: Tom Aldcroft (aldcroft@head.cfa.harvard.edu)
"""
import math
# Define a few constants
cm_per_pc = 3.0856775813057289536e+18
c = 299792.458 # velocity of light in km/sec
km_per_ly = 3600*24*365.25*c # km per light-year
Tyr = 977.8 # coefficent for converting 1/H into Gyr
arcsec_per_rad = 206264.806
_outvals_str = ('z H0 WM WV WK WR',
'DA DA_Gyr DA_Mpc DA_cm',
'DL DL_Gyr DL_Mpc DL_cm',
'DCMR DCMR_Gyr DCMR_Mpc DCMR_cm',
'PS_kpc PS_cm',
'DTT DTT_Gyr',
'VCM VCM_Gpc3',
'age age_Gyr',
'zage zage_Gyr',)
_outvals = (' '.join(_outvals_str)).split()
def cosmocalc(z, H0=71, WM=0.27, WV=None):
"""
Calculate useful values for the supplied cosmology.
This routine returns a dictionary of values in the form ``<name>: <value>``,
where the values are supplied in "natural" units for cosmology, e.g. 1/H0.
In addition various useful unit conversions are done and stored in the
dictionary as ``<name>_<unit>: <value>``. E.g. angular size distance::
'DA': 0.38250549415474988,
'DA_Gyr': 5.2678010166833023,
'DA_Mpc': 1615.1022857909447,
'DA_cm': 4.9836849147807571e+27
Example::
>>> from cosmocalc import cosmocalc
>>> from pprint import pprint
>>> pprint(cosmocalc(3, H0=75, WM=.25))
{'DA': 0.39103776375786625,
'DA_Gyr': 5.0980896720325548,
'DA_Mpc': 1563.0689649039205,
'DA_cm': 4.8231268630387788e+27,
'DCMR': 1.564151055031465,
'DCMR_Gyr': 20.392358688130219,
'DCMR_Mpc': 6252.2758596156818,
'DCMR_cm': 1.9292507452155115e+28,
'DL': 6.25660422012586,
'DL_Gyr': 81.569434752520877,
'DL_Mpc': 25009.103438462727,
'DL_cm': 7.717002980862046e+28,
'DTT': 0.84826379084317027,
'DTT_Gyr': 11.059097795819358,
'H0': 75,
'PS_cm': 2.3383178917293232e+22,
'PS_kpc': 7.5779721961095019,
'VCM': 1.2756009121294902,
'VCM_Gpc3': 1023.7714254161302,
'WK': 0.0,
'WM': 0.25,
'WR': 7.4044444444444448e-05,
'WV': 0.74992595555555552,
'age': 1.0133755371756261,
'age_Gyr': 13.211714670004362,
'z': 3,
'zage': 0.16511174633245579,
'zage_Gyr': 2.1526168741850036}
:param z: redshift
:param H0: Hubble constant (default = 71)
:param WM: Omega matter (default = 0.27)
:param WV: Omega vacuum (default = 1.0 - WM - 0.4165/(H0*H0))
:rtype: dictionary of cosmology values (name_unit = value)
"""
if z > 100:
z = z / 299792.458 # Values over 100 are in km/s
if WV is None:
WV = 1.0 - WM - 0.4165/(H0*H0) # Omega(vacuum) or lambda
age = 0.0 # age of Universe in units of 1/H0
h = H0 / 100.
WR = 4.165E-5 / (h*h) # includes 3 massless neutrino species, T0 = 2.72528
WK = 1 - WM - WR - WV
az = 1.0 / (1 + 1.0*z)
n=1000 # number of points in integrals
for i in range(n):
a = az * (i + 0.5) / n
adot = math.sqrt(WK + (WM/a) + (WR/(a*a)) + (WV*a*a))
age = age + 1./adot
zage = az * age / n
DTT = 0.0
DCMR = 0.0
# do integral over a=1/(1+z) from az to 1 in n steps, midpoint rule
for i in range(n):
a = az + (1-az) * (i+0.5) / n
adot = math.sqrt(WK + (WM/a) + (WR/(a*a)) + (WV*a*a))
DTT = DTT + 1./adot
DCMR = DCMR + 1./(a*adot)
DTT = (1.-az) * DTT / n
DCMR = (1.-az) * DCMR / n
age = DTT + zage
# tangential comoving distance
ratio = 1.0
x = math.sqrt(abs(WK)) * DCMR
if x > 0.1:
if WK > 0:
ratio = 0.5 * (math.exp(x) - math.exp(-x)) / x
else:
ratio = math.math.sin(x) / x
else:
y = x * x
if WK < 0:
y = -y
ratio = 1. + y/6. + y*y/120.
DCMT = ratio * DCMR
# comoving volume computation
ratio = 1.00
x = math.sqrt(abs(WK)) * DCMR
if x > 0.1:
if WK > 0:
ratio = (0.125 * (math.exp(2.*x) - math.exp(-2.*x)) - x/2.) / (x**3 / 3.)
else:
ratio = (x/2. - math.sin(2.*x)/4.)/(x**3 / 3.)
else:
y = x * x
if WK < 0: y = -y
ratio = 1. + y/5. + (2./105.)*y*y
VCM = ratio * DCMR**3 / 3.
VCM_Gpc3 = 4. * math.pi * (0.001*c/H0)**3 * VCM
DA = az * DCMT
DL = DA / (az*az)
# Now convert to some more useful units
Gyr = lambda x: Tyr / H0 * x
Mpc = lambda x: c / H0 * x
cm = lambda x: Mpc(x) * 1e6 * cm_per_pc
DA_Gyr = Gyr(DA)
DA_Mpc = Mpc(DA)
DA_cm = cm(DA)
DL_Gyr = Gyr(DL)
DL_Mpc = Mpc(DL)
DL_cm = cm(DL)
DCMR_Gyr = Gyr(DCMR)
DCMR_Mpc = Mpc(DCMR)
DCMR_cm = cm(DCMR)
DTT_Gyr = Gyr(DTT)
age_Gyr = Gyr(age)
zage_Gyr = Gyr(zage)
PS_kpc = Mpc(DA) * 1000 / arcsec_per_rad
PS_cm = PS_kpc * cm_per_pc * 1000
localvals = locals()
return dict((x, localvals[x]) for x in _outvals)
def get_options():
"""
cosmocalc.py [options] redshift [name_unit [name_unit2 ...]]
Allowed ``name_unit`` values::
DA DA_Gyr DA_Mpc DA_cm
DL DL_Gyr DL_Mpc DL_cm
DCMR DCMR_Gyr DCMR_Mpc DCMR_cm
PS_kpc PS_cm
DTT DTT_Gyr
VCM VCM_Gpc3
age age_Gyr
zage zage_Gyr
H0 WM WV WK WR z
If no ``name_unit`` values are supplied then all the above will be printed."""
from optparse import OptionParser
parser = OptionParser(get_options.__doc__)
parser.set_defaults()
parser.add_option("--H0",
default=None,
type='float',
help="Hubble constant")
parser.add_option("--WM",
default=None,
type='float',
help="")
parser.add_option("--WV",
default=None,
type='float',
help="")
opt, args = parser.parse_args()
return opt, args, parser
def main():
opt, args, parser = get_options()
if len(args) < 1:
parser.error('Need a redshift')
kwargs = dict((key, val) for (key, val) in list(opt.__dict__.items()) if val is not None)
z = float(args[0])
cc = cosmocalc(z, **kwargs)
try:
outlines = []
for outkey in (args[1:] or _outvals):
outlines.append(outkey + ' = ' + str(cc[outkey]))
print('\n'.join(outlines))
except KeyError:
parser.error(outkey + ' is not a valid output name_unit')
if __name__ == '__main__':
main()