Cosmological Units and Equivalencies¶
This package defines and collects cosmological units and equivalencies. We suggest importing this units package as
>>> import astropy.cosmology.units as cu
To enable the main astropy.units
to access these units when searching
for unit conversions and equivalencies, use
add_enabled_units()
.
>>> import astropy.units as u
>>> u.add_enabled_units(cu)
About the Units¶
:hide:
>>> import astropy.units as u
Cosmological Redshift and Dimensionless Equivalency¶
There are numerous measures of distance in cosmology – luminosities, CMB
temperature, the universe’s age, etc. – but redshift is the principal measure
from which others are defined. In cosmology, distance measures are commonly
exasperating to follow in a derivation, because they are used interchangeably.
astropy
provides the redshift
unit and associated equivalencies to
assist in these derivations and unify the distance measures.
Examples¶
To convert to or from dimensionless to “redshift” units:
>>> import astropy.units as u
>>> import astropy.cosmology.units as cu
>>> z = 1100 * cu.redshift
>>> z.to(u.dimensionless_unscaled, equivalencies=cu.dimensionless_redshift())
<Quantity 1100.>
The equivalency works as part of a quantity with composite units
>>> q = (2.7 * u.K) * z
>>> q.to(u.K, equivalencies=cu.dimensionless_redshift())
<Quantity 2970. K>
Since the redshift is not a true unit and is used so frequently, the redshift / dimensionless equivalency is actually enabled by default.
>>> z == 1100 * u.dimensionless_unscaled
True
>>> q.to(u.K)
<Quantity 2970. K>
To temporarily remove the equivalency and enforce unit strictness, use
astropy.units.set_enabled_equivalencies()
as a context.
>>> with u.set_enabled_equivalencies([]):
... try:
... z.to(u.dimensionless_unscaled)
... except u.UnitConversionError:
... print("equivalency disabled")
equivalency disabled
The other redshift equivalency is with_redshift
,
enabling redshift to be converted to other units, like CMB temperature:
>>> from astropy.cosmology import WMAP9
>>> z = 1100 * cu.redshift
>>> z.to(u.K, cu.with_redshift(WMAP9))
<Quantity 3000.225 K>
or the Hubble parameter:
>>> z.to(u.km / u.s / u.Mpc, cu.with_redshift(WMAP9))
<Quantity 1565637.40154275 km / (Mpc s)>
>>> z.to(cu.littleh, cu.with_redshift(WMAP9))
<Quantity 15656.37401543 littleh>
or a physical distance (comoving, lookback, or luminosity):
>>> z.to(u.Mpc, cu.with_redshift(WMAP9, distance="luminosity"))
<Quantity 15418438.76317008 Mpc>
These conversions are cosmology dependent, so if the cosmology changes, so too will the conversions.
>>> excosmo = WMAP9.clone(Tcmb0=3.0)
>>> z.to(u.K, cu.with_redshift(excosmo))
<Quantity 3303. K>
If no argument is given (or the argument is None
), this equivalency assumes
the current default Cosmology
:
>>> z.to(u.K, cu.with_redshift())
<Quantity 3000.7755 K>
To use this equivalency in a larger block of code:
>>> with u.add_enabled_equivalencies(cu.with_redshift()):
... # long derivation here
... z.to(u.K)
<Quantity 3000.7755 K>
Reduced Hubble Constant and “littleh” Equivalency¶
The dimensionless version of the Hubble constant — often known as “little h” —
is a frequently used quantity in extragalactic astrophysics. It is also widely
known as the bane of beginners’ existence in such fields (See e.g., the title
of this paper, which also provides
valuable advice on the use of little h). astropy
provides the
with_H0()
equivalency that helps keep this
straight in at least some of these cases, by providing a way to convert to/from
physical to “little h” units.
Examples¶
To convert to or from physical to “little h” units:
>>> import astropy.units as u
>>> import astropy.cosmology.units as cu
>>> H0_70 = 70 * u.km/u.s/u.Mpc
>>> distance = 70 * (u.Mpc/cu.littleh)
>>> distance.to(u.Mpc, cu.with_H0(H0_70))
<Quantity 100.0 Mpc>
>>> luminosity = 0.49 * u.Lsun * cu.littleh**2
>>> luminosity.to(u.Lsun, cu.with_H0(H0_70))
<Quantity 1.0 solLum>
Note the unit name littleh
: while this unit is usually expressed in the
literature as just h
, here it is littleh
to avoid confusion with
“hours.”
If no argument is given (or the argument is None
), this equivalency assumes
the H0
from the current default Cosmology
:
>>> distance = 100 * (u.Mpc/cu.littleh)
>>> distance.to(u.Mpc, cu.with_H0())
<Quantity 147.79781259 Mpc>
This equivalency also allows a common magnitude formulation of little h scaling:
>>> mag_quantity = 12 * (u.mag  u.MagUnit(cu.littleh**2))
>>> mag_quantity
<Magnitude 12. mag(1 / littleh2)>
>>> mag_quantity.to(u.mag, cu.with_H0(H0_70))
<Quantity 11.2254902 mag>
Reference/API¶
astropy.cosmology.units Module¶
Cosmological units and equivalencies.
Unit 
Description 
Represents 
Aliases 
SI Prefixes 


Reduced/”dimensionless” Hubble constant 
No 


Cosmological redshift. 
No 
Functions¶
Allow redshift to be 1to1 equivalent to dimensionless. 


Convert quantities between measures of cosmological distance. 

Convert quantities between redshift and distance. 

Convert quantities between redshift and Hubble parameter and littleh. 

Convert quantities between redshift and CMB temperature. 

Convert between quantities with littleh and the equivalent physical units. 