# Licensed under a 3-clause BSD style license - see LICENSE.rst
"""Cosmological units and equivalencies."""
import astropy.units as u
from astropy.units.utils import generate_unit_summary as _generate_unit_summary
__all__ = [
"littleh",
"redshift",
# redshift equivalencies
"dimensionless_redshift",
"with_redshift",
"redshift_distance",
"redshift_hubble",
"redshift_temperature",
# other equivalencies
"with_H0",
]
__doctest_requires__ = {("with_redshift", "redshift_distance"): ["scipy"]}
_ns = globals()
###############################################################################
# Cosmological Units
# This is not formally a unit, but is used in that way in many contexts, and
# an appropriate equivalency is only possible if it's treated as a unit.
redshift = u.def_unit(
["redshift"],
prefixes=False,
namespace=_ns,
doc="Cosmological redshift.",
format={"latex": r""},
)
u.def_physical_type(redshift, "redshift")
# This is not formally a unit, but is used in that way in many contexts, and
# an appropriate equivalency is only possible if it's treated as a unit (see
# https://arxiv.org/pdf/1308.4150.pdf for more)
# Also note that h or h100 or h_100 would be a better name, but they either
# conflict or have numbers in them, which is disallowed
littleh = u.def_unit(
["littleh"],
namespace=_ns,
prefixes=False,
doc='Reduced/"dimensionless" Hubble constant',
format={"latex": r"h_{100}"},
)
###############################################################################
# Equivalencies
[docs]
def dimensionless_redshift():
"""Allow redshift to be 1-to-1 equivalent to dimensionless.
It is special compared to other equivalency pairs in that it allows
this independent of the power to which the redshift is raised, and
independent of whether it is part of a more complicated unit. It is
similar to u.dimensionless_angles() in this respect.
"""
return u.Equivalency([(redshift, None)], "dimensionless_redshift")
[docs]
def redshift_distance(cosmology=None, kind="comoving", **atzkw):
"""Convert quantities between redshift and distance.
Care should be taken to not misinterpret a relativistic, gravitational, etc
redshift as a cosmological one.
Parameters
----------
cosmology : `~astropy.cosmology.Cosmology`, str, or None, optional
A cosmology realization or built-in cosmology's name (e.g. 'Planck18').
If None, will use the default cosmology
(controlled by :class:`~astropy.cosmology.default_cosmology`).
kind : {'comoving', 'lookback', 'luminosity'}, optional
The distance type for the Equivalency.
Note this does NOT include the angular diameter distance as this
distance measure is not monotonic.
**atzkw
keyword arguments for :func:`~astropy.cosmology.z_at_value`, which is used to
convert distance to redshift.
Returns
-------
`~astropy.units.equivalencies.Equivalency`
Equivalency between redshift and temperature.
Raises
------
`~astropy.cosmology.CosmologyError`
If the distance corresponds to a redshift that is larger than ``zmax``.
Exception
See :func:`~astropy.cosmology.z_at_value` for possible exceptions, e.g. if the
distance maps to a redshift that is larger than ``zmax``, the maximum redshift.
Examples
--------
>>> import astropy.units as u
>>> import astropy.cosmology.units as cu
>>> from astropy.cosmology import WMAP9
>>> z = 1100 * cu.redshift
>>> d = z.to(u.Mpc, cu.redshift_distance(WMAP9, kind="comoving"))
>>> d # doctest: +FLOAT_CMP
<Quantity 14004.03157418 Mpc>
The reverse operation is also possible, though not always as simple. To convert a
very large distance to a redshift it might be necessary to specify a large enough
``zmax`` value. See :func:`~astropy.cosmology.z_at_value` for details.
>>> d.to(cu.redshift, cu.redshift_distance(WMAP9, kind="comoving", zmax=1200)) # doctest: +FLOAT_CMP
<Quantity 1100.000 redshift>
"""
from astropy.cosmology import default_cosmology, z_at_value
# get cosmology: None -> default and process str / class
cosmology = cosmology if cosmology is not None else default_cosmology.get()
with default_cosmology.set(cosmology): # if already cosmo, passes through
cosmology = default_cosmology.get()
allowed_kinds = ("comoving", "lookback", "luminosity")
if kind not in allowed_kinds:
raise ValueError(f"`kind` is not one of {allowed_kinds}")
method = getattr(cosmology, kind + "_distance")
def z_to_distance(z):
"""Redshift to distance."""
return method(z)
def distance_to_z(d):
"""Distance to redshift."""
return z_at_value(method, d << u.Mpc, **atzkw)
return u.Equivalency(
[(redshift, u.Mpc, z_to_distance, distance_to_z)],
"redshift_distance",
{"cosmology": cosmology, "distance": kind},
)
[docs]
def redshift_hubble(cosmology=None, **atzkw):
"""Convert quantities between redshift and Hubble parameter and little-h.
Care should be taken to not misinterpret a relativistic, gravitational, etc
redshift as a cosmological one.
Parameters
----------
cosmology : `~astropy.cosmology.Cosmology`, str, or None, optional
A cosmology realization or built-in cosmology's name (e.g. 'Planck18').
If None, will use the default cosmology
(controlled by :class:`~astropy.cosmology.default_cosmology`).
**atzkw
keyword arguments for :func:`~astropy.cosmology.z_at_value`
Returns
-------
`~astropy.units.equivalencies.Equivalency`
Equivalency between redshift and Hubble parameter and little-h unit.
Examples
--------
>>> import astropy.units as u
>>> import astropy.cosmology.units as cu
>>> from astropy.cosmology import WMAP9
>>> z = 1100 * cu.redshift
>>> equivalency = cu.redshift_hubble(WMAP9) # construct equivalency
>>> z.to(u.km / u.s / u.Mpc, equivalency) # doctest: +FLOAT_CMP
<Quantity 1565637.40154275 km / (Mpc s)>
>>> z.to(cu.littleh, equivalency) # doctest: +FLOAT_CMP
<Quantity 15656.37401543 littleh>
"""
from astropy.cosmology import default_cosmology, z_at_value
# get cosmology: None -> default and process str / class
cosmology = cosmology if cosmology is not None else default_cosmology.get()
with default_cosmology.set(cosmology): # if already cosmo, passes through
cosmology = default_cosmology.get()
def z_to_hubble(z):
"""Redshift to Hubble parameter."""
return cosmology.H(z)
def hubble_to_z(H):
"""Hubble parameter to redshift."""
return z_at_value(cosmology.H, H << (u.km / u.s / u.Mpc), **atzkw)
def z_to_littleh(z):
"""Redshift to :math:`h`-unit Quantity."""
return z_to_hubble(z).to_value(u.km / u.s / u.Mpc) / 100 * littleh
def littleh_to_z(h):
""":math:`h`-unit Quantity to redshift."""
return hubble_to_z(h * 100)
return u.Equivalency(
[
(redshift, u.km / u.s / u.Mpc, z_to_hubble, hubble_to_z),
(redshift, littleh, z_to_littleh, littleh_to_z),
],
"redshift_hubble",
{"cosmology": cosmology},
)
[docs]
def redshift_temperature(cosmology=None, **atzkw):
"""Convert quantities between redshift and CMB temperature.
Care should be taken to not misinterpret a relativistic, gravitational, etc
redshift as a cosmological one.
Parameters
----------
cosmology : `~astropy.cosmology.Cosmology`, str, or None, optional
A cosmology realization or built-in cosmology's name (e.g. 'Planck18').
If None, will use the default cosmology
(controlled by :class:`~astropy.cosmology.default_cosmology`).
**atzkw
keyword arguments for :func:`~astropy.cosmology.z_at_value`
Returns
-------
`~astropy.units.equivalencies.Equivalency`
Equivalency between redshift and temperature.
Examples
--------
>>> import astropy.units as u
>>> import astropy.cosmology.units as cu
>>> from astropy.cosmology import WMAP9
>>> z = 1100 * cu.redshift
>>> z.to(u.K, cu.redshift_temperature(WMAP9))
<Quantity 3000.225 K>
"""
from astropy.cosmology import default_cosmology, z_at_value
# get cosmology: None -> default and process str / class
cosmology = cosmology if cosmology is not None else default_cosmology.get()
with default_cosmology.set(cosmology): # if already cosmo, passes through
cosmology = default_cosmology.get()
def z_to_Tcmb(z):
return cosmology.Tcmb(z)
def Tcmb_to_z(T):
return z_at_value(cosmology.Tcmb, T << u.K, **atzkw)
return u.Equivalency(
[(redshift, u.K, z_to_Tcmb, Tcmb_to_z)],
"redshift_temperature",
{"cosmology": cosmology},
)
[docs]
def with_redshift(
cosmology=None, *, distance="comoving", hubble=True, Tcmb=True, atzkw=None
):
"""Convert quantities between measures of cosmological distance.
Note: by default all equivalencies are on and must be explicitly turned off.
Care should be taken to not misinterpret a relativistic, gravitational, etc
redshift as a cosmological one.
Parameters
----------
cosmology : `~astropy.cosmology.Cosmology`, str, or None, optional
A cosmology realization or built-in cosmology's name (e.g. 'Planck18').
If `None`, will use the default cosmology
(controlled by :class:`~astropy.cosmology.default_cosmology`).
distance : {'comoving', 'lookback', 'luminosity'} or None (optional, keyword-only)
The type of distance equivalency to create or `None`.
Default is 'comoving'.
hubble : bool (optional, keyword-only)
Whether to create a Hubble parameter <-> redshift equivalency, using
``Cosmology.H``. Default is `True`.
Tcmb : bool (optional, keyword-only)
Whether to create a CMB temperature <-> redshift equivalency, using
``Cosmology.Tcmb``. Default is `True`.
atzkw : dict or None (optional, keyword-only)
keyword arguments for :func:`~astropy.cosmology.z_at_value`
Returns
-------
`~astropy.units.equivalencies.Equivalency`
With equivalencies between redshift and distance / Hubble / temperature.
Examples
--------
>>> import astropy.units as u
>>> import astropy.cosmology.units as cu
>>> from astropy.cosmology import WMAP9
>>> equivalency = cu.with_redshift(WMAP9)
>>> z = 1100 * cu.redshift
Redshift to (comoving) distance:
>>> z.to(u.Mpc, equivalency) # doctest: +FLOAT_CMP
<Quantity 14004.03157418 Mpc>
Redshift to the Hubble parameter:
>>> z.to(u.km / u.s / u.Mpc, equivalency) # doctest: +FLOAT_CMP
<Quantity 1565637.40154275 km / (Mpc s)>
>>> z.to(cu.littleh, equivalency) # doctest: +FLOAT_CMP
<Quantity 15656.37401543 littleh>
Redshift to CMB temperature:
>>> z.to(u.K, equivalency)
<Quantity 3000.225 K>
"""
from astropy.cosmology import default_cosmology
# get cosmology: None -> default and process str / class
cosmology = cosmology if cosmology is not None else default_cosmology.get()
with default_cosmology.set(cosmology): # if already cosmo, passes through
cosmology = default_cosmology.get()
atzkw = atzkw if atzkw is not None else {}
equivs = [] # will append as built
# Hubble <-> Redshift
if hubble:
equivs.extend(redshift_hubble(cosmology, **atzkw))
# CMB Temperature <-> Redshift
if Tcmb:
equivs.extend(redshift_temperature(cosmology, **atzkw))
# Distance <-> Redshift, but need to choose which distance
if distance is not None:
equivs.extend(redshift_distance(cosmology, kind=distance, **atzkw))
# -----------
return u.Equivalency(
equivs,
"with_redshift",
{"cosmology": cosmology, "distance": distance, "hubble": hubble, "Tcmb": Tcmb},
)
# ===================================================================
[docs]
def with_H0(H0=None):
"""Convert between quantities with little-h and the equivalent physical units.
Parameters
----------
H0 : None or `~astropy.units.Quantity` ['frequency']
The value of the Hubble constant to assume. If a
`~astropy.units.Quantity`, will assume the quantity *is* ``H0``. If
`None` (default), use the ``H0`` attribute from
:mod:`~astropy.cosmology.default_cosmology`.
References
----------
For an illuminating discussion on why you may or may not want to use
little-h at all, see https://arxiv.org/pdf/1308.4150.pdf
"""
if H0 is None:
from .realizations import default_cosmology
H0 = default_cosmology.get().H0
h100_val_unit = u.Unit(100 / (H0.to_value((u.km / u.s) / u.Mpc)) * littleh)
return u.Equivalency([(h100_val_unit, None)], "with_H0", kwargs={"H0": H0})
# ===================================================================
# Enable the set of default equivalencies.
# If the cosmology package is imported, this is added to the list astropy-wide.
u.add_enabled_equivalencies(dimensionless_redshift())
# =============================================================================
# DOCSTRING
# This generates a docstring for this module that describes all of the
# standard units defined here.
if __doc__ is not None:
__doc__ += "\n" + _generate_unit_summary(_ns)
