skais_mapper.cosmology

Utilities for handling cosmology-dependent calculations.

Classes:

Name	Description
CosmoModel	Set cosmological parameter for distance calculations, mass projections, etc.

CosmoModel dataclass

CosmoModel(
    omega_m: float = 0.279952,
    omega_l: float = 0.72,
    omega_k: float = 0.0,
    z: float = 0.0,
    c: ac.Constant = (lambda: ac.c)(),
    h: float = 0.718,
    u_H0: au.CompositeUnit = au.km / au.s / au.Mpc,
)

Set cosmological parameter for distance calculations, mass projections, etc.

Parameters:

Name	Type	Description	Default
omega_m	float	matter energy fraction	0.279952
omega_l	float	dark energy fraction	0.72
omega_k	float	curvature fraction	0.0
omega_r	float	radiation energy fraction (will be calculated assuming flat universe if not given)	required
h	float	'little' H (H0 / 100 km/s/Mpc)	0.718
c	ac.Constant	speed of light	(lambda: ac.c)()
z	float	redshift	0.0

Methods:

Name	Description
H	The Hubble parameter at a given scale factor a.
arcsec2kpc	Angular distance d_z from a redshift z within given cosmology.
d_comov	Calculate the comoving distance from scale factor (for solve_ivp).
d_z	Angular distance d_z from a redshift z within given cosmology.
d_z2kpc	Given scale-less distance d, return scaled distance c/H0 * d [kpc].

Attributes:

Name	Type	Description
H0	au.Quantity	The Hubble constant getter.
a	float	The scale parameter getter.
omega_r	float	The radiation density parameter getter.
rho_crit	au.Quantity	The critical density getter.

H0 property writable

H0: au.Quantity

The Hubble constant getter.

a property writable

a: float

The scale parameter getter.

omega_r property writable

omega_r: float

The radiation density parameter getter.

rho_crit property

rho_crit: au.Quantity

The critical density getter.

H

H(a: float | None = None) -> au.Quantity

The Hubble parameter at a given scale factor a.

Parameters:

Name	Type	Description	Default
a	float | None	scale factor	None

Returns:

Type	Description
float	value of the Hubble parameter

Source code in skais_mapper/cosmology.py

def H(self, a: float | None = None) -> au.Quantity:
    """The Hubble parameter at a given scale factor `a`.

    Args:
        a: scale factor

    Returns:
        (float): value of the Hubble parameter
    """
    if a is None and self.z and self.a:
        a = self.a
    elif a is None:
        a = 1.0
    return (
        self.H0
        * (self.omega_m / a**3 + self.omega_r / a**4 + self.omega_k / a**2 + self.omega_l)
        ** 0.5
    )

arcsec2kpc staticmethod

arcsec2kpc(
    z: float,
    dist_z: float | None = None,
    cosmo_model: TCosmo | None = None,
) -> au.Quantity

Angular distance d_z from a redshift z within given cosmology.

Parameters:

Name	Type	Description	Default
z	float	redshift	required
dist_z	float | None	scaled comoving distance	None
cosmo_model	TCosmo | None	cosmological parameter lookup class	None

Return

(float): kpc/arcsec scaling within given redshift and cosmology

Source code in skais_mapper/cosmology.py

@staticmethod
def arcsec2kpc(
    z: float,
    dist_z: float | None = None,
    cosmo_model: TCosmo | None = None,
) -> au.Quantity:
    """Angular distance d_z from a redshift z within given cosmology.

    Args:
        z: redshift
        dist_z: scaled comoving distance
        cosmo_model: cosmological parameter lookup class

    Return:
        (float): kpc/arcsec scaling within given redshift and cosmology
    """
    if dist_z is None:
        dist_z = CosmoModel.d_z(z, cosmo_model=cosmo_model, scaled=True)
    d_kpc_arcsec = (dist_z / au.rad).to(au.kpc / au.arcsec)
    return d_kpc_arcsec

d_comov staticmethod

d_comov(
    a: float, r: float, cosmo_model: TCosmo | None = None
) -> au.Quantity

Calculate the comoving distance from scale factor (for solve_ivp).

Parameters:

Name	Type	Description	Default
a	float	scale factor	required
r	float	distance	required
cosmo_model	TCosmo | None	cosmological parameter lookup class	None

Returns:

Type	Description
float	comoving radial distance (scale-free)

Source code in skais_mapper/cosmology.py

@staticmethod
def d_comov(a: float, r: float, cosmo_model: TCosmo | None = None) -> au.Quantity:
    """Calculate the comoving distance from scale factor (for solve_ivp).

    Args:
        a: scale factor
        r: distance
        cosmo_model: cosmological parameter lookup class

    Returns:
        (float): comoving radial distance (scale-free)
    """
    if cosmo_model is None:
        cosmo_model = CosmoModel()
    return 1.0 / (a * a * cosmo_model.H(a))

d_z staticmethod

d_z(
    z: float | None = None,
    cosmo_model: TCosmo | None = None,
    scaled: bool = False,
) -> au.Quantity

Angular distance d_z from a redshift z within given cosmology.

Parameters:

Name	Type	Description	Default
z	float | None	redshift	None
cosmo_model	TCosmo | None	cosmological parameter lookup class	None
scaled	bool	return result with c/H0 in units of kpc	False

Return

(float): apparent distance d_z

Source code in skais_mapper/cosmology.py

@staticmethod
def d_z(
    z: float | None = None,
    cosmo_model: TCosmo | None = None,
    scaled: bool = False,
) -> au.Quantity:
    """Angular distance d_z from a redshift z within given cosmology.

    Args:
        z: redshift
        cosmo_model: cosmological parameter lookup class
        scaled: return result with c/H0 in units of kpc

    Return:
        (float): apparent distance d_z
    """
    if cosmo_model is None:
        cosmo_model = CosmoModel()
    comov = partial(CosmoModel.d_comov, cosmo_model=cosmo_model)
    if z is None and cosmo_model.a:
        a = cosmo_model.a
    else:
        a = 1.0 / (1.0 + z)
    a_lim = [a, 1]
    res = solve_ivp(comov, a_lim, [0])
    if res["success"]:
        r = res["y"][0]
        D = a * (r[-1] - r[0])
        if scaled:
            return CosmoModel.d_z2kpc(D)
        return D
    raise ValueError(f"No solution found for the inputs z={z}, " f"cosmo_model={cosmo_model}")

d_z2kpc staticmethod

d_z2kpc(
    distance: float | np.ndarray,
    cosmo_model: TCosmo | None = None,
) -> au.Quantity

Given scale-less distance d, return scaled distance c/H0 * d [kpc].

Parameters:

Name	Type	Description	Default
distance	float | np.ndarray	scale-less distance	required
cosmo_model	TCosmo | None	cosmological parameter lookup class	None

Source code in skais_mapper/cosmology.py

@staticmethod
def d_z2kpc(
    distance: float | np.ndarray, cosmo_model: TCosmo | None = None
) -> au.Quantity:
    """Given scale-less distance d, return scaled distance c/H0 * d [kpc].

    Args:
        distance: scale-less distance
        cosmo_model: cosmological parameter lookup class
    """
    if cosmo_model is None:
        cosmo_model = CosmoModel()
    c = cosmo_model.c
    H0 = cosmo_model.H0
    return (distance * c / H0).to(au.kpc)