# -*- coding: utf-8 -*-
# Licensed under a 3-clause BSD style license - see LICENSE.rst
import warnings
import numpy as np
from astropy import units as u
from astropy.utils.decorators import format_doc
from astropy.utils.exceptions import AstropyDeprecationWarning
from astropy.coordinates.angles import Angle
from astropy.coordinates.matrix_utilities import rotation_matrix, matrix_product, matrix_transpose
from astropy.coordinates import representation as r
from astropy.coordinates.baseframe import (BaseCoordinateFrame, frame_transform_graph,
RepresentationMapping, base_doc)
from astropy.coordinates.attributes import (Attribute, CoordinateAttribute,
QuantityAttribute,
DifferentialAttribute)
from astropy.coordinates.transformations import AffineTransform
from astropy.coordinates.errors import ConvertError
from .icrs import ICRS
__all__ = ['Galactocentric']
# Measured by minimizing the difference between a plane of coordinates along
# l=0, b=[-90,90] and the Galactocentric x-z plane
# This is not used directly, but accessed via `get_roll0`. We define it here to
# prevent having to create new Angle objects every time `get_roll0` is called.
_ROLL0 = Angle(58.5986320306*u.degree)
doc_components = """
x : `~astropy.units.Quantity`, optional
Cartesian, Galactocentric :math:`x` position component.
y : `~astropy.units.Quantity`, optional
Cartesian, Galactocentric :math:`y` position component.
z : `~astropy.units.Quantity`, optional
Cartesian, Galactocentric :math:`z` position component.
v_x : `~astropy.units.Quantity`, optional
Cartesian, Galactocentric :math:`v_x` velocity component.
v_y : `~astropy.units.Quantity`, optional
Cartesian, Galactocentric :math:`v_y` velocity component.
v_z : `~astropy.units.Quantity`, optional
Cartesian, Galactocentric :math:`v_z` velocity component.
"""
doc_footer = """
Other parameters
----------------
galcen_coord : `ICRS`, optional, must be keyword
The ICRS coordinates of the Galactic center.
galcen_distance : `~astropy.units.Quantity`, optional, must be keyword
The distance from the sun to the Galactic center.
galcen_v_sun : `~astropy.coordinates.representation.CartesianDifferential`, optional, must be keyword
The velocity of the sun *in the Galactocentric frame* as Cartesian
velocity components.
z_sun : `~astropy.units.Quantity`, optional, must be keyword
The distance from the sun to the Galactic midplane.
roll : `Angle`, optional, must be keyword
The angle to rotate about the final x-axis, relative to the
orientation for Galactic. For example, if this roll angle is 0,
the final x-z plane will align with the Galactic coordinates x-z
plane. Unless you really know what this means, you probably should
not change this!
Examples
--------
To transform to the Galactocentric frame with the default
frame attributes, pass the uninstantiated class name to the
``transform_to()`` method of a coordinate frame or
`~astropy.coordinates.SkyCoord` object::
>>> import astropy.units as u
>>> import astropy.coordinates as coord
>>> c = coord.ICRS(ra=[158.3122, 24.5] * u.degree,
... dec=[-17.3, 81.52] * u.degree,
... distance=[11.5, 24.12] * u.kpc)
>>> c.transform_to(coord.Galactocentric) # doctest: +FLOAT_CMP
<Galactocentric Coordinate (galcen_coord=<ICRS Coordinate: (ra, dec) in deg
( 266.4051, -28.936175)>, galcen_distance=8.3 kpc, galcen_v_sun=( 11.1, 232.24, 7.25) km / s, z_sun=27.0 pc, roll=0.0 deg): (x, y, z) in kpc
[( -9.6083819 , -9.40062188, 6.52056066),
(-21.28302307, 18.76334013, 7.84693855)]>
To specify a custom set of parameters, you have to include extra keyword
arguments when initializing the Galactocentric frame object::
>>> c.transform_to(coord.Galactocentric(galcen_distance=8.1*u.kpc)) # doctest: +FLOAT_CMP
<Galactocentric Coordinate (galcen_coord=<ICRS Coordinate: (ra, dec) in deg
( 266.4051, -28.936175)>, galcen_distance=8.1 kpc, galcen_v_sun=( 11.1, 232.24, 7.25) km / s, z_sun=27.0 pc, roll=0.0 deg): (x, y, z) in kpc
[( -9.40785924, -9.40062188, 6.52066574),
(-21.08239383, 18.76334013, 7.84798135)]>
Similarly, transforming from the Galactocentric frame to another coordinate frame::
>>> c = coord.Galactocentric(x=[-8.3, 4.5] * u.kpc,
... y=[0., 81.52] * u.kpc,
... z=[0.027, 24.12] * u.kpc)
>>> c.transform_to(coord.ICRS) # doctest: +FLOAT_CMP
<ICRS Coordinate: (ra, dec, distance) in (deg, deg, kpc)
[( 86.22349059, 28.83894138, 4.39157788e-05),
( 289.66802652, 49.88763881, 8.59640735e+01)]>
Or, with custom specification of the Galactic center::
>>> c = coord.Galactocentric(x=[-8.0, 4.5] * u.kpc,
... y=[0., 81.52] * u.kpc,
... z=[21.0, 24120.0] * u.pc,
... z_sun=21 * u.pc, galcen_distance=8. * u.kpc)
>>> c.transform_to(coord.ICRS) # doctest: +FLOAT_CMP
<ICRS Coordinate: (ra, dec, distance) in (deg, deg, kpc)
[( 86.2585249 , 28.85773187, 2.75625475e-05),
( 289.77285255, 50.06290457, 8.59216010e+01)]>
"""
[docs]@format_doc(base_doc, components=doc_components, footer=doc_footer)
class Galactocentric(BaseCoordinateFrame):
r"""
A coordinate or frame in the Galactocentric system. This frame
requires specifying the Sun-Galactic center distance, and optionally
the height of the Sun above the Galactic midplane.
The position of the Sun is assumed to be on the x axis of the final,
right-handed system. That is, the x axis points from the position of
the Sun projected to the Galactic midplane to the Galactic center --
roughly towards :math:`(l,b) = (0^\circ,0^\circ)`. For the default
transformation (:math:`{\rm roll}=0^\circ`), the y axis points roughly
towards Galactic longitude :math:`l=90^\circ`, and the z axis points
roughly towards the North Galactic Pole (:math:`b=90^\circ`).
The default position of the Galactic Center in ICRS coordinates is
taken from Reid et al. 2004,
http://adsabs.harvard.edu/abs/2004ApJ...616..872R.
.. math::
{\rm RA} = 17:45:37.224~{\rm hr}\\
{\rm Dec} = -28:56:10.23~{\rm deg}
The default distance to the Galactic Center is 8.3 kpc, e.g.,
Gillessen et al. (2009),
https://ui.adsabs.harvard.edu/#abs/2009ApJ...692.1075G/abstract
The default height of the Sun above the Galactic midplane is taken to
be 27 pc, as measured by Chen et al. (2001),
https://ui.adsabs.harvard.edu/#abs/2001ApJ...553..184C/abstract
The default solar motion relative to the Galactic center is taken from a
combination of Schönrich et al. (2010) [for the peculiar velocity] and
Bovy (2015) [for the circular velocity at the solar radius],
https://ui.adsabs.harvard.edu/#abs/2010MNRAS.403.1829S/abstract
https://ui.adsabs.harvard.edu/#abs/2015ApJS..216...29B/abstract
For a more detailed look at the math behind this transformation, see
the document :ref:`coordinates-galactocentric`.
The frame attributes are listed under **Other Parameters**.
"""
default_representation = r.CartesianRepresentation
default_differential = r.CartesianDifferential
# frame attributes
galcen_coord = CoordinateAttribute(default=ICRS(ra=266.4051*u.degree,
dec=-28.936175*u.degree),
frame=ICRS)
galcen_distance = QuantityAttribute(default=8.3*u.kpc)
galcen_v_sun = DifferentialAttribute(
default=r.CartesianDifferential([11.1, 220+12.24, 7.25] * u.km/u.s),
allowed_classes=[r.CartesianDifferential])
z_sun = QuantityAttribute(default=27.*u.pc)
roll = QuantityAttribute(default=0.*u.deg)
def __init__(self, *args, **kwargs):
# backwards-compatibility
if ('galcen_ra' in kwargs or 'galcen_dec' in kwargs):
warnings.warn("The arguments 'galcen_ra', and 'galcen_dec' are "
"deprecated in favor of specifying the sky coordinate"
" as a CoordinateAttribute using the 'galcen_coord' "
"argument", AstropyDeprecationWarning)
galcen_kw = dict()
galcen_kw['ra'] = kwargs.pop('galcen_ra', self.galcen_coord.ra)
galcen_kw['dec'] = kwargs.pop('galcen_dec', self.galcen_coord.dec)
kwargs['galcen_coord'] = ICRS(**galcen_kw)
super().__init__(*args, **kwargs)
@property
def galcen_ra(self):
warnings.warn("The attribute 'galcen_ra' is deprecated. Use "
"'.galcen_coord.ra' instead.", AstropyDeprecationWarning)
return self.galcen_coord.ra
@property
def galcen_dec(self):
warnings.warn("The attribute 'galcen_dec' is deprecated. Use "
"'.galcen_coord.dec' instead.", AstropyDeprecationWarning)
return self.galcen_coord.dec
[docs] @classmethod
def get_roll0(cls):
"""
The additional roll angle (about the final x axis) necessary to align
the final z axis to match the Galactic yz-plane. Setting the ``roll``
frame attribute to -this method's return value removes this rotation,
allowing the use of the `Galactocentric` frame in more general contexts.
"""
# note that the actual value is defined at the module level. We make at
# a property here because this module isn't actually part of the public
# API, so it's better for it to be accessable from Galactocentric
return _ROLL0
# ICRS to/from Galactocentric ----------------------->
def get_matrix_vectors(galactocentric_frame, inverse=False):
"""
Use the ``inverse`` argument to get the inverse transformation, matrix and
offsets to go from Galactocentric to ICRS.
"""
# shorthand
gcf = galactocentric_frame
# rotation matrix to align x(ICRS) with the vector to the Galactic center
mat1 = rotation_matrix(-gcf.galcen_coord.dec, 'y')
mat2 = rotation_matrix(gcf.galcen_coord.ra, 'z')
# extra roll away from the Galactic x-z plane
mat0 = rotation_matrix(gcf.get_roll0() - gcf.roll, 'x')
# construct transformation matrix and use it
R = matrix_product(mat0, mat1, mat2)
# Now need to translate by Sun-Galactic center distance around x' and
# rotate about y' to account for tilt due to Sun's height above the plane
translation = r.CartesianRepresentation(gcf.galcen_distance * [1., 0., 0.])
z_d = gcf.z_sun / gcf.galcen_distance
H = rotation_matrix(-np.arcsin(z_d), 'y')
# compute total matrices
A = matrix_product(H, R)
# Now we re-align the translation vector to account for the Sun's height
# above the midplane
offset = -translation.transform(H)
if inverse:
# the inverse of a rotation matrix is a transpose, which is much faster
# and more stable to compute
A = matrix_transpose(A)
offset = (-offset).transform(A)
offset_v = r.CartesianDifferential.from_cartesian(
(-gcf.galcen_v_sun).to_cartesian().transform(A))
offset = offset.with_differentials(offset_v)
else:
offset = offset.with_differentials(gcf.galcen_v_sun)
return A, offset
def _check_coord_repr_diff_types(c):
if isinstance(c.data, r.UnitSphericalRepresentation):
raise ConvertError("Transforming to/from a Galactocentric frame "
"requires a 3D coordinate, e.g. (angle, angle, "
"distance) or (x, y, z).")
if ('s' in c.data.differentials and
isinstance(c.data.differentials['s'],
(r.UnitSphericalDifferential,
r.UnitSphericalCosLatDifferential,
r.RadialDifferential))):
raise ConvertError("Transforming to/from a Galactocentric frame "
"requires a 3D velocity, e.g., proper motion "
"components and radial velocity.")
@frame_transform_graph.transform(AffineTransform, ICRS, Galactocentric)
def icrs_to_galactocentric(icrs_coord, galactocentric_frame):
_check_coord_repr_diff_types(icrs_coord)
return get_matrix_vectors(galactocentric_frame)
@frame_transform_graph.transform(AffineTransform, Galactocentric, ICRS)
def galactocentric_to_icrs(galactocentric_coord, icrs_frame):
_check_coord_repr_diff_types(galactocentric_coord)
return get_matrix_vectors(galactocentric_coord, inverse=True)