# -*- coding: utf-8 -*-
# Licensed under a 3-clause BSD style license - see LICENSE.rst
from __future__ import (absolute_import, unicode_literals, division,
print_function)
import numpy as np
from ... import units as u
from ..angles import Angle
from ..representation import CartesianRepresentation, UnitSphericalRepresentation
from ..baseframe import (BaseCoordinateFrame, FrameAttribute,
frame_transform_graph)
from ..transformations import FunctionTransform
from ..errors import ConvertError
from .icrs import ICRS
# 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)
[docs]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,
http://adsabs.harvard.edu/abs/2009ApJ...692.1075G.
The default height of the Sun above the Galactic midplane is taken to
be 27 pc, as measured by
http://adsabs.harvard.edu/abs/2001ApJ...553..184C.
For a more detailed look at the math behind this transformation, see
the document :ref:`coordinates-galactocentric`.
Parameters
----------
representation : `BaseRepresentation` or None
A representation object or None to have no data (or use the other
keywords)
galcen_distance : `~astropy.units.Quantity`, optional, must be keyword
The distance from the Sun to the Galactic center.
galcen_ra : `Angle`, optional, must be keyword
The Right Ascension (RA) of the Galactic center in the ICRS frame.
galcen_dec : `Angle`, optional, must be keyword
The Declination (Dec) of the Galactic center in the ICRS frame.
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_distance=8.3 kpc, galcen_ra=266d24m18.36s, galcen_dec=-28d56m10.23s, z_sun=27.0 pc, roll=0.0 deg): (x, y, z) in kpc
[(-9.6083818980977, -9.400621883358546, 6.520560663896347),
(-21.283023068029138, 18.763340128812384, 7.846938548636718)]>
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_distance=8.1 kpc, galcen_ra=266d24m18.36s, galcen_dec=-28d56m10.23s, z_sun=27.0 pc, roll=0.0 deg): (x, y, z) in kpc
[(-9.407859235565343, -9.400621883358546, 6.520665737962164),
(-21.08239383088295, 18.763340128812384, 7.84798134569032)]>
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)
[(86.22349058727241, 28.8389413808627, 4.391577882957292e-05),
(289.6680265194508, 49.88763881149547, 85.96407345372828)]>
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)
[(86.25852490164378, 28.85773187391088, 2.7562547481200286e-05),
(289.77285254989323, 50.062904565432014, 85.92160096237191)]>
"""
default_representation = CartesianRepresentation
# TODO: these can all become QuantityFrameAttribute's once #3217 is merged
galcen_distance = FrameAttribute(default=8.3*u.kpc)
galcen_ra = FrameAttribute(default=Angle(266.4051*u.degree))
galcen_dec = FrameAttribute(default=Angle(-28.936175*u.degree))
z_sun = FrameAttribute(default=27.*u.pc)
roll = FrameAttribute(default=0.*u.deg)
@classmethod
[docs] 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 ----------------------->
@frame_transform_graph.transform(FunctionTransform, ICRS, Galactocentric)
def icrs_to_galactocentric(icrs_coord, galactocentric_frame):
from ..representation import CartesianRepresentation
from ..angles import rotation_matrix
if isinstance(icrs_coord.data, UnitSphericalRepresentation):
raise ConvertError("Transforming to a Galactocentric frame requires "
"a 3D coordinate, e.g. (angle, angle, distance) or"
" (x, y, z).")
xyz = icrs_coord.cartesian.xyz
# define rotation matrix to align x(ICRS) with the vector to the Galactic center
mat1 = rotation_matrix(-galactocentric_frame.galcen_dec, 'y')
mat2 = rotation_matrix(galactocentric_frame.galcen_ra, 'z')
R1 = mat1 * mat2
# extra roll away from the Galactic x-z plane
R2 = rotation_matrix(galactocentric_frame.get_roll0() - galactocentric_frame.roll, 'x')
# construct transformation matrix
R = R2*R1
# some reshape hacks to handle ND arrays
orig_shape = xyz.shape
xyz = R.dot(xyz.reshape(xyz.shape[0], np.prod(xyz.shape[1:]))).reshape(orig_shape)
# translate by Sun-Galactic center distance along new x axis
xyz[0] = xyz[0] - galactocentric_frame.galcen_distance
# rotate about y' to account for tilt due to Sun's height above the plane
z_d = (galactocentric_frame.z_sun / galactocentric_frame.galcen_distance).decompose()
R = rotation_matrix(-np.arcsin(z_d), 'y')
xyz = R.dot(xyz.reshape(xyz.shape[0], np.prod(xyz.shape[1:]))).reshape(orig_shape)
representation = CartesianRepresentation(xyz)
return galactocentric_frame.realize_frame(representation)
@frame_transform_graph.transform(FunctionTransform, Galactocentric, ICRS)
def galactocentric_to_icrs(galactocentric_coord, icrs_frame):
from ..representation import CartesianRepresentation
from ..angles import rotation_matrix
if isinstance(galactocentric_coord.data, UnitSphericalRepresentation):
raise ConvertError("Transforming from a Galactocentric frame requires "
"a 3D coordinate, e.g. (angle, angle, distance) or"
" (x, y, z).")
xyz = galactocentric_coord.cartesian.xyz
# rotate about y' to account for tilt due to Sun's height above the plane
z_d = (galactocentric_coord.z_sun / galactocentric_coord.galcen_distance).decompose()
R = rotation_matrix(np.arcsin(z_d), 'y')
# some reshape hacks to handle ND arrays
orig_shape = xyz.shape
xyz = R.dot(xyz.reshape(xyz.shape[0], np.prod(xyz.shape[1:]))).reshape(orig_shape)
# translate by Sun-Galactic center distance along x axis
xyz[0] = xyz[0] + galactocentric_coord.galcen_distance
# define inverse rotation matrix that aligns x(ICRS) with the vector to the Galactic center
mat1 = rotation_matrix(-galactocentric_coord.galcen_dec, 'y')
mat2 = rotation_matrix(galactocentric_coord.galcen_ra, 'z')
R1 = mat1 * mat2
# extra roll away from the Galactic x-z plane
R2 = rotation_matrix(galactocentric_coord.get_roll0() - galactocentric_coord.roll, 'x')
# construct transformation matrix
R = R2*R1
# rotate into ICRS frame
xyz = np.linalg.inv(R).dot(xyz.reshape(xyz.shape[0], np.prod(xyz.shape[1:]))).reshape(orig_shape)
representation = CartesianRepresentation(xyz)
return icrs_frame.realize_frame(representation)