synthpop.synthpop_utils.coordinates_transformation

Functions for coordinates transformations following Bovy 2011.

Classes

CoordTrans

Functions

`get_trans_matrix`(→ numpy.ndarray)	creates the transformation matrix between galactic and equatorial coordinates
`getA`(→ numpy.ndarray)	determines the Position Matrix A from Bovy 2011
`dlb_to_rphiz`(→ Tuple[numpy.ndarray, numpy.ndarray, ...)	translates d, l, b into r, theta, z
`dlb_to_xyz`(→ Tuple[numpy.ndarray, numpy.ndarray, ...)	Convert from galactic coordinates an distance
`xyz_to_rphiz`(→ Tuple[numpy.ndarray, numpy.ndarray, ...)	Translate from galactocentric cartesian coordinates into
`lb_to_ad`(→ Tuple[numpy.ndarray, numpy.ndarray])	Conversion from Galactic coordinates to Equatorial coordinates
`ad_to_lb`(→ Tuple[numpy.ndarray, numpy.ndarray])	Conversion from Equatorial coordinates to Galactic coordinates
`uvw_to_vrmulb`(→ Tuple[numpy.ndarray, numpy.ndarray, ...)	Conversion from u,v,w to v_r, mu_l, and mu_b
`uvw_to_vrmuad`(→ Tuple[numpy.ndarray, numpy.ndarray, ...)	Conversion from u,v,w

Module Contents

synthpop.synthpop_utils.coordinates_transformation.get_trans_matrix() → numpy.ndarray

creates the transformation matrix between galactic and equatorial coordinates

Returns

trans_matrix :: transformation matrix between galactic and equatorial coordinates

synthpop.synthpop_utils.coordinates_transformation.getA(longitude_rad: np.ndarray or float, latitude_rad: np.ndarray or float) → numpy.ndarray

determines the Position Matrix A from Bovy 2011 Note that R^T is equivalent to A

Parameters

longitude_rad: float, ndarray: galactic or ecliptic longitude
latitude_rad: float, ndarray: galactic or ecliptic latitude

Returns

Andarray: transformation matrix

class synthpop.synthpop_utils.coordinates_transformation.CoordTrans(sun: synthpop.synthpop_utils.sun_info.SunInfo = None, amp_warp: float = 0, amp_warp_pos: float = None, amp_warp_neg: float = None, r_warp: float = 0, alpha_warp: float = 0, phi_warp_deg: float = 0, phi_warp_rad: float = 0)

sun = None

amp_warp_pos = None

amp_warp_neg = None

r_warp = 0

alpha_warp = 0

phi_warp_rad

warp_correction(r_kpc, phi_rad): Correction for the WARP following Chen X. et al. 2019

dlb_to_rphiz(d_kpc: numpy.ndarray, l_deg: numpy.ndarray, b_deg: numpy.ndarray) → Tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray]

translates d, l, b into r, phi, z

phi increases along the galactic rotation with a zero point at the position of the sun

Parameters

d_kpc : float, ndarray [kpc] l_deg : float, ndarray [degree] b_deg : float, ndarray [degree]

Returns

r : float, ndarray [kpc] phi_rad : float, ndarray [rad]

polar angle follows the rotation of the galaxy zero point is at the sun.

zfloat, ndarray [kpc]: hight above/below the galactic plane

dlb_to_xyz(d_kpc: numpy.ndarray, l_deg: numpy.ndarray, b_deg: numpy.ndarray) → Tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray]

Convert from galactic coordinates an distance to galactocentric cartesian coordinates.

Parameters

l_degfloat, ndarray, [degrees]: galactic longitude
b_degfloat, ndarray, [degrees]: galactic latitude
d_kpcfloat ndarray, [kpc]: distance

Returns

x,y,zfloat nd_array [kpc]: galactocentric cartesian coordinates

rphiz_to_xyz(r_kpc: numpy.ndarray, phi_rad: numpy.ndarray, z_kpc: numpy.ndarray) → Tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray]

Translate from cylindrical cartesian coordinates to galactocentric cartesian coordinates the zero point of z follows the warp of the galaxy.

Parameters

r_kpc : float, ndarray [kpc] phi_rad : float, ndarray [rad]

polar angle follows the rotation of the galaxy zero point is at the sun.

z_kpcfloat, ndarray [kpc]: hight above/below the galactic plane

Returns

x_kpc,y_kpc,z_kpcfloat, ndarray [kpc]: galactocentric cartesian coordinates

xyz_to_rphiz(x_kpc: numpy.ndarray, y_kpc: numpy.ndarray, z_kpc: numpy.ndarray) → Tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray]

Translate from galactocentric cartesian coordinates into cylindrical cartesian coordinates, the zero point of z follows the warp of the galaxy.

Parameters

x_kpc,y_kpc,z_kpcfloat, ndarray [kpc]: galactocentric cartesian coordinates

Returns

r_kpc : float, ndarray [kpc] phi_rad : float, ndarray [rad]

polar angle follows the rotation of the galaxy zero point is at the sun.

z_kpcfloat, ndarray [kpc]: hight above/below the galactic plane

static lb_to_ad(l_deg: numpy.ndarray, b_deg: numpy.ndarray) → Tuple[numpy.ndarray, numpy.ndarray]

Conversion from Galactic coordinates to Equatorial coordinates

Parameters

l_degfloat, ndarray [degree]: Galactic longitude
b_degfloat, ndarray [degree]: Galactic latitude

Returns

a_degfloat, ndarray [degree]: right ascension
d_degfloat, ndarray [degree]: declination

static ad_to_lb(a_deg: numpy.ndarray, d_deg: numpy.ndarray) → Tuple[numpy.ndarray, numpy.ndarray]

Conversion from Equatorial coordinates to Galactic coordinates

Parameters

a_degfloat, ndarray [degree]: right ascension
d_degfloat, ndarray [degree]: declination

Returns

l_degfloat, ndarray [degree]: Galactic longitude
b_degfloat, ndarray [degree]: Galactic latitude

uvw_to_vrmulb(l_deg: numpy.ndarray, b_deg: numpy.ndarray, dist_kpc: numpy.ndarray, u_kmps: numpy.ndarray, v_kmps: numpy.ndarray, w_kmps: numpy.ndarray) → Tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray]

Conversion from u,v,w to v_r, mu_l, and mu_b Using (vr, vl, vb) = R * (u,v,w) from Bovy 2011

Parameters

l_degfloat, ndarray [degrees]: galactic longitude
b_degfloat, ndarray [degrees]: galactic latitude
dist_kpcfloat, ndarray [kpc]: distance
u_kmpsfloat, ndarray [km/s]: rectangular velocity with_out correction for the motion of the sun
v_kmpsfloat, ndarray [km/s]: rectangular velocity with_out correction for the motion of the sun
w_kmpsfloat, ndarray [km/s]: rectangular velocity with_out correction for the motion of the sun

Returns

vr_kmpsfloat, ndarray[km/s]: radial velocity
mu_l_maspyrfloat, ndarray [mas/yr]: proper motion in galactic longitude cos(b) is applied
mu_b_maspyrfloat, ndarray [mas/yr]: proper motion in galactic latitude

uvw_to_vrmuad(l_deg: numpy.ndarray, b_deg: numpy.ndarray, dist_kpc: numpy.ndarray, u_kmps: numpy.ndarray, v_kmps: numpy.ndarray, w_kmps: numpy.ndarray) → Tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray]

Conversion from u,v,w to v_r, mu_l, and mu_b

Parameters

l_degfloat, ndarray [degrees]: galactic longitude
b_degfloat, ndarray [degrees]: galactic latitude
dist_kpcfloat, ndarray [kpc]: distance
u_kmpsfloat, ndarray [km/s]: rectangular velocity with_out correction for the motion of the sun
v_kmpsfloat, ndarray [km/s]: rectangular velocity with_out correction for the motion of the sun
w_kmpsfloat, ndarray [km/s]: rectangular velocity with_out correction for the motion of the sun

Returns

vr_kmpsfloat, ndarray[km/s]: radial velocity
mu_a_maspyrfloat, ndarray [mas/yr]: proper motion in galactic longitude cos(delta) is applied
mu_d_maspyrfloat, ndarray [mas/yr]: proper motion in galactic latitude

vr_bc_to_vr_lsr(l_deg: numpy.ndarray, b_deg: numpy.ndarray, vr: numpy.ndarray) → numpy.ndarray

Conversion of radial velocity from barycentric frame to local standard of rest frame following Beaulieu et al. (2000)

Parameters

l_degfloat, ndarray [degrees]: galactic longitude
b_degfloat, ndarray [degrees]: galactic latitude
vrfloat, ndarray [km/s]: barycentric radial velocity

Returns

vr_lsrfloat, ndarray[km/s]: radial velocity relative to the LSR

synthpop.synthpop_utils.coordinates_transformation.dlb_to_rphiz(d_kpc: numpy.ndarray, l_deg: numpy.ndarray, b_deg: numpy.ndarray) → Tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray]

translates d, l, b into r, theta, z

phi increases along the galactic rotation with a zero point at the position of the sun

Parameters

d_kpc : float, ndarray [kpc] l_deg : float, ndarray [degree] b_deg : float, ndarray [degree]

Returns

r : float, ndarray [kpc] phi_rad : float, ndarray [rad]

polar angle follows the rotation of the galaxy zero point is at the sun.

zfloat, ndarray [kpc]: hight above/below the galactic plane

synthpop.synthpop_utils.coordinates_transformation.dlb_to_xyz(d_kpc: numpy.ndarray, l_deg: numpy.ndarray, b_deg: numpy.ndarray) → Tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray]

Convert from galactic coordinates an distance to galactocentric cartesian coordinates.

Parameters

l_degfloat, ndarray, [degrees]: galactic longitude
b_degfloat, ndarray, [degrees]: galactic latitude
d_kpcfloat ndarray, [kpc]: distance

Returns

x,y,zfloat nd_array [kpc]: galactocentric cartesian coordinates

synthpop.synthpop_utils.coordinates_transformation.xyz_to_rphiz(x_kpc: numpy.ndarray, y_kpc: numpy.ndarray, z_kpc: numpy.ndarray) → Tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray]

Translate from galactocentric cartesian coordinates into cylindrical cartesian coordinates, the zero point of z follows the warp of the galaxy.

Parameters

x_kpc,y_kpc,z_kpcfloat, ndarray [kpc]: galactocentric cartesian coordinates

Returns

r_kpc : float, ndarray [kpc] phi_rad : float, ndarray [rad]

polar angle follows the rotation of the galaxy zero point is at the sun.

z_kpcfloat, ndarray [kpc]: hight above/below the galactic plane

synthpop.synthpop_utils.coordinates_transformation.lb_to_ad(l_deg: numpy.ndarray, b_deg: numpy.ndarray) → Tuple[numpy.ndarray, numpy.ndarray]

Conversion from Galactic coordinates to Equatorial coordinates

Parameters

l_degfloat, ndarray [degree]: Galactic longitude
b_degfloat, ndarray [degree]: Galactic latitude

Returns

a_degfloat, ndarray [degree]: right ascension
d_degfloat, ndarray [degree]: declination

synthpop.synthpop_utils.coordinates_transformation.ad_to_lb(a_deg: numpy.ndarray, d_deg: numpy.ndarray) → Tuple[numpy.ndarray, numpy.ndarray]

Conversion from Equatorial coordinates to Galactic coordinates

Parameters

a_degfloat, ndarray [degree]: right ascension
d_degfloat, ndarray [degree]: declination

Returns

l_degfloat, ndarray [degree]: Galactic longitude
b_degfloat, ndarray [degree]: Galactic latitude

synthpop.synthpop_utils.coordinates_transformation.uvw_to_vrmulb(l_deg: numpy.ndarray, b_deg: numpy.ndarray, dist_kpc: numpy.ndarray, u_kmps: numpy.ndarray, v_kmps: numpy.ndarray, w_kmps: numpy.ndarray) → Tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray]

Conversion from u,v,w to v_r, mu_l, and mu_b Using (vr, vl, vb) = R * (u,v,w) from Bovy 2011

Parameters

l_degfloat, ndarray [degrees]: galactic longitude
b_degfloat, ndarray [degrees]: galactic latitude
dist_kpcfloat, ndarray [kpc]: distance
u_kmpsfloat, ndarray [km/s]: rectangular velocity with_out correction for the motion of the sun
v_kmpsfloat, ndarray [km/s]: rectangular velocity with_out correction for the motion of the sun
w_kmpsfloat, ndarray [km/s]: rectangular velocity with_out correction for the motion of the sun

Returns

vr_kmpsfloat, ndarray[km/s]: radial velocity
mu_l_maspyrfloat, ndarray [mas/yr]: proper motion in galactic longitude cos(b) is applied
mu_b_maspyrfloat, ndarray [mas/yr]: proper motion in galactic latitude

synthpop.synthpop_utils.coordinates_transformation.uvw_to_vrmuad(l_deg: numpy.ndarray, b_deg: numpy.ndarray, dist_kpc: numpy.ndarray, u_kmps: numpy.ndarray, v_kmps: numpy.ndarray, w_kmps: numpy.ndarray) → Tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray]

Conversion from u,v,w to v_r, mu_l, and mu_b

Parameters

l_degfloat, ndarray [degrees]: galactic longitude
b_degfloat, ndarray [degrees]: galactic latitude
dist_kpcfloat, ndarray [kpc]: distance
u_kmpsfloat, ndarray [km/s]: rectangular velocity with_out correction for the motion of the sun
v_kmpsfloat, ndarray [km/s]: rectangular velocity with_out correction for the motion of the sun
w_kmpsfloat, ndarray [km/s]: rectangular velocity with_out correction for the motion of the sun

Returns

vr_kmpsfloat, ndarray[km/s]: radial velocity
mu_a_maspyrfloat, ndarray [mas/yr]: proper motion in galactic longitude cos(delta) is applied
mu_d_maspyrfloat, ndarray [mas/yr]: proper motion in galactic latitude