EpochPropagation#

class pygaia.astrometry.coordinates.EpochPropagation#

Bases: object

Provides methods for transforming the astrometry and radial velocity of a given source to a different epoch.

The formulae for rigorous epoch transformation can be found on the Gaia documentation pages.

mastorad#

Numerical factor to convert milliarcseconds ro radians.

Type:

float

Methods Summary

propagate_astrometry(phi, theta, parallax, ...)

Propagate the astrometric parameters of a source from the reference epoch t0 to the new epoch t1.

propagate_astrometry_and_covariance_matrix(a0, ...)

Propagate the astrometric parameters iand radial proper motion, as well as the corresponding covariance matrix, from epoch t0 to epoch t1.

propagate_pos(phi, theta, parallax, ...)

Propagate the position of a source from the reference epoch t0 to the new epoch t1.

Methods Documentation

propagate_astrometry(phi, theta, parallax, muphistar, mutheta, vrad, t0, t1)#

Propagate the astrometric parameters of a source from the reference epoch t0 to the new epoch t1.

Parameters:

  • phi (float) – Longitude at reference epoch (radians).

  • theta (float) – Latitude at reference epoch (radians).

  • parallax (float) – Parallax at the reference epoch (mas).

  • muphistar (float) – Proper motion in longitude (including np.cos(latitude) term) at reference epoch (mas/yr).

  • mutheta (float) – Proper motion in latitude at reference epoch (mas/yr).

  • vrad (float) – Radial velocity at reference epoch (km/s). Can be set to 0 km/s if not known.

  • t0 (float) – Reference epoch (Julian years).

  • t1 (float) – New epoch (Julian years).

Returns:

phi1, theta1, parallax1, muphistar1, mutheta1, murad1 – Astrometric parameters, including the “radial proper motion” (NOT the radial velocity), at the new epoch.

Return type:

float or array

propagate_astrometry_and_covariance_matrix(a0, c0, t0, t1)#

Propagate the astrometric parameters iand radial proper motion, as well as the corresponding covariance matrix, from epoch t0 to epoch t1.

Code based on the Hipparcos Fortran implementation by Lennart Lindegren.

Parameters:

  • a0 (array_like) – 6-element vector: (phi, theta, parallax, muphistar, mutheta, vrad) in units of (radians, radians, mas, mas/yr, mas/yr, km/s). Shape of a should be (6,) or (6,N), with N the number of sources for which the astrometric parameters are provided. The value of vrad can be set to 0 km/s if the radial velocity is not know. An appropriate uncertainty should then be provided (see below).

  • c0 (array_like) – Covariance matrix stored in a 6x6 element array. This can be constructed from the columns listed in the Gaia catalogue. The units are [mas^2, mas^2/yr, mas^2/yr^2] for the various elements. Note that the elements in the 6th row and column should be: c[6,i] = c[i,6] = c[i,3] * vrad / auKmYearPerSec for i = 1,..,5 and c[6,6] = c[3,3] * (vrad^2+vrad_error^2) / auKmYearPerSec^2 + (parallax*vrad_error/auKmYearPerSec)^2 The shape of c0 should be (6,6) or (N,6,6). If the radial velocity is not know the uncertainty on the radial velocity (vrad_error) should be set to the velocity dispersion of the population the source is drawn from.

  • t0 (float) – Reference epoch (Julian years).

  • t1 (float) – New epoch (Julian years).

Returns:

a, c – Astrometric parameters, including the “radial proper motion” (NOT the radial velocity), and the covariance matrix at the new epoch as a 2D matrix with the new variances on the diagonal and the covariance in the off-diagonal elements.

Return type:

array

propagate_pos(phi, theta, parallax, muphistar, mutheta, vrad, t0, t1)#

Propagate the position of a source from the reference epoch t0 to the new epoch t1.

Parameters:

  • phi (float) – Longitude at reference epoch (radians).

  • theta (float) – Latitude at reference epoch (radians).

  • parallax (float) – Parallax at the reference epoch (mas).

  • muphistar (float) – Proper motion in longitude (including np.cos(latitude) term) at reference epoch (mas/yr).

  • mutheta (float) – Proper motion in latitude at reference epoch (mas/yr).

  • vrad (float) – Radial velocity at reference epoch (km/s). Can be set to 0 km/s if not known.

  • t0 (float) – Reference epoch (Julian years).

  • t1 (float) – New epoch (Julian years).

Returns:

phi, theta – Coordinates the new epoch (in radians)

Return type:

float