Source code for gammapy.utils.coordinates.other

# Licensed under a 3-clause BSD style license - see LICENSE.rst
"""Other coordinate and distance-related functions"""
import numpy as np
from astropy.units import Unit, Quantity

__all__ = [
    "cartesian",
    "galactic",
    "luminosity_to_flux",
    "flux_to_luminosity",
    "radius_to_angle",
    "angle_to_radius",
    "velocity_glon_glat",
    "motion_since_birth",
    "polar",
    "D_SUN_TO_GALACTIC_CENTER",
]

# TODO: replace this with the default from the Galactocentric frame in astropy.coordinates
D_SUN_TO_GALACTIC_CENTER = Quantity(8.5, "kpc")
"""Default assumed distance from the Sun to the Galactic center (`~astropy.units.Quantity`)"""


[docs]def cartesian(r, theta): """ Convert polar coordinates to cartesian coordinates. """ x = r * np.cos(theta) y = r * np.sin(theta) return x, y
[docs]def polar(x, y): """Convert cartesian coordinates to polar coordinates.""" r = np.sqrt(x ** 2 + y ** 2) theta = np.arctan2(y, x) return r, theta
[docs]def galactic(x, y, z, obs_pos=None): """Compute galactic coordinates lon, lat (deg) and distance (kpc) for given position in cartesian coordinates (kpc). """ obs_pos = obs_pos or [D_SUN_TO_GALACTIC_CENTER, 0, 0] y_prime = y + D_SUN_TO_GALACTIC_CENTER d = np.sqrt(x ** 2 + y_prime ** 2 + z ** 2) glon = np.arctan2(x, y_prime).to("deg") glat = np.arcsin(z / d).to("deg") return d, glon, glat
[docs]def luminosity_to_flux(luminosity, distance): """Distance is assumed to be in kpc""" return luminosity / (4 * np.pi * distance ** 2)
[docs]def flux_to_luminosity(flux, distance): """Distance is assumed to be in kpc""" return flux * 4 * np.pi * distance ** 2
[docs]def radius_to_angle(radius, distance): """Radius (pc), distance(kpc), angle(deg)""" return np.arctan(radius / distance)
[docs]def angle_to_radius(angle, distance): """Radius (pc), distance(kpc), angle(deg)""" return np.tan(angle * distance)
[docs]def velocity_glon_glat(x, y, z, vx, vy, vz): """ Compute projected angular velocity in galactic coordinates. Parameters ---------- x : `~astropy.units.Quantity` Position in x direction y : `~astropy.units.Quantity` Position in y direction z : `~astropy.units.Quantity` Position in z direction vx : `~astropy.units.Quantity` Velocity in x direction vy : `~astropy.units.Quantity` Velocity in y direction vz : `~astropy.units.Quantity` Velocity in z direction Returns ------- v_glon : `~astropy.units.Quantity` Projected velocity in Galactic longitude v_glat : `~astropy.units.Quantity` Projected velocity in Galactic latitude """ y_prime = y + D_SUN_TO_GALACTIC_CENTER d = np.sqrt(x ** 2 + y_prime ** 2 + z ** 2) r = np.sqrt(x ** 2 + y_prime ** 2) v_glon = (-y_prime * vx + x * vy) / r ** 2 v_glat = vz / (np.sqrt(1 - (z / d) ** 2) * d) - np.sqrt( vx ** 2 + vy ** 2 + vz ** 2 ) * z / ((np.sqrt(1 - (z / d) ** 2) * d ** 2)) return v_glon * Unit("rad"), v_glat * Unit("rad")
[docs]def motion_since_birth(v, age, theta, phi): """ Compute motion of a object with given velocity, direction and age. Parameters ---------- v : `~astropy.units.Quantity` Absolute value of the velocity age : `~astropy.units.Quantity` Age of the source. theta : `~astropy.units.Quantity` Angular direction of the velocity. phi : `~astropy.units.Quantity` Angular direction of the velocity. Returns ------- dx : `~astropy.units.Quantity` Displacement in x direction dy : `~astropy.units.Quantity` Displacement in y direction dz : `~astropy.units.Quantity` Displacement in z direction vx : `~astropy.units.Quantity` Velocity in x direction vy : `~astropy.units.Quantity` Velocity in y direction vz : `~astropy.units.Quantity` Velocity in z direction """ vx = v * np.cos(phi) * np.sin(theta) vy = v * np.sin(phi) * np.sin(theta) vz = v * np.cos(theta) # Compute new positions dx = vx * age dy = vy * age dz = vz * age return dx, dy, dz, vx, vy, vz