# Licensed under a 3-clause BSD style license - see LICENSE.rst
"""Simulate source catalogs."""
import numpy as np
from astropy.table import Table, Column
from astropy.units import Quantity
from astropy.coordinates import SkyCoord
from ...utils import coordinates as astrometry
from ...utils.coordinates import D_SUN_TO_GALACTIC_CENTER
from ...utils.distributions import draw, pdf
from ...utils.random import sample_sphere, sample_sphere_distance, get_random_state
from ..source import SNR, SNRTrueloveMcKee, PWN, Pulsar
from ..population.spatial import (
Exponential,
FaucherSpiral,
RMIN,
RMAX,
ZMIN,
ZMAX,
radial_distributions,
)
from ..population.velocity import VMIN, VMAX, velocity_distributions
__all__ = [
"make_catalog_random_positions_cube",
"make_catalog_random_positions_sphere",
"make_base_catalog_galactic",
"add_snr_parameters",
"add_pulsar_parameters",
"add_pwn_parameters",
"add_observed_parameters",
]
[docs]def make_catalog_random_positions_cube(
size=100, dimension=3, distance_max="1 pc", random_state="random-seed"
):
"""Make a catalog of sources randomly distributed on a line, square or cube.
This can be used to study basic source population distribution effects,
e.g. what the distance distribution looks like, or for a given luminosity
function what the resulting flux distributions are for different spatial
configurations.
Parameters
----------
size : int
Number of sources
dimension : {1, 2, 3}
Number of dimensions
distance_max : `~astropy.units.Quantity`
Maximum distance
random_state : {int, 'random-seed', 'global-rng', `~numpy.random.RandomState`}
Defines random number generator initialisation.
Passed to `~gammapy.utils.random.get_random_state`.
Returns
-------
table : `~astropy.table.Table`
Table with 3D position cartesian coordinates.
Columns: x (pc), y (pc), z (pc)
"""
distance_max = Quantity(distance_max).to_value("pc")
random_state = get_random_state(random_state)
# Generate positions 1D, 2D, or 3D
if dimension == 1:
x = random_state.uniform(-distance_max, distance_max, size)
y, z = 0, 0
elif dimension == 2:
x = random_state.uniform(-distance_max, distance_max, size)
y = random_state.uniform(-distance_max, distance_max, size)
z = 0
elif dimension == 3:
x = random_state.uniform(-distance_max, distance_max, size)
y = random_state.uniform(-distance_max, distance_max, size)
z = random_state.uniform(-distance_max, distance_max, size)
else:
raise ValueError("Invalid dimension: {}".format(dimension))
table = Table()
table["x"] = Column(x, unit="pc", description="Cartesian coordinate")
table["y"] = Column(y, unit="pc", description="Cartesian coordinate")
table["z"] = Column(z, unit="pc", description="Cartesian coordinate")
return table
[docs]def make_catalog_random_positions_sphere(
size=100, distance_min="0 pc", distance_max="1 pc", random_state="random-seed"
):
"""Sample random source locations in a sphere.
This can be used to generate an isotropic source population
in a sphere, e.g. to represent extra-galactic sources.
Parameters
----------
size : int
Number of sources
distance_min, distance_max : `~astropy.units.Quantity`
Minimum and maximum distance
random_state : {int, 'random-seed', 'global-rng', `~numpy.random.RandomState`}
Defines random number generator initialisation.
Passed to `~gammapy.utils.random.get_random_state`.
Returns
-------
catalog : `~astropy.table.Table`
Table with 3D position spherical coordinates.
Columns: lon (deg), lat (deg), distance(pc)
"""
distance_min = Quantity(distance_min).to_value("pc")
distance_max = Quantity(distance_max).to_value("pc")
random_state = get_random_state(random_state)
lon, lat = sample_sphere(size, random_state=random_state)
distance = sample_sphere_distance(distance_min, distance_max, size, random_state)
table = Table()
table["lon"] = Column(lon, unit="rad", description="Spherical coordinate")
table["lat"] = Column(lat, unit="rad", description="Spherical coordinate")
table["distance"] = Column(distance, unit="pc", description="Spherical coordinate")
return table
[docs]def make_base_catalog_galactic(
n_sources,
rad_dis="YK04",
vel_dis="H05",
max_age="1e6 yr",
spiralarms=True,
n_ISM="1 cm-3",
random_state="random-seed",
):
"""Make a catalog of Galactic sources, with basic source parameters.
Choose a radial distribution, a velocity distribution, the number
of pulsars n_pulsars, the maximal age max_age[years] and the fraction
of the individual morphtypes. There's an option spiralarms. If set on
True a spiralarm modelling after Faucher&Kaspi is included.
max_age and n_sources effectively correspond to s SN rate:
SN_rate = n_sources / max_age
Parameters
----------
n_sources : int
Number of sources to simulate
rad_dis : callable
Radial surface density distribution of sources
vel_dis : callable
Proper motion velocity distribution of sources
max_age : `~astropy.units.Quantity`
Maximal age of the source
spiralarms : bool
Include a spiralarm model in the catalog?
n_ISM : `~astropy.units.Quantity`
Density of the interstellar medium
random_state : {int, 'random-seed', 'global-rng', `~numpy.random.RandomState`}
Defines random number generator initialisation.
Passed to `~gammapy.utils.random.get_random_state`.
Returns
-------
table : `~astropy.table.Table`
Catalog of simulated source positions and proper velocities
"""
max_age = Quantity(max_age).to_value("yr")
n_ISM = Quantity(n_ISM).to("cm-3")
random_state = get_random_state(random_state)
if isinstance(rad_dis, str):
rad_dis = radial_distributions[rad_dis]
if isinstance(vel_dis, str):
vel_dis = velocity_distributions[vel_dis]
# Draw random values for the age
age = random_state.uniform(0, max_age, n_sources)
age = Quantity(age, "yr")
# Draw spatial distribution
r = draw(
RMIN.to_value("kpc"),
RMAX.to_value("kpc"),
n_sources,
pdf(rad_dis()),
random_state=random_state,
)
r = Quantity(r, "kpc")
if spiralarms:
r, theta, spiralarm = FaucherSpiral()(r, random_state=random_state)
else:
theta = Quantity(random_state.uniform(0, 2 * np.pi, n_sources), "rad")
spiralarm = None
x, y = astrometry.cartesian(r, theta)
z = draw(
ZMIN.to_value("kpc"),
ZMAX.to_value("kpc"),
n_sources,
Exponential(),
random_state=random_state,
)
z = Quantity(z, "kpc")
# Draw values from velocity distribution
v = draw(
VMIN.to_value("km/s"),
VMAX.to_value("km/s"),
n_sources,
vel_dis(),
random_state=random_state,
)
v = Quantity(v, "km/s")
# Draw random direction of initial velocity
theta = Quantity(random_state.uniform(0, np.pi, x.size), "rad")
phi = Quantity(random_state.uniform(0, 2 * np.pi, x.size), "rad")
# Compute new position
dx, dy, dz, vx, vy, vz = astrometry.motion_since_birth(v, age, theta, phi)
# Add displacement to birth position
x_moved = x + dx
y_moved = y + dy
z_moved = z + dz
table = Table()
table["age"] = Column(age, unit="yr", description="Age of the source")
table["n_ISM"] = Column(n_ISM, description="Interstellar medium density")
if spiralarms:
table["spiralarm"] = Column(spiralarm, description="Which spiralarm?")
table["x_birth"] = Column(x, description="Galactocentric x coordinate at birth")
table["y_birth"] = Column(y, description="Galactocentric y coordinate at birth")
table["z_birth"] = Column(z, description="Galactocentric z coordinate at birth")
table["x"] = Column(x_moved.to("kpc"), description="Galactocentric x coordinate")
table["y"] = Column(y_moved.to("kpc"), description="Galactocentric y coordinate")
table["z"] = Column(z_moved.to("kpc"), description="Galactocentric z coordinate")
table["vx"] = Column(vx, description="Galactocentric velocity in x direction")
table["vy"] = Column(vy, description="Galactocentric velocity in y direction")
table["vz"] = Column(vz, description="Galactocentric velocity in z direction")
table["v_abs"] = Column(v, description="Galactocentric velocity (absolute)")
return table
[docs]def add_snr_parameters(table):
"""Add SNR parameters to the table.
TODO: document
"""
# Read relevant columns
age = table["age"].quantity
n_ISM = table["n_ISM"].quantity
# Compute properties
snr = SNR(n_ISM=n_ISM)
E_SN = snr.e_sn * np.ones(len(table))
r_out = snr.radius(age)
r_in = snr.radius_inner(age)
L_SNR = snr.luminosity_tev(age)
# Add columns to table
table["E_SN"] = Column(E_SN, description="SNR kinetic energy")
table["r_out"] = Column(r_out.to("pc"), description="SNR outer radius")
table["r_in"] = Column(r_in.to("pc"), description="SNR inner radius")
table["L_SNR"] = Column(L_SNR, description="SNR photon rate above 1 TeV")
return table
[docs]def add_pulsar_parameters(
table,
B_mean=12.05,
B_stdv=0.55,
P_mean=0.3,
P_stdv=0.15,
random_state="random-seed",
):
"""Add pulsar parameters to the table.
For the initial normal distribution of period and logB can exist the following
Parameters: B_mean=12.05[log Gauss], B_stdv=0.55, P_mean=0.3[s], P_stdv=0.15
Parameters
----------
random_state : {int, 'random-seed', 'global-rng', `~numpy.random.RandomState`}
Defines random number generator initialisation.
Passed to `~gammapy.utils.random.get_random_state`.
"""
random_state = get_random_state(random_state)
# Read relevant columns
age = table["age"].quantity
# Draw the initial values for the period and magnetic field
def p_dist(x):
return np.exp(-0.5 * ((x - P_mean) / P_stdv) ** 2)
p0_birth = draw(0, 2, len(table), p_dist, random_state=random_state)
p0_birth = Quantity(p0_birth, "s")
log10_b_psr = random_state.normal(B_mean, B_stdv, len(table))
b_psr = Quantity(10 ** log10_b_psr, "G")
# Compute pulsar parameters
psr = Pulsar(p0_birth, b_psr)
p0 = psr.period(age)
p1 = psr.period_dot(age)
p1_birth = psr.P_dot_0
tau = psr.tau(age)
tau_0 = psr.tau_0
l_psr = psr.luminosity_spindown(age)
l0_psr = psr.L_0
# Add columns to table
table["P0"] = Column(p0, unit="s", description="Pulsar period")
table["P1"] = Column(p1, unit="", description="Pulsar period derivative")
table["P0_birth"] = Column(p0_birth, unit="s", description="Pulsar birth period")
table["P1_birth"] = Column(
p1_birth, unit="", description="Pulsar birth period derivative"
)
table["CharAge"] = Column(tau, unit="yr", description="Pulsar characteristic age")
table["Tau0"] = Column(tau_0, unit="yr")
table["L_PSR"] = Column(l_psr, unit="erg s-1")
table["L0_PSR"] = Column(l0_psr, unit="erg s-1")
table["B_PSR"] = Column(
b_psr, unit="Gauss", description="Pulsar magnetic field at the poles"
)
return table
[docs]def add_pwn_parameters(table):
"""Add PWN parameters to the table.
TODO: document
"""
# Some of the computations (specifically `pwn.radius`) aren't vectorised
# across all parameters; so here we loop over source parameters explicitly
results = []
for idx in range(len(table)):
age = table["age"].quantity[idx]
E_SN = table["E_SN"].quantity[idx]
n_ISM = table["n_ISM"].quantity[idx]
P0_birth = table["P0_birth"].quantity[idx]
b_psr = table["B_PSR"].quantity[idx]
# Compute properties
pulsar = Pulsar(P0_birth, b_psr)
snr = SNRTrueloveMcKee(e_sn=E_SN, n_ISM=n_ISM)
pwn = PWN(pulsar, snr)
r_out_pwn = pwn.radius(age).to_value("pc")
results.append(dict(r_out_pwn=r_out_pwn))
# Add columns to table
table["r_out_PWN"] = Column(
[_["r_out_pwn"] for _ in results], unit="pc", description="PWN outer radius"
)
return table
[docs]def add_observed_parameters(table, obs_pos=None):
"""Add observable parameters (such as sky position or distance).
Input table columns: x, y, z, extension, luminosity
Output table columns: distance, glon, glat, flux, angular_extension
Position of observer in cartesian coordinates.
Center of galaxy as origin, x-axis goes trough sun.
Parameters
----------
table : `~astropy.table.Table`
Input table
obs_pos : tuple or None
Observation position (X, Y, Z) in Galactocentric coordinates (default: Earth)
Returns
-------
table : `~astropy.table.Table`
Modified input table with columns added
"""
obs_pos = obs_pos or [D_SUN_TO_GALACTIC_CENTER, 0, 0]
# Get data
x, y, z = table["x"].quantity, table["y"].quantity, table["z"].quantity
vx, vy, vz = table["vx"].quantity, table["vy"].quantity, table["vz"].quantity
distance, glon, glat = astrometry.galactic(x, y, z, obs_pos=obs_pos)
# Compute projected velocity
v_glon, v_glat = astrometry.velocity_glon_glat(x, y, z, vx, vy, vz)
coordinate = SkyCoord(glon, glat, unit="deg", frame="galactic").transform_to("icrs")
ra, dec = coordinate.ra.deg, coordinate.dec.deg
# Add columns to table
table["distance"] = Column(
distance, unit="pc", description="Distance observer to source center"
)
table["GLON"] = Column(glon, unit="deg", description="Galactic longitude")
table["GLAT"] = Column(glat, unit="deg", description="Galactic latitude")
table["VGLON"] = Column(
v_glon.to("deg/Myr"),
unit="deg/Myr",
description="Velocity in Galactic longitude",
)
table["VGLAT"] = Column(
v_glat.to("deg/Myr"),
unit="deg/Myr",
description="Velocity in Galactic latitude",
)
table["RA"] = Column(ra, unit="deg", description="Right ascension")
table["DEC"] = Column(dec, unit="deg", description="Declination")
try:
luminosity = table["luminosity"]
flux = luminosity / (4 * np.pi * distance ** 2)
table["flux"] = Column(flux.value, unit=flux.unit, description="Source flux")
except KeyError:
pass
try:
extension = table["extension"]
angular_extension = np.degrees(np.arctan(extension / distance))
table["angular_extension"] = Column(
angular_extension,
unit="deg",
description="Source angular radius (i.e. half-diameter)",
)
except KeyError:
pass
return table