# Licensed under a 3-clause BSD style license - see LICENSE.rst
"""Simulate source catalogs."""
import numpy as np
from astropy.coordinates import SkyCoord
from astropy.table import Column, Table
from astropy.units import Quantity
from gammapy.astro.source import PWN, SNR, Pulsar, SNRTrueloveMcKee
from gammapy.utils import coordinates as astrometry
from gammapy.utils.random import (
draw,
get_random_state,
pdf,
sample_sphere,
sample_sphere_distance,
)
from .spatial import (
RMAX,
RMIN,
ZMAX,
ZMIN,
Exponential,
FaucherSpiral,
radial_distributions,
)
from .velocity import VMAX, VMIN, velocity_distributions
__all__ = [
"add_observed_parameters",
"add_pulsar_parameters",
"add_pwn_parameters",
"add_snr_parameters",
"make_base_catalog_galactic",
"make_catalog_random_positions_cube",
"make_catalog_random_positions_sphere",
]
[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, optional
Number of sources. Default is 100.
dimension : {1, 2, 3}
Number of dimensions. Default is 3.
distance_max : `~astropy.units.Quantity`, optional
Maximum distance. Default is "1 pc".
random_state : {int, 'random-seed', 'global-rng', `~numpy.random.RandomState`}
Defines random number generator initialisation.
Default is 'random-seed'.
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(f"Invalid dimension: {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, optional
Number of sources. Default is 100.
distance_min, distance_max : `~astropy.units.Quantity`, optional
Minimum and maximum distance. Default is "0 pc" and "1 pc", respectively.
random_state : {int, 'random-seed', 'global-rng', `~numpy.random.RandomState`}
Defines random number generator initialisation.
Default is "random-state".
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 sources ``n_sources`` and the maximum age ``max_age`` in years. If ``spiralarms``
is True a spiral arm modeling after Faucher&Kaspi is included.
``max_age`` and ``n_sources`` effectively correspond to a SN rate:
SN_rate = ``n_sources`` / ``max_age``
Parameters
----------
n_sources : int
Number of sources to simulate.
rad_dis : callable, optional
Radial surface density distribution of sources.
Default is "YK04".
vel_dis : callable, optional
Proper motion velocity distribution of sources.
Default is "H05".
max_age : `~astropy.units.Quantity`, optional
Maximal age of the source.
Default is "1e6 yr".
spiralarms : bool, optional
Include a spiral arm model in the catalog.
Default is True.
n_ISM : `~astropy.units.Quantity`, optional
Density of the interstellar medium.
Default is "1 cm-3".
random_state : {int, 'random-seed', 'global-rng', `~numpy.random.RandomState`}
Defines random number generator initialisation.
Default is "random-state".
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.
Parameters
----------
table : `~astropy.table.Table`
Table that requires at least columns "age" and "n_ISM" to be defined.
Returns
-------
table : `~astropy.table.Table`
Table with the following entries:
* "E_SN" : SNR kinetic energy
* "r_out" : SNR outer radius
* "r_in" : SNR inner radius
* "L_SNR" : SNR photon rate above 1 TeV
"""
# 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 is given with
the default values.
Parameters
----------
B_mean : float, optional
The mean magnetic field. Default is 12.05 (log Gauss).
B_stdv : float, optional
The standard deviation magnetic field. Default is 0.55.
P_mean : float, optional
The mean period. Default is 0.3 (seconds).
P_stdv : float, optional
The standard deviation period. Default is 0.15.
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.
Parameters
----------
table : `~astropy.table.Table`
Table that requires at least the following columns to be defined:
"age", "E_SN", "n_ISM", "P0_birth" and "B_PSR".
Returns
-------
table : `~astropy.table.Table`
Table with the additional entry "r_out_PWN" which is the outer radius
of the PWN.
"""
# 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 through sun.
Parameters
----------
table : `~astropy.table.Table`
Input table.
obs_pos : tuple, optional
Observation position (X, Y, Z) in Galactocentric coordinates.
Default is None, which uses the Earth's position.
Returns
-------
table : `~astropy.table.Table`
Modified input table with columns added.
"""
obs_pos = obs_pos or [astrometry.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
