# Licensed under a 3-clause BSD style license - see LICENSE.rst
"""Utilities to compute J-factor maps."""
from __future__ import absolute_import, division, print_function, unicode_literals
import numpy as np
import astropy.units as u
__all__ = ["JFactory", "compute_dm_flux"]
[docs]class JFactory(object):
"""Compute J-Factor maps.
All J-Factors are computed for annihilation. The assumed dark matter
profiles will be centered on the center of the map.
Parameters
----------
geom : `~gammapy.maps.WcsGeom`
Reference geometry
profile : `~gammapy.astro.darkmatter.profiles.DMProfile`
Dark matter profile
distance : `~astropy.units.Quantity`
Distance to convert angular scale of the map
"""
def __init__(self, geom, profile, distance):
self.geom = geom
self.profile = profile
self.distance = distance
[docs] def compute_differential_jfactor(self):
r"""Compute differential J-Factor.
.. math ::
\frac{\mathrm d J}{\mathrm d \Omega} =
\int_{\mathrm{LoS}} \mathrm d r \rho(r)
"""
# TODO: Needs to be implemented more efficiently
separation = self.geom.separation(self.geom.center_skydir)
rmin = separation.rad * self.distance
rmax = self.distance
val = [self.profile.integral(_, rmax) for _ in rmin.flatten()]
jfact = u.Quantity(val).to("GeV2 cm-5").reshape(rmin.shape)
return jfact / u.steradian
[docs] def compute_jfactor(self):
r"""Compute astrophysical J-Factor.
.. math ::
J(\Delta\Omega) =
\int_{\Delta\Omega} \mathrm d \Omega^{\prime}
\frac{\mathrm d J}{\mathrm d \Omega^{\prime}}
"""
diff_jfact = self.compute_differential_jfactor()
return diff_jfact * self.geom.to_image().solid_angle()
[docs]def compute_dm_flux(jfact, prim_flux, x_section, energy_range):
r"""Create dark matter flux maps.
The gamma-ray flux is computed as follows:
.. math::
\frac{\mathrm d \phi}{\mathrm d E \mathrm d\Omega} =
\frac{\langle \sigma\nu \rangle}{8\pi m^2_{\mathrm{DM}}}
\frac{\mathrm d N}{\mathrm dE} \times J(\Delta\Omega)
Parameters
----------
jfact : `~astropy.units.Quantity`
J-Factor as computed by `~gammapy.astro.darkmatter.JFactory`
prim_flux : `~gammapy.astro.darkmatter.PrimaryFlux`
Primary gamma-ray flux
x_section : `~astropy.units.Quantity`
Velocity averaged annihilation cross section, :math:`\langle \sigma\nu\rangle`
energy_range : tuple of `~astropy.units.Quantity`
Energy range for the map
Returns
-------
flux : `~astropy.units.Quantity`
DM Flux
References
----------
* `2011JCAP...03..051 <http://adsabs.harvard.edu/abs/2011JCAP...03..051>`_
"""
prefactor = x_section / (8 * np.pi * prim_flux.mDM ** 2)
int_flux = prim_flux.table_model.integral(
emin=energy_range[0], emax=energy_range[1]
)
return (jfact * prefactor * int_flux).to("cm-2 s-1")