# Licensed under a 3-clause BSD style license - see LICENSE.rst
"""Dark matter profiles."""
import abc
import numpy as np
import astropy.units as u
from gammapy.modeling import Parameter, Parameters
from gammapy.utils.integrate import integrate_spectrum
__all__ = [
"DMProfile",
"NFWProfile",
"EinastoProfile",
"IsothermalProfile",
"BurkertProfile",
"MooreProfile",
]
[docs]class DMProfile(abc.ABC):
"""DMProfile model base class."""
LOCAL_DENSITY = 0.3 * u.GeV / (u.cm ** 3)
"""Local dark matter density as given in refenrece 2"""
DISTANCE_GC = 8.33 * u.kpc
"""Distance to the Galactic Center as given in reference 2"""
[docs] def __call__(self, radius):
"""Call evaluate method of derived classes."""
kwargs = dict()
for par in self.parameters.parameters:
kwargs[par.name] = par.quantity
return self.evaluate(radius, **kwargs)
[docs] def scale_to_local_density(self):
"""Scale to local density."""
scale = (self.LOCAL_DENSITY / self(self.DISTANCE_GC)).to_value("")
self.parameters["rho_s"].value *= scale
def _eval_squared(self, radius):
"""Squared density at given radius."""
return self(radius) ** 2
[docs] def integral(self, rmin, rmax, **kwargs):
r"""Integrate squared dark matter profile numerically.
.. math::
F(r_{min}, r_{max}) = \int_{r_{min}}^{r_{max}}\rho(r)^2 dr
Parameters
----------
rmin, rmax : `~astropy.units.Quantity`
Lower and upper bound of integration range.
**kwargs : dict
Keyword arguments passed to :func:`~gammapy.utils.integrate.integrate_spectrum`
"""
integral = integrate_spectrum(self._eval_squared, rmin, rmax, **kwargs)
return integral.to("GeV2 / cm5")
[docs]class NFWProfile(DMProfile):
r"""NFW Profile.
.. math::
\rho(r) = \rho_s \frac{r_s}{r}\left(1 + \frac{r}{r_s}\right)^{-2}
Parameters
----------
r_s : `~astropy.units.Quantity`
Scale radius, :math:`r_s`
rho_s : `~astropy.units.Quantity`
Characteristic density, :math:`\rho_s`
References
----------
* `1997ApJ...490..493 <https://ui.adsabs.harvard.edu/abs/1997ApJ...490..493N>`_
* `2011JCAP...03..051 <https://ui.adsabs.harvard.edu/abs/2011JCAP...03..051>`_
"""
DEFAULT_SCALE_RADIUS = 24.42 * u.kpc
"""Default scale radius as given in reference 2"""
def __init__(self, r_s=None, rho_s=1 * u.Unit("GeV / cm3")):
r_s = self.DEFAULT_SCALE_RADIUS if r_s is None else r_s
self.parameters = Parameters(
[Parameter("r_s", u.Quantity(r_s)), Parameter("rho_s", u.Quantity(rho_s))]
)
[docs] @staticmethod
def evaluate(radius, r_s, rho_s):
rr = radius / r_s
return rho_s / (rr * (1 + rr) ** 2)
[docs]class EinastoProfile(DMProfile):
r"""Einasto Profile.
.. math::
\rho(r) = \rho_s \exp{
\left(-\frac{2}{\alpha}\left[
\left(\frac{r}{r_s}\right)^{\alpha} - 1\right] \right)}
Parameters
----------
r_s : `~astropy.units.Quantity`
Scale radius, :math:`r_s`
alpha : `~astropy.units.Quantity`
:math:`\alpha`
rho_s : `~astropy.units.Quantity`
Characteristic density, :math:`\rho_s`
References
----------
* `1965TrAlm...5...87E <https://ui.adsabs.harvard.edu/abs/1965TrAlm...5...87E>`_
* `2011JCAP...03..051 <https://ui.adsabs.harvard.edu/abs/2011JCAP...03..051>`_
"""
DEFAULT_SCALE_RADIUS = 28.44 * u.kpc
"""Default scale radius as given in reference 2"""
DEFAULT_ALPHA = 0.17
"""Default scale radius as given in reference 2"""
def __init__(self, r_s=None, alpha=None, rho_s=1 * u.Unit("GeV / cm3")):
alpha = self.DEFAULT_ALPHA if alpha is None else alpha
r_s = self.DEFAULT_SCALE_RADIUS if r_s is None else r_s
self.parameters = Parameters(
[
Parameter("r_s", u.Quantity(r_s)),
Parameter("alpha", u.Quantity(alpha)),
Parameter("rho_s", u.Quantity(rho_s)),
]
)
[docs] @staticmethod
def evaluate(radius, r_s, alpha, rho_s):
rr = radius / r_s
exponent = (2 / alpha) * (rr ** alpha - 1)
return rho_s * np.exp(-1 * exponent)
[docs]class IsothermalProfile(DMProfile):
r"""Isothermal Profile.
.. math:: \rho(r) = \frac{\rho_s}{1 + (r/r_s)^2}
Parameters
----------
r_s : `~astropy.units.Quantity`
Scale radius, :math:`r_s`
References
----------
* `1991MNRAS.249..523B <https://ui.adsabs.harvard.edu/abs/1991MNRAS.249..523B>`_
* `2011JCAP...03..051 <https://ui.adsabs.harvard.edu/abs/2011JCAP...03..051>`_
"""
DEFAULT_SCALE_RADIUS = 4.38 * u.kpc
"""Default scale radius as given in reference 2"""
def __init__(self, r_s=None, rho_s=1 * u.Unit("GeV / cm3")):
r_s = self.DEFAULT_SCALE_RADIUS if r_s is None else r_s
self.parameters = Parameters(
[Parameter("r_s", u.Quantity(r_s)), Parameter("rho_s", u.Quantity(rho_s))]
)
[docs] @staticmethod
def evaluate(radius, r_s, rho_s):
rr = radius / r_s
return rho_s / (1 + rr ** 2)
[docs]class BurkertProfile(DMProfile):
r"""Burkert Profile.
.. math:: \rho(r) = \frac{\rho_s}{(1 + r/r_s)(1 + (r/r_s)^2)}
Parameters
----------
r_s : `~astropy.units.Quantity`
Scale radius, :math:`r_s`
References
----------
* `1995ApJ...447L..25B <https://ui.adsabs.harvard.edu/abs/1995ApJ...447L..25B>`_
* `2011JCAP...03..051 <https://ui.adsabs.harvard.edu/abs/2011JCAP...03..051>`_
"""
DEFAULT_SCALE_RADIUS = 12.67 * u.kpc
"""Default scale radius as given in reference 2"""
def __init__(self, r_s=None, rho_s=1 * u.Unit("GeV / cm3")):
r_s = self.DEFAULT_SCALE_RADIUS if r_s is None else r_s
self.parameters = Parameters(
[Parameter("r_s", u.Quantity(r_s)), Parameter("rho_s", u.Quantity(rho_s))]
)
[docs] @staticmethod
def evaluate(radius, r_s, rho_s):
rr = radius / r_s
return rho_s / ((1 + rr) * (1 + rr ** 2))
[docs]class MooreProfile(DMProfile):
r"""Moore Profile.
.. math::
\rho(r) = \rho_s \left(\frac{r_s}{r}\right)^{1.16}
\left(1 + \frac{r}{r_s} \right)^{-1.84}
Parameters
----------
r_s : `~astropy.units.Quantity`
Scale radius, :math:`r_s`
References
----------
* `2004MNRAS.353..624D <https://ui.adsabs.harvard.edu/abs/2004MNRAS.353..624D>`_
* `2011JCAP...03..051 <https://ui.adsabs.harvard.edu/abs/2011JCAP...03..051>`_
"""
DEFAULT_SCALE_RADIUS = 30.28 * u.kpc
"""Default scale radius as given in reference 2"""
def __init__(self, r_s=None, rho_s=1 * u.Unit("GeV / cm3")):
r_s = self.DEFAULT_SCALE_RADIUS if r_s is None else r_s
self.parameters = Parameters(
[Parameter("r_s", u.Quantity(r_s)), Parameter("rho_s", u.Quantity(rho_s))]
)
[docs] @staticmethod
def evaluate(radius, r_s, rho_s):
rr = radius / r_s
rr_ = r_s / radius
return rho_s * rr_ ** 1.16 * (1 + rr) ** (-1.84)