Source code for gammapy.astro.darkmatter.profiles

# 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 ...utils.fitting import Parameter, Parameters
from ...spectrum.utils 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.spectrum.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)