This is a fixed-text formatted version of a Jupyter notebook

Dark matter spatial and spectral models#

Introduction#

Gammapy has some convenience methods for dark matter analyses in ~gammapy.astro.darkmatter. These include J-Factor computation and calculation the expected gamma flux for a number of annihilation channels. They are presented in this notebook.

The basic concepts of indirect dark matter searches, however, are not explained. So this is aimed at people who already know what the want to do. A good introduction to indirect dark matter searches is given for example in https://arxiv.org/pdf/1012.4515.pdf (Chapter 1 and 5)

Setup#

As always, we start with some setup for the notebook, and with imports.

[1]:
from gammapy.astro.darkmatter import (
    profiles,
    JFactory,
    PrimaryFlux,
    DarkMatterAnnihilationSpectralModel,
)

from gammapy.maps import WcsGeom, WcsNDMap
from astropy.coordinates import SkyCoord
from matplotlib.colors import LogNorm
from regions import CircleSkyRegion
import astropy.units as u
import numpy as np
[2]:
%matplotlib inline
import matplotlib.pyplot as plt

Profiles#

The following dark matter profiles are currently implemented. Each model can be scaled to a given density at a certain distance. These parameters are controlled by profiles.DMProfile.LOCAL_DENSITY and profiles.DMProfile.DISTANCE_GC

[3]:
profiles.DMProfile.__subclasses__()
[3]:
[gammapy.astro.darkmatter.profiles.NFWProfile,
 gammapy.astro.darkmatter.profiles.EinastoProfile,
 gammapy.astro.darkmatter.profiles.IsothermalProfile,
 gammapy.astro.darkmatter.profiles.BurkertProfile,
 gammapy.astro.darkmatter.profiles.MooreProfile]
[4]:
for profile in profiles.DMProfile.__subclasses__():
    p = profile()
    p.scale_to_local_density()
    radii = np.logspace(-3, 2, 100) * u.kpc
    plt.plot(radii, p(radii), label=p.__class__.__name__)

plt.loglog()
plt.axvline(8.5, linestyle="dashed", color="black", label="local density")
plt.legend()

print("LOCAL_DENSITY:", profiles.DMProfile.LOCAL_DENSITY)
print("DISTANCE_GC:", profiles.DMProfile.DISTANCE_GC)
LOCAL_DENSITY: 0.3 GeV / cm3
DISTANCE_GC: 8.33 kpc
../../_images/tutorials_api_astro_dark_matter_7_1.png

J Factors#

There are utilities to compute J-Factor maps that can serve as a basis to compute J-Factors for certain regions. In the following we compute a J-Factor map for the Galactic Centre region

[5]:
profile = profiles.NFWProfile()

# Adopt standard values used in HESS
profiles.DMProfile.DISTANCE_GC = 8.5 * u.kpc
profiles.DMProfile.LOCAL_DENSITY = 0.39 * u.Unit("GeV / cm3")

profile.scale_to_local_density()

position = SkyCoord(0.0, 0.0, frame="galactic", unit="deg")
geom = WcsGeom.create(binsz=0.05, skydir=position, width=3.0, frame="galactic")
[6]:
jfactory = JFactory(
    geom=geom, profile=profile, distance=profiles.DMProfile.DISTANCE_GC
)
jfact = jfactory.compute_jfactor()
[7]:
jfact_map = WcsNDMap(geom=geom, data=jfact.value, unit=jfact.unit)
ax = jfact_map.plot(cmap="viridis", norm=LogNorm(), add_cbar=True)
plt.title(f"J-Factor [{jfact_map.unit}]")

# 1 deg circle usually used in H.E.S.S. analyses
sky_reg = CircleSkyRegion(center=position, radius=1 * u.deg)
pix_reg = sky_reg.to_pixel(wcs=geom.wcs)
pix_reg.plot(ax=ax, facecolor="none", edgecolor="red", label="1 deg circle")
plt.legend()
[7]:
<matplotlib.legend.Legend at 0x7fe18d4107f0>
../../_images/tutorials_api_astro_dark_matter_11_1.png
[8]:
# NOTE: https://arxiv.org/abs/1607.08142 quote 2.67e21 without the +/- 0.3 deg band around the plane
total_jfact = pix_reg.to_mask().multiply(jfact).sum()
print(
    "J-factor in 1 deg circle around GC assuming a "
    f"{profile.__class__.__name__} is {total_jfact:.3g}"
)
J-factor in 1 deg circle around GC assuming a NFWProfile is 1.35e+21 GeV2 / cm5

Gamma-ray spectra at production#

The gamma-ray spectrum per annihilation is a further ingredient for a dark matter analysis. The following annihilation channels are supported. For more info see https://arxiv.org/pdf/1012.4515.pdf

[9]:
fluxes = PrimaryFlux(mDM="1 TeV", channel="eL")
print(fluxes.allowed_channels)
['eL', 'eR', 'e', 'muL', 'muR', 'mu', 'tauL', 'tauR', 'tau', 'q', 'c', 'b', 't', 'WL', 'WT', 'W', 'ZL', 'ZT', 'Z', 'g', 'gamma', 'h', 'nu_e', 'nu_mu', 'nu_tau', 'V->e', 'V->mu', 'V->tau']
[10]:
fig, axes = plt.subplots(4, 1, figsize=(6, 16))
mDMs = [0.01, 0.1, 1, 10] * u.TeV

for mDM, ax in zip(mDMs, axes):
    fluxes.mDM = mDM
    ax.set_title(rf"m$_{{\mathrm{{DM}}}}$ = {mDM}")
    ax.set_yscale("log")
    ax.set_ylabel("dN/dE")

    for channel in ["tau", "mu", "b", "Z"]:
        fluxes.channel = channel
        fluxes.table_model.plot(
            energy_bounds=[mDM / 100, mDM],
            ax=ax,
            label=channel,
            yunits=u.Unit("1/GeV"),
        )

axes[0].legend()
plt.subplots_adjust(hspace=0.5)
../../_images/tutorials_api_astro_dark_matter_15_0.png

Flux maps#

Finally flux maps can be produced like this:

[11]:
channel = "Z"
massDM = 10 * u.TeV
diff_flux = DarkMatterAnnihilationSpectralModel(mass=massDM, channel=channel)
int_flux = (
    jfact * diff_flux.integral(energy_min=0.1 * u.TeV, energy_max=10 * u.TeV)
).to("cm-2 s-1")
[12]:
flux_map = WcsNDMap(geom=geom, data=int_flux.value, unit="cm-2 s-1")

ax = flux_map.plot(cmap="viridis", norm=LogNorm(), add_cbar=True)
plt.title(
    f"Flux [{int_flux.unit}]\n m$_{{DM}}$={fluxes.mDM.to('TeV')}, channel={fluxes.channel}"
);
../../_images/tutorials_api_astro_dark_matter_18_0.png
[ ]: