\n",
"**This is a fixed-text formatted version of a Jupyter notebook.**\n",
"\n",
"- Try online [![Binder](https://mybinder.org/badge.svg)](https://mybinder.org/v2/gh/gammapy/gammapy-webpage/v0.8?urlpath=lab/tree/astro_dark_matter.ipynb)\n",
"- You can contribute with your own notebooks in this\n",
"[GitHub repository](https://github.com/gammapy/gammapy/tree/master/tutorials).\n",
"- **Source files:**\n",
"[astro_dark_matter.ipynb](../_static/notebooks/astro_dark_matter.ipynb) |\n",
"[astro_dark_matter.py](../_static/notebooks/astro_dark_matter.py)\n",
"
\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Dark matter utilities\n",
"\n",
"## Introduction \n",
"\n",
"Gammapy has some convenience methods for dark matter analyses in [gammapy.astro.darkmatter](..\/astro/darkmatter/index.rst). These include J-Factor computation and calculation the expected gamma flux for a number of annihilation channels. They are presented in this notebook. \n",
"\n",
"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)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Setup\n",
"\n",
"As always, we start with some setup for the notebook, and with imports."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"from gammapy.astro.darkmatter import (\n",
" profiles,\n",
" JFactory,\n",
" PrimaryFlux,\n",
" compute_dm_flux,\n",
")\n",
"\n",
"from gammapy.maps import WcsGeom, WcsNDMap\n",
"from astropy.coordinates import SkyCoord\n",
"from matplotlib.colors import LogNorm\n",
"from regions import CircleSkyRegion\n",
"import astropy.units as u\n",
"import numpy as np"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"%matplotlib inline\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Profiles\n",
"\n",
"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``"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[gammapy.astro.darkmatter.profiles.NFWProfile,\n",
" gammapy.astro.darkmatter.profiles.EinastoProfile,\n",
" gammapy.astro.darkmatter.profiles.IsothermalProfile,\n",
" gammapy.astro.darkmatter.profiles.BurkertProfile,\n",
" gammapy.astro.darkmatter.profiles.MooreProfile]"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"profiles.DMProfile.__subclasses__()"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The assumed local density is 0.3 GeV / cm3 at a distance to the GC of 8.33 kpc\n"
]
},
{
"data": {
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\n",
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