\n",
"\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/v0.11?urlpath=lab/tree/source_population_model.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",
"[source_population_model.ipynb](../_static/notebooks/source_population_model.ipynb) |\n",
"[source_population_model.py](../_static/notebooks/source_population_model.py)\n",
"
\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Astrophysical source population modeling with Gammapy"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Introduction\n",
"\n",
"The [gammapy.astro.population](..\/astro/population/index.rst) package contains some simple Galactic source population models.\n",
"\n",
"Here we provide some Python code to compute observable parameter distributions for Galactic gamma-ray source populations.\n",
"\n",
"* Observables: Flux, GLON, GLAT\n",
"* Source classes: Pulsar (PSR), Supernova remnant (SNR), pulsar wind nebula (PWN)\n",
"\n",
"References:\n",
"\n",
"* Section 6.2 in the Fermi-LAT collaboration paper [\"The First Fermi-LAT Catalog of Sources Above 10 GeV\"](http://adsabs.harvard.edu/abs/2013arXiv1306.6772T)\n",
"* Axel Donath's bachelor thesis [\"Modelling Galactic gamma-ray source populations\"](http://pubman.mpdl.mpg.de/pubman/item/escidoc:912132:1/component/escidoc:912131/BScThesis_ddonath.pdf), specifically Chapter 4.\n",
"* Casanova & Dingus (2008), [\"Constraints on the TeV source population and its contribution to the galactic diffuse TeV emission\"](http://adsabs.harvard.edu/abs/2008APh....29...63C)\n",
"* Strong (2007), [\"Source population synthesis and the Galactic diffuse gamma-ray emission\"](http://adsabs.harvard.edu/abs/2007Ap%26SS.309...35S)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Setup"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"%matplotlib inline\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import astropy.units as u\n",
"from gammapy.utils.random import sample_powerlaw\n",
"from gammapy.astro import population"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Simulate positions"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"# Spatial distribution using Lorimer (2006) model\n",
"n_sources = int(1e5)\n",
"\n",
"table = population.make_base_catalog_galactic(\n",
" n_sources=n_sources,\n",
" rad_dis=\"L06\",\n",
" vel_dis=\"F06B\",\n",
" max_age=1e6 * u.yr,\n",
" spiralarms=True,\n",
")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Simulate luminosities"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Several source population models, e.g. the 1FHL paper or Strong (2007), use power-law luminosity functions.\n",
"\n",
"Here we implement the \"reference model\" from the 1FHL catalog paper section 6.2."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"# Source luminosity (ph s^-1)\n",
"\n",
"luminosity = sample_powerlaw(x_min=1e34, x_max=1e37, gamma=1.5, size=n_sources)\n",
"table[\"luminosity\"] = luminosity"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Compute observable parameters"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"
\n",
" name dtype unit description \n",
"---------- ------- --------- --------------------------------------\n",
" age float64 yr Age of the source\n",
" n_ISM float64 1 / cm3 Interstellar medium density\n",
" spiralarm str18 Which spiralarm?\n",
" x_birth float64 kpc Galactocentric x coordinate at birth\n",
" y_birth float64 kpc Galactocentric y coordinate at birth\n",
" z_birth float64 kpc Galactocentric z coordinate at birth\n",
" x float64 kpc Galactocentric x coordinate\n",
" y float64 kpc Galactocentric y coordinate\n",
" z float64 kpc Galactocentric z coordinate\n",
" vx float64 km / s Galactocentric velocity in x direction\n",
" vy float64 km / s Galactocentric velocity in y direction\n",
" vz float64 km / s Galactocentric velocity in z direction\n",
" v_abs float64 km / s Galactocentric velocity (absolute)\n",
"luminosity float64 \n",
" distance float64 pc Distance observer to source center\n",
" GLON float64 deg Galactic longitude\n",
" GLAT float64 deg Galactic latitude\n",
" VGLON float64 deg / Myr Velocity in Galactic longitude\n",
" VGLAT float64 deg / Myr Velocity in Galactic latitude\n",
" RA float64 deg Right ascension\n",
" DEC float64 deg Declination\n",
" flux float64 1 / kpc2 Source flux\n"
]
}
],
"source": [
"table = population.add_observed_parameters(table)\n",
"table.info()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Check output"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The simulation is done, you could save the simulated catalog to a file.\n",
"\n",
"Here we just plot a few distributions to check if the results look OK."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
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\n",
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