Numeric GRB Afterglow models

A Python 3 module to calculate GRB afterglow light curves and spectra. Details of the methods can be found in Ryan et al 2019. Builds on van Eerten & MacFadyen 2010 and van Eerten 2018. This code is under active development.

Documentation available at https://afterglowpy.readthedocs.io/

Attribution

If you use this code in a publication, please refer to the package by name and cite "Ryan, G., van Eerten, H., Piro, L. and Troja, E., 2019, arXiv:1910.11691" arXiv link.

Acknowledgements

This work is funded in part by the European Union’s Horizon 2020 Programme under the AHEAD2020 project (grant agreement n. 871158).

Features

afterglowpy computes synchrotron emission from the forward shock of a relativistic blast wave. It includes:

• Fully trans-relativistic shock evolution through a constant density medium.
• On-the-fly integration over the equal-observer-time slices of the shock surface.
• Approximate prescription for jet spreading.
• Arbitrary viewing angles.
• Angularly structured jets, ie. E(θ)
• Spherical velocity-stratified outflows, ie. E(u)
• Counter-jet emission.

It has limited support (these should be considered experimental) for:

• Initial energy injection
• Inverse comption spectra
• Spatially-resolved intensity maps
• Early coasting phase

It does not include (yet):

• External wind medium, ie. n ∝ r^-2
• Synchrotron self-absorbtion
• Reverse shock emission

afterglowpy has been calibrated to the BoxFit code (van Eerten, van der Horst, & Macfadyen 2011, available at the Afterglow Library) and produces similar light curves for top hat jets (within 50% when same parameters are used) both on- and off-axis. Its jet models by default do not include an initial coasting phase, which may effect predictions for early observations.

Installation/Building

afterglowpy is available via pip:

$ pip install afterglowpy

If you are working on a local copy of this repo and would like to install from source, you can the run the following from the top level directory of the project.

$ pip install -e .

Using

This interface will be updated to be more sensible in the VERY near future

In your python code, import the library with import afterglowpy as grb.

The main function of interest isgrb.fluxDensity(t, nu, jetType, specType, *pars, **kwargs). See tests/plotLC.py for a simple example.

jetType can be -1 (top hat), 0 (Gaussian), 1 (Power Law w/ core), 2 (Gaussian w/ core), 3 (Cocoon), or 4 (Smooth Power Law).

specType can be 0 (global cooling time, no inverse compton) or 1 (global cooling time, inverse compton).

For jet-like afterglows (jetTypes -2, -1, 0, 1, 2, and 4) pars has 14 positional arguments:

• 0 thetaV viewing angle in radians
• 1 E0 on-axis isotropic equivalent energy in erg
• 2 thetaC half-width of the jet core in radians (jetType specific)
• 3 thetaW "wing" truncation angle of the jet, in radians
• 4 b power for power-law structure, θ^-b
• 5 L0 Fiducial luminosity for energy injection, in erg/s, typically 0.
• 6 q Temporal power-law index for energy injection, typically 0.
• 7 ts Fiducial time-scale for energy injection, in seconds, typically 0.
• 8 n0 Number density of ISM, in cm^-3
• 9 p Electron distribution power-law index (p>2)
• 10 epsilon_E Thermal energy fraction in electrons
• 11 epsilon_B Thermal energy fraction in magnetic field
• 12 xi_N Fraction of electrons that get accelerated
• 13 d_L Luminosity distance in cm

For cocoon-like afterglows (jetType 3) pars has 14 positional arguments:

• 0 umax Initial maximum outflow 4-velocity
• 1 umin Minium outflow 4-velocity
• 2 Ei Fiducial energy in velocity distribution, E(>u) = E_i u^-k.
• 3 k Power-law index of energy velocity distribution
• 4 Mej Mass of material at `umax' in solar masses
• 5 L0 Fiducial luminosity for energy injection, in erg/s, typically 0.
• 6 q Temporal power-law index for energy injection, typically 0.
• 7 ts Fiducial time-scale for energy injection, in seconds, typically 0.
• 8 n0 Number density of ISM, in cm^-3
• 9 p Electron distribution power-law index (p>2)
• 10 epsilon_E Thermal energy fraction in electrons
• 11 epsilon_B Thermal energy fraction in magnetic field
• 12 xi_N Fraction of electrons that get accelerated
• 13 d_L Luminosity distance in cm

Keyword arguments are:

• z redshift (defaults to 0)
• tRes time resolution of shock-evolution scheme, number of sample points per decade in time
• latRes latitudinal resolution for structured jets, number of shells per thetaC
• rtol target relative tolerance of flux integration
• spread boolean (defaults to True), whether to allow the jet to spread.