1. General description

Among the possible interpretations of the "plateau" feature observed in a large fraction of GRB X-ray afterglows, there is the hypothesis of a newly-born magnetar pumping energy into the forward shock in the form of spin-down radiation.

Under this assumption, this code allows to extract magnetar magnetic field and spin period that better describe the properties of observed plateau in the X-ray afterglow.

The code is written in Python language and is based on the magnetar model formulated in Dall'Osso et al. 2011, A&A, 526, 121 and Stratta et al. 2018, ApJ, 869, 155

2. To run the code

The code runs under Python >= 3.7.x or and requires the following modules:

ipython, astropy, numpy, matplotlib, scipy, pandas, sympy

Python can be simply installed through the Anaconda Individual Edition distribution platform. To create and activate a virtual environment with the required dependencies just type:

conda env create -f magnetar.yml

conda activate magnetar

To run the code:

python loglumfit.py

As an example, the code has predefined default settings for the case of the short GRB 151221A (just press "enter" when a question is prompted).

2.1 Required input

Most of the input are predefined in "set_iniparam" module (see also section 5). The following ones are asked to user while running the code:

GRB name

Once the GRB name is given (e.g. 151221A), the code reads the corresponding data file in the 'data' directory (e.g. ./data/151221A.txt). The data file must have the name of the GRB and extension ".txt".

Data should be in the Swift/XRT Repository format for the 0.3-10 keV "XRT unabsorbed flux light curves" including the corresponding photon indexes.

The right format can be downloaded from the Swift/XRT Repository following these steps:

• select the GRB name
• click the "Burst Analyser" repository (on the top of the page)
• scroll down to the "XRT unabsorbed flux light curves"
• on the wideget (on the left) select "Subplot: Photon Index", "0.3-10 keV flux"
• click on "Data file" and save data in the "data" directory by renaming the file as "GRBname.txt" (e.g. 151221A.txt)

GRB jet half-opening angle in deg

If not known, you can set the jet half-opening angle to 90 deg, i.e. isotropic case, or assume a fiducial value e.g. 5.0 deg

Some useful references where to find GRB estimated jet opening angles are:

• Wang X-G et al. 2018, Apj, 859, 160
• Wang F. et al. 2020, ApJ, 893, 77

GRB redshift

Redshift is required to compare the afterglow luminosity with the magnetar one. If not know, you can put it to a fiducial value (e.g. z=0.5).

See the useful GRB table by J. Greiner and collaborators

3. Output

The code asks if the user wants to save the output. If the answer is yes, then in the "output" directory two files are generated:

• a log file with the GRB name, the best fit model parameters, the start time of the fit, the GRB and magnetar half-opening angles, and the fit statistics. The last column shows the time of the fit, so the user can have an overview of multiple runs for the same source.

• a png file with the afterglow light curve and the best fit models

The file names indicate the GRB name, the magnetar half-opening angle and the rest frame energy band and the morphology used for the lightcurve (e.g. 151221A_30.0deg_1.0_30.0keV_PA.log and 151221A_30.0deg_1.0_30.0keV_PA.png)

4. The code step by step

1. The code first reads the GRB X-ray afterglow flux and photon indexes vs time and print onto the screen the magnetar predefined setting parameters

2. Then it computes and plots the afterglow beamed corrected luminosity light curve by reading the rest frame energy band in "set_iniparam" and applying the K-correction, and by asking for the redshift and the jet opening angle.

3. At this point the code asks to indicate the start and end time of the plateau and of the temporal window we want to consider for the fit

4. Once the afterglow morphology is defined, the code proceeds in computing a first guess model and then in fitting the model to the data.

5. Results from fit are prompted on the screen

5. Magnetar default assumptions

There are a number of assumptions on the magnetar properties that are defined in the "set_iniparam.py" module. Each of these assumptions can be changed as desired.

• The magnetar is assumed to radiate all its energy within a cone of half-aperture "thetamdeg=90" [degrees].
• The magnetar mass and radius are set to M = 1.4 [solar mass] and r0 = 1.2 [10 km]
• The magnetar angular momentum direction forms an angle theta_i = 90 [deg] with the magnetic field direction.
• The magnetar bolometric luminosity is approximated with the luminosity computed in the 1.0-30 keV band, defined with the "Er1" and "Er2" variables. The K-correction will takes into account any change of this band.
• The code keeps the magnetar model coefficient k<1 (where k = (4ε_e dlnt/dlnT), ε_e is the electron energy fraction and dlnt/dlnT describes the dynamical evolution of the shock, see Dall'Osso et al. 2011) and estimate it as k=a2-1 where a2 is the post-plateau decay index
• The code tests the magnetar model with fixed α = (3-n)/2 where n is the braking index. Initial value is se to 0, but any value <1.0 can be given (see Stratta et al. 2018)