En-Tzu Lin

Gamma-ray bursts (GRBs) are intense beams of electromagnetic radiation. The detection of the gravitational wave event GW170817 associated with GRB170817A has proved that the origin of short Gamma-ray bursts are binary neutron star mergers, as shown in figure 1. Relativistic jet launched by the merger interacting with the ambient medium will produce an afterglow across the EM spectrum. Figure 2 shows the afterglow light curve of GW170817. Analyzing the after light curves of GRBs will help us resolve the structure of these jets. The procedure of the entire analysis framework are designed as follows. We generated X-ray light curves from our GRB afterglow model and perform parameter estimation on them under bayesian inference. Posterior distributions are the probability density functions of parameters given the observing data, which is the light curve we gave. We adopted Marcov Chain Monte Carlo(MCMC) sampling method to help us get the posteriors. In order to accelerate the progress, we came up with an idea to replace the likelihood function with a new interpolating function. First, we created a multi-dimensional gird of light curve by simulating each model parameter across a certain range in the parameter space, and stored them into a file. Figure 4 illustrates how light curves look like across different observing angles. After this, for each MCMC sample, instead of calculating the likelihood from our GRB model, which is very time-consuming, it only has to interpolate between the adjacent parameter values stored in our high-dimensional grid. A comparison between the simulated light curve and interpolated light curve are shown in figure 5. Currently, we are considering a gaussian structure jet, that is, with a uniform core within the jet core angle, the energy profile between the jet opening angle and jet core angle will follow a gaussian distribution. We simulated a three-dimensional gird that stored the light curves spanning across different jet core angle(theta_c), observing angle(theta_obs) and observing time(t_obs). The MCMC results of three jet parameters are shown in figure 7. The posterior distributions of theta_c and theta_obs show our code has the ability of recovering the injected parameter values(orange vertical lines), and theta_j was not found due to the lack of information in the 3D grid. In the mean time, the accuracy of the interpolation function should be improved to allow a full parameter estimation. In addition, constraints from gravitational wave observation will be included during the parameter estimation. More jet models will be investigated in the future. The goal of this project is to examine how future multi-messenger observations can help to solve the intrinsic structure of GRB jets.