Afterglow from merger remnant [11]

Fitting and analysis of radio afterglow lightcurves from GW sourcesArvind Balasubramanian, Alessandra Corsi

Abstract

Gravitational Wave observations have given us yet another way to

understand the cosmos. Gravitational wave events are often accompanied by

emission from across the electromagnetic (EM) spectrum. EM follow up

observations help in pushing the boundaries of our understanding of

gravitational physics, nucleosynthesis and cosmology. GW170817 is the first

detection of gravitational waves and light from the merger of two neutron

stars. Radio observations, in particular, and analysis of the broad-band

afterglow of GW170817 in general, led to verification of the predictions of

various jet models. These models are parametrized by a large number of

correlated parameters. Fitting them requires a robust tool like affine invariant

Markov Chain Monte Carlo (MCMC) simulations, that can be used to obtain

the best fit parameters and the errors associated with them. This poster

presents preliminary testing of a dedicated MCMC code, and some ongoing

work to model the expected very-late-time radio emission of GW170817

arising from the interaction between the neutron-rich ejecta and the

surrounding interstellar medium.

Introduction

The merger of compact objects produces gravitational waves and are often accompanied by a delayed emission, termed afterglow, in the X-ray, optical and radio wavelengths. Gravitational waves from such mergers have been observed using the

LIGO and VIRGO detectors in the last few years. The afterglow originates from synchrotron emission from accelerated electrons when the relativistic outflow launched in the merger collides with the external interstellar medium [1]. Many

models have been proposed to explain the lightcurves – evolution of spectral flux density with time, of the afterglow emission and the models generally involve a large number of correlated parameters [2].

Method

References:

[1] Sari et al.1998, ApJ, 497L, 17S

[2] Kasliwal et al. 2017, Science, 358, 1559

[3] Christian Robert and George Casella. Introducing Monte Carlo Methods

with R. Springer 2010

[4] Goodman et al. 2010, CAMCS, 5, 65G

[5] Foreman-Mackey et al. 2013, ascl.soft 03002F

[6] Mooley et al. 2018, Nature, 554, 207M

[7] Hallinan et al. 2017, Science, 358, 1579H

[8] Davide Lazzati. Cocoon Afterglow Lightcurves. http://www.science.orego

nstate.edu/~lazzatid/cocoon.html.

[9] Lazzati et al. 2018, PhRvL, 120, 1103L

[10] Lazzati et al. 2017, ApJ, 848, 6L

[11] Berger, 2014, ARA&A, 52, 43B

Some proposed models for GW170817 [2]

First release: 16 October 2017 www.sciencemag.org (Page numbers not final at time of first release) 14

Fig. 5. Model schematics considered in this paper. In each panel, the eye indicates the line of sight to the observer. (A) A classical, on-axis, ultra-relativistic, weak short gamma-ray burst (sGRB). (B) A classical, slightly off-axis, ultra-relativistic, strong sGRB. (C) A wide-angle, mildly-relativistic, strong cocoon with a choked jet. (D) A wide-angle, mildly-relativistic, weak cocoon with a successful off-axis jet.

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Results and Conclusion

The above fitting method was used to obtain best fit parameters for the GRB afterglow lightcurve of GW170817. The model lightcurves used during the

fit were obtained from [8] ([9] [10]) and the data were obtained from [6] and [7]. The best fit values match published results [9]. The lightcurve with

confidence intervals is shown on the right and the corner plot on the right shows the correlation between the model parameters taken two at a time.

Markov Chain Monte Carlo (MCMC), which is

based on Bayesian inference, is very useful for

problems involving a large number of parameters

and is being increasingly used to perform statistical

data analyses [3][4].

MCMC algorithms set up random walkers that

traverse the parameter space of the problem to not

only getting best fit parameters but also produce a

set of acceptable samples for the posterior. They

generate a collection of states that follow a

desired distribution P(x) using a Markov process

that converges to a stationary distribution π(x) which

satisfies detailed balance :

An example of an affine transformation [4]

[5] (emcee python package)

With the advanced LIGO and collaborations doing electromagnetic follow-up of BNS mergers, we hope to document many sources like GW170817 in

the next few years. More data will help in constraining the possible models which successfully explain such events and open new horizons for exotic

physics happening at these scales. This routine can easily be modified to fit any type of data with a given model.

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