Inverse reconstruction ofjet structure from off-axis
gamma-ray burst afterglows
Kazuya Takahashi & Kunihito Ioka
(Yukawa Institute for Theoretical Physics,Kyoto University)

KT & Ioka (2019) arXiv:1912.01871

Neutron Star Merger Event
GW170817

Gravitational wave
+ EM counterparts(dim) short GRB

macronova (kilonova)
Radio - X-ray afterglow

The afterglow of GRB170817A(Ghirlanda+19, Mooley+18b)(Mooley+18a)

Slowly-rising afterglow light curve
Rapid decline of the afterglow after the peak
Super-luminal apparent motion

We saw a structured jet from off-axis.

We saw astructured jetfrom off-axis.

(Lazzati+17)

Previous studies (e.g., Troja+19, Ghirlanda+19)

This study

Inverse problem

Method
A novelmethodMethodto inversely
reconstruct

A model of structured jets

(Troja+19, van Eerten+10)

shocked thin shell

NS-NSmerger

Inter stellar matter(cold, uniform )jet axis
synchrotron radiation(off-axis) observer
The jet energy has an angle dependence:
Each segment expands as if it were a portion of a spherically
expanding shell (e.g., Kumar & Granot 2003):(cf. Blandford-McKee 1976)

The synchrotron emissivity is given by the standard modelof Sari+98:

A model of structured jets

(Troja+18, van Eerten+10)

jet axisInter stellar matter(cold, uniform )NS-NSmerger
opening angle(off-axis) observer
luminosity distance

The observed flux density at T:

Complicated function ofA model of structured jets

(Troja+18, van Eerten+10)

jet axisInter stellar matter(cold, uniform )NS-NSmerger
opening angle(off-axis) observer
luminosity distance

The observed flux density at T:

How to reconstruct?

Complicated function of

Observer timeafter the merger

jet axis
For a Gaussian jet:Observerdirection

Only a limited region contributes to the observed flux(Why?)For a Gaussian jet:

The contributing region gradually approach the jet axis,
as the time passes. (Why?)Contribution to the flux strongly related Beaming factor

Beamed awayfrom the obs.

Relativistic region

Beamed tothe observer

The contributing region gradually approach the jet axis
as the jet is decelerated, due to beaming effects.

Cutoff angle

General expression for the cutoff angle:: ambient matter number density

All the contributions to the observed flux
― Contribution from the region thathas been seen before:= Contribution fromcontaining the information on
the energy distribution forAll the contributions to the observed flux
― Contribution from the region thathas been seen before:= Contribution fromcontaining the information on
the energy distribution forInversion Formula:

Change rateof the observed flux

Subtracted contribution
from the ever-seen region

where K is defined by

Boundary condition (assumption):forjet truncation angle

The cutoff angle at a given initial time
The jet structure is uniquely reconstructed by integrating
the inversion formula fromto(the jet axis).

ResultsMethod

A non-trivial jetstructure
obtained by ourmethod

Non-trivial Result : Hollow-cone structure

Jet StructureLight Curve
Used forinversion

Inverselyreconstructed
Assumededge structurein Troja et al. (2019)

Parameters:

19

Possible origin of hollow-cone structures(only naïve consideration)
Jet acceleration mechanism?
If the jet is launched by the Blandford-Znajek mechanism,
the energy flux around the jet axis is low ().
(e.g., McKinney 2006, Tchekhovskoy+ 2008, )Structure created through the interaction with the ejecta
during the propagation or at the shock breakout?
Some numerical simulations show the jet structure can bea hollow-cone type.
(e.g., Zhang et al. 2006, Mizuta & Ioka 2013)

Summary
We developed a novel method to inversely
reconstruct jet structures from off-axis GRB
afterglows.
Our method does not assume the functional form ofE(θ).
Our method uniquely obtains E(θ) for a given afterglow
light curve and given parameters.

We found that a hollow-cone jet structure canbe consistent with GRB170817A afterglow.
The method can be applicable to future offaxis GRB afterglows.