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chapter5.tex
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\chapter{Results and Future Work}\label{ch:results-future}
In this report, a framework was developed to compute the EM counterpart produced
when an NSBH binary with a given set of parameters merges. This framework takes as
inputs:
\begin{itemize}
\item The set of binary parameters, which are usually samples from a population
model distribution for each of the binary parameters. Some of these
population models are physically motivated and some are empirical guesses
in situations where a physical model has many complications to consider.
\item The functions used to compute the jet energetics and intrinsic structure.
In the case of the SGRB jet, the former are the functions given in
\cite{kawaguchi_2016} and \cite{foucart_2018} to compute the dynamic and
remnant masses, whereas the latter is the Gaussian structured jet model from
\cite{salafia_2015}, \cite{saleem_2020B}.
\end{itemize}
By using these inputs, the framework simulates the EM counterpart using the
equations described in \ref{sec:ns_in_gw}. Additionally, these events are analysed
from the GW side of things, with the corresponding GW optimal SNR also being
computed under this framework.\\
From these simulations, it is seen that under the assumption that NSBH mergers are
disruptive (which may be a strong assumption to make given the mass ratio
distribution seen by Advanced LIGO/VIRGO), in order to have bright SGRB jets the
binary must have a low mass black hole that is spinning rapidly. This conclusion is
seen from considering the effect of the BH spin distribution on the number of EM
detected events in Table \ref{tab:popln_numbers}. Furthermore this also implies that
by comparing the observed number of SGRB jets which are also detected in the GW
regime as a NS merger, one can make guesses about the nature of the BH spin
distribution in an NSBH binary. One can also compare the predictions that more
physically motivated spin distributions (say, those derived from stellar population
synthesis codes) give for the observed SGRB rates.\\
As for the events from GWTC-1 and 2 which were considered here, it is seen that for
GW190425 and GW190426\_152155, there is a negligible possibility that the event was
an NSBH event which could have produced an SGRB jet consistent with what was
observed by gamma-ray instruments. In the case of GW170817, the posteriors show that
it is probable that the event was an NSBH merger which gave rise to a jet compatible
with what was observed by space-based gamma-ray detectors.\\
With these conclusions in mind, the directions in which this work could be taken in
the future is explored in the next section, in no particular order. These directions
are directly related to loosening the simplifying assumptions made in this work and
serve as a reminder to the applicability of the work.
\section{Future Directions}
\begin{enumerate}
\item In the framework developed here, the spin of the black hole is
assumed to be aligned to the angular momentum of the binary system, and
also it is assumed that the system is non-precessing. The former
assumption is valid to make for the computation of the masses left
outside the BH apparent horizon, since retrograde spins disfavour
disruption nonetheless. However, the BH spins which are tilted with
respect to the angular momentum of the binary can still disrupt
inspiralling NS matter (although to a lesser amount than aligned spins)
and is an assumption that must be relaxed as much as possible. The
relaxation of the latter assumption will introduce complications, since
for a precessing binary system the definition of the inclination angle
changes with time, and so the entire framework will have to be reworked
in order to take care of that new definition.
\item Currently, the microphysics behind the NS Equation of State (EoS) and
the resulting effect it can have on the EM counterpart is not
considered. As was mentioned, it is known qualitatively that `softer'
equations of state can disfavour disruption whereas the `harder'
equations of state aid disruption, and thus would support more energetic
jets. For the purposes of computation within the framework, the NS EoS
is assumed to be the SFHo EoS (see \cite{hempel_2010},
\cite{hempel_2012}) which predicts a NS radius of $\sim 11$ km and a
tidal deformability of around 330 for the NS mass of $1.4$ M$_\odot$,
which is the median mass for GW170817 considered as a BNS merger.
However, from the posterior distributions on tidal deformability for
GW170817 in combination with the constraints on the same from EM
observations of AT2017gfo, a wide range of EoS can explain the observed
properties. Thus, this is a vital area of the parameter space that must
be explored more deeply.
\item The framework in its current state only computes the properties of a
possible SGRB jet from an NSBH merger using the aforementioned fit
formulae. However, as seen from Fig. \ref{fig:nsbh_outflows}, there are
other outflows as well which arise from NSBH mergers such as the optical
kilonova and the jet afterglow. These are non-relativistic outflows and
are thus not affected as drastically by off-axis viewing, unlike the
SGRB jet. Furthermore, for black holes in the `mass gap' region (i.e.
$M_{BH} \sim [3, 5]$ M$_\odot$), the brightness of the kilonova may even
be used to distinguish between NSBH merger events and BNS merger events
(see \cite{barbieri_2019b}). Thus, this component of the EM outflows is
another vital piece of information that is being modelled, and will be
investigated in the future. However, the jet afterglow component is
sensitive to the properties of the environment surrounding the NS
binary, and thus deriving general conclusions from considering this
component requires more careful analysis or simplifying assumptions.
\item It is also assumed currently that the only mechanism for the
extraction of the SGRB jet is via the Blandford-Znajek mechanism, which
kicks in once the disruption of the inspiralling NS occurs, the
remnant matter accretes around the remnant BH, and the magnetic field
around the BH is sufficiently high enough to launch a jet . However,
this may not be the case, and alternative mechanisms have been proposed
which do not rely on tidal disruption of the NS, such as the mechanism
in \cite{east_2021}. Such alternative mechanisms, though exotic, may
explain why EM outflows from NSBH mergers have not been distinctly
observed yet.
\item Once the other assumptions are relaxed, further analysis can be done
to infer the jet and kilonova structure parameters. This can be done by
using GWBENCH or a similar tool which computes the FIM for a particular
set of GW network and source parameters. The FIM can then be used to
forecast the parameter estimates for the component masses, spins,
luminosity distances etc., which will then translate into fluences (for
the associated prompt emission) and magnitudes (for the associated
kilonova) using the underlying fit formulae for each component. Thus, by
comparing these observed quantities with what is predicted, one should
be able to constrain the structure parameters. However, note that this
comes with the caveat that the corresponding NSBH merger must have a
high enough SNR ($\gtrsim 20$) for the analysis in \ref{sec:ns_in_gw} to
be valid. For events with only a moderately high SNR (but still above
the SNR detection threshold), traditional Bayesian parameter inference
must be carried out to compute the posteriors accurately.
\end{enumerate}