[CFT] [CFT] [CFT] CFT]Center for Theoretical Physics, Polish Academy of
Sciences, Al. Lotnikow 32/46, 02–668, Warsaw, Poland Kilonovae from binary
mergers

# What we can learn about compact binary mergers from their kilonova signals?

Agnieszka Janiuk  Joseph Saji  Gerardo Urrutia  [

###### Abstract

Compact binary mergers are sources of gravitational waves, and can be
accompanied by electromagnetic signals. We discuss the possible features in
the kilonova emissions which may help distinguish the black hole - neutron
star mergers from the binary neutron stars. In addition, the amount of ejected
material may depend on whether the system undergoes the creation of a
transient hyper-massive, differentially rotating neutron star. In this
context, the numerical simulations of post-merger systems and their outflows
are important for our understanding of the nature of short GRB progenitor
systems. In this article, we present a suite of GR MHD simulations performed
by the CTP PAS astrophysics group, to model the neutrino driven disk winds and
their contribution to the kilonova emissions. The contribution of the disk
wind to the jet collimation and variability is also briefly discussed.

##  1 Introduction

Short Gamma Ray Bursts (GRBs) are transient events of high energy radiation
released via pulses, lasting from miliseconds up to couple seconds. The
central engine which powers these explosions is composed of a rotating Kerr
black hole and a magnetized accretion disk, extremely hot and dense
($T>10^{9}K$, $\rho>10^{8}$ g cm-3). Under such conditions, the electron gas
is degenerate and beta reactions take place. The microphysics and equation of
state (EOS) of the gas is governed by nuclear physics, and the EOS is no
longer described by an adiabatic law111this law stands an analytic fomula,
with $p=(\gamma-1)u$, where $p$ denotes pressure, $u$ is internal energy, and
$\gamma$ is an adiabatic index, of a value between $4/3$ and $5/3$. The EOS
provides a closing equation for the system of magnetohydrodynamic (MHD)
equations that describe accretion flow evolution, to capture the gas
microphysics.

Compact binaries coalescence (binary neutron star, NSNS, or black hole-neutron
star, BHNS) have been modeled numerically since over 20 years, in the context
of short GRB progenitors (Shibata & Uryū, 2000; Korobkin et al., 2012;
Paschalidis et al., 2015). The postmerger system can be either a hypermassive
neutron star, supported by its differential rotation, or a promptly formed
black hole. Eventually, the relativistic jet is produced, and provides an
electromagnetic counterpart to the gravitational wave (GW). Depending on the
observer’s viewing angle, one may detect a short-weak GRB and its afterglow
emission, from the shocked interstellar medium, as well as other counterparts,
like a kilonova (Metzger, 2019).

The GRBs prompt emission is accompanied by other electromagnetic observables,
emerging on longer timescales. The discovery of a kilonova signal, associated
with the GRB afterglow (Tanvir et al., 2013) has been predicted by Li &
Paczyński (1998). They proposed that the radioactivities from dynamical ejecta
after the NSNS merger can power a distinct electromagnetic signal, in Optical
and Near-Infrared bands. Its characteristics is similar to the supernova, but
is several orders of magnitude fainter: the absolute magnitudes are below
$M_{V}=-16$ at the peak, and rapidly fading, by about $\sim 0.5$ mag per day.
These transients are quite rare, and their rate is estimated at below 1 per
cent of the core collapse supernova rate. However, after the pre-merger
expansion of the dynamical ejecta, also the subsequent accretion can provide a
contribution to the kilonova, if only the disk outflows are fast enough and
not absorbed by precedent ejecta.

Such system can be modeled via numerical simulation (Siegel & Metzger, 2017),
and the heavy unstable isotopes are formed in the rapid neutron capture
process (r-process), while the ejected material is very neutron rich. The blue
and red kilonovae components associated with GRB-GW170817 have been attributed
to post-merger dynamical ejecta, and accretion disk winds (Kilpatrick et al.,
2017).

##  2 Numerical code

The phenomena such as the jet launching via extraction of the black hole
rotational energy, or the expansion of magnetised, neutrino-driven winds from
accretion disk, are well described by ideal MHD simulations in general
relativity (GR MHD). The GR MHD code, HARM (Noble et al., 2006), is a finite
volume, shock capturing scheme that solves hyperbolic system of partial
differential equations of GR MHD. The plasma energy-momentum tensor,
$T^{\mu\nu}$, is contributed by gas and electromagnetic field:
$T^{\mu\nu}={T_{\left(m\right)}}^{\mu\nu}+{T_{\left(em\right)}}^{\mu\nu}$,
where

$\ {T_{\left(m\right)}}^{\mu\nu}=\rho hu^{\mu}u^{\nu}+pg^{\mu\nu};\hskip
28.45274pt{T_{\left(em\right)}}^{\mu\nu}=b^{\kappa}b_{\kappa}u^{\mu}u^{\nu}+\frac{1}{2}b^{\kappa}b_{\kappa}g^{\mu\nu}-b^{\mu}b^{\nu}.$
(1)

Here $u^{\mu}$ is the four-velocity of gas, $u$ denotes internal energy
density, $b^{\mu}$ is magnetic four-vector, and $h$ is the fluid specific
enthalpy. The continuity and momentum conservation equations read:

$\ (\rho u^{\mu})_{;\mu}=0;\hskip 28.45274ptT^{\mu}_{\nu;\mu}=0.$ (2)

They are brought in conservative form, by implementing the Harten, Lax, van
Leer (HLL) solver to calculate numerically the corresponding fluxes. In
addition, magnetic field is evolved according to Maxwell equations

${}^{*}F^{\mu\nu}_{;\mu}=0,$ (3)

where ${}^{*}F$ is the Faraday tensor dual, and the ideal MHD conditions
eliminate three degrees of freedom due to vanishing electric field. The zero
divergence constraint for magnetic field is kept by the numerical scheme.

In the current work, we use the code HARM_COOL_EOS, recently developed in our
group. The microphysics of dense nuclear matter in the GRB engine is treated
with specific tabulated, composition-dependent EOS, with three parameters:
rest-mass density, temperature, and electron fraction. It has to be noted that
in this case the inversion between the EOS (’primitive’) parameters and the
variables advanced by the MHD scheme (’conservative’) is non-trivial task. The
code needs to solve numerically five coupled non-linear equations through the
recovery scheme. After testing several of such schemes, we implemented the
bracketed root-finding 1D scheme proposed by Palenzuela et al. (2015), which
gives minimum errors for the broadest range of temperatures and densities, in
comparison to other tested, 2D and 3D schemes (Janiuk, 2023).

##  3 Results

Figure 1: Accretion rate onto black hole as a function of time. Red line shows
model with $\beta=10$, and thick line is for $\beta=50$.

Figure 2: Normalized magnetic flux on the black hole horizon, as a function of
time for the same models as in Fig. 2

In this section we present preliminary results of the new implementation of
the neutrino leakage scheme in HARM_COOL_EOS, reading the Helmholtz tables
(Fryxell et al., 2000), where the EOS of dense matter is taken as
$P(\rho,T,Y_{e})$ and $\epsilon(\rho,T,Y_{e})$, for wide range of densities
and temperatures. The evolving electron fraction is giving an additional
source term to the energy equation: The neutrino leakage scheme is adapted as
in Rosswog & Liebendörfer (2003) and computes a grey optical depth estimate
along the radial rays for electron neutrinos, anti-neutrinos, and heavy lepton
’nux’.

The quantities plotted in Figures 2 and 2, are showing the accretion rate
through the BH horizon, and magnetic flux on the horizon, respectively. The
accretion rate is anti-correlated with the magnetic flux, indicating that the
magnetic barrier acts on the plasma, pushing it out from the horizon at some
episodes. They are identified as ’magnetically arrested state’ (MAD) and are
more prolonged in the simulation with higher initial magnetisation of the
disk.

Figure 3: Density and magnetic field streamlines in the innermost regions of
the central engine. Snapshot is taken at evolved time of $t=85$ ms, in the
middle of the simulation.

Figure 4: Neutrino emissivity map in the GRB central engine, for the same
model and snapshot as in Fig. 1. Parameters are black hole mass of 3
$M_{\odot}$ and its spin $a=0.9375$

In Figures 4 and 4 we plot the density distribution and neutrino emissivity
for a chosen snapshot at the beginning of the simulation with $\beta=50$ (less
magnetized initial condition, NSNS merger scenario). Turbulent accretion disk
is located in the equatorial plane, and accretes in a ’standard and normal
accretion episode’ (SANE). Neutrino emissivity of the inner densest disk parts
is as high as $10^{30}$ erg s-1 cm-3. The winds become unbound and driven by
magnetic field only above a certain radius, $r\sim 30r_{g}$. The electron
fraction distribution in disk and wind for the same snapshot is visualised in
Fig. 6.

Model | $r_{in}$ | $r_{max}$ | $a$ | $S_{disk}$ | $M_{\rm BH}$ | $\beta$ | $Y_{e,0}^{\rm disk}$ | <$\dot{M}_{\rm out}$>
---|---|---|---|---|---|---|---|---
| [$r_{g}$] | [$r_{g}$] |  | [s] |  |  |  | [$M_{\odot}$ s-1]
FM50 | 4.0 | 9.0 | 0.9735 | 10.0 | 3 | 50 | 0.1 | $2.08\times 10^{-3}$
FM10 | 4.0 | 9.0 | 0.9735 | 10.0 | 3 | 10 | 0.1 | $2.57\times 10^{-2}$
Table 1: Model parameters of the neutrino cooled GRB engine.

In Figure 6 we plot the total (volume integrated) luminosity of neutrinos and
antineutrinos, as a function of time for the whole simulation. Its shallow
decrease with time only weakly reflects the changing mode of accretion (SANE
vs. MAD), while oscillations in the energy output appear quasi-periodic.

Figure 5: Neutrino luminosity as a function of time. Blue and green lines show
electron neutrino and antineutrino fluxes (Lnu1 and Lnu2), integrated over
volume in the disk. Purple lines show the heavy lepton neutrino fluxes (Lnu3).
Thin lines show model with $\beta=10$, and thick lines are for $\beta=50$.

Figure 6: Electron fraction distribution map in the GRB central engine, for
the same model and snapshot as in Fig. 1. Parameters are black hole mass of 3
$M_{\odot}$ and its spin $a=0.9375$, and initial gas-to-magnetic pressure
ratio in the disk $\beta=50$.

The model parameters are summarized in Table 1. We give here also the estimate
for wind mass loss rates.

###  3.1 Nucleosynthesis in GRB accretion disk winds

Synthesis of elements heavier than Iron occurs via rapid neutron capture and
conditions in the unbound outflows from the accretion disks in the GRB engine
are plausible for that process. We have shown that the disk winds are an
important source of mass ejection (Siegel & Metzger, 2017; Janiuk, 2019). The
winds of a highly neutronized material, $Y_{e}\sim 0.1-0.4$, are driven by
magnetic fields and neutrino heating, are expanding into the interstellar
medium with mildly relativistic velocities, and entropy per baryon on the
order of $12-15k_{B}$.

The tabulated equation of state has been implemented in our code instead of
the adiabatic law, and electron fraction evolution is driven by the lepton
number conservation. By means of the tracer particles, we follow the
nucleosynthesis on the streams expanding with the disk wind used as an input
to the nuclear reaction network post-processing. The network contains more
than a thousand isotopes in its database, and takes into account the fission
reactions and electron screening (see Lippuner & Roberts (2017) for details).
All three peaks of the Solar abundance pattern are reproduced. The second and
third maximum are obtained for the Lanthanide- and Actinide-rich ejecta, with
the electron fraction on the order of $Y_{e}\lesssim 0.1$.

The detailed composition pattern of the outflow depends on the engine
parameters: the black hole spin and disk mass, as well as its initial
magnetisation. We postulate therefore, that different types of engines, will
imprint their properties in the observed kilonova signals due to various
composition patterns.

Figure 7: Trajectories of wind particles for two models, representing engine
of binary neutron star merger. Black tracers represent jet outflows, orange-
yellow ones are those representing unbound wind.Panles refer to model FM10
(left) and FM50 (right).

For instance, there are some distinguishable features between BHNS and NSNS
mergers. The average electron fraction is higher for the BHNS case especially
on the equator, predicting a less effective r-process nucleosynthesis (Urrutia
et al., in prep.) The trajectories distributions for the two simulations
listed in Table 1 are depicted in Fig. 7 and show that for FM50 postmerger
system, the fastest tracers reach outer boundary at a later time, and larger
polar angles, than for FM10 case.

##  4 Discussion and Conclusions

Our models do not provide direct method to distinguish between BH-NS and NS-NS
progenitors, but still some features like the mass of ejected material and its
composition, leading to different shape of kilonova lightcurves, are expected.
We can also speculate on the role of magnetic field strength, and possible MAD
episodes, on the variability pattern of the neutrino luminosity. This would
provide some quasi-periodic variable energy input to the jet, and consequently
further shape the wind and jet interface, and affect observed GRB emission
(Urrutia et al. in prep; see also Urrutia & Janiuk, this Proceeding). We
address this issue to the GRB progenitor properties, and try verify the
scenario in which the BHNS progenitors would rather produce less magnetised
disks than NSNS systems (due to magnetic flux conservation).

On 11 December 2021, the Fermi GBM triggered and located GRB 211211A, also
detected by the Swift/BAT. The GBM light curve consists of an exceptionally
bright emission made up of three separate pulses with a duration of about
34.3s (50-300 keV). It was not located in any star-forming region and
associacion with supernova is excluded (Troja et al., 2022). A kilonova
component was nevertheless identified in the UV/optical/infrared by spectral
analysis (Rastinejad et al., 2022). This system seems a puzzle to our
understanding of the short GRB progenitors, however according to Meng et al.
(2023) photosphere model with a structured jet can satisfactorily explain the
peculiar long duration, through the duration stretching effect on the
intrinsic longer ($\sim 3$ s) duration of NS-BH merger. More evidence of the
BHNS merger origin is found, especially the fit of the afterglow-subtracted
optical-NIR light curves by the significant thermal cocoon emission and the
sole thermal red kilonova component.

###### Acknowledgements.

This research was supported in part by the grant 2019/35/B/ST9/04000 from
Polish National Science Center. This research was carried out with the support
of the Interdisciplinary Center for Mathematical and Computational Modeling at
the University of Warsaw (ICM UW), and was also supported in part by PLGrid
Infrastructure, under grant plg-grb6.

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