General relativistic simulations of collapsing binary neutron star mergers with Monte-Carlo neutrino transport Francois Foucart1Matthew D. Duez2Roland Haas3 4Lawrence E.

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General relativistic simulations of collapsing binary neutron star mergers with

Monte-Carlo neutrino transport

Francois Foucart,1Matthew D. Duez,2Roland Haas,3, 4 Lawrence E.

Kidder,5Harald P. Pfeiﬀer,6Mark A. Scheel,7and Elizabeth Spira-Savett1, 8

1Department of Physics & Astronomy, University of New Hampshire, 9 Library Way, Durham NH 03824, USA

2Department of Physics & Astronomy, Washington State University, Pullman, Washington 99164, USA

3National Center for Supercomputing Applications, University of Illinois, 1205 W Clark St, Urbana IL 61801, USA

4Department of Physics, University of Illinois, 1110 West Green St, Urbana IL 61801, USA

5Cornell Center for Astrophysics and Planetary Science, Cornell University, Ithaca, New York, 14853, USA

6Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-14467 Potsdam, Germany

7TAPIR, Walter Burke Institute for Theoretical Physics, MC 350-17,

California Institute of Technology, Pasadena, California 91125, USA

8Department of Physics and Astronomy, Barnard College, 3009 Broadway, Altschul Hall 504A, New York, NY 10027

Recent gravitational wave observations of neutron star-neutron star and neutron star-black hole

binaries appear to indicate that massive neutron stars may not be too uncommon in merging systems.

These discoveries have led to an increased interest in the simulation of merging compact binaries

involving massive stars. In this manuscript, we present a ﬁrst set of evolution of massive neutron

star binaries using Monte-Carlo radiation transport for the evolution of neutrinos. We study a

range of systems, from nearly symmetric binaries that collapse to a black hole before forming a disk

or ejecting material, to more asymmetric binaries in which tidal disruption of the lower mass star

leads to the production of more interesting post-merger remnants. For the latter type of systems,

we additionally study the impact of viscosity on the properties of the outﬂows, and compare our

results to two recent simulations of identical binaries performed with the WhiskyTHC code. We

ﬁnd agreement on the black hole properties, disk mass, and mass and velocity of the outﬂows within

expected numerical uncertainties, and some minor but noticeable diﬀerences in the evolution of the

electron fraction when using a subgrid viscosity model, with viscosity playing a more minor role

in our simulations. The method used to account for r-process heating in the determination of the

outﬂow properties appears to have a larger impact on our result than those diﬀerences between

numerical codes. We also use the simulation with the most ejected material to verify that our newly

implemented Lagrangian tracers provide a reasonable sampling of the matter outﬂows as they leave

the computational grid. We note that, given the lack of production of hot outﬂows in these mergers,

the main role of neutrinos in these systems is to set the composition of the post-merger remnant.

One of the main potential use of our simulations is thus as improved initial conditions for longer

evolutions of such remnants.

I. INTRODUCTION

The last ﬁve years have oﬀered a sudden wealth of

information about the properties of merging compact

objects, thanks to gravitational wave observations by

the LIGO-Virgo-KAGRA collaboration. The latest cat-

alogues of gravitational wave events [1–4] include in

particular two binary neutron star mergers and 2 −5

black hole-neutron star mergers. Interestingly, the neu-

tron stars observed in these systems include objects of

higher mass than what one might have expected from

the observed population of neutron stars in galactic bi-

naries. Galactic observations of compact neutron star

binaries favor low-mass systems [5], even though higher

mass neutron stars are observed in e.g. the popula-

tion of millisecond pulsars [6]. In gravitational wave

observations, we now have a ∼3.4Mbinary neu-

tron star system (GW190425), a (1.7−2.2)Mneu-

tron star in a neutron star-black hole binary (GW200105

162426), and lower mass objects in the neutron star bi-

nary GW170817 and the neutron star-black hole binary

GW191219 163120. Other observed neutron stars have

poorly measured masses, and a few observed compact

objects may be either high mass neutron stars or low

mass black holes (e.g. GW200210 092254). Overall, we

thus observe a much wider range of masses than initially

expected.

As a result, while early simulations of neutron star

binaries focused mostly on low-mass systems, there has

been an increased interest in recent years in modeling

high-mass binaries (see e.g. [7–10]), especially considering

existing deﬁciencies in the semi-analytical models used to

predict the outcome of neutron star mergers in that less

studied part of the available parameter space [10, 11].

Parameter space coverage for these high mass systems

remains however sparser than for lower mass systems.

In this manuscript, we focus speciﬁcally on systems

that collapse to a black hole within ∼1 ms of the col-

lision between the two neutron star cores. There are

eﬀectively two known regimes for such systems. For near

equal-mass systems, there remains only a small amount

of material outside of the forming black hole with enough

angular momentum to avoid being immediately accreted

by the black hole remnant. These systems typically re-

sult in nearly no mass ejection, and low-mass accretion

disks. For more asymmetric systems, on the other hand,

arXiv:2210.05670v2 [astro-ph.HE] 12 Apr 2023

the lower mass neutron star may be of suﬃciently low

compaction to be partially disrupted before merger. In

that case, material in the tidal tail formed during merger

has enough angular momentum to avoid falling into the

black hole. Mass ejection and the formation of massive

disks are then possible.

All of our simulations are performed with the SpEC

code [12], using a self-consistent evolution of Einstein’s

equations and of the equations of general relativistic hy-

drodynamics [13]. We also use our new state-of-the-art

Monte-Carlo radiation transport code [14] to account for

neutrino-matter interactions and neutrino transport. We

note that Monte-Carlo transport is particularly conve-

nient to use for the post-merger evolution of these sys-

tems, as Monte-Carlo methods are very eﬃcient in the

absence of a dense neutron star in the system and our

remnants are all black hole-disk systems. We simulate

a near equal-mass system, as well as a range of unequal

mass binaries, and focus particularly on the properties

of the remnant black hole, the accretion disk, and the

matter and neutrino outﬂows. Two of our systems are

speciﬁcally chosen to match the binary parameters used

in [8], allowing for more detailed comparison of simu-

lations with very diﬀerent numerical methods. We will

see that our results generally show agreement between

the two codes within expected numerical errors, with the

possible exception of the electron fraction of some out-

ﬂows. Diﬀerences in the electron fraction may be due

to diﬀerent viscosity models or neutrino transport algo-

rithms in the simulations.

For the simulation producing the most massive disk

and outﬂows, we also perform a more detailed study of

the impact of subgrid viscosity on the merger, using our

recent implementation of a LES (Large Eddy Simulation)

model [15]. That model is a modiﬁcation of the viscos-

ity model of Radice al [16] used in [8], with a few key

diﬀerences detailed in the methods section. We also use

this simulation to perform a detailed analysis of a new

implementation of Lagrangian tracers in SpEC, aimed

at determining whether diﬀerences between the evolu-

tion of the tracers and the evolution of the ﬂuid lead

to the tracers not being a good sampling of the matter

outﬂows at the end of the simulation. This new imple-

mentation is designed to improve load-balancing of the

tracer evolution, allowing us to follow a larger number of

Lagrangian particles, but has the disadvantage of using

a lower-order time-stepping algorithm than the ﬂuid evo-

lution. For the neutron star merger considered here, we

ﬁnd that the tracers remain a reasonably good sampling

of the ﬂuid (i.e. with errors of the same order as expected

sampling errors), yet we caution that we found much less

encouraging results in simulations of a high-mass black

hole-neutron star system.

Finally, we note that the previously mentioned vis-

cosity model is meant to capture the eﬀective impact

of the Kelvin-Helmholtz instability during merger. Af-

ter merger, the main source of eﬀective viscosity in the

accretion disk is expected to be the magnetorotational

instability (MRI). Accordingly, for the two simulations

forming the most massive disks, we switch to a sub-

grid model for viscosity calibrated to the MRI 5 ms after

merger (following [17]), continuing these simulations up

to 10 ms post-merger in order to reach a relatively settled

black hole-disk post-merger remnant that can be used as

initial condition for longer post-merger simulations.

II. OVERVIEW OF THE SIMULATIONS

In this manuscript, we consider a total of four distinct

binary systems, described in more detail in this section.

First, we simulate three binaries in which the equation of

state of dense matter is modeled using the SFHo equa-

tion of state [18]. The neutron stars in these binaries

have gravitational masses (m1, m2) = (1.61M,1.51M),

(1.80M,1.31M), and (1.78M,1.06M). We then re-

peat the last conﬁguration with the LS220 equation of

state [19].

These systems represent three potential outcome of bi-

nary neutron star mergers with rapidly collapsing rem-

nants. In the ﬁrst case, nearly all of the matter rapidly

falls into the forming black hole, leaving a disk of negli-

gible mass around it and nearly no mass ejection. In the

second case, a low-mass disk (0.04M) forms around the

remnant black hole, and we still do not observe signiﬁ-

cant mass ejection during merger. In the third and fourth

cases, tidal disruption of the low-mass star by its mas-

sive companion leads to the formation of a more massive

disk (∼0.15M) and signiﬁcant mass ejection in a cold

tidal tail (&0.001M). We note that while the least

massive neutron star in these two conﬁgurations has a

very low mass, these systems were chosen because they

match simulations performed in [8] with a diﬀerent code

and diﬀerent treatment of neutrinos and viscosity. This

allows for easy comparisons with our results, and addi-

tionally provides us with an extreme case that should be

useful in the construction of analytical models for rem-

nant disks and matter outﬂows. To test the robustness of

our results, we perform the LS220 simulation at two dif-

ferent resolutions, and with or without subgrid viscosity.

Speciﬁcally, we ran simulations without viscosity; with

viscosity included only after black hole formation; with

viscosity included only up to the contact; and with vis-

cosity included during the entire simulation. The second

and third case here are meant to verify that the subgrid

viscosity does not have an important eﬀect at times when

the Kelvin Helmotz instability is not active. The binary

using the LS220 equation of state is also used to test our

implementation of tracer particles. Finally, we studied

the impact of the number of Monte-Carlo packets during

the inspiral, collapse to a black hole, and post merger

evolution. We note however that most of those changes

had only minor impacts on the outcome of the simula-

tions for the observables discussed in this manuscript,

with the exception of the number of packets used during

the collapse itself (see below).

Name M1M2EoS R1(km) R2(km) ˜

SFHo-161-151 1.61M1.51MSFHo 11.7 11.8 170

SFHo-180-131 1.80M1.31MSFHo 11.5 11.9 360

SFHo-178-106 1.78M1.06MSFHo 11.5 12.0 1450

LS220-178-106 1.78M1.06MLS220 12.2 12.8 2460

TABLE I. Summary of the conﬁgurations simulated in this manuscript. We list the name of the simulation, the gravitational

mass of each neutron star, the equation of state, the radius of each star, and the reduced tidal deformability of the binary. The

last conﬁguration was simulated at two resolutions, as well as with viscosity turned on/oﬀ at diﬀerent times in the evolution.

Initial conﬁgurations for our simulations are con-

structed using the Spells code [20, 21]. We initially build

quasi-circular conﬁguration (i.e. stars without radial ve-

locity at the initial time), which results in residual eccen-

tricities e∼0.01, then perform one round of eccentricity

reduction to obtain orbits with e.0.003, following the

method described in [22]. The near-equal mass system is

initialized ∼4 orbits before contact, while the other three

binaries are evolved for 6 −7 orbits before contact. We

evolve the post-merger remnants for 4 ms after collapse

to a black hole, long enough to be able to extract values

for the mass of the post-merger disk and of the dynamical

ejecta (if any ejecta is produced), as discussed in Sec. IV.

In addition, the two most asymmetric conﬁgurations are

followed up to 10 ms post-collapse with a subgrid viscous

model meant to approximately capture heating and an-

gular momentum transport due to the MRI.

In the rest of this manuscript, we refer to the

four binary systems described in this section using the

names SFHo-161-151, SFHo-180-131, SFHo-178-106, and

LS220-178-106, i.e. the equation of state followed by the

mass of each star, in units of 0.01M. A list of all phys-

ical conﬁgurations is provided in Table I.

III. NUMERICAL METHODS

A. General Relativistic Hydrodynamics

All simulations are performed using the Spectral Ein-

stein Code (SpEC) [12]. SpEC evolves the spacetime

metric using the Generalized Harmonics formulation of

Einstein’s equations using pseudospetral methods [23],

and the general relativistic equations of hydrodynamics

on a separate ﬁnite volume grid [13]. A number of diﬀer-

ent evolution algorithms are available in SpEC, to accom-

modate both simulations with a low-level of microphysics

requiring less dissipative, high-order methods in order to

decrease numerical errors (for waveform modeling), and

simulations with more detailed microphysics for which

phase accuracy during the evolution is not as crucial and

slightly more dissipative methods are preferable for sta-

bility. The simulations presented here fall in the second

category.

The ﬂuid equations are evolved in conservative form

using high-order shock capturing methods (HLL approx-

imate Riemann solver [24] and WENO5 reconstruction

from cell centers to cell faces [25, 26]). Both systems of

equations are evolved in time using third-order Runge-

Kutta time stepping. The evolution of the metric uses

adaptive step sizes, while the evolution of the ﬂuid uses

time steps ∆t= 0.25 min (∆x/cg), with cgthe speed of

light in grid coordinates, and ∆xthe grid spacing. The

minimum is taken over all cells in our computational do-

main. Given the stricter time stepping constraints on the

spectral grid, this results in larger desired time steps on

the ﬁnite volume grid than on the pseudospectral grid.

In practice, we require an integer number of time steps

on the pseudospectral grid for every step on the ﬁnite

volume grid. At the end of each time step on the ﬁnite

volume grid, we communicate metric quantities from the

pseudospectral grid to the ﬁnite volume grid, and ﬂuid

variables in the reverse direction. Values of these quan-

tities at other times are, when needed, extrapolated in

time from the last two communicated values.

The Generalized Harmonics formulation of Einstein’s

equation requires the prescription of a source term Ha

for the evolution of the coordinates xb, which follows the

inhomogeneous wave equation

gab∇c∇cxb=Ha(¯x, gab),(1)

with gab the spacetime metric. The initial value of Ha

is set by requiring that gtt and gti are constant in the

coordinate system corotating with the binary at the ini-

tial time. We then smoothly transition ﬁrst to the har-

monic condition Ha= 0 during inspiral, and then to the

“damped harmonic” prescription from Szilagyi et al. [27]

after contact. Once an apparent horizon is found in our

simulation, we additionally excise the region inside of

that horizon, as described in [28]. More detail on our

numerical methods can be found in [13, 29].

B. Equation of state

The ﬂuid equations require us to prescribe an equa-

tion of state for the dense matter within the neutron

stars. We use tabulated versions of the SFHo [18] and

LS220 [19] equations of state, taken from the Stellar-

Collapse library [30]. These tables provide us with the

internal energy, pressure, and sound speed of the ﬂuid

as a function of baryon density ρ0, temperature T, and

electron fraction Ye. The LS220 equation of state leads

to 1.4Mneutron stars with a radius of 12.7 km, and

a maximum mass for non-rotating neutron stars in iso-

lation of 2.04M. The SFHo equation of state leads to

more compact stars (11.9 km for 1.4Mstars) and a sim-

ilar maximum mass (2.06M). Both lead to macroscopic

properties for neutron stars that are consistent with cur-

rent astrophysical constraints, even though they are not

compatible with all nuclear physics constraints at lower

density. We note that the deﬁnition of the baryon density

is not entirely consistent in diﬀerent equations of state ta-

bles: we deﬁne ρ0=mbnbwith nbthe number density of

baryons and mbthe assumed mass of a baryon. Numer-

ical simulations use a constant mbin evolutions because

they evolve the baryon density of the ﬂuid, but the true

conserved quantity is the number of baryons; that is we

evolve the equation

∇a(mbnbua) = 0 (2)

with uathe 4-velocity of the ﬂuid, taking advantage of the

fact that at constant mb, this is just the equation for the

conservation of baryon number. Any reasonable choice

for mb(proton mass, neutron mass, average mass of a

nucleon in a given nucleus) is however acceptable. This

does not impact the evolution of the ﬂuid, which only

cares about nband the total energy density u=ρ0(1+),

with the speciﬁc internal energy of the ﬂuid – but it does

impact what our simulation considers to be ”rest mass

energy” (ρ0) vs ”internal energy” (ρ0). This distinction

becomes relevant when attempting to determine the fate

of the ejecta, as discussed in Sec. III F. In our tables, the

reference density for the SFHo equation of state is close

to the average mass per baryons of the nuclei formed in

r-process nucleosynthesis, while for the LS220 equation

of state it is the neutron mass.

C. Subgrid viscosity

During the merger of two neutron stars and the

post-merger evolution of neutron star-disk or black

hole-disk systems, we expect signiﬁcant growth of

(magneto)hydrodynamical instabilities. The Kelvin-

Helmholtz instability is active at the interface between

the two colliding stars during merger. After merger, the

MRI is active in the remant disk as well as, possibly,

in some regions of the remnant neutron star. These in-

stabilities drive small scale turbulence that is expected

to play an important role for angular momentum trans-

port and heating of the post-merger remnant. If a dy-

namo mechanism is active in the remnant, they may also

eventually lead to the production of strong magnetically-

driven disk winds and relativistic jets [31–35]. Captur-

ing the growth of these small scale instabilities is how-

ever very costly, and getting converged predictions for

the large scale magnetic ﬁeld post-merger is beyond even

the highest resolution simulations performed so far [36].

A possible alternative to at least qualitatively capture

angular momentum transport and heating in the rem-

nant is to rely on approximate subgrid models explictly

introducing viscosity in the simulations. A few classes

of subgrid models have been used in merger simulations

so far: a relativistic α-viscosity model [37] adapted from

the Israel-Stewart formalism for non-ideal ﬂuids [38], a

simpler (but not fully covariant) turbulent mean-stress

model [16], and the gradient sub-grid scale model of [39].

In the ﬁrst two cases, the stress-energy tensor of the ideal

ﬂuid

Tab,ideal = [ρ0(1 + ) + P]uaub+P gab (3)

(with Pthe pressure of the ﬂuid) is complemented by an

approximate non-ideal piece τab:

Tab =Tab,ideal +τab.(4)

In [39], the magnetic ﬁeld is directly evolved and a sub-

grid magnetic stress tensor is added to the evolution

equations instead.

In this work, some of our simulations use the shear

viscosity model of Radice [16], modiﬁed to match the

expected Newtonian limit for the energy equation and

to impose the expected condition τabua= 0 [15]. The

spatial components of τab are taken from [16]:

τij =−2ρ0lcshW 21

2(∇ivj+∇jvi)−1

3∇kvkγij (5)

with h= 1 + +P/ρ0the speciﬁc enthalpy, csthe sound

speed, Wthe Lorentz factor of the ﬂuid, viits 3-velocity,

and γij the 3-metric on a slice of constant time coor-

dinate. Given a normal vector nato that slice, the 3-

velocity is given by ua=W(na+va), and the 3-metric

by γab =gab +nanb. We can see from this deﬁnition

that the method is not fully covariant, as it requires the

choice of a preferred time direction, and uses covariant

derivatives of the velocity on the spatial slice orthogonal

to that preferred direction.

The length scale lsets the strength of non-ideal eﬀects,

and should be calibrated to the result of simulations cap-

turing magnetic turbulence in the post-merger remnant.

In our simulations using viscosity, during merger, we con-

sider the simple choice l= 30 m, which is expected to be

at the upper end of the range of reasonable values for

the Kelvin-Helmholtz instability in neutron star merg-

ers [16]. We note however that more advanced models in

which ldepends explicitly on the ﬂuid density have been

developed in [40], and a density-dependent mixing length

is in particular using in the simulations of [8] that we are

here using as a comparison point. While our two viscos-

ity schemes are thus fairly similar, they diﬀer both due

to our correction to the time components of the stress-

tensor and due to the choice of a smaller mixing length

at low-density in [8]. As our simulations ﬁnd a lesser im-

pact of viscosity on the properties of the outﬂows, and

we use a larger mixing length, it is however unlikely that

the choice of mixing length alone explains the small dif-

ferences between the two sets of simulations.

For simulations continued up to 10 ms post merger, we

modify the value of lto more closely match the expected

eﬀect of the MRI. Following [17], we choose

l=αvis

ΩKcSρ0

(6)

with αvis = 0.03. We switch to this viscosity model 5 ms

post-merger, after formation of a clear accretion disk.

This subgrid model is expected to qualitatively cap-

ture heating and angular momentum transport. It does

not however capture the eﬀects of a large scale magnetic

ﬁeld. Accordingly, we cannot use this model to study rel-

ativistic jets, gamma-ray bursts, or magnetically-driven

winds. High-resolution 3D MHD simulations would be

required to accomplish those objectives.

Unless otherwise noted, all ﬁgures in this manuscript

for simulations LS220-178-106 and SFHo-178106 are for

the simulations including a subgrid viscosity model. The

simulations without viscosity performed for case LS220-

178-106 are only used to estimate the impact of that

model.

D. Neutrino transport

Neutrinos are evolved using our recently developed

Monte-Carlo algorithm [41]. In this algorithm, neutrino

packets directly sample the distribution function of neu-

trinos, allowing for the evolution of Boltzmann’s equa-

tions of radiation transport. Packets are emitted isotrop-

ically in the ﬂuid frame, sampling the emission spectrum

of neutrinos, then propagate along geodesics. During this

propagation, each packet has a ﬁnite probability of being

absorbed or scattered by the ﬂuid, determined by tab-

ulated values of the absorption and scattering opacities.

We consider 3 species of neutrinos: electron neutrinos

νe, electron antineutrinos ¯νe, and heavy-lepton neutri-

nos νx(which include muon and tau neutrinos and an-

tineutrinos). We use tables generated by the public code

NuLib [30]. We include in the reaction rates absorptions

of νeand ¯νeby neutrons and protons, elastic scattering of

all neutrinos on neutrons, protons, alpha particles, and

heavy nuclei, and emission of νxdue to e+e−pair an-

nihilation and nucleon-nucleon Bremsstrahlung. Inverse

reactions are all calculated assuming Kirchoﬀ’s law. We

currently ignore pair processes for electron type neutri-

nos, inelastic scattering, and all types of neutrino oscil-

lations. Neutrino emissivities η, absorption opacities κa,

and scattering opacities κsare tabulated in 16 energy

bins (logarithmically spaced up to 528 MeV), 82 den-

sity bins (logarithmically spaced between 106and 1015.5

g/cc), 65 temperature bins (logarithmically spaced be-

tween 0.05 and 150 MeV) and 51 values of the electron

fraction Ye(linearly spaced between 0.01 and 0.6).

To handle the densest/hottest regions of neutron

stars, our Monte-Carlo algorithms makes two notable ap-

proximations. In regions with large scattering opacity

(κs∆t≥3), we do not perform each scattering event

individually, but instead directly move packets to a lo-

cation drawn from the solution of a diﬀusion equation

matching the outcome of individual scatterings in the

limit of many neutrino-matter interactions [42, 43]. In

regions with large absorption opacities (κa∆t≥0.5),

we reduce the absorption opacity while keeping the to-

tal opacity κa+κsand the equilibrium energy density

η/κaconstant [41]. This maintains the expected diﬀusion

rate of neutrinos through the star and their equilibrium

energy density, but eﬀectively increase the equilibration

timescale of neutrinos from κ−1

ato (2∆t). This method,

inspired by implicit Monte-Carlo algorithms [44], has the

dual advantage of avoiding stiﬀ coupling between the

neutrinos and the ﬂuid and of avoiding large numbers

of emissions / absorptions during each time step. We

have veriﬁed that for the short timescales considered here

and the ﬂuid conﬁgurations found in merger remnants,

this approximation likely introduces errors that are sig-

niﬁcantly smaller than our current numerical errors [41].

We also note that this approximation is not used much in

the simulations presented in this manuscript, as the bi-

naries evolved in this work rapidly form a black hole-disk

system in which nearly all cells on our computational grid

are optically thin to neutrinos (even if the disk in its en-

tirety is not). This type or remnant is signiﬁcantly easier

to evolve using Monte-Carlo methods than the neutron

star-disk remnants considered in our ﬁrst Monte-Carlo

simulation [14]. A detailed discussion of our Monte-Carlo

algorithm can be found in [41].

In the simulations presented here, we use 106neutrino

packets per species up to the collision of the neutron

stars, and 4 ×107neutrino packets per species (107at

low resolution) thereafter. We note that this high num-

ber of packets is only really needed around the time of

the collapse of the remnant to a black hole. We have also

been able to evolve the post-merger remnant (after black

hole formation) with as few as 106packets, due to the rel-

atively low neutrino luminosity of the remnant and the

fact that it is optically thin to neutrinos. However, after

merger our numerical grid is large enough that evolving

more packets does not signiﬁcant impact the cost of the

simulations (we use 5 ×106grid cells in our post-merger

evolution, and each ﬂuid cell is signiﬁcantly more expen-

sive to evolve than a MC packet).

During the collapse to a black hole, on the other hand,

a high number of packets is actually crucial to the sta-

bility of the evolution, at least with the distribution

of packets currently implemented in the SpEC code 1.

With those methods, the simulations are unstable with

(106,4×106) packets. With 107packets, shot noise re-

mains visible in the composition of the low-density re-

gions, and the average Yeof the outﬂows increases no-

ticeably (see results). With 4 ×107packets, shot noise

is only observed close to the black hole, and the compo-

sition of the outﬂows largely matches expectations for a

cold tidal tail unimpacted by neutrinos. We note how-

ever that the mass, temperature, and structure of the

post-merger accretion disk and the other properties of the

matter outﬂows are not notably impacted by the choice of

1It might be reasonable to simply ignore neutrino interactions in

the very high density, hot matter formed during collapse to a

black hole instead, but we have not so far attempted to do this

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摘要：

GeneralrelativisticsimulationsofcollapsingbinaryneutronstarmergerswithMonte-CarloneutrinotransportFrancoisFoucart,1MatthewD.Duez,2RolandHaas,3,4LawrenceE.Kidder,5HaraldP.Pfeier,6MarkA.Scheel,7andElizabethSpira-Savett1,81DepartmentofPhysics&Astronomy,UniversityofNewHampshire,9LibraryWay,DurhamNH0382...

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General relativistic simulations of collapsing binary neutron star mergers with Monte-Carlo neutrino transport Francois Foucart1Matthew D. Duez2Roland Haas3 4Lawrence E..pdf

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General relativistic simulations of collapsing binary neutron star mergers with Monte-Carlo neutrino transport Francois Foucart1Matthew D. Duez2Roland Haas3 4Lawrence E.

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