Effect of turbulent dissipation on the evolution of a binary neutron
star merger remnant. Turbulence is modeled using a general-relativistic
extension of the classical mixing length prescription. We consider four
value of the mixing length parameter ℓmix : from 0 (no
turbulent dissipation) to 50 meters (extremely efficient turbulence). We
show temperature and density in the meridional plane. The time is in
milliseconds after merger. The white lines are the iso-density contours
for ρ = 1010, 1011, 1012, 1013,
1014, and 5·1014 g·cm−3.
Neutron star merger simulations are extremely computationally challenging.
WhiskyTHC requires 6 hours of calculation on 512 cores to simulate one
millisecond of evolution of a binary. This is for our standard resolution of
180 meters. Doubling the resolution increases the computational cost by a
factor 16. Unfortunately, we know that, during the merger, there are
small-scale magnetohydrodynamical instabilities that generate turbulence with
typical driving scales of few meters or less. These are scales that are
unaccessible to our simulations, even when running on the World's largest
supercomputers. How can we model their effect in simulations?
Our approach is to use turbulence models initially developed for weather
forecast and other "terrestrial" applications. Indeed, WhiskyTHC is the
first, and so far only, code to include an effective, sub-grid scale,
treatment of turbulence. This is based on the general-relativistic (GR)
extension of the large-eddy simulations (LES) method, which we recently
For our first GRLES simulations, we adopted the so-called mixing-length
closure of turbulence and we studied the impact of (sub-grid scale) turbulent
mixing in the evolution of the merger remnant. We found that turbulence could
have a potentially very important role in the evolution of the binary after
contact and might alter the gravitational-wave and neutrino signals from the
binary. On the other hand, for the most conservative values of the mixing
length parameter ℓmix, we found that these effects are
minor. This is very good news for all existing models of the
gravitational-wave emissions from merging neutron star, which did not include
any turbulence model. However, the final words will have to wait until
we will be able to actually measure ℓmix by means of more
restricted, but much higher resolution, GRMHD simulations.
Gravitational wave strain and spectra generated during the collision
of two neutron stars modeled with two different nuclear equations of
state. The DD2 equation of state includes only "normal" nuclear matter,
while the BHBΛφ also includes Λ-hyperons.
Can we use coming gravitational-waves observations of merging neutron
stars to detect the appearance of exotic particles or phase transitions in
nuclear matter at several times nuclear density?
The answer to this question is "yes" according to our most recent
simulations. The typical outcome of neutron star mergers is the formation of
an object, called hypermassive neutron star, which survives only for short
time before collapsing to form a black hole. The densities in this remnant
can be several times larger than the density in the neutron stars before they
collide. Now, we expect that phase transitions or other changes in the nature
of matter in the remnant will be the result of the system re-arranging to
find a new energy minimum. Where does the energy difference go? In
gravitational waves! As a consequence, gravitational waves can be used to
confirm or rule out the appearance of exotic states of matter in these
Binary neutron star merger simulations showing the development and
saturation of the one-armed spiral instability for both "soft" and "stiff"
equations of state.
We recently performed a series of high-resolution simulations of the late
inspiral and merger of neutron star binaries using the high-order methods
implemented in WhiskyTHC.
We studied the development and saturation of an hydrodynamical instability
that has been recently discovered in eccentric neutron star mergers that
included neutron star spin by Paschalidis and collaborators.
We found that this instability is not restricted to eccentric or spinning
neutron star mergers, but that the development of the one-armed spiral
instability is a generic outcome of the merger. Furthermore, if detected in
gravitational-waves, this instability would help constrain unknown parameters
of the equation of state of matter at super-nuclear densities.
Complete gravitational wave spectrum for an M1 = M2 = 1.35 Msun
binary neutron star merger at 10 Mpc with edge-on orientation. We use the
MS1b interaction model to describe the equation of state of neutron stars
(the "stiff" case above).
For this study, we constructed hybrid waveforms by combining our
numerical-relativity waveforms with state-of-the-art effective-one-body
waveforms we generated using a publicly
available code. Using these waveforms, we studied the detectability of
this instability and of other components of the gravitational-wave signal by
ground-based gravitational wave observatories. Unfortunately, we find that
the detection of this instability by Advanced LIGO is unlikely, but
might be possible for third generation detectors such as the Einstein Telescope.
We released the complete hybrid gravitational waveforms on
Counterpart and Nucleosynthetic Yield of Neutron Star Mergers
Rest mass density in the orbital plane for a binary coomposed of a
1.4 and a 1.2 solar mass neutron stars. The top panels show a simulation
that does not account for turbulent viscosity, while the bottom panels show
a simulation that included a treatment for turbulent viscosity. The black
countours enclose matter that is gravitationally unbound. Viscous heating
of the tidal stream between the primary and the secondary stars can
significantly enhance the mass loss from the binary.
Light curve modeling of the
kilonova that followed
GW170817 revealed the
presence of a few percent of solar mass of material ejected with large
velocity of about 0.3 c. Extant neutron star merger simulations find that
material is indeed ejected with large velocities during the collision between
the stars. However, the amount of the fast-moving ejecta is significantly
smaller than that required by the kilonova models. It appears that something
is missing in the current simulations.
We have recently performed the first simulations of unequal mass binary
neutron star mergers that included a sub-grid treatment of turbulent
viscosity. These new simulations show a new mechanism for mass ejection
during mergers. We find that mass exchange streams between the neutron star
prior to merger become super-heated due to the effects of turbulent
viscosity and reach temperatures as high as 20 MeV (230 billion Kelvins!).
The thermal pressure then drives powerful outflows with high velocities.
Viscous-dynamical ejecta might explain the fast outflows seen for GW170817.
Our simulations also make two predictions that could be tested. First,
they predict that some of the ejecta expand so rapidly that some of the
neutrons might escape capture by seed nuclei during the decompression. The
neutrons would then decay on a timescale of minutes and produce a bump in the
UV bands on a time scale of an hour. in the first hour of the merger. Second,
the radio fluency from GW170817 might reveal the presence of a substantial
amount of fast-moving ejecta in the next few months or years.
Visualization of the electron fraction in a binary neutron star
merger simulation. The blue color denotes neutron rich material, while the
red color denotes material with electron fraction 0.5 (i.e., equal number
of neutrons and protons).
We present a comprehensive study of mass ejection, nucleosynthesis, and
associated electromagnetic counterparts from binary neutron star mergers. In
the course of 2 years, we have performed 59 neutron star merger simulations
with a microphysical treatment of neutron star merger. We find that typically
a few 10-3 solar masses of material are ejected dynamically during
the mergers. The amount and the properties of these outflow depend on binary
parameters and on the NS equation of state (EOS). A small fraction of these
ejecta, typically 10-6 solar masses, is accelerated by shocks
formed shortly after merger to velocities larger than 0.6 c and produces
bright radio flares on timescales of weeks, months, or years after merger.
Their observation could constrain the strength with which the NSs bounce
after merger and, consequently, the EOS of matter at extreme densities. The
dynamical ejecta robustly produce second and third r-process peak nuclei with
relative isotopic abundances close to solar. The production of light
r-process elements is instead sensitive to the binary mass ratio and the
neutrino radiation treatment. Accretion disks of up to 0.2 solar masses are
formed after merger, depending on the lifetime of the remnant. In most cases,
neutrino- and viscously-driven winds from these disks dominate the overall
outflow. Finally, we generate synthetic kilonova light curves and find that
kilonovae depend on the merger outcome and could be used to constrain the NS
Estimated outcomes for the viscous evolution of a binary neutron
star system producing a stable remnant after merger. The grey shaded area
shows the set of all rigidly-rotating equilibrium configurations. The solid
line is a conservative estimate of the mass ejection and a possible
trajectory for the viscous evolution. The blue shaded region denotes the
range of all possible outcomes of the viscous evolution, for which we
identify two possible regimes. The first corresponds to the "normal"
ejection of matter due to nuclear recombination of the disk. The second to
the case in which more massive outflows are produced as the remnant settles
to a rigidly-rotating equilibrium. We find that the merger remnant has
enough angular momentum to unbind more than 0.1 solar masses of
The outcome of neutron star mergers depends on the total mass of the
system and on the poorly known equation of state of dense nuclear matter.
Binaries with mass significantly larger than the maximum mass for a
nonrotating neutron star result in prompt black-hole formation. Binaries with
lower masses, but above the maximum mass of isolated rigidly rotating neutron
stars, result in the formation of so-called hypermassive neutron
stars, objects temporarily supported against gravitational collapse by
the large differential rotation. Lower mass systems could produce remnants
that are stable even after the effective viscosity due to turbulence has
removed the differential rotation.
The identification of the outcome of the merger of binary neutron star
systems with different masses would yield a precise measurement of the
maximum mass of neutron stars. This, in turn, would constraint the equation
of state of matter at extreme densities. It is therefore important to
identify signatures indicative of the formation of long-lived remnants.
In a recent work, we studied the formation of long-lived merger remnants
in our simulations. We showed that these are born with so much angular
momentum that they will inevitabily become unstable under the action of
turbulent angular momentum transport, which will try to bring them to
solid-body rotation. The result is expected to be the launching of massive
neutron rich winds. These, in turn, could produce particularly luminous kilonova counterparts that
would be smoking gun evidence for the formation of massive or such objects if
detected by future UV/optical/infrared follow ups on gravitational waves
events or short gamma-ray bursts.
Ejecta and disk mass (top panel) and black-hole formation time
(lower panel) as a function of the tidal parameter Λ for binary
neutron star systems. Each point condenses the results of a full 3D
Neutron star mergers generically result in the ejection of a small
fraction (0.1% - 1%) of a solar mass of neutron rich material. As these
ejecta expands and cools, they may undergo the so-called
and produce heavy nuclei, like gold. The radioactive decay of by-products
of the r-process can power an UV/optical/infrared transient known as
During the merger, material is ejected from the neutron stars because of
tidal torques and shocks. Most of this material is bound and forms an
accretion disk around the merger remnant, a massive neutron star or a black
hole. A small fraction achieves velocities in excess of the escape velocity
and is unbound. Additionally, a substantial fraction of the disk (10% - 40%)
becomes unbound over a timescale of a second due to magnetic and neutrino
processes in the disk.
We constructed a large database of neutron star merger simulations, the
largest to date with fully general-relativistic simulations and with a
microphysical treatment of the neutron star equation of state. For each
simulation we estimated the dynamical ejecta and the disk masses. We used
this data to provide a unified interpretation of gravitational-wave and
electromagnetic observations of
GW170817. Our results
showed that the observation of a kilonova implies a constraint on the
presently unknown neutron star equation of state, complementary to that
derived by LIGO/Virgo on the basis of the gravitational-wave data alone.
Binary neutron star merger simulation with microphysics performed with WhiskyTHC.
With the aim of studying this process, we performed binary neutron star
merger simulations using a temperature- and composition-dependent nuclear
equation of state and including neutrino cooling and heating. The focus of
this study was to understand the role of weak reactions in shaping the
morphology and composition of the outflows and the final abundances.
Final abundances. The HY runs included no weak interactions. The LK
simulations included neutrino emission and electron/positron captures.
Finally, the M0 simulations included both neutrino emission and absorption,
as well as electron/positron captures.
We performed simulations with different microphysics modules in WhiskyTHC
switched on or off to be able to measure their relative importance. We used
the nuclear reaction network code
SkyNet to estimate the
final yields of the ejecta for each of these runs.
We found the final abundances of nuclei with atomic mass number A > 120
to be insensitive to weak reactions. On the other hand, the abundances of
lighter nuclei are affected in a qualitative and quantitative way by weak
reactions. The reason for this is that heavy nuclei are mostly synthesized in
the cold and catalyzed part of the ejecta due to tidal interactions, while
lighter nuclei are also synthesized in shock- and neutrino-driven outflows,
which undergoes weak reprocessing within the timescale of our simulations.
Turbulent Neutrino-Driven Convection in Core-Collapse Supernovae
The impact of resolution in numerical simulations of neutrino-driven
convection in core-collapse supernovae. The reference resolution is a
typical resolution used in 3D simulations, while 2x, 4x, and 12x are,
respectively, 2, 4, and 12 times higher resolution.
Neutrino-driven convection plays an important role in the explosion of
core-collapse supernovae. However, since it results in the creation of small
scale flow structures that are difficult to capture numerically, it is also a
serious obstacle to the development of accurate supernova simulations.
Quantifying these aspects has been the aim of my research.
One of the main finding of our work is that the
numerical viscosity inherent to any scheme can interfere with the turbulent
cascade in such a way as to trap energy at large scale (the so-called
bottleneck effect). This explains why low resolution simulations are
artificially more prone to explosion, something that had been already observed
before. It also suggests that some peculiar properties of neutrino driven
convection reported in the literature might be numerical artifacts. One in
particular is the rather flat kinetic energy spectrum observed in simulations
that is difficult to explain from a turbulence theory point of view.
Neutrino-driven convection. Compensated velocity power-spectra at
different resolutions. As the resolution increases, the slope predicted by
Kolmogorov's theory is recovered.
We used the high-order methods implemented in WhiskyTHC to attack this
problem and carry out simulations of neutrino-driven convection in
core-collapse supernovae at unprecedented resolutions. We found that the
predictions from Kolmogorov's classical theory of turbulence
are indeed recovered. However, this happens only at extremely high
resolutions, 15 times or more higher than current high-resolutions global
Driven relativistic turbulence. Logarithm of the Lorentz factor minus 1.
WhiskyTHC was used to perform the first systematic study of stationary,
isotropic, turbulence in the relativistic regime.
For that study, we performed 4 batches of simulations, labelled "A", "B",
"C", and "D". For the A runs we simulated sub-relativistic turbulence, while
the B, C, and D simulations had increasingly relativistic flows. We studied the
way in which turbulence changes as the flow becomes relativistic using data
from all of these simulations, which we performed at multiple resolutions.
Driven relativistic turbulence. Compensated velocity power-spectra
for different resolutions (64^3, 128^3, 256^3, and 512^3 grid points) and for
increasingly relativistic flows (A, B, C, and D).
We found that turbulence becomes increasingly intermittent as the fluid
becomes relativistic. However, somewhat surprisingly, we find low order
velocity statistics, such as the power-spectrum, to be in good agreement with
the prediction of Kolmogorov's classical theory of turbulence.