When two black holes (BHs) interact, they lose
energy through gravitational waves and spiral towards each other. They
eventually merge to give rise to a single black hole that is characterized
only by its mass, spin, and velocity (or "kick").
The merger of binary BHs is a very
complicated process that requires numerical simulations to accurately
predict the outcome. These simulations are very expensive, taking about a
month on a supercomputer to run. In recent years, several
surrogate models for these simulations have been developed. These
models are trained against a large number of numerical simulations, using
some fancy interpolation methods. In the end, the surrogate can reproduce
the result of the simulation as accurately as the simulation itself, but in
a fraction of a second, and on your laptop, rather than a month on a supercomputer!
In our new package, binaryBHexp, we use these surrogate models to
visualize the evolution of binary black hole systems. You can now generate
visualizations at any point in the parameter space, in a few seconds,
without needing to do a full numerical simulation! These visualizations are
described in detail in our paper [arXiv:1811.06552].
On this page you'll find a number of example
explorations that highlight what you can learn
about black hole mergers
with binaryBHexp. For quick access, use
the table of contents above.
Let's go!
Visualizations
Enough background, let's see some movies!
Precessing binary black hole
Here we see a precessing binary black hole merger.
The black holes are shown as oblate spheres, with arrows indicating their
spins. The orbital angular momentum is indicated by the pink arrow at the
origin. The colors in the bottom-plane shows the value of the plus
polarization of the GW as seen by an observer at that location; red means
positive and blue means negative, notice the quadrupolar pattern of the
radiation. In the subplot at the bottom, we show the plus and cross
polarizations as seen from the camera viewing angle. Our time steps are
chosen such that there are 30 frames per orbit during the
inspiral-merger-ringdown; this ensures that the movie slows down near the
merger, and it's easier to observe the dynamics. After the ringdown, we
speed up the movie to exaggerate the kick.
Here the BH spins are misaligned w.r.t the angular
momentum direction. Therefore, the spins, the angular momentum, and the
orbital plane all precess during the inspiral. It is interesting to see how
the remnant spin direction is very close to the direction of the orbital
angular momentum near merger. This animation corresponds to Fig. 1 of
[arXiv:1811.06552].
Precessing binary BH with varying camera angle
Here we show the same animation, but with a varying
camera angle. In the plot at the bottom we see how the waveform changes
based on the viewing angle; this is because the different (spin-weighted
spherical harmonic) modes combine with different weights based on the
observer viewing angle. Notice how the GW signal is strongest along the
direction of orbital angular momentum and weakest in perpendicular
directions. This animation corresponds to Fig. 4 of [arXiv:1811.06552].
Aligned-spin binary black hole
Here the spins are aligned w.r.t the angular
momentum direction, and there is no precession. Due to symmetries, the
remnant spin is also aligned, while the remnant velocity is restricted to
the orbital plane.
Orbital hangup effect
Here we demonstrate the "orbital hangup effect". On
the left, both black hole spins are aligned with the orbital angular
momentum. In the middle, the black holes are nonspinning. On the right,
both spins are anti-aligned with the orbital angular momentum. All three
cases start at the same orbital frequency, however, due to the orbital
hangup-up effect, the aligned (anti-aligned) case takes a longer (shorter)
time to merge than the nonspinning case. As a result the aligned system
also loses more energy to gravitational waves, and the final mass is
smaller. On the other hand, because the anti-aligned spins reduce the total
orbital angular momentum of the system, the final spin is lesser in the
right case. The nonspinning case is intermediate between these two.
In these cases, due to the symmetries present, the
final kick is zero. Unlike the other animations in this page, here we use
uniform time steps between movie frames. Even though the start frequency is
the same, the length of the waveform is different in each case, and
therefore the BHs merge at different times. This animation corresponds to
Fig. 5 of [arXiv:1811.06552].
Super-kick
In this case, notice how the spins line up in a
single plane close to the merger. This is believed to be necessary to cause
super-kicks, or very high remnant velocities. Notice how fast the final
black hole flies away compared to the above cases; that is about c/100,
where c is the speed of light! This is larger than the escape velocity of
even the most massive galaxies in the Universe, and such a binary would get
kicked out of its host galaxy. This animation corresponds to Fig. 6 of
[arXiv:1811.06552].
Sinusoidal-kicks
The kick velocity is very sensitive to the
orientation of the component spins near merger. Here we show several cases
that have equal-mass BHs, with anti-parallel spins lying in the orbital
plane at t=−100M. Each evolution is initialized with a different orbital
phase or, equivalently, performing an overall rotation of the spins about
the z-axis. The remnant kick changes dramatically with the phase of the
spins at merger; notice the sinusoidal nature of the final kick magnitude.
This animation corresponds to Fig. 7 of [arXiv:1811.06552].
Downloading these movies
You can download these movies by right-clicking on
them. On Chrome choose "Save Video As..", and similar for other browsers.
You can also get them directly from our Github repo as follows. Don't forget to credit us.
git clone git@github.com:vijayvarma392/binaryBHexp.git
cd binaryBHexp/docs/movies/
Generating your own visualizations
Since this package does not rely directly on
numerical simulations, you can generate new visualizations yourself, on
your laptop! These instructions have been tested for MacOS and Linux.
Short version
Our package, binaryBHexp, takes one command to
install and one command to run.
Installation
This package is available on
PyPI,
and can be installed using pip. This adds a new shell command called
binaryBHexp.
By clicking and dragging on the movie as it plays,
you can change the viewing angle, and see the waveform change. For more
options, do:
binaryBHexp -h
Long version
Installation
This package is available on PyPI, and can be installed using pip.
pip install binaryBHexp
You can also get the package from our
Github repo as follows.
git clone git@github.com:vijayvarma392/binaryBHexp.git
cd binaryBHexp
Prerequisites
This package relies on the surrogate models, NRSur7dq2 and surfinBH . These are
automatically installed with the pip installation. For the Github version,
these can be installed using pip.
pip install NRSur7dq2
pip install surfinBH
Usage
If you installed the binaryBHexp package with pip,
it should have added a new shell command called binaryBHexp, which you can
use as shown below. Instead, if you are using the Github version, the
script can be found in the repository, and you need to replace binaryBHexp
with ./binaryBHexp in the following.
You can save the video to file with the --save_file
option. Use this option if the live rendering is slow. You can generate
this aligned-spin movie with the following
command:
Please credit us, and cite our paper
[arXiv:1811.06552] and this website, if you use these visualizations in
your work, presentations or outreach. You can use the following bibtex keys:
@article{Varma:2018rcg,
author = "Varma, Vijay and Stein, Leo C. and Gerosa, Davide",
title = "{The binary black hole explorer: on-the-fly
visualizations of precessing binary black holes}",
journal = "Class. Quant. Grav.",
volume = "36",
year = "2019",
number = "9",
pages = "095007",
doi = "10.1088/1361-6382/ab0ee9",
eprint = "1811.06552",
archivePrefix = "arXiv",
primaryClass = "astro-ph.HE",
Note = {\href{https://vijayvarma392.github.io/binaryBHexp/}{https://vijayvarma392.github.io/binaryBHexp/}},
SLACcitation = "%%CITATION = ARXIV:1811.06552;%%"
}