Let's Simulate Neutron Stars
What is a Neutron Star?
A neutron star is a star formed when stars 4-8 times larger than the sun explode into supernovas. When these stars explode they leave behind their cores which start to collapse the material it just exploded back together. The material begins to press itself so tightly together that it forms what we know as a neutron star. We call it a neutron star because the protons and electrons in the exploded matter press against each so intensely that they form neutrons.
Neutron stars generally have a diameter of 20km. However, they are so dense that their gravitational pull is 2 billion times greater than Earth. A section of them about 5-6 inches long can weigh a billion tons. The makeup of their core is unknown, but there are many theories on what lies inside them. Their pull is strong enough to create gravitational lensing. Gravitational lensing bends radiation, and allows you to visually see the backside of a star.
Neutron stars also have a very fast rotation speed. It can spin several times a second. Sometimes as fast as 43,000 times a minute. Their spinning speed is controlled by their angular momentum as they compress and shrink.
Most neutron stars are considered pulsars. Pulsars are neutron stars that have pulses of radiation that take place over a few milliseconds or seconds. They were first discovered in 1967 by Jocelyn Bell Burnell.
They also have very strong magnetic fields, and emit particles of matter from their poles. These particles form beams of light. Their magnetic fields are not aligned with their axis, this creates a unique effect when they are viewed. The particles that are emitted from their axis, get swept up into their magnetic fields, and spin around them. Pulsars are also thought of as lighthouses. In the sense that when they rotate they emit a beam of light that sweeps around the sky.
As of 2010, 1,800 pulsars have been found. Some of them have their own solar systems.
Magnetic fields play a huge part in defining neutron stars from other stars in the universe.
The magnetic field strength of the stars affects its surface tension. On the surface of a neutron star the strength of this can range from 104-1001 teslas. Teslas are a measurement for magnetic induction. These tesla levels have not been observed anywhere else in the universe. Fun fact,T fields have been used in laboratory settings to levitate living frogs.
The variations in magnetic field strength that neutron stars give off allow them to have a unique spectra, and create the pulses that give pulsars their names.
Neutron stars with the strongest magnetic fields are called magnetars. The ranges of their fields are between 108-1001 teslas. Magnetars are also called soft gamma repeaters and anomalous X-ray pulsars. They emit X-rays and gamma rays when their magnetic fields shift, and their outer crust cracks. This is also known as a starquake. These starquakes cause fireballs to rise out of the star, and then become trapped in the magnetic field. The field is also so strong that it will polarize the vacuum of space.
No one is sure where these magnetic fields come from. It is hypothesized that these stars contain a magnetic flux over their surface area. This flux remains the same as the star shrinks, and then increases the magnetic field in the process. However, there are many lacking details to this theory.
Let’s learn more about gamma rays. Not the Incredible Hulk kind.
In astronomy, gamma ray bursts(GRBs), and huge explosions full of energy that travel through the universe. They are the brightest electromagnetic events in the universe, and can last from a few seconds to several hours. After the initial explosion, different types of radiation are emitted until it completely fades away. This can be made up of X-ray, ultraviolet, optical, infrared, microwave and radio waves.
Binary neutron stars are thought to emit short bursts of GRBs. These are thought to happen when the crust of the star shatters, and the edges of the pieces continue to collide. Most of the gamma rays released by a neutron star will be more than our sun will release over its entire lifetime.
There is one scary part of GRBs, if a neutron star was close enough to Earth, and released a burst of gamma rays our way, it could result in a mass extinction event. However, lucky for us, all large GRBs have been observed outside the milky way.
GRBs were first detected in 1967 by the vela satellites. These satellites were first designed to detect nuclear weapon tests going on, on the surface of the Earth. These gamma ray bursts confused scientists and the military. This confusion started the creation of many hypothetical models of where these gamma rays were coming from. However, it wasn’t confirmed till 1997 that neutron stars were emitting these signatures.
Gamma rays are also thought to be released when a neutron star collides with a blackhole. These merging events are thought to release bursts lasting less than a few seconds.Depending on how fast the blackhole swallows the star.
When neutron stars collide, they also release short GRBs as well.
Now there are two other types of gamma ray bursts that exist that are not closely linked to neutron stars. But I think they are worth discussing.
Long gamma-ray bursts, and GRBs that last longer than two seconds. These are the most observed gamma ray events, as they are the easiest to detect. They have the brightest “afterglows”, or radiation after their main event. They are mostly linked to galaxies with rapid star formation, and collapsing supernovas.
Ultra long gamma ray bursts are GRBs that last longer than 10,000 seconds. They are thought to be caused by supermassive stars collapsing, tidal disruption events, or newly born magnetars. Only a small number of them have ever been detected.
Rotation and Spin
Due to their angular momentum in their formation process. The more their core shrinks the faster their spin becomes. Their spin can be likened to the way figure skaters spin. When they hold out their arms they spin slower. When they pull their arms in, they speed up.
Neutron stars are thought to be powered by their rotational speeds. The brightness or “luminosity” of the stars is correlated to their rotational speeds. Based on the type of star, the luminosity can be directly related to their spin down or up speeds. It is also thought that the luminosity can be linked to how active the magnetic fields of the star are.
There are two changes of rotational speed for a neutron star. Spin up and spin down. Let’s talk about each.But fits let’s mention something called a P-P dot diagram.
These diagrams can be used to map the rotational speed of a star of a period of time The first “P” stands for the periodic time of the rotational period of the star. The second “P” stands for the periodic time over a selected unit of time. These diagrams can be used to map rotation-powered pulsars, X-ray pulsars, high-energy emission pulsars, binary pulsars, and many more.
The P and P formula allow the minimum value of the magnetic fields of the stars to be calculated. They can also be used to calculate the age of pulsars, the spin down “brightness” of the star, and the loss of rotational energy the star might have.
The magnetic field of a neutron star is directly linked to the rotation of it. When a neutron star starts to slow, the magnetic field of the star also decreases. When three stars become very old, it may take them a few seconds to complete one full rotation. This continues until the star ages so much it completely stops turning. This is called a spin down.
When the spin down is complete, the neutron star can no longer be detected.
Neutron stars can increase their rotational speed over time. This process is known as a spin up. When the star absorbs surrounding matter from other stars, this increases its rotation rate, and reshapes the star. When this process occurs, it can speed up the star’s rotational speed over a hundred times a second.
The faster rotating neutron star known in the universe is PSR J1748-2446ad. It rotates 716 - 1122 times per second.
Previously, we mentioned that starquakes are events that happen on a neutron star’s surface. However, they also cause something called glitches to happen.
Glitches are sudden increases in a star’s rotational speed. They are thought to happen directly after a starquake, or by vortices from the superfluid in the star’s core.
There are also something called anti-glitches that occur in stars. These are sudden and random decreases in a star’s rotational speed.
Other Neutron Star Variants
We’ve mentioned a few different variants of neutron stars already. But let’s talk about other different types that are worth mentioning.
Neutron stars are classified by how they can be detected and what characteristics they exhibit. There are rotationally powered neutron stars that can only be detected through X-ray and gamma ray detectors. As well as X-ray bursters that showcase rapid increases and decreases in luminosity. These stars can be detected through the electromagnetic spectrum. They often have another star orbiting around them called a donor star.
The way X-ray bursters emit X-rays is by absorbing material from their donor star. When the material disappears into the main star’s event horizon, the material falls into the surface and hydrogen and helium start to fuse. This produces bursts of X-rays.
The mass of a neutron star system also factors in if the system has a donor star. The mass of a star is calculated in Solar Masses.
Another type of neutron star is a soft gamma repeater. (SGR) These are astronomical objects that emit large bursts of gamma rays and X-Rays. They are thought to be a type of magnetar or a type of neutron star with large disks of matter around them.
There are many known variants of X-ray bursters and neutron stars. But let’s talk about a few that are hypothetical.
An exotic star is a theoretical compact star composed of particles other than electrons, protons, neutrons, or muons. It also prevents its own gravitational collapse by the pressure it creates and it’s own quantum properties. Exotic stars also include quark stars(made of quarks),preon stars(made of prions, a hypothetical particle), and strange stars(made of strange matter).
These stars are theoretical because we don’t fully understand how the matter that creates them behaves. There is also no confirmed or easy way of detecting these stars. We also don’t currently have the technology. But we can look for predicted observable phenomena they might give off.
NASA, and Computational Simulations
Let’s look into some scientific simulations of neutron stars. Starting out with the center of a neutron star.
We can’t confirm what material exactly makes up the center of a neutron star, due to its extreme environment. However, there have been some developments in how the matter inside the star should behave.
NICER(Neutron star Interior Composition Explorer), on the international space station, has been making some great observations for NASA. Especially, when it comes to measuring how dense and “squeezable” the matter inside the stars are.
NICER has been doing observations of a pulsar PSR J0740+6620 (J0740 for short). It is the largest neutron star ever recorded, and it is over 3,600 light years away from Earth. The star is estimated to be over 2.1 times the size of our Sun.
Because neutron stars are so closely related to blackholes, by studying their matter, we can technically observe matter before it implodes and creates a blackhole. From these NASA observations, scientists have been able to conclude that the inner core of massive neutron stars are more dense than predicted.
The NICER explorer is also extremely accurate.It can measure the arrival of X-rays in less than 100 nanoseconds. It can track a pulsar’s brightness to see how it varies when it spins. Then it takes this data and estimates how much the star is distorting spacetime.
Even with NICER hard at work, down on Earth there have been some teams of scientists creating simulations of colliding neutron stars. When these stars collide together, sometimes the output is a blackole that swallows all the remaining debris. So how can we detect a collision like this if all the evidence of the stars is now gone? Well some researchers at Penn State University have figured out how.
Turns out when these celestial bodies collide, gravitational waves emerge away from the impact area. We can also detect these waves with detectors like LIGO in the USA, and Virgo in italy. They also found out through their simulations that the resulting blackhole doesn’t always swallow all the radiation from it’s two stars. Depending on the size of the two colliders, this can have a lasting impact on how much radiation is produced. If one is bigger than the other, then it will tear the smaller star apart, and allow some of the radiation to escape before the blackhole formation. These signatures can then be used to detect more blackholes.
LIGO has recently confirmed these merging events in the Universe while using these detection methods. It detected it’s first in 2017, and another in 2019.
The first merging event it witnessed was between two neutron stars of the same size. The second was between a larger star, and a smaller one. In order to see how messy and radioactive this second collision was, scientists used Pittsburgh Supercomputing Center's Bridges platform and the San Diego Supercomputer Center's Comet platform, to run a simulation of their data.
The team used about 500 computing cores, and over 20 separate instances. The simulation was so big it required over 100 times the usual amount of memory for an average astrophysical simulation.
Their simulation pretty much confirmed what researchers at State Penn predicted.the larger star tore the smaller one apart, and the absorption of the matter into the larger star formed a blackhole. But some of the smaller star matter didn’t drift into the blackhole straight away, and created a wave of electromagnetic radiation.
Berkeley Lab’s National Energy Research Scientific Computing Center (NERSC),is also doing simulations of gravitational wave signals. They published their findings in an issue of the scientific journal Classical and Quantum Gravity.
One of the studies they did modeled the first milliseconds of when a blakhole and a neutron star merge. The other models they created simulate the formation of disks of matter after they merge together, and the matter ejected from the collision.
They estimated that the matter leftover from a blackhole and star collision includes gold, platinum, and some other radioactive elements. They also estimated that the speed that this matter travels away is around 20,000-60,000 miles per second.Or one third the speed of light.
Their simulations are also very customizable, and allow them to add more physical information to them after the fact.
VFX Simulations and Further Visualization
There have also been some other interesting sims of neutron stars as well.
There have been a few studies of monte carlo simulations and the propagation methods of neutron stars throughout the Universe. It is estimated that gravitational waves also help scatter these stars randomly about the Universe.
By entering a starting population of stars, a birth kick velocity, an estimated star formation rate, and variable for gravitational potential for formation, scientists were able to better understand how neutron stars form across the universe. As well as where to find them, and how they could evolve into pulars, manetars, and other variations. These simulations also took into account the spin up and spin down rates of the stars.
Monte Carlo simulations are also used to simulate radiation from neutron stars. These simulations are usually time dependent, and use Fokker-Planck code to determine lepton population in stars. They also take into account the accretion rate, stellar surface field, and level of wave turbulence around them. The results so far have suggested that X-ray pulsars give off accretion-powered emissions.
So you might be wondering, has anyone simulated a neutron star using Houdini? Or are there any great examples of them in VFX? Well, yes there are.
I know personally from some buddies that neutron stars are visualized at planetariums, and they sometimes use Houdini. There are also some very talented Houdini artists out there that take time out of their day to create examples of these stars on their own.You can find some great examples on vimeo and on artstation.
Other than space animations, there aren't too many good on screen references or examples of neutron stars in film. There are several mentioned by name in various Star Trek tv shows.However, when they are shown, they aren’t the most accurate stars in the world.
So I would suggest we need to change that. :)
Personally. If you are going to simulate these stars on your own, You’ll need to figure out what part or functions of the star you should add into your simulation. Decide whether you’d like to do a close up of the star’s surface, the magnetic fields, the exotic particles emitted from them, anything really.
Remember, scientists have to use super computers to simulate neutron star data. However, as visualization artists, more than likely we’ll be working with previously released images, known facts, and developing certain parameters for different aspects of the star. So try and figure out if there is an easy way to generate your results.
Creating a custom ball of fire will probably involve some vex. Probably sparse pyro as well, as that is a faster pyro solver than the legacy pyro tools in Houdini. There is a great tutorial floating around on how to simulate the sun. So in an open source sense, that might be a great starting point for your neutron star simulation.
As of 2021, some very interesting developments have happened when it comes to photographing neutron stars. As well as visualizing them.
On the ISS(International Space Station), there is a star detector on it called the Neutron Star Interior Composition Explorer.NICER for short. As mentioned in a previous chapter. It looks for X-ray information cooking towards us from the rest of the universe. Lately, scientists aimed NICER towards a pulsar 1,100 light years away. It’s name is J0030.Two teams, one from The University of Amsterdam, and another from The University of Maryland were able to take data from this star and map it’s entire surface. Their creation was a beautiful blue picture of a star.
Pulsars are like blackholes. They are incredibly dense and very small. Their huge gravitational well also makes them incredibly hard to observe. This gravitational warping also makes a pulsar appear larger than it actually is. But because these scientists were observing the star through its pattern of X-rays, they were able to better observe the surface, and see where the signals were directly coming from.
They found that this particular star is about 1.3-1.4 times heavier than the mass of our sun, and it is about 16km wide. Which is incredibly smaller than our sun. Our sun is about 1.3 million km across.
These teams were even able to photograph the hotspots of the star, which changed the overall opinion on where hotspots are located on a pulsar. Turns out there are not two of them located on the poles of the star, rather there are 2-3 of them in the southern hemisphere. These hotspots push matter from the star into outer space.
Photographing these hotspots would have taken a regular bunch of computers over a decade to render. However, the supercomputers on NICER took less than a month to process.