Einstein’s theory of gravity has been tested in lots of ways, from the slow precession of Mercury’s orbit, to the detection of gravitational waves. So far the theory has passed every test, but that doesn’t necessarily mean it’s completely true. Like any theory, general relativity is based upon certain assumptions about the way the universe works. The biggest assumption in relativity is the principle of general equivalence. 

The equivalence principle was proposed by both Galileo and Newton, and basically states that any two objects will fall at the same rate under gravity. Barring things like air resistance, a bowling ball and a feather should fall at the same rate. Experiments that have tested the principle of equivalence show it’s a good approximation at the very least.

In Newtonian gravity, this just means that the gravitational force on an object is proportional to its mass, so even if the equivalence principle is only an approximation we could still use Newtonian gravity. But Einstein’s theory of relativity, gravity isn’t a force, but simply an effect of the warp and weft of spacetime. In order for this to be true, the equivalence principle can’t be approximately true, it has to be exactly true. If objects “fall” due to the bending of space itself, then everything must fall at the same rate, because they are all in the same spacetime.

But there’s an interesting twist to this principle. One of the things relativity predicts is that mass and energy are related. This is where Einstein’s most famous equation, E = mc², comes into play. Normally the “relativistic mass” of an object is effectively the same as its regular mass, but objects like neutron stars have such strong gravitational and electromagnetic fields that their relativistic mass is a bit larger than the mass of their matter alone. If the gravitational force on an object is proportional to its mass-energy, then a neutron star should fall slightly faster than lighter objects. If Einstein is right, then a neutron star should fall at exactly the same rate as anything else.

A few years ago, astronomers discovered a system of three stars orbiting closely together. Two of them are white dwarf stars, while the third is a neutron star. The neutron star is also a pulsar, which means it emits regular pulses of radio energy. The timing of these pulses are determined by the rotation of the neutron star, which is basically constant. Any variation in the timing of the pulses is therefore due to the motion of the neutron star in its orbit. In other words, we can use the radio pulses to measure the motion of the neutron star very precisely.

Each of the stars in this system is basically “falling” in the gravitational field of the others. Recently a team of astronomers observed this system to see if the neutron star falls at a different rate different from Einstein’s prediction. Their result agreed with Einstein. To within 0.16 thousandths of a percent (the observational limit of their data) the neutron star falls at the same rate as a white dwarf.

Once again, Einstein’s gravitational theory is right.

Paper: A. Archibald et al. Testing general relativity with a millisecond pulsar in a triple system. 231st meeting of the American Astronomical Society, Oxon Hill, Md. (2018)

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The first elements to appear in the Universe were hydrogen and helium, created soon after the big bang. Other elements on the periodic table are produced through nuclear interactions within stars. Lighter elements such as carbon, nitrogen and oxygen are formed through nuclear fusion in a star’s core, but heavier elements such as gold are formed through catastrophic events such as a supernova explosion or the collision of neutron stars. It’s known as r-process nucleosynthesis (due to the rapid neutron interactions) and is still a bit of a mystery. 

We can distinguish r-process elements not only by their presence in stars, gas and dust, but also by their relative abundances. The r-process abundances are distinctly different from other nucleosynthesis methods such as the s-process (slow neutron) that occurs in the late stage fusion of large stars. So we know that heavier elements can are produced through r-process events, but one of the big debates has been over which type of events create the most heavy elements.

There’s basically been two schools of thought. One is that core-collapse supernova are the main factor. These are fairly common on a cosmic scale, but the amount of heavy elements released in a particular supernova is relatively low. In this model a galaxy would be seeded with a low but steady flow of heavy elements. The other idea is that stellar collisions create most heavy elements. The collision of two neutron stars, for example, is fairly rare, but the amount of heavy elements released from such an explosion would be quite high. In this model heavy elements are seeded into a galaxy in bursts every now and then. The challenge is to determine which model is right.

Recently astronomers found evidence that the collision model seems to be the right one. They looked at the abundance of elements in a dwarf galaxy known as Reticulum II. They found that the 9 brightest stars in this galaxy have heavy element abundances 100 to 1,000 times greater than seen in other similar galaxies. This would imply that the abundance of r-process elements was unusually high during their formation, which is what you would expect if they are produced at high quantities in rare events. It seems clear, then that stellar collisions play a major role in the production of heavy elements.

Since gold is one of those heavy elements, you could say that the collision of neutron stars causes a galaxy to enter a gilded age.

Paper: Alexander P. Ji, et al. R-process enrichment from a single event in an ancient dwarf galaxy. Nature 531, 610–613 (2016) doi:10.1038/nature17425

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How do you weigh a star? If two stars orbit each other, then we can determine their masses by their orbits. Since each star pulls gravitationally on the other, the size of their orbits and the speed at which they orbit each other allows us to calculate their masses using Kepler’s laws. But if a star is by itself, we have to use indirect methods such as its brightness and temperature to estimate their mass. While this can work reasonably well for main sequence stars like our Sun, it doesn’t work well for neutron stars due their small size and extreme density. But new work in Science Advances has found an interesting way to determine the mass of a type of neutron star known as a pulsar.

Neutron stars have a mass greater than our Sun, but are only about 20 kilometers (12 miles) wide. They are so dense that their magnetic fields are incredibly strong. So strong that they channel lots of radio energy away from their magnetic poles. As a neutron star rotates, these beams of radio energy sweep around like a lighthouse. If the beam is oriented toward Earth, then we observe these beams as short pulses of radio energy. Each pulse marks a single rotation of the star (known as its rotational period). We can measure the timing of these pulses very precisely, and one thing we notice is that period of a pulsar gradually lengthens as its rotation slows over time.

Basic structure of a neutron star. Image by Wikipedia user Brews ohare. CC BY-SA 3.0.

But every now and then the rotational period of pulsar will jump a bit, indicating that its rotation has increased. These jumps are known as glitches, and they are due to interactions between the core of the neutron star and its outer crust. As a neutron star loses energy, it is the crust that slows down over time. The interior of the star is a superfluid, and so continues to rotate at a steady rate. Over time the difference in rotation becomes severe enough that the interior transfers some of its rotational speed to the crust, slowing down the core and speeding up the crust so that the two are more in sync.

How a pulsar glitches.

Just how much rotation is transferred, and how often such a glitch occurs, depends upon the exact nature of a neutron star’s interior. That’s where this new work comes in. The team took glitch data from the Vela pulsar spanning 45 years, and compared it to several models of neutron star interiors. They found that only one model matched the observed glitches. When they compared this model to another pulsar (PSR J0537−6910) spanning about 14 years, it also agreed with the same model. From the glitch data the team was able to pin down the interior structure of these neutron stars.

What’s interesting about this result is that the superfluid model that fits the glitch data can be used to determine the mass of a pulsar. Since the interior of a neutron star must be below a critical temperature to be superfluid, the glitch data tells us about the internal temperature of the star. Since neutron stars don’t produce heat through fusion like main sequence stars, they gradually cool over time. Larger (more massive) neutron stars cool more slowly than smaller ones. If we know how old the neutron star is (and thus how long it has been cooling) then we can use its age and the critical temperature to determine the mass of the neutron star. Often we can determine the age of a neutron star by studying the remnant of the supernova that formed it, or by using x-ray observations to study its surface temperature.

Since the ages of the Vela pulsar and PSR J0537−6910 are known, the team calculated their masses. They found the Vela pulsar has a mass of 1.5 Suns, and PSR J0537−6910 has a mass of 1.8 Suns. More pulsars will need to be studied to see if their glitch patterns follow the same model, but if the method holds up we’ll be able to determine the mass of a pulsar even when it’s all alone.

This article originally appeared on Forbes.

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Yesterday I talked about millisecond pulsars, and the way in which they might gain such rapid rotation. Another property of millisecond pulsars is that they demonstrate very clearly that pulsars are neutron stars. It all has to do with their rapid rotation and the physics of centripetal (or centrifugal) force.

When you stand on the Earth, there are two basic forces acting on you. The first is gravity, where the attraction of Earth’s mass tries to pull you to the center of our planet. The second is the ground, which prevents you from moving through it by pushing up on you. This is often called the normal force. Standing on the ground, these two forces are in balance. The weight of gravity is countered by the normal force of the ground, which is why you can stay put.

If the Earth weren’t rotating, then these two forces would be equal in magnitude. But since the Earth rotates, the normal force is very slightly smaller than the attraction of gravity. Just how much smaller depends on where you are on the Earth, but it is smallest if you are standing on the equator. You can see why that is if you’ve ever been in a car going around a corner. As the car turns, it feels like you are being pulled slightly outward, away from the turning car. This is sometimes called a centrifugal force, and it has to do with the fact that your body (like any object with mass) would like to keep moving in a straight line at a constant speed. To change your direction (and keep you in your seat) the car has to push you in the direction of the turn. Whenever you are pushed in some direction, it feels like you are being pulled in the opposite direction, so it feels like you are being pulled outward. A similar thing occurs when your car accelerates, and it feels like you are being pulled back into your seat.

As you stand upon our rotating planet, a similar thing occurs. You are moving around in a circle, once per day, so your direction is always changing. Your body would like to keep moving in a straight line, but Earth’s gravity keeps changing your direction. Earth’s gravity is more than strong enough to overcome your centrifugal force, so the normal force of the ground also acts to keep you on the ground. But the normal force doesn’t have to counteract all of gravity, just the extra gravity beyond the centrifugal force.

Diagram of a pulsar Source: NRAO

Now suppose we could spin our spherical world faster and faster. As we are standing on its surface, we would have a tendency to fly off the world due to its rotation. The gravity is stronger than the centrifugal force, so we stay put. But if we could spin the world faster and faster, we would reach a point where the centrifugal force is equal to the force of gravity. Spin the world any faster, and we would fly off. Earth’s gravity wouldn’t be strong enough to hold us. The surface gravity of a planet or star depends upon its density, so far a given density for a planet/star, there is a maximum rate of rotation. Any faster and it would fly apart. Put another way, if we measure the rotation of a planet or star, we know its minimum density.

When we do the math, we find we can calculate that minimum density in grams per cubic centimeter by taking 140 million and dividing it by the square of an object’s period in seconds. So for the Earth, the period is 24 hours or 86,400 seconds. Plug that into our equation and we get a minimum density of about 0.02 g/cc. The Earth’s real density is about 5 g/cc, well above that minimum.

Pulsars are kind of like cosmic light houses. As they rotate they sweep out a beam of radio waves from their magnetic poles. If those poles are pointing in our direction, we can hear each rotation as a pulse. The fastest millisecond pulsar has a rotation of 716 times a second, or a rotational period of 1.4 milliseconds. Plug that into our equation, and you get a minimum density of about 7 x 10¹³ g/cc. Thats that’s about 7 billion kilograms per sugar cube volume, which is an unimaginably high density. It also happens to be a bit less than the density of atomic nuclei.

So pulsars are as dense as atomic nuclei, only several kilometers in diameter. We call them neutron stars.

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A millisecond pulsar is a neutron star that is rotating about 600 to 700 times a second. Because of their strong magnetic fields, they produce strong beams of radio energy from the regions of their magnetic poles, and as they rotate these beams can point in our direction. As a result, we observe these neutron stars as radio bursts that pulse every 1 – 10 milliseconds. Hence their name.

Millisecond pulsars are rotating about as fast as neutron star can rotate, which makes them a bit of a mystery. Left by themselves, a pulsar gradually slows down over time. That means millisecond pulsars are either very young neutron stars that formed at near maximal rotation, or there must be some mechanism that causes them to spin more rapidly.

It’s generally thought that the latter process is the more common. A neutron star that is part of a binary system with a red giant companion can capture material from the companion star. As the material is captured, the angular momentum (rotation) of the material is transferred to the neutron star, thus increasing its rotation. This would explain why millisecond pulsars are often old pulsars with a companion. While this mechanism was initially proposed decades ago, over the years we’ve gathered a lot of evidence to support it.

When neutron stars are actively capturing material from their companion, the energy released as it falls to the neutron star produces intense x-rays. Such x-ray producing systems are known as x-ray binaries. These x-ray binaries can be quite active, but the radiation emitted by them tends to push the accreting material away. Thus over time an active x-ray binary will become less active, eventually entering a quiet period after which it may become active again. In the late 1980s it was observed that some x-ray binaries in the late stage of their active period contain radio millisecond pulsars. In 1998 a millisecond pulsar was observed within an active x-ray binary. Then in 2009 an accretion disk was discovered around a millisecond pulsar, indicating that the pulsar had been accreting material in the past.

Then last year in Nature new evidence was presented that further verifies the mechanism. The paper presents observations of an x-ray transient known as IGR J18245–2452. An x-ray transient is an object that emits x-rays for a time, then goes quiet for a time. There are several types of x-ray transients, but this particular one is a neutron star with a companion. In the past it had been observed as a radio pulsar. It then entered an active period and begin emitting x-rays with millisecond pulsations. After an active period of about a month, the x-rays went quiet, and the neutron star began to emit radio pulses again.

This not only demonstrates a clear connection between x-ray binaries and millisecond pulsars, but that these objects can shift between the two states on a fairly rapid pace. It seems that some neutron stars really do eat and run.

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It’s a well known law of physics that the speed of light (in a vacuum) is always the same, regardless of your frame of reference (essentially your vantage point). But this isn’t entirely true. It actually depends on how you define “speed”.

There are different ways to define speed, which is easy to see if you think about a car. One way to determine the speed of a car would be to look at the speedometer. If it says you are travelling 50 miles per hour (80 kilometers per hour), then that is the car’s speed at that moment in time. We sometimes call this the instantaneous speed. Another way to determine the car’s speed is to time how long it takes the car to travel a certain distance. So if we observe the car travel 50 miles in one hour, then we would say its speed if 50 mph. This is known as an average speed.

So what does this have to do with the speed of light? After all, if the speed of light is constant, doesn’t that mean the instantaneous speed and average speed will always be the same? They would be if light always travelled in a straight line (in flat space), but we know that space is actually curved. Gravity is the result of the curvature of space and time around a mass, so near a large mass like the Sun space is not flat. This means the average speed isn’t necessarily the same as the instantaneous speed.

We can see this with the car example again. Suppose two towns were 100 miles apart, and connected by a perfectly straight road. Then suppose we travel in a car with cruise control set at exactly 50 mph. The instantaneous velocity of the car is constant, so we would expect the travel time between the cities to be exactly 2 hours. But halfway on our journey, there is a bit of construction, so we must take a slight detour. Our speed remains 50 mph, but because of the detour our path is not perfectly straight. So instead of 2 hours, it takes us a bit longer, say 2 hours and 4 minutes. Thus the average speed is 48.4 mph.

We see this same effect with light. The mass of the Sun warps space near it, therefore light passing near the Sun has a slight detour. That means light from a planet on the other side of the solar system from earth reaches us a tiny bit later than we would otherwise expect. The first measurement of this time delay was in the late 1960s by Irwin Shapiro. Radio signals were bounced off Venus from Earth when the two planets were almost on opposite sides of the sun. The measured delay of the signals’ round trip was about 200 microseconds, just as predicted by general relativity. This effect is now known as the Shapiro time delay, and it means the average speed of light (as determined by the travel time) is slightly slower than the (always constant) instantaneous speed.

This effect has been used to determine the mass of certain neutron stars. In 2010, as described in a paper from Nature, a binary system consisting of a neutron star and a white dwarf was observed. The neutron star is a pulsar, meaning that it sweeps out a beam of intense energy as it rotates (kind of like a lighthouse). We see this as repeating radio pulses.

The two stars orbit each other in such a way that the white dwarf almost passes in front of the pulsar each orbit. This means the radio pulses pass close to the white dwarf before reaching us, and experiences a Shapiro time delay. Since the amount of the delay depends on the amount of spatial warping, which depends on the mass of the white dwarf, the team could use the delay to determine the mass of the white dwarf. Knowing that, they could determine the mass of the neutron star.

What they found was that this particular neutron star (PSR J1614-2230) is the most massive neutron star currently known, with a mass of about twice the Sun. It is so massive that we aren’t entirely sure how it exists.

In our everyday lives, a flight delay can be a bit of an annoyance. For light, a flight delay is a useful astronomical tool.

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In the 1990s the ROSAT x-ray observatory made an all-sky survey. By 2001, seven soft x-ray sources were found from the survey data, and shown to be neutron stars. They came to be known as the magnificent seven.

The magnificent seven differ from most neutron stars in the way they appear to us. Most of the neutron stars we observe are either young and hot, meaning they are sources of hard x-rays, or they are pulsars, meaning that their magnetic fields are aligned in such a way that it sweeps a beam of intense energy in our direction like a lighthouse.

The seven are cooler than other neutron stars. While young neutron stars can have surface temperatures of more than a million Kelvin, the seven have temperatures of 500,000 to 800,000 Kelvin, and they lack the hard x-ray spectrum of other neutron stars. Neutron stars cool over time, so by their temperatures they are middle-aged, being about 100,000 years old or so.

The light they give off follows a blackbody pattern, which is how we know their temperatures. This also means we can calculate something called the flux density. The flux density is a measure of the amount of light an object gives off per unit area. If you know the flux density and size of an object, then you can calculate its brightness, or absolute magnitude. This is useful because we can also measure how bright an object appears (apparent magnitude), and by comparing the two we can calculate the object’s distance.

The difficulty is that we don’t know the precise size of these neutron stars. From what we know of neutron stars in general they are likely between 12 and 20 kilometers in diameter, but it’s hard to be more precise. From their apparent brightness, this means they are between 500 to 1500 light years away, which is fairly close.

Ideally it would be nice to have an alternative distance measurement to compare with. For stars in this distance range we could use the method of parallax, which is similar to the depth perception of human vision. By measuring the position of a star at different times of the year (when the Earth has moved from one side of its orbit to the other), we can observe the apparent shift of the star relative to more distant stars. With a bit of trigonometry we can accurately determine a star’s distance. But these neutron stars don’t give off much visible light, so that trick doesn’t work with them.

Still, we do have some indirect evidence that our distance estimates are reasonable. Stars are not fixed in space, but instead are moving relative to each other. For distant stars this motion is too small to observe directly, but close stars exhibit this as proper motion, or the gradual changing of position relative to other stars. Large proper motion is an indication that a star is relatively close. We’ve observed such a proper motion with some of these neutron stars, as seen in the image above. This shift in only a few years is a good indication of the closeness of the neutron stars.

Because of their closeness and age, the magnificent seven provide an opportunity to learn more about the structure of neutron stars. In particular, further observation should provide insight on the equation of state of a neutron star’s interior, which would help us understand the interactions of dense, high-temperature nucleons.

Learning more about that would be pretty magnificent indeed.

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A neutron star is the remnant of a large supernova. When a large star explodes, a remnant of its core is compressed so tightly that the electrons are squeezed into protons, resulting in a mass of neutrons. A neutron star typically has a mass of about 2 solar masses, but it is only about 12 kilometers in diameter. Imagine taking two suns and squeeze it into the size of a small city, and you get the idea of how incredibly dense these objects are.

Neutron stars are often represented as a simple mass of neutrons, but we know that they actually have a complex structure. Just as the Earth has a crust, mantle and core, a neutron star has an iron crust, neutron mantle and core. We know from variations the rotation rate of pulsars that neutron stars undergo “starquakes”, that they likely have mountains (assuming you can call a rift a couple meters high a mountain range). They are geologically active. We also know they have atmospheres.

Just how we observe the atmosphere of a 12 kilometer wide neutron star light years away is pretty interesting. The surface temperature of a young neutron star is about a million Kelvin. This means it radiates a significant amount of light in the x-ray spectrum. If a neutron star had no atmosphere, then light should follow a distribution known as the blackbody curve. In other words, with no atmosphere the x-ray light should depend only on the surface temperature of the neutron star. But if it has an atmosphere, then the atmosphere will absorb some of the light and emit light at a different wavelength. So the x-ray spectrum would measurably differ from a blackbody spectrum. Just how it differs would depend upon the makeup and thickness of the atmosphere.

In 2009, Wynn Ho and Craig Heinke published a paper analyzing the x-ray spectrum of a neutron star known as Cassiopeia A. (Actually, Cassiopeia A is the name of the supernova remnant where the neutron star resides.) This is a young neutron star about 11,000 light years away. They found that the x-ray emission did not match a blackbody spectrum well, so they compared the spectrum to various model atmospheres such as pure hydrogen, helium, carbon, nitrogen, and oxygen. They found the best match to be a carbon atmosphere.

This carbon atmosphere isn’t like anything we’ve experienced. It’s only about 4 centimeters thick, and while it is “gaseous”, its density is about the same as diamond (3.5 grams/cc). Over time this atmosphere is expected to change. The gravity is so intense that carbon would eventually settle out of the atmosphere while lighter elements such as hydrogen and helium accumulate. Eventually even the lighter elements would settle to the surface.

But Cassiopeia A is still young, so for now it can enjoy its diamond sky.

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A while back I wrote about a phenomena known as fast radio bursts (FRBs). These short bursts of radio energy have been a bit of a puzzle. On the one hand they they have all the appearance of being astronomical in nature. For one thing, the frequencies of the signal are spread out so that higher frequencies arrive before lower ones. This is known as dispersion, and is an indicator having traveled through the interstellar medium. On the other hand, the signals are unusually strong, and their short duration is similar to radio interference from sources on Earth.  They’ve also only been detected at one radio telescope (the Parkes radio telescope in Australia). That is, until now.

It turns out another FRB was detected at the Arecibo observatory in Puerto Rico. It was actually detected in 2012, but an analysis of this event has recently been published in the Astrophysical Journal. Analysis of this radio burst shows it has the same overall properties as the ones observed at Parkes, which gives credence to the Parkes events being astronomical. But in this paper the authors take the analysis further.  They looked at the dispersion measure and found that the burst had a dispersion three times larger than the maximum dispersion found in objects within our galaxy in that region.  Since the amount of dispersion is a property of the amount of interstellar medium a signal passes through, this means the signal must come from well beyond our galaxy.  So the event is not only astronomical in nature, it is intergalactic.

So it seems that the mystery over the legitimacy of these FRBs is solved, but that leads us to the question about the cause of these bright radio bursts. One idea is that they could be caused by massive neutron stars as they collapse into black holes. Other possibilities could be neutron star mergers, or possibly even evaporating black holes (though this is a bit of a stretch). But now that we’ve identified FRBs, we can look for more of these events in radio observation data. By some estimates there could be 10,000 such events a day. Their short duration simply makes them easy to overlook.

It seems what was thought as merely distant noise is actually evidence of interesting new astrophysics.

Paper: L. G. Spitler et al., Fast Radio Burst Discovered in the Arecibo Pulsar ALFA Survey, The Astrophysical Journal (2014).

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Yesterday I talked about quark stars. These are hypothetical stars similar to neutron stars, but smaller and a bit more massive. Their gravity and density would be enough that instead of being largely made of neutrons (which are made of up and down quarks), they would be made of free up, down and strange quarks. If such quark stars exist, they would lie between neutron stars and solar mass black holes.

But how can we tell a quark star from a neutron star? If it has reached a stable state, then a quark star should be smaller than a neutron star, say 10 – 12 miles in diameter versus 15 – 20 miles in diameter, as you can see in the figure below. This is a difference of only a few miles. Given that these stars are light years away, making measurement of a star’s size precise enough to tell them apart is a huge challenge. It would help if we had a complete equation of state for a quark star so that we could compare things like size and temperature, but we don’t. So it can be very difficult to distinguish a quark star from a neutron star. That’s assuming quark stars exist, which we aren’t sure is the case.

Credit: CXC/M. Weiss

In 1992 a possible quark star was discovered, named RX J1856.5-3754 (great name, eh?) and it’s measured diameter was about 12 miles, which would make it too small to be a neutron star. But this was assuming it was about 200 light years away, and it was later determined to be about 400 light years away. As a result it is closer to 17 miles in diameter, which makes it too big to be a quark star. Measurements of its temperature also confirm it is a neutron star. This happens to be one of the closest neutron stars to Earth, and even then it took a great deal of effort to pin down its size. So it isn’t very likely that we will be able to distinguish quark stars from neutron stars by their size. At least not with our current instruments.

There may be another way to distinguish them. Neutron stars are quite hot when they form, with surface temperatures of several hundred thousand Kelvin. Since they don’t have any way to generate heat, they gradually cool over time. A neutron star massing 2 – 3 solar masses will eventually cool and shrink slightly until it reaches a stable state where the neutron pressure balances its gravity. But a more massive neutron star would cool and shrink until it reaches a critical point. If it is too massive to stabilize as a neutron star, it will reach a point where the up and down quarks can collide hard enough to become strange quarks. This would induce a phase change from neutron matter to strange matter (a mixture of up, down and strange quarks) within a few milliseconds.

This phase change would also produce large quantities of neutrinos. The quark star would be so dense that the neutrinos couldn’t escape all at once. But they could escape faster than photons. This means that after the phase change a quark star would cool faster than a neutron star. Interestingly, we’ve seen just this effect in a star known as 3C 58. This object appears to be a neutron star, but is cooling faster than expected. It’s possible then that 3C 58 is a quark star.

Of course to know for sure, we need to pin down its size and other properties. It might just be an unusual neutron star. So 3C 58 is a candidate quark star, not a confirmed one. There are a handful of other candidates as well.

At the moment, though, there is no confirmed quark star. They remain a hypothetical possibility.

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Imagine a star twice as massive as the Sun, compressed to the size of a city. All that matter squeezed into a sphere about 15 miles wide. Such an object is known as a neutron star. The matter of a neutron star is so dense and its gravity is so strong that atoms cannot support themselves. Instead they collapse, with the electrons being squeezed into the nuclei until what remains is a mass of neutrons. Hence the name.

The exact structure of a neutron star is still a bit of a mystery. At a broad level, they are just large balls of neutrons, but they have strong gravitational and magnetic fields that can affect their structure, and then there are the neutrons themselves. How do we understand “stuff” made out of neutrons, when what we see around us are made of atoms? The key is to determine its equation of state.

The equation of state of a material determines its bulk properties. If you’ve had a chemistry class you are likely familiar with the ideal gas law, which describes how the pressure, temperature and volume of a gas are related. The ideal gas law is an equation of state for a simple gas.

We have observed the gas law experimentally, but we can also derive its properties mathematically using kinetic theory. Since a gas tends to be relatively low density, we can treat the atoms or molecules almost as billiard balls that bounce against each other. Modelling a gas in this way gives us the ideal gas law.

Equations of state are the key to understanding stars and the like, because stars are a balance between the weight of the star’s matter and its pressure. Knowing the equation of state for a star’s material means we can calculate things such as size and temperature. Likewise if we know a stars size and temperature we can gain an understanding of the equation of state.

Neutrons (and electrons) obey a different equation of state from that of a simple gas. It is derived from Fermi-Dirac statistics, which takes into account what is known as quantum degeneracy pressure. If you are familiar with the Pauli exclusion principle, which states that no two electrons can occupy the same state, then you are familiar with one example of degeneracy pressure. The basic idea of degeneracy pressure is that there is a minimum volume into which you can squeeze a neutron. Beyond that limit the degeneracy pressure gets too large for you to overcome.

This doesn’t mean you can never overcome that pressure. You can overcome the degeneracy pressure if you have enough mass. Based on the neutron equation of state that limit is a bit more than 3 solar masses. Anything bigger than that, and the neutron star is so massive it collapses into a black hole. A similar thing occurs with white dwarfs. In a white dwarf star the weight of its mass is balanced by the degeneracy pressure of the electrons. As long as the white dwarf is less than 1.4 solar masses (the Chandrasekhar limit), then everything is fine. But if the white dwarf has more mass, then it will collapse into a neutron star.

There is, however, one important difference. Electrons are elementary particles, which means they aren’t made of anything smaller. So when a white dwarf is more massive than the Chandrasekhar limit it can’t do anything but collapse into a neutron star. But neutrons aren’t elementary particles. They are made up of a trio of quarks. So when if the mass of a neutron star is close to the neutron limit, then it might not collapse into a black hole. It might collapse into a quark star.

In a quark star, instead of being clumped into neutrons the quarks would move freely, making the star a mass of quarks, as you can see in the figure above. Of course this means that a quark star needs an entirely different equation of state. This is further complicated by the fact that the interior of quark stars would have so much heat and energy that some of the neutron quarks (up and down quarks) could transform into strange quarks. (Not strange in that they are weird, but strange because they are named strange quarks). The interior of a quark star could then be strange matter, and we don’t know exactly what its equation of state would be.

We don’t have a solid theoretical understanding of quark matter, but most models predict that quark stars would be slightly smaller than neutron stars. The one catch is that the largest quark stars could be as large as the smallest neutron stars, so it might be difficult to distinguish them. There have been a few observations of stars that might be quark stars, but so far there are no confirmed quark stars.

Then again it might be the case that quark stars are unstable. This would mean that large neutron stars might enter a short quark star period before collapsing into a black hole, but there would never be a long-lived quark star. We aren’t really sure at this point.

In the end it will all come down to their equation of state.

The post Equations of State appeared first on One Universe at a Time.

About a year ago in Nature astronomers reported evidence of an anti-glitch in the magnetar 1E 2259+586. You might remember from yesterday’s post that a magnetar is a neutron star with an extremely strong magnetic field. This particular magnetar is also a pulsar, meaning that the intense x-ray beams that stream from the magnetar’s polar region happen to be aligned so that we see it flash regularly. You can think of a pulsar as a kind of cosmic lighthouse, if you will.

The rate at which a pulsar flashes is determined by the rate at which it rotates. So if you see a pulsar flash 10 times a second, you know it rotates once every tenth of a second. (It can be a bit more complicated than that, but you get the idea). The rotation of a pulsar is usually pretty regular. Pulsars can gradually slow down over thousands or millions of years due to its radiated energy, but this is a gradual process.

Occasionally, however, a pulsar will speed up just a bit in a very short time (on the order of minutes). This rapid speed-up is known as a glitch. After a glitch the pulsar will return to its previous speed within weeks or months, and then continue with its gradual, thousands-year slowdown.

It is generally thought that these glitches are due to changes in the shape of the neutron star. Because of their rotation, neutron stars should bulge a bit at their equator. The faster their rotation, the greater the bulge. As a neutron star gradually slows down, its equatorial bulge would tend to decrease. But it’s thought that the neutron matter in the crust of the star is fairly rigid. This means that as the pulsar gradually slows down, stresses would build up in the pulsar’s crust. This would eventually reach a breaking point. The crust would then collapse to form a more stable, less bulgy shape. Because of this new shape, the pulsar would speed up a bit, just like a spinning figure skater who spins faster when she pulls her arms inward.

We have observed lots of glitches in pulsars, and they all behave in a similar way. But the Nature article presents an observation of an anti-glitch. In other words, researchers observed a rapid slowdown in this particular magnetar. You can see this slowdown in the graph below. Such an anti-glitch is very strange, because it means either it was caused by an external interaction, or our understanding of neutron stars will need to be revised.

The slowdown of this magnetar actually happened in two stages. There was an initial anti-glitch, and then a second shift that could be modeled as a glitch or a second anti-glitch, depending on how you look at it. This means the magnetar had a quick slowdown, then a second adjustment a little while later. This could have been caused by a twisting and reconnection of the star’s magnetic field. On the Sun, such phenomena causes solar flares and coronal mass ejections. If a similar process occurred on the magnetar, then it could slow it down by transferring some of the angular momentum from the star to the material ejected and the magnetic field. But such a process would likely cause an x-ray burst during both the initial anti-glitch and the secondary readjustment. Such activity was observed during the first anti-glitch, but not the second, so this doesn’t seem very likely.

The alternative is that the magnetar is rotating differentially. That is, the superfluid core of the magnetar is rotating at a different speed than its crust. If that is the case, then as the crust shifted it could some rotation from the superfluid to the crust. The resulting transfer would cause the initial slowdown, and then the secondary shift would be caused by later readjustment into a more stable state. This model matches the observations, but it would mean that neutron stars can rotate differentially, which we didn’t think happened. If that’s the case, then we will need to reexamine the glitch model as well, since that may be caused by differential rotation as well.

So it looks like we’ll need to look at pulsar glitches a bit more closely.

The post Glitch and Anti-Glitch appeared first on One Universe at a Time.