Astronomy

How Would a Neutron Star Actually Appear?

How Would a Neutron Star Actually Appear?


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Having seen many pictures produced by artists of neutron stars and planets that orbit some of them, I was wondering how a pulsar would appear to a human being, in visible light (assuming the intense radiation etc. doesn't kill us in the process).

As I understand, the pulsar's beam is projected from the star's magnetic poles rather than rotational poles, which are not necessarily in line with each other. Given that pulsars rotate extremely quickly and the beam could be visible across vast distances - such as if it were shining through the pulsar's nebula - would it appear as a straight line, curved line or perhaps a cone? This is assuming the beam can be seen in visible light.

Given the incredible density of neutron stars and their small physical sizes, would the night sky be visibly distorted to the point where (for example) just after sunset on a hypothetical planet, one could possibly observe other planets near or behind the star that would otherwise be blocked by it?

Given their small surface areas, would a neutron star still appear as luminous as say, the Sun, at a similar distance? How close would you have to get to a neutron star for its apparent magnitude to match the Sun's from Earth?


Your question is too general, you need to get to specific examples.

First, very few neutron stars are pulsars. Pulsars are either a brief phase during a pulsar's spin-down at the start of a neutron star's life, or they are the product of the spin-up of a neutron star in a binary system. Most neutron stars fall in neither of these categories.

A standard neutron star will look like any other star at a similar temperature. Most of them will be very hot indeed - 100,000 K or more, though the cooling histories of neutron stars are still uncertain and depend on some exotic physics. Such an object is "white hot" - it emits black body radiation at all frequencies visible to the eye (as well as lots more at UV wavelengths).

How close would you have to get for it's apparent luminosity/magnitude to match the Sun? Well that depends on the size and temperature of the neutron star. Most are thought to have a diameter of 20 km. The way you would do the calculation is equate the blackbody radiative flux per unit area at a given distance to the solar radiation constant of about 1300 W per square metre. However, there are two wrinkles for a neutron star: First, the radiation is gravitationally redshifted, so the temperature we measure is lower than the temperature at the surface. Second, General Relativity tells us that we can see more than just a hemisphere of the neutron star - i.e. we can see around the back - and this increases the flux we observe. These are roughly factor of two effects, so just to get an order of magnitude estimate, ignore GR and assume a 10 km radius NS with $T=10^{5}$ K.

Using Stefan's law for a blackbody, then at a distance $d$, we have that $$frac{4 pi r^2}{4pi d^2} sigma T^4 = 1300 W m^{-2},$$ where $sigma$ is the Stefan-Boltzmann constant.

For $r=10$ km, then $d=7 imes 10^{8}$ m, which is coincidentally about a solar radius. Of course this distance depends on the square of the temperature, so a younger NS with $T=10^6$ K, then $d sim 1$ au.

These are the distances where the total flux at all wavelengths would be similar to that from the Sun. To do the calculation just for the visible range we need to account for the bolometric correction, which converts a visual magnitude to a bolometric magnitude. The bolometric correction for the Sun is $sim 0$, whereas the bolometric correction for a very hot star could be -5 mag. This means that only 1% as much flux from the hot neutron star emerges in the visible band compared with sunlight. This means that the distances calculated above, if we require the visual brightness of the neutron star be similar to the Sun, must be reduced by a factor of 10.

To turn to pulsars. Note that the pulsed radiation does have an optical component and pulsed optical radiation has been seen from a number of pulsars. Optical synchrotron emission would just appear to be a periodic, intense brightening of the pulsar, as the beam sweeps across the line of sight. If you were not in the line of sight, then you would not see the pulsed optical emission. If you could observe the beam passing through nebulosity or some other medium around the pulsar then yes there may well be some effects you could see in terms of ionisation or scattered light coming from along the beam path.

Lastly, the gravitational lensing effect. Yes, this should be strong close to a neutron star. The deflection angle (in radians) is given by $$ alpha = frac{4GM}{c^2 b},$$ where $b$ is how close the light passes to the neutron star and $M$ is the neutron star mass. Expressing $b$ in terms of the 10km radius of the neutron star: $$ alpha simeq 0.83 left(frac{M}{1.4M_{odot}} ight) left(frac{b}{10 km} ight)^{-1},$$ where strictly speaking this formula is only valid for $alpha ll 1$.

So consider a planet directly behind the neutron star at a distance of 1 au. The light from this would only need to be bent through an angle of $sim 2 imes 10 km/1 au sim 10^{-7}$ radians in order to be seen from a planet diametrically opposite at a distance of 1 au. So this is easily possible. However, the image would likely be highly distorted, especially if the neutron star was spinning. It would not look dissimilar to this simulated black hole image, but with a bright neutron star in the middle rather than a black disc.


I can kind of give an answer, but I welcome correction.

I was wondering how a pulsar would appear to a human being, in visible light

It wouldn't look like much in the visible light spectrum unless there was a significant nebula, then we might see the effect of the pulsar on the nebula, but not the pulsar itself. X-rays and radio waves aren't visible, and if the pulsar wasn't directed at us, we wouldn't see it pass through empty space.

Neutron Stars are generally too hot for us to see. If one was to cool down significantly, to maybe 10 or 20 thousand degrees on the surface, then it might glow visibly blue and look like the brightest star in the sky, still just a point in the sky, but the brighest point in the sky at 1 AU.

But mostly they're too hot to glow in visible light.

What you might see from 1 AU from a Neutron Star could be the accretion disk. Matter that falls into a Neutron Star gets very hot and the energy if impact is far greater than the energy of fission, so as matter gets close to the Neutron star and spirals in, you're probably talking x-rays and gamma rays, but you might see a visibly glowing accretion disk at some distance out, perhaps in a gradually decaying orbit. In effect, what you could see would depend on what's around the Neutron star than it would depend on the star itself.

As I understand, the pulsar's beam is projected from the star's magnetic poles rather than rotational poles, which are not necessarily in line with each other. Given that pulsars rotate extremely quickly and the beam could be visible across vast distances - such as if it were shining through the pulsar's nebula - would it appear as a straight line, curved line or perhaps a cone

The problem here is, you can't see the beam. You see light as it's pointed towards you, you can't see a light beam in space (even if it's visible light).

You can see a beam not pointed at you in the atmosphere because of reflection off dust and water molecules in the air.

(see little picture)

In space, matter is far more spread out. It's true that a pulsar can light up part of a nebula, though the nebula may also glow on it's own anyway (I'm not 100% sure on that), but a Nebula is very large and very spread out. To see it from the naked eye, I don't think you'd see much other than perhaps a large glow.

If you could see a pulsar beam, it takes light 8 minutes to for light to travel 1 AU, and a pulsar can rotate hundreds of times, perhaps thousands of times in 8 minutes, so if you could actually see the beam, it would be enormously curved, like a spiral. The light itself would travel in a straight line but since the source of the light was rapidly rotating it would appear like this (picture below), if there was sufficient material for the light to reflect off of (which there probably wouldn't be, not within 1 AU).

In reality, it would look nothing like that, but if you could see the the beam, that's what it would look like. What that spiral looks like from a single point is a pulsar, off, on, off, on, off, on, etc.

Also, the light never travels in a spiral, it travels in a direct line away from the Pulsar, but like the water spiral here, which falls down in a straight line, but it looks like it falls in a spiral (if that makes sense).

Given the incredible density of neutron stars and their small physical sizes, would the night sky be visibly distorted to the point where (for example) just after sunset on a hypothetical planet, one could possibly observe other planets near or behind the star that would otherwise be blocked by it?

Well, for starters, without a sun there, planets would probably not be visible. If the Neutron Star glowed brightly due to a hot accretion disk you couldn't see anything behind it cause the brightness of it would make seeing light bent around it pale by comparison.

Now if the Neutron star was dark, to our eyes, then we could see gravity lensing around it, but stars, not planets cause planets would be dark. (The moon would be very dark too, visible more by what it blocks than what it shines). The lensing would be quite small however. Visible lensing would only be a few times the diameter of the Neutron star, maybe 100 miles across, which, 93 million miles away is really tiny. You might see some odd warping of a star here or there when properly lined up, but to see any interesting visible lensing you'd need a pretty powerful telescope.

Given their small surface areas, would a neutron star still appear as luminous as say, the Sun, at a similar distance? How close would you have to get to a neutron star for its apparent magnitude to match the Sun's from Earth?

Kind of touched on this above. The Neutron Star can give off a lot of energy in it's pulsar beam, but it's mostly x-rays, not visible light. How bright it is would depend on how much material is falling into it at the time, so there's no right answer to how close the Earth would need to be to have equal brightness. It's a different kind of brightness too, mostly not visible light. But there's no way to answer that question cause it depends on too many things.

When a Neutron star is just formed (which usually happens after a supernova so there's enormous energy released), but when the star just forms, it's maybe 12-15 miles in diameter but it's surface temperature can be (guessing) perhaps a billion degrees, though it cools very quickly. A very young Neutron Star might emit more energy to our sun, though much of it would be in Neutrinos that would largely pass through the Earth. But that level of energy output wouldn't last long. It would cool down to about a million degrees within a few years. Source.


If we assume that the pulsar's surface is like that of other neutron stars, unless the beam is pointed at you, it will look like other neutron stars. RX J1856.5-3754 (https://en.wikipedia.org/wiki/RX_J1856.5-3754) is one of very few neutron stars we can see at optical wavelengths. It has a visual magnitude of 25.6 at ≈61 parsecs (the Sun's apparent visual magnitude at that distance would be about 8.75). Turning the cranks I get an absolute visual magnitude MV of 21.67 and a visual luminosity of ≈.00000018. Taking the square root, I'd need to be about .00043 AU away, or about a tenth the diameter of the Sun for it to be as bright as the Sun is from Earth, visually. At only 14 km or so in diameter, it would very small, about 4.7% the apparent diameter of the Sun--not much more than a point. But as noted above, the actual, bolometric, luminosity of the neutron star would be much, much higher. A person looking at it (unprotected) from that distance it would be blinded and fried in short order. One might also be far enough down the gravity well at that distance that the relativistic effects that dim the star would be less and the star would appear even brighter. And one might note some tidal effects as well. This situation calls for the "General Products Hull" Larry Niven used for his story, "Neutron Star!"


The statement that a Pulsar will look like a black body with a high temperature does is not supported by the evidence. Optical measurements of the Crab Pulsar show a flat spectrum see this. This is a result of the optical emission being from synchrotron radiation rather than the hot surface.

The recent Gaia DR2 results include the Crab Pulsar as DR23403818172572314624 this has a BP-RP colour of 1.0494 which equates to a temperature of around 5,100 K from the DR2 HR diagram. This is very similar to the temperature shown in the DR2 data. This needs to be used with caution as the calibration is for a star with a 'Black Body' atmosphere rather than an 'atmosphere' radiating due to synchrotron Radiation. See this for the full DR2 data.

We don't know how large the radiating 'atmosphere' is but a rough idea could be calculated from the DR2 data in the link above. However the parallax (distance) uncertainty is quite large so would need a better distance measurement.


How Would a Neutron Star Actually Appear? - Astronomy

Q&A: Supernova Remnants and Neutron Stars

Q:
How bright would this glow be compared to other self luminous and reflective objects (i.e., what magnitude would it appear to be at one AU)?

What how strong would this glow be in different parts of the spectrum (i.e., visible light, IR, etc.)?

A:
A neutron star is born very hot (leftover heat from when the star was still "normal" and undergoing nuclear reactions) and gradually cools over time. For a 1 thousand to 1 million year old neutron star, the surface temperature is about 1 million Kelvin (whereas the Sun is 5800 K).

I will continue to make comparisons to the Sun (one reason is that it is at a distance of 1 AU). To determine it's intrinsic brightness, we need to know the size of the neutron star, which turns out to be about 10 km. The Sun is much bigger (solar radius 7x10 5 km). The intrinsic brightness or luminosity is proportional to the square of the size and the fourth power of the temperature the luminosity of a neutron star compared to the Sun is (10/7x10 5 ) 2 x (10 6 /5800) 4 , which is about 1. Therefore, a 1 million Kelvin neutron star is about the same intrinsic brightness as the Sun.

However, because it is much hotter, it is brightest at X-ray wavelengths [whereas the Sun is brightest at visual wavelengths this is just like a hotter blowtorch is blue (or shorter wavelength), and a cooler one is red.] So if you had X-ray eyes, a neutron star at a distance of 1 AU would appear as bright as the Sun (in visual). On the other hand, a neutron star is quite a bit dimmer at visual wavelengths it turns out to be about -10th magnitude at visual at a distance of 1 AU, ie a little dimmer than the Moon.


2 Answers 2

We believe neutron stars cool down very fast, compared to other stellar remnants, so that they are only "hot" for a comparatively short time. Therefore despite their novel phase/ state, their magnetic/ superfluidity/ possible reheating phenomenae, and possible infalling material, most neutron stars quickly become cold, dead, tiny, unobservable cinders in just a few million years. In between they would presumably be ordinary black body sources, and radiate in the visible spectrum depending on their temperature as they cool, but you'd have to be EXTREMELY close to see them as more than dots, or at all..

We can't be certain because they cease to be currently observable via light, X rays or other electromagnetic radiation within a short time, of perhaps a few hundreds of thousands or.millions of years.

There could be accretion effects, and lensing effects, but in both cases they are very limited in scale and visibility by the neutron star's tiny size - unlike black holes which can apparently be any size, neutron stars can only be tiny, tiny objects (typically 10 miles across,1.4 times the mass of our sun, maximum mass believed to be a little larger, between 2.3 and 3.0 solar masses). If they gained much more mass via accretion, collision, or other means, they'd just collapse into a black hole.


How massive can neutron stars be?

Emission of gravitational waves during a neutron star merger. Credit: Goethe-Universität Frankfurt am Main

Astrophysicists at Goethe University Frankfurt set a new limit for the maximum mass of neutron stars: They cannot exceed 2.16 solar masses.

Since their discovery in the 1960s, scientists have sought to answer an important question: How massive can neutron stars actually become? By contrast to black holes, these stars cannot gain in mass arbitrarily past a certain limit there is no physical force in nature that can counter their enormous gravitational force. For the first time, astrophysicists at Goethe University Frankfurt have succeeded in calculating a strict upper limit for the maximum mass of neutron stars.

With a radius of about 12 kilometres and a mass that can be twice as large as that of the sun, neutron stars are amongst the densest objects in the universe, producing gravitational fields comparable to those of black holes. Whilst most neutron stars have a mass of around 1.4 times that of the sun, massive examples are also known, such as the pulsar PSR J0348+0432 with 2.01 solar masses.

The density of these stars is enormous, as if the entire Himalayas were compressed into a beer mug. However, there are indications that a neutron star with a maximum mass would collapse to a black hole if even just a single neutron were added.

Together with his students Elias Most and Lukas Weih, Professor Luciano Rezzolla, physicist, senior fellow at the Frankfurt Institute for Advanced Studies (FIAS) and professor of Theoretical Astrophysics at Goethe University Frankfurt, has now solved the problem that had remained unanswered for 40 years: With an accuracy of a few percent, the maximum mass of non-rotating neutron stars cannot exceed 2.16 solar masses.

The basis for this result was the "universal relations" approach developed in Frankfurt a few years ago [www.goethe-university-frankfurt.de/60913695/15]. The existence of "universal relations" implies that practically all neutron stars "look alike," meaning that their properties can be expressed in terms of dimensionless quantities. The researchers combined these "universal relations" with data on gravitational-wave signals and the subsequent electromagnetic radiation (kilonova) obtained during the observation last year of two merging neutron stars in the framework of the LIGO experiment. This simplifies calculations tremendously because it makes them independent of the equation of state. This equation is a theoretical model for describing dense matter inside a star that provides information on its composition at various depths in the star. Such a universal relation therefore played an essential role in defining the new maximum mass.

The result is a good example of the interaction between theoretical and experimental research. "The beauty of theoretical research is that it can make predictions. Theory, however, desperately needs experiments to narrow down some of its uncertainties," says Professor Rezzolla. "It's therefore quite remarkable that the observation of a single binary neutron star merger that occurred millions of light years away combined with the universal relations discovered through our theoretical work have allowed us to solve a riddle that has seen so much speculation in the past."

The research results were published as a Letter of the Astrophysical Journal. Just a few days later, research groups from the USA and Japan confirmed the findings, despite having so far followed different and independent approaches.

Gravitational-wave astronomy is expected to observe more such events in the near future, both in terms of gravitational-wave signals and in the more traditional frequency ranges. This will further reduce uncertainties about maximum mass and lead to a better understanding of matter under extreme conditions. This will be simulated in modern particle accelerators, for example at CERN in Switzerland or the FAIR facility in Germany.


As I understand it, at the surface of a neutron star, most light is emitted in the X-ray range. In the visible range, red is emitted at about the same as blue and the other colors, so it would appear white to human eyes.

Everything in the universe is spinning. Spinning planets and their spinning moons orbit around spinning stars, which orbit spinning galaxies. Like all stars, our sun rotates on its axis. You can’t tell because staring at the sun long enough will permanently damage your eyeballs.


What does a neutron star actually look like?

Title: (1) The relativistic “looks” of a neutron star, H.P. Nollert, H. Ruder, H. Herold and U. Krauss, in Astronomy and Astrophysics and (2) Light Deflection Near Neutron Stars, U. Krauss, in Relativistic Astrophysics

Status: Open access, see here and here

Today we will look at two papers which attempt to answer the question posed in the title – what does a neutron star look like up-close? In the process, they illustrate (1) a cool feature of relativity which means we can see the far-side of a neutron star from a single vantage point and (2) that this feature is relevant for understanding astrophysical observations.

In the absence of a gravitational field, photon orbits are straightforward – they travel in straight lines! However, in the presence of a strong gravitational field, this is no longer the case. The gravitational forces of a massive body will cause the fabric of space around it to curve. The denser the object, the more spacetime will curve. Photons will follow the contours of space time and therefore travel along curved orbits.

This is true even for stars that are not particularly dense (such as our Sun) – there will still be a small deflection of light that travels past the Sun due to the curvature of spacetime in that region (see Figure 1). This effect was predicted by Einstein and successfully measured in 1919. This was achieved by taking photographs of a region of the sky centered on the Sun during a total solar eclipse (the solar eclipse meant that the positions of stars in that region were visible and not washed out by light from the Sun). Then, another photograph was taken of those same stars when the Sun was far from that patch of the sky. The two photographs where then compared and the conclusion was that light was indeed deflected, confirming the prediction of general relativity.

Figure 1: The gravity of the Sun bends the spacetime around it. Light will follow along the curved spacetime fabric. As the light from a background star passes by the Sun, it is deflected, and therefore the apparent position of the star is different to the actual position of the star. Image source: http://hyperphysics.phy-astr.gsu.edu/hbase/Relativ/grel.html

Photon orbits around a neutron star

As in the case of the Sun, the gravity around a neutron star causes the spacetime to bend around it. A neutron star contains the mass of the Sun compressed into an object that is the size of a city. Therefore, relativistic effects such as the deflection of light will be even more pronounced near a neutron star compared to the Sun. Understanding the trajectories of photons is crucial for determining what a relativistic object such as a neutron star will look like.

We usually think about space as being three dimensional, i.e. described in terms of three co-ordinates, say . However, in General Relativity, we need four co-ordinates, including time, i.e. . The four co-ordinates are closely interlinked the value of the fourth co-ordinate (time) has an effect on the other three co-ordinates, hence we need it for a complete description of the geometry of spacetime.

For an object with spherical symmetry (which is very relevant for astrophysics, where gravitating bodies will typically have spherical geometry) the curvature of spacetime will be described by the Schwarzschild metric. This metric tells us how the spacetime will curve near a neutron star and, in particular, how the curvature will change as a function of the mass of the neutron star. To read more about the Schwarzschild metric, you can find some background here and here.

If we consider the equatorial motion of a photon (i.e. we only care about trajectories along a plane through the equator of the star), then the motion of the photon can be described with three co-ordinates, () where and are polar co-ordinates (see Figure 2).

Figure 2: Polar co-ordinates describe the geometry of an equatorial slice through a neutron star. Image source: http://www1.kcn.ne.jp/

The equations of motion can be solved numerically to find the trajectory of a photon (i.e. the angular position of the photon at a particular radius .) We notice that the trajectory is a function of the parameter which is called the impact parameter. The impact parameter is the distance of the photon from a line through the centre of the star (see Figure 3).

Figure 3. This figure demonstrates the definition of the impact parameter b.The black dot corresponds to the centre of the neutron star.

The value of the impact parameter determines what kind of motion will occur around the neutron star. There are two different regimes: (1) and (2) where is the critical value of the impact parameter. Some examples of the two types of orbits are shown below for the two regimes in Figure 4 and 5 respectively. One thing we notice about the motion of photons in the vicinity of a neutron star is that not only can the photons be deflected as in the case of our Sun, the photons can fall into orbits around the neutron star (see Figure 4).

Figure 4: Orbits of a photon around a neutron star in the regime , with increasing from top to bottom. Figure 2 in “Light Deflection Near Neutron Stars”.

Figure 5: Photon orbits around a neutron star in the regime , with with decreasing from top to bottom. Figure 3 in “Light Deflection Near Neutron Stars”.

Radiation from the neutron star surface

Due to the extreme deflection of photons around a neutron star, what a neutron star looks like is different to the physical reality. Our human minds have adapted to Earth’s gravity and assume that the paths taken by all photons are straight. This is not a valid assumption on the surface of a neutron star, where the gravitational forces are 2×10 11 times stronger than on Earth.

The radiation emitted by the neutron star bends in such a way that parts of the rear surface (which would normally be invisible) become visible (see Figure 6). In fact, it is possible for photons to trapped along an orbit (see Figure 4), therefore causing the entire surface to be visible. The mass of an object determines its Schwarzschild radius . An object with a radius smaller than its Schwarschild radius will be a black hole. Therefore, the closer the the object’s radius is to the Schwarschild radius, the more “black-hole”-like it is, and the more spacetime will curve around it.

Therefore, the quantity that determines the amount of deflection experienced by a photon near a neutron star is the ratio of the Schwarzschild radius to the radius of the neutron star $ latexR/r_s$. As this quantity decreases, more and more of the rear surface of the neutron star is visible, as depicted in Figure 6.

Figure 6: Four images of neutron stars with the same radius but different masses and hence different . The ratio decreases from top to bottom. Figure 6 in “Light Deflection Near Neutron Stars”.

Pulse profiles from neutron stars

Understanding light deflection around neutron stars is important for determining its X-ray pulse profile. This phenomenon is discussed in detail in this astrobite the authors of today’s bite summarise a simple model which I will discuss briefly here. In an accreting X-ray binary (which is a neutron star in a binary system that accretes from its non-neutron star companion), matter is channeled along the magnetic field lines to the poles, where the kinetic energy is turned into X-ray radiation. We observe regular pulses of this X-ray radiation as the neutron star rotates. Naturally, the radiation emitted close to the poles of the neutron star will be affected by light deflection due to general relativity.

Figure 7: X-ray pulse profiles from an accreting x-ray binary for (right column) and (left column). corresponds to the flux from one of the polar caps and corresponds to the flux from the other polar cap. is the flux from both polar caps combined. Increased photon deflection (i.e. decreasing reduces the modulation in the flux. Figure 12 in “Light Deflection Near Neutron Stars”.

X-ray emission comes from the poles of the neutron star. Without any light deflection, both poles of the neutron star are only visible during part of the period of the neutron star and vanish at other times, therefore the X-ray flux will modulate over the neutron star’s period. When is small (the neutron star is very compact), there is substantial light deflection and therefore almost the entire surface of the neutron star is visible all the time. Because both poles are visible all the time, we always see an X-ray flux. This means there will be essentially no flux modulation when is small, as seen in Figure 7.

Relativity is not simply a vital building block of fundamental theoretical physics, it plays a direct role in observational astrophysics. We can use it to understand the radiation we receive from extreme, compact objects such as neutron stars and even learn more about the mysterious content of their interiors – for a more detailed discussion of this topic, check out this astrobite!


Stephen Hawking's favorite places in the universe (pictures)

Now imagine you could take all three of these stars and run them through the biggest compactor in the universe, smashing them down to create an exotic object -- a sphere only 19 miles (30 km) across.

Put even more simply, it's like taking those three massive stars and compressing them down to be roughly the size of the city of Denver.

"Neutron stars are as mysterious as they are fascinating," said Thankful Cromartie, a graduate student at the University of Virginia and a fellow at NRAO. "These city-sized objects are essentially ginormous atomic nuclei. They are so massive that their interiors take on weird properties. Finding the maximum mass that physics and nature will allow can teach us a great deal about this otherwise inaccessible realm in astrophysics."

The measurement of this neutron star actually came as part of NRAO's search for gravitational waves .

"At Green Bank, we're trying to detect gravitational waves from pulsars," said West Virginia University professor Maura McLaughlin. "In order to do that, we need to observe lots of millisecond pulsars, which are rapidly rotating neutron stars. This [discovery] is not a gravitational wave detection paper but one of many important results which have arisen from our observations."

Neutron stars and pulsars are the densest "normal" objects that we know of. The only thing more dense is a black hole, which is certainly not normal. As such, this specific pulsar discovery is as close as we've ever come to defining the line between the normal and the most puzzling, mysterious and exotic objects in existence.


How Would a Neutron Star Actually Appear? - Astronomy

If the core mass is between 1.4 and 3 solar masses, the compression from the star's gravity will be so great the protons fuse with the electrons to form neutrons. The core becomes a super-dense ball of neutrons. Only the rare, massive stars (about 8 to 25 solar masses) will form these remnants in a supernova explosion. Neutrons can be packed much closer together than electrons so even though a neutron star is more massive than a white dwarf, it is only about the size of a city.

The neutrons are degenerate and their pressure (called neutron degeneracy pressure) prevents further collapse. Neutron stars are about 30 kilometers across, so their densities are much larger than even the incredible densities of white dwarfs: 200 trillion times the density of water (one sugar cube volume's worth has a mass = mass of humanity)! The superior resolution of the Hubble Space Telescope has enabled us to directly image a few of these very small objects in visible light. The first image in visible light of a lone neutron star is shown in the figure below (the arrow points to it). Even though it is over 660,000 K, the neutron star is close to the limit of HST's detectors because it is at most 27 kilometers across. This one is at most 400 light years away. The closest known neutron star is about 200 light years away.

Pulsars

Normal variable stars (stars near the end of their life in stages 5 to 7) oscillate brightness by changing their size and temperature. The density of the star determines the pulsation period---denser stars pulsate more quickly than low density variables. However, normal stars and white dwarfs are not dense enough to pulsate at rates of under one second. Neutron stars would pulsate too quickly because of their huge density, so pulsars must pulsate by a different way than normal variable stars. A rapidly rotating object with a bright spot on it could produce the quick flashes if the bright spot was lined up with the Earth. Normal stars and white dwarfs cannot rotate fast enough because they do not have enough gravity to keep themselves together they would spin themselves apart. Neutron stars are compact enough and strong enough to rotate that fast. The pulsar at the center of the Crab Nebula rotates 30 times every second. In the figure below, it is the left one of the two bright stars at the center of the Hubble Space Telescope image (right frame).

(Click the triangle in the top right corner to view the animation and click it again to reset it)

The 1/1000th of second burst of energy means that the pulsars are at most (300,000 kilometers/second) × (1/1000 second) = 300 kilometers across. This is too small for normal stars or white dwarfs, but fine for neutron stars (they are actually less than 30 kilometers across). When neutron stars form, they will be spinning rapidly and have very STRONG magnetic fields (10 9 to 10 12 times the Sun's). The magnetic field is the relic magnetic field from the star's previous life stages. The magnetic field is frozen into the star, so when the core collapses, the magnetic field is compressed too. The magnetic field becomes very concentrated and much stronger than before.

Why would neutron stars be fast rotators? Conservation of angular momentum! Just as a spinning ice skater can spin very fast by pulling in her arms and legs tight about the center of her body, a star will spin faster when it brings its material closer to its center. The angular momentum of an object = its mass × its equatorial spin speed × its radius. The mass remains constant. In order to keep the angular momentum constant the spin speed must increase if the radius decreases. This will keep the product of spin speed × radius the same value. A slowly rotating red giant star will have the same angular momentum when it becomes a tiny, fast rotating neutron star. See the Angular Momentum appendix for other examples.

Lighthouse Model

The neutron star's magnetic field lines converge at the magnetic poles, so the charges get focused and a narrow cone of non-thermal radiation is beamed outward. If the beam sweeps past Earth, you see a flash of light. However, given the wide range of angles the magnetic poles could be aligned in space, it is more likely that the beam will miss the Earth. There are probably many more pulsars out there that cannot be detected because their beams do not happen to cross our line of sight.

The energy of the non-thermal radiation beam comes from the rotational energy of the pulsar. Since the light energy escapes, the production of the energy beam robs energy from the pulsar, so the pulsar's rotation slows down (angular momentum does slowly decrease). Another equivalent way to view the process is from Newton's 3rd law of motion. The magnetic field exerts a force on the charged particles, speeding them up. The charged particles exert a reaction force on the magnetic field slowing it and the pulsar down. Eventually, the pulsar dies away when the neutron star is rotating too slowly (periods over several seconds long) to produce the beams of radiation.

Every now and then, a ``glitch'' is seen in the pulse rate of a pulsar. The pulsar suddenly increases its spin rate. What causes this is the neutron star suddenly shrinks by about 1 millimeter. The spin rate suddenly increases to conserve angular momentum. The spin rate can be greatly increased if the pulsar is in a close binary system and its companion dumps gas onto the pulsar. The pulsar gains angular momentum from the incoming gas and ramps up its spin rate as more gas falls onto it. The pulsars that spin hundreds of times per second are thought to be the result of such a transfer.


Astronomy Picture of the Day Index - Stars: Neutron Stars

| Today's APOD | Title Search | Text Search | Editor's choices for the most educational Astronomy Pictures of the Day about neutron stars:

APOD: 1988 November 28 - A Lonely Neutron Star
Explanation: How massive can a star get without imploding into a black hole? These limits are being tested by the discovery of a lone neutron star in space. Observations by the Hubble Space Telescope have been combined with previous observations by the X-ray ROSAT observatory and ultraviolet EUVE observatory for the isolated star at the location of the arrow. Astronomers are able to directly infer the star's size from measurements of its unblended brightness, temperature, and an upper limit on the distance. Assuming that the object is a neutron star of typical mass, some previous theories of neutron star structure would have predicted an implosion that would have created a black hole. That this neutron star even exists therefore allows a window to the extreme conditions that exist in the interiors of neutron stars.

APOD: 1998 April 25 - Supernova Remnant and Neutron Star
Explanation: A massive star ends life as a supernova, blasting its outer layers back to interstellar space. The spectacular death explosion is initiated by the collapse of what has become an impossibly dense stellar core. However, this core is not necessarily destroyed. Instead, it may be transformed into an exotic object with the density of an atomic nucleus but more total mass than the sun - a neutron star. A neutron star is hard to detect directly because it is small (roughly 10 miles in diameter) and therefore dim, but newly formed in this violent crucible it is intensely hot, glowing in X-rays. These X-ray images from the orbiting ROSAT observatory may offer a premier view of such a recently formed neutron stars' X-ray glow. Pictured is the supernova remnant Puppis A, one of the brightest sources in the X-ray sky, with shocked gas clouds still expanding and radiating X-rays. In the inset close-up view, a faint pinpoint source of X-rays is visible which is most likely the young neutron star, kicked out by the asymmetric explosion and moving away from the site of the original supernova at about 600 miles per second.

APOD: 1998 July 23 - X Ray Pulsar
Explanation: This dramatic artist's vision shows a city-sized neutron star centered in a disk of hot plasma drawn from its enfeebled red companion star. Ravenously accreting material from the disk, the neutron star spins faster and faster emitting powerful particle beams and pulses of X-rays as it rotates 400 times a second. Could such a bizarre and inhospitable star system really exist in our Universe? Based on data from the orbiting Rossi X-Ray Timing Explorer (RXTE) satellite, research teams have recently announced a discovery which fits this exotic scenario well - a "millisecond" X-ray pulsar. The newly detected celestial X-ray beacon has the unassuming catalog designation of SAX J1808.4-3658 and is located a comforting 12,000 light years away in the constellation Sagittarius. Its X-ray pulses offer evidence of rapid, accretion powered rotation and provide a much sought after connection between known types of radio and X-ray pulsars and the evolution and ultimate demise of binary star systems.

APOD: 2005 May 15 - On the Origin of Gold
Explanation: Where did the gold in your jewelry originate? No one is completely sure. The relative average abundance in our Solar System appears higher than can be made in the early universe, in stars, and even in typical supernova explosions. Some astronomers now suggest that neutron-rich heavy elements such as gold might be most easily made in rare neutron-rich explosions such as the collision of neutron stars. Pictured above is a computer-animated frame depicting two neutron stars spiraling in toward each other, just before they collide. Since neutron star collisions are also suggested as the origin of short duration gamma-ray bursts, it is possible that you already own a souvenir from one of the most powerful explosions in the universe.


Segment Transcript

IRA FLATOW: This is Science Friday. I’m Ira Flatow. About 130 million years ago, two neutron stars collided, and that collision created a universe shaking explosion so big astronomers are calling it a kilonova that rippled space-time and splattered the cosmos with a cocktail of heavy metals, including lots of gold, about 200 times the mass of Earth in gold. This week astronomers announced that they had spotted the signals from that collision both in gravitational waves, like waves like the ones LIGO detected from merging black holes, and in signals across the range of the electromagnetic spectrum from optical light to gamma waves. It sounded like this.

Oh, that little chirp right there at the end. I hope you could hear that because it was kind of faint. And joining me now to talk about what makes that observation so important and what it means for our understanding of the universe are my guests– Vicky Kalogera is a professor in the Department of Physics and Astronomy at Northwestern University in Evanston, Illinois. She’s also a member of the LIGO Scientific Collaboration. Welcome.

VICKY KALOGERA: Hi, happy to be with you.

IRA FLATOW: Nice to have you. Daniel Holtz is an associate professor at the University of Chicago and the Kavli Institute for Cosmological Physics and a member of the LIGO Scientific Collaboration as well. Welcome, Daniel.

DANIEL HOLZ: Thank you. It’s so great to be here.

IRA FLATOW: Dr. Kalogera, tell me exactly what exactly did astronomers see, what was the signal, or all the signals.

VICKY KALOGERA: Well, what’s amazing with this discovery is that we didn’t just see, but we actually also heard. So first on August 17th early on, we heard more than 100 seconds of gravitational waves coming from the in-spiral, the death spiral of a pair of neutron stars. They were going one around the other until they came so close that they actually collided. So the gravitational waves came first, and we heard them with the LIGO detectors– laser interferometers in the US.

And then two seconds later, a cascade of waves across the whole electromagnetic spectrum started. It started with gamma rays, the most energetic light we have and continued with optical light, also later x-rays, and eventually radio waves. That continued over hours, days, and weeks. This combination of gravitational waves and electromagnetic waves coming from one cosmic source has never been observed before. So this was one amazing first.

IRA FLATOW: And Dr. Holz, why is this such a big deal? What do we learn from neutrons colliding that we would not know from black holes colliding?

DANIEL HOLZ: There is an incredible range of new science here. And it’s really hard to pick out what’s most exciting. I mean, we learn about speed of gravitational waves. We’ve now learned that the speed of gravity is the same as the speed of light. We’ve learned where the gold and the platinum in the universe is made, or at least a good fraction of it. We’ve also been able to measure the scale of the universe in a whole new way. I mean, these are all completely new developments all from this one discovery.

IRA FLATOW: Our number, 844-724-8255 if you’d like to talk about it. You can also tweet us @scifri. Dr. Kalogera, explain for us what a neutron star is, how big it is, how it’s different than a black hole.

VICKY KALOGERA: So a neutron star is actually the most compact star that nature can form. And it is still not as compact as a black hole. But it’s still a star in the sense that it is really made of matter, regular particles, primarily neutrons. And that’s why we call it the neutron star. Now it comes from the demise of very massive stars about 10 or 20 times the mass of the sun. When those stars ran out of nuclear fuel, they cannot not support themselves against their own gravity.

So the inner parts of those stars collapse under their own gravity. But eventually they don’t become black holes. They don’t become points. But instead they manage to support themselves because of nuclear pressure, and they manage to become neutron stars. Now these are very small. They’re as big as– since both Daniel and I are in the Chicago area– they are about the size of the city of Chicago. But they have a mass which is 1 and 1/2 times the mass of the sun. One teaspoon full of that neutron star matter is as heavy as the whole mountain of Everest.

VICKY KALOGERA: So this is extremely dense matter, which has very peculiar properties. We don’t have these kinds of properties on our planet. So the only way to study this kind of material is really by studying cosmic sources like this collision.

IRA FLATOW: And how do you know from looking at the data that last year’s observations were black holes merging, and this event is neutron stars? How do you know that?

VICKY KALOGERA: So this we know in two different ways. First, the gravitational waves signals are very different. So they both have this characteristic sound that you played in the beginning of the segment, which was the chirp like sound– whoop– except, when it is neutron stars, the signaling gravitational waves is much longer.

So we heard it play much longer. In this case, it was more than 100 seconds. So long signals imply small masses. And that tells us that we are dealing with neutron stars given what else we know in astronomy and astrophysics. But there is now, one might ask, why wouldn’t it be small black holes, about 1 and 1/2 times the mass of the sun but black holes.

IRA FLATOW: Yeah, I’ll ask it.

VICKY KALOGERA: And there we need the electro-magnetic waves. The fact that we saw light right after the collision means we had at least one neutron star.

IRA FLATOW: That’s really interesting. And Dr. Holz, a lot has been made about how much gold came out of this collision. What is the connection between this event and the heavy metals like gold in there? Why so much?

DANIEL HOLZ: Well, one of the interesting things about the way the elements are made– so we have a very nice picture of how this is all made from the very big bang, where the big bang makes some lighter elements like hydrogen and helium and then those elements form stars and the stars burn and produce heavier elements. And that story works all the way to iron. And it works very well, and it kind of accounts for everything we’ve seen– but not past iron.

So heavier elements like gold and platinum– we’ve had trouble explaining how there is as much gold and platinum as there is, for example, in our galaxy when we make observations. And this now helps address that question. What we’ve seen through measuring the light, through measuring everything with our optical telescopes and these other telescopes, what we’ve now measured are signatures that indicate all these heavier elements are being made and they’re being spewed out into the galaxy where this thing resides.

And so we’re actually watching the movie of the formation of that gold and platinum, and a lot of it as you said. It’s many, many times the mass of the Earth in gold and in platinum. There’s also uranium. There are a bunch of other things being produced and then being spewed out. And so now we can say this is where it all comes from.

IRA FLATOW: Do we know– do we think that these collisions are common, producing gravitational waves between either black holes or gravitational waves from neutron stars– pretty common?

DANIEL HOLZ: You can go, Vicky.

VICKY KALOGERA: It’s OK, Daniel. We both know the answer. So I would say– so we have had suspicions of how common these collisions are. But with this one observation, we’ve actually gotten a much better picture. It turns out that they are very rare as we expected. But not as rare as they could have been. So in terms of numbers, in a galaxy like our own, these collisions maybe happen a dozen times, maybe a few dozen times per millions of years. So that’s rare.

IRA FLATOW: That’s rare, but they could be coming in from other parts. My question is, if these are coming from different places, different neutron stars, let’s say, or different black holes, and they’re actually warping the space around them and sending a wave, a gravitational wave, what happens if two of them meet, two gravitational waves one from two different collisions meet in space? What happens at the juncture, like the ripples in the pond– two ripples when they meet– what happens to the gravitational wave?

DANIEL HOLZ: So what’s interesting about that is the very first paper I ever wrote– the very first project when I was an undergraduate– was on that specific question. And I showed that if you had really strong gravitational waves crashing into each other, you could make black holes. But for what we’re talking about here, with our detectors on Earth, we had to build a state of the art detector. We pushed the technology to the very edge, and we barely, barely detected anything. And so even if we had multiple sources of gravitational waves all coming at the same time, it would still barely register. Unfortunately, it’s very difficult to make extremely strong waves all colliding in the same place.

IRA FLATOW: So it’s not like– I’m thinking waves in a pond. You see how they build up– waves in the ocean. But you’re saying these are so weak, you wouldn’t get any buildup.

DANIEL HOLZ: That’s exactly right.

IRA FLATOW: And we’re also thinking of standing waves, things like that.

DANIEL HOLZ: That’s right. I mean, it would be great if we could do stuff with these waves. But we haven’t come up with a way to do that.

IRA FLATOW: Well, I’m thinking, if the waves come together and they crest really high– so if you’re warping space-time like that, could you tunnel through it and get to the other side in shorter amount of time?

DANIEL HOLZ: To be honest, part of the inspiration for that first paper was this analog of these rogue waves in the ocean, where every now and then you get this massive wave because everything comes in phase. And it’s exactly as you said. If you have, in principle, really strong gravitational waves, they could generate this huge curvature of space-time and just collapse that black hole. But we don’t think that happens.

IRA FLATOW: Let me see if I can get a phone call in. Let’s go to Wayne in Warner Robins, Georgia. Hi, Wayne.

WAYNE: Hello. Thank you for letting me on the show, the radio. My question to your panel is that, is the gold that we have here on earth made here on earth or did it come from outer space from this neutron planet implosion, or explosion.

IRA FLATOW: Good question. So the gold we have here on earth is from some collision of neutron stars? What do you think?

DANIEL HOLZ: My money would be on that it’s coming from something what we call a kilnova, exactly these sorts of things– that sometime in the past, probably many millions of years ago, there was a collision like this in our Milky Way galaxy. And it spewed a bunch of gold out and– actually, this would be probably much, much longer now I’m talking about it. It’d probably be billions of years ago. And when the Earth formed, some of that gold was part of its formation.

IRA FLATOW: You just blew my mind on this thing.

VICKY KALOGERA: That gold exists in the gas that surrounds the sun. It becomes planets. It goes into our mountains, and we get it in the mines. And we make our jewelry and our watches. But it’s not made in the earth. It pre-exists.

IRA FLATOW: I’m Ira Flatow. This is Science Friday from PRI, Public Radio International, talking with Daniel Holz and Vicky Kalogera, who just, as I say, blew my mind. This gold is much more valuable then. When you think of where it came from, how much more valuable it must be?

DANIEL HOLZ: Well, and you can see part of the reason we’re so excited now– I mean, to have figured this out. It’s pretty good.

IRA FLATOW: So is this part of the excitement of the neutron star collision discovery? I mean, what other things are blowing your mind about this discovery? Are you measuring the universe more accurately or are we measuring constance more accurately?

DANIEL HOLZ: So something I’m particularly excited about is this ability to measure the expansion of the universe much more accurately, or at least in a completely different way. And so by using this event, by the fact that we’ve detected it both in gravitational waves and in light, we can do an absolutely unique sort of measurement that we’ve talked about and we’ve wanted to do for a long time, but we’ve never been able to do before. And now we’ve done it, and we can measure this expansion– how quickly the universe is expanding around us right now. And by doing that, we get an overall sense of the scale of the universe and the age of the universe. And it’s beautiful. We’ve done the measurement.

IRA FLATOW: And have we had to change our idea about that yet? Do we know what it is?

DANIEL HOLZ: We know what it is. There are still some errors. It’s the very first time we’ve done it. But it’s consistent with what we’ve known before. and the whole picture just kind of fits together. And that’s remarkable because we’ve never been able to do this before. And yet, it all kind of works.

VICKY KALOGERA: There is one other first with this discovery. I mean, it’s amazing. As Daniel said earlier, there’s so many scientific new conclusions we’re drawing in one event that we’re all excited. The other first is that we’ve had, for 50 years, explosions and gamma rays that we’ve been observing. They started our observations– in the community, started in the late 60s. And over the 50 years, we have suspected theories developed that maybe they are coming from collisions of two neutron stars. But we never had proof.

For the first time with this discovery and the addition of the observations of gravitational waves, now we know we’re dealing with a collision of two neutron stars from the gravitational waves. And two seconds later, we see the gamma ray emission arriving. And we finally have proof that collisions of neutron stars are producing these short bursts of gamma rays. That’s another first that came within the first few minutes, and the understanding came within the first few hours of the community analyzing the data.

IRA FLATOW: Because gamma rays have always been mysterious. And now we know they come from the collision of neutron stars.

VICKY KALOGERA: We have an actual proof.

IRA FLATOW: So we’ve settled on gold and gamma rays all at the same time.

VICKY KALOGERA: And the expansion of the universe.

IRA FLATOW: And the expansion of the universe. What else?

DANIEL HOLZ: And the speed of gravity.

IRA FLATOW: Oh, that’s been verified?

DANIEL HOLZ: Yup. So this was the first time we could measure that gravitational waves go at the speed of light. Now the theory says that it has to, and this is what everyone expected. But now we’ve measured it. We showed– I mean, that gamma rays and gravitational waves arrived at Earth after traveling for over 100 million years. They arrived at Earth within two seconds of each other. So their speeds are to 15 decimal places are the same.

IRA FLATOW: We now have something to really be happy about for this weekend. Wow.

VICKY KALOGERA: And for much longer. This is only the beginning.

DANIEL HOLZ: That’s the truth.

IRA FLATOW: Well, we’ll hoist a beer to all you guys and gals for the work you’ve done. Thank you very much, Vicky Kalogera, and Daniel Holz, both members of the LIGO scientific collaboration. Thank you both for taking time to be with us today– very, very informative. Thanks again.

VICKY KALOGERA: Thank you. Thank you.

DANIEL HOLZ: Thank you for having us.

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