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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?

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    $\begingroup$ Not related to your question, but what things would look like on the surface of a Neutron Star is much more interesting. Because of the way light bends, the sky when standing on the surface of a Neutron Star would be squeezed into a tiny circle and the planet would visibly appear to rise up around you, taking up most of what you can see. apod.nasa.gov/htmltest/gifcity/nslens_ul.html $\endgroup$ – userLTK Dec 15 '15 at 21:10
  • $\begingroup$ @userLTK It's a fascinating link, and a negatively curved horizon would be amazing to see to say the least! $\endgroup$ – user10106 Dec 16 '15 at 12:21
  • $\begingroup$ Does anyone know if such "ultracompact" neutron stars actually form? $\endgroup$ – Steve Linton Jun 1 '18 at 9:43
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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 $$\frac{4 \pi r^2}{4\pi d^2} \sigma T^4 = 1300\ W\ m^{-2},$$ where $\sigma$ is the Stefan-Boltzmann constant.

For $r=10$ km, then $d=7 \times 10^{8}$ 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: $$ \alpha \simeq 0.83 \left(\frac{M}{1.4M_{\odot}}\right) \left(\frac{b}{10 km}\right)^{-1},$$ 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 $\sim 2 \times 10\ km/1\ au \sim 10^{-7}$ 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.

distorted images

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  • $\begingroup$ A very interesting answer. I had imagined a neutron star's luminosity would be higher than what would be calculated due to light emitted from its 'far side' being bent towards an observer, but I did not realise it would also be redshifted in such a way as to make the star appear cooler. $\endgroup$ – user10106 Dec 16 '15 at 12:30
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    $\begingroup$ Does the lensing increase the observed flux in this case? Thinking in terms of light rays emitted from the surface, some emitted nonradially from the back hemisphere will be seen, but this also means that some emitted from the front hemisphere that "would have been" observed won't be, because they will bend to miss the observer. ... For a hypothetical nonrotating neutron star, spherical symmetry implies only the redshift matters due to energy conservation. For a more realistic one, it would depend on relative orientation. $\endgroup$ – Stan Liou Dec 16 '15 at 17:35
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    $\begingroup$ @StanLiou that does sound correct. It can't be brighter in all directions. $\endgroup$ – Rob Jeffries Dec 16 '15 at 20:47
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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.

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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)

http://cache1.asset-cache.net/xt/516070391.jpg?v=1&g=fs1|0|FLF|70|391&s=1

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).

http://orig10.deviantart.net/193f/f/2011/095/d/9/spiral_by_10binary-d3dbvut.png

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.

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    $\begingroup$ Mostly wrong. Just picking up on a major point. A blackbody at a hot temperature radiates more energy at all wavelengths than a cooler object with the same emitting area. As they cool down, neutron stars become less visible. $\endgroup$ – Rob Jeffries Dec 15 '15 at 22:18
  • $\begingroup$ Visible to x-ray telescopes or visible to the Human eye? The question was about visible to the Human eye. $\endgroup$ – userLTK Dec 15 '15 at 22:57
  • $\begingroup$ At all wavelengths. $\endgroup$ – Rob Jeffries Dec 15 '15 at 23:10
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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!"

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