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A neutron star is a type of compact star that can result from the gravitational collapse of a massive star after a supernova. Neutron stars are the densest and smallest stars known to exist in the Universe; with a radius of only about $11–11.5~\text{km}$ (7 miles), they can have a mass of about twice that of the Sun.

I am not yet ready to consider the formation of such a planet, as a planet orbiting what is now a neutron star would have been destroyed instantly during that star's supernova phase.

For the sake of this question, let's go ahead and consider that this Earth-like planet was placed here by advanced alien species after the star's supernova collapse.

The average surface temperature of an average neutron star is around $10^{6}~\text{K}$, which is a fair bit more than our Sun's modest $5.7\cdot 10^{3}~\text{K}$. Not to say that this is the only problem, but it is the obvious one that I would like addressed in an answer.

Is a large orbit to compensate for such heat feasible? Will the neutron star's gravitational pull allow for a stable orbit?


This question itself deals with the orbit, radiation exposure, and placement of the planet, another question will probably ask about the biology; however, most of these answers make prospects pretty dim.

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Related: Can a planet survive a supernova? – Samuel Feb 1 at 20:51
    
Actually, we've detected planets near neutron stars (pulsars). Pulsar B1620-26 has one planet at ~23 AU, and Pulsar B1257+12 has 3 planets, extremely close to it. The theory is that the stars didn't blow away ALL of the matter in the system during the supernova, and the remains coalesced into a new planet(s). en.wikipedia.org/wiki/Pulsar_planet – R. Daughtry Feb 2 at 7:47
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Since answers are mentioning photosynthesis, are you looking for a planet that is Earth-like in size and composition, or Earth-like in biology? If you are prepared to accept a planet similar to Earth with completely different biology deriving energy from x-rays, then it's easier to give you a positive answer. – trichoplax Feb 2 at 13:20
    
Temperature only matters to the blackbody radiation, really. You need to account for the fact that the surface area of the star dropped considerably - the increased temperature is nowhere near enough to sustain the original overall energy output. It's not the heat that kills you, it's the hard radiation :) – Luaan Feb 2 at 15:16
    
I can't speak to "Earth-like", but the presence of planets around a neutron star is a non-issue. The first exoplanet ever discovered orbits a neutron star within a system of three planets and possibly an asteroid belt. The system is thought to have formed from the supernova remnant after the original star exploded. en.wikipedia.org/wiki/PSR_B1257%2B12 – ApproachingDarknessFish May 31 at 21:41
up vote 8 down vote accepted

I don't exactly trust this wiki on the subject, but I think for the purposes here it will be close enough (the data and conclusions look correct to me).

Nope!

According to that page, if Sol was a neutron star, Earth would be subjected to the same planetary temperatures as Uranus (that's a fair bit colder than Earth is now) despite the increased solar temperature.

The biggest problem is going to be the massive X-Ray output by the star, which...is suffice to say, not terribly healthy. Those higher stelar temperatures lead to an increase in the energy of the light coming off the star: each photon has more energy, and more energy means shorter wavelengths. Minutephysics has a short video on this that explains it better than I can.

Stable orbits though? Absolutely. Neutron stars don't have "weird" gravity, because gravity is just gravity and you can make a stable orbit around just about anything (provided the universe has three dimensions of space).

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"you can make a stable orbit around just about anything" - that's not strictly true. Gravitational fields from other bodies, as well as irregularities in the mass distribution of the main body make it quite difficult sometimes. – Ordous Feb 2 at 13:01
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@Ordous: you can make a stable orbit around anything sufficiently small. If the sun works, then a neutron star works actually better. – leftaroundabout Feb 2 at 14:24

I'd say...

Yes!*

* with a huge if.

Gravity is actually a non-issue. The gravity exerted by a 1.1 Sol-mass neutron star, the minimum allowed by the Chandrasekhar limit for a white dwarf, is exactly... 1.1 Sols, same for a 1.1-Sol black hole.

Your problem is to find a Goldilocks zone for your planet, and the main issue is X-rays. here comes the huge if: An atmosphere saturated with phosphorescent materials, such as zinc sulfide or strontium aluminate, able to work as a dampener by intercepting the high-energy X-ray photons and emitting lower-energy photons at infra-red (thermal) levels.

[edit]

After reading the comments, I went and did a bit of research. Turns out that diamonds irradiated and activated by X-rays emit light in the optical spectrum. So another rather fashionable solution would be to encase environments under diamond domes.

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Comments are not for extended discussion; this conversation has been moved to chat. – Serban Tanasa Mar 1 at 18:02

The orbit: sure it's feasible. Gravity is gravity, it doesn't matter what the source is. We could replace the sun with a black hole, and as long as it was the same mass all the planets would keep revolving exactly the same (with the minor exception of Earth experiencing a sudden loss of all life).

So for your neutron star, it's exactly the same. Ballpark it as having a mass of 1.5 solar masses (per Wikipedia). Now, we'd need to shift orbits out a little bit to accommodate for the mass increase, but that's just a matter of messing with the numbers.

To deal with the other part of your question, the temperature, neutron stars are about a thousand times hotter than the sun, as you said, but the emissions are mainly x-rays and gamma rays. Those don't interact with matter as much as lower energy emissions like from our sun. As a result, they're hotter, but don't warm a planet as much as a normal star at the same distance.

So we're left with a dilemma of needing to be further away to balance the mass increase, but closer to balance the temperature. And, of course, the dilemma that the output of the star is x-rays and gamma rays, which aren't exactly conducive to life in large quantities. Ultimately won't work, unfortunately.

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"Sudden loss of all life." I don't think it would be that sudden. Afterall, we wouldn't even notice for a whole 8 minutes. ;) – Draco18s Feb 1 at 20:31
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"sudden loss of life" is what's wrong with this answer. Surface would freeze over quite slowly. Geothermal energy could support humans for years in deep mines. And ultimately, rift oasis would probably never notice that something happened up there, as those ecosystems are not tied to our. – Agent_L Feb 2 at 14:03

Neutron stars, while small, have a lot of mass. A neutron star with a diameter of 22 kilometers could have twice the mass of the sun, so large orbits are possible.

Actually, because of the threat of time dilation a large orbit may be necessary.

Unfortunately, while the surface is a lot hotter, it's also a lot smaller, which means that the actual amount of heat coming off of it is less.

It's like an acetylene blowtorch compared to a propane space heater. While the blowtorch is a lot hotter, it is also smaller, so a space heater can easily out heat it.

The radiation it produces may be an issue too.

Edit:
Actually, the radiation could be useful. Since the planet is possibly an artifact, then the creators would have taken it into account.
So if the planet was heavy in x-ray absorbing materials like metals, it would warm up a lot more than normal dirt in sunlight, and to a greater depth. This absorbed energy would then be radiated out as heat.

The earth's atmosphere absorbs a lot of radiation. With a thick enough atmosphere the radiation could be knocked down from deadly to "don't stand in the sun to long"

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Because of the ratio of X-rays to visible light is about a million to a billion to one, no atmosphere can protect us. By the time you're close enough to get enough visible light for plants you're already frying from the heat. You're also being bombarded by so many X-rays even if they're all absorbed by the atmosphere they still transfer heat so your planet fries even more in a super greenhouse effect. See my answer for details. – Schwern Feb 1 at 21:40
    
Convert the energy and vary orbital distance or living depth if needed for repairs. – Cees Timmerman Feb 2 at 14:19
    
@Schwern So you shield the crap out of it with a massive electromagnetic field, and maybe some active shielding too, since these are beings that can create a planet so why not. Put it at an orbital distance where the radiation won't be to much, and maybe something to either convert some of the x-rays to visible light with orbiting scintillators or other artificial light, or engineer plants that don't need visible light. Of course a main line star would be easier, but there might be useful reasons to have a place to study a neutron star from. – AndyD273 Feb 2 at 17:36
    
@AndyD273 Photons (X-rays) have no charge, so an electromagnetic shield doesn't help. What it does help against is charged particles (solar wind & solar flares), but that's something we haven't even gotten into. Using scintillators has already been mentioned. Once we start "engineering plants that don't need visible light" we're moving beyond "Earth-like". – Schwern Feb 2 at 20:11

What you're asking is if a neutron star has a habitable zone. The answer is NO. Either all plants die from lack of sunlight, or it's too hot, or you're sterilized by X-rays.

To be habitable you need an orbit where there's enough light for photosynthesis to work, the right temperature for liquid water, and not too much high-energy light (X-rays, gamma rays) to overwhelm being absorbed by the atmosphere (which makes things even hotter).

As far as liquid water is concerned you can probably find one for a neutron star, they're typically about 1 to 2 times the mass of the Sun and put out about $\frac{1}{3}$ the energy, so it would have to be closer than the Earth is to our Sun, but not so close we need to worry about being torn apart by tidal forces at about 700,000 km.

I'm not going to go into that further because there's a bigger problem: the type of radiation.

A typical neutron star has a surface temperature of $6\cdot 10^{5}~\text{K}$ (100 times hotter than the Sun). From this we can determine what type of radiation will be most powerful using Wien's displacement law for blackbody radiation.

$\text{max wavelength} = \frac{\text{Wien's displacement constant}}{\text{surface temperature}}$

As you can see, wavelength will drop as the surface temperature gets higher. Since the Sun puts out lots of visible light, and a neutron star is 100 times hotter, this isn't going to go well for our new Earth. When we plug in the numbers...

$\text{max wavelength} = \frac{2.90\cdot 10^{−3}~\text{K m}}{6\cdot 10^{5}~\text{K}} = 4.833\cdot 10^{-9}~\text{m}$

About 5 nanometers which puts us firmly into X-rays. This is bad for life.

While Earth's atmosphere absorbs most everything with more energy than visible light the Sun doesn't put out a lot of X-Rays in the first place.

Source: http://www.windows2universe.org/sun/spectrum/multispectral_sun_overview.html

Note that graph is exponential, our Sun is putting out a million times more visible light than X-rays, our atmosphere can handle that. Our neutron star slides that line to the left. The maximum output will be firmly in X-rays. It will be putting out a million times more X-rays than our Sun. It will also be putting out 1,000 times less visible light causing problems for photosynthesis.

Because a neutron star puts out about $\frac{1}{3}$ the energy of our Sun, we only need to be a little closer to get enough heat. But because there's 1,000 times less little visible light than the Sun, we need to be much, much closer for photosynthesis to work. But that close we'll be fried by heat. Getting closer to get 1,000 times more visible light also gives us 1,000 times more X-rays which puts us at a billion times the X-rays from our Sun! Our atmosphere cannot protect us from that, or if it could the absorbed energy transferred to heat would fry us even further.

An atmosphere engineered to deal with this would need to reflect (not absorb) most of the energy coming from the neutron star, while still letting through nearly all of the visible light, and still be friendly to life as we know it. I don't think such an atmosphere is possible.

Alternatively, riffing on this answer, the atmosphere would need to convert X-ray radiation into visible light while still being acceptable to life. This reaction, if balanced correctly, would allow the planet to generate enough visible light for plants and heat for liquid water while protecting the surface from X-rays. I don't know of any substance which could do this, but I'm not a chemist.

Sources:

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Couldn't the atmosphere convert the absorbed x-rays to lower-frequency waves? – Paŭlo Ebermann Feb 1 at 21:54
    
@PaŭloEbermann I just added that possibility, but I don't know of a substance which could do that, and be suspended in the atmosphere (I'll allow humans could replenish it), and not be hostile to life. Do you? – Schwern Feb 1 at 21:56
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Maybe even putting a metal shield between the planet and the star? It absorbs the x-rays (and actually everything from the star), becomes hot (but not that hot as the star itself), and starts emitting light itself? (Just like a piece of Dyson sphere.) I guess the distance to the star can to be calibrated for temperature, and the size + distance to planet for quantity of light which reaches the planet. – Paŭlo Ebermann Feb 1 at 22:00
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@PaŭloEbermann It may be possible. Let's ignore the problem of how we get all that mass into space (we use lead to stop X-rays). With enough mass anything should be able to stop X-rays. You need to select something which absorbs X-rays and, once in thermal equilibrium, is hot enough to glow in visible light yet remains stable. Sounds like a good question. – Schwern Feb 1 at 22:50
    

As Many people have pointed out, finding a gravitational equilibrium is relatively simple and the largest obstacle to overcome is the emission spectrum of the Neutron star. The ratio of these factors leaves no habitable zone, however...

Delving into a creative realm, you could theoretically make an inverse Dyson Sphere around the planet of a material(s) that can efficiently and effectively absorb the radiation from the Neutron star and emit it at reasonable energy levels to the surface of the planet. Although this approach is in no way feasible, with abundant resources and technology a solution could be found.

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See also this question. – Cees Timmerman Feb 2 at 14:17

No.

Everyone has been dismissing the neutron star's gravitation as irrelevant because gravity is gravity. Unfortunately, in this case it isn't.

The goldilocks zone scales at the square root of the luminosity.

Neutron star luminosity: Around 1 millionth of the sun ?

Earth's orbital radius: 150,000,000km.

Neutron star goldilocks zone: 150,000km.

Now for the killer: The Roche limit.

2.423 * radius * cube root (density/satellite density)

radius: around 10km density: low bound: 3.7E14 g/cm^3 ? (Note: I converted units here) satellite density: 5.51 g/cm^3 (Earth)

density ratio: 67,150,635,208,711 cube root: 40,645

2.423 * 10km * 40,645 = 984,828km

Oops, a planet that's warm enough gets torn to pieces pronto.

(Not to mention that you have a year that's measured in minutes.)

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That article has the luminosity wrong because their temperature is an order of magnitude too low (5x10^4K instead of 5x10^5K). Since temperature is raised to the fourth power in the Luminosity Formula I get anywhere from 1/100th to 1/5th the luminosity of the Sun depending on if I plug in 5x10^5K or 10^6K as the star's temperature. – Schwern Feb 3 at 19:45

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