# Trying to survive a passing neutron star by burrowing deep in the planet's crust?

Situation: My colony is threatened by a passing neutron star. It turns out this planet is part of a binary system and once every several hundred years it passes by a neutron star, which irradiates its surface. I'm trying to figure out a way for the colonists to survive the impending cataclysm. Assume they don't have access to interstellar ships.

My question has two parts:

1. What if they dig deeper into the planet's core? Could the layers of rock shield them from the worst of the radiation? (Assume they have tech to pull this off).
2. Is there anything else they could do to shield themselves from this catastrophe, short of leaving the planet?

Edit: It's an older, non-pulsar neutron star. I would like for the neutron star to have an accretion disk (I would love for the colonists to witness it accrete away some of their main star's mass), but I can dispense with that if necessary. I would also like for it to pass close by enough for the colonists to feel some of the tidal forces and gravitational waves but not enough to kill them.

• How close will the neutron star pass to the planet, and does it have an accretion disk? Jul 10 '21 at 2:54
• Does "turns out" imply this is a surprise to them? Because a neutron star sounds like one of those things you really should've noticed before you set up your colony. Jul 10 '21 at 2:57
• A neutron star is what's left over after a supernova, which would have blasted away all the atmosphere and most of the surface of the planet. A lifeless, airless world doesn't seem like the place one would want to put a colony. Jul 10 '21 at 3:40
• If the pass is close enough to douse the world in radiation, is it also close enough for tidal forces to knead the core and crust into activity and cause killer quakes that squish the new underground communities? Jul 10 '21 at 3:46
• @Cadence, haha yes, it's a surprise! and a big part of the story is how and why that came about. Jul 10 '21 at 13:27

## 1 Answer

I think they'll be okay.

Let's start by figuring out what we're up against. Neutron stars can produce high-energy radiation through two means: thermal and non-thermal emission. Thermal emission is just the light emitted by a black body. Young neutron stars that have begun cooling (a couple of years old - younger than this one) have temperatures of $$\sim10^6$$ Kelvin. Assuming a radius of roughly 10 km, the Stefan-Boltzmann law predicts that a young neutron star should have a luminosity about 19% that of the Sun. The thermal emission peaks somewhere near the cutoff between ultraviolet and x-rays, meaning that a lot of this will be dangerous to humans.

If the neutron star is behaving like a pulsar, it will also emit non-thermal radiation through synchrotron emission. You probably know pulsars best from radio observations, but in the most energetic pulsars, most of the rotational energy of the pulsar is actually converted to x-rays and gamma-rays; there's a weak correlation between the frequency of light and the fraction of the spin-down energy that goes into that frequency band.$$^{\dagger}$$ The power released by a typical pulsar with period $$P$$ and period time derivative $$\dot{P}$$ is $$\dot{E}\approx4\times10^{31}\;\text{erg s}^{-1}\left(\frac{\dot{P}}{10^{-15}}\right)\left(\frac{P}{\text{s}}\right)^{-3}$$ This usually comes out to a few percent of a solar luminosity, so it's fair to say that our neutron star should have a total luminosity - including thermal and non-thermal emission - of roughly $$0.25L_{\odot}$$. Ish. And that's generous, because your neutron star is certainly older, which thanks to cooling might drop this by 1-2 orders of magnitude. At any rate, I think we can assume that this is mostly the sort of high-energy radiation we'd prefer to avoid.

(Brief interlude: You've mentioned that the neutron star has an accretion disk but that it's not behaving like a pulsar. That's a bit odd for two reasons: 1) the neutron star would have to have been in a close orbit to its companion star in order to accrete that matter in the first place, which seems incompatible with a planet remotely near the habitable zone, and 2) neutron stars accreting matter gain angular momentum, which increases their rotational speeds and turn them into millisecond pulsars, as the increase in angular momentum also turns on the not-overly-well-understood pulsar emission mechanism. In other words, I'd be surprised to see a neutron star with an accretion disk not emitting pulses of radiation. Coupled with the strangeness of having an accretion disk while in a wide orbit, I'd like to dispute that part of the premise!)

The flux on the planet depends on how far from the neutron star it is. Let's say the closest approach is around 100 AU; a pass on the order of 10 AU or less has a decent risk of causing orbital problems, particularly if there are other planets in the system (thank you to Loren Pechtel for confirming this!). The flux on the surface is then about 0.034 Watts per square meter.$$^{\ddagger}$$ If an unshielded human weighing 80 kg (cross-sectional area of something like 2 square meters?) was exposed to this amount of radiation for one year, they'd receive a dose of about 27,000 Sieverts. As I understand it, we'd want to reduce this below 1 Sievert to significantly reduce the risk of radiation sickness. Not great.

However, we could absolutely build shielding. Lead has a half-value layer of 4.8 mm against gamma rays, so we could lower the radiation by the requisite four or so orders of magnitude with 15 times this length. Not bad. Even if the distance to the neutron star is an order of magnitude lower, raising the dosage by a factor of 100, we'd still need lead shielding of something like 10 cm, if my numbers are correct. Dirt itself has a half-value layer of 115 cm, so 25 meters of dirt would provide adequate shielding from the worst-case 10 AU-approach scenario.

Let's briefly discuss gravitational effects, since you've brought up tidal forces and gravitational waves. Tidal forces would be minimal since at interplanetary distances there's no difference gravitationally between a $$\sim1.5M_{\odot}$$ neutron star and a $$\sim1.5M_{\odot}$$ main sequence star; tidal forces are only important quite close to the surface. Gravitational waves are a possibility from tiny imperfections in the neutron star's surface on the order of millimeters or so (we ironically call them "mountains"). Mountains on a neutron star at a distance of 100 AU should produce a strain on the order of $$\sim10^{-20}$$, give or take a couple orders of magnitude (Lasky 2015), which won't cause problems.

I'm sure these numbers are off by a bit - a factor of 10 here, a factor of 3 there. I've likely overestimated the thermal radiation and the high-energy contribution from non-thermal radiation, and I think I've also overestimated how close the neutron star can be without having affecting the planet's orbit. The point, though, is that even if I'm wrong by 1-2 orders of magnitude, a mine shaft a kilometer or so deep should be cozy enough against whatever a neutron star can thrown at these colonist. And that's probably substantially overkill.

Anyway, time to start digging.

$$^{\dagger}$$Handbook of Pulsar Astronomy, Lorimer & Kramer. Also my reference for other bits of this answer.

$$^{\ddagger}$$This is slightly inaccurate because the non-thermal pulsed radiation will not be emitted equally in all directions. A reasonable assumption is that the beam covers about 10% of the sky at a given time (although this depends on the pulse period), meaning the flux when it sweeps across the planet will be higher than in the case of isotropic emission. Conversely, there's no guarantee the beams will cross the planet at all.

• 27000 Sievert, not great, not terrible. Jul 10 '21 at 12:10
• I think your 10AU is too close. Just tried a simulation in Universe Sandbox, a 1 solar mass black hole with a periapsis at 10AU and an apoapsis at 100AU. One pass, I would say Earth is still inhabitable. Saturn and Neptune are gone, though, Jupiter's periapsis is near Mercury and Uranus' is near Venus. Jul 10 '21 at 18:32
• 2nd pass: Jupiter is safe, Uranus and Mars are gone, Earth's habitability is questionable. 3rd pass: Jupiter and Pluto are gone, Earth is still of questionable habitability. 4th pass: A few Kupier belt objects that were stolen got returned, Earth still questionable. Jul 10 '21 at 18:47
• Retrying at 20AU. First pass: Uranus, Neptune ejected, Pluto stolen, Earth looks ok. 2nd pass: Pluto returned. 3rd pass: Pluto taken again, Saturn ejected. The inner system seems safe. Jul 10 '21 at 19:27
• @LorenPechtel - Maybe you could post your experiment. It would be nice if youtube had some videos using Universe Sandbox that were other than massive collisions. I considered getting it but it seemed like all you could do was whack stuff into other stuff. Not that there is anything wrong with that. Jul 10 '21 at 22:29