How long would we survive an approaching neutron star?

Question

I recently came across PSR B1620−26. A neutron star that captured a sun like star with an orbiting planet. The system went through several stages of development, but through it all the orbiting planet remained relatively unscathed. At least in terms of it wasn't destroyed, wasn't ejected from the system, its orbit didn't change much if at all.

Image source: https://esahubble.org/images/opo0319e/

So my question is, if our solar system faced a similar situation, how long would we, here on Earth, survive? What kind of effects would it have on us as it approached? At what distance would we first notice harmful effects? Could the neutron star make it all the way to the sun and form a binary system without greatly affecting us?

I've been approaching this under the assumption that the neutron star is moving directly toward the sun at an angle perpendicular to the solar system's orbital plane. I've been treating the neutron star as a blackbody, and I've been using the these parameters in my own approach to solving this question:

• The neutron star has a radius of around 10 km.
• The neutron star has a mass of 1.35 solar masses, or 2.7x10³⁰ kg.
• The supernova that birthed this neutron star happened at around 100 light-years. The supernova would have been damaging to Earth if it had occurred within 50 light-years, so I chose a distance much greater to allow for some error. However, this is more or less an arbitrary number that I selected to make calculations more convenient.
• The neutron star is moving at a speed relative to us of around 500 km/s. The solar system has a speed of 200-220 km/s. If the neutron star received an average speed from the pulsar kick when it formed, then it would have a speed between 200-500 km/s. I'm assuming the neutron star is moving at an angle perpendicular to the solar system's orbital plane. This means it must have a speed between 1-20 km/s if the solar system and neutron star are moving in the same direction, or a speed between 400-720 km/s if they are moving in opposite directions. I chose the scenario where they are moving in opposite directions, the sun with a speed of 200 km/s, and the neutron star with a speed of 300 km/s. (Thanks PM 2Ring for pointing me to pulsar kicks)
• The age of the neutron star is around 60,000 years old. This I calculated with the distance of 100 light-years and the speed of 500 km/s.
• The temperature of the neutron star is around 400,000 kelvin. I calculated this by assuming that the neutron star cooled to 1,000,000 kelvin within the first 10,000 years of life. Now it's in the stage where photon cooling through soft x-ray emissions is the dominant cooling method. Which means that we can calculate the star's temperature by knowing that as time quadruples, temperature halves. (I learned this from a different question that ProfRob answered, so thanks ProfRob for that and the comment.)
• Radiation for the neutron star peaks at 7 nm which is in the x-ray range. I calculated this using Wien's Displacement Law.
• I'm not entirely sure on this point, but I believe the radiation from the neutron star is about 1% visible light, 41% ultraviolet, and 58% x-ray and gamma (mostly x-ray).
• The neutron star's total energy flux is 1.45x10¹⁵ W/s. I calculated this using the Stefan-Boltzmann Law.
• The neutron star's intrinsic luminosity is 1.82x10²⁴ W. Compared to the sun's intrinsic luminosity of 3.83x10²⁶ W, the neutron star only radiates about 0.48% as much energy. This really surprised me. I expected the neutron star's energy output to exceed the sun's since it's so much hotter. If I understand right, it's the neutron star's much smaller radius that makes its energy output this small.
• The equation below calculates the apparent magnitude for the neutron star.

$$A=-2.5\log\left( \frac{\left( \frac{\left( 1.82 \cdot 10^{24} \right)}{4\pi R^2} \right)}{1365} \right) - 26.8$$

Where: A is the apparent magnitude for the neutron star. 1.82x10²⁴ W is the intrinsic luminosity of the neutron star. R is the distance from Earth to the neutron star in meters. 1365 W/m² is the radiant flux for sun at 1AU. And -26.8 is the apparent magnitude for the sun at 1AU.

(Hopefully I got the equation correct.) This is as far as I've been able to get. I haven't been able to figure out how the neutron star's magnetic field affects the situation.

Taking all this into account, if I understand everything correctly, the neutron star wouldn't have much effect on Earth as it approached. This due to the intrinsic luminosity being so much smaller than the suns. And because most of the neutron stars radiation is in the UV, x-ray, gamma spectrum which the Earth's atmosphere blocks for the most part. If it were to get very close, within .1 AU (as Anders Sandberg commented) then it would start to impact Earth, but at that distance I expect gravity would have a much stronger effect than radiation.

This means that if such a situation were to occur in our solar system, we should be able to watch the neutron star as it approached without it harming us. And if our conditions happened to be the same as they were for PSR B1620−26 b, then we could potentially end up in a new binary star system.

EDIT Something I overlooked (as ProfRob pointed out in his answer below) is that this neutron star would be a pulsar. I’ve tried to take this along with a few more things into account to come up with a more complete answer to my original question. Here’s my thoughts:

Because this neutron star is a pulsar, it must be emitting beams of radiation out of its magnetic poles. Unless the magnetic poles happen to align with the star's poles, then the beams will definitely shine on Earth as the neutron star approaches. Unless we are very unlucky, I think the neutron star's relative speed of 500 km/s will mean the beams only shine on us for a brief moment. Potentially just seconds. This should mean essentially no damage from the beams.

For the pulsar wind nebula, I must admit, I didn’t know this existed, so I will default to the information in ProfRob’s answer below. Though, if my understanding is correct, Earth should start to see some effects from the pulsar wind nebula (PWN) when the neutron star is about 1 light-year away, with effects increasing as it gets closer. If I were to speculate, I’d say these effects might be similar to that of a strong solar flare, but as if the solar flare were constant. These effects might include: more frequent auroras, radio blackouts, damage to satellites. Another effect could be an increase in risk of cancer with the overall increase in radiation, even if most of it is blocked by the atmosphere. These effects would last for around 1,200 years if the neutron star maintained a speed of 500 km/s as it passed through the solar system.

All this leads me to believe that if we faced a similar situation to PSR B1620−26 b, a close encounter with a neutron star, we would most likely come out relatively unharmed. It seems certain that it would cause some harm, but would it drive us to extinction or leave the planet a desolate wasteland? No, I don’t think so. So how long would we survive an approaching neutron star? The odds seem good that we would likely survive the whole time and beyond. But I could be wrong and I welcome corrections.

Thanks again to the commentors! Appreciate any answers, corrections, or comments! Thanks!

Answer 1

The following was too long for a comment, but I don't claim it is an answer.

The first part is easy. At a relative velocity of 500 km/s, the neutron star will race, probably almost unperturbed, through the Solar System. There is no chance of it being captured into a binary system - this would require a significant third body to absorb sufficient kinetic energy to allow the neutron star to be captured.

The dynamical effects on the Solar System would depend on exactly how close it came. The probability of an approach within radius $r$ declines as $\sim r^2$. The effects could be catastrophic or not very significant. The only way to answer this would be a suite of N-body simulations of the encounter. Because the neutron star is travelling so fast, I doubt any effects on Earth would be felt until it was almost upon us. For example, a 1% perturbation in gravitational force would occur when it was about 10 au away and potentially only a month away from its closest approach. In other words, there wouldn't be a slow perturbation to the Earth's orbit - any big changes would happen on a timescale less than the orbital period of the Earth.

The second aspect to this is radiation damage. I concur with your assessment of the temperature and luminosity of the neutron star, but you have forgotten that a neutron star aged 60,000 years will almost certainly be a rapidly rotating, highly energetic pulsar.

A reasonable comparison object might be the Vela pulsar, with an age of around 11,000 years. The pulsar, with a rotation period of about 0.1 s, is surrounded by a magnetosphere and a pulsar wind nebula that are powered by the spindown of the pulsar. This non-thermal emission, at radio to gamma ray wavelengths, amounts to around $10^{30}$ Watts in the case of the Vela pulsar, and dwarfs the thermal emission from the neutron star surface. It is a few thousand times more luminous than the Sun, but a much larger fraction of the luminosity emerges at high energies - UV-gamma ray. It emits almost a solar luminosity in hard X-rays and gamma rays. In other words, the pulsar would be $>10$ orders of magnitude more luminous than the Sun at these wavelengths. See Fang-Wu et al. (2018).

How close that can get before being very damaging to life on Earth? I don't know - that seems to be a question for life scientists and meteorologists. But my guess is, even if the pulsar were not unfavourably orientated, beaming radiation towards the Earth, there would be problems if it came within a light year. The pulsar wind nebula itself has a radius of about a light year, so to add to the radiation, there would be a significant population of relativistic charged particles to contend with.