How big a black hole is needed for this story?

Question

The story begins in classic disaster film style. A small rogue black hole is approaching our Solar System. It isn’t going to get close enough to destroy everything, but it will agitate our Sun, causing horrific solar flares as it reaches perihelion. Those flares are going to bake the Earth’s surface in fatal levels of radiation. Conservative estimates suggest that it will take a thousand years for the planet’s magnetic fields to recover, at which time it will be fit for recolonization.

We don’t have FTL travel and we’ve only got a decade to prepare, so the world unites in an effort to build a fleet of generation ships capable of holding ten thousand souls, plus a Noah’s ark assortment of domesticated animals. The trick will be to keep that viable gene pool alive for a thousand years in deep space. The finest minds alive work on the problem, but there is just no way to bring even a fraction of the oxygen, food and water needed.

In desperation, an insane plan is adopted.

The ships will launch about a year before perihelion and will proceed on a collision course with the approaching black hole. At the moment when the singularity passes closest to our Sun, the ships will dive into its gravity well, slingshoting in close enough to the event horizon to cause significant time dilation.

Emerging after half an orbit of the hole (by firing Orion nuclear engines to reach escape velocity), they will race back towards earth, arriving just before the life support supplies run out. If the time dilation does what it should, the fleet's two year round trip, will find an Earth more than a thousand years older and completely healed.

Now for my question…

What combination of black hole size/mass and distance from our Solar System would make this story viable?

• It needs to get close enough that an Orion nuclear drive (and maybe a sun-dive/slingshot outbound maneuver) can get our ships there in a relatively short time (so that we don’t run out of life support on the way there).
• It needs to be small enough that it doesn’t rip Earth out of its orbit as it passes by. It can take the rest of the planets, but Earth and our moon have to survive.
• It needs to be big enough that it can generate enough time dilation that a thousand years can pass on Earth during the fleet’s one or two year journey.

One additional question…

Is it believable that a cosmically short-term interaction with a distant black hole, could temporarily cause our sun to intensify, throwing off solar flare for a few years before settling back down to normal?

Answer 1

That's some extreme time dilation.

It is possible, but the black hole needs to be insanely massive for your ship to orbit it without falling into the event horizon and have the proper amount of time pass.

Gravitational time dilation goes like this:

$$t_0 = t_f \sqrt{1-{{r_0}\over{r}}}$$

Where,

• $t_0$ is the proper time between events A and B for a slow-ticking observer within the gravitational field
• $t_f$ is the coordinate time between events A and B for a fast-ticking observer at an arbitrarily large distance from the massive object
• $r$ is the radial coordinate of the observer (which is analogous to the classical distance from the center of the object, but is actually a Schwarzschild coordinate)
• $r_0 = {{2GM}\over{c^2}}$ is the Schwarzschild radius of M.

I initially solved this by estimating the insane minimum distance of 1km from the event horizon. This was supposed to be a minimum bound for the size of the black hole, but it appears to not be insane enough. You said you wanted half an orbit, a slingshot, it's hard to say how long that would take. I'm guessing a tenth of one year; about five weeks.

$$0.1\ year = 1000\ years \sqrt{1-{{r_0}\over{r_0 + 1000\ meters}}}$$

Solving this gives a Schwarzschild radius of about 99,999,999,000 meters. Which requires 33,851,584 solar masses to produce. This would be a supermassive black hole larger than the one at the center of our galaxy. Larger by almost an order of magnitude.

To have such a thing pass near enough to our solar system that the ship could get there in one year is likely to do more than make our sun fizzle a bit. Placing the black hole farther away means it needs to be even more massive in order to make up for the extra travel time. Which might not work anyway because the ship would also have to orbit in less time, which starts to become impossible as the black hole gets larger.

To make this story plausible, the elapsed time needs to be significantly reduced. Unfortunately that reduction would likely need to be to less than ten years. Even getting closer to the black hole doesn't solve it. Getting to just ten meters away still requires a black hole of around 338,500 solar masses. But, 1km was already insane and very likely impossible to achieve.

I don't think a passing black hole is a viable method for "intensifying" our Sun's weather. I can't think of anything you could do to the Sun to make it act weirdly for only 1000 years, it's been around for so much longer than that.

Answer 2

This is probably more of a comment than an answer, but as I don't have enough reputation to comment I'll see how this goes:

Have you considered using a cosmic string instead of a black hole? You might be able to still get the time dilation effect due to the string acting like it has high mass, and the crew could travel along the length of the string as it passes near the solar system so they exit at the other end of the string, still near the solar system but at a time when the string has passed out of harm's way (rather than with the black hole where they would exit very far from where they started).

Answer 3

I suppose I'll address the solar flares angle, since nobody appears to have tried that yet.

My main objection here is that an external source will have a very hard time causing solar flares. Solar flares are, at their hearts, magnetic phenomena. While the exact mechanism behind them is unknown, one fundamental component is charged particles traveling along magnetic field lines, formed inside the star. There are various ideas as to the events that lead to these particles being ejected: kink instabilities in coronal loops (Wood & Priest (1979)), coronal mass ejections (discussed in Zhang et al. (2001)), or more exotic structures (Kusano et al. (2012)). A good overview of many different theories is given in Shibata (2011).

The point is, an external source is most likely not going to cause solar flares. It's true that black holes can have magnetic fields, but, as I explained here, they are generated by the accretion disk surrounding the black hole, not the black hole itself. You would need to have it bring its accretion disk along with it for it to have a magnetic field itself, which would really screw up the Solar System in other ways - and still probably not cause solar flares, unless you take into account the other extreme consequences of a black hole entering the Solar System.