What cosmological event could snuff out the sun without destroying Earth?

[onomatomanic]

^ Exactly. And the post mfb's was in reply to specified that this is a "massive black hole", so we don't even have to rely on its conforming to the known/predicted mass range. No capture is possible between the two stellar-mass objects without the assistance of at least one other in that range.

 

[mfb]

Thanks Drakkith and onomatomanic.

To quantify the ability of our solar system to catch massive objects:
Assume that a massive, slow-moving object (10km/s far away) approaches our solar system. Assume that its mass is small compared to the mass of sun (the reason will become clear later). How can we capture it? Gravitational interaction with a planet. It has to dump enough energy to fall below escape velocity - and it has to do so in a single interaction, as two significant interactions with planets in a single pass through the solar system are extremely unlikely.
The best geometry is a head-on approach to a massive, fast-moving planet, with a very near miss: With the approximation that all objects are point-masses, the planet will be shot in the opposite direction, getting a velocity kick of twice the relative velocity. Real planets have a finite size, which can limit the maximal momentum transfer to lower values, but I will neglect this issue here.


We need massive, fast-moving planets close to the sun... I will begin with Jupiter here and consider Mercury afterwards:

Jupiter orbital velocity 13km/s
Escape velocity (solar system) at its distance: sqrt(2)*13km/s = 18.38km/s
Velocity of incoming object at Jupiter orbit: sqrt(10^2+18.38^2) km/s = 20.93km/s

Relative velocity: 20.92km/s+13km/s = 33.92km/s.
=> Jupiter velocity change 2*33.92km/s = 67.85km/s
Required velocity change of incoming object: (20.93-18.38)km/s=2.54km/s.

=> maximal mass of incoming object: 67.85/2.54 = 26.7 Jupiter masses = 0.026 solar masses.

Mercury: Orbital velocity 47.87km/s, maximal mass of incoming object 317 mercury masses = 0.055 Jupiter masses.

As you can see, Jupiter's mass dominates the results - even with Earth in a mercury orbit, 317 Earth masses would be about one Jupiter mass (and not 26.7).


This gives 26.7 Jupiter masses = 0.026 solar masses as an upper limit for any reasonable capturing process in the solar system.


What happens if we take the finite size of the objects into account? Objects with 26.7 Jupiter masses are brown dwarfs, with a size similar to Jupiter.
Escape velocity scales with sqrt(M/r), at twice the Jupiter radius (closest possible flyby without touching) this corresponds to 60km/s*sqrt(26.7/2)=220km/s. Based on an initial relative velocity of 33.92km/s, the velocity at closest approach is sqrt(220^2+33.92^2)km/s=222.6km/s.

Calculate the (minimal) eccentricity:
$e=\sqrt{1+\frac{2\epsilon h^2}{\mu^2}}$ with ε=1/2 (33.92km/s)^2, h=4*(jupiter radius)*(222.6km/s) and μ=G*26.7*(jupiter mass)
=> e=1.175
This gives a maximal deflection of 2.04 or 117° - in other words, only ~85% of the maximal velocity change can be used and the maximal mass is even lower. And a minimal separation of 2 Jupiter radii is not possible anyway - the brown dwarf is extremely dense, its Roche limit for Jupiter will be significantly larger.

I would expect ~15 Jupiter masses as a more reasonable number.

 

[CCWilson]

How about a relatively slow moving black hole of the mass of the sun? Could that be captured into a binary?

 

[Drakkith]

How about a relatively slow moving black hole of the mass of the sun? Could that be captured into a binary?

Doesn't matter. The Sun, and most everything else in the solar system, would fall towards a black hole, as it falls towards the Sun, with both the Sun and the BH gaining velocity the whole way and being flung out after closest approach. Once away from each other their relative velocity would be similar to what it was before the encounter. Stellar mass black holes are also not the mass of the Sun, but on the order of around 3+ solar masses. There is no known way for a black hole to form with just 1 solar mass.

 

[Ryan_m_b]

There is no known way for a black hole to form with just 1 solar mass.

At first I wondered about a larger black hole shrinking over time to one this size but the universe isn't old enough by far to allow for that type of time scale.

To the OP how about a very small black hole falling into the sun? Over time the sun will shrink and dim as it falls in (though I'm not sure how the exact process will go). As it's sci fi you don't have to explain exactly how this small black hole was formed, you could even mention it baffled scientists but they've got bigger things to deal with now.

 

[mfb]

If we allow very improbable events, there are two small loopholes:

- let a brown/red dwarf scratch the surface of sun, capturing ~2*10^(-4) brown/red dwarf masses, and let it get very close to a planet afterwards (probably Jupiter) to give it some angular momentum. It will end in an extremely eccentric orbit, but bound in the solar system. This needs additional perturbations to get some stable system afterwards, but at least it is possible.
The same would be possible with a black hole of << 1 solar mass, but unless there are primordial black holes with that mass they do not exist.

- the sun could probably perform a similar capturing mechanism around a black hole, swallowing a planet afterwards to get some angular momentum. This event would ruin the whole solar system, some planets would fly away and the others would get completely new orbits afterwards.

 

[CCWilson]

Doesn't matter. The Sun, and most everything else in the solar system, would fall towards a black hole, as it falls towards the Sun, with both the Sun and the BH gaining velocity the whole way and being flung out after closest approach. Once away from each other their relative velocity would be similar to what it was before the encounter. Stellar mass black holes are also not the mass of the Sun, but on the order of around 3+ solar masses. There is no known way for a black hole to form with just 1 solar mass.

I understand that a black hole formed by the collapse of a massive star would be at least 2 1/2 solar masses in size - and that's the size of the black hole in my story. However, don't some physicists believe that some black holes may have formed near the big bang by some mechanisms that we don't fully understand that could indeed give us smaller black holes currently?

 

[Drakkith]

I understand that a black hole formed by the collapse of a massive star would be at least 2 1/2 solar masses in size - and that's the size of the black hole in my story. However, don't some physicists believe that some black holes may have formed near the big bang by some mechanisms that we don't fully understand that could indeed give us smaller black holes currently?

I've never heard of that, but I'm not an astrophysicist or cosmologist, so I really can't say for certain.

 

[mfb]

Could exist, but remains unconfirmed. It would be quite surprising if the first detection happens within our solar system ;).