How much energy would it take to ignite a brown dwarf?

Question

The Halo video game's extended universe book Halo: Evolutions describes the Battle of Psi Serpentis, in which a superjovian planet is converted into a brown dwarf via massive nuclear bombardment of its core, destroying the vastly more powerful pursuing Covenant alien fleet.

The Covenant fleet regrouped and pursued Cole's fleet until a group of Insurrectionist vessels emerged from slipspace. Led by the heavily modified Bellicose, they opened fire on the Covenant, losing a quarter of their number. Once they attacked they smashed through the Covenant formation and withdrew from the system. Cole himself moved Everest deeper into Viperidae's gravity well while the UNSC fleet proceeded to disengage. The Admiral then issued a broadcast to the pursuing Covenant ships, boasting of his own achievements while scoffing at their claim to righteousness. Sensing and accepting the challenge, the Covenant moved to attack Everest, but their plasma was deflected by the magnetosphere of the planet.

Cole moved Everest past the point of no return from Viperidae's gravity well, and launched a barrage of missiles at the lead ship in the Covenant formation. Nuclear fire destroyed the ship but there was little damage done to the rest of the fleet.

While the Covenant fleet was distracted by the barrage, Cole had launched one hundred Shiva nuclear warheads into Viperidae's unstable core. The resulting ignition caused the planet to go nova, undergoing stellar fusion and briefly becoming a brown dwarf. The resulting shockwave obliterated all of the Covenant ships, reduced Viperidae to a smoldering rock, and presumably destroyed Everest.

Is such a battle tactic actually valid, in the sense that would launching a large number of nuclear weapons at the core of a superjovian planet be sufficient to cause it to ignite into a brown dwarf? If so, how much energy is required to make this happen?

Answer 1

$2.55\times10^{45}\text{ Joules}$. But it probably won't work.

There are a few things we need to get straight here, namely, the differences between brown dwarfs and giant planets. Here are two of the most important:^[1]

• Mass. Brown dwarfs are, at the lower mass end, greater than ~13 Jupiter masses, and there's a murky transition zone between low-mass brown dwarfs and high-mass gas giants (see Burgasser). Other categories of object, like sub-brown dwarfs, only serve to muddle the waters. But most brown dwarfs are in the dozens of Jupiter masses, extending to about 80 Jupiter masses. So to make a super-Jupiter (actually a technical term) a brown dwarf, you'd have to increase its mass. As Samuel calculated, this change in mass comes out to ~2.55$\times$10⁴⁵ Joules.
• Structure. Structure is very important when analyzing substellar objects. Brown dwarfs don't really have layers, while gas giants typically do. So you'd need to somehow figure out a way to get rid of all the layers of matter in a gas giant to make it more like a brown dwarf. Composition is a related factor, although many of the same compounds (even besides hydrogen and helium) are present in brown dwarfs. This answer on Physics Stack Exchange (which is fantastic) states that you would need a deuterium layer for fusion to happen as is the case in a brown dwarf, which makes sense.

You'd need to change both of these things in order to turn a gas giant into even a low-mass brown dwarf.

There's also one more issue: Setting off a nuclear explosion wouldn't do much (surprising, right?). Why? Well, you could set off a whole bunch of nuclear weapons, thereby raising the temperature and pressure in a certain volume. But you would have a tough time sustaining the necessary conditions for hydrogen fusion (at least ~10⁷ Kelvin, for the p-p chain). Obviously, nuclear weapons reach this temperature, but they quickly cool. The temperature would quickly drop, as would pressure. You might get a little bit of fusion going, but I doubt it would be enough to sustain hydrogen fusion - unless you increased the mass. This document found that no runaway fusion would be possible in an Earth-like atmosphere, and I suspect that similar mechanisms of energy loss would exist here, making it impossible for fusion to happen as you intend.

It would be much easier to reach conditions necessary for deuterium fusion - and I would assume that that requires a lower starting temperature - but a sustained reaction would be just as hard.

For fun, here's how fast thermal radiation emission drops (again, from here):

Note that this would, of course, be increased if you increased the number of weapons detonated (would 100 really be enough?). That said, I'd be worried about how you propose to bring the weapons so deep into the brown dwarf. I would think that before reaching the core, where the conditions for fusion would be best, temperatures and pressures could cause premature detonation, leading to a much less effective use of the weapons.

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Some other random criticisms of the scenario:

• Viperidae most likely did not have any heavier elements inside it, so it would not turn to "rock" afterwards. I don't know what the result would be, but a substantial portion might remain as gas.
• A gas giant should not have an "unstable core".
• There isn't a "point of no return" from the "gravity well", as Viperidae is not a black hole, although perhaps this referred to low fuel levels.
• The shockwave might not be too powerful unless material was ejected to carry it. Space is not a vacuum, but it still doesn't (in general) conduct shockwaves too well unless the medium is dense enough.

I take it, however, that you don't really care about these points that much.

Answer 2

In short, no, this isn't a valid battle tactic. A nuclear weapon would have little to no effect on even a small gas giant. The key isn't energy, it's mass.

A nuclear bombardment from orbit might have a total detonated yield in the gigatons or even teratons of TNT. That sounds like a lot, and it is, if you are considering what it would do to conditions on our own planet. However, that's not even a drop in the bucket of the forces and energies at work inside a gas giant, never mind a superjovian.

The key, as I said, is mass. It takes about 25-40 Jupiter masses before you start seeing sustained deuterium burning (depending on the exact makeup of the giant, the amount of solar gain from its star and what, exactly, you consider enough sub-fusion activity to draw a line in the sand between gas giant and brown dwarf). If the planet's currently around 20 M_J, you'd have to feed 5 additional Jupiters' worth of mass into the gas giant to even have a chance of seeing a net energy output from deuterium burning. We have nothing anywhere near the technology needed to move this kind of mass in anything approaching a war timescale. If we did, the tactic of igniting a superjovian to make it a weapon would be superfluous; you could simply carve a large chunk out of a nearby moon and throw it at your pursuers in a high-speed shotgun blast of Europe-sized asteroids.