Will stars live longer if they consume more hydrogen?

I heard that stars would live longer if they consumed more hydrogen and material from their 'environment'. Is that true? For example, if the sun consumed all of the gas giants, would it live a little bit longer?

• On a related topic, you could greatly extend the Sun's life by starlifting material from the Sun, filtering out heavier elements and returning the hydrogen. This would extend the time until the core "choked" and converted to fusing Helium. Mar 30 '20 at 21:14

Adding mass of similar composition to the Sun would effectively turn the Sun into a higher-mass main-sequence star. That would not increase the gravitational pressure, it would lower it, because it would cause the Sun to expand to lower density. It would also cause the Sun to fuse hydrogen faster, to the point that it would actually reduce the lifetime of the Sun, not increase it. All this can be seen by consulting models of higher-mass main-sequence stars.

If it seems counterintuitive that adding mass would weaken the gravity, this is because the core must self-regulate its fusion rate to match the rate that light is escaping, and simply adding mass would upset that balance unless the Sun expanded to recover it. Note that main-sequence star models do not particularly care about the history of how the mass got there, they are simply the only equilibrium models that have the appropriate mass and composition and are undergoing core fusion.

• Somehow there's a really really bad analogy to "hot water freezes faster than cold" here. Jun 13 '18 at 15:11
• Could a mass infusion really late in the stars life still result in a net increase. eg if 99% of the hydrogen was used up, and adding 1% of a stellar mass of hydrogen did anything less than doubling the burn rate it'd end up a net increase. This might only be relevant for stars that are fully convective from the core to surface like red dwarfs (otherwise you need a way to bring the fresh fuel down to the core). Jun 13 '18 at 16:07
• The problem is, we would assume you cannot inject the hydrogen into the core, it would settle in the envelope. Even if we assumed it somehow managed to get mixed evenly throughout the star, a 1% increase in mass would not double the 1% hydrogen in the core, because something like 70% of the star would still be mostly hydrogen. So you're right that changing the composition could do interesting things, but it would be hard to do. Jun 13 '18 at 21:16

The sun has a mass of $1.989*10^{30}$ kg. Jupiter's mass is $1.898*10^{27}$ kg. That's only about 0.1% of the sun's mass. From a simple estimation, the sun consumes about $4.4*10^9$ kg of hydrogen per second via nuclear fusion. Therefore, it burns about 1 Jupiter Mass every 1.4 million years. Considering the fact that the sun is about 5 billion years old, and will live another 5 billion years, this would increase the sun's lifetime by about 0.1%. This is ultimately a negligible contribution.

Saturn and the other gas giants are all an order of magnitude smaller than Jupiter, so their contributions would be even smaller - just a few hundred thousand years.

In addition, this is all assuming that all of the mass added by the planets we've added is being used for fusion. In reality, Jupiter is only about 90% Hydrogen. Also, adding more mass to the sun would cause it to fuse hydrogen a little more quickly, to counteract the increased gravitational pressure its core would experience. This is why giant stars die more quickly than smaller stars. So this would slightly counteract the increased lifetime from the added fuel.

TL;DR smashing all the gas giants into the sun wouldn't meaningfully change its lifetime.

• Not only would it counteract the added fuel, it would mean adding fuel would actually shorten the Sun's life. (But yes, only very little.) Also, surprisingly, adding mass to the Sun would not result in increasing the gravitational pressure, it would reduce it. The Sun would actually expand a little, and its density would drop, and its core temperature would rise and it would burn its fuel faster. Jun 13 '18 at 5:12
• @KenG I would like to see you expand this to an answer, since this is the interesting point, not comparing the mass of Jupiter and the Sun. I think the answer is complicated and certainly depends how the mass is added. Jun 13 '18 at 6:07
• This answer fails to point out that Jupiter actually has a similar composition to the Sun. All things being equal, making a bigger star leads to faster nuclear fusion and shorter lifetimes. Jun 13 '18 at 6:09
• But wouldn't the sun get more fuel? Jun 13 '18 at 22:21
• More fuel yes, but it would burn it even faster because the larger star would trap and leak more light. Jun 16 '18 at 11:23