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It occurred to me later that our aliens actually could penetrate the core. All you have to to is target your sun with a gas planet traveling at very high velocities. A small red-giant is about 20 solar diameters, so lets assume a radius of 12 million km. The radius of 12 million km can be traversed at .1 c in about 400 seconds. Since the photosphere is not very dense, the gas planet could hit the core largely intact. Note, that .1 c may simply be faster than needed -- .01c means 4000 seconds (1.1 hours) to reach the core, don't know the lowest speed that would allow you to hit the core which depends on the size and the planet and what percentage needs to penetrate the core.

I am pretty sure that this would be a bad day for our aliens though as the impact would cause huge solar solar flares, and the sudden influx of new hydrogen fuel would perhaps react at a greatly accelerated pace since the core temps are much hotter than those needed to fuse hydrogen.

But, instead of dropping in a planet, why not drop in a big lump of frozen hydrogen enough for say 1 minute worth of fusion, 42 billion metric tons of hydrogen. Now the splash "crater" and solar flares are much smaller and I am pretty sure that most of the hydrogen can still penetrate to the core. Optimize the size and speed of your hydrogen ice balls and repeat as needed.

Even given this strategy, I still don't think it actually helps out the aliens. The core will become even hotter as most of the new fuel burns much faster than the current helium/carbon, etc. core. So the existing core will simply burn faster. I think you have to remove the heavy atoms in the core at the same time you refuel it to actually drop the core temperature. We hit the magic tech required level once again.

So, still no happy answer. But maybe this gives someone an idea for saving the day.

They go back in time to when their sun was young and hydrogen rich and encase the entire star in a oversize General Products Hull that neatly encases their sun. Or perhaps, they are just good planners and don't need to travel back in time.

Due to the GP hull, the sun lasts longer than it otherwise would since it is not wasting its hydrogen on solar flares and solar wind. In the late stages, the additional pressure on the star keeps the star from even going into the giant/supergiant phase as the helium burning phase kicks in. During the main sequence phase, the fuel losses are actually quite minor, but they because quite large in the later stages of a star.

If the stellar radiation becomes too intense over time, your can even activate the Slaver stasis shield, turning on and off the sun rapidly, adjusting the duty cycle to match the desired level of radiation. This would also obviously extend the stars life.

This should extend the useful life of their sun by many millions, if not billions of year. If they are emotionally similar to the Puppeteers, they would perhaps prefer this method over evacuation anyway. It is similar to the Puppeteers solution to their problem in that respect.

I've read the Fleet of Worlds and know how the Puppeteers build a hull, so this is not completely practical at that level, but perhaps an alternate hull construction technique would be possible, or just another similar technology.

Sadly, the real answer for the question as postulated is that it cannot be done. 10 years in not enough time to make any difference sans time travel. Even if you have fully advanced Von-Neuman machines at your service, you can't make a change to the core of your sun in ten years. No non-magical machine can penetrate to to core of a star and alter its composition. To prevent a nova, you have to change the core. And if you have magic tech, surely you could evacuate to safety,

They go back in time to when their sun was young and hydrogen rich and encase the entire star in a oversize General Products Hull that neatly encases their sun. Or perhaps, they are just good planners and don't need to travel back in time.

Due to the GP hull, the sun lasts longer than it otherwise would since it is not wasting its hydrogen on solar flares and solar wind. In the late stages, the additional pressure on the star keeps the star from even going into the giant/supergiant phase as the helium burning phase kicks in. During the main sequence phase, the fuel losses are actually quite minor, but they become quite large in the later stages of a star.

If the stellar radiation becomes too intense over time, your can even activate the Slaver stasis shield, cycling on and off the sun rapidly (hundreds of time per second you would not even notice), adjusting the duty cycle to match the desired level of radiation. This would also obviously extend the stars life.

This should extend the useful life of their sun by many millions, if not billions of year. If the alien race is emotionally similar to the Puppeteers, they would perhaps prefer this method over evacuation anyway. It is similar to the Puppeteers solution to their problem in that respect.

I've read the Fleet of Worlds and know how the Puppeteers build a hull, so this is not completely practical at that level, but perhaps an alternate hull construction technique would be possible, or just another similar technology.

Sadly, the real answer to the question as postulated is that it cannot be done. 10 years is not enough time to make any difference sans time travel. Even if you have fully advanced Von-Neuman machines at your service, you can't make a change to the core of your sun in ten years. No non-magical machine can penetrate to to core of a star and alter its composition because of the temperature are hot enough to turn all matter into plasma quickly. 

To prevent a nova, you must change the core. And if you have magic tech, surely you could evacuate to safety,

They go back in time to when their sun was young and hydrogen rich and encase the entire star in a oversize General Products Hull that neatly encases their sun. Or perhaps, they are just good planners and don't need to travel back in time.

Due to the GP hull, the sun lasts longer than it otherwise would since it is not wasting its hydrogen on solar flares and solar wind. In the late stages, the additional pressure on the star keeps the star from even going into the giant/supergiant phase as the helium burning phase kicks in. During the main sequence phase, the fuel losses are actually quite minor, but they because quite large in the later stages of a star.

If the stellar radiation becomes too intense over time, your can even activate the Slaver stasis shield, turning on and off the sun rapidly, adjusting the duty cycle to match the desired level of radiation. This would also obviously extend the stars life.

This should extend the useful life of their sun by many millions, if not billions of year. If they are emotionally similar to the Puppeteers, they would perhaps prefer this method over evacuation anyway. It is similar to the Puppeteers solution to their problem in that respect.

I've read the Fleet of Worlds and know how the Puppeteers build a hull, so this is not completely practical at that level, but perhaps an alternate hull construction technique would be possible, or just another similar technology.

They go back in time to when their sun was young and hydrogen rich and encase the entire star in a oversize General Products Hull that neatly encases their sun. Or perhaps, they are just good planners and don't need to travel back in time.

Due to the GP hull, the sun lasts longer than it otherwise would since it is not wasting its hydrogen on solar flares and solar wind. In the late stages, the additional pressure on the star keeps the star from even going into the giant/supergiant phase as the helium burning phase kicks in. During the main sequence phase, the fuel losses are actually quite minor, but they because quite large in the later stages of a star.

If the stellar radiation becomes too intense over time, your can even activate the Slaver stasis shield, turning on and off the sun rapidly, adjusting the duty cycle to match the desired level of radiation. This would also obviously extend the stars life.

This should extend the useful life of their sun by many millions, if not billions of year. If they are emotionally similar to the Puppeteers, they would perhaps prefer this method over evacuation anyway. It is similar to the Puppeteers solution to their problem in that respect.

I've read the Fleet of Worlds and know how the Puppeteers build a hull, so this is not completely practical at that level, but perhaps an alternate hull construction technique would be possible, or just another similar technology.

Sadly, the real answer for the question as postulated is that it cannot be done. 10 years in not enough time to make any difference sans time travel. Even if you have fully advanced Von-Neuman machines at your service, you can't make a change to the core of your sun in ten years. No non-magical machine can penetrate to to core of a star and alter its composition. To prevent a nova, you have to change the core. And if you have magic tech, surely you could evacuate to safety,