Have you seen "Star Trek Generations" movie from 1984?

A key plot device in a movie is that the bad guy launches a "trilithium" probe at a star. The probe stops the nuclear reactions, causing the star to implode, creating a shockwave that destroys its solar system.

Bang!

That made for nice (1994-nice) special effects, but of course it was completely wrong,

Why?

Nuclear reactions in the core don't keep the star stable (on short timescales), the star is stable because it is made of hot gas, and hot gas ("ideal gas") resists gravity via pressure.

In fact you can create a perfectly good model of the Sun (and most of other stars) without (initially) worrying about the fusion - it is a very secondary (but also very important) factor.

So what would have happened if we somehow ("dilithium") were able to switch the fusion off?

Yes, as @PowerDNS_Bert just replied, we would quickly notice that the Solar neutrinos are missing.

But, from the outside (Earth), there would be no difference. The Sun would still be shining happily, and there definitely would be no bang of any kind (boring for the movie!)

But how can Sun still shine, if there is no energy generated in its core?

Short answer: think about the interior of a star as its "retirement account", and fusion as its "income".

If they stop paying me, I will (probably) not explode, and I will still be spending (some) money.

But on a longer timescale, months and years, not having an income anymore (why do they call it "fixed income, by the way?) would definitely change my behavior.

That is also true for a star, but with much longer timescale involved.

What is that timescale? For our Sun, it is about 30 million years, and in general, it is called Kelvin–Helmholtz timescale:

https://en.wikipedia.org/wiki/Kelvin%E2%80%93Helmholtz_mechanism

which is basically how much energy ("saved money") does a star keep inside it, divided by its luminosity ("rate of spending")

So, photons keep leaking out of the "retired" no-fusion Sun (which is still hot, and hot gas makes photons, so it is going to be luminous), but they are not being replenished, so eventually the Sun will stop shining, right?

Wrong!

It would be true if the Sun was just a cloud of gas sitting out there in space, not bound by gravity.

But our Sun is a whole bunch of gas (1 Solar mass, in fact :), bound by its own gravity, so as the photons leak out, our Sun shrinks and gradually gets HOTTER!

So, if we somehow switched the fusion off inside the Sun, it would start (slowly) shrinking, getting hotter, and actually getting brighter (more luminous)!

That is not always the case: young stars, when they shrink, become hotter, but less luminous https://en.wikipedia.org/wiki/Hayashi_track

However, our fusion-less Sun would evolve along so-called Henyey evolutionary track: https://en.wikipedia.org/wiki/Henyey_track

slowly getting hotter and more luminous (again, no fusion).

OK, but then what? It can't just keep shrinking forever, while getting more and more powerful!

(again, this is all a hypothetical scenario of a fusion-less Sun)

(and now I leave you on this nice cliff-hanger :)

We do plan to continue this, but we need to pull together some papers/numbers - it is not entirely trivial (this being a hypothetical situation, so not that well studied).

So for now, watch the reruns instead.

OK, let's resume our "fusion inside the Sun is gone, hijinks ensue" hypothetical scenario.

The pseudo-Sun keeps contracting while becoming hotter and more luminous, but at some point it will stop.

Why?

Electron degeneracy pressure!

What?

At some point, as star's density grows, electrons are so close to each other that quantum exclusion principle kicks in: namely, two electrons are not allowed to simultaneously occupy the same quantum state: https://en.wikipedia.org/wiki/Electron_degeneracy_pressure

The pseudo-Sun stops contracting!

Basically, at that point our pseudo-Sun becomes a ~1 solar mass white dwarf: https://en.wikipedia.org/wiki/White_dwarf

Given mass-radius relation for white dwarfs (below), it will be about 0.01 Solar radii, with an average density of 10^6 grams/CC (million times water density)!

So we started with a ~1 Solar radius star, now shrunk to ~0.01 Solar radii, while, which, while collapsing, released large amounts of photon energy ("light"), obtained from converting gravitational potential energy to 1/2 internal heat, 1/2 photons ("virial theorem").

Hot!

How much energy is that? We use an equation below (assuming 3/5 ~ 1, don't get too emotional :) for gravitational binding energy https://en.wikipedia.org/wiki/Gravitational_binding_energy

and we get ≈ 4×10^43 Joules ≈ 4×10^50 ergs

(assuming I did not screw up the math, let me know if I did).

Half of that energy

≈ 2×10^43 Joules ≈ 2×10^50 ergs

will be released as photons between the initial ~1 Solar radius stage and the final ~0.01 Solar radii stage.

OK, just like the pseudo-Sun, we will pause here for now.

But you can enjoy an actual image of the nearest white dwarf to us, Sirius B, taken with Hubble (hint: not the giant thing in the middle): https://www.nasa.gov/multimedia/imagegallery/image_feature_468.html

Picking up the story of the hypothetical "pseudo-Sun" where for whatever reason (aliens?!) the nuclear reactions in the core have been stopped.

Recap: such a star would not explode, quite the opposite - it would start shrinking, but slowly, gradually increasing its brightness.

What we have described so far - shrinking, and then stopping due to electron degeneracy pressure - was all rather easy to deduce.

The next step - how long it takes between stopping nuclear reactions and the pseudo-Sun effectively becoming a white dwarf - is harder to calculate.

Why?

We do know how much energy can be released - ≈ 2×10^43 Joules ≈ 2×10^50 ergs - but it is not trivial to know the luminosity without actual calculations.

So, like any good astronomer, I will just take an Order of Magnitude approach, and I will say that it was ~10 L_Sun.

So now we just take

≈ 2×10^50 ergs

divide by 10 L_Sun, and you get

≈ 5×10^15 seconds or ≈ 1.6×10^8 years - 160 million years!

This is just a OoM guess, but a reasonable one - I am sure some of the people reading it can do a better calculation.

So if the Evil Aliens come to our Solar System, and they decide to destroy us by somehow stopping the nuclear reactions in the core of our Sun, we don't need to panic - we have many millions of years to figure out the solution (or to destroy ourselves first, just to spite them).

Quick update -- Local Stellar Evolution Expert says:

"True, Henyey would be what you’d get for a radiative star contracting in a homologous fashion. For a free free opacity you’d have L ~ R^-0.5, so L would go up by 10 if R dropped by 100. .."

Yay!

But there is a caveat:

"However, once you get closer to degeneracy, you switch to a conductive T gradient that is pretty small and the sign changes. So it’s fair to say somewhat brighter initially."

So overall, not a bad guess on our part. Lower luminosity extends the lifetime.

"But wait, there's more!"

Remember that ≈ 2×10^50 ergs of energy that was radiated away while the pseudo-Sun was shrinking?

Another ≈ 2×10^50 ergs of energy was stored inside the Sun in thermal motions of particles (proton, electron, some helium), and that can be used to generate more photons!

So now the pseudo-Sun is no longer shrinking, but it is still shining, just like white dwarfs do - it would be a every unusual white dwarf that we don't see in nature, but that is the beauty of hypothetical of scenarios and imagination.

So what happens?

At this point I have decided that I need somebody who does this every day to actually verify my story, and Jared Goldberg ( @aurimontem - thanks Jared!) ran some quick stellar evolution models with fusion switched off.

Here is a teaser - radius vs. time plot for our scenario:

When we return, I will show more plots made by @aurimontem, but in the meantime you can check out his scientific papers using ADS:

https://ui.adsabs.harvard.edu/search/fq=%7B!type%3Daqp%20v%3D%24fq_database%7D&fq_database=database%3A%20astronomy&q=author%3A(%22%5Egoldberg%22%20%22bildsten%22)&sort=date%20desc%2C%20bibcode%20desc&p_=0

So, as a reminder, I went to Jared ( @aurimontem: https://www.physics.ucsb.edu/people/jared-austin-goldberg), and he quickly run the MESA stellar evolution code to see in details what happens ( http://mesa.sourceforge.net/ ).

Overall, my guesses were pretty good, but there are some details worth spending more time on.

Let's look at what happen with the luminosity of our pseudo-Sun as a function of time.

As expected, it initially goes up, reaching a peak value of ~5 L_Sun some ~50 million years from the "trilithium event".

That is as expected, but a bit less luminous than my initial guess.

The truth is, the fact that the luminosity actually goes up initially is not that trivial to explain - let's just say that has something to do with how the "opacity" works inside a star, and I am not yet ready to explain opacity on Twitter :)

Then, still looking at the evolution of the luminosity, our pseudo-Sun starts to fade, but it is not until ~100 million years after the "event" that it drops below the initial value of 1 L_Sun.

After that, the star resembles a white dwarf more and more,
dimming rather quickly.

Let's look at another plot that @aurimontem made: evolution of our pseudo-Sun in surface temperature-luminosity diagram (log-log scale), color coded by time since the event.

Big dots mark 10^6, 10^7, 10^8, 10^9, and 10^10 (10 billion!) years.

As our pseudo-Sun shrinks, its surface temperature increases, eventually reaching ~25,000 Kelvin (compared to 5,800 K these days).

So our-alien attacked Sun would have been smaller on the sky, but even more painful to look at!

(no, I am not going to post that picture)

OK, one final plot that @aurimontem made: he went "nuts" (probably just took few minutes), and run stellar evolution tracks for several stars with different mass with fusion and with no fusion at all, see below:

Here, there was no "alien event", the star is either allowed to fuse hydrogen into helium, or not.

It becomes immediately clear what the fusion really is good for: it allows the star to basically sit there for billions of years in a very stable configuration - Main Sequence!

This was a fun thread to run - this is a neat problem that I have been asking graduate students at various exams for many years now :)

Thanks @aurimontem and his adviser Lars Bildsten for such a quick reaction to my whimsical, late evening e-mail!

And an immediate update: in the meantime, Jared ( @aurimontem) run these hypothetical evolution models with a smaller time step, and there are some small differences, so here they are, just for fun (please don't use these in any actual publication, obviously):

In summary:

If Evil Aliens, who obviously have some super-advanced technology, but apparently never took an astrophysics course, try to destroy the Earth by stopping the nuclear fusion in the core of our Sun, they will be disappointed!