Would ripping the core from a Sun-like star cause it to explode?
I'm well aware that a Sun-like star is incapable of producing a supernova at the end of its life. However, would removing the core or a fraction of it, trigger an explosion from the star collapsing in on itself? Removing, in this case, means actually taking somewhere else, both the mass and energy that may be present. Would the collapse be violent enough to light a more energetic and runaway fusion reaction or produce antimatter as may be the case with a hypernova?
If an explosion occurs how might it compare to an actual supernova?
Don't worry about the mechanism that removes the core; for the sake of the question I'm only concerned with the effect.
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Let's think about why a supernova happens in a massive star. You probably know that after a star develops an iron core, further nuclear fusion is not possible on a large scale. Yes, you can produce heavier elements via neutron capture, which indeed happens during supernovae (via the r-process) and inside massive stars (via the s-process), but conditions simply aren't suitable enough to form them at any significant rates inside massive stars, let alone the Sun. Therefore, you no longer have a source of outward pressure in the core (although the outer layers will still be fusing lighter nuclei in shell-burning processes).
Previously, the star was in hydrostatic equilibrium; the outward pressure balanced the inward gravitational force. However, the inner pressure is now gone - as is the case with your coreless Sun - and so the core begins to collapse. What happens next is a little complex; I'm going to quote from an answer I wrote on Astronomy:
- At high enough densities ($\rho\sim10^9\text{ g/cm}^3$), electron capture becomes important, where a proton and electron combine to form a neutron and an electron neutrino: $$e^-+p\to n+\nu_e$$ Simultaneously, beta decay may occur, where a neutron decays to a proton, electron and electron antineutrino: $$n\to p+e^-+\bar{\nu}_e$$ However, beta decay becomes less important than electron capture at this point.
- Electron capture reduces electron degeneracy pressure in the core, which leads to accelerated core collapse. Degeneracy pressure is important in the cores of many stars, but in extremely massive stars - red supergiants included - it simply isn't enough to stop the collapse.
- At densities below $\sim10^{11}\text{ g/cm}^3$, neutrinos can carry away energy, and the initial burst leaves the star within about ten seconds. However, core collapse quickly leads to much greater densities, and when $\rho\sim4\times10^{11}\text{ g/cm}^3$, neutrinos are trapped. They scatter off nuclei, and transfer energy to electrons. Electron-nuclei scattering is also important, and may be dominant at higher energies.
- At $\rho\sim2.5\times10^{14}\text{ g/cm}^3$, the core undergoes a "bounce", and the supernova explosion fully begins. A shock wave propagates into the outer core, and more neutrinos are produced via electron capture.
- Neutrinos still trapped in/by the stellar remnant are released about ten seconds later. Neutrino pair production, too, leads to rapid cooling. Some of these neutrinos may contribute to a revival of the shockwave.
What if we could quickly stop the densities from reaching high enough that electron capture becomes less important, stalling both accretion and the outward rejuvenating burst of neutrinos? That would provide support against further collapse, and stop the outward shockwave from every forming, because there would be no bounce. In fact, we can do this easily in the case of the Sun, given that we should expect to see a lower core density than in massive stars.
Now, those lower densities mean neutrinos are less likely to interact with the outer layers of the star; thus, they should escape, carrying their energy harmlessly away. This should make the bounce weaker, if it happens at all - another reason I'd argue that the supernova may not occur.
Another advantage we may have is that the Sun's core is not degenerate; rather, it is supported by thermal pressure. I suspect this should make it more stable. The analogy I see used a lot, and which I prefer, is that of a thermostat, which was mentioned in the linked notes above. In a star, if the pressure decreases, so does the temperature and fusion rate. The star then collapses a little until it reaches higher densities, increasing fusion rate, temperature and pressure until it is stable once more. I'm guessing that this is what would happen for a coreless Sun. The density would presumably never be high enough for electron capture to occur, and so the shockwave would never happen. You wouldn't have a supernova, because you'd have something to counter the collapse: nuclear fusion.
Here's another little tidbit: electron capture is more likely to happen with free protons than with heavier nuclei (see Balasi et al. (2015)), meaning that if you had plenty of heavy metals in your coreless Sun, perhaps electron capture could happen less dramatically, slowing the core collapse and perhaps preventing the bounce.
Finally, I've been debating whether or not I should mention a helium flash. Again, I have no idea how fusion in the coreless Sun would occur as material moved towards the center, but there's a chance you could see brief runaway fusion (similar to what happens in a helium flash) that would then be damped, albeit a reaction of hydrogen fusion, not helium fusion. I'm still not sure how that would affect the possibility of a bounce.
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