The year is XXXX, or maybe XX,XXX (or maybe even XXX,XXX, though that'd be less than ideal). Humanity has been prospering for the past few millenia, and has stretched out to the stars. I will skip all the geopolitics but will note that, due to lowering birth rates, the population has stabilised at a few dozen billion, and that the Solar System and Earth in particular are considered the centre of human civilisation and still hold most of human population, despite the actual reach of humanity spanning a large chunk of the galaxy (in particular, a largely-automated industry spans millions of systems to supply humanity with resources for grand projects).
Humanity is not alone, though they are currently the most advanced; this is used as a political excuse to overspend on millitary installations for defense, as various human nations posture to be the best "protectors of Earth". As a result, the Solar System has become the most defended place in the galaxy. Compared to the millitary capabilities of all other known civilisations, this is completely overkill, but most people like it that way.
At least until a new invader arrives from outside the galaxy. After razing several alien systems (while leaving the planets intact and harvesting them of resources), and spreading terror across all non-human civilisations, an attack is mounted on the center of humanity itself. The technological marvel that are the Solar defense installations hold up... until, seeing that the battle isn't going their way, the rest of the invading force shows up, with the entire fleet literally swarming the system with of billions of capital-class ships. Humanity's millitary defense, the marvel of the galaxy, is utterly overwhelmed and crumbles, and the invading fleet pours down on the ground to raze the planet like they have done to so many others in the galaxy.
Seeing the human population being decimated and with irreversible defeat upon them, the emergency war council, with mandate from every human nation, takes their final decision: they activate the Solar System's doomsday switch, wiping from existence Earth, its neighbouring planets, and the entirety of the unstoppable alient fleet currently stationed near the center of the Solar System.
What is the lowest tech level with which such a doomsday device could be achieved?
It must be:
- Rapid. While razing the planets and setting up resource harvesting might take some time, the main fleet has little reason to stick around, and may be gone elsewhere (to split up again and keep destroying systems) within a few days. Additionally, in an emergency, assume it will take the alien ships on the order of a few hours to escape FTL (and sub-light drives are negligible); if the "doomsday shockwave" propagates slower-than-light, this must be taken into account.
- Inconspicuous, and/or resilient to attack. Something like a megastructure around the Sun would probably be targeted by the invading force. The doomsday device should be usable once all other defenses have crumbled.
- Comprehensive. At least everything inside the asteroid belt (~4AU from the Sun) should suffer extremely heavy damage. The goal is to reliably wipe out a high-tech fleet of terror, but as a benchmark, planets in range should ideally be destroyed to the point of being unrecognisable (if some central mass is left that, in a few million years, re-accretes into a new planetoid, that's fine). Bonus if the entire planterary system is annihilated (let's say ~50AU), but if there's a significantly easier method which can only wipe the inner regions that would still be the preferred one.
On the low tech end, you could release enough energy to counteract the Earth's gravitational binding energy (e.g. through a large antimatter deposit located in the mantle, whose containment is disabled), and blow up the planet. That would be a big blow to the fleet around it, but the solar system is pretty big, and even the planetary debris will likely leave most of the ships stationed around mostly intact. In particular, over a few days, they will only have the chance to make a fraction of an orbit around the Sun.
On the very high tech end, one could imagine something like releasing some strange matter into the Sun, causing it to collapse into a strange star, and then you can probably handwave how it could cause a chain reaction across the entire system (combined with the energy release from the collapse). Or, veering away from pseudoscience but much more heavily into pseudoengineering, maybe an installation a couple of light days away - far enough to escape notice and damage during the battle - capable of hurling a black hole through the solar system at near light speed. Both of these, however, are quite implausible based on our current understanding of reality.
Is there any way to do this which sits between those two, i.e. achieves enough damage to wipe at least the inner solar system within the required timeframe, but can be at least somewhat grounded in far-future tech without ridiculous handwavium?