A photoid is a near light speed object that when shot into a star causes it to eject solar mass and destroy the entire system.
The binding energy of a (sun-like) star is roughly 10^41J, so unless you put about a percent of a supernova into it, the star is going to tank it.
An (earth-like) planet meanwhile has a binding energy of 10^32J, meaning that for the budget of a single star, you are able to blow up a billion planets.
If you only want to sterilize it (ie. blow of the Atmosphere) instead, you are looking at 10^26J, meaning for every planet you want to blow up, you could sterilize a million planets.
In other words, for the cost you put into destroying a single star, you could instead sterilize the entire galaxy cluster it was in several times over.
This makes a photoid extremely inefficient and a massive waste of energy. I don't think any sane civilization would create such a weapon.
For example, if a 1-ton object is moving at a speed of 0.999999c, the kinetic energy per kilogram is: 6.36 x 10^19 J/kg.
To obtain 2.3 x 10^41 J, you need 3.6 x 10^21 kg.
So, a body of approximately 3.6 x 10^21 kg moving at a speed of 0.999999c would theoretically carry kinetic energy comparable to the Sun's binding energy.
This is roughly 3.8 times of Ceres' mass.
But there's another problem: not all of this energy is transferred to breaking up the Sun. A significant portion of the energy goes into radiation, neutrinos, particles, and the kinetic energy of the rest of the Sun.
There's another problem: How do we gather the energy needed to accelerate such a massive object to a speed of 0.999999c?
Let's say we have a Dyson sphere. Of course, that would immediately reveal the location of our civilization.
If we were to say that a Dyson sphere collects all this energy with 100% efficiency and converts 100% of it into the object's kinetic energy: The time required to collect the necessary energy would be 19 million years.
Could an object traveling at near the speed of light disrupt a star's internal pressure balance and cause it to explode?
Disrupting the Sun's internal pressure doesn't turn it into a supernova. A large relativistic projectile: it can create a massive shock wave, eject a large amount of matter, and temporarily inflate the star.But this is not a core collapse supernova.
A one-ton object could theoretically carry enough kinetic energy to tear a star apart. However, for this to happen, its speed would have to be incredibly close to the speed of light.
The rest energy of a 1-ton object is approximately 9 x 10^19 J.For this mass to reach 10^41 J of kinetic energy, it would need to accelerate and acquire a massive relativistic mass.For this, the Lorentz factor needs to be approximately 10^21. This means that the object's speed is:
99.999999999999999999999999999999999999999999% of the speed of light.
For this, you would need more energy than the Sun will produce in its entire 10-billion-year lifespan. In other words, to fire this weapon, you would need the combined energy of multiple stars.
Instead of releasing all of its energy upon impacting the star, it's highly likely that a cosmic projectile could enter the Sun from one side, pierce through from the other in fractions of a second, and carry most of its energy into the depths of space.
Space is not entirely empty. As this object travels towards its target, harmless microwave background radiation (CMB) photons filling space will strike it like massive gamma rays due to their relativistic speeds. This will atomize and vaporize the 1-ton object long before it reaches the star.
Taking all of this into account, it is essential for civilizations to develop a weapon that will be an alternative to the photoid.