How do astrophysicists study astroparticles?
Some on Earth, some in space.
Since everything is the same everywhere in the universe; the atoms, the waves, and the laws of physics. Astrophysicists can simulate the extreme conditions particles undergoes in the universe, such as traveling at near the speed of light and enduring temperature millions and even billions of degrees.
Most famous facilities are the Large Hadron Collider and CERN.
But we do have telescopes and particles detectors here on Earth too, such as LIGO and IceCube.