Is Limb Darkening because at centre we are directly looking core, whereas at limbs we are seeing only photospheric part? Is limb darkening of the Sun because at centre we are directly looking the core and different zones, whereas at limbs we are seeing only the photospheric part (and less beneath photospheric part)? Or there is some other physics behind this phenomenon?
We can't see the core, but we can see deeper into the photosphere of the sun. The deeper layers of the photosphere are hotter and brighter, and this is the cause of limb darkening.