Question

How is it possible for white dwarf stars to have lower luminosity than the sun even though the sun is cooler than white dwarfs?

Answer 1

Size of a white dwarf is small.

Explanation:

So luminosity is also low.

Answer 2

A white dwarf may be hot but it is not generating energy, it is losing it.

Explanation:

A white dwarf is the remains of a star after fusion reactions have finished. The core collapse which creates a white dwarf makes it initially very hot. It can be over `100,000K`.

White dwarfs emit radiation while they cool down over a very long time period. They are very small and have very low luminosity.

A star like the Sun on the other hand is constantly producing energy from fusion reactions in the core. Although the surface temperature may only be `6,000K`, the core is at `14,000,000K` and constantly producing energy. Hence the Sun is much larger and much more luminous.

Red giant stars are even cooler at less than `4,000K`. They still have fusion reactions taking place in or around the core. They are very large and very much more luminous than the Sun.