Why can the accretion disk around a neutron star release so much more energy than the accretion disk around a white dwarf, even though the two stars have approximately the same mass?

Neutron stars are incredibly dense remnants of massive stars that have undergone supernova explosions. They are fascinating celestial objects with unique characteristics.
Neutron stars form when the core of a massive star collapses under gravity as the outer layers are blown away in a supernova. This collapse forces protons and electrons to combine and form neutrons, resulting in an extremely dense object.
Typical neutron stars have a mass similar to that of the sun but are only about 10 kilometers in diameter. This extraordinary density means that a sugar-cube-sized amount of neutron-star material would weigh about a billion tons on Earth.
Because of their small radii, neutron stars have incredibly strong gravitational fields. This results in high gravitational potential energy, which becomes significant when discussing energy release from accretion disks.

White dwarfs are remnants of stars like our sun that have exhausted their nuclear fuel and shed their outer layers. These remnants form when a star has expelled its outer layers, leaving behind a dense core which cools and contracts into a white dwarf.
Unlike neutron stars, white dwarfs are slightly less dense with typical radii around 10,000 kilometers, making them much larger in comparison. Yet, they are still very dense because they pack a sun-like mass into a relatively small volume the size of Earth.
White dwarfs no longer undergo fusion reactions and instead shine by radiating away the residual thermal energy left from their previous stages. Since they are less dense than neutron stars and have larger radii, their gravitational potential energy is lower, affecting the overall energy released by their accretion disks.

Gravitational potential energy is key to understanding why accretion disks around neutron stars release more energy compared to those around white dwarfs. This energy depends on both the mass of the star and its radius and is described by the formula U = - \frac{GMm}{r} Here,

• \(G\) is the gravitational constant, a measure of the strength of gravity in the universe.
• \(M\) is the mass of the star, either neutron star or white dwarf in our case.
• \(m\) is the mass of the accreted material.
• \(r\) is the radius of the star.

Since neutron stars have much smaller radii compared to white dwarfs, the gravitational potential energy (U) in absolute value is much higher for neutron stars. This means that as material accretes (falls onto the star), the energy released is much greater for neutron stars due to their stronger gravitational fields.
In summary, the significant difference in radii between neutron stars and white dwarfs leads to a stark contrast in gravitational potential energy, explaining the differences in energy release observed.