Question

What astronomical objects are X-ray sources?

Answer 1

Black hole.

Explanation:

Answer is black hole.

Answer 2

If dust and gas falls into an object to generates X-rays then the object must be either a neutron star or a black hole.

Explanation:

Neutron stars and black holes are small and don't emit light in their own right. Both, especially neutron stars, can have very strong magnetic fields.

A neutron star of black hole can be in a cloud of dust, or better, part of a binary system with another star. In this case gas and dust fall into the body forming an accretion disk.

If there is a strong magnetic field or the accretion disk material gets very hot then radiation is produced. This is often in the X-ray range. This radiation makes the object visible as an X-ray source.

So, the objects emitting X-rays is probably a neutron star but could be a black hole.