A normal star's core consists of Hydrogen but a white dwarf is itself the core and it consists of stellar ash. So the degeneracy pressure is exerted when this stellar ash becomes very dense (In other words when the white dwarf becomes very dense). Am I right? The density of a white dwarf is so much that a small cup of white dwarf material would be equal to the weight of 25 elephants. But why is the stellar ash so dense is another question?