White dwarfs are dense, hot, inert cores of low-mass stars made primarily of the element carbon, which requires a temperature of to begin fusion. low-mass stars like the sun do not have enough mass to reach such a high temperature.

It needs a temperature of a 600 Million K to start a fusion. First generation stars were very massive (>30 M) because they were born in warmish clouds (100k) that required higher density for gravity to overcome thermal pressure. If the white dwarf the radius gets smaller.