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# 4.4 White dwarf composition and cooling

The simplest type of white dwarf, resulting from the collapse of a star of very low main-sequence mass () in which no helium burning has occurred, would be composed entirely of helium. Such objects are referred to as He white dwarfs, with masses . However we are unlikely to find isolated He white dwarfs in the Galaxy for the following reason. The He white dwarfs form from stars with very low mass. Such stars have main-sequence lifetimes of ~ 1011 years, or around 10 times the age of the Universe, so have not had time to evolve into white dwarfs yet. Any He white dwarfs that are seen must have formed as part of a binary star system that has undergone a phase of mass transfer which has altered the mass and composition of one or both of its components.

Low-mass stars, with , undergo helium burning, producing carbon and oxygen in their cores. They lose some mass while on the AGB and so typically end their lives with masses of . Even intermediate-mass stars, with , lose so much mass as giants that only remains to form the white dwarf. These carbon/oxygen cores are supported against further collapse by degenerate electrons, and hence do not attain the temperatures required to initiate carbon burning. The remnants of low- and intermediate-mass stars are therefore CO white dwarfs, with masses .

There is a narrow range of massive stars, with , whose remaining cores are massive enough to collapse and ignite carbon (forming oxygen, neon and magnesium), but which ultimately fall below the Chandrasekhar limit owing to continued mass loss. When this carbon burning terminates, these stars will be supported by degenerate electrons again and will contract no further, leaving ONeMg white dwarfs, with masses typically in the range .

Stars with retain enough of their mass during mass loss that their cores continue to exceed the Chandrasekhar limit; at the end of each burning phase, their cores contract and heat up more. These stars complete all of the advanced burning phases, including silicon burning to form iron. Their endpoints will be explored in later sections of this course.

As there are no nuclear energy sources active in a white dwarf, its luminosity is due solely to the slow leakage of thermal energy into space, as radiation. It takes ~ 109 y for white dwarfs to fade to . As white dwarfs fade, they also cool. The luminosity of white dwarfs is provided by thermal leakage rather than slow gravitational contraction because white dwarfs are degenerate, so their temperature and pressure are decoupled. As they cool, the pressure remains constant so the radius is unchanged. Hence there is no release of gravitational potential energy. As white dwarfs cool and fade in the H–R diagram, they do so along lines of constant radius (see Figure 1).

Figure 1 (repeated) A schematic H–R diagram indicating the locations of four regions where most stars are found. The vertical axis shows stellar luminosity in solar units or absolute visual magnitude; the horizontal axis shows surface temperature in kelvins, spectral type, or colour index defined as the difference between B and V magnitudes. (Notice that temperature increases to the left.) Diagonal lines of constant stellar radius are also shown and some notable named stars are indicated.
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