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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The figure illustrates a schematic H–R diagram indicating the locations of four regions where most stars are found. The horizontal axis has three ranges of information: (1) T in kelvin, (2) spectral type, and (3) colour index B minus V. The following points are marked on the horizontal axis, from left to right in logarithmic spacing at unequal distances. For T in kelvin: 40000, 30000, 20000, 10000, 5000, 3000, and 2000. For spectral type: O (about 30000), B (between 20000 and 10000), A (below 10000), F (between 7000 and 6000), G (about 5000), K (below 5000), M (above 3000), and L (above 2000). Colour index: negative 0.4 (between 40000 and 30000), 0 (at about 10000), and 1.5 (above 3000). The vertical axis is labelled M subscript V and ranges from 15 (at the bottom) to negative 10 (at the top) in decrements of 5 units, and L divided by L subscript solar and ranges from 10 raised to the negative fourth power (at the bottom) to 10 raised to the sixth power (at the top) in increments of 100 units. Diagonal parallel lines of constant stellar radius labelled 0.001 R subscript solar, 0.01 R subscript solar, 0.01 R subscript solar, 1 R subscript solar, and 10 R subscript solar from the vertical axis move toward the bottom right until the horizontal axis or the right vertical axis. The main-sequence region starts from the top left end and moves toward the bottom right end. The following stars are marked on the main sequence from the top to bottom: Zeta Puppis, Achernar, Regulus, Sirius A, Procyon A, Sun, 61 Cygni A, 61 Cygni B, Barnard’s Star, Proxima Centauri, and Wolf 359. The white dwarfs region is in the bottom left corner of the graph. Some of the white dwarfs are Sirius B (top left), Procyan B (bottom right), and Van Maanen 2 (bottom right of Procyan B). The red giants are on the top right. Some of the red giants (from bottom to top) are Pollux, Arcturus, and Aldebaran A. The supergiants region is at the top of the graph. Some of the supergiants are as follows: Rigel A (top left), Betelgeuse (top right), and Canopus (below and between Rigel A and Betelgeuse). The stars in the region between 10000 K and 7000 K are bluish-white. Moving to the right, the colours become white (around 5000 K), yellowish-white (between 5000 K and 3000 K), and orangey-white (between 3000 K and 2000 K).

Figure 1 (repeated) A schematic H–R diagram indicating the locations of four regions where most stars are found. The vertical axis shows ...