Planetary systems that orbit white dwarf stars can be studied via spectroscopic observations of the stars themselves. Numerous white dwarfs are seen to have accreted mostly rocky minor planets, the remnants of which are present in the stellar photospheres. The elemental abundances in the photospheres unveil the bulk compositions of the accreted parent bodies with a precision far greater than can be attained with any other technique currently available to astronomers. The most significant discovery, overall, is that rocky extrasolar planets have bulk elemental compositions similar to those of Earth and other rocky objects in our solar system. The white dwarf studies reveal that many extrasolar minor planets (asteroids) are differentiated, possessing analogs of terrestrial crust, mantle and core; this finding has important implications for the origin of our own solar system.
1) OverviewDiscovery of planetary systems around stars other than our Sun has been a dream of scientists extending back centuries in time. This fascination derives, no doubt, from the question "Are we alone in the Universe?"Well before the first extrasolar planets were discovered astronomers had considered a variety of planet detection techniques. These are discussed in other chapters in this book and include the indirect techniques of astrometry, transits, and precision radial velocity. In addition, one can directly image extrasolar planets via reflected starlight at visible wavelengths or by infrared radiation emitted by self-luminous warm planets. So-called "microlensing" is an additional indirect planet discovery technique that was first noted theoretically only as recently as 1964 (Liebes 1964). But it then took 40 years for this technique to yield its first planet (Bond et al 2004).The purpose of the present chapter is to describe a planetary system discovery technique that is applicable only to white dwarf stars. Whereas all of the above techniques were realized theoretically well before they were observationally successful, the technique of identifying planetary systems around white dwarfs came literally out of the blue --where c is an integration constant that is zero where the mass of Z at time zero is also zero (the typical assumption). For the He-rich DB white dwarfs, the settling times are expected to be long due to the need to settle through large convective layers. In these cases the large values for t z suggest that often t/t z << 1 so that exp(-t/t z ) and exp(t/t z ) approach unity and the solution becomesWe can assume that during this buildup of element Z in the convective layer the rate of accretion is effectively constant, yieldingwhere t is the timescale over which the element is being added. For any two elements, Z1 and Z2, taking their ratio eliminates the time variable such that the mass ratio in the white dwarf faithfully reflects the same ratio in the parent body that is being accreted:This shows clearly the advantage of using elemental ratios; timescales cancel and measured ratios can be interpreted directly as the c...