Although we have little clue about the physical characteristics of the exoplanets before they were pulverized, all the components that make up the terrestrial planets - Mercury, Venus, Earth, Mars and the asteroids - are present in the white dwarfs' dust. The proportions of these elements are about as "Earth-like" as it gets.
There is one white dwarf, called PG0843+516, that stands out from the other three; it has an overabundance of iron, nickel and sulfur in its atmosphere. These particular elements are found in the cores of rocky planets. During planetary evolution, gravity pulls these elements into the core - a process known as "differentiation." Differentiation will occur in large rocky worlds like Earth, forming a core, mantle, crust and, probably, tectonic activity.
Also, as the white dwarfs' gravity should consume these elements very quickly, the fact that they have been spotted in the star's atmosphere indicates a rocky planetary body is being ripped to shreds right now.
In all four white dwarfs, the researchers estimate 1 million kilograms of planetary material must be raining down into the stars every second. This is significant as they are witnessing the final stages of these star systems' death throes.