KIC 12557548 (Kepler Input Catalogue 12557548) is a K-type orange dwarf star, smaller and cooler than the sun, but likely to shine for a lot longer. It has an estimated surface temperature of about 4400 K (4127 ° C), compared to 5778 K (5505 °C) for the sun, and is probably about 70% as large. The star is occulted by a transiting object every 15.685 hours, but these occultations, while extremely regular, reduce the apparent output of the star be an irregular amount.
On 12 January 2012 a paper by a team of scientists lead by Saul Rappaport of the Department of Physics and the Kavli Institute for Astrophysics and Space Research at the Massachusetts Institute of Technology, appeared on the arXiv online database at Cornell University Library in which they examine the KIC 12557548 system in more depth, using data from the Kepler Space Telescope combined with observations by the 1.6 m telescope at the Observatoire Astronomique du Mont-Mégantic
The only reasonable explanations of a regular occultation of a star is another body close to our line of sight which regularly interfere with our view of the star, and another body in the same system, orbiting the star. Rappaport et al. were unable to find another star close enough to our line of sight to interfere with our view of KIC 12557548, leaving another body in the same system as the only explanation.
The short period for the object suggests that it must be very close to the parent star; since KIC 12557548 is a fairly small star, a large object in a close orbit, such as a second star, or a brown dwarf, would be extremely unstable. This makes the most likely object a planet, and a fairly small one at that. However the available data does not support a small solid object, which would reduce the light output from the star by a regular amount. Rappaport et al. experimented with the idea of two or more planets with similar or related orbits but could not come up with a stable model for this.
The model that Rappaport et al. eventually came up with involves a small planet, 0.1 times the mass of the Earth or 1.8 times the mass of Mercury and a radius of 0.5 times that of the Earth or 1.3 times that of Mercury, orbiting very close to the parent star. The closeness of the star superheats the surface of the planet, causing rocks to sublimate (turn from a solid to a gas without passing through a liquid phase) from the surface of the planet. Since rocks are largely made up of mixtures of minerals, the escaping gasses would take a lot of small grains of still solid minerals with them, similar to the ash plume of a volcano. The upshot of this would be a small planet that produces a tail similar to a comet, made up of escaping gasses laden with mineral grains.
Models of the planet with its tail seen from (a) stellar north and (b) further out within the plain of the system. The red circle represents the star. From Rappaport et al. (2012).
Rappaport et al. consider that the planet would have to be quite small for this effect to work, since a larger planet's gravity would prevent minerals from escaping, this would only be possible with a small planet with low gravity and no permanent atmosphere. They calculate that such a planet could take about 200 million years to evaporate, though they do not speculate on how the planet could have got into its current position.
See also The strange debris disk of 99 Herculis, Kepler discovers two Cthonian Planets orbiting a subdwarf star, Wasp 19b; a highly irradiated Hot Jupiter and Exoplanets on Sciency Thoughts YouTube.