"The data lead us to postulate that we are witnessing an encounter with an asteroid or in-falling debris from a disk," they write in a paper published to the arXiv pre-print service.
It stands to reason that debris from a star system may persist after the parent star has gone supernova, leaving a rapidly-spinning pulsar in its wake. Planetary bodies, asteroids, dust and gas will therefore collect around the pulsar in the form of a disk. The gravity of the pulsar will inevitably drag some of that mass into it. After some extreme physics right near the surface of the dense matter, the in-falling matter will abruptly alter the pulsar's spin rate and its radiation signature, two distinct signals that PSR J0738-4042 generated in 2005.
ANALYSIS: Pulsar Planets: Strange Worlds Orbiting Undead Stars
The researchers calculated that a mass of a billion tons dropped into the pulsar's magnetosphere, the effects of which can be observed today. As the mass, presumably a moderately-sized asteroid, fell into the pulsar's magnetosphere, getting shredded and material ionized - akin to a magnetic blender. The highly-charged particles from the ex-asteroid then got trapped in the pulsar's magnetic field, blasting out energy and bleeding the spinning stellar husk of its angular momentum, or spin, causing the observed slowdown in pulses.