Although (6478) Gault is a main belt asteroid, it has recently been acting very un-asteroidly. The tail visible here is material coming off the asteroid. The current theory is the YORP effect is causing the material to escape the asteroid’s gravitational field.
The surface of solar system objects absorb energy from the sunlight that hits them. If the object rotates, it re-radiates that energy in the form of infra-red radiation in directions determined by the rotation. This energy output can act like a small reaction jet. Depending on the objects rotation, the energy can over time, change the spin rate. If the spin rate increases enough, the material making up the object may drift off of the surface. This effect is named for four contributors (Yarkovsky–O’Keefe–Radzievskii–Paddack) whose concepts contributed to understanding the process.
(6478) Gault [C:15x300s]
The ATLAS (Asteroid Terrestrial-Impact Last Alert System) telescope in Hawai’i first noticed the tail in early January and a search of archived imagery showed additional evidence of the tail was recorded in December of 2018. Right now there are two distinct debris tails but only one is obvious here. Right now the asteroid is just outside of Mars’ orbit and slightly below the plane of the solar system.
I am still working on recovering from a camera power supply failure but the asteroid was very well placed last night (the 28th) so I went ahead and took the series of images that were used to construct the picture. The images were stacked using the asteroid as the reference point which is why the stars are trailed.