Constraints on the HI Mass for NGC 1052-DF2

We report deep, single-dish 21 cm observations of NGC 1052-DF2, taken with the Green Bank Telescope. NGC. 1052-DF2, proposed to be lacking in dark matter, is currently classified as an ultra-diffuse galaxy in the NGC. 1052 group. We do not detect the galaxy, and derive an upper limit on the H I mass. The galaxy is extremely gas poor, and we find that a 3 sigma M-H (I) detection at a distance of 19 Mpc and using a line width of 3.2 km s(-1) would have an upper limit of M-H (I),(lim) < 5.5 x 10(5) M-circle dot At this mass limit, the gas fraction of neutral gas mass to stellar mass is extremely low, at M-H I/M-star < 0.0027. This extremely low gas fraction, comparable to Galactic dwarf spheroidals and gas-poor dwarf ellipticals, implies that either the galaxy is within the virial radius of NGC. 1052, where its gas has been stripped due to its proximity to the central galaxy, or that NGC. 1052-DF2 is at a distance that is large enough to inhibit detection of its gas. We also estimate the upper limit of the H I mass of NGC. 1052-DF2 resided at 13 Mpc. This would give an H I mass of M-H (I),(lim) < 2.5 x 10(5) M-circle dot, and an H I gas fraction if M-H (I)/ M-star < 0.0024, becoming even more extreme for its environment. While the dark matter fraction would be less extreme at this distance, the neutral gas fraction would be unprecedented for an object in a low-density environment.