The surprisingly low carbon mass in the debris disk around HD 32297

Gas has been detected in a number of debris disks. It is likely secondary, i.e. produced by colliding solids. Here, we report ALMA Band 8 observations of neutral carbon in the CO-rich debris disk around the 15--30 Myr old A-type star HD 32297. We find that C$^0$ is located in a ring at $\sim$110 au with a FWHM of $\sim$80 au, and has a mass of $(3.5\pm0.2)\times10^{-3}$ M$_\oplus$. Naively, such a surprisingly small mass can be accumulated from CO photo-dissociation in a time as short as $\sim$10$^4$ yr. We develop a simple model for gas production and destruction in this system, properly accounting for CO self-shielding and shielding by neutral carbon, and introducing a removal mechanism for carbon gas. We find that the most likely scenario to explain both C$^0$ and CO observations, is one where the carbon gas is rapidly removed on a timescale of order a thousand years and the system maintains a very high CO production rate of $\sim$15 M$_\oplus$ Myr$^{-1}$, much higher than the rate of dust grind-down. We propose a possible scenario to meet these peculiar conditions: the capture of carbon onto dust grains, followed by rapid CO re-formation and re-release. In steady state, CO would continuously be recycled, producing a CO-rich gas ring that shows no appreciable spreading over time. This picture might be extended to explain other gas-rich debris disks.