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 in nature and produced by the colliding solids in these disks. Here, we used ALMA Band 8 to observe emission from neutral carbon at 492 GHz 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 with a surprisingly small mass of $(3.5\pm0.2)\times10^{-3}$ M$_\oplus$. An order of magnitude estimate shows that such a mass can be produced by CO photo-dissociation in a time no longer than $10,000$ yr. We develop a simple evolutionary model to properly account for the reduction in CO photo-dissociation by CO self-shielding and shielding by neutral carbon, following the suggestion by Kral et al (2018). When adopting the commonly used intensity of the interstellar radiation field, to simultaneously reproduce the observed C$^0$ and the previously determined C$^{18}$O masses with our model, a high CO production rate by the debris disk is required, and that gas production started only $\sim$3000 yr ago around this star. By association, its dusty debris disk must also be similarly short-lived. We discuss various scenarios where our conclusion may fail. We conclude that the gas observed around HD 32297 is the result of a recent event, similar to the debris disk around $\beta$ Pictoris.