A linear stability analysis is performed for a plume flow inside a cylinder of aspect ratio 1. The configuration is identical to that used by Lopez and Marques (2013) for their direct numerical simulation study. It is found that the first bifurcation, which leads to a periodic axisymmetric flow state, is accurately predicted by linear analysis: both the critical Rayleigh number and the global frequency are consistent with the reported DNS results. It is further shown that pressure feedback drives the global mode, rather than absolute instability.