Cumulative probability of the circumferential radius for a hydrogen atmosphere model of the 0.4–3 keV XMM-Newton pn data obtained for PSR J1614−2230 by Pancrazi et al. (2012). The solid red line shows the result for a conservative assumption of ﹩{\theta }_{c}=85^\circ ﹩ (i.e., the spot is close the rotational equator; note that for ﹩{\theta }_{c}=90^\circ ﹩ and the known ﹩{\theta }_{{\rm{obs}}}\approx 90^\circ ﹩, ﹩{{Rc}}^{2}/{GM}\lesssim 3.5﹩, or ﹩R\lesssim 10﹩ km for the known mass ﹩M=1.93\;{M}_{\odot }﹩, produces caustics that are ruled out by the data) and the dotted blue line shows the result for ﹩{\theta }_{c}=40^\circ ﹩, which is the magnetic inclination angle found by Venter et al. (2009) from analysis of Fermi gamma-ray data. This figure shows that if the spot is closer to the pole than to the equator the limits are currently somewhat interesting (﹩R\gt 10﹩ km with ∼10% probability), but if the spot is at the equator no realistic radius is significantly disfavored. Note that in this figure and the others we present, there are no meaningful upper limits to the radius because for larger radii a smaller ﹩{\theta }_{c}﹩, a larger spot, or an extra unmodulated emission could produce statistically acceptable fits to the real or synthetic data.