not surprising that all the temperature profiles are essentially identical at $\tau > 1$; indeed, in the diffusion-limited regime that is to be expected. The less obvious and most crucial point is that the profiles remain very similar for $0.1 < \tau < 1$, where they also differ significantly from a grey opacity profile. In our computations of synthetic light curves (see Figure 2), we see that only the photons traveling nearly radially out from the star emerge from slightly deeper than $\tau\sim 1$, and thus most of the photons contributing to the light curve emerge from smaller Thomson depths. Therefore, a grey opacity temperature profile could not possibly produce the same large synthetic pulse fraction, and would not yield a realistic representation of the emergent flux; we *must* use a self-consistent template accounting for depth-dependent opacity.

Figure 2 shows sample X-ray light curves (normalized to a mean of unity) of magnetic NS surface emission, computed using our TTFT method with various template functions $F(\tau)$ depicted in Figure 1. These light curves are for a specific NS surface model (effective temperature and magnetic field distributions) appropriate for the CCO in Kes 79 (see Section 3 for details). We see that 