normal vector $\hat{\bf r}$. Since ${\cal F}=\sigma T_{\rm eff}^4$, we then obtain a one-to-one mapping between $T_0$ and $T_{\rm eff}$ for the given template function $F(\tau)$. (iii) We then adopt the [*ansatz*]{} that for a given surface patch with $T_{\rm eff}$, the atmosphere profile is $T(\tau;T_{\rm eff})=T_0(T_{\rm eff})F(\tau)$, and the emergent radiation intensity can be computed via the method of Section 2.2.

Figure 1 demonstrates the reasoning for the validity of the TTFT method. The top panel presents several self-consistent temperature profiles at different effective temperatures and field strengths provided by Wynn Ho ($B=0$ and $B=2\times 10^{12}$ G models) and by Valery Suleimanov ($B=6.2\times 10^{10}$ G models). We note that all the profiles are very similar in shape, especially for $\tau\go 0.1$, and differ mostly in overall normalization; this is true both with respect to magnetic field strength variation and effective temperature variation. After normalization to the same $T_{\rm eff}=3.8\times
10^6$ K and $B=8.8\times 10^{10}$ G, all the temperature profiles become similar at $\tau\go 0.1$. Therefore, when computing the intensity of photons that emerge from sufficient depth in the atmosphere, the same single temperature template $F(\tau)$ may be used for the entirety of the NS surface.

Note that it is 