Figure 3 presents three sample functions $T_\mathrm{eff}(\theta)$, two at the same value of $B_0$ but different values of $\theta_0$ and one at a lower value of $B_0$. We also include the corresponding $f(\theta)$ curves to clarify the effect of changing $\theta_0$. It is important to note that when the toroidal field strength $B_0$ is sufficiently large, even a very smooth $B_\phi$ profile can produce rather small hot spots. For example, at $B_0=2\times 10^{14}$ G and $\theta_0=40^\circ$, the temperature drops from $T_p\simeq 4\times
10^6$ K

at the magnetic pole to $T_p/2$ at $\theta\sim 3^\circ$, and to $T_p/4$ at $\theta\sim 10^\circ$.

When computing the synthetic X-ray light curves, we split the effective temperature curve into 7-9 bins, with degree-resolution close to the pole, and coarser resolution for the rest of the star. For each bin we create the temperature profile $T(\tau;T_{\rm
  eff})$ at the requisite effective temperature using the TTFT process described in Section 2. Note that since $B_\phi$ vanishes at the NS surface, it does not contribute to the atmospheric physics in any way. We can then compute the light curves for each of the effective temperature distributions depicted in Figure 3.

In addition to $B_0$ and $\theta_0$, the light curves 