synthetic light curves at the photon energy $E=1.5$ keV, using each of the three $T_\mathrm{eff}(\theta)$ functions of Figure 3. The $B_0=2\times10^{14}$ G, $\theta_0=40^\circ$ model (solid line) achieves the required pulse fraction observed in Kes 79 NS. For $B_0=2\times10^{14}$ G, $\theta_0=10^\circ$ model (dashed line), the hot spot is too concentrated with a small area, causing a decrease in pulse fraction. For $B_0=2\times10^{13}$ G, $\theta_0=40^\circ$ model (dot-dashed line), the spot has enough area, but the rest of the star is simply not dark enough, and thus the pulse fraction is small. We therefore conclude that a toroidal magnetic field in the crust of order $B_\phi\sim{\rm a~few}\times10^{14}$ G or higher, rising slowly enough from zero toward the magnetic equator, such that it allows the hot spot to gain enough area, can naturally produce the requisite pulse fraction observed in the Kes 79 NS.

The bottom panel of Figure 4 shows that the pulse profiles at different photon energies are approximately the same (with the pulse fraction slightly higher at $E=5$ keV than at $1.5$ keV), in agreement with the observation of the Kes 79 NS (Halpern & Gotthelf 2010). Note that while we compute the pulse profiles at a single well-defined energy, they 