also depend on two geometrical parameters: the angle between the line of sight and the rotation axis, $\beta$, and the angle between the magnetic dipole axis and the rotation axis, $\theta_B$. We select $\beta$ and $\theta_B$ in order to maximize the pulse fraction. Since, as a rule, emission is strongest for photons emitted parallel to the direction of the magnetic field, we should select $\beta$ and $\theta_B$ to be the same or nearly so, such that at some point during the NS’s rotation, the photons we see are emitted parallel to the magnetic field and the beaming effect is maximized. We also select the angles such that a single-peaked pulse profile is produced (see below for double-peaked profiles). After exploring the available phase space, we settle on $\beta=\theta_B=45^\circ$. This choice is not an overly specific one, however, as there are many other geometrical configurations that result in only slightly smaller pulse fractions. Our selection of $\beta$ and $\theta_B$ maximizes the pulse fraction, and therefore minimizes how “dark” the stellar surface must be away from the hot spots. This selection is therefore the most conservative estimate of the required strength of $B_\phi$.

The top panel of Figure 4 presents the whole-star 