Torque modeling for 4U 0115+63. (a) Light curve of 4U 0115+63 as measured by Swift/BAT. The red curve is the interpolation of the data. (b) Pulsation period as measured by Fermi/GBM. The red curve is the best-fit model of W_III modified by the Doppler shift of the orbit. The green curve is the intrinsic spin-up of the NS. (c) Intrinsic spin-up signal predicted by the model (same as the green curve in panel (b). (d) χ residuals of the spin model. For all panels, the crosses enclosed by gray diamonds have been ignored for the model comparison; we also note the gaps on the time axis.