Title: Discovery of the Free Precession in the Magnetar SGR 1806$-$20 with the ASCA GIS

Abstract: Four X-ray data sets of the Soft Gamma Repeater SGR 1806-20, taken with the Gas Imaging Spectrometer (GIS) onboad ASCA, were analyzed. Three of them were acquired over 1993 October 9-20, whereas the last one in 1995 October. Epoch-folding analysis of the 2.8-12 keV signals confirmed the $\sim 7.6$ s pulses in these data, which Kouveliotou et al. (1998) reported as one of the earliest pulse detections from this object. In the 1995 observation, 3-12 keV pulses were phase modulated with a period of $T =16.4 \pm 0.4$ ks, and an amplitude of $\sim 1$ s. This makes a fourth example of the behavior observed from magnetars. Like in the previous three sources, the pulse-phase modulation of SGR 1806-20 disappeared at $\lesssim 2.5$ keV, where the soft X-ray component dominates. In the 1993 data sets, this periodic modulation was reconfirmed, and successfully phase-connected coherently across the 11 d interval. As a result, the modulation period was refined to $T =16.435 \pm 0.024$ ks. The implied high stability of the phenomenon strengthens its interpretation in terms of free precession of the neutron star, which is deformed to an asphericity of $\sim 10^{-4}$, presumably by the stress of toroidal magnetic fields reaching $\sim 10^{16}$ G. Toroidal fields of this level can be common among magnetars.