Discovery of free precession in the magnetar SGR 1806−20 with the ASCA Gas Imaging Spectrometer

Publications of the Astronomical Society of Japan, 2024, 76(4), 688–701 https://doi.org/10.1093/pasj/psae040 Advance access publication date: 2024 May 25 Discovery of free precession in the magnetar SGR 1806−20 with the ASCA Gas Imaging Spectrometer Kazuo MAKISHIMA,1 ,2 ,∗ Nagomi UCHIDA,3 and Teruaki ENOTO4 ,5 1 Department of Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo, 5-1-5 Kashiwa-no-ha, Kashiwa, Chiba 277-8683, Japan 3 Institute of Space and Astronautical Science, JAXA, 3-1-1 Yoshinodai, Chuo-ku, Sagamihara, Kanagawa 252-5210, Japan 4 Department of Physics, Kyoto University, Kitashirakawa Oiwake-cho, Sakyo-ku, Kyoto, Kyoto 606-8502, Japan 5 Extreme Natural Phenomena RIKEN Hakubi Research Team, Cluster for Pioneering Research, RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan 2 E-mail: Abstract Four X-ray datasets 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, the last one in 1995 October. Epoch-folding analysis of the 2.8–12 keV signals confirmed the ∼7.6 s pulses in these data, which Kouveliotou et al. (1998, Nature, 393, 235) 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 ± 0.4 ks, and an amplitude of ∼1 s. This makes a fourth example of the behavior observed from magnetars. As in the previous three sources, the pulse-phase modulation of SGR 1806−20 disappeared at 2.5 keV, where the soft X-ray component dominates. In the 1993 datasets, 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 ± 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 ∼10−4 , presumably by the stress of toroidal magnetic fields reaching ∼1016 G. Toroidal fields of this level can be common among magnetars. Keywords: stars: individual: SGR 1806-201 — stars: magnetars — stars: magnetic fields — stars: neutron 1 Introduction Consider an axisymmetric rigid body with I1 = I2 = I3 , where Ij is the moment of inertia around the principal axes xˆ j ( j = 1, 2, 3), with xˆ 3 the body’s symmetry axis. When the body is  is confree from external torque, its angular momentum L served, and its dynamics around the center of gravity is split into two modes (Landau and Lifshitz 1996) that degenerate when the body is spherical. One is free precession, wherein  with xˆ 3 rotates (as seen from the inertial frame) around L a constant precession period Ppr = 2π I1 /L, and a constant  . (This should not be confused wobbling angle α relative to L with forced precession that is often observed in a spinning top.) The other is rotation around xˆ3 with a rotation period Prot = 2π I3 /L = Ppr /(1 + ), where  ≡ (I1 − I3 )/I3 is asphericity. When α = 0 and the body’s emission is symmetric around xˆ 3 , we can detect Ppr as the pulsation, whereas Prot is undetectable (see a discussion in sub-subsection 4.3.1). If α = 0 and the emission violates the symmetry around xˆ 3 , the phase of the pulsation at Ppr becomes modulated at the beat period between Ppr and Prot , given as T= −1 Ppr 1  −1 −1 = Prot − Ppr  cos α cos α (1) (Butikov 2006). This pulse-phase modulation (PPM) provides evidence for the free precession in an asymmetrically radiating celestial object that is axially deformed ( = 0) and has α = 0. Although astrophysical examples of free precession remain relatively limited, we have detected its evidence from three magnetars, 4U 0142+61 (Makishima et al. 2014, 2019), 1E 1547.0−5408 (Makishima et al. 2016, 2021a), and SGR 1900+14 (Makishima et al. 2021b). In these objects, the hard X-ray pulses with a period P = Ppr were found to exhibit the PPM effect, with a long period of T ∼ 104 P that can be identified with T in equation (1). Further assuming cos α ∼ 1, we find that these neutron stars (NSs) are deformed to  ∼ P/T ∼10−4 , and perform free precession. Since the centrifugal effect is much smaller (estimated to be  ∼ 10−7 ) in these slowly rotating NSs, the deformation must be due to magnetic stress. Then, the inferred magnetic field becomes B ∼ 1016 G, when combined with a theoretical prediction (Ioka & Sasaki 2004) as  ∼ 10−4 (B/1016 G)2 . (2) Because this B is much higher than the dipole magnetic fields of these objects, Bd = (1–7) × 1014 G, the magnetic fields that cause the deformation are considered to be confined inside these NSs, in the form of toroidal magnetic fields, Bt . To reinforce this scenario, we study SGR 1806−20, with the primary aim to search for the PPM effect. If this phenomenon is common to magnetars, it should also be detected from SGR 1806−20, the prototypical object that connected Received: 2023 December 4; Accepted: 2024 April 18 © The Author(s) 2024. Published by Oxford University Press on behalf of the Astronomical Society of Japan. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited. ∗ Publications of the Astronomical Society of Japan (2024), Vol. 76, No. 4 2 Observations 2.1 The Gas Imaging Spectrometer (GIS) The Gas Imaging Spectrometer (GIS; Ohashi et al. 1996; Makishima et al. 1996) onboard ASCA consists of a pair of identical imaging gas scintillation proportional counters, named GIS2 and GIS3. They are placed at the focal planes of the X-ray Telescope (XRT; Serlemitsos et al. 1995), and cover a wide field of view (0.◦ 75 diameter) with a moderate angular resolution (≈4 ). The GIS also realizes a high sensitivity and a low background, over a broad energy band of 0.7–12 keV, which covers both the HXC and SXC of SGR 1806−20. The modest energy resolution (8% FHHM at 7 keV) of the GIS is sufficient for the present purpose. Being a gas detector, the GIS also has a high time resolution (t = 61 or 488 μs), which is sufficient in the present work, together with a low dead time, which allows detection of burst-like phenomena. 2.2 A brief history We briefly review the dramatic progress of the knowledge on SGR 1806−20 that took place in the mid-1990s. As described in Murakami et al. (1994), the fourth Japanese X-ray satellite ASCA (Tanaka et al. 1994) had been in orbit for 7 months when a burst activity of SGR 1806−20 was detected, after nearly a decade, by CGRO/BATSE on 1993 September 29. At that time, the object was only coarsely (∼1◦ × 4 ) localized by interplanetary burst-timing triangulation. On 1993 October 9 and 10, four short pilot po (...truncated)