Kazuo Makishima

Particles are accelerated to very high, nonthermal energies in space, solar, and astrophysical plasma environments. In cosmic-ray physics, the Hillas limit is often used as a rough estimate (or the necessary condition) of the maximum energy of particles. This limit is based on the concepts of one-shot direct acceleration by a system-wide motional electric field, as well as stochastic and diffusive acceleration in strongly turbulent environments. However, it remains unclear how well this limit explains the actual observed maximum energies of particles. Here, we show, based on a systematic review, that the observed maximum energy of particles—those in space, solar, astrophysical, and laboratory environments—often reach the energy predicted by the Hillas limit. We also found several exceptions, such as electrons in solar flares and jet-terminal lobes of radio galaxies, as well as protons in planetary radiation belts, where deviations from this limit occur. We discuss possible causes of such deviations, and we argue in particular that there is a good chance of detecting ultra-high-energy (∼100 GeV) solar flare electrons that have not yet been detected. We anticipate that this study will facilitate further interdisciplinary discussions on the maximum energy of particles and the underlying mechanisms of particle acceleration in diverse plasma environments.

Utilizing four archival X-ray datasets taken with the Hard X-ray Detector onboard Suzaku, timing studies were performed on three magnetars, 1E 1841−045 (observed in 2006), SGR 0501+4516 (2008), and 1RXS J170849.0−400910 (2009 and 2010). Their pulsations were reconfirmed, typically in an energy range of 12–50 keV. The 11.783 s pulses of 1E 1841−045 and those of SGR 0501+4516 at 5.762 s were periodically phase modulated, with a long period of ≈23.4 ks and ≈16.4 ks, respectively. The pulse-phase modulation was also observed, at ≈46.5 ks, from two datasets of 1RXS J170849.0−400910. In all these cases, the modulation amplitude was 6 to 16% of the pulse cycle. Including previously confirmed four objects, this characteristic timing behavior is now detected from seven magnetars in total, and interpreted as a result of free precession of neutron stars that are deformed to an asphericity of ∼10⁻⁴. Assuming that the deformation is due to magnetic stress, these magnetars are inferred to harbor toroidal magnetic fields of B_t ∼ 10¹⁶ G. By comparing the estimated B_t of these objects with their poloidal dipole field B_d, the B_t/B_d ratio is found to increase with their characteristic age. Therefore, the toroidal fields of magnetars are likely to last longer than their poloidal fields. This explains the presence of some classes of neutron stars that have relatively weak B_d but are suspected to hide strong B_t inside them.

Utilizing four archival X-ray datasets taken with the Hard X-ray Detector onboard Suzaku, timing studies were performed on three magnetars, 1E 1841-045 (observed in 2006), SGR 0501+4516 (2008), and 1RXS J170849.0-400910 (2009 and 2010). Their pulsations were reconfirmed, typically in an energy range of 12-50 keV. The 11.783 s pulses of 1E 1841-045, and those of SGR 0501+4516 with 5.762 s were periodically phase modulated, with a long period of about 23.4 ks and about 16.4 ks, respectively. The pulse-phase modulation was also observed, at 46.5 ks, from two datasets of 1RXS J170849.0-400910. In all these cases, the modulation amplitude was 6 to 16 percent of the pulse cycle. Including previously confirmed four objects, this characteristic timing behavior is now detected from seven magnetars in total, and interpreted as a result of free precession of neutron stars that are deformed to an asphericity of ~10^{-4}. Assuming that the deformation is due to magnetic stress, these magnetars are inferred to harbor toroidal magnetic fields of Bt~10^{16} G. By comparing the estimated Bt of these objects with their poloidal dipole field Bd, the Bt/Bd ratio is found to increase with their characteristic age. Therefore, the toroidal fields of magnetars are likely to last longer than their dipole fields. This explains the presence of some classes of neutron stars that have relatively weak Bd but are suspected to hide strong Bt inside them.

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.

The present study aims to reinforce the evidence for the ∼9 s pulsation in the gamma-ray binary LS 5039, derived from a Suzaku observation in 2007 and a NuSTAR observation in 2016. Through a reanalysis of the NuSTAR data incorporating the orbital Doppler correction, the 9.0538 s pulsation was confirmed successfully even in the 3–10 keV range, where it was undetectable previously. This was attained by perceiving an energy-dependent drift in the pulse phase below 10 keV and correcting the pulse timing of individual photons for that effect. Similarly, an archival 0.7–12 keV data set of LS 5039, taken with the ASCA Gas Imaging Spectrometer in 1999 October, was analyzed. The data showed possible periodicity at about 8.882 s, but again the energy-dependent phase drift was noticed below 10 keV. By correcting for this effect, and for the orbital Doppler delays in the LS 5039 system, the 2.8–12 keV periodicity became statistically significant at 8.891 ± 0.001 s. The periods measured with ASCA, Suzaku, and NuSTAR approximately follow an average period derivative of P ̇ ≈ 3.0 × 10 − 10 s s⁻¹. These results provide further evidence for the pulsation in this object and strengthen the scenario proposed by Yoneda et al. that the compact object in LS 5039 is a strongly magnetized neutron star.

We present the catalog of InterPlanetary Network (IPN) localizations for 199 short-duration gamma-ray bursts (sGRBs) detected by the Konus-Wind (KW) experiment between 2011 January 1 and 2021 August 31, which extends the initial sample of IPN-localized KW sGRBs to 495 events. We present the most comprehensive IPN localization data on these events, including probability sky maps in Hierarchical Equal Area isoLatitude Pixelization format.

X-ray timing properties of the magnetar SGR 1900+14 were studied, using the data taken with Suzaku in 2009 and NuSTAR in 2016, for a time lapse of 114 and 242 ks, respectively. On both occasions, the object exhibited the characteristic two-component spectrum. The soft component, dominant in energies below ∼5 keV, showed a regular pulsation, with a period of P = 5.21006 s as determined with the Suzaku XIS, and P = 5.22669 with NuSTAR. However, in ≳ 6 keV where the hard component dominates, the pulsation became detectable with the Suzaku HXD and NuSTAR only after the data were corrected for periodic pulse-phase modulation, with a period of T = 40 − 44 ks and an amplitude of ≈1 s. Further correcting the two data sets for complex energy dependences in the phase modulation parameters, the hard X-ray pulsation became fully detectable, in 12–50 keV with the HXD and 6–60 keV with NuSTAR, using a common value of T = 40.5 ± 0.8 ks. Thus, SGR 1900+14 becomes a third example, after 4U 0142+61 and 1E 1547−5408, to show the hard X-ray pulse-phase modulation, and a second case of energy dependences in the modulation parameters. The neutron star in this system is inferred to perform free precession, as it is axially deformed by ≈ P/T = 1.3 × 10⁻⁴, presumably due to ∼ 10¹⁶ G toroidal magnetic fields. As a counterexample, the Suzaku data of the binary pulsar 4U 1626−67 were analyzed, but no similar effect was found. These results altogether argue against the accretion scenario for magnetars.

This paper describes an analysis of the NuSTAR data of the fastest-rotating magnetar 1E 1547 − 5408, acquired in 2016 April for a time lapse of 151 ks. The source was detected with a 1–60 keV flux of 1.7 × 10⁻¹¹ erg s⁻¹ cm⁻², and its pulsation at a period of 2.086710(5) s. In 8–25 keV, the pulses were phase-modulated with a period of T = 36.0 ± 2.3 ks, and an amplitude of ∼0.2 s. This reconfirms the Suzaku discovery of the same effect at |$T=36.0 ^{+4.5}_{-2.5}$| ks, made in the 2009 outburst. These results strengthen the view derived from the Suzaku data, that this magnetar performs free precession as a result of its axial deformation by ∼0.6 × 10⁻⁴, possibly caused by internal toroidal magneti fields (MFs) reaching ∼10¹⁶ G. Like in the Suzaku case, the modulation was not detected in energies below ∼8 keV. Above 10 keV, the pulse-phase behaviour, including the 36 ks modulation parameters, exhibited complex energy dependencies: at ∼22 keV, the modulation amplitude increased to ∼0.5 s, and the modulation phase changed by ∼65° over 10–27 keV, followed by a phase reversal. Although the pulse significance and pulsed fraction were originally very low in >10 keV, they both increased noticeably, when the arrival times of individual photons were corrected for these systematic pulse-phase variations. Possible origins of these complex phenomena are discussed, in terms of several physical processes that are specific to ultrastrong MFs.