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We did 194 epochs of simultaneous 2.25/8.60 GHz observations of XTE J1810−197 in 926 days shortly following its reactivation in 2018 with Shanghai Tian Ma Radio Telescope (TMRT). Although its integrated profiles changed with both time and frequency during this period, they could be classified into 12 types according to phase areas of active radiation components. After MJD 59015, XTE J1810−197 turned from the normal emission state into the spiky emission state that was manifesting as a series of bright narrow sub-pulse bursts at both 2.25 and 8.60 GHz. Due to its variable integrated profiles and unsteady rotations, we got the spin frequency ν and spin-frequency derivatives ν ̇ with the piecewise fitting method. In addition, its long-term declining trend of ν was also obtained as ν ̇ = − 3.2 (1) × 10 − 13 s−2 with the linear fitting method based on our observations spanning a comparatively longer period. We found its flux densities went through three stages: sharp decrease, stabilization, and day-to-day fluctuations in our dual-frequency observations. Although the flux density showed different stages, XTE J1810−197 showed a relatively flat spectrum (α > –1) in most observations. Assuming an ideal dipole magnetic field as some previous research works, we obtained the emission heights of XTE J1810−197 were about 7.5(9) × 104 km and 2.38(7) × 104 km at 2.25 and 8.60 GHz, respectively. We also found that its emission heights would decrease rapidly with the degree of magnetic field twisting. [ABSTRACT FROM AUTHOR]

Swift  J1818.0–1607 discovered in early 2020 is not only the fifth magnetar known with periodic radio pulsations but also the fastest rotating one. Simultaneous 2.25/8.60 GHz observations of Swift  J1818.0–1607 were carried out with Shanghai Tian Ma Radio Telescope (TMRT) from MJD 58936 to 59092. The spin-frequency ν and first-order derivative |$\dot{\nu }$| of this magnetar were obtained with piecewise fitting method because of its instable timing properties. We found that the amplitude of short-term |$\dot{\nu }$| fluctuations decreased with time, and the long-term declining trend of ν discovered previously continued in our observations. The best fit long-term |$\dot{\nu }$| were about |$-2.25\times 10^{-11} \, \mathrm{s}^{-2}$| using our observation data spanning 156 d. The derived characteristic age was about 522 yr, supporting the recent viewpoint that this magnetar may be older than initially thought shortly after its discovery. The flux density of this magnetar was increased at both 2.25 and 8.60 GHz during our observations, and its radio spectrum became flatter at the same time. We also detected bright-quiet type emission mode switching in Swift  J1818.0–1607. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the electron Landau level stability and its influence on the electron Fermi energy, , in the circumstance of magnetars, which are powered by magnetic field energy. In a magnetar, the Landau levels of degenerate and relativistic electrons are strongly quantized. A new quantity , the electron Landau level stability coefficient is introduced. According to the requirement that decreases with increasing the magnetic field intensity , the magnetic field index in the expression of must be positive. By introducing the Dirac- function, we deduce a general formulae for the Fermi energy of degenerate and relativistic electrons, and obtain a particular solution to in a superhigh magnetic field (SMF). This solution has a low magnetic field index of , compared with the previous one, and works when and Gauss. By modifying the phase space of relativistic electrons, a SMF can enhance the electron number density , and decrease the maximum of electron Landau level number, which results in a redistribution of electrons. According to Pauli exclusion principle, the degenerate electrons will fill quantum states from the lowest Landau level to the highest Landau level. As increases, more and more electrons will occupy higher Landau levels, though decreases with the Landau level number . The enhanced in a SMF means an increase in the electron Fermi energy and an increase in the electron degeneracy pressure. The results are expected to facilitate the study of the weak-interaction processes inside neutron stars and the magnetic-thermal evolution mechanism for magnetars. [ABSTRACT FROM AUTHOR]