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NICER observed two outbursts from the neutron star low-mass X-ray binary 4U~1730$-$22 in 2021 and 2022, which showed a similar spectral evolution in the hardness-intensity diagram. Seventeen type I X-ray bursts were identified in both outbursts. The X-ray burst spectra showed clear deviations from the blackbody model, firstly $\sim10$ s after onset. Adding the enhanced persistent emission due to the Poynting-Robertson drag or the reflection from the accretion disk both significantly improved the fitting results. We found that 12 out of 17 X-ray bursts showed the photospheric radius expansion (PRE) characteristic. Considering the nine PRE bursts out of ten X-ray bursts observed by Insight-HXMT, 78\% of bursts from 4U~1730--22 exhibited PRE. According to the burst rise time, the duration, the local accretion rate, and the burst fuel composition estimated from recurrence time, we propose that these PRE bursts were powered by pure helium. From the touchdown flux of PRE bursts, we estimate the source distance of $ d=7.54\pm{0.46} (X=0)$ kpc for a canonical neutron star with $M_{\rm NS}=1.4M_\odot$ and $R_{\rm NS}=10~{\rm km}$., 11 pages, 6 figures; Matches the version published in A&A

Type I X-ray bursts are the result of an unstable thermonuclear burning of accreting matter on the neutron star (NS) surface. The quick release of energetic X-ray photons during such bursts interacts with the surrounding accretion disk, which raises the accretion rate due to Poynting-Robertson drag and, thus, a fraction of the burst emission is reflected. We analyzed two photospheric radius expansion bursts in the NS low-mass X-ray binary 4U 1636--536 that took place in 2017, using data from Neutron star Interior Composition Explorer. The time-resolved burst spectra showed clear deviations from a blackbody model. The spectral fitting can be significantly improved by introducing either the enhanced persistent emission (the $f_a$ model) or the reflection from the accretion disk (the \texttt{relxillNS} model). The $f_a$ model provides a higher blackbody temperature and higher burst flux compared with the \texttt{relxillNS} model. The peak fluxes of two bursts from the $f_a$ model, $4.36\times10^{-8}~\mathrm{erg~cm^{-2}~s^{-1}}$ and $9.10\times10^{-8}~\mathrm{erg~cm^{-2}~s^{-1}}$, are slightly higher than the Eddington limits of mixed hydrogen-helium and pure helium bursts from previous observations, respectively. When the disk reflections have been taken into account simultaneously, the peak fluxes are lower to match the preferred values. We find evidence to support the finding that both the Poynting-Robertson drag and disk reflection have been appeared during these two X-ray bursts. Moreover, the disk reflection may contribute $\sim20-30\%$ of the total burst emissions., 8 pages, 7 figures. This version matches the published version

Type-I X-ray burst oscillations are powered by thermonuclear released on the neutron star (NS) surface in low mass X-ray binaries (LMXBs), where the burst oscillation frequencies are close to the NS spin rates. In this work, we report the detection of oscillation at 584.65 Hz during the cooling tail of a type-I X-ray bursts observed from the accreting NS LMXB 4U~1730--22 in 2022 March 20, by the \textit{ Neutron star Interior Composition Explorer} (\textit{NICER}) telescope. The oscillation signal showed a strong Leahy power, $P_{\rm m}\sim54.04$, around 584.65 Hz, which has single trial and multiple trials confidence levels of $7.05\sigma$ and $4.78\sigma$, respectively. The folded pulse profile of the oscillation in the 0.2--10 keV band showed a sinusoidal shape with the fraction amplitude rms of $(12.5\pm1.8)\%$. We found the oscillation frequency showed insignificant upward drifting, i.e., less than 0.3 Hz, during the cooling tail, similar as the behavior appearing in accreting millisecond X-ray pulsars (AMXP), and indicate the source could be an AMXP spinning at 1.71 ms., Comment: matches published version

Superbursts are long duration, rare, and extremely energetic thermonuclear explosions of neutron star low-mass X-ray binaries (NS LMXBs), which are proposed to be due to unstable carbon ignition. We report the superburst properties and consequences from Aql X-1 observed by the Neutron Star Interior Composition Explorer (NICER), the Monitor of All-sky X-ray Image, Swift, and Insight Hard X-ray Modulation Telescope (Insight-HXMT) on the MJD 59130.7. We found two faint type I X-ray bursts 9.44 days after the superburst with a short recurrence time of 7.6 minutes, which is the most accurate measurement of the quenching time in all NS LMXBs with observed superbursts. We also discovered mHz quasi-periodic oscillations in the frequency range 2.7--11.3 mHz immediately after the superburst, before and after the resumption of the first type I X-ray burst from NICER, Swift, and Insight-HXMT observations. For the first time, we observed the transition from superburst, via marginally stable burning to unstable burning in NS LMXBs. We compared the quenching time and the recurrence time of type I X-ray bursts with simulations., Comment: Minor changes to match version published in ApJ

The various types of pulsars are classified in the magnetic and spin period (B-P) diagram, by which one can recognize their properties there. We also investigate the relation of radio pulsars and X-ray neutron stars, and their distribution characteristics, implying their evolution links. B-P diagram is divided by the special lines, e.g. spin-up line and "death line", which indicate the evolution information of pulsars. Like Hertzsprung-Russell (H-R) diagram of showing the stellar evolution or "lives of stars", we try to develop B-P diagram as a function of representing the evolution track of neutron star.

With accretion of mass from an evolving companion star, a neutron star can be spun up to an equilibrium period, which is set by the Kepler orbital period at the magnetosphere radius, expressed as a proportional relation between the spin period and magnetic field strength. The spin-up line relationship can be also expressed as a relation between period (P) and period derivative (Ṗ) for the pulsars with dipole radiation. All binary pulsars should lie below the spin-up line, if they accrete the sufficient masses from companions. So, we investigate the distribution of isolated and binary pulsars in the period (P) and magnetic field (B) diagram to see their positions relative to the spin-up line. It is found that the eight binary pulsars (of total 172) are above the spin-up line, thus we analyze their properties and present the possible process of their formations.

We investigated the spin period evolution of the accreting neutron star (NS) in binary systems, based on the accretion-induced magnetic decay model, while both the accretion spin-up torque and the gravitational wave (GW) emission induced spin-down torque are taken into account. We found that the spin period of millisecond pulsar (MSP) can stop at the value of several milliseconds, if the accretion spin-up torque balances the spin-down torque by the GW radiation. Furthermore, we obtained the minimum spin period of MSP and its relation to the deformation ellipticity of NS that accounts for the NS mass quadrupole moment. The comparisons between the pulsar observations and the model results are discussed in the diagram of magnetic field versus spin period, and the consistency can be obtained.

Using data from the ATNF pulsar catalogue, 186 binary pulsars are shown in the magnetic field versus spin period (B-P) diagram, and their relationship to the spin-up line is investigated. Generally speaking, pulsars in binary systems should be below the spin-up line when they get enough accretion mass from their companions. It is found that there are seven binary pulsars above the spin-up line. Based on the parameters of these seven binary systems, we describe possible reasons why they are above the spin-up line., 3 pages, 1figure, 1table

186 binary pulsars are shown in the magnetic field versus spin period (B-P) dia- gram, and their relations to the millisecond pulsars can be clearly seen. We declaim a minimum accretion rate for the millisecond pulsar formation both from the observation and theory. If the accretion rate is lower than the minimum accretion rate, the pulsar in binary system will not become a millisecond pulsar after the evolution., Comment: 2 pages, 1figure

The bottom magnetic fields of neutron stars (NSs) in LMXBs are found to be proportionally related to their accretion rate, i.e. Z (Atoll) source with Eddington (less Eddington) rate is associated with a stronger value of about B ~109 G (B ~108 G). We discuss the relation between the jet formation of NS and its bottom magnetic field strength, and pointed out that the accretion powered millisecond pulsar will not exclude the jet production, furthermore the appearance of kHz QPOs may be also coexistence with the jets. The observer's viewing angle to the NS rotating axis may be a significant factor for observing the jet, pulsar or kHz QPO.