We have computed an extensive grid of binary evolution tracks to represent low- and intermediate mass X-ray binaries (LMXBs and IMXBs). The grid includes 42,000 models which covers 60 initial donor masses over the range of 1-4 solar masses and, for each of these, 700 initial orbital periods over the range of 10-250 hours. These results can be applied to understanding LMXBs and IMXBs: those that evolve analogously to CVs; that form ultracompact binaries with orbital periods in the range of 6-50 minutes; and that lead to wide orbits with giant donors. We also investigate the relic binary recycled radio pulsars into which these systems evolve. To evolve the donor stars in this study, we utilized a newly developed stellar evolution code called "MESA" that was designed, among other things, to be able to handle very low-mass and degenerate donors. This first application of the results is aimed at an understanding of the newly discovered pulsar PSR J1614-2230 which has a 1.97 solar masses neutron star, orbital period = 8.7 days, and a companion star of 0.5 solar mass. We show that (i) this system is a cousin to the LMXB Cyg X-2; (ii) for neutron stars of canonical birth mass 1.4 solar masses, the initial donor stars which produce the closest relatives to PSR J1614-2230 have a mass between 3.4-3.8 solar masses; (iii) neutron stars as massive as 1.97 solar masses are not easy to produce in spite of the initially high mass of the donor star, unless they were already born as relatively massive neutron stars; (iv) to successfully produce a system like PSR J1614-2230 requires a minimum initial neutron star mass of at least 1.6+-0.1 solar masses, as well as initial donor masses and orbital period of ~ 4.25+-0.10 solar masses and ~49+-2 hrs, respectively; and (v) the current companion star is largely composed of CO, but should have a surface H abundance of ~10-15%.
PSR J1640+2224 is a binary millisecond pulsar (BMSP) with a white dwarf (WD) companion. Recent observations indicate that the WD is very likely to be a $\sim 0.7\,M_{\odot}$ CO WD. Thus the BMSP should have evolved from an intermediate-mass X-ray binary (IMXB). However, previous investigations on IMXB evolution predict that the orbital periods of the resultant BMSPs are generally $<40$ days, in contrast with the 175 day orbital period of PSR J1640+2224. In this paper, we explore the influence of the mass of the neutron star (NS) and the chemical compositions of the companion star on the format…
We report the first hard X-ray (3-79 keV) observations of the millisecond pulsar (MSP) binary PSR J1023+0038 using NuSTAR. This system has been shown transiting between a low-mass X-ray binary (LMXB) state and a rotation-powered MSP state. The NuSTAR observations were taken in both LMXB state and rotation-powered state. The source is clearly seen in both states up to ~79 keV. During the LMXB state, the 3-79 keV flux is about a factor of 10 higher that in the rotation-powered state. The hard X-rays show clear orbital modulation during the X-ray faint rotation-powered state but the X-ray orbital…
Transitional millisecond pulsars (tMSPs) switch, on roughly multi-year timescales, between rotation-powered radio millisecond pulsar (RMSP) and accretion-powered low-mass X-ray binary (LMXB) states. The tMSPs have raised several questions related to the nature of accretion flow in their LMXB state and the mechanism that causes the state switch. The discovery of coherent X-ray pulsations from PSR J1023+0038 (while in the LMXB state) provides us with the first opportunity to perform timing observations and to compare the neutron star's spin variation during this state to the measured spin-down i…
Millisecond pulsars (MSPs) are mainly characterised by their spin periods, B-fields and masses - quantities which are largely affected by previous interactions with a companion star in a binary system. In this paper, we investigate the formation mechanism of MSPs by considering the pulsar recycling process in both intermediate-mass X-ray binaries (IMXBs) and low-mass X-ray binaries (LMXBs). The IMXBs mainly lead to the formation of binary MSPs with a massive carbon-oxygen (CO) or an oxygen-neon-magnesium white dwarf (ONeMg WD) companion, whereas the LMXBs form recycled pulsars with a helium wh…
The transitional millisecond pulsar binary system PSR J1023+0038 re-entered an accreting state in 2013 June, in which it bears many similarities to low-mass X-ray binaries (LMXBs) in quiescence or near-quiescence. At a distance of just 1.37 kpc, PSR J1023+0038 offers an unsurpassed ability to study low-level accretion onto a highly-magnetized compact object. We have monitored PSR J1023+0038 intensively using radio imaging with the Karl G. Jansky Very Large Array, the European VLBI Network and LOFAR, seeing rapidly variable, flat spectrum emission that persists over a period of 6 months. The fl…
PSR J1713+0747 is a binary system comprising millisecond radio pulsar with a spin period of 4.57 ms, and a low-mass white dwarf (WD) companion orbiting the pulsar with a period of 67.8 days. Using the general relativistic Shapiro delay, the masses of the WD and pulsar components were previously found to be $0.28\pm 0.03 M_{\odot}$ and $1.3\pm 0.2 M_{\odot}$ (68% confidence), respectively. Standard binary evolution theory suggests that PSR J1713+0747 evolved from a low-mass X-ray binary (LMXB). Here, we test this hypothesis. We used a binary evolution code and a WD evolution code to calculate e…
The spin-down rate of PSR J1023+0038, one of the three confirmed transitional millisecond pulsars, was measured in both radio pulsar (RMSP) and X-ray pulsar (LMXB) states. The spin-down rate in the LMXB state is only about 27 % greater than in the RMSP state (Jaodand et al. 2016). The inner disk radius, r_in, obtained recently by Ertan (2017) for the propeller phase, which is close to the co-rotation radius, r_co, and insensitive to the mass-flow rate, can explain the observed torques together with the X-ray luminosities, Lx . The X-ray pulsar and radio pulsar states correspond to accretion wi…
Ultra-luminous X-ray sources (ULXs) are those X-ray sources located away from the centre of their host galaxy with luminosities exceeding the Eddington limit of a stellar-mass black hole ($L_X>10^{39}\;{\rm erg\,s}^{-1}$). The discovery of X-ray pulsations in some of these objects (e.g. M82~X-2) suggests that a certain fraction of the ULX population may have a neutron star accretor. We present systematic modelling of low- and intermediate-mass X-ray binaries (LMXBs and IMXBs; donor-star mass range $0.92$--$8.0$~M$_{\odot}$ and neutron-star accretors) to explain the formation of this sub-popula…
The author presented the results on the evolution of NS LMXBs and the formation of UCXBs(Ma & Li 2009 for details), and proposed a scenario for the formation of UCXBs from L/IMXBs with the aid of a CB disk in this work.
In this review I discuss the characteristics and the formation of all classes of millisecond pulsars (MSPs). The main focus is on the stellar astrophysics of X-ray binaries leading to the production of fully recycled MSPs with white dwarf (WD) or substellar semi-degenerate companions. Depending on the nature of the companion star MSPs are believed to form from either low-mass X-ray binaries (LMXBs) or intermediate-mass X-ray binaries (IMXBs). For each of these two classes of X-ray binaries the evolutionary status of the donor star -- or equivalently, the orbital period -- at the onset of the R…
We consider the evolution of millisecond radio pulsars in binary systems with a main-sequence or evolved stellar companion. Evolution of non-accreting binary systems with "eclipsing" milisecond pulsars was described by Kluźniak, Czerny & Ray (1992) who predicted that systems like the one containing the Terzan 5 PSR 1744-24A will in the future become accreting low mass X-ray binaries (LMXBs), while PSR 1957+20 may evaporate its companion. The model presented in the current paper gives similar results for these two objects and allows to obtain diverse evolutionary tracks of millisecond pulsars w…
Although the first millisecond pulsars (MSPs) were discovered 30 years ago we still do not understand all details of their formation process. Here, we present new results from Tauris, Langer & Kramer (2012) on the recycling scenario leading to radio MSPs with helium or carbon-oxygen white dwarf companions via evolution of low- and intermediate mass X-ray binaries (LMXBs, IMXBs). We discuss the location of the spin-up line in the (P,Pdot)-diagram and estimate the amount of accreted mass needed to obtain a given spin period and compare with observations. Finally, we constrain the true ages of ob…
We report NuSTAR observations of the millisecond pulsar - low mass X-ray binary (LMXB) transition system PSR J1023+0038 from June and October 2013, before and after the formation of an accretion disk around the neutron star. Between June 10-12, a few days to two weeks before the radio disappearance of the pulsar, the 3-79 keV X-ray spectrum was well fit by a simple power law with a photon index of Gamma=1.17 +/-0.08 (at 90% confidence) with a 3-79 keV luminosity of 7.4+/-0.4 x 10^32 erg/s. Significant orbital modulation was observed with a modulation fraction of 36+/-10%. During the October 19…
XSS J12270-4859 is an X-ray binary associated with the Fermi LAT gamma-ray source 1FGL J1227.9-4852. In 2012 December, this source underwent a transition where the X-ray and optical luminosity dropped and the spectral signatures of an accretion disc disappeared. We report the discovery of a 1.69 millisecond pulsar (MSP), PSR J1227-4853, at a dispersion measure of 43.4 pc cm$^{-3}$ associated with this source, using the GMRT at 607 MHz. This demonstrates that, post-transition, the system hosts an active radio MSP. This is the third system after PSR J1023+0038 and PSR J1824-2452I showing evidenc…
Transitional millisecond pulsars are systems that alternate between an accreting low-mass X-ray binary (LMXB) state, and a non-accreting radio pulsar state. When at the LMXB state, their X-ray and optical light curves show rapid flares and dips, origin of which is not well understood. We present results from our optical and NIR observing campaign of PSR J1023+0038, a transitional millisecond pulsar observed in an accretion state. Our wide band optical photopolarimetry indicates that the system shows intrinsic linear polarisation, the degree of which is anticorrelated with optical emission, i.e…
The low-mass X-ray binary (LMXB) system FIRST J102347.6+003841 hosts a newly born millisecond pulsar (MSP) PSR J1023+0038 that was revealed as the first and only known rotation-powered MSP in a quiescent LMXB. While the system is shown to have an accretion disk before 2002, it remains unclear how the accretion disk has been removed in order to reveal the radio pulsation in 2007. In this Letter, we report the discovery of gamma-rays spatially consistent with FIRST J102347.6+003841, at a significance of 7 standard deviations, using data obtained by the Fermi Gamma-ray Space Telescope. The gamma-…
The pulsar J1203+0038 rotates with a frequency $ν\approx 592$ Hz and has been observed to transition between a radio state, during which it is visible as a millisecond radio pulsar, and and a Low Mass X-ray Binary state, during which accretion powered X-ray pulsations are visible. Timing during the two phases reveals that during the LMXB phase the neutron star is spinning down at a rate of $\dotν\approx -3 \times 10^{-15}$ Hz/s, which is approximately 27\% faster than the rate measured during the radio phase, $\dotν\approx -2.4 \times 10^{-15}$ Hz/s, and at odds with the predictions of accreti…
Binary millisecond pulsars (BMSPs) are thought to have evolved from low-mass X-ray binaries (LMXBs). If the mass transfer in LMXBs is driven by nuclear evolution of the donor star, the final orbital period is predicted to be well correlated with the mass of the white dwarf (WD), which is the degenerate He core of the donor. Here we show that this relation can be extended to very small WD mass ($\sim 0.14-0.17\,M_\odot$) and narrow orbital period (about a few hours), mainly depending on the metallicities of the donor stars. There is also discontinuity in the relation, which is due to the tempor…
XSS J12270-4859 is the only low mass X-ray binary (LMXB) with a proposed persistent gamma-ray counterpart in the Fermi-LAT domain, 2FGL 1227.7-4853. Here, we present the results of the analysis of recent INTEGRAL observations, aimed at assessing the long-term variability of the hard X-ray emission, and thus the stability of the accretion state. We confirm that the source behaves as a persistent hard X-ray emitter between 2003 and 2012. We propose that XSS J12270-4859 hosts a neutron star in a propeller state, a state we investigate in detail, developing a theoretical model to reproduce the ass…
The $Fermi$-LAT has revealed that rotation powered millisecond pulsars (MSPs) are a major contributor to the Galactic $γ$-ray source population. Such pulsars may also be important in modeling the quiescent state of several low mass X-ray binaries (LMXBs), where optical observations of the companion star suggest the possible existence of rotation powered MSPs. To understand the observational properties of the different evolutionary stages of MSPs, the X-ray and $γ$-ray emission associated with the outer gap model is investigated. For rotation powered MSPs, the size of the outer gap and the prop…
According to the recycling scenario, millisecond pulsars (MSPs) have evolved from low-mass X-ray binaries (LMXBs). Their orbits are expected to be circular due to tidal interactions during the binary evolution, as observed in most of the binary MSPs. There are some peculiar systems that do not fit this picture. Three recent examples are PSRs J2234$+$06, J1946$+$3417 and J1950$+$2414, all of which are MSPs in eccentric orbits but with mass functions compatible with expected He white dwarf companions. It has been suggested these MSPs may have formed from delayed accretion-induced collapse of mas…
We present an analysis of high energy (HE; 0.1-300 GeV) gamma-ray observations of 1FGL J1227.9-4852 with the Fermi Gamma-ray Space Telescope, follow-up radio observations with the Australia Telescope Compact Array, Giant Metrewave Radio Telescope and Parkes radio telescopes of the same field and follow-up optical observations with the ESO VLT. We also examine archival XMM-Newton and INTEGRAL X-ray observations of the region around this source. The gamma-ray spectrum of 1FGL J1227.9-4852 is best fit with an exponentially cutoff power-law, reminiscent of the population of pulsars observed by Fer…
Previous optical and radio observations of the binary millisecond pulsar PSR J1640+2224 have come to inconsistent conclusions about the identity of its companion, with some observations suggesting the companion is a low-mass helium-core (He-core) white dwarf (WD), while others indicate it is most likely a high-mass carbon-oxygen (CO) WD. Binary evolution models predict PSR J1640+2224 most likely formed in a low-mass X-ray binary (LMXB) based on the pulsar's short spin period and long-period, low-eccentricity orbit, in which case its companion should be a He-core WD with mass about $0.35 - 0.39…
When neutrons star low-mass X-ray binaries (NS-LMXBs) are in the low-level accretion regime (i.e., $L_{\rm X}\lesssim 10^{36}\ \rm erg\ s^{-1}$), the accretion flow in the inner region around the NS is expected to be existed in the form of the hot accretion flow, e.g., the advection-dominated accretion flow (ADAF) as that in black hole X-ray binaries. Following our previous studies in Qiao $\&$ Liu 2020a and 2020b on the ADAF accretion around NSs, in this paper, we investigate the radiative efficiency of NSs with an ADAF accretion in detail, showing that the radiative efficiency of NSs with an…
Intermediate-mass binary pulsars (IMBPs) are composed of neutron stars (NSs) and CO/ONe white dwarfs (WDs). It is generally suggested that IMBPs evolve from intermediate-mass X-ray binaries (IMXBs). However, this scenario is difficult to explain the formation of IMBPs with orbital periods ($P_{\rm orb}$) less than 3 d. It has recently been proposed that a system consisting of a neutron star (NS) and a helium (He) star can form IMBPs with $P_{\rm orb}$ less than 3 d (known as the NS+He star scenario), but previous works can only cover a few observed sources with short orbital periods. We aim to…
We study the evolution of close binary systems formed by a normal (solar composition), intermediate mass donor star together with a neutron star. We consider models including irradiation feedback and evaporation. These non-standard ingredients deeply modify the mass transfer stages of these binaries. While models that neglect irradiation feedback undergo continuous, long standing mass transfer episodes, models including these effect suffer a number cycles of mass transfer and detachment. During mass transfer the systems should reveal themselves as low-mass X-ray binaries (LMXBs), whereas when …
We present the results of {\it Chandra} observations of two non-accreting millisecond pulsars, PSRs J1640$+$2224 (J1640) and J1709$+$2313 (J1709), with low inferred magnetic fields and spin-down rates in order to constrain their surface temperatures, obtain limits on the amplitude of unstable $r$-modes in them, and make comparisons with similar limits obtained for a sample of accreting low-mass X-ray binary (LMXB) neutron stars. We detect both pulsars in the X-ray band for the first time. They are faint, with inferred soft X-ray fluxes ($0.3-3$ keV) of $\approx$ $6\times10^{-15}$ and $3\times …
In this work, we investigate the existence of neutron stars (NS) in the framework of $f$($\mathbb{T}$,$\mathcal{T}$) gravity, where $\mathbb{T}$ is the torsion tensor and $\mathcal{T}$ is the trace of the energy-momentum tensor. The hydrostatic equilibrium equations are obtained, however, with $p$ and $ρ$ quantities passed on by effective quantities $\bar{p}$ and $\barρ$, whose mass-radius diagrams are obtained using modern equations of state (EoS) of nuclear matter derived from relativistic mean field models and compared with the ones computed by the Tolman-Oppenheimer-Volkoff (TOV) equations…
The low-mass X-ray binary Cen X-4 is the brightest and closest (<1.2 kpc) quiescent neutron star transient. Previous 0.5-10 keV X-ray observations of Cen X-4 in quiescence identified two spectral components: soft thermal emission from the neutron star atmosphere and a hard power-law tail of unknown origin. We report here on a simultaneous observation of Cen X-4 with NuSTAR (3-79 keV) and XMM-Newton (0.3-10 keV) in 2013 January, providing the first sensitive hard X-ray spectrum of a quiescent neutron star transient. The 0.3-79 keV luminosity was 1.1 x 10^(33) erg/s (for D=1kpc), with around 60 …
