Nuclear-powered X-ray millisecond pulsars are the third type of millisecond pulsars, which are powered by thermonuclear fusion processes. The corresponding brightness oscillations, known as burst oscillations, are observed during some thermonuclear X
-ray bursts, when the burning and cooling accreted matter gives rise to an azimuthally asymmetric brightness pattern on the surface of the spinning neutron star. Apart from providing neutron star spin rates, this X-ray timing feature can be a useful tool to probe the fundamental physics of neutron star interior and surface. This chapter presents an overview of the relatively new field of nuclear-powered X-ray millisecond pulsars.
The Soft X-ray Telescope (SXT) aboard the $AstroSat$ satellite is the first Indian X-ray telescope in space. It is a modest size X-ray telescope with a charge coupled device (CCD) camera in the focal plane, which provides X-ray images in the $sim 0.3
-8.0$ keV band. A forte of SXT is in providing undistorted spectra of relatively bright X-ray sources, in which it excels some current large CCD-based X-ray telescopes. Here, we highlight some of the published spectral and timing results obtained using the SXT data to demonstrate the capabilities and overall performance of this telescope.
An understanding of spin frequency ($ u$) evolution of neutron stars in the low-mass X-ray binary (LMXB) phase is essential to explain the observed $ u$-distribution of millisecond pulsars (MSPs), and to probe the stellar and binary physics, includin
g the possibility of continuous gravitational wave emission. Here, using numerical computations we conclude that $ u$ can evolve in two distinctly different modes, as $ u$ may approach a lower spin equilibrium value ($ u_{rm eq,per}$) for persistent accretion for a long-term average accretion rate ($dot{M}_{rm av}$) greater than a critical limit ($dot{M}_{rm av,crit}$), and may approach a higher effective spin equilibrium value ($ u_{rm eq,eff}$) for transient accretion for $dot{M}_{rm av} < dot{M}_{rm av,crit}$. For example, when $dot{M}_{rm av}$ falls below $dot{M}_{rm av,crit}$ for an initially persistent source, $ u$ increases considerably due to transient accretion, which is counterintuitive. We also find that, contrary to what was suggested, a fast or sudden decrease of $dot{M}_{rm av}$ to zero in the last part of the LMXB phase is not essential for the genesis of spin-powered MSPs, and neutron stars could spin up in this $dot{M}_{rm av}$-decreasing phase. Our findings imply that the traditional way of $ u$-evolution computation is inadequate in most cases, even for initially persistent sources, and may not even correctly estimate whether $ u$ increases or decreases.
A millisecond pulsar having an ellipticity, that is an asymmetric mass distribution around its spin-axis, could emit continuous gravitational waves, which have not been detected so far. An indirect way to infer such waves is to estimate the contribut
ion of the waves to the spin-down rate of the pulsar. The transitional pulsar PSR J1023+0038 is ideal and unique for this purpose, because this is the only millisecond pulsar for which the spin-down rate has been measured in both accreting and non-accreting states. Here we infer, from our formalism based on the complete torque budget equations and the pulsar magnetospheric origin of observed $gamma$-rays in the two states, that PSR J1023+0038 should emit gravitational waves due to a permanent ellipticity of the pulsar. The formalism also explains some other main observational aspects of this source in a self-consistent way. As an example, our formalism naturally infers the accretion disc penetration into the pulsar magnetosphere, and explains the observed X-ray pulsations in the accreting state using the standard and well-accepted scenario. This, in turn, infers the larger pulsar spin-down power in the accreting state, which, in our formalism, explains the observed larger $gamma$-ray emission in this state. Exploring wide ranges of parameter values of PSR J1023+0038, and not assuming an additional source of stellar ellipticity in the accreting state, we find the misaligned mass quadrupole moment of the pulsar in the range of $(0.92-1.88)times10^{36}$ g cm$^2$, implying an ellipticity range of $(0.48-0.93)times10^{-9}$.
We construct a time-dependent relativistic accretion model for tidal disruption events (TDEs) with an $alpha-$viscosity and the pressure dominated by gas pressure. We also include the mass fallback rate $dot{M}_f$ for both full and partial disruption
TDEs, and assume that the infalling debris forms a seed disc in time $t_c$, which evolves due to the mass addition from the infalling debris and the mass loss via accretion onto the black hole. Besides, we derive an explicit form for the disc height that depends on the angular momentum parameter in the disc. We show that the surface density of the disc increases at an initial time due to mass addition, and then decreases as the mass fallback rate decreases, which results in a decrease in the disc mass $M_{rm d}$ with a late-time evolution of $M_{rm d} propto t^{-1.05}$ and $M_{rm d} propto t^{-1.38}$ for full and partial disruption TDEs respectively, where $t$ is the time parameter. The bolometric luminosity $L$ shows a rise and decline that follows a power-law at late times given by $L propto t^{-1.8}$ and $L propto t^{-2.3}$ for full and partial disruption TDEs respectively. Our obtained luminosity declines faster than the luminosity inferred using $L propto dot{M}_f$. We also compute the light curves in various spectral bands.
We report the results from textit{AstroSat} observations of the transient Galactic black hole X-ray binary MAXI J1535-571 during its hard-intermediate state of the 2017 outburst. We systematically study the individual and joint spectra from two simul
taneously observing textit{AstroSat} X-ray instruments, and probe and measure a number of parameter values of accretion disc, corona and reflection from the disc in the system using models with generally increasing complexities. Using our broadband ($1.3-70$ keV) X-ray spectrum, we clearly show that a soft X-ray instrument, which works below $sim 10-12$ keV, alone cannot correctly characterize the Comptonizing component from the corona, thus highlighting the importance of broadband spectral analysis. By fitting the reflection spectrum with the latest version of the textsc{relxill} family of relativistic reflection models, we constrain the black holes dimensionless spin parameter to be $0.67^{+0.16}_{-0.04}$. We also jointly use the reflection spectral component (textsc{relxill}) and a general relativistic thin disc component (texttt{Kerrbb}), and estimate the black holes mass and distance to be $10.39_{-0.62}^{+0.61} M_{odot}$ and $5.4_{-1.1}^{+1.8}$ kpc respectively.
Low-mass X-ray binaries (LMXBs) have a wide range of X-ray properties which can be utilised to reveal many physical conditions of the associated accretion discs. We use the spectral synthesis code CLOUDY to perform a detailed modelling of neutron sta
r LMXBs GX 13+1, MXB 1659--298, 4U 1323--62 and XB 1916--053; and characterise the underlying physical conditions, such as density, radiation field, metallicity, wind velocity, etc. For this purpose we model highly ionised spectra of Fe, Ca, S, Si, Mg, Al in the soft X-ray band, and compare the predicted line flux ratios with the observed values. We also find that the strength and profile of these spectral lines get modified in the presence of magnetic field in the accretion disc. Using this, we estimate an upper limit of the existing magnetic field to be about a few hundred to a few thousand G in the accretion discs of these four LMXBs.
It has recently been shown that the persistent emission of a neutron star low-mass X-ray binary (LMXB) evolves during a thermonuclear (type-I) X-ray burst. The reason of this evolution, however, is not securely known. This uncertainty can introduce s
ignificant systematics in the neutron star radius measurement using burst spectra, particularly if an unknown but significant fraction of the burst emission, which is reprocessed, contributes to the changes in the persistent emission during the burst. Here, by analyzing individual burst data of AstroSat/LAXPC from the neutron star LMXB 4U 1728--34 in the soft state, we show that the burst emission is not significantly reprocessed by a corona covering the neutron star. Rather, our analysis suggests that the burst emission enhances the accretion disk emission, possibly by increasing the accretion rate via disk. This enhanced disk emission, which is Comptonized by a corona covering the disk, can explain an increased persistent emission observed during the burst. This finding provides an understanding of persistent emission components, and their interaction with the thermonuclear burst emission. Furthermore, since burst photons are not significantly reprocessed, non-burst and burst emissions can be reliably separated, which is required to reduce systematic uncertainties in the stellar radius measurement.
The recent fast growth of a population of millisecond pulsars with precisely measured mass provides an excellent opportunity to characterize these compact stars at an unprecedented level. This is because the stellar parameter values can be accurately
computed for known mass and spin rate and an assumed equation of state (EoS) model. For each of the 16 such pulsars and for a set of EoS models from nucleonic, hyperonic, strange quark matter and hybrid classes, we numerically compute fast spinning stable stellar parameter values considering the full effect of general relativity. This first detailed catalogue of the computed parameter values of observed millisecond pulsars provides a testbed to probe the physics of compact stars, including their formation, evolution and EoS. We estimate uncertainties on these computed values from the uncertainty of the measured mass, which could be useful to quantitatively constrain EoS models. We note that the largest value of the central density $rho_{rm c}$ in our catalogue is $sim 5.8$ times the nuclear saturation density $rho_{rm sat}$, which is much less than the expected maximum value $13 rho_{rm sat}$. We argue that the $rho_{rm c}$-values of at most a small fraction of compact stars could be much larger than $5.8 rho_{rm sat}$. Besides, we find that the constraints on EoS models from accurate radius measurements could be significantly biased for some of our pulsars, if stellar $spinning$ configurations are not used to compute the theoretical radius values.
A millisecond pulsar is a neutron star that has been substantially spun up by accretion from a binary companion. A previously unrecognized factor governing the spin evolution of such pulsars is the crucial effect of non-steady or transient accretion.
We numerically compute the evolution of accreting neutron stars through a series of outburst and quiescent phases considering the drastic variation of the accretion rate and the standard disk-magnetosphere interaction. We find that, for the same long-term average accretion rate, X-ray transients can spin up pulsars to rates several times higher than can persistent accretors, even when the spin down due to electromagnetic radiation during quiescence is included. We also compute an analytical expression for the equilibrium spin frequency in transients, by taking spin equilibrium to mean that no net angular momentum is transferred to the neutron star in each outburst cycle. We find that the equilibrium spin rate for transients, which depends on the peak accretion rate during outbursts, can be much higher than that for persistent sources. This explains our numerical finding. This finding implies that any meaningful study of neutron star spin and magnetic field distributions requires the inclusion of the transient accretion effect, since most accreting neutron star sources are transients. Our finding also implies the existence of a submillisecond pulsar population, which is not observed. This may point to the need for a competing spin-down mechanism for the fastest-rotating accreting pulsars, such as gravitational radiation.
