Accretion via disks can make neutron stars in low-mass X-ray binaries (LMXBs) fast spinning, and some of these stars are detected as millisecond pulsars. Here we report a practical way to find out if ...a neutron star in a transient LMXB has reached the spin equilibrium by disk-magnetosphere interaction alone, and if not, to estimate this spin equilibrium frequency. These can be done using specific measurable source luminosities, such as the luminosity corresponding to the transition between the accretion and propeller phases, and the known stellar spin rate. Such a finding can be useful to test if the spin distribution of millisecond pulsars, as well as an observed upper cutoff of their spin rates, can be explained using disk-magnetosphere interaction alone, or additional spin-down mechanisms, such as gravitational radiation, are required. Applying our method, we find that the neutron star in the transient LMXB Aql X-1 has not yet reached the spin equilibrium by disk-magnetosphere interaction alone. We also perform numerical computations, with and without gravitational radiation, to study the spin evolution of Aql X-1 through a series of outbursts and to constrain its properties. While we find that the gravitational wave emission from Aql X-1 cannot be established with certainty, our numerical results show that the gravitational radiation from Aql X-1 is possible, with a g cm2 upper limit of the neutron star misaligned mass quadrupole moment.
The concept of spin equilibrium due to an interaction between the stellar magnetosphere and a thin, Keplerian accretion disk, and a well-known formula of the corresponding equilibrium spin frequency, ...provide a key understanding of spin evolution and the distribution of rapidly spinning neutron stars, viz., millisecond pulsars. However, this concept and formula are for stable accretion, but the mass transfer to most accreting millisecond pulsars is transient and the accretion rate evolves by orders of magnitude during an outburst. In this short and focussed review, we briefly discuss a relatively new concept of the spin equilibrium condition and a new formula for the equilibrium spin frequency for transiently accreting millisecond pulsars. We also review a new method to estimate this equilibrium spin frequency for observed transiently accreting millisecond pulsars, even when a pulsar has not yet attained the spin equilibrium. These will be crucial to probe the spin evolution and distribution of millisecond pulsars, and should also be applicable to all magnetic stars transiently accreting via a thin, Keplerian accretion disk.
ABSTRACT 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 nonsteady 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.
Measurement of at least three independent parameters, for example, mass, radius and spin frequency, of a neutron star is probably the only way to understand the nature of its supranuclear core ...matter. Such a measurement is extremely difficult because of various systematic uncertainties. The lack of knowledge of several system parameter values gives rise to such systematics. Low mass X-ray binaries, which contain neutron stars, provide a number of methods to constrain the stellar parameters. Joint application of these methods has a great potential to significantly reduce the systematic uncertainties, and hence to measure three independent neutron star parameters accurately. Here, we review the methods based on: (1) thermonuclear X-ray bursts; (2) accretion-powered millisecond-period pulsations; (3) kilohertz quasi-periodic oscillations; (4) broad relativistic iron lines; (5) quiescent emissions; and (6) binary orbital motions.
A defining characteristic of modern science is its ability to make immensely successful predictions of natural phenomena without invoking a putative god or a supernatural being. Here, we argue that ...this intellectual discipline would not acquire such an ability without the mathematical zero. We insist that zero and its basic operations were likely conceived in India based on a philosophy of
nothing
, and classify
nothing
into four categories—
balance
,
absence
,
emptiness
and
nonexistence
. We argue that zero is a tangible representation of nonexistence and constitutes all nonzero numbers, which together represent existence. It appears that zero’s journey out of India somewhat separated its mathematical and philosophical aspects, with the former being more valued by some cultures and the latter by others. The European culture, in which modern science grew, largely ignores a philosophy of
nothing
due to a deep-rooted Greek philosophical base, although this science relies on the notion of nonexistence through zero. Consequently, zero is a mere number of convenience without its foundational philosophy in science, and techniques to circumvent zero are developed. We insist that, while such techniques contribute to the progress of science and mathematics within the current framework, a tendency to avoid zero and its philosophy leads to approximations and may hinder a deeper understanding. Finally, we argue that nonexistence may notionally constitute existence, and hence may be the fundamental. This implies that, if a supernatural being
exists
, it is not the fundamental. The independence of modern science from a supernatural being is consistent with this.
Abstract Understanding the spectral evolution along the “Z”-shaped track in the hardness–intensity diagram of Z sources, which are a class of luminous neutron star low-mass X-ray binaries, is crucial ...to probe accretion processes close to the neutron star. Here, we study the horizontal branch (HB) and the normal branch (NB) of the Z source GX 340+0 using AstroSat data. We find that the HB and the NB appear as two different types of X-ray intensity dips, which can appear in any sequence and with various depths. Our 0.8–25 keV spectra of dips and the hard apex can be modeled by the emissions from an accretion disk, a Comptonizing corona covering the inner disk, and the neutron star surface. We find that as the source moves onto the HB, the corona is replenished and energized by the disk and a reduced amount of disk matter reaches the neutron star surface. We also conclude that quasiperiodic oscillations during HB/NB are strongly associated with the corona and explain the evolution of strength and hard lag of this timing feature using the estimated coronal optical depth evolution.
ABSTRACT
A fundamental difference between a neutron star (NS) and a black hole (BH) is the absence of a physical surface in the latter. For this reason, any remaining kinetic energy of the matter ...accreting on to a BH is advected inside its event horizon. In the case of an NS, on the contrary, accreting material is decelerated on the NS surface, and its kinetic energy is eventually radiated away. Copious soft photons produced by the NS surface will affect the properties of the Comptonized component dominating spectra of X-ray binaries in the hard state. Thus, parameters of the Comptonized spectra – the electron temperature kTe and the Compton y-parameter, could serve as an important tool for distinguishing BHs from NSs. In this paper, we systematically analyse heretofore the largest sample of spectra from the BH and NS X-ray binaries in the hard state for this purpose, using archival RXTE/PCA and RXTE/HEXTE observations. We find that the BHs and NSs occupy distinctly different regions in the y − kTe plane with NSs being characterized by systematically lower values of y-parameter and electron temperature. Due to the shape of the boundary between BHs and NSs on the y − kTe plane, their 1D y and kTe distributions have some overlap. A cleaner one parameter diagnostic of the nature of the compact object in X-ray binaries is provided by the Compton amplification factor A, with the boundary between BHs and NSs lying at A ≈ 3.5–4. This is by far the most significant detection of the imprint of the event horizon on the X-ray spectra for stable stellar-mass BHs.
Burst oscillations during the rising phases of thermonuclear X-ray bursts are usually believed to originate from flame spreading on the neutron star surface. However, the decrease of fractional ...oscillation amplitude with rise time, which provides a main observational support for the flame spreading model, have so far been reported from only a few bursts. Moreover, the non-detection and intermittent detections of rise oscillations from many bursts are not yet understood considering the flame spreading scenario. Here, we report the decreasing trend of fractional oscillation amplitude from an extensive analysis of a large sample of Rossi X-ray Timing Explorer Proportional Counter Array bursts from 10 neutron star low-mass X-ray binaries. This trend is 99.99% significant for the best case, which provides, to the best of our knowledge, by far the strongest evidence of such a trend. Moreover, it is important to note that an opposite trend is not found in any of the bursts. The concave shape of the fractional amplitude profiles for all the bursts suggests latitude-dependent flame speeds, possibly due to the effects of the Coriolis force. We also systematically study the roles of low fractional amplitude and low count rate for non-detection and intermittent detections of rise oscillations, and attempt to understand them within the flame spreading scenario. Our results support a weak turbulent viscosity for flame spreading, and imply that burst rise oscillations originate from an expanding hot spot, thus making these oscillations a more reliable tool to constrain the neutron star equations of state.
ABSTRACT
A millisecond pulsar having an ellipticity, which 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 contribution 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 γ-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 γ-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) × 1036 g cm2, implying an ellipticity range of (0.48–0.93) × 10−9.
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