Millisecond Pulsar XTE Research Articles

Constraining the properties of the thermonuclear burst oscillation source XTE J1814−338 through pulse profile modelling

ABSTRACT Pulse profile modelling (PPM) is a comprehensive relativistic ray-tracing technique employed to determine the properties of neutron stars. In this study, we apply this technique to the Type I X-ray burster and accretion-powered millisecond pulsar XTE J1814−338, extracting its fundamental properties using PPM of its thermonuclear burst oscillations. Using data from its 2003 outburst, and a single uniform temperature hotspot model, we infer XTE J1814−338 to be located at a distance of $7.2^{+0.3}_{-0.4}$ kpc, with a mass of $1.21^{+0.05}_{-0.05}$ M$_\odot$ and an equatorial radius of $7.0^{+0.4}_{-0.4}$ km. Our results also offer insight into the time evolution of the hotspot but point to some potential shortcomings of the single uniform temperature hotspot model. We explore the implications of this result, including what we can learn about thermonuclear burst oscillation mechanisms and the importance of modelling the accretion contribution to the emission during the burst.

Time-scale of twin-peak quasi-periodic oscillations and mass of accreting neutron stars

ABSTRACT Einstein’s general relativity predicts that orbital motion of accreted gas approaching a neutron star (NS) in a NS low-mass X-ray binary (LMXB) system occurs on a time-scale proportional to the NS mass. Radiation of the gas accounts for most of the observed LMXBs variability. In more than a dozen of sources twin-peak quasi-periodic oscillations (QPOs) have been observed. Inspired by the expected proportionality between periods of orbital motion and NS mass we present a straightforward comparison among these sources. We investigate relations between QPO periods and their ratios and identify characteristic time-scales of QPOs associated with individual sources. These time-scales are likely determined by the relative mass of each NS. We show that the characteristic time-scale of the millisecond pulsar XTE J1807.4−294 is longer than for most other NS LMXBs. Consequently, models of QPOs that consider geodesic orbital frequencies imply that the X-ray pulsars’ mass has to be about $50{{\ \rm per\ cent}}$ higher than the average mass of other sources. Consideration of other X-ray pulsars indicates that the exceptionality of XTE J1807.4−294 cannot be related to NS magnetic field in any simple manner. We suggest that QPOs observed in this source can help to discriminate between the proposed versions of the NS equation of state.

M/R estimates for two neutron stars in LMXBs with possible r-mode frequencies detected

The puzzling existence of a number of neutron stars that appear to be in the r-mode instability window supports further investigations of the r-mode frequencies, damping times and saturation amplitudes, especially now in light of the much anticipated and exciting results from LIGO and NICER. It has been suggested by Mahmoodifar and Strohmayer that coherent frequencies found in the RXTE data of the accreting millisecond pulsar XTE J1751-305 and during the 2001 superburst of 4U 1636-536 (one of the accreting sources to be observed by NICER) could, in fact, be r-modes. Based on these observations, we expand here the results of a previous work on relativistic, rotational and differential rotation corrections to the r-mode frequency in order to provide more accurate estimates of the $M-R$ relation for these neutron stars. Finally, we compare our results with predictions from a few realistic tabulated equations of state, providing further constraints that favor more compact models. We find that, if the observed frequencies indeed correspond to r-modes, then the masses of XTE J1751-305 and 4U 1636-536 should lie in the approximate ranges $1.48 - 1.56 M_{\odot}$ and $1.60 - 1.68 M_{\odot}$, respectively.

System mass constraints for the accreting millisecond pulsar XTE J1814-338 using Bowen fluorescence

We present phase-resolved spectroscopy of the millisecond X-ray pulsar XTE J1814-338 obtained during its 2003 outburst. The spectra are dominated by high-excitation emission lines of HeII $\lambda$4686, H$\beta$, and the Bowen blend CIII/NIII 4630-50\AA. We exploit the proven Bowen fluorescence technique to establish a complete set of dynamical system parameter constraints using bootstrap Doppler tomography, a first for an accreting millisecond X-ray pulsar binary. The reconstructed Doppler map of the NIII $\lambda$4640 Bowen transition exhibits a statistically significant (>4$\sigma$) spot feature at the expected position of the companion star. If this feature is driven by irradiation of the surface of the Roche lobe filling companion, we derive a strict lower limit to the true radial velocity semi-amplitude $K_2$. Combining our donor constraint with the well constrained orbit of the neutron star leads to a determination of the binary mass ratio: q = $0.123^{+0.012}_{-0.010}$. The component masses are not tightly constrained given our lack of knowledge of the binary inclination. We cannot rule out a canonical neutron star mass of 1.4 $M_{\odot}$ (1.1 $M_{\odot}$ < $M_1$ < 3.1 $M_{\odot}$; 95%). The 68/95% confidence limits of $M_2$ are consistent with the companion being a significantly bloated, M-type main sequence star. Our findings, combined with results from studies of the quiescent optical counterpart of XTE J1814-338, suggest the presence of a rotation-powered millisecond pulsar in XTE J1814-338 during an X-ray quiescent state. The companion mass is typical of the so-called 'redback' pulsar binary systems ($M_2$ ~ 0.2 $M_{\odot}$).

Excitation of a non-radial mode in a millisecond X-ray pulsar XTE J1751-305

We discuss candidates for non-radial modes excited in a mass accreting and rapidly rotating neutron star to explain the coherent frequency identified in the light curves of a millisecond X-ray pulsar XTE J1751-305. The spin frequency of the pulsar is $\nu_{\rm spin}\cong435$Hz and the identified coherent frequency is $\nu_{\rm osc}=0.5727595\times\nu_{\rm spin}$. Assuming the frequency identified is that observed in the corotating frame of the neutron star, we find that the surface $r$-modes of $l^\prime=m=1$ and 2 excited by $\epsilon$-mechanism due to helium burning in the thin shell can give the frequency ratio $\kappa=\nu_{\rm osc}/\nu_{\rm spin}\simeq0.57$ at $\nu_{\rm spin}=435$Hz. As another candidate for the observed ratio $\kappa$, we also suggest a toroidal crustal mode that has penetrating amplitudes in the fluid core and is destabilized by gravitational wave emission. Since the surface fluid layer is separated from the fluid core by a solid crust, the amplitudes of an $r$-mode in the core, which is destabilized by emitting gravitational waves, can be by a large factor different from those in the fluid ocean. We find that the amplification factor defined as $f_{\rm amp}=\alpha_{\rm surface}/\alpha_{\rm core}$ is as large as $f_{\rm amp}\sim 10^2$ for the $l^\prime=m=2$ $r$-mode at $\nu_{\rm spin}=435$Hz for a $M=1.4M_\odot$ neutron star model. Because of this significant amplification of the $r$-mode amplitudes in the surface fluid layer, we suggest that, when proper corrections to the $r$-mode frequency such as due to the general relativistic effects are taken into consideration, the core $r$-mode of $l^\prime=m=2$ can be a candidate for the detected frequency, without leading to serious contradictions to, for example, the spin evolution of the underlying neutron star.

Implications of an r mode in XTE J1751−305: mass, radius and spin evolution

Recently Strohmayer and Mahmoodifar presented evidence for a coherent oscillation in the X-ray light curve of the accreting millisecond pulsar XTE J1751-305, using data taken by RXTE during the 2002 outburst of this source. They noted that a possible explanation includes the excitation of a non-radial oscillation mode of the neutron star, either in the form of a g-mode or an r-mode. The r-mode interpretation has connections with proposed spin-evolution scenarios for systems such as XTE J1751-305. Here we examine in detail this interesting possible interpretation. Using the ratio of the observed oscillation frequency to the star's spin frequency, we derive an approximate neutron star mass-radius relation which yields reasonable values for the mass over the range of expected stellar radius (as constrained by observations of radius-expansion burst sources). However, we argue that the large mode amplitude suggested by the Strohmayer and Mahmoodifar analysis would inevitably lead to a large spin-down of the star, inconsistent with its observed spin evolution, regardless of whether the r-mode itself is in a stable or unstable regime. We therefore conclude that the r-mode interpretation of the observed oscillation is not consistent with our current understanding of neutron star dynamics and must be considered unlikely. Finally we note that, subject to the availability of a sufficiently accurate timing model, a direct gravitational-wave search may be able to confirm or reject an r-mode interpretation unambiguously, should such an event, with a similar inferred mode amplitude, recur during the Advanced detector era.

CONSTRAINTS ON THE MASS AND RADIUS OF THE NEUTRON STAR XTE J1807-294

The accreting millisecond pulsar XTE J1807-294 is studied through a pulse shape modeling analysis. The model includes blackbody and Comptonized emission from the one visible hot spot and makes use of the Oblate Schwarzschild approximation for ray-tracing. We include a scattered light contribution, which accounts for flux scattered off an equatorial accretion disk to the observer including time delays in the scattered light. We give limits to mass and radius for XTE J1807-294 and compare to limits determined for SAX J1808-3658 and XTE J1814-334 previously determined using similar methods. The resulting allowed region for mass-radius curves is small but is consistent with a mass-radius relation with nearly constant radius (~12 km) for masses between 1 and 2.5 solar masses.

ACCRETION TORQUES AND MOTION OF THE HOT SPOT ON THE ACCRETING MILLISECOND PULSAR XTE J1807-294

We present a coherent timing analysis of the 2003 outburst of the accreting millisecond pulsar XTE J1807-294. We find an upper limit for the spin frequency derivative of 5E-14 Hz/s. The sinusoidal fractional amplitudes of the pulsations are the highest observed among the accreting millisecond pulsars and can reach values of up to 27% (2.5-30 keV). The pulse arrival time residuals of the fundamental follow a linear anti-correlation with the fractional amplitudes that suggests hot spot motion over the surface of the neutron star both in longitude and latitude. An anti-correlation between residuals and X-ray flux suggests an influence of accretion rate on pulse phase, and casts doubts on the use of standard timing techniques to measure spin frequencies and torques on the neutron star.

Searching for pulsed emission from XTE J0929–314 at high radio frequencies

Aims. The aim of this work is to search for radio signals in the quiescent phase of accreting millisecond X-ray pulsars, in this way giving an ultimate proof of the recycling model, thereby unambiguously establishing that accreting millisecond X-ray pulsars are the progenitors of radio millisecond pulsars. Methods. To overcome the possible free-free absorption caused by matter surrounding accreting millisecond X-ray pulsars in their quiescence phase, we performed the observations at high frequencies. Making use of particularly precise orbital and spin parameters obtained from X-ray observations, we carried out a deep search for radio-pulsed emission from the accreting millisecond X-ray pulsar XTE J0929–314 in three steps, correcting for the effect of the dispersion due to the interstellar medium, eliminating the orbital motions effects, and finally folding the time series. Results. No radio pulsation is present in the analyzed data down to a limit of 68 μ Jy at 6.4 GHz and 26 μ Jy at 8.5 GHz. Conclusions. We discuss several mechanisms that could prevent the detection, concluding that beaming factor and intrinsic low luminosity are the most likely explanations.

Does the accreting millisecond pulsar XTE J1814−338 precess?

Precession in an accretion-powered pulsar is expected to produce characteristic variations in the pulse properties. Assuming surface intensity maps with one and two hotspots, we compute theoretically the periodic modulation of the mean flux, pulse-phase residuals and fractional amplitudes of the first and second harmonic of the pulse profiles. These quantities are characterised in terms of their relative precession phase offsets. We then search for these signatures in 37 days of X-ray timing data from the accreting millisecond pulsar XTE J1814-338. We analyse a 12.2-d modulation observed previously and show that it is consistent with a freely precessing neutron star only if the inclination angle is < 0.1 degrees, an a priori unlikely orientation. We conclude that if the observed flux variations are due to precession, our model incompletely describes the relative precession phase offsets (e.g. the surface intensity map is over-simplified). We are still able to place an upper limit on \epsilon of 3.0 x 10^{-9} independently of our model, and estimate the phase-independent tilt angle \theta; to lie roughly between 5 and 10 degrees. On the other hand, if the observed flux variations are not due to precession, the detected signal serves as a firm upper limit for any underlying precession signal. We then place an upper limit on the product \epsilon cos(\theta) of \leq 9.9 x 10^{-10}. The first scenario translates into a maximum gravitational wave strain of 10^{-27} from XTE J1814-338 (assuming a distance of 8 kpc), and a corresponding signal-to-noise ratio of \leq 10^{-3} (for a 120 day integration time) for the advanced LIGO ground-based gravitational wave detector.

Coherence of Burst Oscillations and Accretion-Powered Pulsations in the Accreting Millisecond Pulsar XTE J1814-338

X-ray timing of the accretion-powered pulsations during the 2003 outburst of the accreting millisecond pulsar XTE J1814-338 has revealed variation in the pulse time of arrival residuals. These can be interpreted in several ways, including spin-down and wandering of the fuel impact point around the magnetic pole. In this Letter we show that the burst oscillations of this source are coherent with the persistent pulsations, to the level where they track all of the observed fluctuations. Only one burst, which occurs at the lowest accretion rates, shows a significant phase offset. We discuss what might lead to such rigid phase-locking between the modulations in the accretion and thermonuclear burst emission, and consider the implications for spin variation and the burst oscillation mechanism. Wandering of the fuel impact hot spot around a fixed magnetic pole seems the most likely cause for the accretion-powered pulse phase variations. This means that the burst asymmetry is coupled to the hot spot, not the magnetic pole. If premature ignition at this point (due to higher local temperatures) triggers a burning front that stalls before spreading over the entire surface, the resulting localized nuclear hot spot may explain the unusual burst and burst oscillation properties of this source.

Spin‐up and Phase Fluctuations in the Timing of the Accreting Millisecond Pulsar XTE J1807−294

We performed a timing analysis of the 2003 outburst of the accreting X-ray millisecond pulsar XTE J1807-294 observed by RXTE. Using recently refined orbital parameters we report for the first time a precise estimate of the spin frequency and of the spin frequency derivative. The phase delays of the pulse profile show a strong erratic behavior superposed to what appears as a global spin-up trend. The erratic behavior of the pulse phases is strongly related to rapid variations of the light curve, making it very difficult to fit these phase delays with a simple law. As in previous cases, we have therefore analyzed separately the phase delays of the first harmonic and of the second harmonic of the spin frequency, finding that the phases of the second harmonic are far less affected by the erratic behavior. In the hypothesis that the second harmonic pulse phase delays are a good tracer of the spin frequency evolution we give for the first time a estimation of the spin frequency derivative in this source. The source shows a clear spin-up of $\dot \nu = 2.5(7) \times 10^{-14}$ Hz sec$^{-1}$ (1 $\sigma$ confidence level). The largest source of uncertainty in the value of the spin-up rate is given by the uncertainties on the source position in the sky. We discuss this systematics on the spin frequency and its derivative.

Measuring the spin up of the accreting millisecond pulsar XTE J1751-305

We perform a timing analysis on RXTE data of the accreting millisecond pulsar XTE J1751-305 observed during the April 2002 outburst. After having corrected for Doppler effects on the pulse phases due to the orbital motion of the source, we performed a timing analysis on the phase delays, which gives, for the first time for this source, an estimate of the average spin frequency derivative <nu_dot> = (3.7 +/- 1.0)E-13 Hz/s. We discuss the torque resulting from the spin-up of the neutron star deriving a dynamical estimate of the mass accretion rate and comparing it with the one obtained from X-ray flux. Constraints on the distance to the source are discussed, leading to a lower limit of \sim 6.7 kpc.

Precise determination of orbital parameters in system with slowly drifting phases: application to the case of XTE J1807-294

We describe a timing technique that allows obtaining precise orbital parameters of an accreting millisecond pulsar in those cases in which intrinsic variations of the phase delays (caused, for example, by proper variation of the spin frequency) with characteristic time-scale longer than the orbital period do not allow to fit the orbital parameters over a long observation (tens of days). We show under which conditions this method can be applied along with the results obtained applying this method to the 2003 outburst observed by RXTE of the accreting millisecond pulsar XTE J1807−294 which shows in its phase delays a non-negligible erratic behaviour. We refined the orbital parameters of XTE J1807−294 using all the 90 days in which the pulsation is strongly detected and the method applicable. In this way, we obtain the orbital parameters of the source with a precision more than one order of magnitude better than the previous available orbital solution, a precision obtained to date, on accreting millisecond pulsars, only for SAX J1808.4−3658 analysing several outbursts spanning over seven years and with much better statistics.

Timing of the accreting millisecond pulsar XTE J1814-338

We present a precise timing analysis of the accreting millisecond pulsar XTE J1814-338 during its 2003 outburst, observed by RXTE. A full orbital solution is given for the first time; Doppler effects induced by the motion of the source in the binary system were corrected, leading to a refined estimate of the orbital period, P_orb=15388.7229(2)s, and of the projected semimajor axis, a sini/c= 390.633(9) lt-ms. We could then investigate the spin behaviour of the accreting compact object during the outburst. We report here a refined value of the spin frequency (nu=314.35610879(1) Hz) and the first estimate of the spin frequency derivative of this source while accreting (nu^dot=(-6.7 +/- 0.7) 10^(-14) Hz/s). This spin down behaviour arises when both the fundamental frequency and the second harmonic are taken into consideration. We discuss this in the context of the interaction between the disc and the quickly rotating magnetosphere, at accretion rates sufficiently low to allow a threading of the accretion disc in regions where the Keplerian velocity is slower than the magnetosphere velocity. We also present indications of a jitter of the pulse phases around the mean trend, which we argue results from movements of the accreting hotspots in response to variations of the accretion rate.

The energy dependence of burst oscillations from the accreting millisecond pulsar XTE J1814-338

The nature of the asymmetry that gives rise to Type I X-ray burst oscillations on accreting neutron stars remains a matter of debate. Of particular interest is whether the burst oscillation mechanism differs between the bursting millisecond pulsars and the non-pulsing systems. One means to diagnose this is to study the energy dependence of the burst oscillations: here we present an analysis of oscillations from 28 bursts observed during the 2003 outburst of the accreting millisecond pulsar XTE J1814-338. We find that the fractional amplitude of the ' burst oscillations falls with energy, in contrast to the behaviour found by Muno et al. in the burst oscillations from a set of non-pulsing systems. The drop with energy mirrors that seen in the accretion-powered pulsations; in this respect XTE J1814-338 behaves like the other accreting millisecond pulsars. The burst oscillations show no evidence for either hard or soft lags, in contrast to the persistent pulsations, which show soft lags of up to 50 μs. The fall in amplitude with energy is inconsistent with current surface-mode and simple hotspot models of burst oscillations. We discuss improvements to the models and uncertainties in the physics that might resolve these issues.

Timing Features of the Accretion‐driven Millisecond X‐Ray Pulsar XTE J1807−294 in the 2003 March Outburst

In order to probe the activity of the inner disk flow and its effect on the neutron star surface emissions, we carried out a timing analysis of the Rossi X-Ray Timing Explorer observations of the millisecond X-ray pulsar XTE J1807-294, focusing on its correlated behaviors in X-ray intensities, hardness ratios, pulse profiles, and power density spectra. The source was observed to have a series of broad flares on a timescale of hours to days on top of a decaying outburst in 2003 March. In the flares, the spectra are softened, and the pulse profiles become more sinusoidal. The frequency of kilohertz quasi-periodic oscillation (kHz QPO) is found to be positively related to the X-ray count rate in the flares. These features observed in the flares could be due to the accreting flow inhomogeneities. It is noted that the fractional pulse amplitude increases with the flare intensities in a range of ~2%-14%, comparable to those observed in the thermonuclear bursts of the millisecond X-ray pulsar XTE J1814-338, whereas it remains at about 6.5% in the normal state. Such a significant variation of the pulse profile in the puny flares may reflect the changes of physical parameters in the inner disk accretion region. Furthermore, we noticed an overall positive correlation between the kHz QPO frequency and the fractional pulse amplitude, which could be the first evidence that the neutron star surface emission properties are very sensitive to the disk flow inhomogeneities. This effect should be cautiously considered in the burst oscillation studies.

Discovery of Kilohertz Quasi‐periodic Oscillations and Shifted Frequency Correlations in the Accreting Millisecond Pulsar XTE J1807−294

We report the discovery of twin kilohertz quasi-periodic oscillations (kHz QPOs) in the X-ray flux of XTE J1807-294, the fourth accreting millisecond pulsar (AMP). This is the second AMP exhibiting twin kHz QPOs. In contrast to the first case, SAX J1808.4-3658, the frequency separation Δν between these kHz QPOs is consistent with the pulse frequency (190.6 Hz), not with half that value, confirming for the first time from pulsation measurements the inference, based on burst oscillations, that slow rotators (spin frequency less than 400 Hz) have Δν approximately equal to the spin frequency. While the QPOs move in frequency together over a range of more than 200 Hz, Δν remains constant with an average value of 205 ± 6 Hz. Variability components were found in the 5-130 Hz range, similar to those seen in other LMXBs. The correlations between the QPO and noise frequencies are also similar to those in other sources, but shifted by a factor of 1.59 in kHz QPO frequencies, similar to the factor of 1.45 shift found for SAX J1808.4-3658. Our results argue in favor of a spin-related formation mechanism for twin kHz QPOs and against a spin-related cause of the shift in the frequency correlations.

Analysis of Variability in the Burst Oscillations of the Accreting Millisecond Pulsar XTE J1814−338

The accreting millisecond pulsar XTE J1814-338 exhibits oscillations at the known spin frequency during Type I X-ray bursts. The properties of the burst oscillations reflect the nature of the thermal asymmetry on the stellar surface. We present an analysis of the variability of the burst oscillations of this source, focusing on three characteristics: fractional amplitude, harmonic content and frequency. Fractional amplitude and harmonic content constrain the size, shape and position of the emitting region, whilst variations in frequency indicate motion of the emitting region on the neutron star surface. We examine both long-term variability over the course of the outburst, and short-term variability during the bursts. For most of the bursts, fractional amplitude is consistent with that of the accretion pulsations, implying a low degree of fuel spread. There is however a population of bursts whose fractional amplitudes are substantially lower, implying a higher degree of fuel spread, possibly forced by the explosive burning front of a precursor burst. For the first harmonic, substantial differences between the burst and accretion pulsations suggest that hotspot geometry is not the only mechanism giving rise to harmonic content in the latter. Fractional amplitude variability during the bursts is low; we can only rule out the hypothesis that the fractional amplitude remains constant at the l(sigma) level for bursts that do not exhibit photospheric radius expansion (PRE). There are no significant variations in frequency in any of the bursts except for the one burst that exhibits PRE. This burst exhibits a highly significant but small (= 0.1Hz) drop in frequency in the burst rise. The timescale of the frequency shift is slower than simple burning layer expansion models predict, suggesting that other mechanisms may be at work.

The X‐Ray Position and Optical Counterpart of the Accretion‐powered Millisecond Pulsar XTE J1814−338

We report the precise optical and X-ray localization of the 3.2 ms accretion-powered X-ray pulsar XTE J1814-338 with data from the Chandra X-Ray Observatory as well as optical observations conducted during the 2003 June discovery outburst. Optical imaging of the field during the outburst of this soft X-ray transient reveals an R = 18 star at the X-ray position. This star is absent (R > 20) from an archival 1989 image of the field and brightened during the 2003 outburst, and we therefore identify it as the optical counterpart of XTE J1814-338. The best source position derived from optical astrometry is R.A. = 18h13m3904, decl. = -33°46'223 (J2000). The featureless X-ray spectrum of the pulsar in outburst is best fit by an absorbed power law (with photon index γ = 1.41 ± 0.06) plus blackbody (with kT = 0.95 ± 0.13 keV) model, where the blackbody component contributes approximately 10% of the source flux. The optical broadband spectrum shows evidence for an excess of infrared emission with respect to an X-ray heated accretion disk model, suggesting a significant contribution from the secondary or from a synchrotron-emitting region. A follow-up observation performed when XTE J1814-338 was in quiescence reveals no counterpart to a limiting magnitude of R = 23.3. This suggests that the secondary is an M3 V or later-type star and therefore very unlikely to be responsible for the soft excess, making synchrotron emission a more reasonable candidate.