Pulse Phase Dependence Research Articles

Insights into the phase-dependent cyclotron line feature in XTE J1946+274: an AstroSat and Insight-HXMT view

ABSTRACT XTE J1946+274 is a Be/X-ray binary with a 15.8 s spin period and 172 d orbital period. Using RXTE/PCA data of the 1998 outburst, a cyclotron line around 37 keV was reported. The presence of this line, its dependence on the pulse phase, and its variation with luminosity have been of some debate since. In this work, we present the re-analysis of two AstroSat observations: one made during the rising phase of the 2018 outburst and the other during the declining phase of the 2021 outburst. We also present a new analysis of the Insight-HXMT observations of the source at the peak of the 2018 outburst. We find the source to be spinning up over the course of the outburst and spinning down between the two outbursts. We report the presence of a higher cyclotron line energy using the 2018 AstroSat observation (∼45 keV) and 2018 Insight-HXMT observation (∼50 keV) and a line at ∼40 keV during the declining phase of the 2021 outburst using data from AstroSat. We also investigate the pulse phase dependence of the cyclotron line parameters and find that the line is significantly detected in all the phases of both AstroSat observations, along with showing variation with the pulse phase. This differs from the previous results reported using BeppoSAX and NuSTAR. We explain this behaviour of the cyclotron line to be due to photon spawning and different accretion column radii at the two poles of this neutron star.

Experimental and numerical demonstration of driver pulse spectral width and phase dependence in near-single-cycle pulse post-compression generation

For many years, light-matter interaction in the strong-field regime has benefited from continuous improvement of femtosecond lasers, in terms of peak power or repetition rate. One of the most current major challenges is the achievement of high-energy, near single-cycle pulses. Such performances are of primary interest in attosecond science for producing intense isolated bursts of extreme ultraviolet light through high-harmonic generation in gases or solids. We present here a detailed experimental and numerical study on a helium filled hollow-core fiber-based post-compression stage. Our measurements highlight the importance of the width and phase of the input spectrum on the spectral broadening, and on the resulting post-compressed pulse. Near Fourier-transform-limited pulses as short as 3.5 fs, carrying a 2.5 mJ energy centered at 750 nm at 1 kHz repetition rate, and leading to a compression factor greater than seven, are demonstrated. The numerical results are in good agreement with the experimental data. Here, spectral broadening is governed by the Kerr effect and the self-steepening on the trailing edge of the guided pulse.

Evolution of timing and spectral characteristics of 4U 1901+03 during its 2019 outburst using the Swift and NuSTAR observatories

ABSTRACT We report the results from a detailed timing and spectral study of a transient X-ray pulsar, 4U 1901+03 during its 2019 outburst. We performed broadband spectroscopy in the 1–70 $\rm keV$ energy band using four observations made with Swift and NuSTAR at different intensity levels. Our timing results reveal the presence of highly variable pulse profiles dependent on both luminosity and energy. Our spectroscopy results showed the presence of a cyclotron resonance scattering feature (CRSF) at ∼ 30 keV. This feature at 30 keV is highly luminosity and pulse phase dependent. Phase-averaged spectra during the last two observations, made close to the declining phase of the outburst, showed the presence of this feature at around $30~\rm {keV}$. The existence of CRSF at 30 keV during these observations is well supported by an abrupt change in the shape of pulse profiles found close to this energy. We also found that 30 keV feature was significantly detected in the pulse phase-resolved spectra of observations made at relatively high luminosities. Moreover, all spectral fit parameters showed a strong pulse phase dependence. In line with the previous findings, an absorption feature at around $10~\rm {keV}$ is significantly observed in the phase-averaged X-ray spectra of all observations and also showed a strong pulse phase dependence.

Pulse Phase Variation of the Cyclotron Line in HMXB 4U 1907+09 with AstroSat LAXPC

We present timing and spectral analysis of data from an observation of the High Mass X-ray Binary pulsar 4U 1907+09 with the LAXPC instrument onboard AstroSat. The light curve consisted of a flare at the beginning of the observation, followed by persistent emission. The pulsar continues to spin down, and the pulse profile is found to be double-peaked up to 16 keV with the peaks separated by a phase of $\sim0.45$. Significant energy dependence of the pulse profile is seen with diminishing amplitude of the secondary peak above 16 keV, and increasing amplitude of the main peak upto 40 keV and a sharp decline after that. We confirm earlier detections of the Cyclotron Resonance Scattering Feature (CRSF) in 4U 1907+09 at $\sim 18.5\pm 0.2$ keV in the phase-averaged spectrum with a high detection significance. An intensity resolved spectral analysis of the initial flare in the light curve shows that the CRSF parameters do not change with a change in luminosity by a factor of 2.6. We also performed pulse phase-resolved spectral analysis with ten independent phase bins. The energy and the strength of the cyclotron line show pulse phase dependence that is in agreement with previous measurements. Two features from the current observation: different energy dependence of the two pulse peaks and a strong CRSF only around the secondary peak, both indicate a deviation from a dipole geometry of the magnetic field of the neutron star, or complex beaming pattern from the two poles.

Probing the Cyclotron line characteristics of 4U 1538–522 using AstroSat-LAXPC

ABSTRACT We report the first report on cyclotron line studies with the LAXPC instrument onboard AstroSat of the high-mass X-ray binary pulsar 4U 1538–52. During the observation of source that spanned about 1 d with a net exposure of 50 ks, the source X-ray flux remained constant. Pulse profile is double peaked in low-energy range and has a single peak in high-energy range, the transition taking place around the cyclotron line energy of the source. Cyclotron scattering feature (CRSF) is detected at ∼22 keV with a very high significance in phase-averaged spectrum. It is one of the highest signal to noise ratio detections of CRSF for this source. We performed detailed pulse-phase-resolved spectral analysis with 10 independent phase bins. We report the results of pulse-phase-resolved spectroscopy of the continuum and CRSF parameters. The cyclotron line parameters show pulse phase dependence over the entire phase with a CRSF energy variation of ${\sim }13{{\ \rm per\ cent}}$, which is in agreement with previous studies. We also confirm the increase in the centroid energy of the CRSF observed between the 1996–2004 (RXTE) and the 2012 (Suzaku) observations, reinforcing that the increase was a long-term change.

Changes in the pulse phase dependence of X-ray emission lines in 4U 1626−67 with a torque reversal

We report results from an observation with the XMM-Newton observatory of a unique X-ray pulsar 4U 1626-67. EPIC-pn data during the current spin-up phase of 4U 1626-67 have been used to study pulse phase dependence of low energy emission lines. We found strong variability of low energy emission line at 0.915 keV with the pulse phase, varying by a factor of 2, much stronger than the continuum variability. Another interesting observation is that behavior of one of the low energy emission lines across the pulse phase is quite different from that observed during the spin-down phase. This indicates that the structures in the accretion disk that produce pulse phase dependence of emission features have changed from spin-down to spin-up phase. This is well supported by the differences in the timing characteristics (like pulse profiles, QPOs etc) between spin-down and spin-up phases. We have also found that during the current spin-up phase of 4U 1626-67, the X-ray pulse profile below 2 keV is different compared to the spin-down phase. The X-ray light curve also shows flares which produce a feature around 3 mHz in power density spectrum of 4U 1626-67. Since flares are dominant at lower energies, the feature around 3 mHz is prominent at low energies.

Looking at A 0535+26 at low luminosities with NuSTAR

We report on two NuSTAR observations of the HMXB A 0535+26 taken toward the end of its normal 2015 outburst at very low $3-50$ keV luminosities of ${\sim}1.4\times10^{36}$ erg/s and ${\sim}5\times10^{35}$ erg/s which are complemented by 9 Swift observations. The data clearly confirm indications seen in earlier data that the source's spectral shape softens as it becomes fainter. The smooth, exponential rollover at high energies present in the first observation evolves to a much more abrupt steepening of the spectrum at $20-30$ keV. The continuum evolution can be well described with emission from a magnetized accretion column, modeled using the compmag model modified by an additional Gaussian emission component for the fainter observation. Between the two observations, the optical depth changes from $0.75\pm0.04$ to $0.56^{+0.01}_{-0.04}$, the electron temperature remains constant, and there is an indication that the column decreases in radius. Since the energy resolved pulse profiles remain virtually unchanged in shape between the two observations, the emission properties of the accretion column, however, reflect the same accretion regime. This conclusion is also confirmed by our result that the energy of the cyclotron resonant scattering feature (CRSF) at ${\sim}45$ keV is independent of the luminosity, implying that the magnetic field in the region in which the observed radiation is produced is the same in both observations. Finally, we also constrain the evolution of the continuum parameters with rotational phase of the neutron star. The width of the CRSF could only be constrained for the brighter observation. Based on Monte-Carlo simulations of CRSF formation in single accretion columns, its pulse phase dependence supports a simplified fan beam emission pattern. The evolution of the CRSF width is very similar to that of the CRSF depth, which is in disagreement with expectations.

Cyclotron Lines: From Magnetic Field Strength Estimators to Geometry Tracers in Neutron Stars

With exactly forty years since the discovery of the first cyclotron line in Her X-1, there have been remarkable advancements in the field related to study of the physics of accreting neutron stars -- cyclotron lines have been a major torchbearer in this regard, from being the only direct estimator of the magnetic field strength, a tracer of accretion geometry and an indicator of the emission beam in these systems. The main flurry of activities have centred around studying the harmonic separations, luminosity dependence, pulse phase dependence and more recently the shapes of the line and the trend for long term evolution in the line energy. This article visits the important results related to cyclotron lines since its discovery and reviews their significance. An emphasis is laid on pulse phase resolved spectroscopy and the important clues a joint timing and spectral study in this context can provide, to build a complete picture for the physics of accretion and hence X-ray emission in accreting neutron stars.

Pulse-phase dependence of emission lines in the X-ray pulsar 4U 1626–67

We present results from a pulse phase resolved spectroscopy of the complex emission lines around 1 keV in the unique accretion powered X-ray pulsar 4U 1626-67 using observation made with the XMM-Newton in 2003. In this source, the red and blue shifted emission lines and the line widths measured earlier with Chandra suggest their accretion disk origin. Another possible signature of lines produced in accretion disk can be a modulation of the line strength with pulse phase. We found the line fluxes to have pulse phase dependence, making 4U 1626-67 only the second pulsar after Her X-1 to show such variability. The O~VII line at 0.568~keV from 4U 1626-67 varied by a factor of $\sim$4, stronger than the continuum variability, that support their accretion disk origin. The line flux variability may appear due to variable illumination of the accretion disk by the pulsar or more likely, a warp like structure in the accretion disk. We also discuss some further possible diagnostics of the accretion disk in 4U 1626-67 with pulse phase resolved emission line spectroscopy.

Latest results of pulse phase resolved spectroscopy of cyclotron lines in accretion powered pulsars

We have performed pulse phase resolved spectroscopy of the Cyclotron Resonance Scattering Features (CRSF) of some bright accretion powered X-ray pulsars like 1A 1118-61, Vela X-1, A0535+26, XTE J1946+274, 4U 1907+09, 4U 1626-67 and GX 301-2 using Suzaku observations with long exposures. We have performed the study using different spectral models for the continuum and have obtained similar patterns of variations of the CRSF in all the cases, thus demonstrating the robustness of our results. Pulse phase dependence of the CRSF in XTE J1946+274 has been obtained for the first time, and phase resolved variations of the CRSF in 4U 1907+09 has been compared at factor of ~ 2 difference in luminosity. We have also studied the pulse profiles of these objects near the CRSF energy, and have noticed an increased pulse fraction and/or a change in the pulse shape near the CRSF energy for some sources. The implications of the results are discussed.

BROADBAND SPECTRAL INVESTIGATIONS OF SGR J1550–5418 BURSTS

We present the results of our broadband spectral analysis of 42 SGR J1550-5418 bursts simultaneously detected with the Swift/X-ray Telescope (XRT) and the Fermi/Gamma-ray Burst Monitor (GBM), during the 2009 January active episode of the source. The unique spectral and temporal capabilities of the XRT Windowed Timing mode have allowed us to extend the GBM spectral coverage for these events down to the X-ray domain (0.5-10 keV). Our earlier analysis of the GBM data found that the SGR J1550-5418 burst spectra were described equally well with a Comptonized model or with two blackbody functions; the two models were statistically indistinguishable. Our new broadband (0.5 - 200 keV) spectral fits show that, on average, the burst spectra are better described with two blackbody functions than with the Comptonized model. Thus, our joint XRT/GBM analysis clearly shows for the first time that the SGR J1550-5418 burst spectra might naturally be expected to exhibit a more truly thermalized character, such as a two-blackbody or even a multi-blackbody signal. Using the Swift and RXTE timing ephemeris for SGR J1550-5418 we construct the distribution of the XRT burst counts with spin phase and find that it is not correlated with the persistent X-ray emission pulse phase from SGR J1550-5418. These results indicate that the burst emitting sites on the neutron star need not be co-located with hot spots emitting the bulk of the persistent X-ray emission. Finally, we show that there is a significant pulse phase dependence of the XRT burst counts, likely demonstrating that the surface magnetic field of SGR J1550-5418 is not uniform over the emission zone, since it is anticipated that regions with stronger surface magnetic field could trigger bursts more efficiently.

4U 1909+07: a Hidden Pearl

We present a detailed spectral and timing analysis of the High Mass X-ray Binary (HMXB) 4U 1909+07 with INTEGRAL and RXTE. 4U1909+07 is a persistent accreting X-ray pulsar with a period of approximately 605 s. The period changes erratically consistent with a random walk expected for a wind accreting system. INTEGRAL detects the source with an average of 2.4 cps (corresponding to 15mCrab), but sometimes exhibits flaring activity up to 50 cps (i.e. 300mCrab). The strongly energy dependent pulse profile shows a double peaked structure at low energies and only a single narrow peak at energies above 20 keV. The phase averaged spectrum is well described by a powerlaw modified at higher energies by an exponential cutoff and photoelectric absorption at low energies. In addition at 6.4 keV a strong iron fluorescence line and at lower energies a blackbody component are present. We performed phase resolved spectroscopy to study the pulse phase dependence of the spectral parameters: while most spectral parameters are constant within uncertainties, the blackbody normalization and the cutoff folding energy vary strongly with phase.

Pulse phase dependence of the magnetar bursts

We report here results from a study of X-ray bursts from 3 magnetar candidates (SGR 1806-20, SGR 1900+14 and AXP 1E 2259+586). We have searched for a pulse phase dependence of the X-ray burst rate from these sources. X-ray light curves were obtained with the Proportional Counter Array on-board the Rossi X-ray Timing Explorer during the periods of intense burst activity in these sources. On detailed analysis of the three sources, we found a very significant burst rate for all pulsar phases. However, some locations appear to produce bursts slightly more often, rendering the non-isotropic distribution. Only in the case of SGR 1900+14, there is a clear pulse phase dependence of burst rate.

Studies of orbital parameters and pulse profile of the accreting millisecond pulsar XTE J1807–294

The accreting millisecond pulsar XTE J1807-294 was observed as a Target of Opportunity (ToO) by XMM-Newton on March 22, 2003 after its discovery on February 21, 2003 by RXTE . The source was detected in its bright phase with an observed average count rate of 33.3 cts s-1 in the EPIC-pn camera in the 0.5–10 keV energy band (3.7 mCrab). Using the earlier established best-fit orbital period of 40.0741 ± 0.0005 min from the RXTE observations and considering a circular binary orbit as first approximation, we derived a value of 4.8 ± 0.1 lt-ms for the projected orbital radius of the binary system and an epoch of the orbital phase of MJD 52 720.67415(16). The barycentric mean spin period of the pulsar was derived as 5.2459427 ± 0.0000004 ms. The pulsar's spin-pulse profile showed a prominent (1.5 ms FWHM) pulse, with energy and orbital phase dependence in the amplitude and shape. The measured pulsed fraction in four energy bands was found to be 3.1 ± 0.2% (0.5–3.0 keV), 5.4 ± 0.4% (3.0–6.0 keV), 5.1 ± 0.7% (6.0–10.0 keV) and 3.7 ± 0.2% (0.5–10.0 keV), respectively. Studies of spin-profiles with orbital phase and energy showed significant increase in its pulsed fraction during the second observed orbit of the neutron star, gradually declining in the subsequent two orbits, which was associated with sudden but marginal increase in mass accretion. From our investigations of orbital parameters and estimation of other properties of this compact binary system, we conclude that XTE J1807-294 is very likely a candidate for a millisecond radio pulsar.

BeppoSAX LECS X-ray observations of Hercules X-1

We present 0.1–10 keV observations of Her X-1 obtained with the Low-Energy Spectrometer Concentrator instrument onboard the BeppoSAX satellite during the main on-state of the 35 day cycle. We confirm the existence of an intense 0.093 keV blackbody component and a broad emission feature at 0.94 keV. The pulse phase dependence of these components is similar, suggesting a common origin. This is most likely fluorescent excitation of moderately ionized (ξ ∼ 10–100) material located at the inner edge of the accretion disk.

Pulse phase studies of x-ray emission from GX301-2

Observations of GX301-2 by Tenma have been analyzed to study spectral changes which occur through the 701 second pulse period. Significant spectral dependence on pulse phase is found which varies from observation to observation. Due to the large column densities observed for GX301-2, effects on the observed spectrum caused by scattering in the circumstellar material are important. These were quantified by Monte Carlo simulations. Such effects can account for a significant part, but not all, of the observed variations. The variation of pulse fraction, allowing for scattering effects, implies that the beaming of radiation from the source fluctuates in a way which is not simply dependent on source intensity. Intrinsic dependence on pulse phase is found for spectral index, cutoff energy and e-folding energy. The dependence of spectral index is different for different observations, and shows an asymmetry indicating a significantly non-dipolar magnetic field for GX301-2. The intensity of the iron line has a pulse phase dependence.

X-ray spectra of Hercules X-1. III - Pulse phase dependence in the high-energy continuum

Pulse phase-dependent spectral changes in the high energy (less than 20 keV) continuum of Hercules X-1 were observed. Cyclotron absorption of underlying continua can reproduce the observed angular dependence in the high energy cutoff. Implications of this model, which include the possibility of determining the angular separation between the line of sight and the neutron star magnetic field if the absorbing electron spectrum is known are discussed.