Superorbital Phase Research Articles

A Precessing Stellar Disk Model for Superorbital Modulations of the Gamma-Ray Binary LS I+61° 303

Gamma-ray binary LS I+61° 303 consists of a neutron star orbiting around a Be star with a period of P orb ≃ 26.5 days. Apart from orbital modulations, the binary shows long-term flux variations with a superorbital period of Psup≃4.6yr as seen in nearly all wavelengths. The origin of this superorbital modulation is still not well understood. Under the pulsar wind–stellar outflow interaction scenario, we propose that the superorbital modulations of LS I+61° 303 could be caused by the precession of the Be disk. Assuming X-rays arise from synchrotron radiation of the intrabinary shock, we develop an analytical model to calculate expected flux modulations over the orbital and superorbital phases. The asymmetric two-peak profiles in orbital light curves and sinusoidal-like long-term modulations are reproduced under the precessing disk scenario. The observed orbital phase drifting of the X-ray peak and our fitting of long-term X-ray data indicate that the neutron star is likely orbiting around the star with a small eccentricity and periastron phase around Φp ∼ 0.6. We compare the Corbet diagrams of LS I+61° 303 with other Be/X-ray binaries, and the linear correlation in the Psup–Porb diagram suggests that the precession of the Be disk in LS I+61° 303 is induced by the tidal torque of its neutron star companion.

Swift/XRT observations of superorbital modulations in wind-fed supergiant X-ray binaries

ABSTRACT We present the first Swift/XRT long-term monitoring of 2S 0114+650, a wind-fed supergiant X-ray binary for which both orbital and superorbital periods are known (Porb ∼ 11.6 d and Psup ∼ 30.8 d). Our campaign, summing up to ∼79 ks, is the most intense and complete sampling of the X-ray light curve of this source with a sensitive pointed X-ray instrument, and covers 17 orbital, and 6 superorbital cycles. The combination of flexibility, sensitivity, and soft X-ray coverage of the X-ray telescope (XRT) allowed us to confirm previously reported spectral changes along the orbital cycle of the source and unveil the variability in its spectral parameters as a function of the superorbital phase. For completeness, we also report on a similar analysis carried out by exploiting XRT archival data on three additional wind-fed supergiant X-ray binaries IGR J16418−4532, IGR J16479−4514, and IGR J16493−4348. For these sources, the archival data provided coverage along several superorbital cycles but our analysis could not reveal any significant spectral variability.

Constraining the Evolution of the Unstable Accretion Disk in SMC X-1 with NICER

Neutron star high-mass X-ray binaries with superorbital modulations in luminosity host warped inner accretion disks that occult the neutron star during precession. In SMC X-1, the instability in the warped disk geometry causes superorbital period “excursions”: times of instability when the superorbital period decreases from its typical value of 55 to ∼40 days. Disk instability makes SMC X-1 an ideal system in which to investigate the effects of variable disk geometry on the inner accretion flow. Using the high-resolution spectral and timing capabilities of the Neutron Star Interior Composition Explorer, we examined the high state of four different superorbital cycles of SMC X-1 to search for changes in spectral shape and connections to the unstable disk geometry. We performed pulse phase-averaged and phase-resolved spectroscopy to closely compare the changes in spectral shape and any cycle-to-cycle variations. While some parameters, including the photon index and absorbing column density, show slight variations with superorbital phase, these changes are most evident during the intermediate state of the superorbital cycle. Few spectral changes are observed within the high state of the superorbital cycle, possibly indicating the disk instability does not significantly change SMC X-1's accretion process.

Monitoring observations of SMC X-1’s excursions (MOOSE)–I. Programme description and initial high state spectral results

ABSTRACT SMC X-1 has exhibited three superorbital period excursions since the onset of X-ray monitoring beginning with the Rossi X-ray Timing Explorer's launch in 1995. TheNeutron star Interior Composition Explorer has recently probed a fourth observed excursion beginning in 2021 with our programme monitoring observations of SMC X-1’s excursions (moose). These sensitive new moose data probe different superorbital periods and phases within them. Spectral fits to the high-state continuum during 2021 April to 2022 January show that the intrinsic spectral shapes are characterized by a soft (kT ∼ 0.19 keV) disc component and a hard (Γ ∼ 0.7) power-law tail. When the 2021–2022 NICER observations, taken during an excursion, are compared to 2016 XMM–Newton observations (outside of an excursion), we find little evidence for intrinsic spectral variability across the high states, but find evidence for a >3σ change in the absorption, although we caution that there may be calibration differences between the two instruments. Thus, over different lengths of superorbital periods, we see little evidence for intrinsic spectral changes in the high state. Upcoming studies of the pulse profiles may shed light on the mechanism behind the excursions.

Evolution of the Spin, Spectrum and Superorbital Period of the Ultraluminous X-Ray Pulsar M51 ULX7

Abstract M51 ULX7 is among a small group of known ultraluminous X-ray pulsars (ULXPs). The neutron star powering the source has a spin period of 2.8 s, orbits its companion star with a period of 2 days, and a superorbital period of 38 days is evident in its X-ray lightcurve. Here we present NuSTAR and XMM-Newton data on the source from 2019 obtained when the source was near its peak brightness. We detect the pulsations, having spun up at a rate of 3 ± 0.5 × 10−10 s s−1 since they were previously detected in 2018. The data also provide the first high-quality broadband spectrum of the source. We find it to be very similar to that of other ULXPs, with two disk-like components, and a high-energy tail. When combined with XMM-Newton data obtained in 2018, we explore the evolution of the spectral components with superorbital phase, finding that the luminosity of the hotter component drives the superorbital flux modulation. The inclination the disk components appear to change with phase, which may support the idea that these superorbital periods are caused by disk precession. We also reexamine the superorbital period with 3 yr of Swift/XRT monitoring, finding that the period is variable, increasing from 38.2 ± 0.5 days in 2018–2019 to 44.2 ± 0.9 days in 2020–2021, which rules out alternative explanations for the superorbital period.

KIC 9406652: A laboratory for tilted disks in cataclysmic variable stars. II. Modeling of the orbital light curves

Abstract KIC 9406652, one of the recently identified IW And-type dwarf novae, is the best target for studying the tilted disk in cataclysmic variable stars. In a previous paper by Kimura et al. (2020b, PASJ, 72, 94), we analyzed its Kepler light curves and found that its orbital light curves during the brightening stage were dominated by the reflection effect of the secondary star and varied with the orientation of the tilted disk; the amplitude was maximized at the minimum of the super-orbital signal and the phase of the light maximum shifted to an earlier one with the advance of the super-orbital phase. We argued in that work that this was direct evidence of the retrogradely precessing tilted disk as the secondary star acts like a reflecting object. In order to confirm this interpretation, we have performed numerical modeling of orbital light curves in this paper. We have succeeded in reproducing the main characteristics of the observed orbital light curves by a simple model in which the secondary star is irradiated by the tilted disk. We have also constrained the inclination angle, i, of the binary system and the tilt angle, θ, of the disk purely from photometric considerations. The best-fitting parameter set is found to be i ∼ 45° and $\theta \sim {2{_{.}^{\circ}}0}$, respectively. The orbital inclination thus estimated is consistent with that obtained from the spectroscopic considerations within the uncertainty limit. On the other hand, the tilt angle of the disk could be underestimated by using only the semi-amplitude of super-orbital signals.

A Broadband X-Ray View of the Precessing Accretion Disk and Pre-eclipse Dip in the Pulsar Her X-1 with NuSTAR and XMM-Newton

Abstract We present a broadband X-ray timing study of the variations in pulse behavior with the superorbital cycle in the low-mass X-ray binary Her X-1. This source shows a 35 day superorbital modulation in X-ray flux that is likely caused by occultation by a warped, precessing accretion disk. Our data set consists of four joint XMM-Newton and NuSTAR observations of Her X-1 which sample a complete superorbital cycle. We focus our analysis on the first and fourth observations, which occur during the bright “main-on” phase, because these observations have strongly detected pulsations. We added an archival XMM-Newton observation during the “short-on” phase of the superorbital cycle because our observations at that phase are lower in signal to noise. We find that the energy-resolved pulse profiles show the same shape at similar superorbital phases, and the profiles are consistent with expectations from a precessing disk. We demonstrate that a simple precessing accretion disk model is sufficient to reproduce the observed pulse profiles. The results of this model suggest that the similarities in the observed pulse profiles are due to reprocessing by a precessing disk that has returned to its original precession phase. We determine that the broadband spectrum is well fit by an absorbed power law with a soft blackbody component and show that the spectral continuum also exhibits a dependence on the superorbital cycle. We also present a brief analysis of the energy-resolved light curves of a pre-eclipse dip, which shows soft X-ray absorption and hard X-ray variability during the dip.

KIC 9406652: A laboratory for tilted disks in cataclysmic variable stars

AbstractKIC 9406652 is a cataclysmic variable, sub-classified as an “IW And-type” star, which shows repeated standstills with oscillatory variations terminated by brightening. This system shows negative superhumps, semi-periodic variations having periods slightly shorter than the ∼6 hr orbital period, and super-orbital signals having ∼4 d periods, both of which are believed to originate from a precessing, tilted accretion disk. We have re-examined its Kepler light curve over 1500 d. In accordance with a cycle of IW And-type light variation, the frequency of negative superhumps showed reproducible variation: a rapid drop during the brightening and a gradual increase during the standstill. This is interpreted as a drastic change in the radial mass distribution and the expansion of the tilted disk, which is not expected from the existing models of IW And stars. The constancy in flux amplitudes of the negative superhumps confirms that their light source is the bright spot sweeping across the surface of the tilted disk. The frequencies of the negative superhumps and super-orbital signals varied in unison on long timescales, suggesting their common origin: the tilted disk. The orbital signals at the brightening were dominated by the irradiation of the secondary star and varied with the orientation of the tilted disk; the amplitude was maximized at the minimum of the super-orbital signals, and the light maximum shifted to early orbital phases as the super-orbital phase advanced. This is the first direct evidence that the disk is tilted out of the binary orbital plane and is retrogradely precessing. The tilt angle of the disk inferred from semi-amplitudes of super-orbital signals was lower than 3°. The diversity in light curves of the negative superhumps supports this and suggests that part of the gas stream overflows the disk edge. This study thus offers rich information about the tilted disk in cataclysmic variables.

An ionized accretion disc wind in Hercules X-1

ABSTRACT Hercules X-1 is one of the best-studied highly magnetized neutron star X-ray binaries with a wealth of archival data. We present the discovery of an ionized wind in its X-ray spectrum when the source is in the high state. The wind detection is statistically significant in most of the XMM–Newton observations, with velocities ranging from 200 to 1000 km s−1. Observed features in the iron K band can be explained by both wind absorption and a forest of iron emission lines. However, we also detect nitrogen, oxygen, and neon absorption lines at the same systematic velocity in the high-resolution Reflection Grating Spectrometer grating spectra. The wind must be launched from the accretion disc, and could be the progenitor of the ultraviolet absorption features observed at comparable velocities, but the latter likely originate at significantly larger distances from the compact object. We find strong correlations between the ionization level of the outflowing material and the ionizing luminosity as well as the superorbital phase. If the luminosity is driving the correlation, the wind could be launched by a combination of Compton heating and radiation pressure. If instead the superorbital phase is the driver for the variations, the observations are likely scanning the wind at different heights above the warped accretion disc. If this is the case, we can estimate the wind mass outflow rate, corrected for the limited launching solid angle, to be roughly 70 per cent of the mass accretion rate.

Study of orbital and superorbital variability of LSI +61° 303 with X-ray data

LSI +61° 303 is one of the few X-ray binaries with a Be star companion from which radio, X-rays and high-energy gamma-ray (GeV and TeV) emission have been observed. The nature of the high-energy activity of the system is not yet fully understood, but it is widely believed that it is generated due to the interaction of the relativistic electrons leaving the compact object with the photons and non-relativistic wind of the Be star. The superorbital variability of the system has been observed in the radio, optical and X-ray domains and could be due to the cyclic change of the Be star disc size. In this paper, we systematically review all publicly available data from Suzaku, XMM–Newton, Chandra and Swift observatories in order to measure the absorption profile of the circumstellar Be disc as a function of orbital and superorbital phases. We also discuss short-term variability of the system, found during the analysis and its implications for the understanding of the physical processes in this system.

Orbital and superorbital monitoring of the Be/X-ray binary A0538–66: constraints on the system parameters

We combine the decade long photometry of the Be/X-ray binary system A0538-66 provided by the MACHO and OGLE IV projects with high resolution SALT spectroscopy to provide detailed constraints on the orbital parameters and system properties. The ~420d superorbital modulation is present throughout, but has reduced in amplitude in recent years. The well-defined 16.6409d orbital outbursts, which were a strong function of superorbital phase in the MACHO data (not occurring at all at superorbital maximum), are present throughout the OGLE IV coverage. However, their amplitude reduces during superorbital maximum. We have refined the orbital period and ephemeris of the optical outburst based on ~25 yrs light curves to HJD = 2455674.48 +/- 0.03 + n*16.6409 +/- 0.0003d. Our SALT spectra reveal a B1 III star with vsini of 285 km/s from which we have derived an orbital radial velocity curve which confirms the high eccentricity of e = 0.72 +/- 0.14. Furthermore, the mass function indicates that, unless the neutron star far exceeds the canonical 1.44 Msun, the donor must be significantly undermassive for its spectral type. We discuss the implications of the geometry and our derived orbital solution on the observed behaviour of the system.

Evidence of coupling between the thermal and nonthermal emission in the gamma-ray binary LS I +61 303

The gamma-ray binary LS I +61 303 is composed of a Be star and a compact companion orbiting in an eccentric orbit. Variable flux modulated with the orbital period of ~26.5 d has been detected from radio to very high-energy gamma rays. In addition, the system presents a superorbital variability of the phase and amplitude of the radio outburst with a period of ~4.6 yr. We present optical photometric observations of LS I +61 303 spanning ~1.5 yr and contemporaneous Halpha equivalent width (EW Halpha) data. The optical photometry shows, for the first time, that the known orbital modulation suffers a positive orbital phase shift and an increase in flux for data obtained 1-yr apart. This behavior is similar to that already known at radio wavelengths, indicating that the optical flux follows the superorbital variability as well. The orbital modulation of the EW Halpha presents the already known superorbital flux variability but shows, also for the first time, a positive orbital phase shift. In addition, the optical photometry exhibits a lag of ~0.1-0.2 in orbital phase with respect to the EW Halpha measurements at similar superorbital phases, and presents a lag of ~0.1 and ~0.3 orbital phases with respect noncontemperaneous radio and X-ray outbursts, respectively. The phase shifts detected in the orbital modulation of thermal indicators, such as the optical flux and the EW Halpha, are in line with the observed behavior for nonthermal indicators, such as X-ray or radio emission. This shows that there is a strong coupling between the thermal and nonthermal emission processes in the gamma-ray binary LS I +61 303. The orbital phase lag between the optical flux and the EW Halpha is naturally explained considering different emitting regions in the circumstellar disk, whereas the secular evolution might be caused by the presence of a moving one-armed spiral density wave in the disk.

SPECTRAL ANALYSIS IN ORBITAL/SUPERORBITAL PHASE SPACE AND HINTS OF SUPERORBITAL VARIABILITY IN THE HARD X-RAYS OF LS I +61°303

ABSTRACT We present an INTEGRAL spectral analysis in the orbital/superorbital phase space of LS I +61°303. A hard X-ray spectrum with no cutoff is observed at all orbital/superorbital phases. The hard X-ray index is found to be uncorrelated with the radio index (non-simultaneously) measured at the same orbital and superorbital phases. In particular, the absence of an X-ray spectrum softening during periods of negative radio index does not favor a simple interpretation of the radio index variations in terms of a microquasar's changes of state. We uncover hints of superorbital variability in the hard X-ray flux, in phase with the superorbital modulation in soft X-rays. An orbital phase drift of the radio peak flux and index along the superorbital period is observed in the radio data. We explore its influence on a previously reported double-peak structure of a radio orbital light curve, and present it as a plausible explanation.

SUPERORBITAL PHASE-RESOLVED ANALYSIS OF SMC X-1

The high-mass X-ray binary SMC X-1 is an eclipsing binary with an orbital period of 3.89 d. This system exhibits a superorbital modulation with a period varying between ~40 d and ~65 d. The instantaneous frequency and the corresponding phase of the superorbital modulation can be obtained by a recently developed time-frequency analysis technique, the Hilbert-Huang transform (HHT). We present a phase-resolved analysis of both the spectra and the orbital profiles with the superorbital phase derived from the HHT. The X-ray spectra observed by the Proportional Counter Array onboard the Rossi X-ray Timing Explorer are fitted well by a blackbody plus a Comptonized component. The plasma optical depth, which is a good indicator of the distribution of material along the line of sight, is significantly anti-correlated with the flux detected at 2.5-25 keV. However, the relationship between the plasma optical depth and the equivalent width of the iron line is not monotonic: there is no significant correlation for fluxes higher than ~35 mCrab but clear positive correlation when the intensity is lower than ~20 mCrab. This indicates that the iron line production is dominated by different regions of this binary system in different superorbital phases. To study the dependence of the orbital profile on the superorbital phase, we obtained the eclipse profiles by folding the All Sky Monitor light curve with the orbital period for different superorbital states. A dip feature, similar to the pre-eclipse dip in Her X-1, lying at orbital phase ~0.6-0.85, was discovered during the superorbital transition state. This indicates that the accretion disk has a bulge that absorbs considerable X-ray emission in the stream-disk interaction region. The dip width is anti-correlated with the flux, and this relation can be interpreted by the precessing tilted accretion disk scenario.

An Application of Hilbert-Huang Transform on the Non-Stationary Astronomical Time Series: The Superorbital Modulation of SMC X-1

We present the Hilbert-Huang transform (HHT) analysis on the quasi-periodic modulation of SMC X-1. SMC X-1, consisting of a neutron star and a massive companion, exhibits superorbital modulation with a period varying between ~40 d and ~65 d. We applied the HHT on the light curve observed by the All-Sky Monitor onboard Rossi X-ray Timing Explorer (RXTE) to obtain the instantaneous frequency of the superorbital modulation of SMC X-1. The resultant Hilbert spectrum is consistent with the dynamic power spectrum while it shows more detailed information in both the time and frequency domains. According to the instantaneous frequency, we found a correlation between the superorbital period and the modulation amplitude. Combining the spectral observation made by the Proportional Counter Array onboard RXTE and the superorbital phase derived in the HHT, we performed a superorbital phase-resolved spectral analysis of SMC X-1. An analysis of the spectral parameters versus the orbital phase for different superorbital states revealed that the diversity of <TEX>$n_H$</TEX> has an orbital dependence. Furthermore, we obtained the variation in the eclipse profiles by folding the All Sky Monitor light curve with orbital period for different superorbital states. A dip feature, similar to the pre-eclipse dip of Her X-1, can be observed only in the superorbital ascending and descending states, while the width is anti-correlated with the X-ray flux.

THE PHOTOIONIZED ACCRETION DISK IN HER X-1

We present an analysis of several high-resolution Chandra grating observations of the X-ray binary pulsar Her X-1. With a total exposure of 170 ks, the observations are separated by years and cover three combinations of orbital and super-orbital phases. Our goal is to determine distinct properties of the photoionized emission and its dependence on phase-dependent variations of the continuum. We find that the continua can be described by a partial covering model which above 2 keV is consistent with recent results from \rxte studies and at low energies is consistent with recent \xmm and \sax studies. Besides a powerlaw with fixed index, an additional thermal blackbody of 114 eV is required to fit wavelengths above 12 \AA ($\sim$ 1 keV). We find that likely all the variability is caused by highly variable absorption columns in the range (1 -- 3)$\times 10^{23}$ cm$^{-2}$. Strong Fe K line fluorescence in almost all observations reveals that dense, cool material is present not only in the outer regions of the disk but interspersed throughout the disk. Most spectra show strong line emission stemming from a photoionized accretion disk corona. We model the line emission with generic thermal plasma models as well as with the photoionization code XSTAR and investigate changes of the ionization balance with orbital and superorbital phases. Most accretion disk coronal properties such as disk radii, temperatures, and plasma densities are consistent with previous findings for the low state. We find that these properties change negligibly with respect to orbital and super-orbital phases. A couple of the higher energy lines exhibit emissivities that are significantly in excess of expectations from a static accretion disk corona.

SPECTROSCOPIC SIGNATURES OF THE SUPERORBITAL PERIOD IN THE NEUTRON STAR BINARY LMC X-4

We present the first high-resolution X-ray study of emission line variability with superorbital phase in the neutron star binary LMC X-4. Our analysis provides new evidence from X-ray spectroscopy confirming accretion disk precession as the origin of the superorbital period. The spectra, obtained with the Chandra High-Energy Transmission Grating Spectrometer (HETGS) and the XMM-Newton Reflection Grating Spectrometer (RGS), contain a number of emission features, including lines from hydrogen-like and helium-like species of N, O, Ne, and Fe, a narrow O VII RRC, and fluorescent emission from cold Fe. We use the narrow RRC and the He-alpha triplets to constrain the temperature and density of the (photoionized) gas. By comparing spectra from different superorbital phases, we attempt to isolate the contributions to line emission from the accretion disk and the stellar wind. There is also evidence for highly ionized iron redshifted and blueshifted by ~25,000 km/s. We argue that this emission originates in the inner accretion disk, and show that the emission line properties in LMC X-4 are natural consequences of accretion disk precession.

Superorbital variability of X-ray and radio emission of Cyg X-1 - II. Dependence of the orbital modulation and spectral hardness on the superorbital phase

We discover a pronounced dependence of the strength of the X-ray orbital modulation and the hardness in Cyg X-1 in the hard state on its superorbital phase. Our results can be well modelled as a combination of two effects: the precession of the accretion disc (which causes the superorbital flux modulation) and the orbital-phase dependent X-ray absorption in an accretion bulge, located at the accretion disc edge close to the supergiant companion but displaced from the line connecting the stars by about 25^o. Our findings are supported by the distribution of the X-ray dips showing concentration towards zero superorbital phase, which corresponds to the bulge passing through the line of sight. We Fourier analyse our model, and find it explains the previous finding of asymmetric beat (between the orbital and superorbital modulations) frequencies in the observed power spectrum, provided the disc precession is prograde. We find no statistically significant changes of the orbital modulation with the superorbital phase in the 15-GHz radio data. This absence is consistent with the radio being emitted by a jet in the system, in which case the orbital modulation is caused by wind absorption far away from the disc. We also find that both the X-ray and radio fluxes of Cyg X-1 in the hard state on time scales >10^4-s have lognormal distributions, which complements a previous finding of a lognormal flux distribution in the hard state on 1-s time scales. We point out that the lognormal character of the flux distribution requires that flux logarithms rather than fluxes themselves should be used for averaging and error analysis. We also provide a correct formula for the uncertainty of rms of a light curve for the case when the uncertainty is higher than the measurement.