Superorbital Variability Research Articles

Determination of X-ray pulsar geometry with IXPE polarimetry

Using observations of X-ray pulsar Her X-1 by the Imaging X-ray Polarimetry Explorer, we report on a highly significant ($>17\sigma$) detection of the polarization signal from an accreting neutron star. The observed degree of the linear polarization of $\sim$10\% is found to be far below theoretical expectations for this object, and stays low throughout the spin cycle of the pulsar. Both the polarization degree and the angle exhibit variability with pulse phase, which allowed us to measure the pulsar spin position angle 57(2) deg and the magnetic obliquity 12(4) deg, which is an essential step towards detailed modelling of the intrinsic emission of X-ray pulsars. Combining our results with the optical polarimetric data, we find that the spin axis of the neutron star and the angular momentum of the binary orbit are misaligned by at least $\sim$20 deg, which is a strong argument in support of the models explaining stability of the observed super-orbital variability with the precession of the neutron star.

Orbital variability of the optical linear polarization of the γ-ray binary LS I +61° 303 and new constraints on the orbital parameters

We studied the variability of the linear polarization and brightness of the γ-ray binary LS I +61° 303. High-precision BVR photopolarimetric observations were carried out with the Dipol-2 polarimeter on the 2.2 m remotely controlled UH88 telescope at Mauna Kea Observatory and the 60 cm Tohoku telescope at Haleakala bservatory (Hawaii) over 140 nights in 2016−2019. We also determined the degree and angle of the interstellar polarization toward LS I +61° 303 using two out of four nearby field stars that have Gaia’s parallaxes. After subtracting the interstellar polarization, we determined the position angle of the intrinsic polarization θ ≃ 11°, which can either be associated with the projection of the Be star’s decretion disk axis on the plane of sky, or can differ from it by 90°. Using the Lomb-Scargle method, we performed timing analyses and period searches of our polarimetric and photometric data. We found statistically significant periodic variability of the normalized Stokes parameters q and u in all passbands. The most significant period of variability, PPol = 13.244 ± 0.012 d, is equal to one half of the orbital period Porb = 26.496 d. The fits of the polarization variability curves with Fourier series show a dominant contribution from the second harmonic which is typical for binary systems with circular orbits and nearly symmetric distribution of light scattering material with respect to the orbital plane. The continuous change of polarization with the orbital phase implies co-planarity of the orbit of the compact object and the Be star’s decretion disk. Using a model of Thomson scattering by a cloud that orbits the Be star, we obtained constraints on the orbital parameters, including a small eccentricity e < 0.2 and periastron phase of ϕp ≈ 0.6, which coincides with the peaks in the radio, X-ray, and TeV emission. These constraints are independent of the assumption about the orientation of the decretion disk plane on the sky. We also extensively discuss the apparent inconsistency with the previous measurements of the orbital parameters from radial velocities. By folding the photometry data acquired during a three-year time span with the orbital period, we found a linear phase shift of the moments of the brightness maximum, confirming the possible existence of superorbital variability.

Modelling of 35-d superorbital cycle of B and V light curves of IMXB HZ Her/Her X-1

ABSTRACT The X-ray binary Her X-1 consists of an accreting neutron star and the optical component HZ Her. The 35-d X-ray superorbital variability of this system is known, since its discovery in 1972 by the Uhuru satellite and is believed to be caused by forced precession of a warped accretion disc tilted to the orbital plane. We argue that the observed features of the 35-d optical variability of HZ Her can be explained by free precession of the neutron star with a period close to that of the forced disc. The model parameters include (a) the X-ray luminosity of the neutron star; (b) the optical flux from the accretion disc; and (c) the tilt of the inner and outer edges of the accretion disc. A possible synchronization mechanism based on the coupling between the neutron star free precession and the dynamical action of non-stationary gas streams is discussed.

H.E.S.S. and Fermi-LAT observations of PSR B1259–63/LS 2883 during its 2014 and 2017 periastron passages

Context. PSR B1259–63/LS 2883 is a gamma-ray binary system consisting of a pulsar in an eccentric orbit around a bright Oe stellar-type companion star that features a dense circumstellar disc. The bright broad-band emission observed at phases close to periastron offers a unique opportunity to study particle acceleration and radiation processes in binary systems. Observations at gamma-ray energies constrain these processes through variability and spectral characterisation studies. Aims. The high- and very-high-energy (HE, VHE) gamma-ray emission from PSR B1259–63/LS 2883 around the times of its periastron passage are characterised, in particular, at the time of the HE gamma-ray flares reported to have occurred in 2011, 2014, and 2017. Short-term and average emission characteristics of PSR B1259–63/LS 2883 are determined. Super-orbital variability is searched for in order to investigate possible cycle-to-cycle VHE flux changes due to different properties of the companion star’s circumstellar disc and/or the conditions under which the HE gamma-ray flares develop. Methods. Spectra and light curves were derived from observations conducted with the H.E.S.S-II array in 2014 and 2017. Phase-folded light curves are compared with the results obtained in 2004, 2007, and 2011. Fermi-LAT observations from 2010/11, 2014, and 2017 are analysed. Results. A local double-peak profile with asymmetric peaks in the VHE light curve is measured, with a flux minimum at the time of periastron tp and two peaks coinciding with the times at which the neutron star crosses the companion’s circumstellar disc (~tp ± 16 d). A high VHE gamma-ray flux is also observed at the times of the HE gamma-ray flares (~tp + 30 d) and at phases before the first disc crossing (~tp − 35 d). The spectral energy range now extends to below 200 GeV and up to ~45 TeV. Conclusions. PSR B1259–63/LS 2883 displays periodic flux variability at VHE gamma-rays without clear signatures of super-orbital modulation in the time span covered by the monitoring of the source with the H.E.S.S. telescopes. This flux variability is most probably caused by the changing environmental conditions, particularly at times close to periastron passage at which the neutron star is thought to cross the circumstellar disc of the companion star twice. In contrast, the photon index remains unchanged within uncertainties for about 200 d around periastron. At HE gamma-rays, PSR B1259–63/LS 2883 has now been detected also before and after periastron, close to the disc crossing times. Repetitive flares with distinct variability patterns are detected in this energy range. Such outbursts are not observed at VHEs, although a relatively high emission level is measured. The spectra obtained in both energy regimes displays a similar slope, although a common physical origin either in terms of a related particle population, emission mechanism, or emitter location is ruled out.

A Study of the 20 day Superorbital Modulation in the High-mass X-Ray Binary IGR J16493-4348

Abstract We report on Nuclear Spectroscopic Telescope Array (NuSTAR), Neil Gehrels Swift Observatory (Swift) X-ray Telescope (XRT), and Swift Burst Alert Telescope (BAT) observations of IGR J16493-4348, a wind-fed supergiant X-ray binary showing significant superorbital variability. From a discrete Fourier transform of the BAT light curve, we refine its superorbital period to be 20.058 ± 0.007 days. The BAT dynamic power spectrum and a fractional root mean square analysis both show strong variations in the amplitude of the superorbital modulation, but no observed changes in the period are found. The superorbital modulation is significantly weaker between MJD 55,700 and MJD 56,300. The joint NuSTAR and XRT observations, which were performed near the minimum and maximum of one cycle of the 20 day superorbital modulation, show that the flux increases by more than a factor of two between superorbital minimum and maximum. We find no significant changes in the 3–50 keV pulse profiles between superorbital minimum and maximum, which suggests a similar accretion regime. Modeling the pulse-phase-averaged spectra we find a possible Fe Kα emission line at 6.4 keV at superorbital maximum. This feature is not significant at superorbital minimum. While we do not observe any significant differences between the pulse-phase-averaged spectral continua apart from the overall flux change, we find that the hardness ratio near the broad main peak of the pulse profile increases from superorbital minimum to maximum. This suggests the spectral shape hardens with increasing luminosity. We discuss different mechanisms that might drive the observed superorbital modulation.

VHE observations of binary systems performed with the MAGIC telescopes

The improvement on the Imaging Air Cherenkov Technique (IACT) led to the discovery of a new type of sources that can emit at very high energies: the gamma-ray binaries. Only six systems are part of this exclusive class. We summarize the latest results from the observations performed with the MAGIC telescopes on different systems as the gamma-ray binary LS I [Formula: see text]303 and the microquasars SS 433, V404 Cygni and Cygnus X-1, which are considered potential VHE gamma-ray emitters. The binary system LS I [Formula: see text] 303 has been observed by MAGIC in a long-term monitoring campaign. We show the newest results of our search for super-orbital variability also in context of contemporaneous optical observations. Besides, we will present the results of the only super-critical accretor known in our galaxy: SS 433. We will introduce the VHE results achieved with MAGIC after 100[Formula: see text]h of observations on the microquasar Cygnus X-1 and report on the microquasar V404 Cyg, which has been observed with MAGIC after it went through a series of exceptional X-ray outbursts in June 2015.

LMC X–4: Different Types of Long-Term Variability

AbstractThis talk presented a summary of our study of different types of long-term variability in the high-mass X-ray binary LMC X-4, by taking advantage of more than 43 years of measurements in the X-ray domain. In particular, we investigated the 30-day cycle of modulation of the X-ray emission from the source (super-orbital or precessional variability), and refined the orbital period and its first derivative. We showed that the precession period in the time-interval 1991–2015 is near its equilibrium value of Psup = 30.370 days, while the observed historical changes in the phase of this variability can be interpreted in terms of the ‘red noise’ model. We obtained an analytical law from which the precession phase can be determined to within 5% throughout the entire time-interval under consideration. Our analysis revealed for the first time that the source is displaying near-periodic variations of its spin period, on a time-scale of roughly 6.8 years, thus making LMC X-4 one of the (few) known binary systems that show remarkable long-term spin–torque reversals.

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.

Optically thick envelopes around ULXs powered by accreating neutron stars

Magnetized neutron stars power at least some ultra-luminous X-ray sources. The accretion flow in these cases is interrupted at the magnetospheric radius and then reaches the surface of a neutron star following magnetic field lines. Accreting matter moving along magnetic field lines forms the accretion envelope around the central object. We show that, in case of high mass accretion rates $\gtrsim 10^{19}\,{\rm g\,s^{-1}}$ the envelope becomes closed and optically thick, which influences the dynamics of the accretion flow and the observational manifestation of the neutron star hidden behind the envelope. Particularly, the optically thick accretion envelope results in a multi-color black-body spectrum originating from the magnetospheric surface. The spectrum and photon energy flux vary with the viewing angle, which gives rise to pulsations characterized by high pulsed fraction and typically smooth pulse profiles. The reprocessing of radiation due to interaction with the envelope leads to the disappearance of cyclotron scattering features from the spectrum. We speculate that the super-orbital variability of ultra-luminous X-ray sources powered by accreting neutron stars can be attributed to precession of the neutron star due to interaction of magnetic dipole with the accretion disc.

Super-orbital variability of LS I +61°303 at TeV energies

The gamma-ray binary LS I +61$^{\circ}$303 is a well established source from centimeter radio up to very high energy (VHE; E$>$100 GeV). Its broadband emission shows a periodicity of $\sim$26.5 days, coincident with the orbital period. A longer (super-orbital) period of 1667 $\pm$ 8 days was discovered in radio and confirmed in optical and high energy (HE; E>100 MeV) gamma-ray observations. We present a four-year campaign performed by MAGIC together with archival data concentrating on a search for a long timescale signature in the VHE emission. We focus on the search for super-orbital modulation of the VHE peak and on the search for correlations between TeV emission and optical determination of the extension of the circumstellar disk. A four-year campaign has been carried out by MAGIC. The source was observed during the orbital phases when the periodic VHE outbursts have occurred ($\phi$=0.55-0.75). Additionally, we included archival MAGIC observations and data published by the VERITAS collaboration in these studies. For the correlation studies, LS I +61$^{\circ}$303 has also been observed during the orbital phases where sporadic VHE emission had been detected in the past ($\phi$=0.75-1.0). These MAGIC observations were simultaneous with optical spectroscopy from the LIVERPOOL telescope. The TeV flux of the periodical outburst in orbital phases $\phi$=0.5--0.75 was found to show yearly variability consistent with the $\sim$4.5 years long-term modulation found in the radio band. This modulation of the TeV flux can be well described by a sine function with the best fit period of $1610\pm 58$ days. The complete dataset span two super-orbital periods. There is no evidence for a correlation between the TeV emission and the mass-loss rate of the Be star but this may be affected by the strong, short timescale (as short as intra-day) variation displayed by the H$\alpha$ fluxes.

Orbital and superorbital variability of LS I +61 303 at low radio frequencies with GMRT and LOFAR

LS I +61 303 is a gamma-ray binary that exhibits an outburst at GHz frequencies each orbital cycle of $\approx$ 26.5 d and a superorbital modulation with a period of $\approx$ 4.6 yr. We have performed a detailed study of the low-frequency radio emission of LS I +61 303 by analysing all the archival GMRT data at 150, 235 and 610 MHz, and conducting regular LOFAR observations within the Radio Sky Monitor (RSM) at 150 MHz. We have detected the source for the first time at 150 MHz, which is also the first detection of a gamma-ray binary at such a low frequency. We have obtained the light-curves of the source at 150, 235 and 610 MHz, all of them showing orbital modulation. The light-curves at 235 and 610 MHz also show the existence of superorbital variability. A comparison with contemporaneous 15-GHz data shows remarkable differences with these light-curves. At 15 GHz we see clear outbursts, whereas at low frequencies we see variability with wide maxima. The light-curve at 235 MHz seems to be anticorrelated with the one at 610 MHz, implying a shift of $\sim$ 0.5 orbital phases in the maxima. We model the shifts between the maxima at different frequencies as due to changes in the physical parameters of the emitting region assuming either free-free absorption or synchrotron self-absorption, obtaining expansion velocities for this region close to the stellar wind velocity with both mechanisms.

Superorbital variability of the X-ray flux in the Be-donor binaries SXP 138, GX-304, and γ Cas

RXTE observations of the X-ray binary systems SXP 138, GX-304, and γ Cas in 1997–2011 have shown for the first time that these objects (X-ray binaries with Be donors) display X-ray flux variations on timescales of ∼1000 days. This timescale is about 10 times longer than their orbital periods, and is comparable to the total time of the observations. The observed variations are apparently not strictly periodic and represent stochastic variability, as is characteristic of such systems in the optical. γ Cas is considered as an example. The series of optical observations of this system available in the AAVSO database covers 78 years, and is much longer than the timescale of the variability studied. Our analysis of this series has shown that γ Cas variability on a timescale of tens of years is predominantly stochastic with a power-law spectrum.

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.

Unveiling the super-orbital modulation of LS I + 61°303 in X-rays

AbstractWe found evidence for the super–orbital modulation in the X-ray emission of LS I + 61°303 from the longest monitoring date by the RXTE. The time evolution of the modulated fraction in the orbital light curves can be well fitted with a sinusoidal function having a super-orbital period of 1667 days. However, we have found a 281.8±44.6 day shift between the super-orbital variability found at radio frequencies and our X-ray data. We also find a super-orbital modulation in the maximum count rate of the orbital light curves, compatible with the former results, including the shift.

UNVEILING THE SUPER-ORBITAL MODULATION OF LS I +61°303 IN X-RAYS

From the longest monitoring of LS I +61 303 done to date by the Rossi X-ray Timing Explorer (RXTE) we found evidence for the long-sought, years- long modulation in the X-ray emission of the source. The time evolution of the modulated fraction in the orbital lightcurves can be well fitted with a sinusoidal function having a super-orbital period of 1667 days, the same as the one reported in non-contemporaneous radio measurements. However, we have found a 281.8 \pm 44.6 days shift between the super-orbital variability found at radio frequencies extrapolated to the observation time of our campaign and what we found in the super-orbital modulation of the modulated fraction of our X-ray data. We also find a super-orbital modulation in the maximum count rate of the orbital lightcurves, compatible with the former results, including the shift.

The doubling of the superorbital period of Cyg X-1

We study properties of the superorbital modulation of the X-ray emission of Cyg X-1. We find that it has had a stable period of about 300 d in soft and hard X-rays and in radio since 2005 until at least 2010, which is about double the previously seen period. This new period, seen in the hard spectral state only, is detected not only in the light curves but also in soft X-ray hardness ratios and in the amplitude of the orbital modulation. On the other hand, the spectral slope in hard X-rays, >20 keV, averaged over superorbital bins is constant, and the soft and hard X-rays and the radio emission change in phase. This shows that the superorbital variability consists of changing the normalization of an intrinsic spectrum of a constant shape and of changes of the absorbing column density with the phase. The maximum column density is achieved at the superorbital minimum. The amplitude changes are likely to be caused by a changing viewing angle of an anisotropic emitter, most likely a precessing accretion disc. The constant shape of the intrinsic spectrum shows that this modulation is not caused by a changing accretion rate. The modulated absorbing column density shows the presence of a bulge around the disc centre, as proposed previously. We also find the change of the superorbital period from about 150 d to about 300 d to be associated with almost unchanged average X-ray fluxes, making the period change difficult to explain in the framework of disc-irradiation models. Finally, we find no correlation of the X-ray and radio properties with the reported detections in the GeV and TeV gamma-ray range.

Superorbital variability in hard X-rays

We present the results of a study with the \emph{Swift} Burst Alert Telescope in the 14 -- 195 keV range of the long-term variability of 5 low mass X-ray binaries with reported or suspected super-orbital periods -- 4U 1636-536, 4U 1820-303, 4U 1916-053, Cyg X-2 and Sco X-1. No significant persistent periodic modulation was detected around the previously reported periods in the 4U 1916-053, Cyg X-2 or Sco X-1 light curves. The $\sim$170 d period of 4U 1820-303 was detected up to 24 keV, consistent with variable accretion due to the previously proposed triple system model. The $\sim$46 d period in 4U 1636-536 was detected up to 100 keV, with the modulation in the low and high energy bands found to be phase shifted by $\sim180^\circ$ with respect to each other. This phase shift, when taken together with the near-coincident onset of the $\sim$46 d modulation and the low/hard X-ray state, leads us to speculate that the modulation could herald transient jet formation.

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.

Superorbital variability of X-ray and radio emission of Cyg X-1 – I. Emission anisotropy of precessing sources

We study theoretical interpretations of the ∼150-d (superorbital) modulation observed in X-ray and radio emission of Cyg X-1 in the framework of models connecting this phenomenon to precession. Precession changes the orientation of the emission source (either disc or jet) relative to the observer. This leads to emission modulation due to an anisotropic emission pattern of the source or orientation-dependent amount of absorbing medium along the line of sight or both. We consider, in particular, anisotropy patterns of blackbody-type emission, thermal Comptonization in slab geometry, jet/outflow beaming and absorption in a coronaltype medium above the disc. We then fit these models to the data from the Rossi X-ray Timing Explorer All-Sky Monitor, CGRO BATSE and the Ryle and Green Bank radio telescopes, and find relatively small best-fitting angles between the precession and the orbital planes, ∼10 ◦ − 20 ◦ . The thermal Comptonization model for the X-ray emission explains well the observed decrease in the variability amplitude from 1 to 300 keV as a result of a reduced anisotropy of the emission due to multiple scatterings. Our modelling also yields the jet bulk velocity of ∼(0.3‐0.5)c, which is in agreement with the previous constraint from the lack of an observed counterjet and the lack of short-term X-ray/radio correlations.