Superorbital Period Research Articles

The Photometric Study of EX Dra: A Dwarf Nova Exhibiting a Titled and Precessional Disk

We present a photometric study of EX Dra, a dwarf nova that has been extensively observed by the Transiting Exoplanet Survey Satellite. The data reveal the occurrence of 20 complete outbursts, exhibiting several intriguing and rare characteristics. The light curves exhibit a distinct superorbital signal with a period of approximately P sor ∼ 4.39(7) days, along with a negative superhump showing an approximate period of P nsh ∼ 4.805(1) hr, indicating that the accretion disk is tilted and undergoing precession with the period of P sor. In addition, the time-varying nature of P sor suggests that the precession period is fluctuating.The eclipsing light minima O – C analysis during quiescence shows an oscillation with period of 3.9(5) days, which is a little shorter than the superorbital period. We contend that this is unlikely to be a sudden alteration of the orbital period, but rather, it is influenced by the tilt and precession of the accretion disk. Notably, we found an amplitude shift in the outburst behavior from 3.5 mag with a periodicity of about 26 days to an amplitude of around 2.5 mag with a periodicity of about 12 days, which persisted for 14 yr before reverting. Furthermore, we have extracted quasiperiodic oscillations in the plateau at the noneclipsed phases, characterized by periods ranging between 37 and 40 minutes.

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.

A New Puzzling Periodic Signal in GeV Energies of the γ-Ray Binary LS I+61°303

LS I+61°303 is a high-mass X-ray binary system comprising a massive Be star and a rapidly rotating neutron star. Its spectral energy distribution across multiwavelengths categorizes it as a γ-ray binary system. In our analysis of LS I+61°303 using Fermi Large Area Telescope observations, we not only confirmed the three previously discussed periodicities of orbital, superorbital, and orbital–superorbital beat periods observed in multiwavelength observations, but also identified an additional periodic signal. This newly discovered signal exhibits a period of ∼26.3 days at a ∼7σ confidence level. Moreover, the power spectrum peak of the new signal gradually decreases as the energy increases across the energy ranges of 0.1–0.3, 0.3–1.0, and 1.0–500.0 GeV. Interestingly, a potential signal with a similar period was found in data obtained from the Owens Valley Radio Observatory 40 m telescope. We suggest that the newly discovered periodic signal may originate from a coupling between the orbital period and the retrograde stellar precession period.

Owens Valley Radio Observatory monitoring of LS I +61°303 completes three cycles of the super-orbital modulation

Context. The high-mass X-ray binary LS I +61°303 is composed of a Be-type star and a compact object in an eccentric orbit. The emission from this source is variable and periodic across the electromagnetic spectrum, from radio to very high-energy γ rays. The orbital period has been determined as P1 ≈ 26.5 d, and the source also features a super-orbital period with a value of Plong ≈ 4.6 years. Long-term monitoring of the binary by the Owens Valley Radio Observatory (OVRO) at 15 GHz has now completed 13.8 years, which corresponds to three full cycles of the super-orbital period. This is exactly one long-term cycle more than in the previous publication about OVRO observations of this source. Aims. Our aim is to investigate the presence and the stability of periodic signals in the radio data and to test if they are in agreement with previous results. This will contribute to the understanding of the physical processes behind the non-thermal emission from this source. Methods. We performed a timing analysis of the OVRO radio light curve and made use of the generalized Lomb-Scargle periodogram. We also combined the OVRO data with the full archive of previous radio observations and computed the discrete autocorrelation function. Results. The most powerful features in the periodogram of the OVRO data are two peaks at P1 = 26.49 ± 0.05 d and P2 = 26.93 ± 0.05 d, which are well separated from each other and clearly stand out above the very low noise level. The previously detected long-term period is still present in these new radio data, and our measurement is Plong = 1698 ± 196 d. Dividing the OVRO data into three segments of equal length showed that the two periods, P1 and P2, are present in the periodogram of each of the consecutive long-term cycles. Our analysis of the full radio archive resulted in the detection of the same three periods, and the autocorrelation function showed a regular pattern, proving the continuity of the decades-spanning stability of the super-orbital modulation. In addition, we report a possible systematic modulation of the radio flux density with a timescale of approximately 40 years that has so far remained unnoticed. Conclusions. The physical model of a relativistic jet whose mass loading is modulated with the orbital period P1 and is precessing with the slightly larger period P2, giving rise to a beating with period Plong, had previously been able to reproduce the radio and gigaelectron volt emission from this source. The ongoing presence and the stability of the periodic signals imply that this model is still the most plausible explanation for the physical processes at work in this source.

Periodically modulated FRB as extreme mass ratio binaries

ABSTRACT The activity of at least one repeating fast radio burst (FRB) source is periodically modulated. If this modulation is the result of precession of the rotation axis and throat of an accretion disc around a black hole, driven by a companion that is also the source of accreted mass, then it may be possible to constrain the mass of the black hole. The dynamics is analogous to that of superorbital periods in ordinary mass-transfer binaries in which the accreting object may be a stellar-mass black hole, a neutron star or a white dwarf, but in the FRB source it may be an intermediate-mass black hole. In a semidetached (mass-transferring) binary, the orbital period is nearly proportional to the −1/2 power of the mean density of the mass-losing star and nearly independent of the mass of the primary, but the ratio of precessional to orbital periods scales approximately as the −2/3 power of the mass ratio for small mass ratios (massive accretors). Assuming a value for the secondary’s density and identifying the observed modulation period as a disc precession period would determine the mass ratio and the mass of the black hole. This model and magnetar-SNR (supernova remnant) models make distinguishable predictions of the evolution of the rotation measure that may soon be tested in FRB 121102.

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.

Disc precession in Be/X-ray binaries drives superorbital variations of outbursts and colour

ABSTRACT Superorbital periods that are observed in the brightness of Be/X-ray binaries may be driven by a misaligned and precessing Be star disc. We examine how the precessing disc model explains the superorbital variation of (i) the magnitude of the observed X-ray outbursts and (ii) the observed colour. With hydrodynamical simulations, we show that the magnitude of the average accretion rate on to the neutron star, and therefore the X-ray outbursts, can vary by over an order of magnitude over the superorbital period for Be star spin–orbit misalignments ≳70° as a result of weak tidal truncation. Most Be/X-ray binaries are redder at optical maximum when the disc is viewed closest to face-on since the disc adds a large red component to the emission. However, A0538-66 is redder at optical minimum. This opposite behaviour requires an edge-on disc at optical minimum and a radially narrow disc such that it does not add a large red signature when viewed face-on. For A0538-66, the misalignment of the disc to the binary orbit must be about 70–80° and the inclination of the binary orbit to the line of sight must be similarly high, although restricted to <75° by the absence of X-ray eclipses.

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.

LAMOST J2043+3413—a Fast Disk Precession SW Sextans Candidate in Period Gap

We present follow-up photometric observations and time-series analysis of a nova-like, SW Sextans-type, cataclysmic variable (CV) candidate, LAMOST J204305.95+341340.6 (hereafter J2043+3413), with a Gaia G-band magnitude of 15.30 and a distance of 990 pc, which was identified from the LAMOST spectrum. The photometric data were collected with the Tsinghua-NAOC 0.8 m telescope (TNT), Transiting Exoplanet Survey Satellite (TESS), Zwicky Transient Facility (ZTF), and ASAS-SN. The TESS light curve reveals the presence of two prominent periods of 2.587(8) hr and 1.09(5) days, corresponding to the orbital and superorbital (precession) period, respectively. The TNT data obtained in 2020 shows a possible quasiperiodic oscillation of 1426 s. The precession period is about three times shorter than that of CVs with similar orbital periods, indicating an unusually fast precessing accretion disk. The ZTF data is found to show a sudden decline of ∼0.4 mag on MJD 58979. From the intermittent behavior of the eclipse, we deduce that J2043+3413 is an intermediate inclination system of CV, similar to V795 Her, which is also situated in the period gap.

Flux-resolved Spectropolarimetric Evolution of the X-Ray Pulsar Hercules X-1 Using IXPE

We conduct a spectropolarimetric study of the accreting X-ray pulsar Hercules X-1 using observations with the Imaging X-ray Polarimetry Explorer (IXPE). IXPE monitored the source in three different epochs, sampling two “Main-on” and one “Short-on” state of the well-known super-orbital period of the source. We find that the 2–7 keV polarization fraction increases significantly from ∼7% to 9% in the Main-on state to ∼15%–19% in the Short-on state, while the polarization angle remains more or less constant or changes slightly, ∼47°–59°, in all three epochs. The polarization degree and polarization angle are consistent with being energy independent for all three epochs. We propose that in the Short-on state, when the neutron star is partially blocked by the disk warp, the increase in the polarization fraction can be explained as a result of the preferential obstruction of one of the magnetic poles of the neutron star.

Superorbital periods of Be/X-ray binaries driven by stellar spin precession

ABSTRACT Superorbital periods are observed in the optical light curves of many Be/X-ray binaries yet their origin has remained somewhat elusive. We suggest that precession of the spin axis of the Be star can drive superorbital periods, particularly for short orbital period binaries. We consider the short orbital period ($P_{\rm orb}=16.6\, \rm d$) and highly eccentric (eb = 0.72) Be/X-ray binary A0538−66 that has a superorbital period of $421\, \rm d$. First, we show that the spin axis precession time-scale is about twice the observed superorbital period. Then, with hydrodynamic simulations we show that the Be star decretion disc can remain locked to the equator of the precessing Be star. At each periastron passage of the neutron star, material is accreted into a disc around the neutron star. The neutron star disc nodally precesses on the same time-scale as the Be star disc and therefore both discs can contribute to the observed superorbital period. For wider and less eccentric binary systems, the Be star disc can have a larger radial extent and more complex behaviour is expected as a result of disc warping and breaking.

Monitoring observations of SMC X-1’s excursions (MOOSE) – II. A new excursion accompanies spin-up acceleration

ABSTRACTSMC X-1 is a high-mass X-ray binary showing superorbital modulation with an unstable period. Previous monitoring shows three excursion events in 1996–1998, 2005–2007, and 2014–2016. The superorbital period drifts from ≳60 to ≲40 d and then evolves back during an excursion. Here, we report a new excursion event of SMC X-1 in 2020–2021, indicating that the superorbital modulation has an unpredictable, chaotic nature. We trace the spin-period evolution and find that the spin-up rate accelerated 1 yr before the onset of this new excursion, which suggests a possible inside-out process connecting the spin-up acceleration and the superorbital excursion. This results in a deviation of the spin-period residual, similar to the behaviour of the first excursion in 1996–1998. In further analysis of the pulse profile evolution, we find that the pulsed fraction shows a long-term evolution and may be connected to the superorbital excursion. These discoveries deepen the mystery of SMC X-1 because they cannot be solely interpreted by the warped-disc model. Upcoming pointed observations and theoretical studies may improve our understanding of the detailed accretion mechanisms taking place.

The ultraluminous X-ray source M 81 X-6: a weakly magnetised neutron star with a precessing accretion disc?

Context. Thanks to their proximity, ultraluminous X-ray sources (ULXs) represent a privileged astrophysical laboratory to study super-Eddington accretion. Current open questions concern the nature of the compact object, which is still hard to determine in those cases where pulsations are not directly detected, and the mechanisms responsible for the spectral changes observed in many ULXs. Aims. We investigate the nature of the ULX M 81 X-6, which has been suggested to harbour a neutron star (NS), by studying its long-term X-ray spectral and temporal evolution, with the goal of assessing the astrophysical phenomena responsible for its spectral changes. Methods. Using the rich set of available archival data from XMM-Newton, Chandra, NuSTAR, and Swift/XRT, we tracked the evolution of the source on the hardness-intensity diagram and inferred the different emitting regions of the system and their geometry, as well as the mechanisms responsible for the spectral transitions. Results. We find that the source oscillates between two main states: one characterised by a hard and luminous spectrum and the other at low hardness and luminosity. The properties of the soft component remain constant between the two states, suggesting that changes in the mass-transfer rate are not driving the spectral transitions. Instead, the bi-modal behaviour of the source and the known super-orbital period would point to the precession of the accretion disc. Here, we tested two theoretical models: (1) Lense-Thirring precession, which can explain the super-orbital period if the NS has a magnetic field B ≲ 1010 G, supporting the idea of M 81 X-6 as a weakly magnetised NS, and (2) precession due to the torque of the NS magnetic field, which leads to B ≳ 1011 G. However, the latter scenario, assuming M 81 X-6 shares similar properties with other NS-ULXs, is disfavoured because it would require magnetic field strengths (B > 1015 G) much higher than those known for other pulsating ULXs. We further show that the contribution from the hard component attributed to the putative accretion column sits just below the typical values found in pulsating ULXs, which, together with the low value of the pulsed fraction (≤10%) found for one XMM-Newton/pn observation, could explain the source’s lack of pulsations. Conclusions. The spectral properties and variability of M 81 X-6 can be accounted for if the accretor is a NS with a low magnetic field. Under the hypothesis of Lense-Thirring precession, we predict a spin period of the NS of a few seconds. We encourage future X-ray pointed observations to look for pulsations and/or spectral signatures of the magnetic field.

Detection of 125.5-day optical periodic modulation of the neutron star M51 ULX-8

ABSTRACT Studying Ultraluminous X-ray sources (ULXs) in the optical wavelengths provides important clues about the accretion mechanisms and the evolutionary processes of X-ray binary systems. In this study, three (C1, C2, and C3) possible optical counterparts were identified for well-known neutron star (NS) candidate M51 ULX-8 through advanced astrometry based on the Chandra and Hubble Space Telescope (HST) observations, as well as the GAIA optical source catalogue. Optical periodic modulation of 125.5 d with an amplitude of 0.14 mag was determined for C3, which has evidence to represent the optical nature of ULX-8 using one-year (2016–2017) 34 HST Advanced Camera for Surveys (ACS)/Wide Field Camera (WFC) observations. Moreover, surprisingly, the observed optical fluxes of C3 exhibit a bi-modal distribution. This could mean that there is a possible correlation between the optical and the X-ray flux variabilities of the ULX-8. The possible scenarios which are frequently mentioned in the literature proposed for the nature of optical emission and optical super-orbital period. The most probable scenario is that the optical emission could have originated from the accretion disc of the ULX-8.

CEN X–3 AS SEEN BY MAXI DURING SIX YEARS

The aim of this work is to study both light curve and orbital phase spectroscopy of Cen X-3 taking advantage of the MAXI/GSC observation strategy. These studies allow delimiting the stellar wind properties and its interactions with the compact object. From the analysis of the light curve, we have estimated the orbital period of the binary system and also found possible QPOs around a superorbital period of Psuperorb = 220 ± 5 days. Both orbital phase-averaged and phaseresolved spectra were extracted and analysed in the 2.0–20.0 keV energy range. Two models have described spectra satisfactorily, a partial absorbed Comptonization of cool photons on hot electrons plus a power law, and a partial absorbed blackbody plus a power law, both modified by adding Gaussian lines. The high value of the X-ray luminosity in the averaged spectrum indicates that the accretion mode is not only due to the stellar wind.

Precession and Jitter in FRB 180916B

ABSTRACT Recent CHIME/FRB observations of the periodic repeating fast radio bursts (FRB) 180916B have produced a homogeneous sample of 44 bursts. These permit a redetermination of the modulation period and phase window, in agreement with earlier results. If the periodicity results from the precession of an accretion disc, in analogy with those of Her X-1, SS 433, and many other superorbital periods, the width of the observable phase window indicates that the disc axis jitters by an angle of about 0.14 of the inclination angle, similar to the ratio of 0.14 in the well-observed jittering jet source SS 433.

The Variability Behavior of NGC 925 ULX-3

We report the results of a 2019–2021 monitoring campaign with Swift and associated target-of-opportunity observations with XMM-Newton and NuSTAR, examining the spectral and timing behavior of the highly variable ultraluminous X-ray source (ULX) NGC 925 ULX-3. We find that the source exhibits a 127–128-day periodicity, with fluxes typically ranging from 1 × 10−13 to 8 × 10−13 erg s−1 cm−2. We do not find strong evidence for a change in period over the time that NGC 925 ULX-3 has been observed, although the source may have been in a much lower flux state when first observed with Chandra in 2005. We do not detect pulsations, and we place an upper limit on the pulsed fraction of ∼40% in the XMM-Newton band, consistent with some previous pulsation detections at low energies in other ULXs. The source exhibits a typical ULX spectrum that turns over in the NuSTAR band and can be fitted using two thermal components. These components have a high temperature ratio that may indicate the lack of extreme inner disk truncation by a magnetar-level magnetic field. We examine the implications for a number of different models for superorbital periods in ULXs, finding that a neutron star with a magnetic field of ∼1012 G may be plausible for this source. The future detection of pulsations from this source would allow for the further testing and constraining of such models.

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.

A step towards unveiling the nature of three cataclysmic variables: LS Cam, V902 Mon, and SWIFT J0746.3-1608

ABSTRACT We have carried out detailed time-resolved timing analyses of three cataclysmic variables (CVs) namely LS Cam, V902 Mon, and SWIFT J0746.3-1608, using the long-baseline, high-cadence optical photometric data from the Transiting Exoplanet Survey Satellite. Our analysis of LS Cam observations hints the presence of a superorbital period of ∼4.025 ± 0.007 d along with negative and positive superhump periods of ∼3.30 and 3.70 h, respectively. These results can be explained as an interaction of nodal and apsidal precession of the accretion disc with orbital motion. For the other two sources, V902 Mon and SWIFT J0746.3-1608, we have found evidence of a beat period of 2387.0 ± 0.6 and 2409.5 ± 0.7 s, respectively, which were not found in earlier studies. Our results presented in this study indicate the change in the accretion mode during the entire observing period for both sources. For V902 Mon, an apparent orbital period derivative of (6.09 ± 0.60) × 10−10 was also found. Moreover, the second harmonic of orbital frequency dominates the power spectrum of SWIFT J0746.3-1608, suggestive of ellipsoidal modulation of the secondary star. Present analyses suggest that LS Cam could be a superhumping CV, whereas V902 Mon and SWIFT J0746.3-1608 are likely to be variable disc-overflow accreting intermediate polars.

Disc precession to explain the superorbital modulation of LMC X-4: results from the Swift monitoring campaign

ABSTRACT We studied the spectral changes of the high-mass X-ray binary system LMC X-4 to understand the origin and mechanisms beyond its superorbital modulation (30.4 d). To this aim, we obtained a monitoring campaign with Swift/XRT (0.3–10 keV) and complemented these data with the years-long Swift/BAT survey data (15–60 keV). We found a self-consistent, physically motivated, description of the broad-band X-ray spectrum using a Swift/XRT and a NuSTAR observation at the epoch of maximum flux. We decomposed the spectrum into the sum of a bulk + thermal Comptonization, a disc reflection component, and a soft contribution from a standard Shakura–Sunyaev accretion disc. We applied this model to 20 phase-selected Swift spectra along the superorbital period. We found a phase-dependent flux ratio of the different components, whereas the absorption column does not vary significantly. The disc emission is decoupled with respect to the hard flux. We interpret this as a geometrical effect in which the inner parts of the disc are tilted with respect to the obscuring outer regions.