The violent past of Cygnus X-2

Cygnus X-2 appears to be the descendant of an intermediate-mass X-ray binary (IMXB). Using Mazzitelli's stellar code we compute detailed evolutionary sequences for the system and find that its prehistory is sensitive to stellar input parameters, in particular the amount of core overshooting during the main-sequence phase. With standard assumptions for convective overshooting a case B mass transfer starting with a 3.5-M_⊙ donor star is the most likely evolutionary solution for Cygnus X-2. This makes the currently observed state rather short-lived, of order 3 Myr, and requires a formation rate > 10⁻⁷–10⁻⁶ yr⁻¹ of such systems in the Galaxy. Our calculations show that neutron star IMXBs with initially more massive donors (≳4 M_⊙) encounter a delayed dynamical instability; they are unlikely to survive this rapid mass transfer phase. We determine limits for the age and initial parameters of Cygnus X-2 and calculate possible dynamical orbits of the system in a realistic Galactic potential, given its observed radial velocity. We find trajectories which are consistent with a progenitor binary on a circular orbit in the Galactic plane inside the solar circle that received a kick velocity ≤200 km s⁻¹ at the birth of the neutron star. The simulations suggest that about 7 per cent of IMXBs receiving an arbitrary kick velocity from a standard kick velocity spectrum would end up in an orbit similar to Cygnus X-2, while about 10 per cent of them reach yet larger Galactocentric distances.     

X-ray timing behaviour of Cygnus X-2 at low intensities

It is known that the overall (mean) intensity of the low-mass X-ray binary Cyg X-2 varies on time-scales from a day to months, independently of the variations on time-scales of hours to a day by which the source moves between the horizontal, normal and flaring branches.
We present RXTE PCA observations of Cyg X-2, taken when its overall intensity was near its lowest values, in 1996 October and 1997 September. For the first time we perform a study of the fast timing behaviour at such low intensities. During the 1996 October observations, the source was in the left part of the horizontal branch, and during the 1997 September observations was most likely in the lower parts of the normal branch and flaring branch.
We find that the properties of the very low-frequency noise during the 1997 September observations are consistent with a monotonic decrease in its strength and power-law index as a function of overall intensity. In contrast, the strength of the ∼6 Hz normal branch quasi-periodic oscillations does not vary monotonically with overall intensity. They are strongest at medium overall intensity and weaker both when the overall intensity is low and when the overall intensity is high.     

Normal-branch quasi-periodic oscillations during the high-intensity state of Cygnus X-2

Using data obtained with the Rossi X-ray Timing Explorer , we report the detection of a 5-Hz quasi-periodic oscillation (QPO) in the bright low-mass X-ray binary and Z source Cygnus X-2 during high overall intensities (the high-intensity state). This QPO was detected on the so-called normal-branch and can be identified with the normal-branch QPO or NBO. Our detection of the NBO is the first one during times when Cygnus X-2 was in the high-intensity state. The rms amplitude of this QPO decreased from 2.8 per cent between 2 and 3.1 keV to <1.9 per cent between 5.0 and 6.5 keV. Above 6.5 keV, its amplitude rapidly increased to ∼12 per cent rms above 16 keV. The time lags of the QPO were consistent with being zero below 5 keV (compared with the 2–3.1 keV band), but they rapidly increased to ∼70 ms (140°) around 10 keV, above which the time lags remained approximately constant near 70 ms. The photon energy dependences of the rms amplitude and the time lags are very similar to those observed for the NBO with other satellites ( Ginga , EXOSAT ) at different (i.e. lower) intensity states.     

The X-ray spectrum of Cyg X-2

The spectra of disc accreting neutron stars generally show complex curvature, and individual components from the disc, boundary layer and neutron star surface cannot be uniquely identified. Here we show that much of the confusion over the spectral form derives from inadequate approximations for Comptonization and for the iron line. There is an intrinsic low-energy cut-off in Comptonized spectra at the seed photon energy. It is very important to model this correctly in neutron star systems as these have expected seed photon temperatures (from either the neutron star surface, inner disc or self-absorbed cyclotron) of ≈1 keV, clearly within the observed X-ray energy band. There is also reflected continuum emission which must accompany the observed iron line, which distorts the higher energy spectrum. We illustrate these points by a reanalysis of the Ginga spectra of Cyg X-2 at all points along its Z track, and show that the spectrum can be well fitted by models in which the low-energy spectrum is dominated by the disc, while the higher energy spectrum is dominated by Comptonized emission from the boundary layer, together with its reflected spectrum from a relativistically smeared, ionized disc.     

Optical spectroscopy and Doppler tomography of Cygnus X-2

We present phase resolved optical spectroscopy and Doppler tomography of V1341 Cygni, the optical counterpart to the neutron star low-mass X-ray binary (LMXB) Cygnus X-2 (Cyg X-2). We derive a radial velocity (RV) curve for the secondary star, finding a projected RV semi-amplitude of   K ₂= 79 ± 3 km s⁻¹  , leading to a mass function of  0.51 ± 0.06 M_⊙, ∼30  per cent lower than the previous estimate. We tentatively attribute the lower value of K ₂ (compared to that obtained by other authors) to variations in the X-ray irradiation of the secondary star at different epochs of observations. The limited phase coverage and/or longer timebase of previous observations may also contribute to the difference in K ₂. Our value for the mass function implies a primary mass of  1.5 ± 0.3 M_⊙  , somewhat lower than previous dynamical estimates, but consistent with the value found by analysis of type-I X-ray bursts from this system. Our Doppler tomography of the broad He  ii λ4686 line reveals that most of the emission from this line is produced on the irradiated face of the donor star, with little emission from the accretion disc. In contrast, the Doppler tomogram of the N  iii λ4640.64 Bowen blend line shows bright emission from near the gas stream/accretion disc impact region, with fainter emission from the gas stream and secondary star. This is the first LMXB for which the Bowen blend is dominated by emission from the gas stream/accretion disc impact region, without comparable emission from the secondary star. This has implications for the interpretation of Bowen blend Doppler tomograms of other LMXBs for which the ephemeris may not be accurately known.     

X-ray spectral evolution of low-mass X-ray binary GX 349+2

We present the results of a systematic investigation of spectral evolution in the Z source GX 349+2, using data obtained during 1998 with the Proportional Counter Array (PCA) on-board the RXTE satellite. The source traced a extended normal branch (NB) and flaring branch (FB) in the colour–colour diagram (CD) and the hardness-intensity diagram (HID) during these observations. The spectra at different positions of the Z-track were best fitted by a model consisting of a disc blackbody and a Comptonized spectrum. A broad (Gaussian) iron line at ∼6.7 keV is also required to improve the fit. The spectral parameters showed a systematic and significant variation with the position along the Z-track. The evolution in spectral parameters is discussed in view of the increasing mass accretion rate scenario, proposed to explain the motion of Z sources in the CD and the HID.     

An XMM–Newton observation of the neutron star X-ray transient 2S 1803−245 in quiescence

We observed the neutron star X-ray transient 2S 1803−245 in quiescence with the X-ray satellite XMM–Newton , but did not detect it. An analysis of the X-ray bursts observed during the 1998 outburst of 2S 1803−245 gives an upper limit to the distance of ≤7.3 kpc, leading to an upper limit on the quiescent 0.5–10 keV X-ray luminosity of  ≤2.8 × 10³² erg s⁻¹  (3σ). Since the expected orbital period of 2S 1803−245 is several hours, this limit is not much higher than those observed for the quiescent black hole transients with similar orbital periods.     

A signature of the donor star in the extra-galactic X-ray binary LMC X−2

Two nights of phase-resolved medium-resolution Very Large Telescope spectroscopy of the extra-galactic low-mass X-ray binary LMC X−2 have revealed a 0.32 ± 0.02 d spectroscopic period in the radial velocity curve of the He  ii λ4686 emission line that we interpret as the orbital period. However, similar to previous findings, this radial velocity curve shows a longer term variation that is most likely due to the presence of a precessing accretion disc in LMC X−2. This is strengthened by He  ii λ4686 Doppler maps that show a bright spot that is moving from night to night. Furthermore, we detect narrow emission lines in the Bowen region of LMC X−2, with a velocity of   K _em= 351 ± 28 km s⁻¹  , that we tentatively interpret as coming from the irradiated side of the donor star. Since K _em must be smaller than K ₂, this leads to the first upper limit on the mass function of LMC X−2 of   f ( M ₁) ≥ 0.86  M_⊙  (95 per cent confidence), and the first constraints on its system parameters.     

Warped accretion discs and the long periods in X-ray binaries

Precessing accretion discs have long been suggested as explanations for the long periods observed in a variety of X-ray binaries, most notably Her X-1/HZ Her. We show that an instability of the response of the disc to the radiation reaction force from the illumination by the central source can cause the disc to tilt out of the orbital plane and precess in something like the required manner. The rate of precession and disc tilt obtained for realistic values of system parameters compare favourably with the known body of data on X-ray binaries with long periods. We explore other possible types of behaviour than steadily precessing discs that might be observable in systems with somewhat different parameters. At high luminosities, the inner disc tilts through more than 90°, i.e., it rotates counter to the usual direction, which may explain the torque reversals in systems such as 4U 1626−67.     

The radial velocity of the companion star in the low-mass X-ray binary 2S 0921–630: limits on the mass of the compact object

In this paper we report on optical spectroscopic observations of the low-mass X-ray binary 2S 0921–630 obtained with the Very Large Telescope. We found sinusoidal radial velocity variations of the companion star with a semi-amplitude of  99.1 ± 3.1 km s⁻¹  modulated on a period of 9.006 ± 0.007 d, consistent with the orbital period found previously for this source, and a systemic velocity of  44.4 ± 2.4 km s⁻¹  . Owing to X-ray irradiation, the centre of light measured by the absorption lines from the companion star is probably shifted with respect to the centre of mass. We try to correct for this using the so-called K -correction. Conservatively applying the maximum correction possible and using the previously measured rotational velocity of the companion star, we find a lower limit to the mass of the compact object in 2S 0921–630 of   M_X sin³ i > 1.90 ± 0.25 M_⊙  (1σ errors). The inclination in this system is well constrained since partial eclipses have been observed in X-ray and optical bands. For inclinations in the range  60° < i < 90°  we find  1.90 ± 0.25 < M_X < 2.9 ± 0.4 M_⊙  . However, using this maximum K -correction we find that the ratio between the mass of the companion star and that of the compact object, q , is 1.32 ± 0.37, implying super-Eddington mass-transfer rates; however, evidence for that has not been found in 2S 0921–630. We conclude that the compact object in 2S 0921–630 is either a (massive) neutron star or a low-mass black hole.     

The photometric evolution of FU Orionis objects: disc instability and wind–envelope interaction

We present the results of a photometric monitoring campaign of three well-studied FU Orionis systems (FU Orionis, V1057 Cygni and V1515 Cygni) undertaken at Maidanak Observatory between 1981 and 2003. When combined with photometric data in the literature, this data base provides a valuable resource for searching for short time-scale variability – both periodic and aperiodic – as well as for studying the secular evolution of these systems. In the case of V1057 Cyg (which is the system exhibiting the largest changes in brightness since it went into outburst) we compare the photometric data with time-dependent models. We show that prior to the end of the 'plateau' stage in 1996, the evolution of V1057 Cyg in the V –( B − V ) colour–magnitude diagram is well represented by disc instability models in which the outburst is triggered by some agent – such as an orbiting planet – in the inner disc. Following the end of the plateau phase in 1996, the dimming and irregular variations are consistent with occultation of the source by a variable dust screen, which has previously been interpreted in terms of dust condensation events in the observed disc wind. Here we instead suggest that this effect results from the interaction between the wind and an infalling dusty envelope, the existence of this envelope having been previously invoked in order to explain the mid-infrared emission of FU Orionis systems. We discuss how this model may explain some of the photometric and spectroscopic characteristics of FU Orionis systems in general.     

The harmonic and sideband structure of the kilohertz quasi-periodic oscillations in Sco X-1

We use data from the Rossi X-ray Timing Explorer to search for harmonics and sidebands of the two simultaneous kilohertz quasi-periodic oscillations (kHz QPOs) in Sco X-1. We do not detect any of these harmonics or sidebands, with 95 per cent confidence upper limits to their power between ∼1 and ∼10 per cent of the power of the upper kHz QPO. The oscillations produced at these frequencies may be attenuated in a scattering corona around the neutron star. We find that upper limits to the unattenuated power of some of the strongest theoretically predicted harmonics and sidebands are as low as ∼2 per cent of the unattenuated power of the high-frequency QPO in Sco X-1.     

MS 1603.6+2600: an accretion disc corona source?

We have observed the eclipsing low-mass X-ray binary MS 1603.6+2600 with Chandra for 7 ks. The X-ray spectrum is well fit with a single absorbed power law with an index of ∼2. We find a clear sinusoidal modulation in the X-ray light curve with a period of  1.7 ± 0.2 h  , consistent with the period of 1.85 h found before. However, no (partial) eclipses were found. We argue that if the X-ray flare observed in earlier X-ray observations was a type I X-ray burst, then the source can only be an accretion disc corona source at a distance of ∼11–24 kpc (implying a height above the Galactic disc of ∼8–17 kpc). It has also been proposed in the literature that MS 1603.76+2600 is a dipper at ∼75 kpc. We argue that, in this dipper scenario, the observed optical properties of MS 1603.6+2600 are difficult to reconcile with the optical properties one would expect on the basis of comparisons with other high-inclination, low-mass X-ray binaries, unless the X-ray flare was not a type I X-ray burst. In that case, the source can be a nearby soft X-ray transient accreting at a quiescent rate, as was proposed by Hakala et al., or a high-inclination source at ∼15–20 kpc.     

Dwarf nova oscillations and quasi-periodic oscillations in cataclysmic variables – II. A low-inertia magnetic accretor model

The dwarf nova oscillations observed in cataclysmic variable (CV) stars are interpreted in the context of a low-inertia accretor model, in which accretion on to an equatorial belt of the white dwarf primary causes the belt to vary its angular velocity. The rapid deceleration phase is attributed to propellering. Evidence that temporary expulsion rather than accretion of gas occurs during this phase is obtained from the large drop in extreme ultraviolet flux.
We show that the quasi-periodic oscillations are most probably caused by a vertical thickening of the disc, moving as a travelling wave near the inner edge of the disc. This alternately obscures and 'reflects' radiation from the central source, and is visible even in quite low inclination systems. A possible excitation mechanism, caused by winding up and reconnection of magnetic field lines, is proposed.
We apply the model, deduced largely from VW Hyi observations, to re-interpret observations of SS Cyg, OY Car, UX UMa, V2051 Oph, V436 Cen and WZ Sge. In the last of these we demonstrate the existence of a 742-s period in the light curve, arising from obscuration by the travelling wave, and hence show that the two principal oscillations are a dwarf nova oscillation and its reprocessed companion.     

The 1997 hard-state outburst of the X-ray transient GS 1354−64/BW Cir

We present observations of the 1997 outburst of the X-ray transient GS 1354−64 (BW Cir) at X-ray, optical and, for the first time, radio wavelengths; our results include upper limits to the linear and circular polarization for the radio data. The X-ray outburst was unusual in that the source remained in the low/hard X-ray state throughout; the X-ray peak was also preceded by at least one optical outburst, suggesting that it was an 'outside-in' outburst – similar to those observed in dwarf novae systems, although possibly taking place on a viscous time-scale in this case. It therefore indicates that the optical emission was not dominated by the reprocessing of X-rays, but that instead we see the instability directly. While the radio source was too faint to detect any extended structure, spectral analysis of the radio data and a comparison with other similar systems suggest that mass ejections, probably in the form of a jet, took place and that the emitted synchrotron spectrum may have extended as far as infrared wavelengths. Finally, we compare this 1997 outburst of GS 1354−64 with possible previous outbursts and also with other hard-state objects, both transient and persistent. It appears that a set of characteristics – such as a weak, flat-spectrum radio jet, a mHz QPO increasing in frequency, a surprisingly high optical/X-ray luminosity ratio, and the observed optical peak preceding the X-ray peak – may be common to all hard-state X-ray transients.