Luminous X-ray binaries (L ;SPMgt; 10 erg/s) are often classified as Low Mass X-ray Binary (LMXBs) and High Mass X-ray Binary (HMXBs) systems depending on the mass of the donor star. While this classification leaves unspecified the nature of the accreting collapsed object (which indeed can be a NS or a black hole in either class), it allows to distinguish the phenomenology of the X-ray sources and their optical counterpart in a natural way (see Table 1.1).
Periodic X-ray pulsations with periods ranging from 0.069s to 1455s are present in a large number ( 35) of HMXBs. This signal originates from the beamed radiation which is produced close to the magnetic poles of the young accreting neutron star with a surface field of 10 G. Due to the misalignment of the magnetic and rotational axes, the neutron star rotation modulates the X-ray intensity in a light-house fashion. Period or phase changes introduced by the binary motion allow to measure some of the orbital parameters of these systems. Together with the duration of the X-ray eclipse (which is present in several HMXBs) and the Doppler velocity and photometric modulation of the optical star, these measurements provide the absolute orbital solution and the masses of the two components. Secular spin period changes arise because of the torque exerted on the neutron star magnetosphere by the accreting matter (Henrichs 1983 and reference therein; Frank, King & Raine 1992; King 1995). X-ray pulsations from luminous X-ray binaries provide an incontrovertible signature of accretion onto a magnetised neutron star.
Table: Classification of NS in X-ray binaries
All but 8 known X-ray pulsators are associated with HMXBs and their origin is still unclear (see Appendix §A.2 for more details). Much more frequent instead, is the phenomenon of (type I) X-ray bursts (see below). Pulsations are not expected from the old neutron stars in bursting sources if their magnetic field has decayed to 10 G, a value below which accretion is not significantly funneled close to the magnetic poles. On the other hand, LMXBs are likely to be progenitors of the old, ``recycled'' millisecond pulsars which are found in increasing number especially in globular clusters (see van den Heuvel 1991 for a detailed review). In this case the neutron star magnetic field of 10 - 10 G inferred from the radio pulsar observations should also characterise the LMXBs stage, and low amplitude X-ray pulsations in the millisecond range would be expected if accretion occurs preferentially along the magnetic field lines. To date the search for fast pulsations in the persistent emission from LMXBs gave negative results (see Wood et al. 1991 and Vaughan et al. 1994). Recently coherent pulsations at a period of 2.75ms were discovered in five out of seven bursts from the bright X-ray source 4U1728-34 (Strohmayer et al. 1996).
About 45 pulse periods has been discovered so far with periods between 70ms and 1455s (see also Appendix, §A.2). The intrinsic pulse periods measured for a number of X-ray pulsars have been sufficiently well measured over the past decades to provide important information regarding the torques exerted on the NSs by the accreting material. Examining the pulse period histories of these pulsars, it is apparent that three types of behaviour are present: the pulse period shows a linear decrease with time, with erratic variations around the trend, an almost constant value of the pulse period, and a steady increase in pulse period (for a review see Rappaport & Joss 1983; Nagase 1989; White, Nagase & Parmar 1995). The spin-up trend in most of the X-ray pulsars towards secular decrease in the period can be understood in terms of torques exerted by the matter accreting onto the NS which can be calculated for the case where the matter has roughly circular Keplerian velocities at the magnetosphere of the NS. The rate of change, , of the intrinsic pulse period P is related to the X-ray luminosity and the physical properties of the NS itself (Ghosh & Lamb 1979):
where the dimensionless function f is expected to be of order of unity for a NS. The observed spin-up timescale ranges from 100 to 100000 yr. From the pulse timing analysis of the transient source EXO2030+375, Parmar et al. (1989) obtained a clear dependence of on the luminosity as - by directly measuring the over a wide range of luminosity. This observed dependence is consistent with the accretion torque theory for disc fed pulsators developed by Ghosh & Lamb (1979), eq. ().
An equilibrium is reached when the NS magnetosphere corotates with the inner edge of the disc, i.e. when equals . Close to corotation, the fields line in the transition zone (where magnetic field begins to thread the disc) are swept backwards, and a negative torque is exerted on the NS (see also §1.1.1). The NS is then spun down, even accretion still continue.
No overall trend in the pulse period history is expected for those systems (both wind or disc driven) where inhomogeneities in the accretion flow occur.
Type I X-ray bursts have been observed from 40 LMXB sources so far. Bursts are described as sudden rise of X-ray luminosity which typically lasts for tens of seconds, a characteristic cooling in the decay phase and recur on timescales of hours (see Fig. 1.1). These bursts account for only a small fraction of the time-averaged luminosity of LMXBs. They originate from thermonuclear flashes in the freshly accreted matter on the surface of a weak magnetised neutron star. In general, burst profiles depend strongly on photon energy; decays are much shorter at high photon energies than a low energies. This energy dependence corresponds to a softening of the burst spectrum during the decay, which is the result of the cooling of the NS photosphere. Burst intervals can be regular or irregular on time scale of hours to days: they range from 5 min to days; burst activity can stop as well for periods from days to months. In some cases, a relation has been observed between burst profile and the persistent emission. The persistent flux of 4U1820-303 (Clark et al. 1977) increased by a factor 5 while the burst interval gradually decreased by 50%. In a few LMXBs the bursting activity ceases when the persistent emission X-ray luminosity increases above a level of 10 erg/s (van Paradijs & Lewin 1988 and references therein).
The time dependent energy spectra of X-ray bursts are usually well described by a blackbody spectrum. The result of the spectral analysis of type I bursts show that during burst decay, one finds often that the blackbody radius is approximatively constant while, during expansion phase the luminosity remains approximatively constant.
For 10 sources strong burst-like events, lasting up to 1500s, have been observed. It is believed that during these bursts the luminosity becomes so high (close to the Eddington limit) that temporarily the atmosphere of the NS, expands due to the radiation pressure, possibly through the formation of a stellar-wind outflow of material from the NS. After the luminosity decreases below the Eddington limit, the photosphere contracts.
Beside type I bursters there is one ``abnormal'' X-ray sources, namely Rapid Burster, which display bursts on shorter time scale. Rapid Burster, when active, displays both type I bursts and bursts produced in quick succession with recurrence intervals as short as 7s. The latter features are known as type II bursts and are thought to be related with spasmodic episodes of accretion (Lewin, van Paradijs & Taam 1995 and references therein). Moreover, quasi periodic oscillations (QPOs) of 2-5 Hz were discovered in Rapid Burster in several long type II bursts (Tawara et al. 1982; Stella et al. 1988a, 1988b). No QPOs have been observed to date in any type I burst from this source. It is presently unclear whether the QPOs observed have any relation to other forms of QPOs observed in LMXBs.
Type I and II bursts usually do not occur in X-ray pulsar binaries because the strong magnetic field ( 10 G) of young neutron stars confines the infalling plasma to the polar caps, thereby increasing dramatically the accretion rate per unit area (compared to weakly magnetic neutron stars) and giving rise to steady (as opposed to flash-like) thermonuclear burning in the accreting material (Fujimoto, Hanawa & Miyaji 1981; Hanawa & Fujimoto 1984). A transient X-ray source was observed recently for the first time by -ray CGRO satellite (Fishman et al. 1995; Kouveliotou et al. 1996; Finger, Wilson & van Paradijs 1996). GRO J1744-28 was soon noticed to possess properties which differ from those of other known high-energy burst source. In particular, the bursts seen in GRO J1744-28 have some similarities with the type II bursts seen in the Rapid Burster (the thermonuclear flashes model of type I bursts has been ruled out based on energetics arguments; Kouveliotou et al. 1996), and are also likely to involve some unknown accretion instability. Moreover, coherent X-ray pulsations at a period of 467 millisecond with nearly sinusoidal profile were detected. The requirement to have sub-Keplerian velocities at the magnetosphere radius for the infalling matter implies , which is consistent with arguments supporting accretion-induced magnetic field decay in NS (Taam & van den Heuvel 1986; Romani 1990).
An important issue concerning X-ray pulsators is the study of pulse profiles as an indicator of X-ray emission geometry. The pulse profile of X-ray pulsators shows great variety from source to source, ranging from sinusoidal-like profiles, to highly structured and energy-dependent modulations (4U1626-67, Her X-1, 4U0900-40, etc; Rappaport & Joss 1983; White, Kallman & Swank 1983). The shape of the periodic signal contains information on the emission geometry from the regions close to the NS magnetic poles where accretion is concentrated. Detailed modelling of the emission pattern emerging from the accreting polar cap(s) of a NS has shown that beamed emission and complex pulse profiles can be produced primarily because of the effects of the magnetic field and the interaction of the radiation with the infalling matter. The preferred beaming direction depends on whether a stand-off shock and, therefore, a dense deceleration region are present above the polar cap. For high luminosity ( erg/s) a radiative shock is expected to form. In this case photons will escape preferentially from the sides of the high density post-shock accretion column, giving rise to a fan-beam pattern. For lower luminosities ( erg/s) the infalling material might be decelerated in a collisionless shock above the polar cap possibly arising from plasma instabilities, or by Coulomb and nuclear collisions at the NS surface. If the latter occurs, the emission region will be located in a thin layer on the NS surface and radiative transfer effects in the strong magnetic field will favor photons escaping in the direction of the field lines, therefore giving rise to a pencil-beam pattern. If a collisionless shock occurs a fan-beam is likely to form, as in the high-luminosity case (Basko & Sunyaev 1976; Mészáros 1984).
The orbital periods of X-ray binaries have been determined from the observation of one or more of the following features: eclipses, smooth periodic modulation, periodically recurring X-ray absorption features, periodically recurring transient X-ray outbursts, pulsar arrival time variations, radial-velocity variations and pulsar-orbital beat period. The orbital periods range from 0.19hr to 398 hr and from 4.8hr and 187days for LMXBs and HMXBs, respectively.
The supergiant systems typically are eclipsing and show extreme intensity and absorption variability on all timescales. The shorter orbital period systems have circular orbits, whereas the longer period systems are eccentric. In LMXBs eclipses are instead rare (see Table 1.1) even if the system is viewed almost edge-on and the compact X-ray source is hidden by the disc. X-rays are still seen because they are scattered in a photo-ionised corona above the disc. As a consequence the source will appear extended and the eclipse partial. The orbital modulation shapes are almost sinusoidal with, in many cases, a minimum close to the partial eclipse due to the partial occultation of an accretion disc corona (ADC) by a structure near the rim of the disc caused by its interaction with the incoming gas stream (X1822-371, X0748-676, etc.; see White, Nagase & Parmar 1995 for a review and Fig. 1.3). A handful of LMXBs show also irregular dips, a sudden decrease of the source intensity, that usually recur periodically. These dips are due to material which is projected above the disc plane by a splash point, where the gas stream from the companion hits the accretion disc. A total of ten dipping sources are known so far.
To account for all these orbital features, the observed properties of LMXBs should depend on the viewing angle (see White, Nagase & Parmar 1995). At a low inclination (;SPMlt; 70 ), no X-ray dips or eclipses are seen, but an optical modulation from the X-ray heated companion may still reveal the orbital period. At an intermediate inclination, periodic dipping behaviour is seen which is caused by a structure at the edge of the accretion disc; in a few cases, a very brief eclipse by the companion may be seen. In high inclination systems ( 80%), the central X-ray source is hidden behind the disc rim, but X-ray scattered via an ADC are still seen giving rise to a partial eclipse.
During the search of expected fast pulsations in LMXBs, a different phenomenon was discovered in an increasing number of bright LMXBs: namely oscillations with frequencies of 1-1000 Hz and a poor coherence. These quasi periodic oscillations (QPOs) display large frequency variations on timescale as short as tens of seconds and, therefore, cannot represent the rotation of the NS. Their phenomenology is very complex, and different QPO modes have been identified which correspond to a different spectral and activity states (Lewin et al. 1988; Stella 1988). A number of sources show a mode in which the QPO frequency, , increases with the source luminosity. This property played a key role in the development of QPO models: the correlation is suggestive of the presence of a NS magnetosphere which is compressed for increasing accretion rates. In the beat frequency model (BFM), the interaction between the disc and the magnetosphere causes the accretion flow to be modulated at the beat frequency between the disc Keplerian frequency at the magnetosphere boundary, , and the NS spin frequency . In this case the QPO frequency is approximatively given by
where is the magnetic dipole field at the neutron star surface in units of 10 Gauss, the X-ray luminosity in units of 10 erg s . The equation above assumes also that the rest energy of the accreting matter is converted into X-ray with a constant efficiency of 10%. When used to fit the relation observed in bright LMXBs like GX 5-1, Sco X-1 and Cyg X-2 (see Fig. 1.4), this model predicts a NS spin frequency of Hz, and a surface magnetic field of , in agreement with the idea that these systems contain a weakly magnetised NS which has been spun up by accretion (Lamb et al. 1985). Periodic pulsations at the NS spin frequency are expected as well in the BFM, although their amplitude might be drastically reduced by the effects of electron scattering. However in the absence of measurements of the magnetic field strength and the NS spin period, it is difficult to use LMXBs to verify the validity of the BFM.
Quite recently (van der Klis et al. 1996a, 1996b, 1996c; Lewin et al. 1996; van Paradijs et al. 1996; Strohmayer et al. 1996) very fast QPOs (600-1200 Hz) were detected in several LMXBs thanks to the unprecedented time resolution and effective area of the XTE satellite detectors. In the case of the LMXB 4U1608-52 (Berger et al. 1996) narrow QPO peaks at frequencies between 850 and 890 Hz were detected on Mar. 3 and 6, while a broad peak around 690 Hz on Mar. 9. The root mean square amplitude of QPOs increases steadily from 5% at 2 keV to 20% at 12 keV.
When an X-ray colour colour diagram was assembled from observations in the 1.5-30 keV band (Fig. 1.5) it was soon noticed that different X-ray source classes (either persistent and transient) occupied different regions of the diagram (White & Marshall 1984). The horizontal axis is the spectral hardness ratio (7-30/3-7 keV) while the vertical axis represents the softness ratio (1.5-3/3-10 keV). The former indicates the spectral hardness while the latter the intrinsic absorption measure. Based on these differences and those obtained similarly in the energy intervals below 1 keV and above 10 kev, several spectral components were identified. They are briefly outlined below:
Besides persistent sources the X-ray sky is populated by a number of transient sources which remain in their quiescent state for most of the time and sporadically undergo bright outbursts with peak luminosities of erg/s , durations ranging from weeks to months, and recurrence timescales of 1-10 years or longer. Throughout the years a very clear analogy of the X-ray characteristics of bright transient sources with those of persistent sources has emerged. In particular, a number of X-ray transients display coherent X-ray pulsations or bursts, testifying to the presence of neutron stars, which undergo sporadic surges of accretion. Like in the case of persistent sources, X-ray bursting transients have low mass companions and relatively soft X-ray spectra, whereas X-ray pulsations are usually observed from transients in Be-star high mass binaries which are characterised by hard X-ray spectra extending up to tens of keV (White, Kaluzuenski & Swank 1984). The identification of the optical counterparts of bright transients, in crowded and often heavily absorbed regions of the galactic plane, is often made easier by the optical flux increase associated with the outburst. In the case of low mass systems, in particular, the reprocessing of high energy radiation can induce an increase of more than a factor of 100 above the quiescent optical flux level (Lewin & Joss 1983). Contrary to the case of persistent low mass X-ray binaries, detailed photometric and spectroscopic studies of the companion star are often possible in low mass transient sources, due to the fact that in the quiescent state their optical spectrum is not dominated by the reprocessing of X-ray radiation or by the emission from the accretion disc around the collapsed object.
X-ray transient sources are also extremely useful as they allow to investigate accretion onto collapsed stars over a range of X-ray luminosities, and therefore, accretion rates, much larger than persistent sources.
In the case of hard X-ray transients, the outburst is driven by sporadic accretion phenomena over a wide interval of accretion rates onto the magnetosphere of NSs. For low , the magnetosphere radius is generally larger than the corotation one and matter is ejected because of super-Keplerian drag exerted by magnetosphere on the infalling matter (centrifugal inhibition). As increases the magnetosphere radius is forced to shrink ( ) and if becomes smaller than , accretion onto the NS surface sets in, giving rise to the beginning of an outburst. Centrifugal inhibition acts again at the end of an outburst because, for decreasing , increases till the condition is met resulting in a sudden ``turn off'' of the X-ray emission.