KHz QPOs

In February 1996, only 2 months after its launch the Rossi X-Ray Timing Explorer (RXTE) discovered kilohertz quasi-periodic oscillations (kHz QPOs) in the well known LMXB Sco X-1 [39]. They appear as two simultaneous peaks (twin peaks) in the power spectrum (Fig. 15.8). Today, some 20 LMXBs (both Z and Atoll type) with QPO peaks between 200 and 1 300 Hz are known. The frequency of both peaks usually increases with increasing X-ray flux, while the separation stays nearly constant. For reviews on observations and the basic physical interpretation see [39] and [40]. Variations in this frequency range had long been expected because this is close to the natural dynamic time scale around compact objects like NS or stellar black holes. The orbital frequency around a NS is given by

1 "color" is defined as the ratio of count rates in adjacent energy intervals kHzQPOs

Exira noise component

1 10 100 1000 Frequency (Hz)

Fig. 15.8 Power Density Spectrum of Sco X-1 (after [1])

vorb = 1200Hz (rorb/15km)-3/2 m^, with m14 being the mass of the NS in units of 1.4 M0. The maximum frequency is then reached at the innermost stable circular orbit (ISCO), which in a Schwarzschild geometry is given by 3 times the Schwarzschild radius (Risco = 3Rs = 6GM/c2 = 12.5kmm1.4): Visco = 1580Hz/m\A. The spin-orbit beat-frequency model, as already discussed earlier for low frequency QPOs, can provide a basic understanding of the observed features: calling the upper and lower frequency (of the two twin peaks) v2 and v1, respectively, and identifying v2 with vorb and v1 with the beat frequency between vorb and vspin, then v1 = vbeat = v2 - vspin. This would identify the spin frequency with the difference between the two observed kilohertz peaks, in agreement with the expectation that vspin is constant. Only a single sideband (vorb - vspin) is observed, as expected from a rotational interaction, with spin and orbit in the same sense. In the sonic point beat-frequency model, the preferred orbital radius is essentially identified with the inner edge of the accretion disk. The above interpretation has received very strong support by the observations of burst oscillations (Sect. 15.6.3) and by the discovery of bursting ms X-ray pulsars, which are believed to show the NS spin frequency directly (see later; it appears, that for some sources the difference between the twin kHz QPO frequencies is vspin for others it is vspin/2).

15.6.3 Bursters

In weakly magnetized NS, the accretion disk can come close to the surface of the NS and the material can trickle down to this surface in a quasi radial-symmetric way. The liberated gravitational energy gives rise to some steady X-ray emission. If the temperature and the density is high enough, the accreted material, mostly hydrogen, can peacefully fuse into helium. When sufficient helium is produced and critical values of density and temperature are reached, helium burning can start. This

Time (s) since 01:22:23 (IDS) Time (s) since 12.17.21 (TDB)

Fig. 15.9 Thermonuclear bursts and frequency development of burst oscillations [32]

Time (s) since 01:22:23 (IDS) Time (s) since 12.17.21 (TDB)

Fig. 15.9 Thermonuclear bursts and frequency development of burst oscillations [32]

process, however, is unstable and resembles an explosion event, producing what we observe as an X-ray burst: a fast rise (<1-10s) in X-ray flux with a subsequent exponential decay (with a duration typically between 10 s and a few minutes), see Fig. 15.9. The time between bursts is typically from 1 h to a few hours. A review about X-ray bursts is given in [28].

The first such X-ray bursts were observed in 1975 through observations with the Dutch X-ray satellite ANS from a neutron star inside globular clusters [21], which was soon followed by the discovery of a dozen X-ray bursters with SAS-3 [27]. Today, about 65 X-ray burst sources are known, situated mainly in globular clusters and in the galactic bulge region. They are members of an old population. The above picture, called the thermonuclear flash model, was soon developed on the basis of solid physical evidence. The measured spectra were consistent with black-body emission, and it was found that the characteristic temperature decreases when the burst fades, also evidenced by a faster decay at higher photon energies. Furthermore, the absolute fluxes and temperatures measured toward the end of many bursts from objects in the galactic bulge (providing an estimate of the distance to the sources) were consistent with the radiation coming from objects of 10-15 km diameter [28], just what is expected from a NS. Since a solid surface is needed for the fusion to take place, the X-ray burst sources must be NS, not black holes. If the luminosity of the steady flux is compared with the integrated burst flux a factor of —100 is found, which is close to the expected ratio of gravitational energy to nuclear energy of the accreted material. Finally, an interesting correlation [28] was found between the time interval since the previous burst and the strength of the burst: the longer the waiting time is, the more nuclear fuel can accumulate for the next burst. There is evidence, particularly in strong bursts, that there is a photospheric radius expansion during the early phases of the burst where the X-ray luminosity reaches the Eddington limit. Any additional energy available is put into kinetic and potential energy of the expanding atmosphere. Bursts from thermonuclear flashes with the characteristics described earlier are called Type I bursts. From seven LMXB superbursts have been observed with decay times between 1 and 6 h and —100 times more energetic than regular bursts. They are thought to be due to unstable burning of carbon rather than helium [24].

15.6.3.1 The Rapid Burster

The necessity to distinguish between two types of bursts came with the discovery of an object called the Rapid Burster (RB) [28,38]. As the name suggests, the rate of bursts is very high with intervals between bursts as short as —7 s (and no longer than —1 h). These bursts do not show the characteristic softening during their decay, as found in Type I bursts. They are, therefore, called Type II bursts. In addition to Type II bursts, the RB generally also shows Type I bursts with the usual characteristics. But there can be periods with only one type of bursts or with no bursts at all. In Type II bursts the strength of the burst correlates with the time interval to the next burst, not the previous one as in Type I bursts. If the RB is burst active, the integrated X-ray flux of Type II X-ray bursts from the RB is about 120 times greater that that of the Type I bursts [28], suggesting gravitational energy behind Type II bursts. For some time, the RB was the only object showing Type II bursts, now we know a second object, GRO 1744-28 [15], also called the Bursting Pulsar (see later).

Many models have been proposed to explain Type II bursts (for references and a discussion see [28]). They all involve some sort of gating mechanism, which -due to an instability - allows to (partially) empty a reservoir of material which can then suddenly fall down to the surface of the NS and cause the X-ray burst. The observed linear correlation of the energy of the burst and the time to the next burst for the RB is very suggestive of a relaxation oscillator: when in one burst the reservoir was emptied to a high degree, it will take a longer time to replenish it again, while a partial emptying will result in a short waiting time to the next burst. It is, however, not entirely clear whether the storage medium is the accretion disk itself or the magnetosphere and which type of instability triggers the gate to open. The RB and GRO 1744-28 must distinguish themselves from all other bursters (showing ordinary Type I bursts) by special physical parameters or conditions. The strength of the magnetic field may be one parameter, but then GRO 1744-28 is a pulsar, the RB is not.

15.6.3.2 The Bursting Pulsar

For about 20 y, the Rapid Burster (RB) was the only object showing Type II bursts, until BATSE on December 2, 1995 detected such bursts from a transient X-ray source close to the Galactic Center (GRO J1744-28) [15]. On top of this, the new source established itself as a new type of X-ray source: one day before the onset of the burst activity coherent X-ray pulsations with a period of 0.467 s were discovered [46]. GRO J1744-28 was dubbed the Bursting Pulsar (BP). Until its discovery, it was believed that coherent pulsations and X-ray burst activity were mutually exclusive in X-ray sources, since the former were associated with highly magnetized NS, the latter with weakly magnetized NS. Most likely, the BP has a magnetic field of intermediate strength (—1011 G) and undergoes strong magnetically guided accretion (albeit gated, as in the RB), which suppresses thermonuclear (Type I) burst activity. Coherent pulsations at the spin period are seen in the persistent flux as well as in bursts [46]. Today, we know two sisters of the BP - objects showing coherent pulsations and (Type I) burst oscillations at the same frequency. However, they belong to the recently identified class of accreting ms X-ray pulsars (Sect. 15.6.4).

15.6.3.3 X-Ray Burst Oscillations

If a thermonuclear burst ignites on the surface of a rotating NS, one might expect to see signs of the rotation because of nonisotropic emission due to patchy burning or the influence of the magnetic field. The first oscillation with a drifting frequency around 363 Hz was observed by RXTE in early 1996 in a Type I burst from 4U 1728-34 [40]. Today, 13 objects (out of the 65 bursters) have been found to exhibit oscillations in Type I bursts [32]. The frequencies range from 270 to 620 Hz. Figure 15.9 shows examples of burst profiles with the development of the frequency of the oscillations throughout the bursts. There is an upward drift (by a few %) toward an asymptotic frequency. Taking a simple model for the frequency drift into account, the oscillations can be accepted as coherent. Also, in a given source the end frequency is stable (within measurement uncertainties) from burst to burst, even if they are years apart. The modulation is generally sinusoidal (with very little harmonic content). These findings have led to the interpretation that the observed end frequency is equal to the rotational frequency of the NS. This conclusion is strongly supported by burst oscillations of two bursting millisecond pulsars (Sect. 15.6.4) in which exactly the same frequency is measured in the persistent flux and in the thermonuclear bursts. It is, however, not clear why nonisotropies in the emission of the bursting ms pulsars remain for —15 s, while it is believed that the nuclear explosion engulves the entire NS surface within 1 s from the ignition, and why the frequency shows this development in time [32].

It is interesting to note, that among the 13 known ms burst oscillators eight objects also show twin kilohertz QPOs. However, only for four of those is the frequency difference between the two kHz QPO peaks nearly equal to the frequency observed during the bursts, in the other four cases it is close to half the frequency during the burst. Interestingly, the former group has vburst < 400 Hz, while for the latter vburst > 400 Hz [31].

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