UvA-DARE (Digital Academic Repository) Correlated timing and spectral variations of the soft X-ray transient Aquila X-1: evidence for an atoll classification

Based on Rossi X-Ray T iming Explorer data, we discuss the classiÐcation of the soft X-ray transient Aquila X-1 in the Z/atoll scheme and the relation of its kilohertz quasi-periodic oscillations (kHz QPOs) properties to the X-ray colors. The color-color diagram shows one elongated (““ banana ÏÏ) structure and several ““ islands ÏÏ of data points. The power spectra of the island are best represented by a broken power law whereas those of the banana by a power law below D1 Hz plus an exponentially cuto† component at intermediate frequencies (30È60 Hz). The parameters of these two components change in correlation with the position of the source in the color-color diagram. Based on the pattern that the source shows in the color-color diagram and its aperiodic variability, we conclude that Aquila X-1 is an atoll source. We have also investigated the possible correlation between the frequency of the kHz QPOs and the position of the source in the color-color diagram. The complexity seen in the frequency versus count rate diagram is reduced to a single track when the frequency is plotted against hard or soft color. Subject headings : accretion, accretion disks È stars : individual (Aquila X-1) È stars : neutron È X-rays : stars


INTRODUCTION
The X-ray burst source and soft X-ray transient Aquila X-1 displays X-ray variability on all timescales. Usually the source is in its quiescent state with a very low X-ray luminosity, typically D1033 ergs s~1 (Verbunt et al. 1994). Within intervals of months to years, it shows outbursts characterized by a gradual increase in Ñux to a level that sometimes is comparable to the Crab pulsar but at other times is 2 orders of magnitude fainter. The periodicity of these long-term outbursts is unstable with recurrent periods of D125 and 309 days (Priedhorsky & Terrell 1984 ;Kitamoto et al. 1993). The rise time is typically 10 days ; the source remains at a Ñux maximum for 5È10 days and then decays back to quiescence in typically 30È50 days (Campana et al. 1998 ;Kitamoto et al. 1993). The spectrum is soft, and no regular pulsations have been detected (Cui et al. 1998 ;Zhang, Yu, & Zhang 1998a). During outbursts, Aquila X-1 displays type I X-ray bursts (Zhang et al. 1998a) that can be explained in terms of runaway thermonuclear burning of matter on the surface of the neutron star. As in many other low-mass X-ray binaries (LMXBs), kilohertz quasi-periodic oscillations (kHz QPOs) have been detected in the persistent Ñux of Aquila X-1 (Zhang et al. 1998a ;Cui et al. 1998). These kHz QPOs occurred in the frequency range 740È830 Hz, had a Q-value of over (\l QPO /*l QPO ) 100, and had an average fractional rms amplitude of 7%. kHz QPOs may be caused by orbital motion of gas around the neutron star very close to its surface (see van der Klis 1999 for a recent review).
Recent deep optical and infrared images and lowresolution spectroscopy of this system suggest that the mass-donating companion is a V \ 21.6 K7 V star, located at an estimated distance of 2.5 kpc (Callanan, Filippenko, & 1999 ;Chevalier et al. 1999) and not the V \ 19.2 K1 Garc• a IV star west, previously assumed to be the candidate 0A .48 (Chevalier & Ilovaisky 1991 ;Shahbaz, Casares, & Charles 1997). At radio wavelengths, Aquila X-1 is unusual in being one of the only neutron star binaries to exhibit radio emission (Hjellming & Han 1995).
The late-type optical counterpart and the episodic outbursts deÐne Aquila X-1 as a soft X-ray transient (SXT), whereas the existence of type I bursts denotes a low magnetic Ðeld neutron star companion (as opposed to black hole). Prior to EXOSAT , LMXBs were classiÐed on the basis of their X-ray luminosity (Schulz, Hasinger, & 1989) into two classes : high-and low-luminosity Tru mper systems. The low-luminosity systems included the so-called X-ray bursters. Thanks to its wide orbit and large collecting area, the EXOSAT satellite allowed long, uninterrupted observations and detailed X-ray timing analysis. Taking into account the rapid aperiodic variability, it turned out that LMXBs could be divided into two di †erent subclasses, Z and atoll sources, deÐned by the patterns that these sources display in X-ray color-color diagrams and the properties of the rapid X-ray variability (Hasinger & van der Klis 1989, hereafter HK89). The classiÐcation of Aquila X-1 in this scheme is not certain. Rossi X-Ray T iming Explorer (RXT E) data has suggested that Aquila X-1 is an atoll source (Cui et al. 1998), though some properties appear anomalous. In this paper we investigate the correlated X-ray timing and spectral variations of Aquila X-1 and present evidence for its classiÐcation as an atoll source.

OBSERVATIONS
The data used in this work were retrieved from the public RXT E archive and correspond to two di †erent sets of observations. The Ðrst one took place between 1997 February 16 and March 10 and consists of 12 separate observations (one every 2 days, roughly), with a total usable time of about 96 ks (see Zhang et al. 1998a). These data correspond to the decay phase of an outburst. The observations during the second set, 1997 August 11ÈSeptember 10, were conducted at a typical rate of once or twice per day and produced approximately 168 ks of usable data. These observations began halfway through the rising phase of another outburst and Ðnished halfway through the decay phase. Five type I X-ray bursts (two of them were already reported in Zhang et al. 1998a) as well as kHz QPOs were present in the data. The bursts were excluded from our analysis. Another four snapshots taken during the rising phase of the 1998 FebruaryÈMarch outburst (Cui et al. 1998) were also analyzed in order to compare our results with those of other authors.
RXT E carries two pointed instruments, the Proportional Counter Array (PCA) developed to cover the lower part of the energy range (2È60 keV) and the High Energy X-ray Timing Experiment (HEXTE) sensitive to X-rays between 15 and 250 keV. These instruments are equipped with collimators yielding an FWHM of 1¡. In addition, RXT E carries an All-Sky Monitor (ASM) that scans about 80% of the sky every orbit. In this work we analyzed data from the PCA only since its large collecting area (D6500 cm2) makes it the most appropriate instrument for timing studies.

Color-Color Diagram
Background-subtracted light curves corresponding to the energy ranges 2.0È3.5 keV, 3.5È6.0 keV, 6.0È9.7 keV, and 9.7È16.0 keV were used to deÐne the soft and hard colors as SC \ 3.5È6.0/2.0È3.5 and HC \ 9.7È16.0/6.0È9.7, respectively. In a few of the observations, one or two of the Ðve detectors of the PCA were switched o † ; we only used the three detectors which were always on to calculate these count rates and normalized the count rates to Ðve detectors. The color-color diagram of Aquila X-1 is shown in Figure 1.
FIG. 1.ÈColor-color diagram of Aquila X-1. The soft and hard colors are deÐned as the ratio of count rates in the bands 3.5È6.0 keV and 2.0È3.5 keV, and 9.7È16.0 keV and 6.0È9.7 keV, respectively. The contribution of the background has been subtracted, but no dead-time correction was applied to the data (the dead-time e †ects on the colors are less than 1%). Each point in the banana branch ( Ðlled circles) and in the island with the lowest hard color ( Ðlled squares) represents 64 s of data, 128 s in the middle island (open circles), and 768 s in the extreme island (open squares). We show the typical error bars in the banana and the island states. Black and gray symbols indicate segments with and without kHz QPOs, respectively. Vertical lines deÐne the regions into which the banana branch was divided. NOTE.ÈIn the island state, the HFN is represented by a broken power law ; in the banana state, the HFN is represented by a power law with an exponential cuto † (see text). Errors are based on a scan in s2 space using *s2 \ 1.
a Refers to the regions deÐned in the color-color diagram (see text). b 1È100 Hz rms amplitude (%). c Broken power law ; slope below the break. d Broken power law ; break frequency (Hz). e Broken power law ; slope above the break. f Background-subtracted count rate for the full PCA (counts s~1). g 0.001È1 Hz rms amplitude (%).
The data points in this color-color diagram fall into several distinct groups, the hard color being the deÐning quantity. The statistical scatter in the uppermost (open squares) and middle (open circles) groups in Figure 1 is considerable. These groups of points come from observations at the very end (after March 5) of the decay of the 1997 March outburst. The lower branch corresponds to observations from the rest of the 1997 FebruaryÈMarch run and from the entire 1997 AugustÈSeptember run. The points represented with Ðlled squares correspond to the 1998 March 2 observation. The mean PCA intensity of each group is given in Table 1. At the rising part of the 1997 AugustÈSeptember outburst, the source moved smoothly from left to right along the lower elongated branch and moved back from right to left during the decay phase. During the 1997 FebruaryÈMarch outburst, the source also moved toward lower soft colors as the intensity decreased.
In order to measure the source luminosity in the di †erent states spanned in the color-color diagram, we extracted energy spectra and Ðtted an absorbed blackbody plus power-law model to the data. An iron line at 6.4 keV was added if necessary. The 2È10 keV X-ray luminosity, assuming a distance of 2.5 kpc, varies from 2.0 ] 1034 ergs s~1 in the uppermost group to 3.2 ] 1035 ergs s~1 in the middle one. The elongated lower group of points presents the highest count rate. Here the source luminosity increases from left to right, from 2.4 ] 1036 to 3.9 ] 1036 ergs s~1.
These structures in the color-color diagram and associated count rate di †erences are similar to those of typical atoll sources. The upper and middle group of points can be associated with the so-called island state, whereas the more elongated lower part would then represent the banana state. By only looking at the position occupied by the points of the 1998 observation, it is not possible to tell whether they deÐne an island or a banana state, and an analysis in terms of the aperiodic variability is needed. In any case they seem to indicate that the transition between the two spectral states is smooth. The gap between the branches is probably observational : no data were obtained for 2 days between the banana and the island and for 3 days between the island and the extreme island states during the 1997 observations.
In order to investigate the variability of Aquila X-1 as a function of the position in the color-color diagram, we divided the color-color plane into several regions as shown in Figure 1. The two island branches deÐne the Ðrst two groups. The banana branch was divided so that each region contains approximately the same amount of data. We then approximated the shape of the banana branch with a spline and used the parameter to measure positions along this S a spline et al. 1999). We set to 2 at (SC, HC) \ (Me ndez S a (1.732,0.338) and to 3 at (SC, HC) \ (2.045,0.320). The intermediate positions are obtained through spline interpolation between the two deÐning values. This could be done for the banana branch only since the discontinuity between the island and banana branches does not allow one to deÐne a unique path. We arbitrarily assigned the values 1.1 and 1.5 to the two island states. In this way each one of the regions in which we had divided the colorcolor diagram is then characterized by a value of the parameter S a .

Noise Components
In order to study the source variability at low frequencies (¹512 Hz), we divided the 2È60 keV PCA light curve (no energy selection was done) of each observation into 256 s segments and calculated the Fourier power spectrum of each segment up to a Nyquist frequency of 1024 Hz. The high-frequency end (950È1024 Hz) of the power spectra was used to determine the underlying Poisson noise, which was subtracted before performing the spectral Ðtting. The power spectra were normalized to fractional rms squared per Hertz (van der Klis 1995). In a few observations, one or two of the Ðve PCA units were switched o †. We have used only those observations for which the Ðve detector units were switched on. This implied a loss of D11% of the data. To avoid contributions to the power from the kHz QPOs, we restricted the spectral Ðtting to the frequency interval (1/256)È512 Hz. The 256 s power spectra were then grouped according to the position of the source in the color-color diagram : for each region in the banana and each island state, one mean power spectrum was obtained.
The power spectra were Ðtted using two broad noise components called the very low frequency noise (VLFN) and the high-frequency noise (HFN). These two components are mathematically represented by a power law and a power law times an exponential cuto †, respectively (HK89). The VLFN accounts for the low-frequency part of the spectrum, whereas the HFN dominates at higher frequencies. Figure 2 shows six power spectra corresponding to di †erent positions in the color-color diagram ; all the island states and the lower, middle, and upper banana states are shown.
While the VLFN plus HFN model can satisfactorily describe the banana-state power spectra, it does not provide good Ðts for the faintest of the two island-state (S a \ 1.1) power spectra. Ford & van der Klis (1998) used a broken power law plus one low-frequency (10È50 Hz) Lorentzian, possibly representing Lense-Thirring precession (Stella & Vietri 1998), to Ðt the island-state power spectra of the atoll source 4U 1728[34. In Aquila X-1 we Ðnd that a simple broken power law gives good Ðts to the power (s l 2 ¹ 1.2) spectra in both island states. Although described by di †erent mathematical functions, the cuto † power law of the banana state and the broken power law of the island state are likely to represent the same type of noise component, namely HFN. To be consistent, we have used the broken power-law model to Ðt the power spectra of the island states. Figure 3 shows the variation of the amplitude (as fractional rms) of the VLFN (circles), HFN (squares), and broken power-law (triangles) components. The latter refers to the island states.
Unlike the HFN component, the amplitude of the VLFN component does not show any clear trend but remains at D6%È7% rms, irrespective of the position that the source occupies in the banana. The maximum strength of the HFN is found during the island phases (rms \ 34% and 18% for the upper and lower island states, respectively). This is in contrast to the results of Cui et al. (1998), who did not detect such an HFN component in the Ðrst observations of the 1998 FebruaryÈMarch outburst (MJD 50,875È50,877) despite the inference from the color diagrams that these data were in an island state. These authors discuss the absence of an HFN in the island state as an unusual phenomenon. We have reanalyzed the Ðrst four observations in the Cui et al. (1998) paper and found that there is, in fact, an HFN component with an rms of 6.0%^0.3% (Fig. 2, Table  1) in the Ðrst two observations. As expected in the island, there is no VLFN (1.6% upper limit, 95% conÐdence level).  The mean hard and soft colors of the corresponding points are HC \ 1.84, SC \ 0.34 and HC \ 1.86, SC \ 0.31 for the Ðrst and second observations, respectively. That is, in our color-color diagram, they lie between the lower island and the banana states. This distribution of the island points in the color-color diagram suggests a continuous transition between the island and banana groups. The other two observations produced points in the banana only.

kHz QPOs and the Color-Color Diagram
For the kHz QPO analysis, we produced power spectra using 64 s data segments and a Nyquist frequency of 2048 Hz. kHz QPOs were only observed in a speciÐc range in the color-color diagram, namely the lower banana near S a \ 2.32 (Fig. 1, Ðlled circles). The 2È60 keV fractional amplitudes of the kHz QPOs ranged from D4.5% to D11.7%. We did not detect QPOs in the upper part of the banana with a 95% conÐdence upper limit of 1.4% rms or in the island with an upper limit of D8%. Figure 4 shows the dependence of the frequency of the QPOs as a function of the 2È16 keV PCA count rate. The two parallel groups at the lower left of the plot (open circles, gray circles) correspond to the 1997 FebruaryÈMarch observations (Zhang et al. 1998b), while the rest come from the 1997 AugustÈSeptember set of observations. et al. (1999) found that there is a much better Me ndez correlation between the frequency of the kHz QPOs in 4U 1608[52 and the position of the source on the color-color diagram than between frequency and Ñux. Similarly, the multivalued dependence of on X-ray Ñux in Aquila X-1 l QPO is reduced to a single relation when is plotted against l QPO the parameter, which in our case is just a measure of the S a soft color (Fig. 5). The hard color is not as sensitive to changes in the kHz QPO frequency in Aquila X-1 as it is in 4U 1608[52 (Kaaret et al. 1998 ;). Me ndez

DISCUSSION
We have measured the color and timing properties of the LMXB Aquila X-1 and found a behavior similar to that of other low-luminosity LMXBs. The color-color diagram shows the classical atoll shape with the banana and island states. The island state is not deÐned by a single group of FIG. 3.ÈVLFN (circles) and HFN (squares, triangles) fractional rms (1È100 Hz, full energy band) as a function of the parameter (see text). S a The two triangles correspond to the island and extreme island state and were obtained using a broken power-law function. The values for these S a two points were arbitrarily chosen.
points, but it is split into a number of di †erent groups as in other atoll sources, e.g., 4U 1636[53 (Prins & van der Klis 1997) and 4U 1608[52 (Yoshida et al. 1993). The lowest count rate and Ñuxes are detected in the island state with the hardest color and increase as the hard color decreases.  Based on the similarity of the color-color diagram of Aquila X-1 to that of other atoll sources, it seems likely that Aquila X-1 can be placed in the group of atoll sources. However, the information provided by the color-color diagram is, by itself, not always sufficient to classify the source state. It is not always possible to make a distinction between Z and atoll sources or between the two spectral states (island/banana) within the atoll class (HK89). Moreover, in some atoll sources the island and banana branches have been seen to shift in the color-color diagram, in both soft and hard colors (Prins & van der Klis 1997). The information obtained from the analysis of the noise components in the power spectra provides the key for an unambiguous classiÐcation.
The preliminary classiÐcation of Aquila X-1 as an atoll source on the basis of the color-color diagram is conÐrmed by the fast-timing analysis. The power spectra of atoll sources (HK89) are characterized by two broad noise components called the very low frequency noise and the highfrequency noise. The relative strengths of these two components vary in anticorrelation with each other and with the inferred mass accretion rate, as measured by M 0 , S a in our analysis : the VLFN component appears at the highest inferred whereas that of the HFN decreases as M 0 , M 0 increases. These two components are present in the power spectra of Aquila X-1 (see Fig. 2 and Table 1). As is commonly seen in atoll sources, the VLFN is most prominent in the banana state, while the HFN dominates the island state. The fractional amplitude of the HFN component decreases as the system moves from the island state to the lower banana and from here to the upper banana. The VLFN component is practically undetectable (rms ¹ 2%) in the island state, and although present in the banana state, its amplitude does not change as expected (see below). Another similarity between the power spectra of Aquila X-1 in the banana state and those of atoll sources is the presence of wiggles in the VLFN (HK89).
The increase of the break frequency as the X-ray count rate (or Ñux) increases and the fact that the largest fractional amplitude and the hardest spectrum are observed in the two island states represent further evidence in favor of an atoll classiÐcation for Aquila X-1 (e.g., 4U 0614]09 ; et Me ndez al. 1997). It is worth noting that all these characteristics are also seen in black hole candidates during the low state, emphasizing the observational similarities between atoll sources and black holes systems (van der Klis 1994).
One of the open questions in atoll sources is whether the transition from the island to the banana states occurs continuously or abruptly, that is, with the source jumping from one state to the other. The trends of the spectral parameters just described seem to indicate that such transition is continuous. This idea would be supported by the 1998 March data (Cui et al. 1998). The upper limit to the rms of the VLFN component in the 1998 March observation (\1.6%, 95% conÐdence) is lower than the value in the banana (5%È 7%), and the rms of the HFN is larger (6% compared to 3.5%). The break frequency Hz follows the same l br B 43 trend as the other two island states, namely, increases as the source moves into the banana.
An interesting di †erence between the island state of 1998 March and the other two island states is the source count rate. While the two 1997 March islands show the lowest PCA intensity, the 1998 March one is comparable to that detected in the lower banana state. It is worth noting that the 1997 island data were collected during the decay of an X-ray outburst, whereas that of 1998 correspond to the rise of the outburst. A hysteresis e †ect may be present.
Our observed VLFN amplitude does not change signiÐcantly in the banana state, contrary to what is observed in other atoll sources. Also, the power-law index of the VLFN becomes less steep as the source moves up in the banana branch, while usually in other atoll sources a slight increase, if any change, occurs. This unusual behavior of the VLFN component may be related to nuclear burning on the surface of the neutron star. In periodic X-ray bursters, like Aquila X-1, the entire surface of the star is rapidly (¹10 s) burned by a fast-propagating thermonuclear instability. This can only happen at low mass accretion rates, where the envelope is convectively combustible most of the time. The convective burning makes it difficult for slower combustion to occur, thus suppressing the VLFN (Bildsten 1993). Yu et al. (1999) reported another unusual aspect of the VLFN in Aquila X-1, namely, its disappearance after a type I burst, in which the 2È10 keV Ñux decreased by about 10% and the kHz QPO frequency fell abruptly by D37 Hz.
Aquila X-1 is unusual among the group of low-mass X-ray binaries with kHz QPOs in that only one kHz QPO has been so far observed. All other sources (Z and atoll) have at least sometimes shown two simultaneous kHz QPOs. Nevertheless, the relationship between the frequency of the kHz QPOs and the X-ray Ñux in Aquila X-1 is very similar to that seen in the atoll sources 4U 1608 [52 et al. 1999) and 4U 0614]091 (Ford et al. 1997) : (Me ndez on timescales longer than D1 day, there is no correlation between the kHz frequency and the X-ray intensity (or Ñux), whereas on short timescales (Dhours), these two quantities correlate remarkably well (Zhang et al. 1998a). We also Ðnd that similarly to other sources, on timescales longer than a day, the QPO frequency correlates much better to color (or than to count rate. S a )

CONCLUSION
We have used RXT E data to carry out a timing analysis with the aim of solving the issue of the classiÐcation of Aquila X-1 in the Z/atoll scheme. Aquila X-1 traces a pattern in the color-color diagram that is consistent with having an island and a banana branch. The PCA intensity correlates with the position of the source in the color-color diagram, decreasing in the sense of upper banana to lower banana to island state.
The power density spectra of the banana states can be described in terms of a power-law component, the so-called very low frequency noise and a cuto † power-law component or high-frequency noise. In the island state, the highfrequency noise component is best described in terms of a broken power law, whereas the very low frequency noise is practically undetectable. The characteristics of the power spectra also change in correlation with the position of the source in the color-color diagram. The amplitude of the high-frequency noise increases as the parameter S a decreases. Finally, we have shown that the soft color (via the parameter) correlates with the frequency of the kHz S a QPO.
Based on the correlation of the X-ray spectral properties of Aquila X-1 (its position in the color-color diagram) and its fast-timing behavior, we conclude that Aquila X-1 is an atoll source. This work was supported by the Netherlands Foundation for research in astronomy (ASTRON) under grant 781-76-017, the Netherlands Research School for Astronomy (NOVA), and the NWO Spinoza grant 08-0 to E. P. J. van den Heuvel. P. R. acknowledges support from the European Union through the Training and Mobility Research Network grant ERBFMRX/CT98/0195. M. M. is a fellow of the Consejo Nacional de Investigaciones y de la Argentina. This Cient• Ðcas Te cnicas Repu blica research has made use of data obtained through the High Energy Astrophysics Science Archive Research Center Online Service, provided by the NASA/Goddard Space Flight Center.