MULTI-INSTRUMENT X-RAY OBSERVATIONS OF THERMONUCLEAR BURSTS WITH SHORT RECURRENCE TIMES

In this paper, we name the different kinds of bursts using the conventions of Boirin et al. (2007). Bursts with recurrence (waiting) times shorter than 1 hr are referred to as short waiting time (SWT) bursts, while longer recurrence time bursts are long waiting time (LWT) bursts. The 1 hr boundary is chosen to discriminate between the two distinct groups of bursts we observe (Section 3.5). A burst event is defined as a series of bursts, where any two or more subsequent bursts are separated by an SWT. We refer to an event with one, two, three, or four bursts as a single, double, triple, or quadruple burst, respectively. Furthermore, we call a double, triple, or quadruple burst a multiple-burst event. For the bursts within a multiple-burst event, we use the terms first burst and follow-up burst, where the former refers to the LWT burst and the latter to any SWT burst in the event.

Because SWT bursts are rare, we need a large sample of bursts to study them well. We use a preliminary version of the Multi-INstrument Burst ARchive (MINBAR), which is a collection of Type I bursts that are observed with different X-ray instruments, and that are all analyzed in a uniform way. MINBAR is a continuation of the effort which started with the RXTE PCA burst catalog by Galloway et al. (2008), combined with the many X-ray bursts observed with the WFCs on BeppoSAX (e.g., Cornelisse et al. 2003). The catalog will be presented in full in a forthcoming paper. Currently it contains information on 3402 bursts from 65 sources, among which are 136 SWT bursts (MINBAR version 0.4). In comparison, Galloway et al. (2008) report 1187 bursts from 48 sources, among which are 84 bursts with a short recurrence time, in that paper defined as <30 minutes (MINBAR contains 110 SWT bursts using this criterion).

The Rossi X-ray Timing Explorer (RXTE) was launched on 1995 December 30. One of the instruments on board is the Proportional Counter Array (PCA; Jahoda et al. 2006), consisting of five proportional counter units (PCUs) which observe in the 1 to 60 keV energy range. The PCA has a large collecting area of 8000 cm² (1600 cm² for each PCU). The PCUs are co-aligned and have a collimator that gives a 1° FWHM field of view (FOV). As part of the primary mission objective of RXTE, the PCA gathered a large amount of exposure time on the galactic LMXB population. The observations we use have an average duration of 78 minutes. We use all data that were publicly available in 2008 July (compared to 2007 June for Galloway et al. 2008).

The High-Energy X-ray Timing Experiment (HEXTE; Gruber et al. 1996) on RXTE consists of two clusters of NaI/CsI scintillation detectors that allow for observations in the 15 to 250 keV energy range. If available, we combine PCA and HEXTE observations to obtain a broadband X-ray spectrum, when studying the persistent flux of bursting sources.

The all-sky monitor (ASM) on RXTE consists of three scanning shadow cameras (SSCs) on a rotating beam that image a large part of the sky each satellite orbit, in a series of short 90 s observations. The SSCs observe in the 1.5 to 12 keV energy range.

A few months after RXTE, the BeppoSAX observatory was launched in 1996 April (Boella et al. 1997), and it was operational until 2002 April 30. On board were two WFCs that faced in opposite directions (Jager et al. 1997). The WFCs were sensitive in the 2 to 28 keV bandpass and each camera imaged at any time 40° × 40° of the sky using a coded mask aperture. Biyearly observations of the Galactic center were performed, resulting in a large exposure time for many of the LMXBs in the Galaxy (in't Zand et al. 2004). the WFC observations have a mean duration of 255 minutes. We use all the WFC data.

For the majority of the bursters, which are located near the Galactic center, we gather a total net exposure time of approximately 50 days.

Both observatories were placed in a low Earth orbit of approximately 96 minutes. During the observation of a particular source, the source is obscured by the Earth for a typical duration of approximately 36 minutes per orbit. Furthermore, when the satellites passed through the South Atlantic Anomaly (SAA), the detectors were turned off to prevent damage. This introduces data gaps of 13 to 26 minutes long. The precise length of the different data gaps depends on the latitude of the source with respect to the satellite orbit, which was different for BeppoSAX and RXTE.

We briefly discuss the process of the burst analysis. The generation of data products for the different instruments is handled identically to the studies by Galloway et al. (2008) and Cornelisse et al. (2003). Our method of burst analysis is in principle the same as for those studies, but extra care was taken to ensure that results from different instruments are directly comparable. For more details of the analysis of PCA and WFC data, we refer to Galloway et al. (2008) and Cornelisse et al. (2003), respectively.

To find burst occurrences, we generate light curves for each instrument, for each known bursting source. In the light curves we locate all events that rise significantly above the background, e.g., exceeding the mean flux level by at least four times the standard deviation. These events are checked by eye for the characteristic profile of a fast rise and an exponential-like decay.

Next, time-resolved spectroscopy is performed on the candidate bursts. We divide the individual bursts in time intervals, such that we obtain for each interval a burst spectrum with similar and sufficient statistics. The net burst spectrum is obtained by subtracting the spectrum of the persistent emission observed during the entire observation, excluding the burst (e.g., Kuulkers et al. 2002). We fit the burst spectra with a blackbody model, taking into account the effects of interstellar absorption (Morrison & McCammon 1983; solar abundances from Anders & Ebihara 1982). From this we find a blackbody temperature and radius, as well as the unabsorbed flux. By extrapolating the fitted blackbody model beyond the observed energy range, we obtain the bolometric unabsorbed flux. Integrating the flux over the burst yields the burst fluence.

The decay time is determined by fits to the burst light curve. We obtain the net burst light curve by subtracting the persistent flux, as measured in the entire observation, excluding the burst. We start fitting the decay when the flux drops below 90% of the peak flux. This has the advantage that we are less sensitive to the Poisson noise at the peak or to the effects of radius expansion. The decay of many bursts is fit well by two exponentials, with two exponential decay times. For some bursts, two exponentials did not yield a statistically better fit than a single exponential. For those bursts we report only a single decay time. It should be noted that not for all bursts a good fit was obtained, but the "best" fit still provides a qualitative description of the burst decay.

The determination of the burst decay time is currently not done uniformly for the different instruments. For the PCA the bolometric flux is used, while for the WFCs the flux in counts per second is used. We compared the decay times obtained for 15 bursts that have been observed by both instruments. On average, the decay times for the WFC bursts are (22 ± 7)% longer than for the PCA bursts. Although the decay timescales are not fully compatible across the different instruments, we can still use them to differentiate between short bursts and the longer bursts with the rp-process tail.

We obtain the persistent flux for each burst by fitting the spectrum from the entire observation, excluding the burst. By extending the fitted spectral model (typically a comptonized spectrum or a blackbody + power law; see Galloway et al. 2008 for details) outside the observed energy range, we determine the bolometric correction. The uncertainty in the bolometric correction can be as small as 10%, when we combine RXTE PCA and HEXTE observations to obtain a broadband spectrum. The BeppoSAX WFCs, however, do not have such broad energy coverage, and some PCA observations suffer from source confusion, which leads to an increased uncertainty in the bolometric correction of up to 30%.

To convert flux to luminosity and fluence to energy, we multiply by 4πd², with d being the distance to the source. We use the distances from Kuulkers et al. (2003) for globular cluster sources, and from Galloway et al. (2008; distances from photospheric-radius expansion bursts observed with the PCA) and Liu et al. (2007) for the other sources. Most measurements of the distance have an uncertainty of the order of 30%. Combined with a 30% error in the bolometric correction, this leads to an uncertainty in the luminosity and the fluence of up to approximately 70%.

The persistent X-ray emission from an LMXB mainly originates from the inner part of the accretion disk, and, therefore, is a measure of the mass accretion rate (e.g., Galloway et al. 2004b). We express the mass accretion rate $\dot{M}$ in terms of the Eddington limited accretion rate ${\dot{M}_{\rm Edd}}$ by equating their ratio to the ratio of the persistent luminosity L and the Eddington luminosity for hydrogen accreting sources L_Edd = 2 × 10³⁸ erg s⁻¹: $\dot{M}/{\dot{M}_{\mathrm{Edd}}}$ = L/L_Edd. L_Edd depends on the neutron star mass and the hydrogen fraction of the accreted material (e.g., Bildsten 1998), both of which are not known to great precision for most LMXBs. The current observational constraints on the mass (Lattimer & Prakash 2007) introduce an uncertainty of several tens of percents. Furthermore, we assume that the accretion process has an efficiency of 100%. It is possible that part of the matter leaves the system in a jet, such as observed in black-hole binaries (e.g., Fender et al. 2005). In this paper, however, we neglect this possibility and assume that the luminosity is a good measure of the mass accretion rate. We also neglect any anisotropy factors that may arise from the inclination of the disk with respect to the line of sight; because the inclination is ill-constrained for most LMXBs, we assume isotropic emission.

The combined uncertainties are quite large, but this only plays a role when we compare different sources. It is, however, of no consequence when we compare the bursts of any single source. We will still compare different sources, but one must be careful to keep these uncertainties in mind.

The MINBAR catalog contains X-ray bursts from 65 sources, 15 of which exhibit SWT bursts (Table 1), i.e., bursts with a recurrence time shorter than 1 hr. We exclude the Rapid Burster, which is known to exhibit Type II bursts, which are not of thermonuclear origin (e.g., Lewin et al. 1993). Interestingly, no multiple-burst events are detected from candidate and confirmed ultra-compact binaries (UCXBs). The companion star in a UCXB is thought to be an evolved star, donating hydrogen-poor matter to the neutron star (in't Zand et al. 2005). For confirmed UCXBs the binary period has been measured, while candidates are identified by tentative measurements of the period, by a low optical to X-ray flux, or by stable mass transfer at rates below 1% of the Eddington limited rate. We employ the list of (candidate) UCXBs from in't Zand et al. (2007), which omits candidates proposed on the basis of their X-ray spectrum, which is likely a less reliable method. From these sources we find 229 bursts, none of which are SWT bursts. The frequent burster 4U 1728-34 (GX 354-0) is suspected of being a UCXB based on its bursting behavior (Galloway et al. 2008). Five hundred and forty-three bursts of this source are present in MINBAR, but no multiple-burst events. As this strongly suggests that SWT bursts are limited to hydrogen-rich accretors, we exclude in our studies the list of (candidate) UCXBs from in't Zand et al. (2007), with the addition of 4U 1728-34.

GX 17+2 and Cyg X-2 exhibit bursts at accretion rates close to the Eddington limit (e.g., Kuulkers et al. 2002), while most LMXBs do not show bursts above approximately 10% of Eddington (e.g., van Paradijs et al. 1988; Cornelisse et al. 2003). Of these two sources, Cyg X-2 exhibits SWT bursts. Due to the high accretion rate, however, the amount of matter accreted in between the bursts is enough to account for the amount of fuel burned in the bursts. Furthermore, Galloway et al. (2008) find indications that (some of) the bursts of GX 17+2 and Cyg X-2 could be Type II bursts. For these reasons, we exclude these two sources as well.

The bursts from EXO 1745-248, located in the globular cluster Terzan 5, exhibit only weak evidence for cooling, which means that their thermonuclear origin is not firmly established, and that they possibly are Type II bursts. Another sign that the bursting behavior is anomalous, is the fact that most sources in Table 1 exhibit more double bursts than triples and quadruples, while EXO 1745-248 has one of each. We exclude the source in our studies.

4U 1746-37, located in the globular cluster NGC 6641, exhibits both faint and bright bursts. Galloway et al. (2004a) found in PCA observations that the faint bursts occur at very regular intervals, unaffected by the occurrence of bright bursts, and vice versa. This lead to the speculation that the faint bursts originate from a different LMXB that is also located in NGC 6641. We, therefore, exclude the bursts from this source.

After excluding the mentioned sources, we consider 44 hydrogen-rich accretors from which we observe 2274 single, 56 double, 7 triple, and 2 quadruple events.

While the WFCs are imaging instruments, the PCA is not. The PCA's collimators restrict the FOV to 1° FWHM. Especially in crowded regions, such as near the Galactic center, multiple X-ray sources may be in the FOV. For the sources in Table 1, we check the RXTE ASM light curves for any nearby bright X-ray sources that were active at the time of PCA burst observations. This is the case for 2S 1742-294 and SAX J1747.0-2853. Those bursts, for which we cannot reliably measure the persistent flux, are excluded from our studies.

The problem is small for SAX J1747.0-2853, because most of its bursts were observed with the WFCs, and we have a reliable measurement of the persistent flux for all three SWT bursts. For 2S 1742-294 the problem of source confusion plays a role for 61 bursts, including 12 out of 16 SWT bursts. Most of these bursts, including all SWT bursts, occur in the time interval MJD 52175–52195. The persistent flux as measured with the WFCs for bursts from that period varies by less than 10%. We assign the mean WFC persistent flux to those PCA bursts.

We define the recurrence time as the time since the previous burst from the same source in the catalog. Due to the frequent data gaps (Section 2.3), we must keep in mind that these are upper limits. Performing Monte Carlo simulations, we investigate the effect of the data gaps on the number of observed SWT and LWT bursts.

We generate a series of 10⁶ burst occurrence times and check which bursts fall in data gaps. We use EXO 0748-676 as a template: we generate LWT and SWT bursts with an SWT fraction of 30%; we use the mean LWT and SWT recurrence times 3.0 hr and 12.7 minutes, respectively (Boirin et al. 2007); we position the bursts in time following a Gaussian distribution around the LWT or SWT t_recur, with a width of 16% of either t_recur (mean variability in persistent flux of a series of persistent sources; Keek et al. 2006) to model variations in the mass accretion rate. To check which of these bursts would be observed in the presence of data gaps, we assume a 96 minute satellite orbit, containing a 36 minute data gap due to Earth occultation. The presence and duration of data gaps due to the SAA depends on the position of the source and the satellite at the time of the observation. We model SAA data gaps by placing a 20 minute gap at a random phase of each orbit.

Only 49% of the generated bursts is "observed", the rest coincide with a data gap. When a burst is missed, the recurrence time of the next burst, as seen from the previously detected burst, is incorrectly found to be longer: in the distribution of observed recurrence times a long tail of bursts is present at longer t_recur than present in the original distribution (Figure 1). There are also bursts in between the Gaussian peaks of SWT and LWT bursts, but their number is less than 10% of the total number of SWT bursts. Because most of these bursts have t_recur < 60 minutes, we still consider them as SWT bursts.

Zoom In Zoom Out Reset image size

The fraction of bursts that are SWT bursts, is reduced when one or more bursts in a multiple-burst event occur during a data gap. While we start our simulations with an SWT fraction of 30%, the observed distribution has a fraction of 20%. We repeat the simulations with different values of the SWT t_recur. The total fraction of detected bursts remains the same, but the SWT fraction drops from 30% to 10% for increasing t_recur, until t_recur exceeds the duration of the Earth occultation data gap (Figure 2).

Zoom In Zoom Out Reset image size

Repeating the simulations with different durations of the Earth-occultation data gap, the SWT fraction drops by only a few percent for longer data gaps, until the fraction quickly goes to 0, when an SWT recurrence time no longer fits in the observed part of the orbit (Figure 3).

Zoom In Zoom Out Reset image size

A similar decrease of the SWT fraction is expected if the duration of the observation is less than the SWT recurrence time. While the average exposure times of both the PCA and the WFCs exceed 1 hr, a substantial part of the observations had a shorter recurrence time: 19% of the WFC exposures and 66% of the PCA exposures were shorter than 1 hr.

The instruments we use have different detection limits. The WFCs had a substantially larger FOV than the PCA, which results in a higher background level. Furthermore, the PCA has a 46 times larger collecting area than each WFC. Consequently, we are able to find fainter bursts in PCA data than in WFC data (Figure 4). This is especially important for the SWT bursts, as they have been found to be on average fainter than the LWT bursts (e.g., Boirin et al. 2007). In the PCA data, we find SWT bursts with peak flux F_peak as low as 1.6 × 10⁻¹⁰ erg cm⁻² s⁻¹, while in the WFC data the faintest SWT burst has F_peak = 3.6 × 10⁻⁹ erg cm⁻² s⁻¹. As a result, we find many more SWT bursts with the PCA: for the PCA we find 76 SWT bursts out of a total of 910 bursts, and for the WFCs we find 14 SWT bursts out of 1560 bursts.

Zoom In Zoom Out Reset image size

We plot for all bursts the recurrence time t_recur as a function of the persistent luminosity L_pers (Figure 5). While most bursts have a recurrence time of at least several hours, there is also a group of SWT bursts with t_recur < 1 hr. There is an intrinsic spread in t_recur due to, for example, variations in the mass accretion rate, or variations in the temperature in the neutron star envelope. We investigate whether the short recurrence times can be explained as the tail of the distribution of the long recurrence times. For this distribution we assume a Gaussian, even though it is not certain whether this is correct far from the mean. The data gaps modify the observed distribution, especially toward longer t_recur (Section 3.3). The leading part of the Gaussian, however, is not modified substantially, apart from the overall lower number of observed bursts due to the lower net exposure time (Figure 1). We fit a Gaussian to the distribution of recurrence times between 1 and 3 hr with the center fixed at 3 hr. Extrapolating the best fit toward shorter t_recur, we predict 5.6 SWT bursts. The Poisson probability for the observed number of SWT bursts of 76, is negligibly small (P ≲ 10⁻¹⁰). Therefore, the short recurrence times follow a separate distribution.

Zoom In Zoom Out Reset image size

There is a separation between bursts with short (≲0.5 hr) and long (≳1 hr) recurrence times. Above L_pers ≳ 6 × 10³⁶ erg s⁻¹, however, there are some bursts that have recurrence times of 30 to 60 minutes. Comparing the recurrence time distributions of SWT bursts (t_recur < 1 hr) at persistent luminosities below and above L_pers = 6 × 10³⁶ erg s⁻¹, a Kolmogorov–Smirnov (K-S) test yields P = 0.16, which means we can exclude at 84% that both distributions are the same. This is not a strong constraint, mainly due to the small number of bursts with L_pers < 6 × 10³⁶ erg s⁻¹. It is, however, consistent with the behavior of EXO 0748-676 during EXOSAT, XMM-Newton, and Chandra observations, that resulted in relatively large data sets, where SWT bursts with recurrence times exceeding 30 minutes only occurred when the persistent flux was larger (Gold 1968; Gottwald et al. 1987b; Boirin et al. 2007; Appendix).

There are SWT bursts at all values of L_pers where LWT bursts are observed, with the possible exception of L_pers ≳ 3 × 10³⁷ erg s⁻¹, although this may be a statistical effect due to the lower number of bursts.

The α-parameter is defined as the ratio of the persistent fluence between bursts and the burst fluence. Assuming a burst fluence of 2.2 × 10³⁹ erg—the average fluence of MINBAR single bursts from hydrogen-rich accretors—we draw lines of constant α; α ≃ 40 is a typical value for many bursters, while α ≃ 1000 is observed for superbursters (e.g., in't Zand et al. 2003). The effective α-value for the SWT bursts is far below α = 40, which is the expected value for thermonuclear ignition of mixed hydrogen/helium fuel, highlighting the requirement for ignition of unburned fuel left-over from the previous burst.

We find the shortest recurrence time reported so far ⁴: 3.8 minutes for a double burst from 4U 1705-44, detected with the WFCs at MJD 51233.89.

We use the persistent luminosity L_pers as a measure of the mass accretion rate (Section 2.5). A K-S test finds that the distributions of all SWT and LWT as a function of L_pers are compatible (P = 0.10; Figure 6): there are multiple-burst events at all mass accretion rates where normal bursts occur. This does not hold, however, for all individual sources. We investigate a few frequent bursters more closely. For EXO 0748-676, the distributions of single and multiple bursts are compatible (P = 0.73); 4U 1636-53 and 2S 1742-294 exhibit multiple bursts only in a small L_pers interval, while single bursts occur in a wider range of L_pers. The small L_pers intervals for these two sources do not seem to coincide. The uncertainty in the luminosity, however, is large (Section 2.5), so the intervals may still be consistent.

Zoom In Zoom Out Reset image size

We find SWT bursts for only 15 of the 44 hydrogen-rich accretors. For most of the sources we can attribute the lack of SWT bursts to the low number of bursts detected per source. There are, however, two bursters, KS 1731-260 and GS 1826-24, from which we have detected over 300 LWT bursts per source, but no SWT bursts.

The position in so-called color–color diagrams, S_Z, is regarded as a tracer of the mass accretion rate (Hasinger & van der Klis 1989). We compared the distribution of S_Z for LWT and SWT bursts observed with the PCA from eight sources for which S_Z is well defined: 4U 1608-522, 4U 1636-536, 4U 1702-429, 4U 1705-44, 4U 1728-34, KS 1731-260, Aql X-1, and XTE J2123-058, omitting 4U 1746-37 as explained in Section 3.1 (Galloway et al. 2008). While LWT bursts have associated S_Z values of up to 2.8, SWT bursts all have S_Z ≲ 2. Therefore, we find that SWT bursts are restricted to the so-called island state, while LWT bursts also occur in the "banana" branch. A K-S test yields P ≃ 10⁻³, confirming that the S_Z distributions for LWT and SWT bursts are different. Most of the SWT bursts from the frequent burster 4U 1636-53 occurred with 1.5 ≲ S_Z ≲ 2.0. KS 1731-260 exhibits only a few LWT bursts in that range. This suggests that SWT bursts occur mainly in a small S_Z interval, and that the lack of SWT bursts from the latter source is caused by the low number of observed bursts in that range. Note that we observe SWT bursts with S_Z as low as 0.8, so the interval is not the same for all sources.

We consider 2415 bursts from hydrogen-accreting sources. 76 have a short recurrence time: the overall SWT fraction is (3.1 ± 0.4)%. The 1σ uncertainty is derived from the Poisson uncertainties in the number of (SWT) bursts. As a function of persistent luminosity there is some variation in the SWT fraction, but there is no clear trend (Figure 7). The weighted mean of the SWT fraction in the range of L_pers where SWT bursts are observed is (2.3 ± 0.3)% for all hydrogen-rich accretors, (13 ± 4)% for 4U 1636-536, (16 ± 4)% for 2S 1742-294, and (6 ± 2)% for EXO 0748-676.

Zoom In Zoom Out Reset image size

We compare these fractions to XMM-Newton and Chandra observations of EXO 0748-676. In 2003, the XMM-Newton EPIC PN observed double and triple bursts from EXO 0748-676 with an SWT fraction of (32 ± 7)% (Boirin et al. 2007). Homan et al. (2003) find in XMM-Newton EPIC PN and MOS observations from 2000 and 2001, four single and four double bursts, which result in an SWT fraction of (33 ± 19)%. Chandra ACIS-S observations from 2001 and 2003 exhibit 41 bursts with an SWT fraction of (27 ± 9)% (see the Appendix). The weighted mean of these rates is (30 ± 5)%. An important difference in the data of on the one hand XMM-Newton and Chandra, and on the other hand RXTE and BeppoSAX, is the frequent data gaps in observations of the latter observatories. From Monte Carlo simulations we found that data gaps reduce an SWT fraction of 30% to 20% (Section 3.3). This is significantly higher than the (6 ± 2)% we obtain from MINBAR. We repeat the simulations for 4U 1636-536 and 2S 1742-294, using the mean SWT recurrence times from MINBAR: 16.2 minutes and 20.5 minutes, respectively. The obtained SWT fractions, respectively 18% and 16%, are consistent within 1.3σ with the fractions from MINBAR.

The discrepancy for EXO 0748-676 may arise because of the fact that the WFCs are less sensitive to fainter bursts than the PCA or the instruments on XMM-Newton and Chandra. Taking only the PCA bursts into account, we find SWT fractions of (11 ± 6)% for EXO 0748-676, (13 ± 4)% for 4U 1636-53, and (23 ± 6)% for 2S 1742-294, all of which are within 1.5σ from the fractions found from the Monte Carlo simulations.

Two frequent bursters exhibit no SWT bursts: KS 1731-26 and GS 1826-24. Combining the number of LWT bursts observed from these sources, we derive an upper limit to the SWT fraction of 0.14%. This is over 20 times smaller than the SWT fraction we find for all hydrogen-accreting sources combined.

From time-resolved spectral analysis of the bursts, we obtain the blackbody temperature and the burst energetics. The peak temperature of the first bursts in multiple-burst events is on average higher than the peak temperature of the SWT bursts (Figure 8). A K-S test shows that the temperature distributions for single bursts and first bursts are not compatible (P ≃ 10⁻¹²).

Zoom In Zoom Out Reset image size

We compare the peak luminosity and the fluence of single bursts to those in multiple-burst events (Figures 9 and 10). The SWT bursts have on average a lower peak luminosity and a lower fluence. The energetics of the first bursts does not follow the same distributions as the single bursts (P ≲ 10⁻²). By adding the fluence of all bursts in a multiple-burst event, we calculate the total event fluence (Figure 11). Multiple-burst events are on average more energetic than single burst events, but do not have a higher fluence than the most energetic single bursts.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Summarizing, SWT bursts are on average weaker and cooler than LWT bursts, but the combined fluence in multiple-burst events is on average 8% higher than the fluence of single-burst events.

The two component exponential provides a good fit to many bursts. If the two-component decay does not provide a significantly better fit than the one-component, we use the latter. We compare the longest decay timescales of all bursts in Figure 12. On average, the SWT bursts decay faster than the other bursts. K-S tests show that all distributions are incompatible (P ≲ 10⁻²).

Zoom In Zoom Out Reset image size

The spin frequency ν_spin of an accreting neutron star is measured in observations of accretion-powered pulsations or burst oscillations. Both mechanisms are thought to arise from hotter and, hence, brighter spots on the surface rotating in and out of view. Currently ν_spin is known for 25 accreting neutron stars, 19 of which are bursters (e.g., Galloway 2008). Among them are five sources that exhibit SWT bursts (Table 1). They are concentrated toward the high-frequency part of the distribution for all bursting sources (Figure 13). Since we only have five multiple-bursting sources with a known spin frequency, we cannot exclude that this bias is the result of the small sample.

Zoom In Zoom Out Reset image size

There could be a selection effect: sources with a higher mass accretion rate accrete more angular momentum, causing them to spin up faster. Furthermore, their burst rate is higher, making it easier to detect a rare multiple-burst event. We check the MINBAR catalog for the number of bursts from these sources as a function of the spin frequency (Figure 13). There is roughly an equal number of bursts observed at higher and at lower ν_spin, so the selection effect is not present.

There are a few hydrogen-accreting sources of which we detected a large number of bursts, but no SWT bursts (Section 3.6). One of these sources, KS 1731-260, is known to have a large spin frequency of ν_spin = 524 Hz (Smith et al. 1997).

To illustrate the properties of LWT and SWT bursts, of which we have shown the distributions using a large number of bursts from the catalog, we consider the quadruple burst from 4U 1636-53 (Figure 14). The four bursts occurred within 54 minutes, and the time between the burst onsets is 18.2 minutes, 17.9 minutes, and 16.8 minutes, respectively. As indicated in Figure 14, the first burst has by far the longest decay time τ. The first burst has a peak flux and fluence that is over seven times larger than any of the three SWT bursts. The peak blackbody temperature (kT) of the four bursts is, respectively, (1.67 ± 0.02) keV, (1.06 ± 0.06) keV, (1.51 ± 0.06) keV, and (1.50 ± 0.04) keV: again the first burst has the highest value. The combined net burst fluence of the quadruple event is (2.93 ± 0.05) 10³⁹erg, which is 35% higher than the average fluence of single bursts from this source and 27% higher than the fluence of the first burst from the quadruplet. This means that at least 27% of the available fuel did not burn in the initial burst.

Zoom In Zoom Out Reset image size

We perform time-resolved spectroscopy of the bursts, and find that SWT bursts are on average less bright and reach a lower blackbody temperature at the peak than the LWT bursts. The fluence of SWT bursts is on average lower, but the combined bursts in a multiple-burst event are as energetic as the most energetic single bursts. This is in agreement with the XMM-Newton observations of EXO 0748-676 analyzed by Boirin et al. (2007). In contrast to that investigation, however, we find that the distributions of these quantities for single and for first bursts of multiple-burst events are not compatible according to K-S tests. It is possible that our improved statistics allows us to see a disparity that previously went unnoticed.

Several ideas have been put forward to explain SWT bursts in an attempt to answer the two main questions: how to preserve fuel during a burst for the next burst, and how to reignite this fuel on a timescale of approximately 10 minutes. Subsequent bursts with short recurrence time may take place in different regions of the neutron star surface. The accreted matter may be confined by a magnetic dipole field to the poles of the neutron star, or perhaps the burning front of a burst is stalled at the equator if the inflow of matter from the accretion disk is particularly strong there. This would provide an explanation for double bursts, but the triple and quadruple bursts that we observe would require a more complicated configuration of the magnetic field. Furthermore, Boirin et al. (2007) find for EXO 0748-676 that there is no evidence for a difference in the X-ray emitting region during the different bursts of multiple-burst events. Also, they find indications that SWT bursts burn a fuel mixture with a lower hydrogen content, which would not be the case if different regions of pristine accreted material are burned. We, therefore, favor the scenario where SWT bursts take place in different layers on top of each other (Fujimoto et al. 1987). For this to work, the thermonuclear burning during the flash must be halted before the hydrogen and helium is depleted.

We observe no SWT bursts from any of the 16 (candidate) ultra-compact sources from which in total 229 bursts have been observed with the PCA and WFCs. For this reason, we excluded these sources from our analyses. For the hydrogen-accreting sources we found that a fraction of 3.1% of all bursts are SWT bursts. If we assume the same SWT fraction for the most frequently bursting confirmed UCXB, 4U 1820-303, we expect 1.7 SWT bursts out of the 54 bursts observed by the PCA and WFCs. The Poisson probability of detecting no SWT bursts when expecting 1.7, is 0.18. Taking into account the bursts from all confirmed and candidate UCXBs, we expect 7 SWT bursts, and the probability of a non-detection is less then 10⁻³.

Based on its bursting behavior, 4U 1728-34 is a suspected UCXB (Galloway et al. 2008). If we include the 543 observed by the PCA and WFCs from this source, the expected number of SWT bursts is 23, and the probability of detecting none is 10⁻¹⁰.

No SWT bursts are observed from UCXBs, but only from sources that are thought to accrete hydrogen-rich matter. This suggests that the nuclear burning processes involving hydrogen, i.e., the hot CNO cycle, the αp-process, and the rp-process, are important for creating SWT bursts. The rp-process is a series of proton captures and β-decays, that creates heavy isotopes with mass numbers up to approximately 100 (Schatz et al. 2001). In this reaction chain there might be a nuclear waiting point with the correct timescale to interrupt and reignite the thermonuclear burning, for example the timescale for spontaneous β-decay of an isotope. We find, however, a broad distribution of short recurrence times t_recur (Figure 5), which argues against a single waiting point in the reaction chain (see also Boirin et al. 2007). Note that we do not detect SWT bursts from all hydrogen-rich accretors, the two frequent bursters KS 1731-26 and GS 1826-24 being the best examples. This means that merely accreting hydrogen is not enough to produce SWT bursts.

The decay profile of an X-ray burst is shaped by two processes. First there is radiative cooling on a thermal timescale. For normal bursts, which ignite at a typical column depth of y ≃ 10⁸ g cm², this timescale is τ_therm ≃ 10 s. A second process, that slows down the decay, is prolonged thermonuclear burning through the rp-process, which lasts up to approximately 100 s (Schatz et al. 2001). For EXO 0748-676 Boirin et al. (2007) found SWT bursts to lack the second slower decay component, while the first bursts clearly exhibit a two-component exponential decay. We confirm that this holds true for the other sources with SWT bursts as well. This supports the conclusion by Boirin et al. (2007) that follow-up bursts must occur in a layer with a significantly reduced hydrogen content.

in't Zand et al. (2009) found observations where the burst decay can be followed for several thousands of seconds. They explain the long tail as due to the cooling of a deeper layer below the bursting layer, that is heated by the burst. One of these long tails is detected for the first burst in a triple event of EXO 0748-676. The tail continues to decay uninterrupted while the second and third bursts occur. This is consistent with the idea that SWT bursts occur in a layer above the ignition depth where the first burst occurs. Taking into account that SWT bursts are less energetic, the deeper layer would not be heated substantially by the SWT bursts and continues to cool.

SWT bursts are observed over the entire range of mass accretion rates $\dot{M}$ where LWT bursts are observed. For some individual sources, however, the SWT bursts occur in a smaller $\dot{M}$ interval than LWT bursts. This is supported by the position in the color–color diagram where SWT bursts are observed (Section 3.6; Galloway et al. 2008). Other frequent bursters exhibit no SWT bursts at all, even though the ranges of $\dot{M}$ we observe from sources with and without SWT bursts overlap. Because of the large uncertainty in converting flux to accretion rate, the precise overlap is uncertain.

At low accretion rates, SWT recurrence times t_recur are mostly restricted to 3.8 minutes ≲ t_recur ≲ 40 minutes. Above approximately $0.05\,{\dot{M}_{\mathrm{Edd}}}$, where the Eddington limited mass accretion rate ${\dot{M}}_{\mathrm{Edd}}$ corresponds to a persistent luminosity of L_Edd = 2 × 10³⁸ erg s⁻¹ for hydrogen-accreting sources, recurrence times occur also in the range 40 minutes ≲ t_recur ≲ 60 minutes. At $0.05\,{\dot{M}_{\mathrm{Edd}}}$; a transition between two bursts regimes is predicted by Fujimoto et al. (1981; see also Bildsten 1998). For lower accretion rates all accreted hydrogen burns in a stable manner, and the burst ignites in a hydrogen-poor layer. At higher rates there is no time to burn all hydrogen, and the burst ignites in a layer containing a substantial fraction of both hydrogen and helium. It may be that the latter regime allows for short recurrence times as long as an hour, while the former regime does not.

The spin frequency ν_spin is not known for most accreting neutron stars, as it requires the observation of X-ray pulsations or burst oscillations (e.g., Galloway 2008). For five sources with short recurrence times ν_spin is known: all five are fast spinning neutron stars with ν_spin ≳ 500 Hz (Table 1). The fast rotation could be required for the occurrence of multiple-burst events. It induces rotational instabilities, for example shear instabilities (e.g., Fujimoto 1988), and instabilities due to a rotationally induced magnetic field (Spruit 2002), that mix the neutron star envelope on a timescale of approximately ten minutes (Piro & Bildsten 2007; Keek et al. 2009). If the thermonuclear burning during a flash is halted before it reaches higher layers, the hydrogen and helium in those layers will be mixed down. On a 10 minute timescale it reaches the depth where temperature and density are sufficiently high to create the thermonuclear runaway for the next burst.

At accretion rates higher than $0.05\,\dot{M}_{\mathrm{Edd}}$, we find bursts with short recurrence times as long as an hour. We mentioned that this may be related to the transition to a different burst regime. The timescale for rotational mixing depends strongly on the thermal and compositional profile of the neutron star envelope (e.g., Heger et al. 2000 for the case of massive stars), which may vary for different burning regimes or even different bursts. This could provide an explanation for the spread in the observed recurrence times. Further theoretical study is necessary to better understand this.

The occurrence of multiple-burst events in sources with high rotation rates has consequences for the hypothesis that strong magnetic fields at the neutron star surface contain accreted matter at the poles. This would explain multiple bursts as caused by the burning of different magnetically confined patches at the poles. The presence of a strong magnetic field, however, would allow for the transportation of angular momentum away from the neutron star, causing it to spin slower. The observations of short recurrence time bursts preferentially at high ν_spin seems in contradiction with this, which disfavors the magnetic-confinement scenario.

KS 1731-260 spins at a high frequency of 524 Hz, accreted hydrogen-rich material, and exhibited many bursts (369 in MINBAR). No short recurrence times were observed. Therefore, while a high rotation rate may support the occurrence of SWT bursts, it is not possible to discriminate between sources with and without SWT bursts based on this property alone. Possibly a combination of fast rotation and a mass accretion rate within a certain range (see previous section) are required for short recurrence times.

We investigate the SWT fraction: the number of bursts that have a short recurrence time with respect to the total number of observed bursts. We determine this fraction, at the persistent luminosities where SWT bursts are observed, for three frequent bursters with SWT bursts: EXO 0748-676, 4U 1636-53, and 2S 1742-294. XMM-Newton and Chandra observations of EXO 0748-676 find an SWT fraction of (30 ± 5)%. Our burst sample is obtained from RXTE PCA and BeppoSAX WFC observations, which contain data gaps due to Earth occultations and due to the SAA. Monte Carlo simulations show that the data gaps reduce an SWT fraction of 30% to 20%. An additional problem is the fact that the WFCs are less sensitive to fainter bursts than the PCA or the instruments on XMM-Newton and Chandra. Especially for EXO 0748-676 we find a much lower SWT fraction than from the XMM and Chandra observations. Taking only the PCA bursts into account, we find SWT fractions of (11 ± 6)% for EXO 0748-676, (13 ± 4)% for 4U 1636-53, and (23 ± 6)% for 2S 1742-294, all of which are within 1.5σ from the SWT fractions we obtain from Monte Carlo simulations, with an initial SWT fraction of 30%. Therefore, in the range of mass accretion rates where SWT bursts occur, approximately 30% of the bursts have a short recurrence time.