X-ray burst induced spectral variability in 4U 1728–34^††thanks: Based on observations with INTEGRAL, an ESA project with instruments and science data centre funded by ESA member states (especially the PI countries: Denmark, France, Germany, Italy, Switzerland, Spain) and with the participation of Russia and the USA.

4U 1728–34, often referred to as the “slow burster”, is a persistent “atoll” source towards the direction of the Galactic center, at a distance of roughly 5.2 kpc (Galloway et al., 2008). The first X-ray bursts from 4U 1728–34 were detected already by the SAS-3 satellite (Hoffman et al., 1976). Since then practically all X-ray observatories have observed X-ray bursts from the source.

The Galactic hydrogen column density towards 4U 1728–34 is high, $N_{\text{H}}=2.6\times {10}^{22}c{m}^{-2}$ (Worpel et al., 2013), and the source has a faint 15th Ks magnitude near-infrared counterpart (Marti et al., 1998). There are hints of about 11 minute periodicity that is likely due to binary orbital modulations, making 4U 1728–34 a candidate ultra-compact X-ray binary (Galloway et al., 2010). The neutron star spin frequency is measured to be about 363 Hz from X-ray burst oscillations (Strohmayer et al., 1996).

RXTE/PCA observations have shown that 4U 1728–34 undergoes the typical hysteresis pattern between hard and soft spectral states (e.g., Muñoz-Darias et al. 2014). In the hard state the X-ray bursts are almost exclusively Eddington-limited photospheric radius expansion bursts (Galloway et al., 2008; Zhang et al., 2016), although the peak fluxes show a weak dependency with the properties of the persistent emission (Galloway et al., 2003).

We have analyzed all the available archival X-ray data of 4U 1728–34 spanning from the INTEGRAL launch in 2002, until the end of 2014, thus covering 12 years. We used data from the JEM-X instruments that are sensitive in the 3–35 keV range with an angular resolution of $3\text{arcmin}$ (Lund et al., 2003) as well as IBIS/ISGRI (sensitive in 15 keV to 10 MeV range, with $12\text{arcmin}$ angular resolution; Ubertini et al. 2003). As JEM-X1 was operational almost 10 years out of the 12 we analyzed, we extracted spectral data from JEM-X1 and used JEM-X2 only to fill the gaps in the long term light curve. We limited our analysis to observations where the off-axis angle between the source location and spacecraft pointing was less than 4 degrees. The selection criteria guaranteed that 1) the measured fluxes and hardness ratios were not affected by “ghosts” towards the edges of the fully coded field-of-view (FoV) of JEM-X that may contaminate the light curves and images, and 2) 4U 1728–34 was always within the fully coded FoV in IBIS/ISGRI. This allowed us to accumulate about 2.7 Ms of dead time corrected exposure on 4U 1728–34. The data were reduced using standard procedures with the INTEGRAL Offline Science Analysis (OSA) version 10.2, provided by the ISDC.¹¹1ISDC Data Centre for Astrophysics, http://www.isdc.unige.ch/

The X-ray bursts were identified using 1 s binned JEM-X light curves in the 3–25 keV band. We first computed the mean and standard deviation of the source count rate within one “science window” (typically 30 min to one hour duration). When the rate exceeded 6$\sigma$ of the persistent level we identified the potential onset of an X-ray burst. The burst detection was confirmed by fitting the burst decay using an exponential function, and extracting the image of the field within a time interval restricted to the burst duration, to discard contamination to the source light curve by other sources in the FoV. The burst search resulted in a sample of 409 X-ray bursts.²²2We note that part of this work is also fed into a larger type-I X-ray burst database, MINBAR, see http://burst.sci.monash.edu/minbar 4U 1728–34 produces predominantly bright He-rich bursts that typically reach the Eddington limit (Galloway et al., 2008), and thus we have likely not missed any bursts that occurred during the analyzed science windows. The burst detection was therefore rather straightforward given that the peak count rate during bursts were always roughly 350 cps, more than an order of magnitude above the persistent emission level. We identified the burst onset time as the first time bin that exceeded 10 per cent of the burst peak flux the 1 s JEM-X light curves. In the subsequent analysis we use this onset value also for extracting the averaged X-ray burst spectra from the JEM-X1 and IBIS/ISGRI instruments.

Because the X-ray burst peak fluxes are similar and the bursts display similar cooling time scales (particularly in the hard state, see Galloway et al. 2003; Zhang et al. 2016), we can stack the bursts together to extract a spectrum of increased S/N ratio at energies above $\sim 40$ keV. An averaged burst spectrum was accumulated from the individual burst spectra, each integrated over a 9 s time interval (1–10 s from the burst onset). This integration time was selected to ensure that we exclude the burst rise and cover the burst peak, allowing that enough counts are collected to perform JEM-X and ISGRI spectral extraction. The stacked JEM-X1 and IBIS/ISGRI X-ray burst light curves and the spectral extraction interval are shown in Fig. 1 for the bursts that occurred in the hard state.

To characterize the persistent emission we extracted the source light curve in the 3–8 and 8–25 keV bands, using time units of one science window. We computed the hardness ratios between these two bands, to determine the source spectral state classification. To avoid burst contribution to the light curve, we always excluded a 300 s interval around the X-ray burst in those science windows where a burst was detected. In addition, we discarded five observations where the persistent 3–25 keV flux was below 5 mCrab. This was done to ensure that 4U 1728–34 was significantly detected in both 3–8 and 8–25 keV bands.

During the 12 years of INTEGRAL observations the persistent (accretion) emission level of 4U 1728–34 has clearly changed (see Fig. 2). In the first 6 years – from 2003 through 2008 – the 3–25 keV persistent emission varied from a few mCrab up to 40 mCrab on time-scales of weeks. In contrast, from 2009 up until 2013, the persistent level was consistently at around 10 mCrab, with only modest fluctuations in spectral hardness. Only during the visibility season of autumn 2014, 4U 1728–34 started to exhibit significantly higher persistent fluxes again.

To characterize the persistent emission, we computed a hardness-intensity diagram (HID) that is shown in Fig. 3. The hardness is defined as the ratio between 8–25 keV and 3–8 keV fluxes, such that hardness of unity corresponds to a Crab-like spectrum. The total flux is computed in the 3–25 keV band. The HID is somewhat similar to Falanga et al. (2006, fig. 3), who analyzed the X-ray bursts and persistent emission during 2003–2004. With 12 years of data, we have now accumulated an order of magnitude more data to study the spectral properties of 4U 1728–34 up to higher energies.

We divided the observations into 4 groups based on the HID. Groups 1, 2 and 3 represent the high-, intermediate- and low flux soft states (SS1, SS2, and SS3 hereafter); and the group 4 corresponds to the hard state HS (“island state”). The SS1 group have 3–25 keV fluxes above 25 mCrab, in the SS2 group the flux is in the 15–25 mCrab range and the SS3 group have fluxes below 15 mCrab. The HS and SS3 are easily distinguished using the simultaneous 25–40 keV band ISGRI flux measurement. The ISGRI count rate histogram has a peak centered around zero (where the SS1 and SS2 observations are located), and another one around 10 cps. We therefore define the HS bursts as those where the ISGRI persistent count rate is higher than 5 cps, and SS3 where the rate is less than 3 cps. The bursts where the ISGRI count rate was 3–5 cps are considered ambiguous, and are not put to either group (they are shown with gray symbols in Figs 2 and 3).

The energy spectra of the persistent emission for the 4 separate groups are shown in Fig. 4, and the best fitting parameters are given in Table 1. The HS spectrum, shown in Fig. 4a, stands out with significantly detected emission up to $\sim$200 keV. It can be described by a combination of several two component xspec models (see, e.g., Tarana et al. 2011) that are multiplied by the tbabs absorption model (Wilms et al., 2000), with the hydrogen column density fixed to the interstellar value of $N_{\text{H}}=2.6\times {10}^{22}{\text{cm}}^{-2}$ (Worpel et al., 2013). One possible model is thermal Comptonization (e.g., nthcomp; Zdziarski et al. 1996; Życki et al. 1999) plus a powerlaw tail or, alternatively, the powerlaw tail can be replaced by a reflection component (e.g., reflect; Magdziarz & Zdziarski 1995). Statistically neither of these models can be rejected, although in the better fitting reflection model we find both the reflection fraction Refl $\sim$ 1 and the electron temperature $T_{\text{e}}>255$ keV unusually high for a NS in the hard state.

In the soft state, the soft X-ray spectra (and timing properties) of most NS-LMXB can be described by a two-component dual-thermal model, where the cooler component is emitted by the accretion disc and the hotter one by the spreading layer (Gilfanov et al., 2003; Revnivtsev & Gilfanov, 2006; Revnivtsev et al., 2013). A hard X-ray tail can be also detected in the soft state, (see e.g., Asai et al. 1994 and discussion below). For this reason we fitted the soft state spectrum with a model tbabs $\times$ (bb $+$ diskbb $+$ powerlaw). The soft state spectra in the three groups shown in Fig. 4b have similar shapes, while they are clearly different from the HS spectrum. The only significant difference between the SS groups is the intensity of the thermal components, likely set by a factor of 3 variation in the mass accretion rate between SS1 and SS3. The accumulation of 12 years of data allowed us to detect, for the first time, a significant hard X-ray tail up to $\sim$80 keV in SS spectra of 4U 1728–34 (the powerlaw component). While tail dominates the X-ray emission above $\sim$40 keV, the powerlaw index can not be constrained and it was fixed to the best-fitting value found for the hard state spectrum. We interestingly see that the tail does not seem to be variable while the soft X-ray flux changes in between the groups.

We detected 123 X-ray bursts in the hard state simultaneously with JEMX-1 and ISGRI. By stacking the X-ray burst spectra in the 1-10 second intervals from the bursts onset time (see Fig. 1), we could accumulate enough exposure time to detect the Comptonized emission from 4U 1728–34 up to $\sim$80 keV and measure if there are any significant burst-induced changes in the hard X-ray tail. The average X-ray burst and persistent emission spectra during the hard state are shown in Fig. 5. In the observed spectra, shown in count space in Fig. 5a, we see a factor of three drop of the burst emission in the 40–80 keV band with respect to the persistent emission; the significance of the flux drop is about 3.4$\sigma$ in the 40–50 keV band and 1.8$\sigma$ in the 50–80 keV band.

We modeled the burst-averaged spectrum using an absorbed black body plus the nthcomp and powerlaw components responsible for the persistent emission. First, we held the persistent emission parameters fixed at the values found excluding the burst intervals. We find a mean blackbody temperature of $T_{\text{bb}}=2.59\pm 0.03$ keV and an average flux of $F_{\text{bb}}=[3.63\pm 0.10]\times {10}^{-8}ergc{m}^{-2}{s}^{-1}$ (3–20 keV band). The burst temperature is lower and the flux is roughly 50 per cent of the average peak flux measured by RXTE/PCA instrument (Galloway et al., 2008), which is reasonable as our burst spectrum covers both the Eddington limited phase and the beginning of the cooling phase (see Fig. 1) during which the black body temperature and radius change significantly. From Fig. 5b it is evident that the burst spectrum drops below the persistent emission level above $\sim$35 keV. The detection in the 40–50 keV band is significant (but marginal in the 50–80 keV range) even if the blackbody spectrum drops off exponentially, indicating that the persistent spectrum still produces the hard X-ray tail, only its intensity diminishes during the burst. The spectral fit is extremely poor though, ${\chi }_{\text{red}}^2\sim 6$, partly because of the flux drop above 40 keV, but also due to the residuals below 30 keV. An important factor is also the fact that we needed to extract the spectrum combining 123 spectra of 9 s interval each, during which the black body temperature is bound to be slightly variable, which may partly be causing the poor fit.

We obviously can not add several new model parameters, but we note that the data above 40 keV is consistent with the powerlaw component. By assuming that the powerlaw component remains constant, and that the nthcomp component disappears during the burst above the 40 keV range, the fit improves slightly and we can estimate the high energy flux loss during the burst. The estimated flux loss is roughly $F_{\text{loss}}\sim 3.6\times {10}^{-10}ergc{m}^{-2}{s}^{-1}$ in the $40-200$ keV band, which is one per cent of the measured mean burst flux. On the other hand, rather than removing the nthcomp component, we also allowed the electron temperature and powerlaw index to vary during the burst (compare the light red and purple dotted lines in Fig. 5). We find that the fit is improved significantly, to ${\chi }_{\text{red}}^2\approx 1.15$ (for 6 degrees of freedom), if during the X-ray burst the nthcomp electron temperature cools down to $T_{\text{e}}=3.5\pm 0.2$ keV and the photon index decreases to $\Gamma ={1.15}_{-0.03}^{+0.04}$ (powerlaw component was left unchanged). In this case, the burst black body temperature and flux are significantly lower, $T_{\text{bb}}={1.95}_{-0.14}^{+0.13}$ and $F_{\text{bb}}=[2.3\pm 0.3]\times {10}^{-8}ergc{m}^{-2}{s}^{-1}$ (3–20 keV band) compared to the standard black body fit with non-variable persistent emission components.