3 Observations and analysis

For our investigation we analysed data obtained by the Proportional Counter Array (PCA) onboard Rossi X-ray Timing Explorer (RXTE) and the Wide Field Cameras (WFCs) onboard the "Satellite per Astronomia X'' (BeppoSAX). RXTE and BeppoSAX have been operational for more than five years, and have observed most of the bright globular cluster X-ray sources. We complement these with results reported in the literature.

3.1 RXTE/PCA

The PCA (2-60 keV; Bradt et al. 1993) combines a large collecting area (maximum of $\simeq$6500 cm²) with high time resolution (down to $\mu$s). This is ideal to study spectral variations on short time scales, such as which occur during X-ray bursts. We inspected light curves from the publicly available RXTE database of globular cluster X-ray bursters (up to January 2002, using the RXTE Master Catalog) at 1 s time resolution using the data collected in the STANDARD 1 mode. If more than one X-ray burst from an individual source was found, we analysed the bright X-ray bursts (which presumably reach the highest luminosity and may exhibit photospheric radius expansion).

We (re)analysed the X-ray bursts seen by the RXTE/PCA, all in a similar way, using the latest information available on the response of the instrument at the relevant times. Data were recorded in various modes (apart from the two standard modes) at high time resolution. We used the data from the Burst Catcher (2 ms resolution; 4U 1722-30), Event (either 16, 125 or 500 $\mu$s; MX 0513-40, MXB 1730-335, 4U 1820-30, 4U 2129+12), or GoodXenon (4U 1746-37, H1825-331) modes. The two former modes provide data in 64 channels covering the whole PCA energy range, while the latter provide data in all 256 channels available. The GoodXenon modes data were stored for every 2 s; the high count rates reached during maximum of the X-ray bursts from 4U 1746-37 and H1825-331 therefore resulted in data losses near the end of the 2 s buffers. Spectra accumulated during these data losses were not taken into account. During the X-ray bursts reported here all Proportional Counter Units (PCUs) were on, except for MX 0513-40 (only PCUs 0, 1, 2, 3 on) and 4U 2129+12 (only PCUs 0, 2, 3 on). We created time resolved spectra at 0.25 s resolution throughout the whole X-ray burst. For a uniform analysis and in order to have as many photons as possible we used information from all PCU layers and as many PCUs as possible. The count rate spectra were dead-time corrected and a 1% systematic uncertainty was included. The X-ray bursts seen from GRS 1747-312 (in 't Zand et al. 2002, in preparation) were analysed in a similar way as the other X-ray bursts seen with the RXTE/PCA described here. During the observation of one of these X-ray bursts, used in our sample, only PCUs 0, 2, 3 were on.

 

 

Table 3: Spectral fit results for Crab (pulsar plus nebula) observations, using an absorbed power law (Eq. (2)), for various instruments (for the RXTE/PCA we also give the values for different PCUs combined). Errors on the fit parameters were not always given by other authors; also sometimes $\Gamma$ and N_H were fixed to the "canonical'' values. Although quoted by various authors, we note that the value of $N_H=3 \times 10 ^{21}$ cm^-1 for the "canonical'' spectrum is not derived by Toor & Seward (1974) themselves. Toor & Seward (1974) list various estimates of N_H derived by other authors; the average (no weighting) and the weighted average of these estimates are $2.8 \pm 0.5$ and $2.3 \pm 0.2 \times 10 ^{21}$ cm^-1, respectively. The references are: [1] Toor & Seward (1984), [2] this paper (Sect. 3.5), [3] Wilms et al. (1999), [4] Barr et al. (2000), [5] Christian & Swank (1997), [6] Parmar & Smith (1985), [7] Turner et al. (1989), [8] in 't Zand (1999), [9] Cusumano, G. (2002, private communication). The last column gives the observed X-ray flux, F_X, in 10^-8 erg cm^-2 s^-1in the 3-20 keV energy band, uncorrected for interstellar absorption.

instrument	$\Gamma$	A	NH	commentsa	ref	FX
"canonical''	2.10 $\pm$ 0.03	9.7 $\pm$ 1.0	3		[1]	2.38
RXTE/PCA
PCUs 0,1,2,3	2.119 $\pm$ 0.003	12.2 $\pm$ 0.1	3	7.10	[2]	2.89
PCUs 0,2,3	2.104 $\pm$ 0.003	12.0 $\pm$ 0.1	3	7.10	[2]	2.93
all PCUs	2.130 $\pm$ 0.003	12.8 $\pm$ 0.1	3	7.10	[2]	2.96
all PCUs	2.187	13.3	2.54	2.2.1	[3]	2.75
all PCUs	2.18	13.5	3.3	2.36	[4]	2.82
Einstein/MPC	2.1	9.5	3.45b		[5]	2.13
EXOSAT/ME	2.1	9.53	3		[6]	2.16
Ginga/LAC	2.08 $\pm$ 0.03	9.15 $\pm$ 0.5	3		[7]	2.17
BeppoSAX/WFC #1	2.1	9.77 $\pm$ 0.26	3c		[8]	2.31
BeppoSAX/WFC #2	2.1	9.93 $\pm$ 0.05	3c		[8]	2.35
BeppoSAX/MECSd	2.093 $\pm$ 0.001	9.15 $\pm$ 0.01	3.34 $\pm$ 0.04	Nov. 1998	[9]	2.09

^a Version of response matrices.

^b Value taken from Schattenburg & Canizares (1986).

^c Value of $N_{\rm H}$ was not quoted by the author. We assume here $N_{\rm H} = 3 \times 10 ^{21}$ cm^-1.

^d Spectral fits to Crab observations taken in 2000 and 2001.

3.2 BeppoSAX/WFCs

The WFCs onboard BeppoSAX are two coded aperture cameras (Jager et al. 1997). They point in opposite directions of one another and perpendicular to the Narrow-Field Instruments on the same satellite. The field of view of each WFC is 40 by 40 square degrees full-width to zero response with an angular resolution of about 5 arcmin in each direction. It is ideal to catch fast (seconds to minutes) phenomena at (un)expected places in the X-ray sky, such as X-ray bursts. Although it has a much lower collecting area (factor of $\sim$50 less than the RXTE/PCA), it has a much larger field of view (factor of $\sim$40 larger than the RXTE/PCA). Moreover, a large amount of time is devoted to the Galactic Center region (see, e.g., in 't Zand 2001), so that a considerable part of the X-ray burster population is being monitored. In this paper we use those type I X-ray bursts from globular clusters which showed either long enough expansion/contraction phases (typically >10 s, see e.g., Cocchi et al. 2001), or X-ray bursts which had a short ($\sim$sec) expansion/contraction phase but which were bright, such as those from 4U 1820-30, so that we have enough signal to noise for a meaningful X-ray spectral analysis during that phase.

Figure 2: Spectral fit results for the net X-ray burst emission of short ( $\protect\mbox{$\la$ }$30 s) X-ray bursts from five globular cluster X-ray sources seen by the RXTE/PCA. The values are plotted on a logarithmic time scale; they have also been logarithmically rebinned in time for clarity. From top to bottom: bolometric black-body luminosity, $L_{\rm bb}$, in 1038 erg s-1, black-body temperature, k $T_{\rm bb}$, apparent black-body radius, $R_{\rm bb}$, and goodness of fit expressed in reduced $\chi ^2$, $\chi ^2_{\rm red}$. $L_{\rm bb}$ and $R_{\rm bb}$ are derived using the distances quoted in Table 1. Note that only the temperature axis has been kept the same for all the sources, and that the $R_{\rm bb}$ and $\chi ^2_{\rm red}$ axes for 4U 1820-30 have a logarithmic scale. T=0 s corresponds to UT 1999 May 26 06:53:08, 1998 February 19 14:29:51, 2000 October 2 15:18:55, 1996 October 27 09:01:51 and 1997 May 2 17:32:45, for MX 0513-40, MXB 1730-335, XB 1745-25, 4U 1746-37 and 4U 1820-30, respectively.

Figure 3: Same as Fig. 2 but for three long X-ray bursts from three other globular cluster X-ray sources seen by the RXTE/PCA. Note that the $R_{\rm bb}$ and $\chi ^2_{\rm red}$ axes for 4U 1722-30 and 4U 2129+12 have a logarithmic scale. T=0 s corresponds to UT 1996 November 8 07:00:29, 1998 November 27 05:45:11 and 2000 September 22 13:47:37, for 4U 1722-30, H1825-331 and 4U 2129+12, respectively.

From the WFC data time resolved dead-time corrected spectra were determined for each X-ray burst. Different integration times were used, so that each spectrum had a similar signal to noise. This was 10 in most cases. For a few X-ray bursts from 4U 1722-30 and the only X-ray burst from 4U 2129+12, however, this resulted in only a few time resolved spectra in which case we could not determine whether it exhibited photospheric radius expansion or not. For these we lowered the signal to noise down to 5. The X-ray bursts from 4U 1820-30 typically last less than 25 s with rather short photospheric radius expansion phases (see e.g. Figs. 2 and 5); for the X-ray burst spectra from this source, therefore, we also used a signal to noise of 5.

We performed our spectral analysis (black-body radiation subjected to interstellar absorption) in the 3-20 keV energy band for the RXTE/PCA and 2-20 keV energy band for the BeppoSAX/WFC. For all the X-ray bursts seen with the RXTE/PCA and BeppoSAX/WFC, we subtracted the pre-burst persistent emission from the X-ray burst spectra (see e.g. Kuulkers et al. 2002, and references therein). The interstellar absorption, $N_{\rm H}$, was fixed to the values given in Table 2. These values are mostly from the best fitting models (disk black-body plus a Comptonized component [see Titarchuk 1994]) to wide-band X-ray spectral data from the BeppoSAX/NFI of the persistent emission by Sidoli et al. (2001) and Parmar et al. (2001). However, MXB 1730-335 and XB 1733-30 were too faint in their observations used, whereas no BeppoSAX/NFI observations have been done for XB 1745-25. For MXB 1730-335 we, therefore, used the value of $N_{\rm H}$ from BeppoSAX/NFI results by Masetti et al. (2000), when the source was on, whereas for XB 1733-30 we used the value of $N_{\rm H}$ from power-law fit results to EXOSAT/ME spectra reported by Parmar et al. (1989); the latter value of $N_{\rm H}$ is consistent with that reported from ROSAT/PSPC observations by Verbunt et al. (1995): $1.8 \times 10 ^{22}$ cm^-2. For XB 1745-25 we used the persistent source spectrum in outburst as observed by the BeppoSAX/WFCs to constrain $N_{\rm H}$, see Appendix A; this value is also more or less consistent with that derived from ROSAT/PSPC observations by Verbunt et al. (1995): $2 \times 10 ^{22}$ cm^-2. Finally, the uncertainties quoted from the X-ray spectral fits are 1 $\sigma$ errors, using $\Delta\chi^2=1$.

3.3 X-ray spectral analysis

As noted in Sect. 1.1 the X-ray burst emission may not be entirely Planckian. Also, a different spectral model has an impact on the inferred bolometric luminosity. When determining the observed bolometric X-ray flux from our X-ray spectral fits we do not take this into account, even when the X-ray spectral fits are satisfactory. In principle an assessment of the observed bolometric X-ray flux using various spectral models is warranted (see e.g. Damen et al. 1990). However, since the "true'' X-ray burst emission is still rather uncertain, such an assessment will be somewhat elusive, and outside the scope of this paper. We, therefore, assume that the X-ray spectra at maximum flux are Planckian and that the unabsorbed bolometric X-ray flux may be determined using

$$F = \sigma T ( R / d )^2,$$ (3)

where T is the black-body temperature (or "color'' temperature), R the neutron star photospheric radius, and d the distance to the source.

3.4 Literature values

In Appendix B we give an account, focused on the bolometric X-ray burst peak fluxes, of all the X-ray bursts seen from globular cluster X-ray sources presented in the literature. These fluxes are also tabulated in Table B.1. The fluxes per source are ordered per instrument. If an instrument did not see a radius expansion burst we give the maximum bolometric flux reached during a single X-ray burst, or a range in bolometric peak fluxes if there is more than one X-ray burst observed with an instrument. In the latter case sometimes also a value is quoted for individual (set of) X-ray bursts, i.e. either the maximum observed peak flux or the average bolometric peak flux of a subset. We note that errors are not always given in the literature.

3.5 Cross calibration of different instruments

It has been noted before that the spectral analysis of RXTE/PCA data of the Crab (pulsar plus nebula) results in observed fluxes which are about 20% higher than those derived from Crab data taken with other instruments (see e.g. Tomsick et al. 1999; Wilms et al. 1999; Kuiper et al. 1999; Barret et al. 2000). Although the calibration of the RXTE/PCA instrument has been improved, the absolute calibration has still not been optimized (see e.g. Jahoda 2000). We, therefore, analysed data sets of the Crab, in order to quantify the effect on our analysis. We created spectra using data recorded by the STANDARD 2 mode, with either all PCUs, PCUs 0, 1, 2, 3, or PCUs 0, 2, 3 summed. The analysis was done in the same way as described above for our globular cluster X-ray sources. Background was subtracted from the Crab spectra, which was estimated using the 2002, February 26 background models. For the spectral model of the Crab (pulsar plus nebula) we used a power law subjected to interstellar absorption:

$$N_{\rm ph} = A ~ E^{-\Gamma}e^{-N_{\rm H}\sigma(E)},$$ (4)

where $N_{\rm ph}$ is the flux in photons s^-1 cm^-2 keV^-1, A the normalization in photons s^-1 cm^-2 keV^-1 at 1 keV, E the photon energy, $\Gamma$ the power-law photon index, $N_{\rm H}$ the interstellar hydrogen column density, and $\sigma$ the photo-electric absorption cross section from Morrison & McCammon (1983). $N_{\rm H}$ was fixed to $3 \times 10 ^{21}$ cm^-1. Our spectral fit results to Crab data obtained on 2000, November 21 are shown in Table 3, together with the "canonical'' Crab X-ray spectrum, and the results from other X-ray instruments. For the instruments onboard SAS-3, Hakucho and Granat (with which X-ray bursts were seen and which were used in our investigation) we do not have X-ray spectral information regarding the Crab. The instruments onboard SAS-3 and Hakucho provided count rates in only a few energy channels. In those cases it seems likely that they were calibrated by using the "canonical'' Crab spectrum.

It is clear from Table 3 that the power-law normalization, A(as well as the observed unabsorbed 3-20 keV flux, F_X), derived for the RXTE/PCA differs very significantly from those derived by other instruments. In order to account for this discrepancy we introduce a scale factor when modeling the observed count rate spectra (note that this results in a correction to the black-body flux and black-body radius, which we use in this paper). These scale factors were determined by comparing the absorbed Crab flux observed with the RXTE/PCA with the absorbed Crab flux estimated from the "canonical'' Crab spectrum, in the 3-20 keV band (i.e., the energy range used in this paper). This is, of course, a crude correction, since the Crab spectral shape (power law) differs from that of X-ray burst spectra (black body). The scale factors are 1.242, 1.211 and 1.227, respectively, when all PCUs are used, only PCUs 0, 1, 2, 3, or only PCUs 0, 2, 3. After taking into account

the correction factors in our RXTE/PCA spectral analyses, the final bolometric X-ray burst peak fluxes are more comparable to those obtained with other instruments (see Table B.1).