3 Broad band spectrum

 

 

Table 2: Goodness of fits for 1-200 BeppoSAX spectrum.

Model$^\dag$	$\chi^2_\nu$	$\nu$
wa$\times$(diskbb+pexrav)	3.703	116
wa$\times$(diskbb+comptt)	3.609	116
wa$\times$(diskbb+po$\times$highecut)	3.453	116
wa$\times$(pexriv)	2.538	117
wa$\times$(diskbb+po$\times$highecut+bbody)	2.012	114
wa$\times$(diskbb+pexrav+gauss)	1.968	113
wa$\times$(diskbb+pexrav+laor)	1.788	112
wa$\times$(diskbb+pexriv+gauss)	1.737	112
wa$\times$(diskbb+pexriv+laor)	1.664	111
wa$\times$(bbody+comptt+laor)	1.473	113
wa$\times$(bbody+comptt+gauss)	1.458	113
wa$\times$(diskbb+comptt+gauss)	1.432	113
wa$\times$(diskbb+comptt+laor)	1.424	113
wa$\times$(diskbb+po$\times$highecut+laor)	1.386	112
wa$\times$(diskbb+po$\times$highecut+gauss)	1.348	113
wa$\times$(diskbb+po$\times$highecut+gauss)$\times$edge	1.308	111
wa$\times$(diskbb+comptt+gauss)$\times$edge	1.308	111

$^\dag$wa = interstellar absorption following Morrison & McCammon (1983), comptt = Comptonized spectrum, gauss = Gauss function, edge = 1 for $E<E_{\rm e}$ and 1 - exp($E/\tau$) for $E>E_{\rm e}$, po = power law, highecut = 1 for $E<E_{\rm b}$ and exp( $-E/E_{\rm f}$) for $E>E_{\rm b}$, bbody = single-temperature black body radiation, diskbb = disk black body (Mitsuda et al. 1984); pexriv = Compton reflection against an ionized medium (Magdziarz & Zdziarski 1995); pexrav = Compton reflection off a neutral medium (Magdziarz & Zdziarski 1995).

The flux was fairly stable during the NFI observation; on a time scale of an hour the variability of the source did not exceed the 5% level. The shape of the 1 to 200 keV spectrum can be characterized by an absorbed power law, with a photon index of 1.7, which is moderately cut off above 60 keV by an exponential with an e-folding energy of 130 keV. There is no strong soft component which is typical of many bright X-ray transients. We tested the spectrum against various continuum models that are applicable to X-ray binaries, for instance a (cut-off) power law, a Comptonized spectrum, bremsstrahlung radiation, and disk black-body radiation. Data were restricted to 1-4 keV for LECS, 1.6-10.5 keV for MECS, 7-34 keV for HP-GSPC, and 15-200 keV for PDS. None of the continuum models adequately describe the data (see cases in Table 2 for which $\chi^2_\nu$ exceeds 2). The primary reason for this is a narrow-band spectral component between 4 and 9 keV which is not represented in these models. In Fig. 5, we present the residuals with respect to the best-fit model when excluding the 4-9 keV range from the fitting. A narrow-band emission feature is apparent, with a peak that is near the energy expected for the Fe-K line complex. The feature is seen in its entirety with the MECS, and is partly confirmed by HP-GSPC data. To accommodate the emission feature, we tested two models in combination with a variety of continuum models. The emission-feature models include a broad Gaussian line, optionally supplemented by an absorption edge, and an emission line that is relativistically broadened by Doppler shifts due to orbital motion of the emitting material around a compact object and to gravitational redshift. For the latter, the model as formulated by Laor (1991) for a rotating compact object was employed. In this model, we fixed the outer radius at 400$R_{\rm g}$ and the power-law index of the emissivity-radius dependence at -3. None of the fixed parameters are in fact constrained by the data.

Figure 5: 2-11 keV NFI data of SAX J1711.6-3808 divided by the best-fit Comptonized model, excluding 4-9 keV in the fit.

 

 

Table 2: Spectral fit parameters of the four most acceptable models to the BeppoSAX spectrum. A systematic flux uncertainty of 1% per channel was added in quadrature to the statistical error. Errors are 90% confidence per parameter of interest (i.e., from range in each parameter for which $\chi ^2$ is smaller than minimum $\chi ^2$ plus 2.71).

Model	wa$\times$(po$\times$highecut+diskbb+gauss)
$N_{\rm H}$	2.83+0.08-0.09 1022 cm-2
disk bb $kT_{\rm in}$	0.94+0.27-0.14 keV
photon index $\Gamma$	$1.65\pm0.01$
$E_{\rm b}$	54.0+3.4-3.3 keV
$E_{\rm f}$	127+10-11 keV
Gauss $E_{\rm line}$	6.33 +0.24-0.22 keV
Gauss line width	2.79 +0.48-0.60 keV (FWHM)
Gauss line flux	4.8+1.3-1.5 10-3 phot s-1 cm-2
$\chi^2_\nu$	0.999 (113 d.o.f.)
Model	wa$\times$(po$\times$highecut+diskbb+laor)
$N_{\rm H}$	2.86+0.04-0.04 1022 cm-2
disk bb $kT_{\rm in}$	0.74+0.58-0.14 keV
photon index $\Gamma$	1.64+0.01-0.01
$E_{\rm b}$	54.5+3.6-2.5 keV
$E_{\rm f}$	128+8-10 keV
Laor $E_{\rm line}$	6.34 +0.18-0.22 keV
Laor $R_{\rm in}$	$4.5^{+1.0}_{-2.6}R_{\rm g}^\dag$
Laor line flux	3.8+0.6-0.4 10-3 phot s-1 cm-2
Laor inclination	86$\fdg$3 +3.7-0.3
$\chi^2_\nu$	0.992 (113 d.o.f.)
Model	wa$\times$(diskbb+comptt+gauss)
$N_{\rm H}$	2.65+0.14-0.11 1022 cm-2
disk bb $kT_{\rm in}$	0.83+0.13-0.23 keV
kT seed photons	1.00+0.20-0.38 keV
kT plasma	25.5+1.5-0.5 keV
optical depth	2.19+0.04-0.11 (disk)
	5.04+0.08-0.23 (sphere geometry)
Gauss $E_{\rm line}$	6.37+0.20-0.19 keV
Gauss line width	2.58+0.43-0.51 keV (FWHM)
Gauss line flux	$(3.9\pm1.0)~10^{-3}$ phot s-1 cm-2
$\chi^2_\nu$	1.102 (111 d.o.f.)
Model	wa$\times$(diskbb+comptt+laor)
$N_{\rm H}$	2.85+0.04-0.06 1022 cm-2
disk bb $kT_{\rm in}$	0.86+0.09-0.13 keV
kT seed photons	<0.2 keV
kT plasma	25.7+1.5-0.6 keV
optical depth	2.17+0.05-0.10 (disk)
	5.01+0.09-0.19 (sphere geometry)
Laor $E_{\rm line}$	6.26+0.18-0.10 keV
Laor $R_{\rm in}$	$3.9^{+1.1}_{-1.9}R_{\rm g}^\dag$
Laor line flux	4.2+0.5-0.6 10-3 phot s-1 cm-2
Laor inclination	86$\fdg$5 +3.5-0.2
$\chi^2_\nu$	1.101 (113 d.o.f.)

$^\dag$ $R_{\rm g}=GM/c^2$.

The continuum models consist of a disk black body (according to Mitsuda et al. 1984) plus either a (high-energy cut off) power law plus, a Comptonized thermal spectrum (Titarchuk 1994; Titarchuk & Lyubarskij 1995; Hua & Titarchuk 1995) or a power-law model reflected off cold or ionized material (following Magdziarz & Zdziarski 1995). The results for the goodness of fit are presented in Table 2. Formally, the values for $\chi^2_\nu$ are not acceptable. For the best fit, the chance probability is as small as about 1%. We attribute this to calibration uncertainties. With the introduction of a reasonable systematic flux uncertainty of 1% per channel, $\chi^2_\nu$ decreases to 1.0. In Table 3, we present the parameter values for four of the best-fit models. We chose to not consider absorption edges because the evidence for their existence is not convincing. Also we chose the disk black body model for the soft excess because single-temperature black body radiation does not fit PCA data (see Sect. 4). Although one of the four is the best fit, the other 3 are consistent at the 1 sigma level. We conclude that 1) the fitted line width is very broad, much larger than the spectral resolution of the MECS (33% versus 8% FWHM); 2) the emission line is consistent with being symmetric with a shape that can either be modeled with a broadened Gauss function or a relativistically broadened emission line with a fairly high inclination angle; 3) the absorption edge is not mandated by the data; 4) reflection models are inconsistent with the data (they particularly have a problem with explaining the high-energy cutoff); 5) both non-reflected continuum models give nearly equally as good a description of the data and 6) the data do not discriminate between single-temperature or multi-temperature black body models.

The disk black body accounts for 9% of the 1-10 keV unabsorbed flux or 3% in the 1-200 keV band. The absorbed flux in 3 to 20 keV is $1.53\times 10^{-9}$ erg cm^-2 s^-1; the unabsorbed flux in the 1 to 200 keV band is $5.0\times 10^{-9}$ erg cm^-2 s^-1. The equivalent width of the broad emission feature is between 0.35 and 0.50 keV, depending on the model.