5 Constraining intervening LMC gas columns

In Paper I I have determined the $N^{\rm LMC}_{\rm HI}$ values by performing X-ray spectral fitting for individual AGN. Here a different method, a hardness ratio analysis, has been chosen to constrain absorbing column densities. The chosen sample of AGN and candidate AGN comprises the AGN sample given in Paper I (22 AGN) and 64 additional candidate background X-ray sources. For 20 AGN and candidate AGN values (with 1$\sigma$ errors) for the total LMC hydrogen absorbing column density $N^{\rm LMC}_{\rm H}$ could be derived and for additional 11 candidate AGN a range. For further 54 candidate AGN only 1$\sigma$ upper limits to the LMC gas column could be derived (and in addition in one case a 1$\sigma$ lower limit). It follows that the values derived for $N^{\rm LMC}_{\rm H}$ from the hardness ratio analysis are consistent with the values for the LMC absorbing column density derived from X-ray spectral fitting of Paper I.

I briefly outline the hardness ratio analysis method which has been applied. I simulated powerlaw tracks in the $H\!R1$ - $H\!R2$ plane for a wide range of powerlaw photon indices $-\Gamma = (0.8{-}3.0)$. I compared the location of the hardness ratio error ellipses of individual AGN and candidate AGN with respect to these tracks to infer the absorbing column densities of LMC gas in the direction of individual background X-ray sources. I assumed that the powerlaw photon indices of background sources are in the range $-\Gamma = (2.0{-}2.5)$, which is the range of powerlaw photon indices derived by Brinkmann et al. (2000) from the X-ray spectra of a large sample of AGN. In the simulations reduced metallicities (-0.3 dex relative to galactic interstellar absorption abundances) have been assumed for the LMC gas and galactic interstellar abundances for the galactic foreground gas. In Table 1 the values for the galactic and LMC hydrogen column density $N^{\rm gal}_{\rm HI}$ and $N^{\rm LMC}_{\rm HI}$ are given which have been derived from 21-cm H  I surveys of the LMC field performed with the Parkes radio telescope (Brüns et al. 2001, see also Dickey & Lockman 1990). Gas columns derived from 21-cm measurements can be separated into a galactic and a LMC component due to the different systemic velocities of both components. In addition the total LMC absorbing hydrogen column density $N^{\rm LMC}_{\rm H}$ derived from the hardness ratio analysis is given.

Figure 6: Correlation between LMC hydrogen absorbing column density (after galactic foreground gas has been removed) as derived from the hardness ratio analysis compared with the LMC hydrogen absorbing column density derived from the X-ray spectral fit (cf. Paper I). The dashed line gives the linear relation for which both LMC column density determinations are equal.

In Fig. 6 I show the correlation between the LMC hydrogen absorbing column density derived with the hardness ratio analysis in comparison with the LMC hydrogen absorbing column density derived from the X-ray spectral fit (Paper I). There is a linear correlation between the LMC gas columns determined by both methods which gives reliability to the LMC gas columns derived by both methods.

Figure 7: LMC hydrogen absorbing column density (after galactic foreground gas has been removed) as derived from the hardness ratio analysis assuming constraints on the powerlaw photon index (cf. Table 1). Upper panel: AGN (additional to the sample from Paper I) for which a best-fit has been determined (the best-fit value is given as filled circle and 1$\sigma$ error bars are drawn) and AGN for which an $N_{\rm H}$ range, band, has been determined and for which the mean value is shown as a filled triangle and 1$\sigma$ error bars are drawn with small cross bars. Lower panel: AGN for which only upper limits (and in one case a lower limit) to the LMC gas columns has been determined. With dashed lines the dependences on the molecular mass fraction $f=0,\ 0.1,\ 0.3$ and 0.8 are indicated.

I present in Fig. 7 the comparison between the LMC gas columns inferred from the 21-cm H  I Parkes survey and the LMC gas columns inferred from the hardness ratio analysis for background sources in addition to those for which X-ray spectral fitting has been performed in Paper I (for 6 AGN a best-fit for the LMC $N_{\rm H}$ value, for 7 AGN a range of values, for 50 AGN upper limits and for one AGN a lower limit is given). The values for the LMC gas columns inferred from the hardness ratio analysis agree in most cases within the uncertainties with the LMC H  I columns inferred from the Parkes survey.

5.1 Deriving constraints on the LMC metallicity

It is assumed that AGN have canonical powerlaw photon indices $-\Gamma = 2.0$ to 2.5 in the ROSAT PSPC band. From simulations, tracks for constant powerlaw indices $-\Gamma$ and a galactic foreground absorbing column of $3\times 10^{20}\ {\rm cm^{-2}}$ have been derived in the $H\!R1$ - $H\!R2$ plane by varying the LMC absorbing column density $N_{\rm H}$.

For the LMC gas hybrid models have been used assuming a constant foreground hydrogen column due to the Milky Way gas of $3\times 10^{20}\ {\rm cm^{-2}}$. In the simulations the metallicity has been varied from -0.8 dex to +0.5 dex in steps of 0.05 dex. In addition $-\Gamma$ has been varied from 2.1 to 2.4 for the AGN and from 1.4 to 1.7 for the X-ray binaries. Three AGN (HP 54, HP 380 and HP 1094, cf. Paper I) with accurately determined values for the hardness ratios $H\!R1$ and $H\!R2$ could be used to constrain the metallicity. From the location of these AGN in the $H\!R1$ - $H\!R2$ plane metallicities somewhat in excess of galactic metallicities X>0.1 can be excluded. Metallicities as low as X=-0.7 were found to be consistent with the data.

The size of the sample has been extended in a next step and the mean metallicity of the intervening LMC gas and the powerlaw slope of the flux have been determined in a least-square grid search. This search has been performed for two different samples, an AGN sample with 14 objects and an X-ray binary sample with 9 objects (cf. Table 1). These objects were taken from a sample selected in this work and, in addition, only objects with accurate hardness ratios $\delta H\!R<0.20$ were used.

Figure 8: Upper panel: confidence contours (99%) for 14 candidate AGN with catalog number 1, 37, 54, 101, 147, 380, 411, 561, 653, 876, 1040, 1094, 1181, and 1247 (Haberl & Pietsch 1999) and hardness ratio errors $\delta HR<0.20$) in the $\Gamma$ - X plane. Lower panel: confidence contours for 9 X-ray binaries (XRB) with catalog number 41, 106, 184, 204, 252, 436, 1001, 1225, and 1325 and $\delta HR<0.20$ in the $\Gamma$ - X plane.

From the formal fit it is found that the powerlaw slope $\Gamma$ and the metallicity X can be constrained for both samples (the AGN and the X-ray binary sample). In the case of the AGN, the errors in the hardness ratios of the AGN have been increased by a factor of 1.4. The range of metallicities which is derived in this way is in agreement with the range of tracks for different metallicities which is covered by the used data points. In the case of the X-ray binaries, a systematic offset of 0.03 in the values of the hardness ratios has been assumed in the fit. This avoids that the least-square fit is biased towards the data points with very small error bars in the hardness ratio values as derived for the bright X-ray binaries (e.g. LMC X-1). This has the effect of increasing the parameter range for a given confidence (e.g. the 99% confidence which is shown in Fig. 8).

In Fig. 8 the confidence contours are shown for the 14 AGN and the 9 X-ray binaries in the $H\!R1$ - $H\!R2$ plane. It is found that for the X-ray binaries the powerlaw slope can be confined to $-\Gamma = 1.45$ to 1.6 and the metallicity to X = -0.5 to +0.0 (99% confidence). For the 14 AGN (Fig. 8) I find that the powerlaw slope can be confined to $-\Gamma = 2.2$ to 2.3 and the metallicity to X = -0.6 to +0.15 (99% confidence). The best-fit metallicity is -X = 0.4 for X-ray binaries and X = -0.15 for AGN respectively.

The value for the metallicity which has been found from the AGN and the X-ray binary sample is consistent with the metallicity of -0.2 to -0.6 derived for the LMC (cf. Pagel 1993; Russell & Dopita 1992). The powerlaw photon index derived for the AGN sample of $-\Gamma = 2.2$ to 2.3 is consistent with the powerlaw slope derived for AGN type spectra (cf. discussion in Paper I). The powerlaw photon index derived for the X-ray binaries $-\Gamma = 1.45$ to 1.6 is steeper than the canonical value of $-\Gamma \sim1.0$ (see also Sect. 6). Apparently for the LMC X-ray binaries steeper powerlaw photon indices are observed in the ROSAT PSPC band. From spectral fitting applied to bright LMC X-ray binaries (LMC X-1, LMC X-2, LMC X-3 and LMC X-4) follows that simple powerlaw spectra cannot explain the absorbed spectra and more complicated spectral shapes have to be fitted.