4.3 Data analysis and results
4.3.4 The Fe abundance within the MCs
In this Section we make use of the measurements of the EW of the Fe-Kα line from the
spectral analysis of the stacked PN spectra (written in 4.5) to infer the mean Fe abundance across the MCs under study. To proceed towards this, we first derive an expression for Fe-line equivalent width. As discussed in Sunyaev & Churazov (1998), the Fe-Kα line flux
(F64) induced by ionisation of a MC by a powerful X-ray source can be written as
F64 =
Ω
4πD2 ZFe τT I8keV photons cm
−2s−1, (4.1)
where Ω is the solid angle (in units 4π) subtended by the diffuse cloud from the per- spective of the radiation source, D the distance to the GC, ZF e the Fe abundance within
1The nominal values for the energy peak of the Fe-K
α and Cu Kα lines have been taken from
102 line reverberation in Galactic Centre molecular clouds
the MC, andτT is the optical depth for Thomson scattering (based on the angular averaged
Thomson cross section). Here I8keV is the photon output of the source at 8 keV in units of
photon s−1 keV−1.
If we assume we are dealing with a small element of the cloud, then the scattered signal at 6.4 keV at an angle θ is
S64=
Ω
4πD2 τT(θ) I8keV(6.4/8)
−Γin photons cm−2s−1keV−1, (4.2)
where Γin is the photon index of incident continuum. Therefore we can write the EW
of the Fe-Kα line with respect to the reflected continuum as:
EWFe−Kα = ZFe τT τT(θ) 6.4 8.0 Γin ∼ 644 ZFe [0.75×(1 + cos2(θ))] eV (4.3)
The same factor applies to all the cloud elements provided the cloud is not optically thick, and hence to the cloud as a whole. The equivalent width is thus independent of LX,
but it does depend on the spectral slope of the incident (and hence reflected) continuum
i.e.,harder spectra produce relatively more 6.4 keV photons.
Using this last formula we have attempted to calculate the average Fe abundance, mak- ing the reasonable assumption that ZF e is constant across the nine clouds. The weighted
mean of the EW of the Fe-Kα inferred from the spectral analysis of the nine clouds is
1.01±0.12 keV, where we used the inverse of the squared error to assign a weight to the different measurements. Moreover, we assume the clouds to be uniformly distributed in the region 25◦ .θ .155◦, i.e. we assume the distance along the line of sight of the clouds to be lower than twice the projected distance. From this assumption we can calculate the mean value for the geometrical function in formula 4.3 to be
1 + cos2(θ) = 1.33.
Substituting the weighted mean for the EW and the geometrical factor value into equation 4.3, we obtain the mean value for the Fe abundance to be ZF e=1.56±0.19 Z.
This important result confirms a higher than solar metallicity for MCs and (presumably) the interstellar medium generally found in the GC region.
Another interesting application of equation 4.3 is the study of the geometry of the illu- mination process. These calculations might indeed turn to be a powerful tool for inferring the distribution of the MCs Fe-Kα bright MCs in the CMZ. In Fig.4.7 we show both the
EW dependence on the geometry (for different Fe abundances) and the ZF e dependence
on the scattering angle for different values of the EW of the 6.4-keV line. Both panels in Fig.4.7 can help us in estimating the line of sight distance of the clouds relative to the plane including Sgr A*. The ZF e=1.56 Z curve in the left panel of Fig.4.7 (plotted in
red) is intersected by the blue lines corresponding to the clouds with lower values of the EW in correspondence ofθ values of 0.6-0.9 and 2.2-2.5; this might give the line of sight of the C, B1, A, DS1 and DS2 clouds to be about the same of the projected one (scattering angles around 45 and/or 135 degrees). The highest EW values also intersect the ZF e=1.56
4.3 Data analysis and results 103
Figure 4.7: Left panel: The predicted EW (from equation 3) plotted against the scattering angle (θ) measured between the direction of incident radiation on the cloud and the line of sight, for different values of the Fe abundance (the red curve is for Z=1.56, see text). The blue horizontal lines show the EW measurements for the nine MCs in our data set - ordered from top to the bottom as follows: B2, F, D, E, C, B1, A, DS1 and DS2 MCs. For clarity, here we plot only the value of the EW, without the error bars. Right panel: The Fe abundance inferred for the different MCs using equation (3) as a function of the scattering angle. The different curves show the ZF e-θdependance for each value of the EW
measured in the MCs. The dashed-dotted black line represents the averaged metallicity value (ZF e=1.56) found across our set of MCs.
red curve if the error bars on these quantities are taken into account, giving these clouds a scattering angle close to 90 deg, therefore resulting in a limited line of sight distribution. The same applies for the plot in the right panel of Fig.4.7; considering the error bars (90% confidence levels), the MCs with the highest EW of the 6.4-keV line meet the ZF e=1.56
line at angles close to 90 degrees (short line of sight distance).
In all of these calculations, we assumed that the MCs are illuminated by the same powerful X-ray source, in a pure XRN scenario. However, we note that these clouds, especially the ones located (in projection) in the vicinity of the Radio Arc (i.e. those in the bridge subregions and in G0.11-0.11), could be subject to intense cosmic-ray particle bombardment, a process which would result in a boosting of the EW of the Fe-Kαline. Any
adjustment of the 6.4-keV line flux arising from photoionisation would of course impact on estimates of line of sight distance derived from the above methodology. We will discuss this issue further in the Section 4.3.7.