Fitting a Model of the F-K and O-K edges

As with PKS 2155-304 (see the C-K edge web page), I extracted the observed count spectrum, n(E), for the Mk 421 observation in October 2002 (obs ID 4148, from F. Nicastro). This time, the C-K edge model was included with the 2PL model fit gives N(E), allowing the depth of the edge to vary using a single depth parameter. The optical depth due to absorption is computed as -ln[n(E)/N(E)], plotted in Fig. 1.

Fig. 1: Modeling the 12-25 Å region of the Mk 421 X-ray spectrum. The O-K edge, which is deepest near 23 Å, has a resonance feature near 23.3 Å and a deep edge near 23.0 Å. Other narrow features in this region are associated with the source or the interstellar medium. The 18 Å edge is modeled using Henke optical constants for fluorine with slight modifications.

The structure of the O-K edge is very similar to the O-K edge found in the ACIS-S optical blocking filter. The model was taken from a spectral decomposition of the OBF and then matched to the Henke optical constants in the 18-21 Å region for extrapolation shortward of 18 Å. This model has a resonance feature that shows up as a deep narrow absorption line near 23.3 Å that is clearly detected.

The edge at 18 Å is attributed to fluorine. Fig. 2 shows that the edge cannot be identified with redshifted Fe-L

Fig. 2: The 18 Å edge is compared to two models. The dotted line represents possible Fe-L absorption, redshifted to z=0.025. The lines are too narrow to fit the data. The F-K edge, however, fits very well without shifting. F-K and Fe-L opacity data were kindly provided by Adam Hitchock of McMaster University.

The F-K edge EXAFS was fit by a similar method used to fit the C-K EXAFS. First, the Henke optical constants were obtained from the CXRO web site. Then, the edge was positioned at lam_fk = 18.03 Å and the EXAFS was fit using the form

1 + A exp( -x/dampscale ) * cos( freq * x )

where x = (lam_fk - lambda) / lam_fk. The constants of the adjustment were estimated (chi-by-eye): A = 0.6, dampscale = 4./lam_fk, and freq = 2 lam_fk/8.5. Note the similarity of the parameters to that used in fitting the C-K edge, where A = 0.4, dampscale = 4./lam_ck, and freq = 2 lam_ck/16. The result is shown in Fig. 1. The overall fit to the Mk 421 data in the 0.22-1.0 keV region is shown in Fig. 3 and expanded in Fig. 4. The jumps near 0.38 keV and 0.48 keV are locations of transitions from data on both a BI and an FI chip to where there is only data on FI chips (the 0.38-0.48 keV range) so the jumps are caused by slight inaccuracy in the BI/FI QE correction.

Fig. 3: Fit to the observed spectrum of Mk 421, where the contaminant absorption is included in the model so the C-K and F-K edges are apparent. The overall fit is good to better than 3% except in the 0.38-0.48 keV region where the relative uncertainties between FI QEs and BI QEs dominate. Below 0.25 keV, the spectrum deviates from the model due to losses from the pulse height distribution as low pulse height events fall below the event threshold.

Fig. 4: Counts vs. wavelength at the edges of F-K (top) and O-K (bottom). The overall structure is modeled to better than 3% and the only remaining features are intrinsic to the source (or to the gas between the target and the telescope, see Nicastro et al., 2003, in preparation). There is a slight normalization error in the F-K edge region due to the systematic effects of correcting for the relative error in the BI QEs compared to the FI QEs.


Herman Marshall
Last updated August 12, 2003