Limits on a broad iron line

Is there evidence for a relativistically-broad iron line once the narrow lines have been modeled? To answer this question, we add a relativistic iron line to the spectral fit using two models to describe its profile; the Schwarzschild model of Fabian et al. (1989) as implemented in the diskline model of XSPEC package, and the near-extreme Kerr model of Laor (1991) as implemented in XSPEC's laor model. The energy of the emission line, $E_{\rm broad}$, was allowed to vary across the range of possible Fe K$\alpha$ transition energies, 6.40keV to 6.97keV (rest-frame). The inner radius of the emitting region $r_{\rm in}$, the emissivity index of the disk $\beta$, the viewing inclination $i$, and the line normalization are also free parameters in the fit. The outer radius of the line emitting region was fixed at $r=1000r_g$ (where $r_g=GM/c^2$). The improvement in the goodness of fit was $\Delta\chi^2=11$ and $\Delta\chi^2=10$ (for 5 additional degrees of freedom) for the diskline and laor models, respectively. Such a change is not significant at the 90% level.

Thus, we have not obtained a detection of a broad iron emission line in the EPIC-pn spectrum of NGC 4593. In order to obtain a meaningful upper limit to the equivalent width of any broad iron line, we must specify its shape (since the data is incapable of doing that itself). We can proceed either empirically or theoretically. Empirically, we can assume that any such line has the ``typical'' profile found in co-added ASCA data by Nandra et al. (1997a), i.e., the diskline model with $E_{\rm broad}=6.4{\rm\thinspace keV}$, $r_{\rm in}=6r_{\rm g}$, $\beta=2.5$, $i=29^\circ$. Using these assumptions, we can set an upper limit (with a 90% confidence level for one interesting parameter) to the broad line equivalent width of $W_{\rm broad}=87{\rm\thinspace eV}$. Theoretically, the simplest model (Shakura & Sunyaev 1973; Novikov & Thorne 1974; Page & Thorne 1974) is one in which the accretion disk is geometrically-thin and radiatively-efficient, extends from the radius of marginal stability to large radii, and with an iron line emissivity that tracks the underlying dissipation (Reynolds & Nowak 2003; Reynolds et al. 2003). Applying such a line profile to the NGC 4593 data in the case of a near-extreme Kerr black hole (with dimensionless spin parameter $a=0.998$) results in an upper limit to the equivalent width of $99{\rm\thinspace eV}$. These are significantly less than the values expected from theoretical reflection models ($\sim 200{\rm\thinspace eV}$ for solar abundances; e.g., Matt, Fabian & Reynolds 1997 and references therein) or observed in the Seyfert galaxy MCG-6-30-15 ($\sim 400{\rm\thinspace eV}$; Fabian et al. 2002). Thus, there appears to be a significant absence of spectral features from a relativistic accretion disk.