Physically motivated relativistic disk models

Table 2: Spectral fits to the MCG$-$6-30-15 EPIC-pn data with relativistic smearing functions corresponding to physical disk models, assuming an underlying power-law continuum. Abbreviations are: PTDISK = smearing model assuming an emissivity profile corresponding to a standard steady-state accretion disk (Novikov & Thorne 1974; Page & Thorne 1974) viewed at an inclination $i$; tPTDISK = same as PTDISK except for the presence of an outer truncation radius at $r=r_{\rm out}$, beyond which there is no X-ray emission or reprocessing; TORQUED = smearing model assuming an emissivity profile corresponding to a steady-state torqued accretion disk (Agol & Krolik 2000) viewed at inclination $i$ with a torque-induced efficiency enhancement of $\Delta \eta$; tTORQUED = same as TORQUED except for the presence of an outer truncation radius at $r=r_{\rm out}$, beyond which there is no X-ray emission or reprocessing. All other abbreviations are given in Table 1.

Model Parameters 2-10keV fitting 0.5-10keV fitting

$$\Gamma 1.73^{+0.4}_{-0.3} 1.77^{+0.05}_{-0.04}$$ ABS(PO+NFE+tTORQUED[iREFL])

$$\log(\xi_{\rm broad}) 3.21^{+0.14}_{-0.15} 3.19^{+0.21}_{-0.22}$$

$$r_{\rm out} 6.3^{+2.0}_{-1.4} 6.3^{+1.8}_{-2.0}$$

$$i 38\pm 4 38^{+4}_{-3}$$

$$\Delta \eta >46 >22$$

$$\chi^2$$ 2068/2103 2978/2891

$$\Gamma 1.75\pm 0.2 1.77^{+0.02}_{-0.07}$$ ABS(PO+NFE+TORQUED[iREFL])

$$\log(\xi_{\rm broad}) 3.19^{+0.25}_{-0.14} 3.21^{+0.11}_{-0.18}$$

$$i <27 <27$$

$$\Delta \eta >193 >200$$

$$\chi^2$$ 2075/2104 2985/2892

$$\Gamma 1.68^{+0.09}_{-0.02} 1.76^{+0.01}_{-0.05}$$ ABS(PO+NFE+tPTDISK[iREFL]

$$\log(\xi_{\rm broad}) 3.5\pm 0.1 3.36^{+0.08}_{-0.15}$$

$$r_{\rm out} 5.6\pm 0.9 5.0^{+1.0}_{-0.7}$$

$$i 34^{+3}_{-4} 35^{+2}_{-4}$$

$$\chi^2$$ 2081/2104 2997/2892

$$\Gamma 1.72\pm 0.02 1.75^{+0.01}_{-0.02}$$ ABS(PO+NFE+PTDISK[iREFL])

$$\log(\xi_{\rm broad}) 3.72^{+0.05}_{-0.07} 3.55^{+0.07}_{-0.04}$$

$$i <8 <6$$

$$\chi^2$$ 2169/2105 3166/2893

Figure 3: Model dissipation profiles for torqued time-independent accretion disks (using expressions from Agol & Krolik 2000). The thick line shows the dissipation profile for a standard non-torqued disk (i.e., one in which the ZTBC applies) around a near-extremal Kerr black hole with spin parameter $a=0.998$. The thin solid lines show the torque-induced dissipation component $D_{\rm tor}$ for spin parameters of (from left to right) $a=0.998$, 0.99, 0.9, 0.5, 0.3, and $0$. Note how the torque-induced dissipation profile becomes more centrally concentrated as the spin parameter is increased. The dashed lines show the torque-induced component of the emitted flux, including the effects of returning radiation. Figure from Reynolds & Nowak (2003).

In the above discussion, we have examined these data with a variety of spectral models. We have found that the need for extreme relativistic effects is robust to different treatments of the soft X-ray complexity, complex absorption, and the use of a Comptonisation model instead of a simple power-law to describe the primary X-ray continuum.

Until now, we have employed a phenomenological model for the radial dependence of the disk emissivity, assuming that it can be described by a power-law form $\epsilon \propto r^{-\beta }$ truncated by inner and outer radii $r_{\rm in}$ and $r_{\rm out}$. While this is an extremely useful parameterization, it does not correspond to any particular physical disk model. Given the quality of these data, we can go beyond these simple power-law emissivity profiles and attempt to constrain physical relativistic smearing models.