Comparison of Relativistic Iron Line Models

The analysis of the broad iron line profile in the X-ray spectra of active galactic nuclei and black hole X-ray binaries allows us to constrain the spin parameter of the black hole. We compare the constraints on the spin value for two X-ray sources, MCG-6-30-15 and GX 339-4, with a broad iron line using present relativistic line models in XSPEC - LAOR and KYRLINE. The LAOR model has the spin value set to the extremal value a=0.9982, while the KYRLINE model enables direct fitting of the spin parameter. The spin value is constrained mainly by the lower boundary of the broad line, which depends on the inner boundary of the disc emission where the gravitational redshift is maximal. The position of the inner disc boundary is usually identified with the marginally stable orbit which is related to the spin value. In this way the LAOR model can be used to estimate the spin value. We investigate the consistency of the LAOR and KYRLINE models. We find that the spin values evaluated by both models agree within the general uncertainties when applied on the current data. However, the results are apparently distinguishable for higher quality data, such as those simulated for the International X-ray Observatory (IXO) mission. We find that the LAOR model tends to overestimate the spin value and furthermore, it has insufficient resolution which affects the correct determination of the high-energy edge of the broad line.

💡 Research Summary

The paper conducts a systematic comparison of two widely used relativistic iron‑line models in XSPEC—LAOR and KYRLINE—by applying them to high‑quality X‑ray spectra of the Seyfert 1 galaxy MCG‑6‑30‑15 and the black‑hole X‑ray binary GX‑339‑4. The LAOR model, introduced in 1991, assumes an extreme spin (a ≈ 0.9982) and treats the inner disc radius (R_in) as the sole free parameter; the spin is inferred indirectly by associating R_in with the marginally stable orbit (ISCO). In contrast, KYRLINE (Dovčiak, Karas & Yaqoob) allows the spin parameter a to be fitted directly, while also providing flexibility in the emissivity law, inclination, and ionisation state.

Both data sets were reduced with a uniform pipeline: background subtraction, response matrix application, and fitting in the 2–10 keV band with a power‑law continuum plus Galactic absorption. The iron‑line component was modeled first with LAOR, then with KYRLINE, and χ² minimisation (augmented by MCMC sampling) was used to derive parameter uncertainties. For the present observations, the two models yield spin estimates that overlap within statistical errors. In MCG‑6‑30‑15, LAOR’s best‑fit inner radius of ≈1.24 r_g corresponds to a spin of a ≈ 0.98, while KYRLINE directly returns a ≈ 0.95 ± 0.07. For GX‑339‑4, LAOR gives R_in ≈ 2.0 r_g (a ≈ 0.9) and KYRLINE a ≈ 0.85 ± 0.10. The agreement reflects the limited spectral resolution and signal‑to‑noise of current XMM‑Newton and Suzaku data.

To probe the models’ performance under future high‑resolution conditions, the authors simulated spectra expected from the International X‑ray Observatory (IXO). When these synthetic data were fitted, LAOR systematically over‑estimated the spin (a ≈ 0.99) because its fixed‑spin assumption forces the fit to shrink R_in below the true ISCO, and its coarse energy grid fails to reproduce the high‑energy edge of the line accurately. KYRLINE, by fitting a directly, recovered the input spin (a ≈ 0.93 ± 0.02) and correctly identified the inner radius (≈1.5 r_g). The discrepancy demonstrates that LAOR’s limited resolution and lack of spin freedom become significant sources of bias when data quality improves.

The discussion emphasizes that while LAOR remains computationally efficient and historically popular, its built‑in spin constraint and insufficient energy resolution render it unsuitable for precision spin measurements with next‑generation observatories such as Athena, XRISM, or IXO. Moreover, physical scenarios where the disc truncates outside the ISCO (e.g., strong magnetic fields or non‑standard emissivity profiles) can be accommodated more naturally by KYRLINE’s flexible parameterisation.

In conclusion, the study finds that for present‑day data the spin values derived from LAOR and KYRLINE are statistically consistent, but for higher‑quality spectra the LAOR model tends to overestimate spin and mischaracterise the line’s high‑energy wing. Therefore, accurate determination of black‑hole spin in the era of high‑resolution X‑ray spectroscopy should preferentially employ models like KYRLINE that allow direct spin fitting and possess finer energy resolution.