Revisit of Local X-ray Luminosity Function of Active Galactic Nuclei with the MAXI Extragalactic Survey

We construct a new X-ray (2–10 keV) luminosity function of Compton-thin active galactic nuclei (AGNs) in the local universe, using the first MAXI/GSC source catalog surveyed in the 4–10 keV band. The sample consists of 37 non-blazar AGNs at $z=0.002-0.2$, whose identification is highly ($>97%$) complete. We confirm the trend that the fraction of absorbed AGNs with $N_{\rm H} > 10^{22}$ cm$^{-2}$ rapidly decreases against luminosity ($L_{\rm X}$), from 0.73$\pm$0.25 at $L_{\rm X} = 10^{42-43.5}$ erg s$^{-1}$ to 0.12$\pm0.09$ at $L_{\rm X} = 10^{43.5-45.5}$ erg s$^{-1}$. The obtained luminosity function is well fitted with a smoothly connected double power-law model whose indices are $\gamma_1 = 0.84$ (fixed) and $\gamma_2 = 2.0\pm0.2$ below and above the break luminosity, $L_{*} = 10^{43.3\pm0.4}$ ergs s$^{-1}$, respectively. While the result of the MAXI/GSC agrees well with that of HEAO-1 at $L_{\rm X} \gtsim 10^{43.5}$ erg s$^{-1}$, it gives a larger number density at the lower luminosity range. Comparison between our luminosity function in the 2–10 keV band and that in the 14–195 keV band obtained from the Swift/BAT survey indicates that the averaged broad band spectra in the 2–200 keV band should depend on luminosity, approximated by $\Gamma\sim1.7$ for $L_{\rm X} \ltsim 10^{44}$ erg s$^{-1}$ while $\Gamma\sim 2.0$ for $L_{\rm X} \gtsim 10^{44}$ erg s$^{-1}$. This trend is confirmed by the correlation between the luminosities in the 2–10 keV and 14–195 keV bands in our sample. We argue that there is no contradiction in the luminosity functions between above and below 10 keV once this effect is taken into account.

💡 Research Summary

This paper presents a new determination of the local (z ≈ 0) X‑ray luminosity function (LF) of active galactic nuclei (AGNs) in the 2–10 keV band, using the first MAXI/Gas Slit Camera (GSC) source catalog obtained in the 4–10 keV band. The authors select 37 non‑blazar, Compton‑thin AGNs with redshifts 0.002–0.2 from the MAXI catalog, achieving a very high identification completeness (> 97 %). For each source, they gather spectral parameters (photon index Γ and absorption column density N_H) from the literature (ASCA, XMM‑Newton, Suzaku, Swift/XRT) or derive them from MAXI hardness ratios when necessary. These parameters allow conversion of the observed 4–10 keV count rates into intrinsic (absorption‑corrected) 2–10 keV luminosities (L_X), including a reflection component with solid angle Ω = 2π as used in earlier work (Ueda et al. 2003).

The analysis proceeds in two steps. First, the N_H distribution (the “N_H function”) is derived by treating the LF as a delta‑function and correcting the observed N_H histogram for the survey’s flux‑dependent selection bias. The N_H function is discretized into four equal logarithmic bins between log N_H = 20 and 24, and the absorbed fraction ψ(L_X) (the proportion of sources with log N_H = 22–24) is modeled as a decreasing function of luminosity. Second, the LF itself is fitted using a maximum‑likelihood method that simultaneously incorporates the N_H function, the survey area curve, and cosmological volume elements. The LF is well described by a smoothly connected double power‑law: a low‑luminosity slope γ₁ fixed at 0.84, a high‑luminosity slope γ₂ = 2.0 ± 0.2, and a break luminosity L_* = 10^{43.3 ± 0.4} erg s⁻¹. The normalization is set so that the expected number of sources matches the observed 37, with Poisson uncertainties (≈ 1/√N).

Key results include: (1) a clear luminosity dependence of the absorbed fraction: for L_X = 10^{42–43.5} erg s⁻¹ the absorbed fraction is 0.73 ± 0.25, dropping to 0.12 ± 0.09 for L_X = 10^{43.5–45.5} erg s⁻¹, confirming earlier findings that higher‑luminosity AGNs are less likely to be obscured; (2) agreement with the classic HEAO‑1 2–10 keV LF at L_X ≳ 10^{43.5} erg s⁻¹, but a higher space density at lower luminosities, suggesting that the older survey missed a fraction of faint, possibly more absorbed AGNs; (3) a comparison with the Swift/BAT 14–195 keV LF shows that the two LFs are not directly reconcilable by a single photon index. By correlating the 2–10 keV and 14–195 keV luminosities for the same objects, the authors find that the average broadband (2–200 keV) spectral slope Γ depends on luminosity: Γ ≈ 1.7 for L_X ≲ 10^{44} erg s⁻¹ and Γ ≈ 2.0 for L_X ≳ 10^{44} erg s⁻¹. This luminosity‑dependent spectral softening explains why the 10 keV‑band LF appears different from the > 10 keV LF when a fixed Γ ≈ 1.8 is assumed.

The paper discusses the physical implications of a luminosity‑dependent spectrum. A softer spectrum at higher luminosities may reflect changes in the coronal temperature, optical depth, or the geometry of the reflecting material (e.g., larger covering factor). The observed decrease of the absorbed fraction with luminosity supports the “receding torus” scenario, where the dusty torus opening angle widens for more powerful AGNs. The authors argue that once the luminosity‑dependent Γ is taken into account, there is no intrinsic contradiction between the 2–10 keV and > 10 keV LFs, and that the local AGN LF is now better constrained across a wide luminosity range.

In conclusion, the MAXI/GSC survey provides a robust, independently derived local X‑ray LF that confirms earlier trends (luminosity‑dependent obscuration) while revealing a higher number density of low‑luminosity AGNs. The work highlights the necessity of accounting for luminosity‑dependent spectral shapes when comparing LFs derived from different energy bands, and it offers valuable constraints for models of AGN evolution (e.g., LDDE versus LAD). Future surveys with larger samples and broader energy coverage will be essential to refine these results and to explore the physical drivers behind the observed spectral changes.