The origin and physical mechanism of the ensemble Baldwin effect

In order to explore the origin and the underlying mechanism of the BEff, based on the homogeneous sample of 4178 z ≤ 0.8 Seyfert 1s and QSOs with median spectral S/N 10 per pixel in the SDSS DR4, we have conducted a systematic investigation of the line-line and line-continuum correlations for broad and narrow emission lines in the near-UV and optical, from Mg II λ2800 to [O III] λ5007. Our findings are as follows:

(i) The strongest correlations of almost all the emission-line intensity ratios and EWs are with L/L Edd , either positively (e.g. Fe II EW) or negatively (e.g. Mg II EW), rather than with L or M BH ; besides, generally intensity ratios have tighter correlations with L/L Edd than the EWs of the related lines.

(ii) The intensity ratios of Fe II emissions -both narrow and broad -to Mg II have very strong, positive correlations with L/L Edd ; interestingly enough, (narrow Fe II λ4570)/Mg II has a stronger correlation with L/L Edd than the optical and UV (broad Fe II)/Mg II, with Spearman r S = 0.74 versus 0.58 (optical) and 0.46 (UV); see Fig. 1 (Dong et al. 2009a).

These findings argue that Eddington ratio (ℓ ≡ L/L Edd ) 2 is the origin of the BEff, as of other regularities of almost all emission lines (e.g., the Fe II-[O III] anticorrelation, Boroson & Green 1992). This once has been suggested by Baskin & Laor (2004) and Bachev et al. (2004) for the C IV BEff. We propose that the underlying physics is certain self-regulation mechanisms caused by (or corresponding to) L/L Edd ; these mechanisms maintain the normal dynamically quasi-steady states of the gas surrounding the central engine of AGNs (Dong et al. 2009a,b). Briefly, the essential one is that there is a lower limit on the column density (N H ) of the clouds gravitationally bound in the AGN line-emitting region, set by L/L Edd (hereafter the N H -L/L Edd mechanism; see also Fig. 1 of Fabian et al. 2006, Marconi et al. 2008). As L/L Edd increases, the emission strength decreases for high-ionization lines (e.g. C IV) and optically thick lines that are emitted at the illuminated surface (e.g. Lyα) or in the thin transition layer (e.g. Mg II) of the BLR clouds; for low-ionization, optically thin lines such as 2 Eddington ratio is the ratio between the bolometric and Eddington luminosities. Eddington luminosity (L Edd ), by definition, is the luminosity at which the gravity of the central source acting on an electron-proton pair (i.e. fully ionized gas) is balanced by the radiation pressure due to electron Thomson scattering; L Edd = 4πGcM mp/σT, where G, c, M , mp , σT are the gravitational constant, speed of light, mass of the central source, proton mass, Thomson scattering cross-section, respectively. In accretion-powered radiation systems, L/L Edd is often referred to as dimensionless accretion rate ṁ (the relative accretion rate normalized by Eddington accretion rate ṀEdd , ṁ ≡ Ṁ / ṀEdd = ηc 2 Ṁ /L Edd , Ṁ being mass accretion rate and η the accretion efficiency) as ṁ is not an observable; yet the two notations are different both in meaning and in scope of application. Even in the accretion-powered radiation systems like AGNs, L/L Edd (L) is not equivalent to ṁ ( Ṁ ) except in the simple thin accretion disk model of Shakura & Sunyaev (1973). Therefore, we would rather call L/L Edd dimensionless luminosity (ℓ).

Fe II multiplets that originate from the volume behind the Hydrogen ionization front (i.e., from the ionization-bounded clouds only), as L/L Edd increases the emission strength increases. 3 This is schematically sketched in Fig. 2.

I. An implication is that BG92’s PC1, if only the spectral correlations in the UV-optical are concerned, shares the same origin with PC2 that is exactly the He II BEff. A lesson is that we should be more cautious about the premises of blind source separation methods such as Principal Component Analysis.

II. As suggested insightfully by G. Richards (e.g. Richards 2006), the C IV line blueshifting (in other words, blue asymmetry) is the same phenomenon of BEff. The underlying physical picture is clear now: There are two components in the C IV emission, one arising from outflows and the other from the clouds gravitationally bound in the BLR; the fraction of bound clouds that optimally emit C IV line decreases with increasing L/L Edd according to the N H -L/L Edd mechanism.

III. If the observed large scatter of Fe II/Mg II at the same redshift is caused predominately by the diversity of L/L Edd , then once this systematic variation is corrected according to the tight Fe II/Mg II -L/L Edd correlation, it is hopeful to still use Fe II/Mg II as a measure of the Fe/Mg abundance ratio and thus a cosmic clock (at least in a statistical manner ).

Appendix: Not Baldwin Effect, but ell Effect?

This Appendix is to present more results taken

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