Free Access
Issue
A&A
Volume 555, July 2013
Article Number A89
Number of page(s) 16
Section Extragalactic astronomy
DOI https://doi.org/10.1051/0004-6361/201321374
Published online 05 July 2013

© ESO, 2013

1. Introduction

Estimations of black hole mass (MBH) and Eddington ratio (L/LEdd) for large and diverse samples of quasars (Marziani & Sulentic 2012; Shen 2013, and references therein) are needed for both astrophysical and cosmological studies. Until recently the majority of virial black hole MBH estimates have not taken profile diversity into account. Instead, broad-line FWHM measures have been assumed to be valid virial estimators in all quasars. The situation becomes even more complicated when we compare FWHM estimates derived from different lines that often show quite different profile shapes (e.g., Wills et al. 1993; Brotherton et al. 1994; Barthel et al. 1990; Baskin & Laor 2005; Zamfir et al. 2010; Ho et al. 2012). The goal of the present paper is to systematize differences between Hβ and Mgiiλ2800 in the process of comparing the relative merits of FWHM Hβ and Mgiiλ2800 as virial broadening estimators. This is done within the context of a 4D eigenvector 1 parameter formalism.

Interpreting of quasar spectra in the context of a 4D parameter space stemming from eigenvector studies reveals a wide diversity of line profile properties (Sulentic et al. 2000a, 2007; Marziani et al. 2003b, 2010) that are most likely driven by L/LEdd, with MBH and source orientation also playing important roles (Boroson & Green 1992; Marziani et al. 2001; Yip et al. 2004). The 4DE1 (4D eigenvector 1) formalism owes its inception to a principal component analysis study of systematic trends in quasar spectra (Boroson & Green 1992) from the the Palomar-Green (PG) survey. The first eigenvector (E1) included a correlation between [Oiii]λλ4959,5007 and optical Feii strength and an anti-correlation between the latter parameter and FWHM Hβ. Variants of E1 were later found in several studies (e.g. Marziani et al. 1996; Boroson 2002; Grupe 2004; Kuraszkiewicz et al. 2002; Sulentic et al. 2000b, 2002; Yip et al. 2004; Kovačević et al. 2010; Kruczek et al. 2011; Tang et al. 2012; Wang et al. 2006).

The eigenvector 1 was eventually expanded into a 4DE1 parameter space (Sulentic et al. 2000a, 2007) with the addition Civλ1549 profile shift and soft X-ray photon index as important parameters that show some of the strongest intercorrelations. The higher dimensionality involves parameters that are observationally independent and that correspond to different physical processes (see the reviews by Sulentic et al. 2000a and Marziani & Sulentic 2012 for more detailed discussions). Quasars occupy a well defined sequence in the “optical plane” of 4DE1 defined by the FWHM of the Hβ broad component and by the intensity ratio between Feiiλ4570 and Hβ, RFeII = I(Feiiλ4570)/I(Hβ) (Boroson & Green 1992; Sulentic et al. 2002). The 4DE1 optical plane therefore offers a tool that allows for defining and identifying quasar populations or spectral types.

Exploration of the 4DE1 parameter space gave rise to the concept of two quasar populations that, if not truly distinct, are an effective way to distinguish important spectroscopic differences between quasars. Population A sources show a wide range of broad-line widths (FWHM Hβ ~ 600–4000 km s-1) with a majority of sources (in low redshift samples) between FWHM Hβ ~ 1000–4000 km s-1. A few sources with RFeII> 0.5 show FWHM Hβ> 4000 km s-1 which was partial motivation for the Pop. A-B formalism. Population A involves a largely radio-quiet quasar population because few radio-loud quasars (especially with double-lobe Fanaroff-Riley II (FRII) radio morphology) show FWHM Hβ< 4000 km s-1 (Zamfir et al. 2008). Those active galactic nuclei (AGN) with FWHM Hβ ≤ 2000 km s-1 are often referred to as narrow-line Seyfert 1 (NLSy1) sources but there is continuity in source properties over the full Pop. A range of FWHM Hβ.

The Population A definition changes in higher redshift samples because the minimum observed broad-line FWHM of Hβ slowly increases with source luminosity (see Fig. 11 in Marziani et al. 2009; and Dultzin et al. 2011). Population A Hβ profiles are best fit with a single symmetric Lorentz function, while Pop. B are not. Following previous results for Hβ, we fit all Pop. A Mgiiλ2800 profiles with Lorentz functions (Véron-Cetty et al. 2001; Sulentic et al. 2002).

Population B quasars show an even wider range of FWHM Hβ than Pop. A sources. The full observed range is FWHM Hβ = 4000–40 000 km s-1 (Wang et al. 2009), but values FWHM Hβ> 16 000 km s-1 are extremely rare with almost all sources in a low redshift sample between 4000 km s-1 and 12 000 km s-1. Most Pop. B sources show RFeII< 0.5. Population B is a mixed radio-quiet and radio-loud population with the majority of radio-loud sources within population B. Population B sources are different from Pop. A because – most fundamentally – they show composite Hβ profiles. The majority of Pop. B Hβ profiles can be modeled with an (almost) unshifted broad (BC) and redshifted very broad component (VBC). It is usually assumed that the unshifted BC is the same as the single component observed in Pop. A sources while the VBC is something non-virial and apparently unique to Pop. B sources (both radio-quiet and radio-loud). Further discussion of Pops. A and B is provided by Sulentic et al. (2011).

The equation used to estimate MBH can be written, under the assumption that line broadening in quasars is due to virialized motions in the emitting gas, as (1)where ℱ is factor ≈1 that depends on geometry of the emitting gas (e.g., Onken et al. 2004; Graham et al. 2011), rBLR is an emissivity-weighted radial distance of the broad line-emitting region (BLR), and Δv is the virial broadening term, which is customarily measured from the width of a suitable emission line. The most accurate MBH estimates come from reverberation mapping measures of rBLR(e.g. Horne et al. 2004; Denney et al. 2009) coupled with Hβ rms profile widths (FWHM or velocity dispersion σ; Peterson et al. 2004).

We now have ≈60 reverberation derived radii (Bentz et al. 2009, 2010, 2013). The cost in telescope time for such accurate rBLR and rms line width estimates is very high even for the brightest sources. It is clear that we must rely on secondary methods to obtain large numbers of additional MBH estimates, as needed for the analysis of an ever increasing population of cataloged quasars (Schneider et al. 2010; Ross et al. 2012). These methods involve single-epoch FWHM measures and rBLR estimates derived from the apparent correlation between reverberation derived radii and source luminosity measures (the so-called “Kaspi relation”; Kaspi et al. 2005). We suggest that line measures for large source samples can be utilized better if 4D parameter space coordinates for each source are taken into account. This is especially true if 4DE1 coordinates are driven by the source Eddington ratio.

Important issues connected with the use of Eq. (1) involve: 1) the validity of extrapolating the Kaspi relation beyond the range of redshift and source luminosity represented in the reverberation sample and 2) estimation of the virial broadening Δv. There are two sides to virial broadening estimation: a) the choice of a suitable emission line (assumed primarily broadened by virial motions) and b) selection of a suitable parameter (FWHM, σ) to define the virial broadening Δv. Single-epoch FWHM Hβ measures have provided MBH estimates for large samples at low and high redshifts. Measurements of the second moment σ are less useful in the case of a broad lines with more than one component. Beyond redshift z ≳ 0.7 we lose the most trusted source of single-epoch FWHM measures (i.e. Hβ). We can either follow Hβ into the infrared or adopt FWHM measures of other broad lines as virial estimators. We have adopted the former approach, taking advantage of Very Large Telescope (VLT) ISAAC (Moorwood et al. 1998) spectroscopy to follow Hβ through the IR windows and obtain MBH estimates that are as accurate as possible for ≈50 luminous quasars in the range z ≈ 1.0−3.0 (Sulentic et al. 2004, 2006; Marziani et al. 2009). We are currently processing a sample of ≈25 sources where Hβ is redshifted into the K band window (z ≈ 3.0−3.7) beyond which Hβ is lost (Sulentic et al., in prep.).

The strongest available surrogate broad lines that are redshifted into the optical over a wide z range are Civλ1549 and Mgiiλ2800. The region of Ciii]λ1909 is a blend of permitted and semiforbidden lines whose apparent intricacy has deterred previous workers, although there is potential for progress if moderate-resolution, high S/N spectra are available (Marziani et al. 2010, 2011; Negrete 2011; Negrete et al. 2012). Civλ1549 is not recommended as a virial estimator because FWHM Civλ1549 does not even show a correlation with FWHM Hβ (Marziani et al. 1996; Sulentic et al. 2007; Netzer et al. 2007; Shen et al. 2008; Richards et al. 2011). Civλ1549 also shows a blueshift and profile asymmetry in many sources (Gaskell 1982; Brotherton 1996; Sulentic et al. 2007; Richards et al. 2011), which challenges the validity of the virial assumption. Some consistency can be achieved if several cautions and corrections are applied to the Civλ1549 measures (Assef et al. 2011; Denney 2012; Greene et al. 2010, and especially in the 4DE1 context as done by Sulentic et al. 2007), but this is not the road to MBH estimates with uncertainties less than 1 dex. In the 4DE1 context (Sulentic et al. 2000b) both Hβ and Civλ1549 show strikingly different profile properties for Pop. A and B sources. Such differences cannot be easily quantified with low-resolution and/or low S/N spectra.

The rest wavelength of Mgiiλ2800 makes it a potentially valuable ground-based virial estimator from z ≈ 0.4 up to z ≈ 2.1. Rapid improvements in IR spectroscopy also makes Mgiiλ2800 accessible at higher redshifts. It has been measured in K band for the quasar with the highest known redshift, z ≈ 7.085 (Mortlock et al. 2011). Is Mgiiλ2800 a safe Hβ surrogate? The doublet Mg+λλ2796,2803 is a low ionization line (LIL) that has long been thought to be produced in a dense optically thick region where at least part of the Balmer lines arise (Grandi & Phillips 1979; Netzer 1980). A possible complication is that Mgiiλ2800 is a resonance line and therefore often affected by broad (Ganguly & Brotherton 2008) and narrow absorption (Wild et al. 2008). Several authors have attempted to define a relation between Mgiiλ2800 and Hβ to provide consistent MBH estimates from the two lines (McLure & Jarvis 2002; Vestergaard & Peterson 2006; Wang et al. 2009; Shen & Liu 2012; Trakhtenbrot & Netzer 2012). Mgiiλ2800 is assumed to be a virial estimator as reliable as Hβ because their line widths are correlated. The latest studies, however, show considerable scatter (and deviation from parity) in the FWHM Hβ vs. FWHM Mgiiλ2800 correlation. There is strong evidence that the FWHM of Mgiiλ2800 is about 20% smaller than FWHM Hβ (Wang et al. 2009) in many sources.

We report here on a more detailed comparison of Hβ and Mgiiλ2800 as virial estimators. This work goes beyond several recent works that consider line shape properties (shifts and asymmetries, the presence of a very broad component) that could weaken or invalidate the virial assumption. Such a more detailed study requires separate consideration of sources with FWHM Hβ less than or greater than 4000 km s-1 (Pops. A and B respectively; cf. Pops. 1 and 2 of Collin et al. 2006). Results for Pop. A sources were presented in a companion paper (Marziani et al. 2013, hereafter Paper I). The majority (≈80%) of Pop. A sources show an unshifted Mgiiλ2800 profile that is significantly less broad (~20%) than Hβ making it the virial estimator of choice. Population A Hβ profiles are best fit with a single symmetric Lorentz function. Gaussian fits to Pop. A profiles will result in a systematic overestimation of MBH. This paper focuses mainly on Pop. B sources where broader and more complex lines are observed. A subset of Pop. A sources shows a significant Mgiiλ2800 blueshift (Paper I) making FWHM Hβ a safer virial estimator. These sources can be described as the youngest least-evolved quasars with strong ongoing star formation among all quasars in the present sample (e.g., Sulentic et al. 2000a; Mathur 2000; Wang et al. 2006; Sani et al. 2010). Extreme values of RFeII appear to be an empirical signature of quasar youth perhaps reflecting extreme low ionization and metal enrichment as well (cf. Paper I).

The advent of the Sloan Digital Sky Survey (SDSS) makes an accurate direct comparison of Hβ and Mgiiλ2800 possible using the brightest 600+ quasars where both lines appear in the spectra (Sect. 2 describes the sample of SDSS quasars). Individually most of these spectra are too noisy (typically S/N < 5 in the continuum near the two lines) to yield good measures and, therefore, a reliable application of MBH – FWHM – relations. We want to move beyond single-epoch measures of the past 20 years involving random samples that yield the same result – quasar black hole masses with mean MBH ~ 8.5 ± 1.5 (see the paradoxical result of Croom 2011). We think that the best path to accomplishing this goal involves generating median composite spectra in the 4DE1 context (Sulentic et al. 2002, Sect. 3). The composites can provide very high S/N line profiles from which more accurate measures can be obtained. Results for line profiles and trends are given in Sect. 4. Our findings are discussed in Sect. 5 which presents the necessary cautions and calibration factors that can ultimately yield improved MBH values. We only briefly analyze (Sect. 5.5) a luminosity-dependent scaling law, such as the one recently presented in Trakhtenbrot & Netzer (2012) as well as the determination of ℱ, which is a distinct and very complex problem (e.g., Collin et al. 2006; Netzer & Marziani 2010; Graham et al. 2011; Park et al. 2012).

2. Sample selection and spectral binning

2.1. Sample selection

Spectral binning offers the possibility of generating much higher S/N composite spectra using the SDSS database if a binning context can be identified. We searched SDSS-DR7 for sources cataloged as type-1 AGN (quasars) in the redshift range 0.4−0.75 and with magnitudes brighter than ≈18.5 in the g, r or i bands. Below the assumed magnitude limit, the low S/N of individual spectra make it difficult to estimate even FWHM Hβ and RFeII well enough to permit reliable bin assignments. We also searched the list of Zhou et al. (2006) in order to include type-1 AGN showing broad line FWHM Hβ< 1000 km s-1. Such sources are not identified as quasars in SDSS but show strong FeII emission characteristic of type 1 AGN. The resultant sample consisted of 716 quasars. The next step involved discarding very noisy spectra and some sources with unusually red colors (obviously reddened quasars where Mgiiλ2800 was very weak or absent) thus reducing the sample (the same one considered in Paper I) to 680 quasars. Narrow and broad absorption line sources were excluded from the sample unless, in the case of narrow absorption lines, the absorption was judged insufficient to affect our ability to measure broad line binning parameters.

2.2. Spectral binning

Spectral binning in the 4DE1 optical plane maps sources using measures of FWHM Hβ vs. RFeII = W(Feiiλ4570) / W(Hβ) ≈ I(Feiiλ4570)/I(Hβ), where Hβ refers to measures of the broad line profile of Hβ (HβBC) corrected for narrow line Hβ emission as well as any contamination from [Oiii]λλ4959,5007, Heiiλ4686, and Feii emission (Sulentic et al. 2002). Recent works, including the present one consider the intensity ratio rather than the ratio of equivalent widths. Spectral types are defined by binning in intervals of RFeIIRFeII = 0.5, from A1 [RFeII< 0.5] to A4 [1.5 ≤ RFeII< 2.0]) and FWHM (ΔFWHM Hβ = 4000 km s-1, from A1 (FWHM Hβ ≤ 4000 km s-1) and B1 to B1++ [12 000 km s-1FWHM Hβ< 16 000 km s-1]). Separating the sample into spectral types will allow us to avoid the danger of mixing sources together that show very different spectral line profile properties. Insofar as Hβ and Feii measures reflect physical conditions in the BLR, the bins isolate sources with similar values of density, ionization parameter, and L/LEdd (see e.g., Marziani et al. 2001, 2010). Binning allows us to also take the complexity of line profiles into account, and to separate, at least in a heuristic way, major flux contributions that are due to gas that is not likely to be virialized (i.e., the redshifted very broad component of Hβ in Pop. B sources). Bin assignments were made as described in Paper I. We made a final inspection supplemented by IRAF SPLOT measures for sources falling near bin boundaries. A few dozen sources were moved into adjacent bins but none of this fine tuning is likely to have had much effect on resultant median composites. Two bins (A2 and B1) are most densely populated while our binning contains enough sources to permit generation of composites for eight bins that span the FWHM Hβ and RFeII ranges occupied by the majority of low redshift type 1 sources (with an inferred 2 dex range in Edditington ratio, 0.01 ≲log  L/LEdd ≲ 1 that is the one of luminous type-1 AGN; Woo & Urry 2002; Marziani et al. 2003b; Kollmeier et al. 2006; Davis & Laor 2011).

Table 1

Sample: number of sources in each spectral type.

Table 1 gives the number of sources (Ntot) in each bin. Boldface numbers indicate spectral types for which a composite spectrum was constructed. The separation into Pop. A and B sources almost evenly divides low redshift z < 1.0 quasar samples (45% Pop. B in Zamfir et al. 2010, and 54% in this study). Bin B2 was almost devoid of sources in previous studies of low-luminosity sources (Marziani et al. 2003a; Zamfir et al. 2010), while it accounts for 3% of the present sample. Sources with B2 spectra are more numerous at high luminosity where they account for ≲20% of our VLT/ISAAC sample (Marziani et al. 2009). Given the shape of the source distribution in the 4DE1 optical plane and the crudeness of the binning, it is likely that bin A1 is a blend of A2 and B1 sources. The B2 composite is mainly due to spectra of sources whose location in the 4DE1 optical plane is close to the boundary of A2 and B1. In other words, it could be that B2 sources are a physically diverse mixture (Marziani et al. 2001). More than anything else, B2 provides a hints of the confusing results that one would obtain by mixing B1 and A2 spectra. Data and measures on B2 are reported but scantily discussed.

2.3. Radio loud sub-samples

The entire sample of 680 binned quasars was cross-correlated against the Faint Images of the Radio Sky at Twenty-Centimeters (FIRST) catalogue (Becker et al. 1995). Radio maps and catalog data for 163 FIRST-detected sources were used to isolate radio-loud (RL) quasars from the general radio-quiet (RQ) population. The majority of RL sources belong to Pop. B (Sulentic et al. 2003; Zamfir et al. 2008). Most radio-detected RQ sources show core-dominated (CD), sometimes core-jet morphology. Sources were classified as RL lobe-dominated (LD) when a visual inspection revealed a complex, usually double-lobe structure. All sources except one1 have radio power log Pν ≥ 31.6 at 1.4 GHz (Pν in units of erg s-1 Hz-1), the nominal lower specific power for Fanaroff-Riley II (FRII) sources. The radio morphology defines the classical RL phenomenon with the weakest FRII sources that provide an empirical lower limit for this activity. Compact sources were considered core-dominated (CD) RL if their rest frame specific emission was above the FRII lower limit, as in Zamfir et al. (2008). This corresponds roughly to RK = 70 as defined in Kellermann et al. (1989). The lower limit of radio power in FRII sources excludes all or most radio-detected RQ sources that appear as CD in FIRST. Table 1 reports the number of sources in each bin along with the numbers of FIRST detections (NFIRST). FIRST nondetections (i.e. undetected RQ sources) and detections are tabulated in Cols. 3 and 4. FIRST should detect all RL sources in the redshift range under consideration. Radio detections were assigned an FRII or CD morphology (numbers of sources are in Cols. 5 and 6) based on inspection of FIRST images.

3. Generation and analysis of composite spectra

Three steps preceded generation of composite spectra: 1) assignment of sources to spectral bins as described in the previous section; 2) deredshifting of source spectra using SDSS z values; and 3) application of a second-order correction connected with a known bias in SDSS redshift estimates (Hewett & Wild 2010). Accurate rest frame definition can be a serious problem. Knowledge of the rest frame is important for identification and physical interpretation of internal broad and narrow line shifts that show a wide velocity range. They differ widely from source to source and depend on ionization state (Gaskell 1982; Tytler & Fan 1992). The technique used for redshift computation in SDSS is reliable but not accurate enough to yield uncertainties as low as ≈30 km s-1 (Hewett & Wild 2010). The [Oiii]λλ4959,5007 line strength is a known E1 correlate with [Oiii]λλ4959,5007 becoming weaker, broader, and hence more difficult to measure as one proceeds from the B to the A1 bin and along the sequence from bin A1 to A4 (Sulentic et al. 2002; Zamfir et al. 2010). Bin A3 and A4 sources show a systematic [Oiii]λλ4959,5007 blueshift with respect to low ionization narrow lines. The shift amplitude in these “blue outliers” is also believed to be related to the E1 sequence (Zamanov et al. 2002; Marziani et al. 2003b; Komossa et al. 2008; Hu et al. 2008).

Wavelengths of the three most prominent narrow lines [Oii]λ3727, Hβ, and [Oiii]λ5007 were measured whenever detected. Systematic shifts were computed by taking an average of the three lines in each source spectrum and clipping individual measurements in cases of disagreement because of poor data or intrinsic blueshift of [Oiii]λ5007. This means that only two lines could be used for redshift determination in several cases. In a few cases (especially in A3 and A4 bins, where oxygen lines can be very weak) only HβNC could be used or, failing that, the adopted SDSS z value. The “bias” in the SDSS redshift determination is larger for extreme A bins but relatively small for Pop. B and bin A1 sources. This is not surprising, since bin B1 shows stronger and sharper narrow lines that permit more accurate redshift determinations with the SDSS algorithm.

After sample selection, bin assignments, and redshift correction we generated median composite spectra for Hβ and Mgiiλ2800. RL and RQ composites were also constructed for bin B1. Wavelength uncertainties of composite spectra were quantified by measuring a posteriori additional low-ionization narrow lines. Systematic effects were found to be small, with a radial velocity difference Δvr ≲ 25 km s-1. The dispersion in radial velocity is σΔvr ≲ 50 km s-1 for all bins in line with estimations of Hewett & Wild (2010). In practice this means that any line is assumed to be unshifted if σΔvr ≲ 100 km s-1.

3.1. Hβ and MgIIλ2800 spectral range

Interpretation of the Hβ and Mgiiλ2800 spectral ranges closely follows previous work (Boroson & Green 1992; Marziani et al. 2003a) and has been discussed in Paper I. We only mention that emission blends near Mgiiλ2800 are mainly due to Feii, which is modeled with the FeiiUV emission template provided by the last model in Table 1 in Brühweiler & Verner (2008). The main results presented in this paper were also tested with an additional empirical template produced by Tsuzuki et al. (2006). Fei emission was detected in Paper I, but appears to be fainter (along with any contribution due to Balmer continuum) in B spectral types. Adopted ranges for the multicomponent fitting analysis are 2600–3050 Å and 2400–3100 Å for Pops. A and B, respectively. Known noniron lines in this region include [Neiv] 2423.8, [Oii] 2471.0, semi-forbidden Alii] 2669.95, O iii 2672.04, and most probably Hei 2945.11.

thumbnail Fig. 1

Predicted intensity ratio of the doublet the Mg+ lines as a function of ionization parameter U and hydrogen density nH. Contour lines are drawn in steps of 0.1 from 1.0 to 2.0.

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thumbnail Fig. 2

Spectra of Hβ (left panels) and of Mgiiλ2800 (right panels) for spectral types B1 to B1++ (from top to bottom). The horizontal scales are in rest frame wavelength [Å] or radial velocity, with the origin set at the rest frame wavelength. The black lines shows the original, continuum-subtracted spectrum, and the dashed magenta line the model with all emission line components. The thick black line is the BC; the thick red line shows the VBC. The green lines trace the Fe iiopt and FeiiUV contribution, and the gold lines various contributions associated to the NLR (HβNC, [Oiii]λλ4959,5007, and Mgiiλ2800 narrow component when appropriate). Excess emission at λ ≳ 2900 Å visible in this and in the next two figures is likely due to a combination of Fei and Balmer continuum emission.

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3.1.1. The ratio of the MgIIλ2800 lines

The intensity ratio of the Mgiiλ2800 doublet R = I(Mg iiλ2796.35)/I(Mg iiλ2803.53) 2 due to transitions should be 2:1 in the pure optically thin case. In the case of infinite optical depth, the ratio should be 1:1 (i.e., if lines are fully thermalized). For intermediate conditions the ratio depends on electron density, temperature, and column density. Under standard assumptions the condition for thermalization on the product ionization parameter times hydrogen density nH is UnH ≳ 1.7 × 107 cm-3 (Laor et al. 1997; Hamann et al. 1995). We therefore expect an R value close to 1:1 for likely values of U and nH in both the BLR and the very broad line region (VBLR) associated with the VBC. An array of CLOUDY (Ferland et al. 1998) simulations predicts the intensity ratio as a function of hydrogen density nH and ionization parameter U (Fig. 1; a fixed hydrogen column density of 1024 cm-2 and solar abundances are assumed).

thumbnail Fig. 3

Spectra of Hβ (left) and of Mgiiλ2800 (right) for spectral type B2. Meaning of symbols/line colors is the same of the previous figure.

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The individual lines are too broad, hence too blended, to permit reliable direct measurement. A priori values must be assumed for BC and VBC (the latter only for Pop. B sources) and the values could be different in lieu of the different physical conditions expected for the BLR and the VBLR (Marziani et al. 2010). In the BLR, log U = −2.75, log  nH = 12.50 yield R≈ 1.3:1. The observed ratio R in a typical Population A NLSy1 source (I Zw 1) is 1.2. We assume a standard value of 1.25, noting that a small change of ±0.05 in the doublet ratio does not affect line decomposition and FWHM measurement.

The intensity of Mgiiλ2800 is difficult to compute by photoionization codes because the line is primarily emitted in the partially ionized zone, where a local approximation (i.e., via a local mean escape probability) treatment of radiation transfer is probably inadequate. It is possible that the Mgiiλ2800 lines become fully thermalized at the extreme optical depth of the LIL emitting part of the BLR, justifying the assumptions of a 1:1 ratio. In the following we therefore have considered both cases.

Table 2

Measured parameters on the Hβ and Mgiiλ2800 profiles of composite spectra.

Table 3

Derived quantities from the Hβ and Mgiiλ2800 profiles composite spectra multicomponent analysis.

Mock Mgiiλ2800 profiles were computed for 1:25 and 1:1 cases assuming a wide range of line FWHM. The peak wavelengths used as a reference, whenever the doublet is treated as unresolved, are 2800.1 Å and 2799.4 Å for the 1:1,1.25:1 cases, respectively. These values are found to be almost independent of FWHM. We assumed that the doublet wavelength cannot be shorter than 2799.1 Å, the value obtained for the case R= 1.5:1. Values of R≳ 1.5 are unlikely for the physical conditions expected within the BLR (Fig. 1).

In the VBLR, R≈ 1.5 is appropriate for −1 ≲ log U ≲ −0.5 and for high density values (nH ≳ 1011 cm-3), and only values R≳ 1.7 are unlikely. Considering, however, that the doublet component separation is Δλ ≈ 8 Å ≪ FWHM(VBC), the VBC can be treated as a single line. Under this assumption the doublet ratio is indeterminate.

4. Results

4.1. Broad line profile shapes

Composite spectra for Pop. B sources are shown in Fig. 2, and Fig. 3, after continuum subtraction (Pop. A median spectra were shown in Paper I). Table 2 reports FWHM, asymmetry index A.I., kurtosis κ and centroid at fractional intensity measures for the Hβ and Mgiiλ2800 broad profiles (i.e. after narrow components and Feii subtraction but before broad/very broad component decomposition) of both Pops. A and B spectral types. A.I., κ, and centroids are defined by Eqs. (1)–(3) in Zamfir et al. (2010). We note that A.I. is defined at maximum intensity and with respect to line peak while centroids are relative to the source rest frame. These parameter values provide an empirical description of the profile without any model assumption. Reported uncertainties are at 2σ confidence level and have been computed by measuring the effect on the profile parameters of changes in continuum placement (always less than 2%, due to the extremely high S/N). Full profile measures for the Mgiiλ2800 doublet assumed an unresolved single line. Width measures for Mgiiλ2800 can be converted to a single component width by subtracting 300 km s-1 (Trakhtenbrot & Netzer 2012). Zero point wavelengths set by [Oii]λ3727 and Hβ narrow component agree within an rms of 10 km s-1. Uncertainties were estimated by propagating the zero point rms, the scatter associated with SDSS wavelength calibration and the uncertainty of continuum placement.

The most important results from Table 2 are the difference in line profile properties for Pop. A and B. FWHM differences among Pop. B spectral types arise from the definition of 4DE1 and how it is binned. Population A sources show broader, more symmetric and less shifted Hβ profiles than Mgiiλ2800, with the exception of bins A3 and A4 where a blue asymmetry is observed. Mgiiλ2800 and Hβ both show a symmetric, unshifted profile in bins A1 and A2. The broad Mgiiλ2800 profile appears symmetric but blueshifted by ≈–300 km s-1 in bins A3 and A4 and these are the only sources where FWHM Mgiiλ2800 exceeds FWHM Hβ. This has been seen before and interpreted as evidence of outflows in the highest L/LEdd A3 and A4 sources (Paper I), possibly because of a distinct LIL component connected to the blue shift observed in HILs like Civλ1549.

Population B sources are largely represented by bins B1 and B1+. Figure 2 confirms previous claims (Wang et al. 2009) that FWHM Hβ is systematically broader than FWHM Mgiiλ2800 by approximately 20%. This appears to be true for all B bins as well as bins A1 and A2. Both Hβ and Mgiiλ2800 Pop. B profiles show median red asymmetries; Mgiiλ2800 perhaps shows slightly weaker asymmetries. Centroid shifts are redward and have larger amplitudes in Hβ than Mgiiλ2800. The red asymmetry in the lower half of the profile has previously been interpreted, in the case of Hβ, as a signature of the VBC (Sulentic et al. 2000c, 2002). Apparently Mgiiλ2800 shows a (weaker) VBC component. Much of the excess Hβ profile width may be due to a stronger VBC component. In other words, the measures on line profiles of Pop. B reported in Table 2 suggest that Hβ is more strongly affected than Mgiiλ2800 by nonvirial motions especially toward the line base. However, the VBC cannot be a full explanation of the difference in line width between Mgiiλ2800 and Hβ because A1 and A2 (where no VBC is present) show the same effect.

Somewhat higher kurtosis values are found for broader Pop. B sources since Pop. A profiles are more sharply peaked (cf. Kollatschny & Zetzl 2013, see Sect. 5.3 for interpretation). The kurtosis index is consistent with a single Gaussian profile (κ ≈ 0.44) only for spectral type B1++, since both Hβ and Mgiiλ2800 B1++ profiles are rare, very broad and complex sometimes show double-peaked lines, although not in our sample.

4.2. Multicomponent analysis

IRAF SPECFIT (Kriss 1994) was used to model and decompose line blends and components in Pop. B composites as previously reported for Pop. A composites (Paper I). We assumed a weak Mgiiλ2800 narrow component in Pop. B composites (see Wang et al. 2009 and references therein) constrained to not exceed the ratio Mgiiλ2800/HβNC ≈ 2 (appropriate for log U ~ −2 and log  nH ≈ 4−5). A double Gaussian model involving an unshifted BC and redshifted VBC was used for fits to both lines following previous work on Hβ (Marziani et al. 2009; Figs. 2 and 3). In contrast to Pop. B, the majority of Pop. A profiles were well fit by an (almost) unshifted symmetric Lorentz function. Table 3 presents BC and VBC measures (intensity, peak shift and FWHM) for Hβ and Mgiiλ2800 for B spectral type and for the source PG 1201+436. Uncertainties are 2σ confidence level. Uncertainties of peak shifts were computed by quadratically propagating errors on zero point, wavelength calibration rms and uncertainty provided by the fitting routine (Paper I). Uncertainties reported for the VBC should be considered as formal errors and are computed following the assumption that the best fit is the correct one and that the functional form describing the line component is also correct. The VBC is a broad component with poorly constrained centroid and width. More realistic uncertainties are estimated around 20% for both shift and width measures.

Our operating assumption is that unobscured gas in virial motion should give rise to a reasonably symmetric/unshifted line profile. The BC component is therefore the virial estimator that we are trying to isolate. The use of a double Gaussian model in SPECFIT was motivated by the inflected appearance of the Hβ profile (this is evident in the B1 panel of Fig. 2). Decomposition of the BC/VBC blend was the most uncertain part of the modeling. We derived the ratio of BC/VBC intensity for the two lines from the fit in the B1, B2 and B1+ cases. However, we do not know the shapes of the individual components. A highly redshifted VBC is unlikely to show a symmetric Gaussian profile. Past work has focused on Hβ and has used very high S/N composites like the ones presented here. Past work involving BC+VBC decomposition (Sulentic et al. 2002; Marziani et al. 2009) is limited and shows FWHM Hβ BC and shift values in the range 4000–4800 km s-1 and zero km s-1, respectively, with the relative strength of the VBC possibly increasing with source luminosity.

Modeling is clearly more ambiguous in sources with broader multicomponent profiles. The Mgiiλ2800 profile in Pop. B sources also deviates from a single Gaussian showing a narrower core and more prominent wings. In other words it is more similar to a Lorentz/Voigt profile that can be approximated by the sum of the Gaussians. An attempt to fit Mgiiλ2800 in the B1 composite with a single Lorentzian will reproduce the observed red wing but model the blue one with a significant excess. The sum of two Gaussians, with the broadest one slightly redshifted provides a satisfactory fit (Fig. 2). The introduction of a small shift in the broader Gaussian accounts for the excess flux in the red wing, prominent in Hβ but also detected in Mgiiλ2800. Nonetheless the assumption that the VBC is a shifted symmetric Gaussian is unlikely to be correct for such a redshifted component: nonvirial motions are likely to strongly affect the VBC. We currently have no empirical basis for fitting the VBC with more complex models. Our best current fits suggest that the Mgiiλ2800/Hβ intensity ratio differs for the VBC and BC: with Mgiiλ2800/Hβ ≳ 1.5 for the BC and Mgiiλ2800/Hβ ≲ 1 for the VBC. This result is consistent with the idea that the VBC arises in a higher-onization VBLR near the inner edge of the BLR (Korista & Goad 2004).

thumbnail Fig. 4

Spectrum of Hβ (left panels) and of Mgiiλ2800 (right panels) for the B1++ source PG 1201+436. Color coding is the same as for Fig. 2 save for the blue line that traces a blueshifted peak visible in both Hβ and Mgiiλ2800 (Sects. 4 and 5.3). Horizontal scale is rest frame wavelength or radial velocity shift from rest frame. The vertical scale is specific flux in units of 10-15 erg s-1 cm-2 Å-1.

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Modeling the VBC as a distinct component is further justified by the discovery of sources where the Hβ profile is dominated by the VBC with little or no detected BC (e.g. PG 1416−129 in Sulentic et al. 2000c, and 3C 110 in Marziani et al. 2010). In the course of assembling the sample under consideration in this study we found a few more VBC-dominated sources. The best example involves PG 1201+436 whose Hβ and Mgiiλ2800 profiles are shown in Fig. 4. Most of the broad redshifted Hβ profile is almost certainly VBC with little or no BC emission. The most straightforward interpretation of the Mgiiλ2800 profile is, conversely, BC dominated with much weaker VBC emission. We can use these considerations to cautiously guide SPECFIT in modeling of Mgiiλ2800 in bin B sources with the broadest profiles, i.e., B1++. B1++ sources, however, constitute less than 3% of our sample. They are nonetheless relevant if for no other reason that bin B1++ shows the largest RL fraction in the 4DE1 sequence (Zamfir et al. 2008 and Table 1). This is also the domain of some of the best known sources that show double-peaked profiles (Eracleous & Halpern 2003), although most do not. A BC+VBC profile with peaks near zero + redshift is not a double-peaked profile. The fit for B1++ shown in Fig. 3 assumes a BC-dominated Mgiiλ2800 profile and attempts to maximize Mgiiλ2800 BC intensity and width. It is interesting that the resulting Mgiiλ2800 profile 1) remains less broad than HβBC and 2) requires a VBC component to produce an acceptable fit.

thumbnail Fig. 5

Continuum subtracted spectral ranges of Hβ (top) and Mgiiλ2800 (bottom) for RQ (left), CD (middle) and FRII (right) median composites computed in the B1 bin. Meaning of symbols is the same of the previous figures.

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Results detailed in Table 3 and Figs. 2 and 3 indicate that in Pop. B sources Mgiiλ2800 mimics Hβ by showing a VBC component. They also show that the VBC has a stronger effect on FWHM Hβ when measuring the full profile. In this sense FWHM Mgiiλ2800 BC appears as a safer virial estimator than FWHM Hβ. The BC measures are preferred as virial estimators for both lines with a consistency correction factor taking into account that FWHM Mgiiλ2800 (BC) is 20% narrower than FWHM Hβ for the majority of sources (B bins and bins A1+A2, 90% of our sample). Nonetheless, all measures reported in Tables 2 and 3 for all spectral types excluding A3 and A4 show that the FWHM of any Mgiiλ2800 component is narrower than the equivalent Hβ component. This result is robust since it also holds for the full profile.

Table 3 indicates that B1 sources may show a significant Mgiiλ2800 BC blueshift, with smaller amplitude in km s-1 than the one measured in Pop. A. A low blueshift might also be present for B1++. Part of the BC blueshift might result from modeling the VBC with a symmetric profile and possibly over-subtracting flux from the red side of the BC. It is however unlikely that this accounts for the full effect since a blueshift is also measured for the full profile: a blue-side excess is visible in the median B1 Mgiiλ2800 profile shown in Fig. 2. Table 2 indicates a Mgiiλ2800 blueshift for spectral types B1 and B2 with any blueshift in B1++ BC not detected by our parameterization of the full profile. The relevance of the blue shifts in Pop. B profiles will be further discussed in Sects. 4.4 and 5.

4.3. Radio loud

RL sources, both CD and FRII (Fig. 5) B1 medians show a symmetric (FRII) or redshifted (CD) Mgiiλ2800 line core. The profiles resembles the typical B1 RQ and full sample profiles but there is no hint of possible blue shifts. A shift to the red is observed at intensity level but again the shift amplitude is less than for Hβ. The redward asymmetry is especially prominent in CD sources with a centroid displacement reaching 600 km s-1. The CD and FRII sources do not show any large difference in FWHM since they were both chosen to belong to spectral type B1 by imposing the same condition on FWHM Hβ. Their interpretation is discussed in Sect. 5.4.

4.4. Major trends

We focus on line shifts and widths because they are parameters relevant to the credibility/definition of a virial broadening estimator. Comparison of centroid shift values at different heights in a line give the best way to evaluate asymmetry and line shift. The behavior of Pop. B is different from Pop. A which is showing a redshift that is strongest in the line base resulting in red asymmetric profiles. We assume that modeling and subtracting of a VBC component will enable us to measure the width of a symmetric and unshifted BC virial estimator. Population A sources in bins A1 and A2 yield an FWHM measure requiring no VBC correction. A correction is only needed to make consistent virial estimate using FWHM Hβ and FWHM Mgiiλ2800. In bins A3 and A4 the FWHM Hβ measure is preferred after correcting for a blue asymmetry.

Rather than the amplitude in km s-1, a value normalized by line width provides a more direct evaluation of the “dynamical relevance” of any line shift. We can define the following parameters (2)where the centroid at fractional peak intensity has been normalized by the full width at the same fractional peak intensity FWM. Figure 6 shows the behavior of and of as a function of spectral type (error bars are obtained propagating quadratically the uncertainties in Table 2). A radial velocity vr shift close to a line peak may represent a systematic effect involving the entire emitting region only if it is also seen at and fractional intensities. Figure 6 confirms that the B1 Mgiiλ2800 blueshift is much less relevant than shifts found in bins A3 and A4. We also note that in bin A3 and A4 the shift measured for the full Mgiiλ2800 profile is probably a lower limit, since the profile can be interpreted as the sum of an unshifted line + a blueshifted component (Sect. 3.3 of Paper I). The line base might be affected by the presence of additional kinematic components that, in our interpretation of the line profiles, are the blueshifted component (blue in Marziani et al. 2010) and the VBC for Pop. A and B respectively. Considering the centroids as a function of spectral type, only bins A3 and A4 show a relatively high Hβ blueshift (the peaks are almost unshifted). Bins A1 and A2 show symmetric profiles in both Hβ and Mgiiλ2800. The situation changes in Pop. B where the B1 and B1+ Hβ profiles are strongly redward asymmetric with the B1+ centroid shift reaching ≈800 km s-1. Conversely, the Mgiiλ2800 profile shows a more symmetric shape. There is a significant shift at the intensity level, but its amplitude is ~0.25 that of Hβ. Given the large FWM for Mgiiλ2800, the δ values are lower than in the case of Hβ. Similar considerations apply to intensity – the line intensity level at which the virial broadening is computed: Mgiiλ2800 shows modest amplitude normalized shifts (Fig. 7).

Table 4

Median bolometric luminosity, black hole mass, and Eddington ratio.

thumbnail Fig. 6

Trends in Pops. A and B as a function of spectral type. The upper panel shows the normalized shift , the lower . Filled symbols: Mgiiλ2800; open symbols: Hβ.

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thumbnail Fig. 7

Trends as a function of Eddington ratio L/LEdd. Upper panel: “dynamical relevance” indicator /FWHM for the Mgiiλ2800doublet broad component. Bottom panel: ratio FWHM(Mgiiλ2800)/FWHM(Hβ) for the broad components. The smaller circles refer to measurements made including the VBC contribution of both lines.

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Eddington ratio estimates are needed to infer the physical meaning of differences between A and B spectral types. We computed the median mass from the medians of the fluxes of individual sources in each bin and from FWHM measured on the median composite. We follow the prescriptions of Assef et al. (2011) and Shen & Liu (2012) to compute MBH from Hβ and Mgiiλ2800 line widths respectively. Trends are also preserved with older relations linking the black hole mass to the FWHM and the continuum at 3100 or 5100 Å. The bolometric luminosity needed for L/LEdd has been derived from the luminosity at 5100 Å following Nemmen & Brotherton (2010). Values of bolometric luminosity, MBH, and L/LEdd, which are computed using the BC as a virial broadening estimator, are reported in the first columns Table 4, followed by MBH and L/LEdd computations using the whole profile (treating Mgiiλ2800 as a single line). MBH values derived from BC and presented in Table 4 show a trend toward decreasing MBH from A1 to A4. A constant median L in the bins (log L ~ 46.0) implies a trend toward increasing L/LEdd from A1 to A4. We do not see this trend if we use Mgiiλ2800 measures that reflect the absence of a clear correlation between Hβ and Mgiiλ2800 line profile measures in Pop. A. Population B sources show a more regular behavior that preserves a trend. This is mainly due to the definition of B spectral types based on increasing line width. However, including the VBC leads to an overestimate of log  MBH for both Hβ and Mgiiλ2800 derived masses.

Figure 7 shows the behavior of and of the FWHM ratio between the broad component of Mgiiλ2800 and Hβ as a function of Eddington ratio since the E1 sequence is mainly a sequence of L/LEdd3. The parameter is considered as an appropriate indicator of the dynamical relevance of the shift because FWHM is the virial broadening estimator of choice. The δ trends at and peak intensity as a function of spectral type are also preserved as a function of L/LEdd and are not shown again. The Mgiiλ2800 blueshift starts increasing at log  L/LEdd ~ −0.6, when the A3 and A4 sources behave differently from all other sources, as discussed in Paper I. The marginal blueshift detected at maximum for spectral type B1 becomes untraceable at half intensity. At half maximum the Mgiiλ2800 profile is mostly unperturbed in all B bins (save B2 that includes a tiny minority of sources and is probably a confusing mixup), while the Hβ profile shows a highly significant shift to the red.

5. Discussion

5.1. MgIIλ2800 and Hβ in the Pops. A and B context

Virial estimates of MBH for large quasar samples have been available now for more than ten years (e.g. McLure & Jarvis 2002; McLure & Dunlop 2004). Estimated masses lie within the range log MBH ~6.0−11.0 with uncertainties i.n the range 0.2–0.4 dex at 1σ confidence. The higher uncertainty value in the range appears more realistic when different estimates for the same sources are compared. This is also confirmed when we compare different mean mass estimates for quasar populations (e.g. radio-quiet vs. radio-loud). This situation has led to claims that FWHM measures contain little or no information about black hole mass (Croom 2011) and others arguing that FWHM measures for different lines are equally valid MBH estimators (Vestergaard et al. 2011). We argue that neither of these claims is valid and that the path to a clearer picture lies within the concept of a quasar parameter space like 4DE1. Quasars do not distribute randomly in 4DE1.

Table 5

Conversion factors.

How can we move towards more accurate and consistent MBH estimates for individual quasars and quasar populations? It is unlikely that inconsistencies only stem from comparisons involving spectra of different S/N (Assef et al. 2012). Inconsistencies remain when comparing estimates using the same (i.e. SDSS) spectra. The S/N is certainly an issue but its effect depends upon the structure of the line profiles used as virial estimators (see e.g. Shen et al. 2008, 2011). Lines that are well fit with single unshifted components are likely the most robust in the face of declining S/N. However many broad lines in type 1 AGN show line shifts and asymmetries while others are obviously not well fit with a single component. Fitting lines with a single Gaussian is inappropriate because the profile shapes are rarely approximated well by a single Gaussian. For example, an attempt to fit the Mgiiλ2800 line of spectral type B1 with a single Gaussian would lead to a (bad) fit resulting in an overestimation of FWHM by 700 km s-1. Effects of erroneous assumptions on fitting function depend on S/N in a way that depends on the intrinsic shape and on noise properties. Composites spectra have very high S/N and allow one to focus on systematic effects with minimal measurement (statistical) errors. The challenge is to generate composites in a clear and unbiased way which means binning physically similar quasars.

If any broad lines serve as virial estimators, then Mgiiλ2800 and Hβ are the safest choices. Results presented in this paper suggest that Mgiiλ2800 is the line least affected by profile shifts and asymmetries in 90% of all quasars. We maintain that a first step in the path to progress requires recognition that quasars showing FWHM Hβ< or > 4000 km s-1 (Pops. A and B, respectively) have very different profile properties(Sulentic et al. 2000b; Collin et al. 2006; Zamfir et al. 2010). In other words, the dispersion in estimated MBH  and resultant LEdd  measures is not found by luminosity binning (at fixed z) but rather by binning in the 4DE1 context that reflects differences in BLR kinematics and geometry.

thumbnail Fig. 8

FWHM of Mgiiλ2800 vs. FWHM Hβ on log scale. Left: full profiles, right: only BC (of single component for Mgiiλ2800). Gray dots are the data points of Wang et al. (2009), with the line representing their best fit. The large black spots are the median values for the full profiles of our median spectra. The dot-dashed lines traces the equality relation, and the thin red line a fixed ratio 0.77.

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Figure 8 (left panel) overlays our composite measures of FWHM Hβ vs. FWHM Mgiiλ2800 (with the Mgiiλ2800 doublet treated as a single line) on the individual source measures from Wang et al. (2009). Full profile measures follow the source distribution and the best-fit regression of Wang et al. (2009). The large scatter at the low FWHM end and the convergence of the regression towards parity reflect the unusual behavior of sources in bins A3 and A4 where the FWHM offset between Hβ and Mgiiλ2800 breaks down. The convergence is also affected at the high FWHM end where the prominence of the VBC component increases in Hβ more than in Mgiiλ2800. Figure 8 (right panel) presents our BC values (all Pop. B sources corrected for the VBC) along with the parity line, the Wang et al. (2009) regression and our best fit to the median composite values. The main result is that we find no convergence but rather a constant offset (Mgiiλ2800 ≈ 20% narrower) from bin A2 through all B bins.

5.2. Implications for MBH estimates of quasars: a tentative recipe

The previous analysis suggests the following recipe.

  • 1

    Identify a source as Pop. A or B – on the basis ofFWHM Hβ< or >4000 km s-1, respectively.

  • 2a

    Bin A3 and A4 Mgiiλ2800 profiles are unsuitable as virial estimators. Bin A3 and A4 Hβ profiles are suitable if corrected for strong Feii contamination and for a blue component.

  • 2b

    For A1 and A2, both Hβ and Mgiiλ2800 can be used as estimators without any correction.

  • 3

    For Pop. B, apply correction because of VBC to both Hβ and Mgiiλ2800, as described below.

A correction factor can be defined as the ratio between observed FWHM and BC FWHM: (3)where (4)and FWHM(line)obs is measured on the whole profile (treating the Mgiiλ2800 doublet as a single line). If a single-epoch FWHM measurement is made without consideration of the intrinsic shape then ξ is as reported in Table 5 (ξ values are derived from Tables 3 and 2). The ξ factor is less important for Mgiiλ2800 because the VBC component is always weaker. In the case of Mgiiλ2800 a suitable ξ value is ≈0.85. Table 5 indicates that a simple correction factor ξ ≈ 0.75−0.8 could be applied to Hβ once the object is classified as Pop. B, as suggested by Fig. 8. A simulation degrading the B1 spectrum with a combination of Gaussian and Poissonian noise shows that it is possible to recover a basic estimate of FWHM (with heavy smoothing) down to S/N ≈ 3 (cf. Shen et al. 2008, 2011), even if information on the profile shape is completely lost. We also note that the ξ correction may be accurate when excluding the most luminous sources where the VBC is extremely strong i.e., for Lbol ≳ 1047 erg s-1 (Marziani et al. 2009), or the profile is not too irregular as it is the case of several sources in B1++. The third column of Table 5 lists the multiplicative factor needed to convert from observed FWHM Hβ to FWHM Mgiiλ2800 BC. The last column lists the factor needed to convert the observed Mgiiλ2800 FWHM into FWHM HβBC.

The recipe reported above accounts for our result that the difference between Mgiiλ2800 and HβMBH is positive at high L/LEdd, and negative toward the lower end of the L/LEdd distribution. If no correction is applied then Mgiiλ2800 will be measured as broader than Hβ toward high L/LEdd values (20% in A3 and ≈50% in bin A4). Therefore at high L/LEdd the Mgiiλ2800 masses will be overestimated with respect to Hβ which should actually provide a more reliable estimate. At low L/LEdd the effect of the VBC on FWHM Hβ is stronger yielding an MBH estimate greater than the one from Mgiiλ2800. The agreement with Fig. 1 of Onken & Kollmeier (2008) is quantitative (if rare outlying points in their Fig. 1 are excluded; medians by definition give no or low weight to extremes in a distribution): Δlog  MBH = log  MBH (Mgiiλ2800) – log  MBH (Hβ) ≈ 0.4 dex for bin A4 with log  L/LEdd ≈ –0.2, and Δlog  MBH ≈ −0.4 at log  L/LEdd ≈ −1.7.

Even if A3 and A4 represent only ≈10% of our low redshift sample, high L/LEdd are discovered with increasing frequency in high-z, flux limited samples. A recent study of z < 1.8 sources involving Mgiiλ2800 and Hα finds a small offset in the MBH estimates, in the sense that Mgiiλ2800-derived masses are slightly higher than those from Hβ (Matsuoka et al. 2013). This might indicate an increasing frequency of Mgiiλ2800 profiles affected by non-virial, outflow motions.

5.3. Origin of MgIIλ2800 emission and profile blueshifts

A major result of this paper is that FWHM Mgiiλ2800 is systematically narrower than FWHM Hβ, excluding types A3 and A4. This holds for both the full profile and for all the components identified in the lines: i.e. BC, VBC, blueshifted component. The simplest explanation is that Mgiiλ2800 is emitted at larger radius, on average, than Hβ, assuming that the gas is photoionized by a central continuum source. The emissivity Σ of the two lines was computed as a function of the ionization parameter U using CLOUDY simulations described in Sect. 3.1.1. The dependence on U was then converted to radial distance assuming a constant column density log  nH = 11 [cm-3]. If we approximate Σ with a power law then Σ ∝ rα yields Σ(Mgiiλ2800) ∝ r-0.1 with a steeper trend for Hβ, Σ(Hβ) ∝ r-0.4, if log U ≲ −0.5. Elementary considerations suggest that the different emissivity law can lead to a different shape in the line wings, hence to a different FWHM for the two lines. The energy emitted in the line at distance r can be written as E(r)dr = 4πr2Σ(r)fc(r)dr, where fc is the covering factor. Since the virial assumption implies that the specific energy emitted per unit radial velocity is if fc(r) ∝ r−2 + q. For α = 0.5 and q = 0, E(v) ∝ v-2 which is the same general power law describing Lorentzian line wings. A flatter emissivity law will yield a more peaked profile. Using the emissivity laws for Mgiiλ2800 and Hβ, a 20% width ratio is obtained for reasonable values of q (, cf. Netzer 1990). A more refined scenario involves computing the line profile following a weak-field approximation (Chen et al. 1989; Sulentic et al. 1998). Using the CLOUDY-computed emissivity laws for Hβ and Mgiiλ2800, the profile of Mgiiλ2800 turns out to be systematically narrower than Hβ by ≳10%. The width ratio can be ≈20% if the inner radius of the emitting disk is ≈250 gravitational radii; therefore, the line width ratio and the Lorentzian-like profile shape can be explained in the context of virialialized gas motions.

The Mgiiλ2800 blueshift is most straightforwardly attributed to outflow of the line emitting gas with preferential obscuration of the receding part of the flow Paper I. A blueshift is suspected in the B1 composite (Fig. 2) but is not significant at a 2σ confidence level. The small amplitude of the shifts does not rule out a change in the intrinsic multiplet ratio as an alternative explanation in Pop. B sources: a value R= 2 would yield an effective wavelength close to the one of the transition, 2796.35. If the effective wavelength is close to this value, then any systematic blueshift ≲300 km s-1 will become insignificant. If the blueshift is associated with a low-density, high-ionization component then a value as high as R≈ 1.7 could be possible. However, the absence of any blueshift in bin A1 that is the simplest profile to analyze (1 component, weak Feii) argues against this suggestion.

Outflows driven by line or ionizing photon pressure can accelerate the line-emitting gas to a terminal velocity that is inversely proportional to the square root of the column density Nc and directly proportional to the Eddington ratio, i.e., (5)where vKepl is the Keplerian velocity at the outflow starting radius.

If real, the modest shift observed in the median spectra of B1 and B1++ could be interpreted as the terminal velocity of a radiation driven outflow. This shift could occur even if L/LEdd ~0.01 in gas with moderate column density Nc ~1023 cm-2 (provided that the gas remains optically thick to the ionizing continuum) that may in turn support the idea that resonant lines are driving, at least in part, the acceleration of the outflow (Proga et al. 2000; Ganguly et al. 2007; Sulentic et al. 2007). There is an intriguing similarity in the Mgiiλ2800 and Civλ1549 behavior that may be related to the resonant nature of both lines, but the effects on Mgiiλ2800 appear by far less relevant than on Civλ1549 since the median Mgiiλ2800 profile retains an overall symmetric appearance. The B1 and B1++ profiles are on average only slightly perturbed by blueshifted emission: low Nc gas might produce some scatter among B sources since it is most strongly affected by radiative forces and may become unbound following a continuum luminosity increase (Netzer & Marziani 2010). B1++ sources are likely to be some of the lowest L/LEdd sources. They are unstable in continuum emission and often show strongly variable emission line profiles with irregular shapes (Lewis et al. 2010). They are also rare (≲3% in the present sample) and are interpreted as the most evolved, perhaps dying or starving quasars in the 4DE1 sequence. An example involves the well-studied FRII source 3C 390.3 which belongs to bin B1++ with line profiles characterized by a prominent blueshifted peak that produces a significant net profile blueshift. Another example with extreme velocity offset and large FWHM involves SDSS 0956+5128 (Steinhardt et al. 2012). Even if the interpretation of 3C 390.3 is currently a subject of debate (e.g. Zhang 2011; Dietrich et al. 2012), an application of the method of Negrete et al. (2012) indicates relatively low density and high ionization, which is consistent with the overall properties of the blueshifted component identified in the spectra of many quasars (Marziani et al. 2010). A significant fraction of B1++ sources in the present sample indeed show Mgiiλ2800 profiles with large blueshifts, blueward asymmetries, or both. Therefore, the marginal blueshifts of spectral type B1++ median composite may reflect the somewhat erratic nature of low-density outflowing gas detected in sources whose unstable accretion rate may induce significant continuum fluctuations.

The high S/N of our composite spectra reveals a semi-broad component in the [Oiii]λλ4959,5007 profiles and on the blue side of HβNC. B1 offers the most striking case along with PG 1201+436. In the B1 Hβ composite spectrum the excess flux is explained as a semi-broad component with width and shift similar to the [Oiii]λλ4959,5007 semi-broad component. That feature does not belong to the broad profile and would induce a blueshift of ~−100 km s-1 into the BC model or into the measures of the broad line profile if not adequately taken into account. A similar interpretation is also possible for the small blueshifted “bump” observed in the Hβ and Mgiiλ2800 profiles of PG 1201+436 (blue line in Fig. 4). The bump is modeled with a Gaussian component of width 1500–2500 km s-1 and shift −1500−2000 km s-1. The inferred velocities and widths appear rather extreme compared to other cases where a semi-broad component of [Oiii]λλ4959,5007 is isolated. We can speculate that also this source is showing outflow largely in a region that might be at the boundary between the BLR and the narrow-line region (Zamanov et al. 2002). A more refined analysis of PG 1201+436 is deferred to later work (Sulentic et al., in prep.).

5.4. Radio quiet and radio loud

Core-dominated and lobe-dominated sources show a fairly symmetric profile, with evidence of a redshifted base due to the VBC that is especially prominent in CD sources (e.g., Punsly & Zhang 2011). The red excess is clearly detected also in Mgiiλ2800 (a very convincing case is provided by the blazar 3C 279, Punsly 2013) although the A.I. is significantly lower than Hβ. The absence of any hint of blueshifts in RL profiles could be related to the full suppression of an accretion disk wind, or it could be due to orientation. The B1 bin was defined on a limited range of line width. Therefore we cannot expect to see the systematic FWHM difference mentioned above. In addition the fraction of FRII increases toward bin B1++  i.e., for broader sources. In bin B1 we are probably considering a subsample of FRII that show narrower profile than the majority of the population. If the FWHM is affected by orientation as expected (e.g., Wills & Browne 1986; Sulentic et al. 2003; Rokaki et al. 2003; Runnoe et al. 2013; Zamfir et al. 2008), we are observing sources that tend to be seen at a smaller viewing angle than the general FRII population. If the wind flow follows a bent path over the accretion disk (Elvis 2000) or if the flow is constrained closer to the disk plane, the absence of a blueshift might therefore be related more to orientation than to full suppression of disk winds in RL sources by the pressure of a cocoon associated with the relativistic ejections (Norman & Miley 1984). Disk winds are probably not fully suppressed in radio-loud sources, as indicated by sources like 3C 390.3 and by the discovery of fast outflows in radio-loud AGNs (Tombesi et al. 2010).

5.5. MgIIλ2800 virial broadening and virial product

The FWHM difference between Hβ and Mgiiλ2800 is very important. From the data presented in this paper, with the exception of spectral types A3 and A4, the FWHM (Hβ) ≳ FWHM (Mgiiλ2800) both if the whole profile is considered and if only the broad component is isolated. The FWHM of a line by itself is of limited usefulness in computing MBH following Eq. (1). A virial broadening estimator (let it be a line FWHM or velocity dispersion) should be associated to a typical distance for employing the simple virial relation that is customarily employed in MBH calculations (McLure & Dunlop 2004; Vestergaard & Peterson 2006; Shen et al. 2008; Trakhtenbrot & Netzer 2012).

In principle, there are two main possibilities in the interpretation of the width differences (not mutually exclusive). The smaller Mgiiλ2800 FWHM may imply that (1) Mgiiλ2800 is emitted farther out from the central continuum source according to the virial law Δv ∝ r−1/2. If the FWHM ratio is ≈0.8, then Mgiiλ2800 should occur at a distance that is significantly larger than Hβ, by a factor 1.4; (2) only part of the gas emitting Hβ is emitting Mgiiλ2800. If (1) applies, the scaling relations involving Mgiiλ2800 should be defined with some care since rBLR defined from reverberation mapping of Hβ would suggest shorter distances. In the second case, Mgiiλ2800 can be interpreted as perhaps the “best” estimator, associated to gas very optically thick that responds to continuum changes.

Reverberation mapping studies of Mgiiλ2800 are not yet conclusive, and they leave open the possibility that the average emitting distance of Mgiiλ2800 is larger than for Hβ (Metzroth et al. 2006; Trevese et al. 2007; Woo 2008). In addition to the theoretical considerations of Sect. 5.3 that favor a larger distance for Mgiiλ2800 emission, there is empirical evidence provided by the difference between the Mgiiλ2800 and Hβ profile shape. For Pop. B sources, the Hβ VBC gives rise to a stronger redward asymmetry than in Mgiiλ2800, and suggests that Mgiiλ2800 emission is occurring farther away from the central continuum source. This is consistent with the observation of smaller FWHM(Mgiiλ2800) for both BC and the whole profile for spectral types A1 and A2 that do not show appreciable VBC emission.

The implication of a larger emissivity-weighted distance for Mgiiλ2800 is a shift in the correlation between rBLR (computed from Hβ) and the luminosity at 3000 Å, by ≈0.16 dex in rBLR in Eq. (7) and Fig. 4 of Trakhtenbrot & Netzer (2012). However, Eq. (12) of Trakhtenbrot & Netzer (2012) will be unaffected since the virial factor is scaled to yield the MBH derived from Hβ. The difference is that ℱ should be ≈1.0 and not ℱ ≈ 1.3−1.4 that follows from the assumption that Hβ and Mgiiλ2800 are emitted at the same distance. Scalings adopted in all previous studies assumed that a single ℱ value is appropriate for all quasars. This assumption is most likely incorrect, especially if nongravitational forces are in play. Previous work has suggested a significant ℱ difference between Pops. A and B (Collin et al. 2006). A much needed improvement is therefore an evaluation of ℱ as a function of spectral type or L/LEdd. This is however beyond the scope of the present paper.

6. Conclusion

Both Hβ and Mgiiλ2800 appear to be suitable for MBH virial estimates of black hole mass at least for a large fraction of quasars. Both low ionization lines, however, show profile shifts and asymmetries that must be taken into account if our goal is to improve the poor present-day accuracy of most estimates. Right now, this analysis suggests that masses for Pop. B sources based on Hβ are likely systematically overestimated. Further progress therefore requires subdivision of large quasar samples into Pops. A and B with further subdivision into spectral types facilitating consideration of MBH and/or L/LEdd trends. 4D eigenvector 1 currently offers the most effective context for binning. Such source discrimination cannot be accomplished with L, z binning because sources with very different line profile properties show similar Lbol even when they host super-massive black holes with significantly different masses (i.e. the highest accretors are connected with Pop. A sources involving the lowest black hole masses, effectively blurring any expected mass-luminosity correlation for quasars).

Our ability to distinguish between Pop. A and B sources is fortunately preserved even at low S/N. We defined simple prescriptions with the goal of providing a better approximation of the virial broadening for single-epoch observations.


1

SDSS J093704.05+293704.9 has log Pν ≈ 31.2 at 1.4 GHz but classical FRII morphology.

2

Vacuum wavelengths are used in this paper. Line identification includes the optical wavelength of traditional use. For example, we refer to [Oiii]λ5007 even if the reference wavelength is 5008.2 Å.

3

Our sample bins have median Lbol that is almost constant. This follows from the flux and redshift limits of our sample, and implies that for any trend as function of L/LEdd, there is a corresponding trend with MBH. MBH is a one-way estimator of a quasar evolutionary status. However, the presence of line shifts is more probably associated to the relative balance of gravitation and radiation forces so that we assume in the following that the relevant physical parameter is L/LEdd.

Acknowledgments

P.M. acknowledges Junta de Andalucía, through grant TIC-114 and the Excellence Project P08-TIC-3531, and the Spanish Ministry for Science and Innovation through grants AYA2010-15169 for supporting a sabbatical stay at IAA-CSIC. I.P.-F. acknowledges the postdoctoral fellowship grants 145727 and 170304 from CONACyT Mexico. Funding for the SDSS and SDSS-II has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, the U.S. Department of Energy, the National Aeronautics and Space Administration, the Japanese Monbukagakusho, the Max Planck Society, and the Higher Education Funding Council for England. The SDSS Web Site is http://www.sdss.org/. The SDSS is managed by the Astrophysical Research Consortium for the Participating Institutions. The Participating Institutions are the American Museum of Natural History, Astrophysical Institute Potsdam, University of Basel, University of Cambridge, Case Western Reserve University, University of Chicago, Drexel University, Fermilab, the Institute for Advanced Study, the Japan Participation Group, Johns Hopkins University, the Joint Institute for Nuclear Astrophysics, the Kavli Institute for Particle Astrophysics and Cosmology, the Korean Scientist Group, the Chinese Academy of Sciences (LAMOST), Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, Ohio State University, University of Pittsburgh, University of Portsmouth, Princeton University, the United States Naval Observatory, and the University of Washington.

References

All Tables

Table 1

Sample: number of sources in each spectral type.

Table 2

Measured parameters on the Hβ and Mgiiλ2800 profiles of composite spectra.

Table 3

Derived quantities from the Hβ and Mgiiλ2800 profiles composite spectra multicomponent analysis.

Table 4

Median bolometric luminosity, black hole mass, and Eddington ratio.

Table 5

Conversion factors.

All Figures

thumbnail Fig. 1

Predicted intensity ratio of the doublet the Mg+ lines as a function of ionization parameter U and hydrogen density nH. Contour lines are drawn in steps of 0.1 from 1.0 to 2.0.

Open with DEXTER
In the text
thumbnail Fig. 2

Spectra of Hβ (left panels) and of Mgiiλ2800 (right panels) for spectral types B1 to B1++ (from top to bottom). The horizontal scales are in rest frame wavelength [Å] or radial velocity, with the origin set at the rest frame wavelength. The black lines shows the original, continuum-subtracted spectrum, and the dashed magenta line the model with all emission line components. The thick black line is the BC; the thick red line shows the VBC. The green lines trace the Fe iiopt and FeiiUV contribution, and the gold lines various contributions associated to the NLR (HβNC, [Oiii]λλ4959,5007, and Mgiiλ2800 narrow component when appropriate). Excess emission at λ ≳ 2900 Å visible in this and in the next two figures is likely due to a combination of Fei and Balmer continuum emission.

Open with DEXTER
In the text
thumbnail Fig. 3

Spectra of Hβ (left) and of Mgiiλ2800 (right) for spectral type B2. Meaning of symbols/line colors is the same of the previous figure.

Open with DEXTER
In the text
thumbnail Fig. 4

Spectrum of Hβ (left panels) and of Mgiiλ2800 (right panels) for the B1++ source PG 1201+436. Color coding is the same as for Fig. 2 save for the blue line that traces a blueshifted peak visible in both Hβ and Mgiiλ2800 (Sects. 4 and 5.3). Horizontal scale is rest frame wavelength or radial velocity shift from rest frame. The vertical scale is specific flux in units of 10-15 erg s-1 cm-2 Å-1.

Open with DEXTER
In the text
thumbnail Fig. 5

Continuum subtracted spectral ranges of Hβ (top) and Mgiiλ2800 (bottom) for RQ (left), CD (middle) and FRII (right) median composites computed in the B1 bin. Meaning of symbols is the same of the previous figures.

Open with DEXTER
In the text
thumbnail Fig. 6

Trends in Pops. A and B as a function of spectral type. The upper panel shows the normalized shift , the lower . Filled symbols: Mgiiλ2800; open symbols: Hβ.

Open with DEXTER
In the text
thumbnail Fig. 7

Trends as a function of Eddington ratio L/LEdd. Upper panel: “dynamical relevance” indicator /FWHM for the Mgiiλ2800doublet broad component. Bottom panel: ratio FWHM(Mgiiλ2800)/FWHM(Hβ) for the broad components. The smaller circles refer to measurements made including the VBC contribution of both lines.

Open with DEXTER
In the text
thumbnail Fig. 8

FWHM of Mgiiλ2800 vs. FWHM Hβ on log scale. Left: full profiles, right: only BC (of single component for Mgiiλ2800). Gray dots are the data points of Wang et al. (2009), with the line representing their best fit. The large black spots are the median values for the full profiles of our median spectra. The dot-dashed lines traces the equality relation, and the thin red line a fixed ratio 0.77.

Open with DEXTER
In the text

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