$M_{\rm BH}$
$L/L_{\rm Edd}$
$n_{\rm e}$
$N_{\rm c}$
$R_{\rm FeII}$
$M_{\rm B}$
R$_{\rm g}$
$\; \buildrel < \over \sim \;$
$\; \buildrel > \over \sim \;$
Civ$\lambda$1549$_{\rm NC}$
Civ$\lambda$1549$_{\rm BC}$
Civ$\lambda$1549$_{\rm VBC}$

H$\beta_{\rm BC}$
H$\beta_{\rm VBC}$
H$\beta_{\rm NC}$

Heii$\lambda$1640$_{\rm NC}$
Feii$_{\rm UV}$
Fe ii$_{\rm opt}$
$\delta v_\mathrm{r}$

76087[Fe vii]$\lambda$6087
km s$^{-1}$
erg  s$^{-1}$
$r_{\rm BLR}$
$r_{\rm SF}$
$L_{\rm Edd}$
$m_{\mathrm B}$

and  line broadening
Marziani et al.

The intermediate-ionization lines  as   virial broadening estimators for Population A quasars   [Based in part  on observations made with ESO Telescopes at the Paranal Observatory under programme 082.B-0572(A), and 083.B-0273(A).]

Paola Marziani
0000-0002-6058-4912]Paola Marziani
National Institute for Astrophysics (INAF), Osservatorio Astronomico di Padova, vicolo dell' Osservatorio 5, IT 35122, Padova, Italy
0000-0003-2055-9816]Ascensión del Olmo
Instituto de Astrofisíca de Andalucía, IAA-CSIC, Glorieta  de la Astronomia s/n 18008 Granada, Spain

0000-0002-1656-827X]C. Alenka Negrete
Universidad Nacional Autonóma de México Instituto de Astronomía: Ciudad de Mexico, Distrito Federal, MX 04510, Mexico
0000-0001-5756-8842]Deborah Dultzin
Universidad Nacional Autonóma de México Instituto de Astronomía: Ciudad de Mexico, Distrito Federal, MX 04510, Mexico
0000-0001-9095-2782]Enrico Piconcelli
National Institute for Astrophysics (INAF), Osservatorio Astronomico di Roma, Via Frascati 33, 00040, Monte Porzio Catone (RM), Italy
0000-0001-9155-8875]Giustina Vietri
National Institute for Astrophysics (INAF), Osservatorio Astronomico di Roma, Via Frascati 33, 00040, Monte Porzio Catone (RM), Italy
National Institute for Astrophysics (INAF),  Istituto di Astrofisica Spaziale e Fisica Cosmica, Via A. Corti 12, 20133 Milano, Italy
0000-0002-7843-7689]Mary Loli Martínez-Aldama
Center for Theoretical Physics (PAS), Al. Lotników 32/46, 02-668 Warsaw, Poland
0000-0001-6441-9044]Mauro D'Onofrio
Dipartimento di Fisica e Astronomia,  Università di Padova, Vicolo dell' Osservatorio 3, Padova, Italy
0000-0002-0465-8112]Edi Bon0000-0002-3462-4888]Natasa Bon
Belgrade Astronomical Observatory, Belgrade, Serbia
0000-0002-7630-0777]Alice Deconto Machado
Instituto de Astrofisíca de Andalucía, IAA-CSIC, Glorieta  de la Astronomia s/n 18008 Granada, Spain
0000-0002-3702-8731]Giovanna M. Stirpe
National Institute for Astrophysics (INAF), Osservatorio di Astrofisica e Scienza dello Spazio, Italy,  via Gobetti 93/3,
40129 Bologna, Italy
Tania Mayte Buendia Rios
Universidad Nacional Autonóma de México Instituto de Astronomía: Ciudad de Mexico, Distrito Federal, MX 04510, Mexico

The identification of a virial broadening estimator  in the quasar UV rest frame suitable for black hole mass computation at high redshift has become an important issue. We compare the HI Balmer    line width to the ones of two intermediate ionization lines: the   doublet and the  line, over a wide interval of redshift and luminosity ($0 \lesssim z \lesssim 3.5$;  $ 43 \lesssim \log L \lesssim 48.5$ []), for 48 sources belonging to the quasar population characterized by mid-to-high values of the Eddington ratio (Population A).  The present analysis indicates that the line width  of   and  are highly correlated, and can be considered equivalent for most Population A quasars over five orders of magnitude in luminosity;  for , multiplication by a constant correction factor $\xi \approx 1.25$ is sufficient to bring the FWHM of  in agreement with the one of .  The statistical concordance between  low-ionization and intermediate-ionization lines  suggests that they  predominantly arise from the same virialized part of the broad line region.  However, blueshifts of modest amplitude (few hundred ) with respect to the quasar rest frame  and an excess ($\lesssim 1.1$)  broadening with respect to  are found   in a fraction of our sample.
Scaling laws to estimate  of high redshift quasar using the  and the  line widths  have  rms scatter  $\approx$ 0.3  dex.  The  scaling law takes the form   $\log M_\mathrm{BH} \approx
0.58 \log L_{1700,44} +
2 \log \mathrm{FWHM} + 0.49$ [].

§ INTRODUCTION

The energetics of all accretion-related   phenomena occurring in active galactic nuclei (AGN) can be tied down to the mass of the central black hole.  The mass () of the  black holes at the origin of the AGN phenomenon is now reputed a key parameter in the evolution of galaxies and in cosmology as well <cit.>, and its estimation   has become an important branch of extragalactic research. Black hole mass estimates on large type-1 AGN samples  are carried out employing a deceptively-simple formulation of the virial theorem, under the assumption that all the mass of the system is concentrated in the center of gravity provided by the black hole <cit.>: = $f_\mathrm{S} r_\mathrm{BLR} (\delta v)^{2} / G$, where     $f_\mathrm{S}$ is a structure factor (a.k.a. virial or form factor) dependent on the emitting region geometry and dynamics, the radius  $r_\mathrm{BLR} $ the distance of the line emitting region from the continuum source, and $\delta v$ a suitable measure of the line broadening (e.g., FWHM  or dispersion $\sigma$,     Vestergaard & Peterson, 2006, Peterson et al., 2004). The main underlying assumptions are that the broadening is due to Doppler effect because of the line emitting gas motion, and that the velocity field  is such that the emitting gas remains gravitationally bound to the black hole.

Early UV and optical inter-line shift analysis provided evidence that not all the line emitting gas is bound to the black hole <cit.>.  The scenario emerging from more recent studies is that outflows are ubiquitous in active galactic nuclei.  They occur under a wide range of physical conditions, and are detected in almost every band of the electromagnetic spectrum and on a wide range of spatial scales, from a few  gravitational radii to tens of kpc <cit.>.

At high luminosity, massive outflows provide feedback effects to the host galaxy <cit.>, and are  invoked to account for the -bulge velocity dispersion correlation <cit.>. For $z \gtrsim 4$,  estimates rely on the  high-ionization line, and  the highest-$z$ sources appear to be almost always high-accretors [Bañados et al., 2018, Nardini et al., 2019]. Two studies pointed out  20 years ago the similarity between X-ray and UV properties of high-$z$ quasars and local quasars accreting at high rates  <cit.>. The source of concerns is that  high-ionization lines such as  are subject to a considerable broadening and blueshifts  associated with outflow motions already at low redshift <cit.>. Overestimates of the virial broadening by a factor as large as   $\approx$5 [Netzer et al., 2007, Sulentic et al., 2007, Mejía-Restrepo et al., 2016, Mejía-Restrepo et al., 2018]   for supermassive black holes at high $z$ may even pose a spurious challenge to concordance cosmology <cit.> and lead to erroneous inferences on the properties of the seed black holes believed to be fledgling precursors of massive black holes.

This paper is focused on the measurement of the line width of the UV intermediate-ionization lines  at $\approx 1900$ Å and on their use for black hole mass measurements for large quasar samples, over a wide interval of luminosity and of redshift.  The blend at $\lambda1900$ Å is due, at least in part, to the  doublet and to the  and  lines.   is a resonant doublet ($^{2}P^{o}_{\frac{3}{2},\frac{1}{2}} \rightarrow ^{2}S_{\frac{1}{2}}$) while  and    are due to inter-combination transitions ($^{3}P^{o}_{1} \rightarrow ^{1}S_{0}$) with widely different critical densities ($\approx 2 \cdot 10^{11}$ 3 and $\approx 3 \cdot 10^{9}$ 3, respectively; Zheng, 1988, Negrete et al., 2012). The parent ionic species imply ionization potentials  $15 \lesssim \chi_\mathrm{i} \lesssim 30$ eV, intermediate between the ones of low-ionization lines (LILs), and the ones of high-ionization lines (HILs; $\chi_\mathrm{i} \gtrsim 40-50$ eV).   The intermediate-ionization lines (IILs) at 1900 Å are well-placed to provide a high redshift estimator; they can be observed with optical spectrometers up to $z \sim 4$. Observations can be extended in the NIR (13,500 Å) up to $z \sim 5.7$ without solution of continuity, thereby sampling  a redshift domain that is crucial for understanding  the primordial growth of massive black holes and galaxy formation. In principle,  observations could be extended to the H band to cover the as yet mostly uncharged range $6.5 \lesssim z \lesssim 8$, a feat that may well become possible with the advent of James Webb Space Telescope [Gardner et al., 2006], of the ESO Extremely Large Telescope [Gilmozzi & Spyromilio, 2007], and of the next-generation  large-aperture telescopes <cit.>.

The  quasar main sequence provides much needed discerning abilities for the exploitation of the IILs  <cit.>, as line profiles and intensities of individual sources are not considered as isolated entities, but interpreted as part of consolidated trends in the main sequence context. Broad line measurements involving  line width and   strength are not randomly distributed but instead  define a sequence that has become known as the quasar  “main sequence” (MS; e.g., Sulentic et al., 2000, Shen & Ho, 2014, Panda et al., 2019, Wildy et al., 2019). The  strength is parameterized by the intensity ratio involving  the  blue blend at 4570 Å and broad  i.e., = I()/I(), and the Hydrogen  line width by   its FWHM.  MS sources  with higher    show  narrower broad   (Population A, FWHM()$\lesssim 4000$ ),  and  sources with broader  profiles tendentially show low   (Pop. B with FWHM()$\gtrsim 4000$ , Sulentic et al., 2000, Sulentic et al., 2011). It is also known that   optical and UV observational  properties  are correlated <cit.>. In this paper, the attention is restricted to sources radiating at relatively high Eddington ratio ( $\gtrsim 0.1-0.2$) i.e., to Population A that accounts for the large majority of sources discovered at high $z$. In the course of our analysis we realised that sources radiating at lower Eddington ratio ($0.01\ \lesssim $ $\lesssim 0.1-0.2$) show a different behaviour of the 1900 blend  and will be considered elsewhere.

The coverage of the  spectral range greatly easies the determination of the redshift as well as the positional classification of sources along the MS. In addition, FWHM  has been employed as a virial broadening estimator of  since the earliest single-epoch observations of large samples of quasars, and in more recent times as well <cit.>. The  line is likely to be still the most widely  used line for  computations for low redshift quasars ($z \lesssim 1$).  Our analysis relies on the availability of both  and the 1900 blend lines, as we will consider FWHM  as the reference “virial broadening estimator” (VBE).

Section <ref> introduces the samples used in the present work, covering a wide range in redshift and luminosity, $0 \lesssim z \lesssim 3.5$;  $ 44 \lesssim \log L \lesssim 48.5$ [].  The data were  obtained with instruments operating in  widely different spectral ranges (UV, optical, IR); as a consequence, S/N ratio values vary widely and the uncertainty assessment requires a dedicated approach (Section <ref>, and Appendix <ref>).     The   Section <ref> introduces paired fits to  and the 1900 blend (an atlas is provided in Appendix <ref>), along with several line width measures, and the relation between  and  measurements. A scaling law for  determination equivalent to the one based on  but based on the IIL broadening is discussed in Section <ref>.

§ SAMPLE

Low-luminosity 1900 and  data (FOS$^{\star}$ sample) We considered a Faint Object Spectrograph (FOS) sample from  <cit.> as a low-$L$ and low-$z$  sample. For the sake of the present paper, we restrict the [Sulentic et al., 2007] sample to 28  sources covering the 1900 blend spectral range and with previous measurements for the  profile and  (FOS$^{\star}$ sample). The spectra covering the  spectral range come from <cit.>, as well as   from the SDSS  [York et al., 2000]  and the 6dF (Jones et al., 2004; Table <ref> provides information on  the provenience of of individual spectra). The FOS high-resolution grisms yielded an inverse resolution $\lambda/\delta \lambda \sim 1000$, equivalent to typical resolution of the data of [Marziani et al., 2003] and of the SDSS. The S/N is above $\gtrsim 20$ for both the  optical and UV  low-redshift data. The FOS$^{\star}$ sample has a typical bolometric luminosity $\log L \sim 45.6$ [] and a redshift $z \lesssim  0.5$.

High-luminosity VLT and TNG data for Hamburg-ESO quasars (HE sample) The sample of high-$L$ quasars  includes 10 sources  identified in the Hamburg-ESO survey <cit.> in the redshift range $1.4 \lesssim   z  \lesssim 2.6$.  All HE quasars satisfy the condition on the bolometric luminosity $\log L \gtrsim 10^{47.5}$  and are discussed in detail by <cit.>, where  and  were analyzed. The sample used in this paper is restricted to the 9  Population A sources with VLT/FORS1 spectra and 1 TNG/DOLORES (HE1347-2457) spectrum that cover the 1900 Å blend.   The spectral resolutions  at FWHM  are $\lesssim 300$  and $\lesssim$ 600  for the spectrographs FORS1 and DOLORES, respectively. The resolution of the ISAAC spectra covering H$\beta$  is $\approx$ 300  [Sulentic et al., 2004]. Typical S/N values are $\gtrsim 50$.

Additional high-luminosity sources (ISAAC sample) Additional ISAAC spectra were obtained under programme 083.B-0273(A), for three targets SDSS J005700.18+143737.7, SDSS J132012.33+142037.1,  SDSS J161458.33+144836.9.  They have been reduced following the same procedures employed for the HE quasars. The data will be presented in a forthcoming paper (Deconto Machado et al., in preparation).  Matching rest-frame UV spectra were collected from the SDSS and BOSS [Smee et al., 2013], with a resolving power $R = \lambda$/FWHM $\sim$ 2000.

High-luminosity sources from the WISSH (WISSH sample) We included  near-infrared (NIR) spectroscopic observations of 7 WISSH Population A quasars QSOs [Vietri et al., 2018], obtained with LUCI at the Large Binocular Telescope  and in one case with SINFONI at VLT. Basic information on this sample is provided in Table 1 of Vietri et al., 2018. The matching rest-frame UV spectra are from the SDSS.  The higher resolution implies a somewhat lower S/N with respect to the ISAAC spectra; we restrict our analysis to the spectra above a minimum S/N $\approx\, 15$. Redshifts measured for this paper agree very well with the values reported by Vietri et al., 2018 if the  profile is sharp; they are lower by 300-400  in four cases with relatively shallow profiles due to the different fitting techniques.

Joint  sample  Table <ref>  lists in the following order  source identification, redshift, specific rest-frame flux in the UV at 1700 Å $f_{\lambda,1700}$, S/N at 1700 Å  reference to the origin of the spectrum,  specific flux in the optical at 5100 Å ($f_{\lambda,5100}$),  S/N at 5100 Å, and reference to the origin of the optical spectrum. Table footnotes list references to the flux scale origin, in case the spectrum had uncertain of no absolute spectrophotometric flux calibration.  Notes include the radio loudness classification [Zamfir et al., 2008, Ganci et al., 2019]: radio-loud (RL), radio-intermediate (RI), and radio-quiet (RQ). Only two sources (HE 0043-2300 and 3C 57) are “jetted” in the sense of having a powerful relativistic jet [Padovani, 2017]. HE 0043-2300 is listed as a flat-spectrum radio quasar  with dominant blazar characteristics in the Roma-BZCAT [Massaro et al., 2009], and 3C 57 is a compact-steep source (CSS; O'Dea, 1998, Sulentic et al., 2015).
Two other sources qualify as radio-intermediate (HE 0132-4313 and HE0248-3628), and are briefly discussed
in Appendix <ref>.

Distribution of redshift (left) and of luminosity at 1700 Å (right) for the four sub-samples considered in this paper.

Sample properties

IAU code     Common name     z
$f_{\lambda,1700}$a      S/N$_{1700}$       Ref.b     $f_{\lambda,5100}$a     S/N$_{5100}$     Ref.b      Notes

8cFOS$^\star$ sample

J00063+2012	   	MRK 0335	       	0.0252	   	60.8	   	15	   	S07	    5.92	 	          					              	55	   	M03

J00392-5117	   	[WPV85] 007	       	0.0290	   	2.5		   	15	   	S07	    2.02 c                              	45	   	6dF

J00535+1241	   	UGC 00545	       	0.0605	   	28.2	   	40	   	S07	    5.77	 	                                          	70	   	M03

J00573-2222	   	TON S180	       	0.0620	   	31.8	   	45	   	S07	    14.6   	                                          	55	   	M03

J01342-4258	   	HE 0132-4313	   	0.2370	   	15.2	   	50	   	S07	    1.44 d	                          	15	   	6dF	     RI

J02019-1132	   	3C 057		       	0.6713	   	17.7	   	25	   	S07	    1.90	 	                                 	      	35	   	S15	     CSS

J06300+6905	   	HS 0624+6907	   	0.3702	   	51.7	   	30	   	S07	    5.04 e	                          	40	   	M03

J07086-4933	   	1H 0707-495  	   	0.0408	   	22.2	   	20	   	S07	    2.14 f	                          	35	   	6dF

J08535+4349	   	[HB89] 0850+440    	0.5149	   	5.7		   	20	   	S07	    0.50 	                               	15	   	M03

J09199+5106	   	NGC 2841 UB3	   	0.5563	   	11.0	   	30	   	S07	    1.25 	                               	40	   	SDSS

J09568+4115	   	PG 0953+414	       	0.2347	   	17.1	   	30	   	S07	    2.15 	                               	75	   	M03

J10040+2855	   	PG 1001+291        	0.3298	   	17.2	   	25	   	S07	    1.92 	                               	45	   	M03

J10043+0513	   	PG 1001+054	       	0.1611	   	4.9		   	10	   	S07	    1.50 	                               	30	   	M03

J11185+4025	   	PG 1115+407	       	0.1536	   	11.7	   	20	   	S07	    0.46 	                               	30	   	M03

J11191+2119	   	PG 1116+215	       	0.1765	   	41.3	   	40	   	S07	    2.62 	                               	50	   	M03

J12142+1403	   	PG 1211+143	       	0.0811	   	31.0	   	20	   	S07	    5.45 	                               	40	   	M03

J12217+7518	   	MRK 0205	       	0.0711	   	23.6	   	35	   	S07	    1.73 	                               	55	   	M03

J13012+5902	   	SBS 1259+593	   	0.4776	   	19.1	   	25	   	S07	    0.59 	                               	50	   	M03

J13238+6541	   	PG 1322+659	       	0.1674	   	9.5		   	40	   	S07	    0.71 	                               	35	   	M03

J14052+2555	   	PG 1402+262	       	0.1633	   	22.6	   	25	   	S07	    1.54 	                               	45	   	M03

J14063+2223	   	PG 1404+226	       	0.0973	   	5.8		   	15	   	S07	    1.12 	                               	60	   	M03

J14170+4456	   	PG 1415+451	       	0.1151	   	10.2	   	25	   	S07	    0.86 	                               	35	   	M03

J14297+4747	   	[HB89] 1427+480    	0.2199	   	7.6		   	30	   	S07	    0.30 	                               	55	   	M03

J14421+3526	   	MRK 0478	       	0.0771	   	28.2	   	25	   	S07	    2.04 	                               	55	   	M03

J14467+4035	   	[HB89] 1444+407    	0.2670	   	18.7	   	45	   	S07	    1.02 	                               	20	   	M03

J15591+3501	   	UGC 10120	       	0.0313	   	7.3		   	20	   	S07	    2.29 	                               	55	   	SDSS

J21148+0607	   	[HB89] 2112+059    	0.4608	   	14.9	   	25	   	S07	    0.81 	                               	50	   	M03

J22426+2943	   	UGC 12163	       	0.0245	   	10.9	   	40	   	S07	    0.67 	                               	25	   	M03

8cHE sample

J00456–2243	   	HE0043-2300	   	1.5402	   	15.5	   	115	   	S17	   	3.2	   	70	   	S17	    RL

J01242–3744	   	HE0122-3759	   	2.2004	   	21.7	   	95	   	S17	   	2.2	   	30	   	S17

J02509–3616	   	HE0248-3628	   	1.5355	   	24.2	   	200	   	S17	   	0.8	   	50	   	S17     RI, inv. radio sp.

J04012–3951	   	HE0359-3959	   	1.5209	   	12.1	   	105	   	S17	   	1.8	   	40	   	S17

J05092–3232	   	HE0507-3236	   	1.5759	   	11.7	   	160	   	S17	   	2.1	   	25	   	S17

J05141-3326	   	HE0512-3329	   	1.5862	   	7.7	   	40	   	S17	   	2.7	   	25	   	S17

J11065–1821	   	HE1104-1805	   	2.3180	   	23.9	   	75	   	S17	   	3.0	   	15	   	S17

J13506–2512	   	HE1347-2457	   	2.5986	   	48.0	   	75	   	S17	   	3.9	   	50	   	S17

J21508–3158	   	HE2147-3212	   	1.5432	   	17.0	   	150	   	S17	   	1.7	   	20	   	S17

J23555–3953	   	HE2352-4010	   	1.5799	   	35.5	   	85	   	S17	   	6.3	   	60	   	S17

8cISAAC sample

J00570+1437 	   	SDSSJ005700.18+143737.7 	       	2.6635	   	14.0	   	55	   	       SDSS	   	2.78	   	40	   	D22	     normalized at 5000 Å

J13202+1420 	   	SDSSJ132012.33+142037.1       	   	2.5357	   	8.4	   	40	   	SDSS	   	1.32	   	25	   	        D22	     normalized at 5000 Å

J16149+1448 	   	SDSSJ161458.33+144836.9       	   	2.5703	   	15.3	   	50	   	SDSS	   	2.54	   	45	   	    D22	     normalized at 5000 Å

8cWISSH sample

0801+5210	   	SDSS J080117.79+521034.5	   	3.2565	   	29.4	   	30	   	SDSS	   	4.12	   	20	   	V18

1157+2724	   	SDSS J115747.99+272459.6	   	2.2133	   	4.2		   	15	   	SDSS	    	2.37	   	25	   	V18	     HiBAL QSO

1201+0116	   	SDSS J120144.36+011611.6	   	3.2476	   	17.0	   	30	   	SDSS	   	3.31	   	20	   	V18

1236+6554	   	SDSS J123641.45+655442.1	   	3.4170	   	22.9	   	45	   	SDSS	   	2.30	   	25	   	V18

1421+4633	   	SDSS J142123.97+463318.0	   	3.4477	   	20.9	   	25	   	SDSS	   	3.28	   	15	   	V18

1521+5202	   	SDSS J152156.48+520238.5	   	2.2189	   	59.8	   	80	   	SDSS	   	8.40	   	35	   	V18

2123–0050	   	SDSS J212329.46-005052.9	   	2.2791	   	32.2	   	60	   	SDSS	   	5.75	   	45	   	V18

$^a$ In units of $10^{-15}$  cm$^{-2}$ Å$^{-1}$, in rest frame, not corrected for Galactic extinction.
$^b$ Reference to the origin of the spectra: [Sulentic et al., 2017]; [Sulentic et al., 2007]; [Marziani et al., 2003]; D22: Deconto Machado et al., in preparation; SDSS: SDSS and BOSS, Smee et al., 2013; 6dF: Jones et al., 2004.

$^c$ Uncalibrated 6dF spectrum; flux scale set by a quick-look magnitude as in [Sulentic et al., 2007]. Grupe et al., 1998 luminosity yields $f_{\lambda,5100} \approx 3.1  \cdot 10^{-15}$  cm$^{-2}$ Å$^{-1}$. Very low  $f_{\lambda,1700}/f_{\lambda,5100} \approx 1$ ratio. The $f_{\lambda,1700}$ from the S07 HST/FOS spectrum corresponds to a deep minimum of the UV flux. Later observations show a more than 5-fold increase in the UV continuum  [Leighly et al., 2015].
$^d$ Uncalibrated 6dF spectrum; flux scale set by a quick-look magnitude as in [Sulentic et al., 2007]. Grupe et al., 2010 $V$ luminosity implies $f_{\lambda,5100} \approx  0.86 \cdot 10^{-15}$  cm$^{-2}$ Å$^{-1}$.
$^e$ Uncalibrated   spectrum; flux scale set by a quick-look magnitude as in [Sulentic et al., 2007]. Decarli et al., 2010 yield  $5.24 \cdot 10^{-15}$  cm$^{-2}$ Å$^{-1}$, in close agreement.
$^f$ Uncalibrated 6dF  spectrum; flux scale set by a quick-look magnitude as in [Sulentic et al., 2007]. Giannuzzo & Stirpe, 1996 yield  $1.80 \cdot 10^{-15}$  cm$^{-2}$ Å$^{-1}$, in close agreement.
RL: jetted,$ \log$ $\gtrsim 100$ following Ganci et al., 2019; RI: $10 \lesssim \log$ $\lesssim 100$; CSS: compact steep spectrum radio-source.

§ DATA ANALYSIS

§.§ The quasar main sequence as an interpretative aid

In the following the framework of the quasar MS to make assumptions on line shapes, both in the optical and in the UV spectral ranges. There are several papers that provide a description of the main trends associated with the MS. Fraix-Burnet et al., 2017 reviews  the main multifrequency trends.   Sulentic et al., 2000, Sulentic et al., 2011 review the  case for two different quasar Populations: Population A (at low $z$, FWHM   $\lesssim 4000$ ), and  Population  B (FWHM   $\gtrsim 4000$ ). The limit is luminosity-dependent [Sulentic et al., 2017], and reaches FWHM $\gtrsim$ 5500  at high luminosity $\log L \sim 48$). In the optical plane of the MS defined by FWHM  vs    Population A has been subdivided into 4 spectral types (STs) according to  prominence: A1, with $\lesssim 0.5$; A2, with $0.5 \lesssim$ $\lesssim 1.0$;   A3, with $1.0 \lesssim$ $\lesssim 1.5$;  A4, with $1.5 \lesssim$ $\lesssim 2.0$ <cit.>.  The condition  $\gtrsim 1.0$ restricts the MS to the tip of high  values, and encompasses  10% of objects (referred to as extreme Population A).  At low-$z$ they are mostly narrow-line Seyfert-1 (NLSy1s) driving the MS correlations [Boroson & Green, 1992, Sulentic et al., 2000, Du et al., 2016]. Sources with $\gtrsim 2$ do exist [Lipari et al., 1993, Graham et al., 1996] but they are exceedingly rare (less than 1%) in optically-selected samples <cit.>. We therefore group all sources  with $\gtrsim 1.5$ in  A4.

§.§ Multicomponent $\chi^{2}$-minimization

Resolution and S/N of the available  spectra are adequate for a multicomponent nonlinear fitting analysis using the IRAF routine specfit [Kriss, 1994], involving an accurate deconvolution of , , ,   in the optical, and of ,   and  in the UV. A  $\chi^2$  minimization analysis is necessary in all cases, since the strongest lines are heavily blended together, and the blend involves also features extended over a broad wavelength range, due to  (mainly optical, and  UV to a lesser extent) and  (UV only).

§.§ H$\beta$ line

The  Balmer emission line is a reliable estimator of the “virial” broadening in samples of moderate-to-high luminosity [Wang et al., 2009, Trakhtenbrot & Netzer, 2012, Shen & Liu, 2012]. Typically, the  line profiles are fairly symmetric, and are thought to be dominated by a virialized component <cit.>. Several previous works noted that  shows a Lorentzian-like profile  in sources belonging to Population A <cit.>.  However, the  profiles can be affected by slight asymmetries and small centroid shifts. In Population A they are mostly due to blueshifted excess, often modeled with a blueward asymmetric Gaussian component (BLUE),   strongly affecting the  line profiles, and related to outflows .  In ,  BLUE is  detected as a faint excess on the blue side of the symmetric profile  assumed as the virialized  component of , almost only in extreme Population A (several examples are shown in the Figures of the atlas of Appendix <ref>). Even when the BLUE component is detected, its influence on the  FWHM is modest, leading at most to an increase of the broadening  $\approx 10$%  over the FWHM of the symmetric broad profile [Negrete et al., 2018].

To extract a profile that excludes the blueshifted excess, we considered a model of the  broad  line with the following components (based on the approach of  Negrete et al., 2018):

* the , modeled with an (almost) unshifted Lorentzian profile;

* a blueshifted excess (BLUE) modeled with  a blueshifted Gaussian with free skew parameter [Azzalini & Regoli, 2012]. The skewed Gaussian function has no more outliers than the normal distribution, and retains the shape of the normal distribution on the skewed side. It is consistent with the suppression of the receding side of an optically thin  flow obscured by  an optically thick structure (i.e., the accretion disk);

* the , modeled with a Gaussian,   unshifted with respect to rest frame;

*  emission, modeled with a scaled and broadened template <cit.>, as defined by Negrete et al., 2018;

* , modeled by a core-component (assumed Gaussian and symmetric)  and a semi-broad component (assumed Gaussian but with the possibility of being skewed). This approach has been followed in several previous work <cit.>;

* , broad and narrow component.  is not always detected in the spectra, especially in the case of strong  emission, but the line was included in the fits.

§.§ The 1900 blend

The range 1700 – 2000  is dominated by the 1900Å blend which includes , , , as well as  and   lines.   On the blue side of the blend Siii$\lambda$1816 and Niii]$\lambda$1750 are also detected. The relative intensity of these lines (apart from Niii]$\lambda$1750 that is not affecting the blend and for which further observations are needed) is known to be a function of the location along the quasar main sequence <cit.>. The line profiles and relative intensities are systematically different not only between Population A and B, but also within Pop. A there is a systematic trend of increasing  and decreasing  prominence  with increasing  emission [Bachev et al., 2004].

Our interpretation of the 1900 blend for Population A sources closely follows previous analyses [Baldwin et al., 1996, Wills et al., 1999, Baldwin et al., 2004, Richards et al., 2011, Negrete et al., 2012, Martínez-Aldama et al., 2018]. The fits include the following components (described in detail by Martínez-Aldama et al., 2018):

* , , and , modeled with a  Lorentzian profile.  We assume that the shapes of the strongest lines are consistent with the ones considered for the   broad components   (Lorentzian for Pop. A), and that  FWHM  = FWHM  [Negrete et al., 2013].  The fitting routine   may introduce a systematic blueshift to minimize $\chi^{2}$, in the case the profile is significantly affected by an unresolved blue shifted component, as observed in the case of

*  emission, very intense in extreme Population A spectra,   modeled with an empirical template [Vestergaard & Wilkes, 2001].  Recent photoionization calculations indicate a more  significant  contribution of  emission in correspondence of  [Temple et al., 2020]. However, the new  model spectrum is consistent with the empirical template of Vestergaard & Wilkes, 2001.

The  template  is usually  included with the    peak shift of  free to vary in the interval 1908 – 1915 Å (see Martínez-Aldama et al., 2018). In the case the peak shift is around $1914 $ Å, the  component may be representing more the $\lambda$1914 line anomalously enhanced by  fluorescence than . Considering the severe blending of these two lines, and the   weakness of  in Population A, the relative contribution of  and  $\lambda$1914 cannot be  measured properly. However, if the peak wavelength of the blend around  is close to 1914 Å, the  $\lambda$1914 line was included in the fit;

* , usually fainter than . This line is expected to be stronger in extreme Population A [Negrete et al., 2012];

*  emission, modeled with a scaled and broadened theoretical template    [Bruhweiler & Verner, 2008, Martínez-Aldama et al., 2018]. The  emission is never very strong around 1900 Å, and at any rate  gives rise to an almost flat pseudo-continuum that is not affecting the relative intensity ratios of the , ,  lines. A spiky feature around 1780 Å is identified with UV  multiplet # 191 ($\lambda1785$). In several extreme cases, attempting to scale the  template to the $\lambda1785$ intensity required   large  emission [Martínez-Aldama et al., 2018]. In such cases the $\lambda1785$ feature  may have been  selectively enhanced by  fluorescence over the expectation of the Bruhweiler & Verner, 2008 template. Considering the difficult assessment of the  emission, no  measurements are reported in the present paper.

* a blueshifted excess (BLUE) modeled with  a blueshifted skew Gaussian.  At high luminosity in the HE sample, there are 2 cases (HE0359-3959 and HE1347-2457) where a strong blueshifted component is obviously affecting the profile of the 1900 blend. Other cases are also detected in the WISSH sample (see <ref> for the interpretation of the 1900 blend profiles  involving a blue shifted excess).  For two objects, the BLUE emission is overwhelming and masking the emission of the individual , ,  broad components (Section <ref>). Otherwise,  the appearance of the blend is not suggesting, even at the highest luminosity, the presence of an outflow component spectroscopically resolved (i.e., of significant blueshifted emission as detected in ). Small in  blueshifts do occur, but with amplitude $\ll$ than their FWHM.

§.§ Full profile measurements

We assume that the symmetric and unshifted   is the representative line components of the virialized part of the BLR. It is expedient to define a parameter $\xi$ as follows:

\begin{equation}
\xi_\mathrm{line} = {{\rm FWHM}_\mathrm{vir}/{\rm FWHM}} \label{eq:xi},
\end{equation}

where the FWHM$_\mathrm{vir}$ is the FWHM of the “virialized” component, in the following assumed to be , and the FWHM is the FWHM measured on the full profile (i.e., without correction for asymmetry and shifts)  of any   line. In the case of ,  FWHM  $\approx$ FWHM , and $\xi_\mathrm{H\beta} \approx 1$ (Section <ref>).  For the sake of this work,   and  can be considered almost equivalent, so that we will rely on the  —  decomposition obtained with specfit only in a few instances. The blue excess  is usually faint with respect to   and no empirical correction has been applied.

A goal of the present paper is to derive $\xi$ for  and .  Similarly as for , the  lines are fit by  symmetric functions. This approach has been  applied  in all cases and appears appropriate for the wide majority of spectra ($\approx 90$%),  where there is no evidence of a strong BLUE in  and the  peak position is left free to vary to account for small shifts that might be due to a spectroscopically-unresolved outflowing component.  A few cases for which there is evidence of contamination by a strong blue shifted excess  are discussed in Sect. <ref>.

§.§ Error estimates

The data used in this paper come from an array of instruments yielding spectra with widely different  S/N. In addition, the comparison is between  two emission lines, one of which is relatively strong ($W$()$\sim 100$ Å), and one faint ($W$()$\lesssim 10$ Å in most cases). To make things worse, at low $z$ the  line is also recorded on  lower S/N spectra. These and other systematic differences have to be quantitatively taken into account  in the error estimates. A quality parameter $\mathcal Q$ has been defined for , , and  as the ratio between the line equivalent width and its FWHM multiplied by the S/N ratio measured on the continuum. The  $\mathcal Q$ values can be computed using the parameters reported in Tables <ref> and <ref>. The systematic differences in the spectra covering  and  are reflected in the distribution of  $\mathcal Q$:  and  occupy two different domains (Figures in Appendix <ref>).  The corresponding fractional  uncertainties in FWHM computed from dedicated Markov Chain Monte Carlo (MCMC) simulations or by defining a relation with the $\mathcal Q$ parameter as detailed in Appendix <ref>     are significantly different for the two  lines, being  just a few percent in the FWHM of the narrowest sources with strong and sharp  and at worst $\approx 10$%, but in the range $\approx 10$%  — 50 % for .

§ RESULTS

§.§ Immediate results

The specfit analysis results are provided in form of an atlas (Appendix <ref>) for the FOS$^\star$, HE, ISAAC, and WISSH samples. The  and  spectral range are shown after continuum subtraction, on a normalized flux scale (at 1700 and 5100 Å).  The parameters measured with the specfit analysis or on the full profiles for , and  are reported in Table <ref>. Table <ref> lists, in the following order: identification by IAU code name (Col. 1), rest-frame flux and equivalent width of the  line  (Cols. 2–3). The following columns (Cols. 4–6) report the  profile parameters: FWHM , FWHM , and shift.

Here for shift $s$ we intend  the  radial velocity of the line peak  with respect to the rest frame as defined from the redshift measured  in the  spectral range; parameter  and spectral type (Cols. 7–8);   rest-frame flux, equivalent width, FWHM and shift of the  line  (Cols. 9–12). The FWHM refers to the individual component of the doublet, whereas flux and equivalent width $W$ are measured over the full doublet; flux of  (Col. 13);  flux and FWHM (Cols. 14–15).  The  flux measurement (Col. 16) was obtained by integrating the template over the range 1800 $-$ 2150 Å. The upper limit of the wavelength range set at 2150 Å allows the inclusion of a broad feature peaking at $\approx 2050 - 2080$ Å and mostly ascribed to  emission  [Martínez-Aldama et al., 2018]. Further information on the reported parameters are given in the Table footnotes.   Errors on line widths have been  computed from the numerical simulations described in Appendix <ref> or from the data listed in Tables <ref> and <ref> that yield $\mathcal Q$. The same approach has been followed for errors on line intensities and line shifts.

The values of the  FWHM for the WISSH quasars  are fully consistent
with those reported by Vietri et al., 2018  for all but two targets,
namely SDSS J152156.48+520238.5 and SDSS J115747.99+272459.6,  for which a discrepancy   can
be explained in terms of a different fitting technique.    Intensity ratios computed  between lines in the UV and the optical should be viewed with extreme care. The observations are not synoptical and were not collected with the aim of photometric accuracy.

§.§ FWHM H$\beta$ vs. FWHM

Fig. <ref> shows the FWHM  vs FWHM  full profile. The overall consistency in the FWHM of the two lines is rather obvious from the plot.  In the case of  and , the Pearson’s correlation coefficient is $\approx 0.785$ ($P \sim 5 \cdot 10^{-8}$ of a chance correlation). A best fit with the  ordinary least-squares (OLS) bisector yields

\begin{equation}
\mathrm{FWHM\, {AlIII}}  \approx     (273 \pm  216) +     (0.933 \pm    0.059) \mathrm{FWHM \, H}\beta.
\end{equation}

The two lines are, on average, unbiased estimators of each other, with a 0 point offset that reflects the  tendency of the  lines to be somewhat broader than  but is not statistically significant (the offset by 250  is at less than 1 $\sigma $ confidence level). An orthogonal LSQ fit yields  slope  and offset  consistent with the OLS. The normalized $\chi_\nu^2 \approx 1$ also indicates that the ratio between the FWHM of the two lines is 1 within the uncertainties.  The maximum FWHM $\approx 6000$  is observed for the sources of the highest luminosity (Section <ref>) and is below the luminosity-dependent FWHM limit of Population A.

Fig. <ref>  should be compared to Fig. 3 of <cit.>, where one can see that there is no obvious relation between the FWHM of  and the FWHM of .  For the Pop. A sources    is systematically  broader than , apart from in  two  cases in the HE sample, and   FWHM() shows a broad range of values for similar FWHM  i.e., FWHM() is almost degenerate with respect to .  The  line FWHM values are so much larger than the ones of   making it possible that the    derived from FWHM  might be higher by  even more than one order of magnitude than the one derived from the  FWHM, as pointed out in several past works [Sulentic et al., 2007, Netzer et al., 2007, Marziani & Sulentic, 2012, Mejía-Restrepo et al., 2016]. We remark again that the  line may show a blueshifted  excess in 6 sources in our sample, with convincing evidence in only  two cases (Sect. <ref>) but that the line profile is otherwise well represented by a symmetric Lorentzian. In the case of a blueshifted excess,  the good agreement between FWHM  and FWHM  is in part due to the  emission that, if no blueshifted  emission is allowed,  becomes  very strong in the fit of the 6 sources, and compensate for the blueshifted excess.  is expected to be enhanced in the physical conditions of extreme sources <cit.>. At the same time, including the  line in the fits allows for a standard procedure that does not require identification and  a screening for the sources with a strong blueshifted excess, which apparently follow the correlation between  and  full profile in Fig. <ref>.

§.§ Dependence on spectral type and

§.§.§ FWHM

In Fig. <ref> the data points are color coded according to their original subsamples. Fig. <ref> shows the joint sample FWHM  vs FWHM  full profile color-coded according to ST. There are  systematic differences between the various STs, in the sense that A1 sources have  narrower than  (at the relatively high confidence level of 2$\sigma$), and  and  FWHM are almost equal for ST A2. The   and  FWHM ratio is reversed, in the sense that  is narrower than , for STs A3 and A4 grouped together. The difference between STs is reinforced if only the BC of  is considered (Fig. <ref>), since the FWHM   is slightly lower than the FWHM  of the full  broad profile, with $\xi_\mathrm{H\beta} \approx 0.97 \pm 0.05$ on average, but $\xi_\mathrm{H\beta} \approx 0.79$ for the spectral types A3 and A4.

If we define    $\xi_\mathrm{AlIII}$ = FWHM()/FWHM(), we have the following median values  ($\pm$ semi-interquartile range):

ST     $ \mu_\frac{1}{2}(1/\xi_\mathrm{AlIII}) \pm$ SIQR

A3-A4     1.267 $\pm$ 0.223

A2     1.093 $\pm$ 0.176

A1     0.796 $\pm$ 0.158

A2 is the highest-prevalence ST in Population A, with $\xi \approx 1$. However, across Population A there is a significant trend that implies differences of $\pm 20 - 25$% with respect to unity.     The A3-A4 result is after all not surprising, considering that quasars belonging to these spectral types with the strongest  emission are the sources most affected by the high-ionization outflows detected in the  line. The A1 result  i.e.,   lines narrower than  by $\approx 20$%    comes more as a surprise, and it is intriguing that it is consistent that also for the B Population  is narrower than  (del Olmo et al., in preparation; Marziani et al., 2017).  This result may hint at a small but systematic extra broadening not associated with virial motions in A2.

Top panel: FWHM() vs. FWHM() (full profiles) for the joint sample. Data points are color-coded according to sub-sample: FOS$^\star$ - aquamarine ($\bullet$), HE - blue    ($\bullet$), ISAAC - magenta ($\bullet$), WISSH - purple ($\bullet$). Dot-dashed line:  1:1 relation; filled line:   best fit obtained using the bisector technique; dotted line: best fit using the least orthogonal distance method [Press et al., 1992]. Middle panel:   ratio $r$ of FWHM  over FWHM . The average ratio  $\bar{r}$, the standard deviation  $\sigma_\mathrm{r}$  and the normalized $\chi^{2}_{\nu}$  are reported.  Bottom: same as the middle panel,   with an  expanded scale along the $y$ axis.

Top panel: FWHM() vs. FWHM() (full profiles) for the joint  sample. Data points are color-coded according to spectral type: A1 - aquamarine ($\bullet$),  A2 - blue    ($\bullet$), A3 - magenta ($\bullet$), A4  - purple ($\bullet$).  Bottom: FWHM ratio between   and .  The median ratio $\mu_\frac{1}{2}(r)$=FWHM /FWHM ,  and  SIQR   are reported  for spectral types A1 and A2, and the union of A3 and A4.

Top panel: FWHM() vs. FWHM() for the joint sample. Data points are color-coded according to spectral type as in Fig. <ref>.  Bottom panel:  FWHM ratio between  and , $  1/\xi_\mathrm{AlIII}$.  The median ratio  $\mu_\frac{1}{2}(1/\xi_\mathrm{AlIII})$ and the SIQR     are reported  for spectral types A1 and A2, and for  the union of A3 and A4, as in Fig. <ref>.

Observed spectrophotometric quantities and main sequence classification

6.26 =2pt

IAU code	    5c           SpT        4c           2c
2-6 9-1214-15
F      W          FWHM     FWHM BC          Shift                           		      F                W      FWHM      Shift      F      F       FWHM

1c(1)    	(2)	   (3)	    (4)	   	(5)	    (6)	   	(7)	   	(8)	   	(9)	   	   (10) 	   	(11)         (12)	       (13)	    (14)     (15)          (16)

15cFOS sample

J00063+2012	   	544	$\pm$	14	   	99	   	1790	$\pm$	82	        1802                 	-130	$\pm$20	   	0.527	$\pm$	0.07	   	A2	   	92.5	$\pm$	36.2	   	1.7	   	1691	$\pm$	650	   	110	$\pm$	200	   	316.8	$\pm$	50.6     	345.0	$\pm$	29.0     	800 	$\pm$	77	   		   1579.8	$\pm$	328.9

J00392-5117	   	103	$\pm$	6	   	50	   	1290	$\pm$	100	        1283                 	-10	$\pm$	20	   	0.842	$\pm$	0.09	   	A2	   	8.9		$\pm$	3.0		   	4.6	   	1100	$\pm$	693	   	-90	$\pm$	230	   	21.3	$\pm$	5.1       50.9	$\pm$	7.2         1634	$\pm$	268	    		    90.1	$\pm$	12.3

J00535+1241	   	294	$\pm$	12	   	45	   	1100	$\pm$	64	        1077                 	-30	$\pm$	20	   	1.619	$\pm$	0.06	   	A4	   	184.4	$\pm$	17.2	   	7.2	   	1370	$\pm$	212	   	-300 $\pm$	160	   	321.5	$\pm$	32.5     	277.7	$\pm$	102.3    	1225	$\pm$	324	   		   857.8	$\pm$	148.8

J00573-2222	   	741	$\pm$	23	   	47	   	1070	$\pm$	30	        1019                 	0	$\pm$	10	   	0.737	$\pm$	0.06	   	A2	   	50.2	$\pm$	9.0		   	1.6	   	1473	$\pm$	602	   	-270 $\pm$	240	   	125.8	$\pm$	21.3     	289.7	$\pm$	46.3     	1672	$\pm$	224	   		   184.9	$\pm$	27.3

J01342-4258	   	35	$\pm$	5	   	25	   	1050	$\pm$	565	        1019                 	40	$\pm$	130	   	2.054	$\pm$	0.25	   	A4	   	71.7	$\pm$	16.6	   	5.2	   	4560	$\pm$	945	   	-520 $\pm$	570	   	48.6	$\pm$	22.8     	11.7	$\pm$	3.0      	5456	$\pm$	959	   		   250.6	$\pm$	35.9

J02019-1132	   	122	$\pm$	14	   	66	   	4500	$\pm$	751	        4500                 	30	$\pm$	140	   	0.947	$\pm$	0.15	   	A2	   	41.5	$\pm$	5.5		   	2.4	   	4318	$\pm$	558	   	250	$\pm$	450	   	110.4	$\pm$	40.5     	173.3	$\pm$	28.3     	4318	$\pm$	965	   		   25.3	$\pm$	4.6

J06300+6905	   	167	$\pm$	6	   	140	   	5000	$\pm$	410	        4998                 	90	$\pm$	80	   	0.281	$\pm$	0.11	   	A1	   	137.1	$\pm$	32.4	   	2.9	   	3358	$\pm$	869	   	-480 $\pm$	620	   	261.6	$\pm$	126.6     1119.4	$\pm$ 182.0       2962	$\pm$	504	   	       225.0	$\pm$	37.5

J07086-4933	   	74	$\pm$	5	   	33	   	990		$\pm$	86	    980          40	$\pm$	30	   	1.717	$\pm$	0.11	   	A4	   	48.9	$\pm$	17.3	   	2.2	   	2015	$\pm$	874	   	-140 $\pm$	620	   	120.0	$\pm$	43.6     	39.4	$\pm$	10.4     	2188	$\pm$	432	   		   429.1	$\pm$	50.6

J08535+4349	   	73	$\pm$	6	   	125	   	4090	$\pm$	304	        4080                 	230	$\pm$	80	   	0.277	$\pm$	0.13	   	A1	   	18.3	$\pm$	3.6		   	3.5	   	3135	$\pm$	816	   	500	$\pm$	260	   	50.4	$\pm$	18.5     	59.2	$\pm$	13.7     	1889	$\pm$	342	   		   63.4	$\pm$	12.7

J09199+5106	   	162	$\pm$	9	   	106	   	5310	$\pm$	411	        5310                 	270	$\pm$	80	   	0.878	$\pm$	0.08	   	A2	   	23.6	$\pm$	6.2		   	2.2	   	2817	$\pm$	733	   	200	$\pm$	630	   	55.3	$\pm$	12.9     	103.3	$\pm$	26.7     	3626	$\pm$	507	   		   135.4	$\pm$	39.1

J09568+4115	   	393	$\pm$	6	   	154	   	3710	$\pm$	129	        3710                  	180	$\pm$	30	   	0.185	$\pm$	0.08	   	A1	   	30.6	$\pm$	10.7	   	1.9	   	2019	$\pm$	2111   	160	$\pm$	430	   	50.1	$\pm$	19.8     	188.8	$\pm$	31.2     	1922	$\pm$	354	   		   157.2	$\pm$	23.8

J10040+2855	   	135	$\pm$	7	   	63	   	1940	$\pm$	151	        1900                  	-40	$\pm$	40	   	0.953	$\pm$	0.09	   	A2	   	84.3	$\pm$	26.9	   	5.7	   	2602	$\pm$	666	   	-70	$\pm$	430	   	141.7	$\pm$	32.2     	140.7	$\pm$	37.2     	1943	$\pm$	361	   		   101.0	$\pm$	16.6

J10043+0513	   	136	$\pm$	7	   	90	   	1850	$\pm$	143	        1800                  	-110$\pm$	40	   	0.694	$\pm$	0.08	   	A2	   	25.6	$\pm$	9.6		   	6.2	   	2898	$\pm$	1041   	-60	$\pm$	480	   	72.7	$\pm$	19.3     	73.7	$\pm$	21.6     	1828	$\pm$	344	   		   117.0	$\pm$	20.5

J11185+4025	   	39	$\pm$	1	   	83	   	2030	$\pm$	95	        2050                  	50	$\pm$	20	   	0.588	$\pm$	0.07	   	A2	   	36.7	$\pm$	12.0	   	3.5	   	2638	$\pm$	2688   	230	$\pm$	390	   	55.7	$\pm$	21.8     	95.5	$\pm$	22.4     	1963	$\pm$	464	   		   190.9	$\pm$	24.6

J11191+2119	   	406	$\pm$	17	   	147	   	3230	$\pm$	179	        3230                  	40	$\pm$	20	   	0.439	$\pm$	0.07	   	A1	   	180.9	$\pm$	50.0	   	5.3	   	3089	$\pm$	651	   	120	$\pm$	390	   	413.7	$\pm$	73.8     	510.3	$\pm$	92.2     	2450	$\pm$	437	   		   883.6	$\pm$	138.3

J12142+1403	   	644	$\pm$	25	   	111	   	1800	$\pm$	92	        1800                  	80	$\pm$	20	   	0.424	$\pm$	0.06	   	A1	   	80.9	$\pm$	34.7	   	2.9	   	2922	$\pm$	1649   	-160 $\pm$	530	   	117.4	$\pm$	39.1     	349.3	$\pm$	72.9     	1609	$\pm$	291	   		   420.3	$\pm$	77.8

J12217+7518	   	224	$\pm$	11	   	135	   	4120	$\pm$	280	        4120                  	300	$\pm$	30	   	0.255	$\pm$	0.07	   	A1	   	69.1	$\pm$	22.0	   	3.2	   	3149	$\pm$	804	   	-310 $\pm$	430	   	217.9	$\pm$	45.6     	226.4	$\pm$	58.5     	2246	$\pm$	416	   		   178.7	$\pm$	29.4

J13012+5902	   	37	$\pm$	2	   	57	   	3310	$\pm$	257	        2520                  	130	$\pm$	60	   	1.365	$\pm$	0.09	   	A3	   	136.0	$\pm$	25.0	   	8.8	   	4347	$\pm$	590	   	-160 $\pm$	630	   	141.8	$\pm$	42.1     	74.0	$\pm$	30.9     	5215	$\pm$	519	   		   487.2	$\pm$	95.7

J13238+6541	   	69	$\pm$	4	   	94	   	2930	$\pm$	182	        2930                  	-80	$\pm$	80	   	0.497	$\pm$	0.07	   	A1	   	12.7	$\pm$	6.9		   	1.4	   	2326	$\pm$	1075   	-320 $\pm$	770	   	57.3	$\pm$	19.0     	160.5	$\pm$	30.0     	2076	$\pm$	399	   		   42.2	$\pm$	6.9

J14052+2555	   	73	$\pm$	4	   	91	   	2300	$\pm$	158	        2300                  	-90	$\pm$	30	   	1.15	$\pm$	0.08	   	A3	   	93.3	$\pm$	28.3	   	4.8	   	2073	$\pm$	491	   	480	$\pm$	410	   	184.2	$\pm$	38.2     	42.7	$\pm$	14.7     	801	    $\pm$	155	   		   559.7	$\pm$	90.4

J14063+2223	   	70	$\pm$	6	   	59	   	1630	$\pm$	151	        1530                  	-10	$\pm$	30	   	1.1		$\pm$	0.11	   	A3	   	33.1	$\pm$	5.1		   	6.8	   	1937	$\pm$	604	   	-180 $\pm$	410	   	62.2	$\pm$	12.1     	31.2	$\pm$	14.6     	1703	$\pm$	496	   		   121.8	$\pm$	26.8

J14170+4456	   	51	$\pm$	6	   	63	   	2290	$\pm$	217	        1620                  	0	$\pm$	70	   	1.182	$\pm$	0.13	   	A3	   	57.6	$\pm$	4.1		   	6.4	   	2104	$\pm$	353	   	-80	$\pm$	250	   	119.4	$\pm$	20.4     	121.7	$\pm$	22.5     	2010	$\pm$	234	   		   161.2	$\pm$	22.0

J14297+4747	   	48	$\pm$	2	   	151	   	2840	$\pm$	153	        2840                  	300	$\pm$	30	   	0.392	$\pm$	0.05	   	A1	   	14.7	$\pm$	5.7		   	2.1	   	2519	$\pm$	965	   	280	$\pm$	490	   	29.5	$\pm$	8.3       92.4	$\pm$	19.5        1795	$\pm$	325	   	 	   79.2	$\pm$	14.0

J14421+3526	   	114	$\pm$	7	   	55	   	1630	$\pm$	169	        1610                  	-140$\pm$	20	   	1.357	$\pm$	0.09	   	A3	   	105.8	$\pm$	32.1	   	4.0	   	1832	$\pm$	433	   	-260 $\pm$	410	   	229.5	$\pm$	46.9     	448.2	$\pm$	101.3    	2007	$\pm$	366	   		   559.7	$\pm$	90.4

J14467+4035	   	77	$\pm$	3	   	74	   	2430	$\pm$	131	        2360                  	30	$\pm$	30	   	1.327	$\pm$	0.06	   	A3	   	62.4	$\pm$	6.6		   	3.6	   	2611	$\pm$	745	   	120	$\pm$	360	   	142.6	$\pm$	33.3     	106.5	$\pm$	27.7     	2059	$\pm$	435	   		   373.6	$\pm$	51.4

J15591+3501	   	121	$\pm$	7	   	44	   	1010	$\pm$	105	        1000                 	100	$\pm$	20	   	1.424	$\pm$	0.10	   	A3	   	21.1	$\pm$	2.7		   	3.3	   	967		$\pm$	185	   	180	$\pm$	340	   	64.3	$\pm$	8.5       152.4	$\pm$	20.2        1534	$\pm$	239	   	        150.4	$\pm$	17.9

J21148+0607	   	86	$\pm$	4	   	119	   	3330	$\pm$	228	        3320                 	0	$\pm$	30	   	0.781	$\pm$	0.08	   	A2	   	119.0	$\pm$	34.2	   	9.3	   	3999	$\pm$	883	   	10	$\pm$	400	   	295.2	$\pm$	55.0     	297.1	$\pm$	54.4       2995	$\pm$	535	   		   131.9	$\pm$	20.9

J22426+2943	   	29	$\pm$	2	   	47	   	1000	$\pm$	149	        1000                 	-20	$\pm$	40	   	0.821	$\pm$	0.15	   	A2	   	18.2	$\pm$	2.5	       	1.7	   	1410	$\pm$	207	   	-290 $\pm$	370	   	52.3	$\pm$	4.8       108.1	$\pm$	28.9        1507	$\pm$	344	   		    75.2	$\pm$	10.3

15cHE sample

J00456–2243	   	229	$\pm$	9	   	68	   	4150	$\pm$	370	   	4146                190	$\pm$	60	   	0.37	$\pm$	0.10	   	A1	   	54.0	$\pm$	4.7		   	4.1	   	3299	$\pm$	261	   	10	$\pm$	190	   	93.0	$\pm$	16.0	   	230.0	$\pm$	63.7	   	3295	$\pm$	474	   		   	82.0	$\pm$	15.1

J01242–3744	   	111	$\pm$	10	   	48	   	3250	$\pm$	469	   	3250                0	$\pm$	100	   	1.155	$\pm$	0.14	   	A3	   	102.0	$\pm$	28.8	   	5.3	   	4543	$\pm$	981	   	10	$\pm$	390	   	94.0	$\pm$	20.5	   	 0.0	 	 			   	 	…   		   	146.0	$\pm$	23.0

J02509–3616	   	39	$\pm$	3	   	44	   	4480	$\pm$	504	   	4480                -20	$\pm$	120	   	0.531	$\pm$	0.13	   	A2	   	69.0	$\pm$	4.9		   	3.1	   	4164	$\pm$	345	   	20	$\pm$	130	   	122.0	$\pm$	13.8	   	18.0	$\pm$	2.3		   	3990	$\pm$	537	   		   				0.0

J04012-3951	   	88	$\pm$	9	   	50	   	5049	$\pm$	652	   	3957                -20	$\pm$	80	   	1.103	$\pm$	0.14	   	A3	   	70.0	$\pm$	8.6		   	6.2	   	6003	$\pm$	673	   	-150	$\pm$380   	39.0	$\pm$	9.9		   	17.0	$\pm$	8.8		   	2052	$\pm$	356	   		   	122.0	$\pm$	16.9

J05092–3232	   	149	$\pm$	8	   	67	   	3880	$\pm$	403	   	3880                -130$\pm$	80	   	0.311	$\pm$	0.10	   	A1	   	48.0	$\pm$	6.8		   	4.3	   	4193	$\pm$	574	   	-50	$\pm$	450	   	96.0	$\pm$	32.3	   	56.0	$\pm$	15.4	   	2500	$\pm$	467	   		   	34.0	$\pm$	6.2

J05141-3326	   	228	$\pm$	15	   	82	   	3702	$\pm$	415	   	3700                0	$\pm$	80	   	0.656	$\pm$	0.07	   	A2	   	57.0	$\pm$	5.6		   	7.5	   	3998	$\pm$	291	   	20	$\pm$	550	   	129.0	$\pm$	39.0	   	67.0	$\pm$	17.2	   	2255	$\pm$	435	   		   	81.0	$\pm$	15.4

J11065–1821	   	366	$\pm$	35	   	121	   	4647	$\pm$	702	   	4646                -50	$\pm$	110	   	0.557	$\pm$	0.11	   	A2	   	108.0	$\pm$	29.6	   	4.9	   	4570	$\pm$	951	   	0	$\pm$	390	   	205.0	$\pm$	37.1	   	113.0	$\pm$	30.8	   	3138	$\pm$	576	   		   	95.0	$\pm$	14.8

J13506–2512	   	162	$\pm$	29	   	37	   	6087	$\pm$	1346   	5795                0	$\pm$	180	   	1.266	$\pm$	0.23	   	A3	   	404.0	$\pm$	101.9	   	9.5	   	6087	$\pm$	1259   	-1480	$\pm$620   	269.0	$\pm$	52.5	   	17.0	$\pm$	9.6		   	2190	$\pm$	652	   		   	543.0	$\pm$	67.0

J21508–3158	   	120	$\pm$	9	   	66	   	5452	$\pm$	741	   	5450         0	$\pm$	130	   	0.816	$\pm$	0.10	   	A2	   	104.0	$\pm$	13.1	   	7.0	   	5078	$\pm$	513	   	-360	$\pm$190   	139.0	$\pm$	43.3	   	66.0	$\pm$	19.0	   	4095	$\pm$	696	   		   	75.0	$\pm$	10.2

J23555–3953 	   	318	$\pm$	21	   	46	   	3639	$\pm$	481	   	3640         0	$\pm$	100	   	0.549	$\pm$	0.08	   	A2	   	99.0	$\pm$	8.9		   	3.2	   	3979	$\pm$	547	   	0	$\pm$	270	   	150.0	$\pm$	27.0	   	0.0	 					       	…   		      370.0	$\pm$	70.2

15cISAAC sample

J00570+1437	   	219	$\pm$	15	   	86.3	   	3901	$\pm$	377	   	3535                          -20	$\pm$	70	   	0.838	$\pm$	0.10	   	A2	   	120.0	$\pm$	32.7	   	10.2	   	4360	$\pm$	904	   	-510	$\pm$	380	   	99.0	$\pm$	21.2	   	56.0	$\pm$	16.7	   	3370	$\pm$	637	   		   	57.9	$\pm$	9.0

J13202+1420	   	122	$\pm$	7	   	97.0	   	4262	$\pm$	325	   	4290                          -150 $\pm$	80	   	0.282	$\pm$	0.05	   	A1	   	45.0	$\pm$	5.3	   	6.5	   	2838	$\pm$	674	   	-710	$\pm$	280	   	78.0	$\pm$	23.9	   	96.0	$\pm$	25.5	   	3282	$\pm$	523	   		   	48.0	$\pm$	7.8

J16149+1448	   	231	$\pm$	21	   	91.5	   	4332	$\pm$	277	   	4177                          -80	$\pm$	40	   	0.423	$\pm$	0.10	   	A1	   	51.0	$\pm$	4.5	   	4.1	   	4906	$\pm$	470	   	30	$\pm$	310	   	169.0	$\pm$	21.9	   	128.0	$\pm$	32.6	   	3499	$\pm$	712	   		   	0.3	$\pm$	0.04

15cWISSH sample

J0801+5210	   	294	$\pm$	36	   	71	   	5620	$\pm$	784	   	5648        -128	$\pm$	140	   	0.55	$\pm$	0.15	   	A2	   	269.8	$\pm$	22.6	   	10.7	   	6783	$\pm$	747    	-270	$\pm$	400	   	285.3	$\pm$	33.8	   	171.6	$\pm$	47.0	   	4576	$\pm$	934	   		   	49.3	$\pm$	9.7

J1157+2724	   	87	$\pm$	7	   	37	   	3169	$\pm$	298	   	3161        -128	$\pm$	100	   	1.68	$\pm$	0.17	   	A4	   	26.4	$\pm$	3.1		   	6.7	       	2484	$\pm$	715    	-560	$\pm$	590	   	95.2	$\pm$	11.4	   	66.6	$\pm$	15.9	   	2913	$\pm$	512	   		   	1.6		$\pm$	0.2

J1201+0116	   	211	$\pm$	23	   	59	   	4085	$\pm$	779	   	4095        -134	$\pm$	140	   	0.60	$\pm$	0.15	   	A2	   	126.1	$\pm$	16.6	   	9.0	       	4548	$\pm$	814    	-710	$\pm$	620	   	141.0	$\pm$	21.8	   	94.4	$\pm$	23.8	   	3100	$\pm$	770	   		   	2.4		$\pm$	0.4

J1236+6554	   	141	$\pm$	15	   	60	   	5674	$\pm$	976	   	5669         225    $\pm$	130	   	0.52	$\pm$	0.12	   	A1	   	106.4	$\pm$	35.2	   	5.3	       	4644	$\pm$	1262   	-520	$\pm$	440	   	163.5	$\pm$	39.5	   	3.5		$\pm$	2.7		   	4317	$\pm$	998	   		   	          0.0

J1421+4633	   	214	$\pm$	27	   	66	   	5584	$\pm$	556	   	4646             -21	$\pm$	140	   	0.99	$\pm$	0.20	   	A2	   	174.5	$\pm$	63.2	   	10.0	   	4901	$\pm$	1594   	-1030	$\pm$	470	   	151.6	$\pm$	44.5	   	0.0	 	 		 		   	 	 	 		 	   		   	251.0	$\pm$	43.3

J1521+5202	   	188	$\pm$	23	   	21	   	4366	$\pm$	851	   	4343          81    $\pm$	150	   	1.15	$\pm$	0.18	   	A3	   	212.6	$\pm$	27.9	   	4.1	       	4650	$\pm$	914    	-510	$\pm$	760	   	271.8	$\pm$	26.0	   	1.8		$\pm$	0.5		   	1248	$\pm$	385	   		   	251.7	$\pm$	47.8

J2123$-$0050	   	296	$\pm$	24	   	51	   	4793	$\pm$	1082   	4426         -61	$\pm$	80	   	1.12	$\pm$	0.11	   	A3	   	179.3	$\pm$	20.6	   	6.6	       	4737	$\pm$	518    	-610	$\pm$	340	   	218.6	$\pm$	35.3	   	226.1	$\pm$	53.0	   	4519	$\pm$	703	   		   	23.7	$\pm$	3.8

(1) JCODE identification  of the object; (2)   total flux of H$\beta$ (sum of all broad line components);  (3)  equivalent width of the full  profile, in Å; (4) FWHM H$\beta$ measured on the full profile, in ;   (5) FWHM H$\beta$ measured on the broad component (), in ;  (6) peak shift of the  broad profile;  (7)  parameter; (8) spectral type SpT following Sulentic et al., 2002; (9) total flux of the  doublet;  (10)  equivalent width in Å; (11) FWHM of the individual line components of the  doublet; (12) shift of , in units of ; (13) flux of ;  (14) flux of ;  (15)  FWHM; (16)    flux of  computed over the range between 1800 – 2150 Å. All measurements are in the quasar rest frame and line fluxes are all in units of 10$^{-15}$ erg s$^{-1} $ cm$^{-2}$.

§.§.§ Shifts

In addition to shifts with respect to the rest frame, we consider also the shift $s^\star$ defined as  the radial velocity difference between the peak position of the Lorentzian function describing the individual components of the  doublet with respect to the quasars rest frame  and the peak position of  and  (reported in Table <ref>) i.e., $s^\star(\mathrm{AlIII}) = s(\mathrm{AlIII}) - s(\mathrm H\beta)  $. We adopt this definition  because   the spectral resolution and the intrinsic line width make it   difficult  to resolve the outflow in the   profile. In the   and  profiles, and even in the ones of , it is possible to isolate a blue-shifted excess that contributes most of the  flux in several cases, superimposed to a symmetric profile originating in the low ionization part of the BLR. In the case of , this approach is more difficult, in part because of the low S/N (a blueshifted contribution as faint as the one of  would be undetectable for , especially in the FOS spectra), in part because of the intrinsic rarity of sources with a strong blue-shifted excess.  In addition,  the  is often overwhelmed by the , making it difficult to accurately measure its width and shift.  The shifts of  broad profile with respect to the rest frame set by the  are usually modest, and the median is consistent with 0, $\mu(s(\mathrm H\beta))\approx 0 \pm 65$ . The shift estimators $s^\star$ and $s$ therefore yield results that are in close agreement.

Fig. <ref>  shows   that the $s^\star$ amplitude  is relatively modest for spectral type A3. ST A4 shows a larger shift, associated with an increase in the FWHM  with respect to , although with a large scatter. This is due to  an outstanding case,  HE0132-4313, a NLSy1 with FWHM  / FWHM  $\approx 5$, a behaviour frequent for the  in strong  emitters but apparently rarer for .

Taken together, the FWHM and shift data suggest that major discrepancies are more likely for the relatively rare, stronger  emitters, ST A3 and A4. The left panel of Fig. <ref> shows that only A4 has a median shift that is significantly different from 0.  A4 sources  are relatively rare sources (4 in our sample, and $\approx$ 3 % in [Marziani et al., 2013]). In addition to the shift amplitude in , the line shift normalized by line width may be a better description of the “dynamical relevance” of the outflowing component [Marziani et al., 2013]. The    parameters
$\delta(\frac{i}{4}) =   {c(\frac{i}{4})}/{\mathrm{FW}\frac{i}{4}\mathrm{M}}, i=1,2,3, $
yield the centroids $c(\frac{i}{4})$ at fractional peak intensity $\frac{i}{4}$  normalized by the full width at the same fractional peak intensity FW$\frac{i}{4}$M.  In the case of the  shifts as defined above, $\delta$ can be approximated as $\delta(\mathrm{AlIII}) \approx
{s(\mathrm{AlIII})}/{\mathrm{FWHM(AlIII)}}. $ The values of the $|\delta$ $|$  are $\lesssim 0.05$ (right panel of Fig. <ref>) save in the case of spectral  type A4 where $\delta \approx -0.1$.

Left, upper panel: behavior  of shift $s^\ast$ of  with respect to rest frame as a function of the spectral type. Reported values are sample medians and  error bars are SIQR. Left bottom panel: same, for the ratio FWHM  over FWHM . Right: parameter $\delta$() as a function of spectral type.

§.§ Dependence on luminosity

§.§.§ FWHM

An important clue to the interpretation of the  broadening is provided by the trends with luminosity.  Fig. <ref> shows FWHM  vs. FWHM  with data points color-coded according to luminosity. There is no significant deviation from equality for the FWHM of  and .  At higher luminosity, both the  and the  line become broader, and the largest line widths are measured on the ESO, ISAAC and WISSH samples.  The ratio $r$ = FWHM  / FWHM   $\approx 1/\xi$    also does not depend on luminosity: dividing the sample by about one half at $\log L_{1700}$ = 46 [erg s$^{-1}$] yields median $r$ values for the subsamples above and below this limit  that are very close to 1 (lower panel of Fig. <ref>).

The statistical equality between FWHM  and FWHM  is not breaking down at any luminosity, at least within the limit sets by our sample and data quality. The explanation resides in the fact that both line FWHM increase in the same way with luminosity, as shown by the left, top panel  of Fig. <ref>.
The trends  for , , and  alike ( is discussed in Section <ref>)  can be explained if the broadening of the line is basically set by the virial velocity at the luminosity-dependent radius of the emitting region, $r _\mathrm{BLR} \propto L^\frac{1}{2}$. Under the standard virial assumption, we expect that FWHM(H$\beta$) $\propto M_\mathrm{BH}^{\frac{1}{4}} \left( L/L_\mathrm{Edd}\right)^{-\frac{1}{4}} f_\mathrm{S}(\theta)^{-\frac{1}{2}}$, with $f_\mathrm{S}$ assumed to be mainly dependent of the angle $\theta$ between the accretion disk axis and the line of sight [Mejía-Restrepo et al., 2018]. Equivalently, FWHM(H$\beta$) $\propto L^{\frac{1}{4}} \left(L/L_\mathrm{Edd}\right)^{-\frac{1}{2}} f_\mathrm{S}(\theta)^{-\frac{1}{2}}$. While   is changing in a narrow range (0.2 — 1) and $f_\mathrm{S}$ is also changing by a factor a few,    is instead spanning around 4 orders of magnitude. Over such a broad ranges of masses or, alternatively,  luminosity, we might expect that the dominant effect in the FWHM increase is associated right with mass or luminosity.    In  Fig. <ref>  the trend expected for FWHM(H$\beta$) $\propto L_{1700}^\frac{1}{4}$ is overlaid to the data points, and is consistent with the data in the luminosity range $44.5 \lesssim \log L_{1700} \lesssim 47.5$ [], where a fivefold increase of the FWHM of both  and  is seen.

Top panel: FWHM() vs. FWHM() for the joint sample. Data points are color-coded according to luminosity at 1700 Å, from red (lowest; $\log L_{1700} \sim 44$) to blue (highest, $\log L_{1700} \sim 47$). Bottom panel:  FWHM ratio of  and .  The median ratios  $\mu_\frac{1}{2}{r}$ and the SIQR ${r}$  are reported   for more luminous  ($\log L \ge\ 46$  [erg/s]) and less luminous ($\log L < 46$) quasars.

and  profile parameter comparison as a function of luminosity.   Left panel: behavior of FWHM  and    (upper half) and of the ratio FWHM()/FWHM() as a function of $\log L$ at 1700 Å. The filled line traces the expected increase of the FWHM in a virialized system with $L^\frac{1}{4}$.   The data point are identified on the basis  of spectral type as in Fig. <ref>. The yellow band marks the region where FWHM()/FWHM()=1 within the errors: the median value of the uncertainty of the ratios,  $ \approx \pm $25%.  Right panels: shifts of    and  (upper half), and their difference  $s^\star$ as a function of $\log L$(1700) (lower half).  The vertical dotted lines join  and  parameters for the same object (e.g., they are not error bars).

§.§.§ Shift

The  blueshifts  involve  radial velocities  that are relatively modest  (right panel of Fig. <ref>).   shifts exceed 1000  only in two cases of extreme luminosity.  Even if we see some increase toward higher $s$ values in the highest luminosity range, several high-luminosity sources remain unshifted within the uncertainties.   If we consider the dependence of shifts on luminosity,  at high $L$ there is an increase in the range of blueshifts involving values that are relatively large (several hundred ; Fig. <ref>). The parameter $\delta$ as a function of $L$ has a more erratic behaviour (Fig. <ref>), but only at the highest $L£$  $\delta \approx -0.1$, and  the effect of the line shift is at a 10% level. Fig. <ref> is consistent with    blueshifts becoming more frequent and of increasing amplitude with luminosity.

Parameter $\delta$() as a function of luminosity. Median values are plotted for 1 dex luminosity intervals. Error bars are sample SIQR.

§.§ FWHM  and FWHM

The  line has been considered as a possible virial broadening estimator, and has been a target of reverberation mapping monitoring [Trevese et al., 2007, Trevese et al., 2014, Lira et al., 2018, Kaspi et al., 2021]. The problem in Population A is that  shows a strong gradient in its intensity. In spectral type A1,  is by far the strongest line in the 1900 Å blend, but its prominence decreases with increasing , i.e., going toward spectral type A3 [Bachev et al., 2004]. In spectral types A3 and A4   is  affected by  the severe blending with  and  emission (much more severe than for ), and  may  become so weak to the point of being barely detectable or even undetectable  [Vestergaard & Wilkes, 2001, Negrete et al., 2014, Temple et al., 2020, Bachev et al., 2004, Martínez-Aldama et al., 2018]. In addition, the  line has a rather low critical density, and its intensity is exposed to the vagaries of density and ionization fluctuations much more than , whose emission is highly efficient in dense  gas over a broad range of ionization levels <cit.>.  The measurements of the   width   might be inaccurate in  extreme Population A if  contamination is strong.  It is therefore legitimate to expect a greater dispersion in the width relation of  with .

The FWHM of  is shown against the FWHM of  full profile in Fig. <ref>, upper panel. Error bars show uncertainties computed following the prescription of Appendix <ref>.  Not surprisingly, the scatter in the FWHM ratio between  and  is larger than in the case of .  The top and  middle  panels of Fig. <ref> show that there is a significant deviation from unity, although for relatively  narrow  profiles around 2000  the FWHM   is close to the 1:1 line.  The $\chi_\nu^2$ is much higher than 1. The bottom panel shows the ratio between FWHM  and FWHM   color-coded according to  strength. The limit was set at normalized intensity (roughly equal to  equivalent width) $I = $ 10. The trend for sources above this limit implies  FWHM = $\xi_\mathrm{CIII]}$ FWHM $\approx$  0.77 FWHM .

We didn’t detect any strong difference in the trend with luminosity of   and  FWHM, as it has been the case for  and . The two lines follow a similar trend with luminosity at 1700 Å (Fig. <ref>).
No shift analysis was carried out for  due to the severe blending with  and .

The narrower profile of  indicates a higher distance from the central continuum source than the one obtained from , if the velocity field is predominantly virial [Peterson & Wandel, 2000]. This result is also consistent with the findings of  Negrete et al., 2013 who, using  intensity ratios in a photoionization  estimate of the emitting region radius, obtained  much larger radii than the ones obtained from reverberation mappings of .

Top panel: FWHM() vs. FWHM() for the joint sample. Data points are color-coded according to spectral types, as for Fig. <ref>. Middle panel:  FWHM ratio of  and ,  The median ratio  $\mu_\frac{1}{2}({r})$, with $r =$ FWHM /FWHM ,   and the SIQR are reported. Bottom panel: same ratio with the data color-coded according to  intensity: normalized intensity $> 10$ (red) and $\le 10$ (blue). Values of  $\mu_\frac{1}{2}({r})$ and   SIQR  are reported for stronger  and weaker   emitters.

and  profile parameter comparison as a function of luminosity.   Top panel: Behavior of FWHM  and    (upper half) and of the ratio FWHM()/FWHM() as a function of $\log L$ at 1700 Å.
The data point are color-coded on the basis  of spectral type.  As in Fig. <ref>, the filled line traces the expected increase of the FWHM in a virialized system with $L^\frac{1}{4}$.  The yellow band marks the region where FWHM()/FWHM() $\approx$ 0.8 within the errors. The width of the band has been  set by  the median value of the uncertainty of the ratios,  $\pm$ 0.17.   The vertical dotted lines join  and  parameters for the same object.

§.§ A  scaling law based on

The goal is to obtain an  estimator based on  that is consistent with  the scaling law derived for . In this context, the process is much simpler than in the case of , where large blueshifts introduced a significant correction and a second-order dependence on luminosity of FWHM  could not be bypassed.   The  and  widths of the two lines grow in a similar trend with $L$ (Fig. <ref>). The  scaling law can be derived in the form $\log M_\mathrm{BH} = \alpha \cdot \log L + 2 \cdot \log \mathrm{FWHM} + \gamma$ by minimizing the scatter and any systematic deviation of      estimated from  with respect to the -derived masses  from the Vestergaard & Peterson, 2006 scaling law:

\begin{equation}
\log M_\mathrm{BH}\, (\mathrm{H\beta})  \approx  0.5 \log L_{5100,44} +
2 \log \left(\mathrm{FWHM}(\mathrm{H\beta}) \right) + 0.91,
\end{equation}

where   $L_{5100,44}$ is the rest frame luminosity  $\lambda L_\lambda$ at 5100 Å in units of $10^{44}$ , and the FWHM  is in ,
considering that no correction is needed  to FWHM   (i.e., $\xi_\mathrm{AlIII} \approx 1$).   The Vestergaard & Peterson, 2006 scaling law is a landmark that has been applied in hundreds of quasar studies. However, the Vestergaard & Peterson, 2006  scaling law  provides individual estimates with large error bars in relative estimates  ($\approx$0.5 dex at 1$\sigma$, see the discussion in their paper).  This is a limit to the precision of any scaling law based on the match with the one based on . The large error bars of individual mass estimates can be mainly explained on the basis of   orientation effects [Marziani et al., 2019] and of trends along the spectral types of the main sequence [Du & Wang, 2019].

If this condition is enforced, the relation between  from  and from   (Fig. <ref>) can be written as:

\begin{equation}
\log M_\mathrm{BH}(\mathrm{AlIII})  \approx (1.000 \pm 0.043) \log M_\mathrm{BH}(\mathrm{H\beta}) - (0.001\pm 0.367). \label{eq:eqmass}
\end{equation}

The  scaling law takes the form, with the FWHM in :

\begin{eqnarray}\label{eq:masslaw}
\log M_\mathrm{BH}\, (\mathrm{AlIII}) & \approx & (0.579^{+0.031}_{-0.029}) \log L_{1700,44} + \\ \nonumber
&& 2 \log \left(\mathrm{FWHM}(\mathrm{AlIII}) \right) + (0.490^{+0.110}_{-0.060}),
\end{eqnarray}

with an rms scatter  $\sigma \approx 0.29$.   Figure <ref> suggests the presence of a well-behaved distribution with a few outlying points. The relation of Eq. <ref> considers the FWHM of 47 sources.  One data point has been excluded applying a $\sigma$ clipping algorithm  (the one A4 outlier, HE0132-4313). This selective procedure is justified by the fact that only some of the most extreme sources of Population A (not all of them) show large blueshifts and only one (HE0132-4313) a  FWHM in excess to  by a large factor, deviating at more than 3 times the sample rms. Removal of HE0132-4313 provides however only a minor, not significant change in the fitting parameters.   The scaling law parameter uncertainties have been estimated computing the coefficients $\alpha$ and $\gamma$ over a wide range of values and defining the interval where agreement  between  from  and  (Eq. <ref>) is satisfied within  1.00$\pm 1 \sigma$ for the best-fitting slope and  $0.00 \pm 1 \sigma$ for the intercepts (respectively $\approx$0.043 and $\approx$0.367, as per Eq. <ref>).  Due to some scatter in FWHM relation at FWHM    $\sim$ 1000  and the possibility of predominantly face-on orientation  [Mejía-Restrepo et al., 2018] the  estimates at  $\lesssim 10^7$  should be viewed with care  due to the paucity of data points.

It is important to remark that this result, unlike the one on   estimates, is obtained without any correction on the measured FWHM. The  and  relation should be considered equivalent with respect to  estimates in large samples of Population A sources. No scaling law $r_\mathrm{BLR}  -  L$ has been ever derived from reverberation mapping on the  lines. However, it is reassuring that the luminosity exponent ($\approx  0.579^{+0.031}_{-0.029}$) deviates by about $1 \sigma$ from the one entering the scaling law  $r_\mathrm{BLR}  -  L$ derived by Bentz et al., 2013 for .

Decimal logarithm of black hole mass in units of solar masses  computed from the  relation of Vestergaard & Peterson, 2006 based on FWHM  vs. the one computed from the  FWHM following Eq. <ref>, with sub-samples identified by color according to their spectral types.  The filled line traces Eq. <ref>, while the dot-dashed line is the equality line.   The bottom panel shows the residuals as a function of the  derived from  .  Average values of the $\log $  differences, standard deviation and normalized $\chi_\nu^2$ are reported  for the joint  sample minus one outlier with $\delta > 1$  (top row). The bottom rows yields the median and the SIQR.

§.§ A  scaling law based on

An  approach analogous to the one adopted for  was also applied to .  The goal is   to obtain an  estimator based on  that is consistent with  the scaling law derived for . The process is again much simpler than in the case of , where large blueshift introduced a significant correction and a second-order dependence on luminosity of FWHM  could not be bypassed.   Considering that only a very simple  correction is needed  to FWHM , $\xi_\mathrm{CIII]} \approx 1.25$, the  scaling law can be derived in the form $\log M_\mathrm{BH} = \alpha \cdot \log L + 2 \cdot \log {\xi_\mathrm{CIII]}} \mathrm{FWHM} + \gamma$ by minimizing the scatter and any systematic deviation of      estimated from  with respect to the -derived masses.  Figure <ref>  suggests the presence of a well-behaved distribution with a few outlying points. The condition

\begin{equation}
M_\mathrm{BH}(\mathrm{CIII]})  \approx (1.000 \pm 0.053) M_\mathrm{BH}(\mathrm{H\beta}) + (0.000\pm 0.454)
\label{eq:eqmassc3}
\end{equation}

is satisfied if  the  scaling law takes the form:

\begin{eqnarray}\label{eq:masslawc3}
\log M_\mathrm{BH}\, \mathrm{CIII]} & \approx & (0.6765 \pm 0.0450) \log L_{1700,44} + \\ \nonumber
&& 2 \log \left({\xi_\mathrm{CIII]}}\mathrm{FWHM}(\mathrm{CIII]}) \right) + (0.332 \pm 0.120),
\end{eqnarray}

with an rms scatter  $\sigma \approx 0.35$ (excluding 1 outlier, for 44 objects). The scaling law parameter uncertainties have been estimated varying the coefficients $\alpha$ and $\gamma$ as for the  case.

The    scaling law  is derived with a simple correction on the measured FWHM . The  and  relation should be considered equivalent with respect to  estimates in large samples of Population A sources. Care should however be taken to consider sources in which  can be measured ($W \gtrsim 10$Å) and to identify extreme objects, as discussed in Section <ref>.   In addition, the heterogeneity of the sample and the possibility of different trends in different FWHM domains (FWHM () $\approx$ FWHM() if FWHM $\lesssim$ 3000 ) makes the scaling law with    more reliable.

Decimal logarithm of black hole mass in units of solar masses  computed from the  relation of Vestergaard & Peterson, 2006 based on the  spectral range vs. the one computed from the  data following Eq. <ref>, with spectral types color-coded as in Fig. <ref>.  As for Fig. <ref>,  the filled line traces Eq. <ref>, while the dot-dashed line is the equality line.   The lower panel shows residuals as a function of  derived from  .  Average, standard deviation, and $\chi_\nu^2$ of the  $\log$  difference are reported on the top-row  of the inside caption; the bottom row reports median and SIQR.

§ DISCUSSION

Decimal logarithm of black hole mass in units of solar masses  computed from the  scaling law based on FWHM  (Eq. <ref>) vs. the one computed from the  FWHM following Eq. <ref>.  The filled line traces an unweighted least square fit; the dot-dashed line is the equality line.

In the following we first compare the scaling laws obtained for  and (Sect. <ref>).

The present work detects systematic shifts of  toward the blue. Even if they are on average slightly above the uncertainties, it is interesting to analyze them in the context of systematic shifts affecting the prominent high and  low-ionization lines of  and  (Section <ref>), and to consider more in detail sources in  the spectral type where  are broader than the  ones  (Section <ref>).

§.§ Consistency of scaling laws

The scaling laws derived for  and  are mutually consistent. Black hole mass estimates are shown in Fig. <ref>. An unweighted lsq fit yields slope $0.975 \pm  0.043$, consistent with unity, and intercept $0.246 \pm 0.371$, with an rms scatter $\approx$ 0.302. The median difference  of the mass values obtained with the two scaling laws is $\mu(\log M_\mathrm{BH} \mathrm{(CIII])} - \log M_\mathrm{BH} \mathrm{(AlIII)}) \approx 0.06 \pm 0.20$ (SIQR).

The  $r_\mathrm{BLR}  -  L$ implicit in Eq. <ref> is consistent with the  $r_\mathrm{BLR}  -  L$ relation derived for  in a previous study [Trevese et al., 2014], and only slightly higher than the one derived in the early study of  <cit.>. More high S/N spectroscopic observations, including monitoring, should be carried out to explore  the full potential of the 1900 Å blend lines and especially of   as VBEs.

The scaling law derived from the  line is consistent with the -based scaling law [Marziani et al., 2019]: Fig. <ref> indicates only a slight bias   (less than the SIQR $\approx$ 0.2 dex, and the  rms $\approx $ 0.3 dex), as the  scaling law apparently overestimates the  by  $\approx 20$% and $\approx 40$% with respect to the  estimates based on   and , respectively. Considering that the -based scaling law requires a large correction ($\xi_\mathrm{CIV}$ can be as low as $\approx$ 0.2) to the  FWHM dependent on both line shift and luminosity, the  scaling law should be preferred in case observations of both  and  are available.

Decimal logarithm of black hole mass in units of solar masses computed from the -based scaling law of [Marziani et al., 2019] vs the ones   computed from the  relation of Vestergaard & Peterson, 2006 based on FWHM  (blue) and  from the  FWHM following Eq. <ref> (black). The dot-dashed is the equality line.   The bottom panel shows the residuals as a function of . Median  and SIQR  of the $\log $  differences $\delta \log M_\mathrm{BH} = \log M_\mathrm{BH}$ CIV $- \log M_\mathrm{BH}$  and $\delta \log M_\mathrm{BH} = \log M_\mathrm{BH}$ CIV $- \log M_\mathrm{BH}$   are reported in the inside caption.

§.§ Shifts of  vs shifts of  and

Fig <ref> shows the  peak shifts reported in Table <ref> vs. the centroid at half maximum of  from [Sulentic et al., 2007], [Sulentic et al., 2017],  Deconto-Machado et al. (2022, in preparation), and  the “peak" shift given by Vietri et al., 2018 for the four subsamples of the present work. The  shift is usually very modest, and a factor of $\sim 10$  lower than the shift measured for .  The  and  shifts are however significantly correlated (Pearson's correlation coefficient $\approx 0.54$, with a significance $P \approx 1. - 2\cdot10^{-3}$):

\begin{equation}
s(\mathrm{AlIII}) \approx (0.114 \pm 0.026) c({\frac{1}{2}})(\mathrm{CIV}) + (50.0 \pm 68.5) \mathrm{km\ s^{-1}}.   \end{equation}

Shift $s$ of   vs shift of  with respect to rest frame. Data points are identified according to  the spectral type, with the same color code of Fig. <ref>. The filled and dot-dashed lines trace an unweighted least square fit and  the equality line, respectively. The grey bands identify uncertainties ranges in radial velocity $\pm 400$ where the lines are not significantly shifted. Squares refer to the c($\frac{1}{2}$)  in the case the excess emission on the blue side of  has been ascribed to . See Section <ref>.

The slope is shallow, but the correlation indicates that the shifts in  and  are likely to be due to the same physical effect.  If we ascribe the small displacements observed in the peak shift $s$ of  to the effect of  outflows, the outflow prominence is much lower than in the case of , both in terms of radial velocity values and of $\delta$.

As mentioned,  shifts and FWHM are correlated, implying that the broader the line, the higher the shift amplitude becomes [Coatman et al., 2016, Sulentic et al., 2017].
The  shows a   consistent behavior, but apparently masked by the much lower shift amplitudes; the presence of   blueshifts  appears to be statistically  significant  at very high luminosity, and for spectral type A3 and A4.   When  shows large blueshifts i.e., for high  or very high luminosity, the  line becomes broader than  (even if the two lines remain in fair agreement). We see a relation between  line shift and widths: in ST A3 and A4, where shifts are larger, the  FWHM exceeds the one of  (Figure <ref>).

The  and  results on line shifts are also consistent with  the ones obtained for . Small amplitude blueshifts of  a few hundreds  were measured on the full line profile of   [Marziani et al., 2013]. For  the separation of a BLUE component and a symmetric Lorentzian  has been possible  on  median composite spectra because of the high S/N and of the peaky line core of the  line.   The same operation is not feasible for individual  profiles that are often significantly affected by noise, and in some cases even barely above noise.  The ,  and  are all resonance lines that may be subject to selective line-driven acceleration [Murray & Chiang, 1997, Proga, 2007, Risaliti & Elvis, 2010]. The different velocity amplitudes most likely reflect the difference in the line emitting region distance from the continuum source and in physical properties, such as ionization parameter, density and column density.

Rare sources with large shift amplitudes in
are expected to be intrinsically infrequent even at the redshift where luminous quasars were fairly common ($z \approx 1.5 - 2$) and, even if over-represented because of a Malmquist-type bias, they  are outstanding and  pretty easily recognizable, especially in large samples of AGN (Sect. <ref>).   The most striking case directly resembling  is the one of HE0132-4313  which is an object of fairly low luminosity and an outlier in the plots FWHM  vs FWHM . Sources with large shift amplitude may be excluded or flagged if black hole mass estimates are being carried out.

§.§ xA quasars

There are 16  sources   meeting the criterion $\gtrsim 1$ in the joint sample. The wide majority of these sources shows  blueshift with respect to .  The average shift is rather modest, $\approx -250$ although for 7 of them, $s \lesssim -250$ . Six  objects show evidence of a strong excess on the blue side of the 1900 blend. Fits to the 1900 blend of these sources following the standard approach are shown in Appendix <ref>. The fits have been repeated by allowing for an extra BLUE in the 1900 blend, represented as a skewed Gaussian (Fig. <ref>). The blueshifted excess  in some cases cannot be distinguished from   strong  emission. The  emission line can be of strength comparable to  in the condition of low ionization and high density derived for the virialized component [Negrete et al., 2012].

In two cases (e.g., HE0359-3959,and  SDSS J152156.48+520238.5) the blueshifted excess is so overwhelming that  emission cannot account for the excess unless the  line itself is significantly blueshifted. These are perhaps the best cases supporting the evidence for a significant BLUE in . It is reasonable to assume  that the blueshifted excess is mainly due to , being  a resonant line for which BALs are also observed. Broad absorption components are observed in the  profile, even if  rarely, and with terminal radial velocity of the absorption through  much lower than the one of  [Gibson et al., 2009].

The Eddington ratio values derived from the continuum luminosity at 1700 Å (after Galactic extinction correction) multiplied by a bolometric correction factor  $k_\mathrm{bol} \approx$ 3.5, and from the  estimated from Eq. <ref>  range between $\approx 0.2$  and $\approx 1.5$.  If the luminosity-dependent $k_\mathrm{bol}$ is applied to   the 1700 Å  continuum, $0.2 \lesssim $$\lesssim 1.1$.   Both estimates confirm that all quasars of the presented sample are within the range expected for Pop. A sources. The xA sources are at the high end of the  distribution, with $\mu(\log$)$\approx -0.18$, and the  BLUE sources are even more extreme with $\mu(\log$)$\approx -0.105$. Extreme radiation forces may  make it possible  to blow out rather dense/high column density gas from the virialized region associated with the emission of the low- and intermediate ionization lines [Netzer & Marziani, 2010]. Sources showing a strong BLUE in  could be the most extreme accretors,  perhaps in a particular “blow-out” phase of the quasar  evolution <cit.>.

Analysis of the 1900 Å blend  for the estreme Population A sources with excess emission on the blue side of .  Abscissa scales are rest-frame wavelength in Å and radial velocity from rest frame wavelength of .  Ordinate scale is  normalized specific flux by the value at 1700 Å.  The black lines identify , . The blueshifted excess BLUE is traced by a thick blue line. Green lines trace the adopted  (pale) and  (dark) templates. Note that  emission is almost absent, as all of the emission on the red side of  can be ascribed to .

A related issue is whether sources with a strong blue-shifted component in  can be empirically  distinguished from the rest of Pop. A quasars, without resorting to the knowledge of the rest frame. The FWHM of the whole blend (i.e., of the sum of all lines after continuum subtraction) is clearly affected by spectral type: going from A1 to A4 we see an overall decrease of prominence in , and an increase in  with respect to the other line. The blue-shifted excess should further increase the FWHM of the blend. The parameter

\begin{equation}
\mathcal{A} = \frac{\mathrm{FWHM_{1900}}}{\left(10^{\log (\lambda L_\lambda)_{1700} - 44}\right)^{0.25}}
\end{equation}

normalizes the FWHM of the whole blend $\mathrm{FWHM}_{1900}$ (i.e., the sum of all line components) because of the increase of the line width with luminosity by a factor $L^\frac{1}{4}$. Fig. <ref> shows the distribution of the $\mathcal{A}$ for the sources of ST A1 and A2, A3 and A4, and the 6 quasars for which the 1900  blend was fit with the addition of a blue-shifted excess. The distributions of A1+A2 and A3+A4 are significantly different at a 3$\sigma$ confidence level according to a K-S test. However, there is considerable overlap around $\mathcal{A} \approx 3000$ , making it difficult to unambiguously distinguishing between xAs, xAs with blue-shifted excess and other sources.

The distribution of the parameter $\mathcal{A}$, as defined in Sect. <ref>, for three groups of quasars: spectral types A1+A2,  A3+A4, and the 6 quasars with a blue shifted excess fit to the 1900 Å blend (Fig. <ref>).

§.§.§ Consistency of UV and optical classification for extreme Population A

Extreme quasars can be identified by employing selection criteria in the optical and UV  [Marziani & Sulentic, 2014]. The consistency of the selection criteria is however little tested, since observations covering both the 1900 Å range and the  one are still rare. In the joint sample    most sources with $\gtrsim 1$ also satisfy  the UV intensity-ratio conditions /$> 0.5$, and $>$. Figure <ref> shows the location of the data points identified according to spectral type (defined by ranges of the optical parameter ; A3 and A4 satisfy the condition $\gtrsim$ 1 by definition)  in  the plane defined by the UV ratios / vs. /.  There are several borderline cases,  but only one in which the criteria are  not satisfied: J15591+3501 with intensity ratios /$\approx 2.38 \pm 0.45$, and /$\approx 0.33 \pm 0.06$. For J14421+3526, the feature at $\approx 1910$ Å is most likely a blend of  and . In this case, only an upper limit can be assigned to the  intensity, and the UV selection criteria may  not have been violated. The reason of the discordance for  J15591+3501 is not clear.   The    majority of objects ($\approx 80$%) in Figure <ref>    supports the equivalence between the two xA selection criteria suggested by [Marziani & Sulentic, 2014].  Apart from borderline cases, five  A2 sources (4 if we exclude J1421+4633 with $\approx$ 0.99) out of 19 enter    the domain of the xA (the grey shaded area of Figure <ref>). These sources appear to be genuine xA in terms of the UV intensity ratios, but have lower than expected  ($0.5 \lesssim $ $\lesssim$ 1). It is intriguing that the  four sources all belong to the high-$z$ samples. The possibility of systematic differences as a function of redshift in the relative abundance of iron with respect to carbon and $\alpha$ elements   should be further investigated <cit.>.

The distribution of xA   sources  in the plane defined by the intensity ratios  / vs /. The area associated with xA sources is the lower-left shaded box. Sources are color coded according to spectral type as in the previous Figures.

§ SUMMARY AND CONCLUSION

The present investigation has shown a substantial equivalence of  and  and  as virial broadening estimators for Population A quasars, thereby providing a  tool suitable for  estimates up to $z \lesssim 4$ from observations obtained with optical spectrometers. More in detail, the  salient  results of the present investigation  can be summarized as follows:

* the  and  FWHM are highly correlated and, in the joint sample of 48 Population A sources, can be considered statistically equivalent   over 4 orders of magnitude in luminosity (Sections <ref> and <ref>).

* The FWHM ratio between  and  increases with increasing  or, equivalently, from spectral type A1 to A4  (Sect. <ref>).  Extreme Pop. A sources appear to be 20% broader than the sample average, while spectral type A1 20 % narrower than spectral type A2.

*  Systematic blueshifts are revealed in ; however, in most cases the amplitude of the blueshifts is modest or smaller than the uncertainties, reaching a sample median for spectral types A3 and A4 of just $\approx -160$  (Sections <ref> and <ref>).

*  The line FWHM of ,  and  increases with luminosity as a function of $L^\frac{1}{4}$, as expected for a virial velocity field of the line emitting gas (Sect. <ref>).

*  The following scaling law between  and luminosity and FWHM : $\log M_\mathrm{BH}\, (\mathrm{AlIII})   \approx   (0.579^{+0.031}_{-0.029}) \log L_{1700,44} +    2 \log \left(\mathrm{FWHM}(\mathrm{AlIII}) \right) + (0.490^{+0.110}_{-0.060}) $ (Eq. <ref> in Sect. <ref>)   provides an estimate of  with an rms scatter of $\approx$ 0.3 dex with respect to the -derived masses,      for $\gtrsim 10^7$ .

* An  analogous scaling law has been defined also for   (Eq. <ref> in Sect. <ref>). The measurement of the   FWHM is however more strongly affected by the severe blending and by the  weakness  in sources with high . The  scaling law requires a constant correction factor to the FWHM of , $\xi_\mathrm{CIII]} \approx  1.25$.  The scaling laws derived from  and  line width are mutually consistent (Sect. <ref>).

*  Although  shift amplitudes are $\approx \frac{1}{10}$ the shifts of  (Section <ref>),  it is   unclear  whether  can be exploited as a virial luminosity estimator for extreme Population A sources  (Section <ref>): the  profile is strongly affected by a blueshifted excess in several extreme Pop. A sources (Sect. <ref>).  The majority of quasars show consistency between FWHM  and , and  a minority of sources that show FWHM $\gg$ FWHM  might be easy to recognize in large samples. The extent of systematic effects should however be analyzed  by a thorough study of a very large sample of xA sources with full coverage of the optical and UV rest-frame ranges from 1000 to 5500 Å.

These results show that the  line is a good UV substitute of  and can be used for black hole mass estimations  with the  advantage to be at the rest-frame of the source.
The results on FWHM   should be compared with the ones obtained for  [Marziani et al., 2019], where the equivalence was obtained at the expense of corrections that were dependent on the accurate knowledge of the quasar rest frame, and therefore not fully achievable without additional measurements in spectral ranges distinct from the one of : the  line is the narrow low ionization line closest in wavelength to  and offers a reliable rest frame estimator [Bon et al., 2020], but is very rarely covered  along with .

The authors are grateful for the contribution of Jack Sulentic to the early development of this paper.

PM, AdO and ADM acknowledge financial support from from the Spanish grants MCI PID2019-106027GB-C41 and the State Agency for Research of the Spanish MCIU through the “Center of Excellence Severo Ochoa" award for  the Instituto de Astrofísica de Andalucía (SEV-2017-0709).  ADM acknowledges the support of the INPhINIT fellowship from “la Caixa" Foundation (ID 100010434).The fellowship code is LCF/BQ/DI19/11730018.
PM  was supported  by  the Hypatia of Alexandria visiting grant  during a two-month stay in  2020 at the Instituto de Astrofísica de Andalucía  where part of the analysis was carried out. NB and EB acknowledge the support of Serbian Ministry of Education, Sci-ence and Technological Development, contract number 451-03-68/2022-14/200002. DD acknowledges support from grant PAPIIT UNAM IN-113719.

Funding for the Sloan Digital Sky Survey (SDSS) has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Aeronautics and Space Administration, the National Science Foundation, the U.S. Department of Energy, the Japanese Monbukagakusho, and the Max Planck Society. The SDSS Web site is http://www.sdss.org/.

The SDSS is managed by the Astrophysical Research Consortium (ARC) for the Participating Institutions. The Participating Institutions are The University of Chicago, Fermilab, the Institute for Advanced Study, the Japan Participation Group, The Johns Hopkins University, Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, University of Pittsburgh, Princeton University, the United States Naval Observatory, and the University of Washington.

NUMPY (Oliphant, 2015);  R (R Core Team, 2019);   SuperMongo (Lupton & Monger, 1996).

§ ESTIMATION OF  UNCERTAINTIES

§.§ Bayesian estimates

Uncertainties were estimated following a Bayesian approach, considering the likelihood function

\begin{equation}
\log {\mathcal L} \propto - \sum_{i} \frac{(f_\mathrm{i} - m_\mathrm{i}({\bf \Theta}))^2}{2\sigma_\mathrm{i}^2} \propto -\frac{1}{2} \log \chi^2,
\end{equation}

where $f_\mathrm{i}$ are the specific flux values as a function of wavelength (or of pixel number), $\sigma_\mathrm{i}$ the uncertainty in $f_\mathrm{i}$ (in practice from the S/N set constant over the spectrum), $m_\mathrm{i}({\bf \Theta})$ the expectation value for the multicomponent model ${\bf \Theta}$ of the spectrum obtained via a specfit analysis. The ${\bf \Theta}$ can be any set of free parameters employed in the fits: intensity, shift and width of each line, intensity, shift and width of each template.  Priors were specified for several parameters in terms of a range of permitted values. The posteriors of  the model parameters ${\bf \Theta}$ (for instance, the distributions of FWHM  and   given the data) were obtained by creating a random walk with a modified Metropolis-Hasting algorithm: a new candidate set of model parameters ${\bf \Theta}$ was randomly generated, and screened by an accettance parameter $\alpha$. The set ${\bf \Theta}$ included model parameters believed to significantly affect the line widths (in practice, most of the parameters included in the specfit analysis). For example, the  lines were modeled with two components, a “core" component represented by a symmetric Gaussian, and a semi-broad component modeled by a skew Gaussian. The template  emission was scaled, shifted and broadened as done in the specfit procedure.
The dispersion of  the   posterior distribution of each spectral  parameter was assumed to yield its uncertainty $\delta$ at $1 \sigma$ confidence level.

§.§ The quality parameter ${\mathcal Q}$

The next step was to connect the uncertainty in FWHM, shift and intensity to a quality parameter  ${\mathcal Q}$, which may turn useful in case very late samples of quasars are analysed.   The quality parameter

\begin{equation}
{\mathcal Q} = \log_{10}\frac{W}{\mathrm{FWHM}} \cdot {\frac{\mathrm S}{\mathrm N}}
\end{equation}

defined as the product of the S/N times a line  equivalent width $W$ divided by its FWHM, increases with S/N and line prominence over the continuum and decreases with increasing line widths. The signal in each resolution element is proportional to the ratio $W$/FWHM, which is a measurement of the sharpness of the line, as  obviously ${\mathcal Q} \propto \log_{10}\frac{I_\mathrm{peak} \cdot \mathrm{FWHM}}{\mathrm{FWHM} I_{\mathrm{c}}} \cdot {\frac{I_\mathrm{c}}{\mathrm N}} \propto \frac{I_\mathrm{peak}}{\mathrm N}$.  The quality parameter ${\mathcal Q}$obviates to the inadequacy of the S/N measurement carried out on the continuum. By multiplying it by the ratio $W$/FWHM we compute a more apt average S/N for   a line depending on its strength and width.
The parameter ${\mathcal Q}$ is larger for sharp lines in spectra with high S/N in the continuum.  The large differences in S/N, line width and line strength between  and  is reflected in the distribution of the ${\mathcal Q}$ parameter, shown in Fig. <ref>.

To be of any practical use, the  ${\mathcal Q}$ parameter needs to be anchored to estimates of the uncertainties. The posterior distributions of the spectral parameters were computed for about 30 sources.    Fig. <ref> shows a well-defined trend between ${\mathcal Q}$ and the fractional uncertainty  $\delta$FWHM/FWHM for ,  , and  derived from the MCMC simulations. Especially for large ${\mathcal Q}$ values, the scatter is relatively modest, and the relation between the   parameter FWHM, flux and shift and  $\log {\mathcal Q}$ can be written in a linear form, save for the fractional uncertainty of FWHM  that is best fit by $\delta \mathrm{FWHM}/\mathrm{FWHM} \approx 1/(a + b\log {\mathcal Q}) $. Table <ref> provides the coefficients $a$ and $b$ of the best fits along with ${\mathcal Q}$ domain. The FWHM relations  were obtained by a non-linear fit algorithm implemented in R [R Core Team, 2019], and  are shown as the thick lines in Fig. <ref>.

Relation between fractional uncertainties and ${\mathcal Q}$

Parameter       $a$      $b $      $\log{\mathcal Q}$ domain

FWHM$a$      0.100     –0.125     $\approx -0.8 \ldots 0.5$

F$b$         0.0666     –0.07022

Shift$c$     66    -0.112

FWHM$d$      10.96     6.15     $\approx -1.6 \ldots -0.6$

F$b$     0.061     $-0.2277$

Shift$c$      180     $-219.7$

FWHM$a$      0.160     –0.026     $\approx -2.5 \ldots 0.0$

F$b$       $-0.026$     $-0.292$

F$b$     -0.04755     0.07520     $\approx -0.8 \ldots 0.5$

a $\delta \mathrm{FWHM}/\mathrm{FWHM} \sim a + b \log{\mathcal Q}$
b$\delta F/F \sim a + b \log {\mathcal Q}$
c$\delta s = a + b \log {\mathcal Q}$ []
d $\delta \mathrm{FWHM}/\mathrm{FWHM} \sim 1/(a + b
\log{\mathcal Q})$

Left: distribution of the $\log$ of parameter ${\mathcal Q}$ parameter for  (blue) and  (red) for the joint sample considered in this paper. Right: distribution of  $\log {\mathcal Q}$  differences between  and .

Relation between the fractional uncertainty ${\delta \mathrm{FWHM}}/{\mathrm{FWHM}}$ and the  logarithm of parameter ${\mathcal Q}$. Red spots are for ,  black for , blue for . The thick lines trace the relations reported in Table <ref>  for the FWHM of  (black) and  (blue).

§  AND 1900 BLEND PAIRED COMPARISON

The results of line profile fitting for the 1900 blend and  are shown in the following figures: Fig. <ref> for the FOS sample, Fig. <ref> for the HE sample, Fig.  <ref> for the FOS sample, and Fig.  <ref> for the WISSH sample. All spectra have been continuum subtracted and normalized by the 5100 Å () and 1700 Å (1900 blend) specific flux.

Analysis of the  spectral range (left) and of  1900 Å blend (right), for the sources of the $FOS^\ast$ subsample.  Abscissa scales are rest-frame wavelength in Å and radial velocity from rest-frame. Ordinate scale is  normalized specific flux by the value at 5100 Å and at 1700 Å. The dashed magenta lines trace the sum of all emission components of the model.  The black lines identify the  broad component  (left), and , , and   (right).  The blue line the blueshifted excess in the  profile. Green lines trace the adopted  (pale) and  (dark) templates.  Golden  lines trace narrow emission lines or line components.

Analysis of  and of the 1900 Å blend for Pop. A sources (cont.).

Analysis of  and of the 1900 Å blend for Pop. A sources (cont.).

Analysis of the 1900 Å blend, for 10 Pop. A sources of the HE sub-sample. Meaning of color coding is the same as in Fig. <ref>.

Analysis of  and of the 1900 Å blend for Pop. A  sources of the ISAAC sample. Meaning of color coding is the same of the previous Figures in the Appendix.

Analysis of  and of the 1900 Å blend for Pop. A sources of the WISSH sample. Meaning of color coding is the same of the previous Figures in the Appendix.

§ NOTES ON INDIVIDUAL OBJECTS

J01342-4258  Extreme of extreme Population A. Strong feature at 2080 Å, extreme  emission. In the UV spectrum a strong shelf of emission extends from the red end of the 1900 Å blend to  beyond 1950 Å. Inverted radio spectrum not accounted for by the classical synchrotron scenario.

J02019-1132 The CSS source 3C 57 shows a spectrum of Pop. A in the optical range. Analyzed by Sulentic et al., 2015.

HE 0248–3628 Candidate high-frequency peaking object which could be associated with an incerted or self-abosbed spectrum in 5 – 20 GHz frequency domain [Massardi et al., 2016]. We speculate that HE 0248–3628 and J01342-4258 could be both objects whose radio emission is not due to a relativistic jet but to thermal sources [Ganci et al., 2019].

J09199+5153 Luminous quasar, considered with “unusually strong optical   emission"  [Sulentic et al., 1990]. The  $\approx 0.8$ confirms that optical  emission is prominent, but not extraordinarily so. The  UV spectrum is definitely not xA, and is consistent with the A2 classification based on the optical spectrum.

J07086-4933 Bad spectrum contaminated by heavy absorptions;  lower limit.

HE 0043-2300 Apart from 3C 57, the only source truly “jetted” radio loud.

HE 0359-3959 High-luminosity analogous of J01342-4258; extreme  blueshift and extremely low ionization in the virialized BLR [Martínez-Aldama et al., 2017].

J1157+2724 This WISSH source has a significant difference in the redshift estimated for the present work and the one published by Vietri et al., 2018 which is estimated  from the narrow  component, 2.2133 vs	2.2170. The difference is significant. The larger redshift of Vietri et al., 2018 would imply larger shifts of .

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