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Mon. Not. R. Astron. Soc. 337, 275­292 (2002)

The correlation of line strength with luminosity and redshift from composite quasi-stellar object spectra
S. M. Croom,1 K. Rhook,1 E. A. Corbett,1 B. J. Boyle,1 H. Netzer,2 N. S. Loaring,3 L. Miller,3 P. J. Outram,4 T. Shanks4 and R. J. Smith5
1 2 3 4 5

Anglo-Australian Observatory, PO Box 296, Epping, NSW 1710, Australia School of Physics and Astronomy, Tel-Aviv University, Tel-Aviv 69978, Israel Department of Physics, Oxford University, Keble Road, Oxford OX1 3RH Physics Department, University of Durham, South Road, Durham DH1 3LE Astrophysics Research Institute, Liverpool John Moores University, 12 Quays House, Egerton Wharf, Birkenhead CH41 1lD

Accepted 2002 July 24. Received 2002 July 23; in original form 2002 June 27

ABSTRACT

We have generated a series of composite quasi-stellar object (QSO) spectra using over 22 000 ° individual low-resolution (8-A) QSO spectra obtained from the 2dF (18.25 < bJ < 20.85) and 6dF (16 < bJ 18.25) QSO Redshift Surveys. The large size of the catalogue has enabled us to construct composite spectra in relatively narrow redshift ( z = 0.25) and absolute magnitude ( M B = 0.5) bins. The median number of QSOs in each composite spectrum is 200, yielding typical signal-to-noise ratios of 100. For a given redshift interval, the composite spectra cover a factor of over 25 in luminosity. For a given luminosity, many of the major QSO emission lines (e.g. Mg II 2798, [O II] 3727) can be observed over a redshift range of 1 or greater. Using the composite spectra we have measured the line strengths (equivalent widths) of the major broad and narrow emission lines. We have also measured the equivalent width of the Ca II 3933 K absorption feature caused by the host galaxy of the active galactic nuclei (AGN). Under the assumption of a fixed host galaxy spectral energy distribution (SED), the correlation seen between Ca II K equivalent width and source luminosity implies L gal L 0.42 ± 0.05 .Wefind QSO strong anticorrelations with luminosity for the equivalent widths of [O II] 3727 and [Ne V] 3426. These provide hints to the general fading of the NLR in high-luminosity sources, which we attribute to the NLR dimensions becoming larger than the host galaxy. This could have important implications for the search for type 2 AGN at high redshifts. If average AGN host galaxies have SEDs similar to average galaxies, then the observed narrow [O II] emission could be solely a result of the host galaxy at low luminosities ( M B -20). This suggests that the [O II] line observed in high-luminosity AGN may be emitted, to a large part, by intense star-forming regions. The AGN contribution to this line could be weaker than previously assumed. We measure highly significant Baldwin effects for most broad emission lines (C IV 1549, C III] 1909, Mg II 2798, H ,H ) and show that they are predominantly caused by correlations with luminosity, not redshift. We find that the H and H Balmer lines show an inverse Baldwin effect and are positively correlated with luminosity, unlike the broad ultraviolet lines. We postulate that this previously unknown effect is caused by a luminosity-dependent change in the ratio of disc to non-disc continuum components. Key words: galaxies: active ­ quasars: emission lines ­ quasars: general ­ galaxies: stellar content.

1

INTR ODUCTION

E-mail: scroom@aaoepp.aao.gov.au
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The correlation of quasi-stellar object (QSO) emission-line properties with luminosity is a straightforward yet potentially highly informative test of standard physical models for active galactic

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2 2.1 D ATA Generation of composite spectra

nuclei (AGN). Since the discovery of an anticorrelation between the equivalent width (W ) of the C IV 1549 emission line and the continuum luminosity (L) by Baldwin (1977), a significant amount of effort has been expended to quantify this relationship (hereinafter referred to as the Baldwin effect), and investigating similar correlations with other QSO emission lines (Baldwin et al. 1989; Zamorani et al. 1992; Green, Forster & Kuraszkiewicz 2001). The results have revealed that the anticorrelation with luminosity is relatively weak, typically W L , with =-0.2 and a large scatter. Similar correlations have been seen in most other broad emission lines including Mg II 2798, C III] 1909, Si IV+O IV] 1400 and Ly with -0.4 < < -0.1 (Green et al. 2001). It has also been claimed (Green et al. 2001) that the Baldwin effect may be dominated by an even stronger anticorrelation with redshift. However, in the magnitude-limited QSO samples that have been studied to date, it is extremely difficult to disentangle the effects of redshift and luminosity. It it typically only possible to access 1­1.5 mag at any given redshift, given the steep slope of the QSO luminosity function for magnitudelimited samples with B < 19.5 (Boyle, Shanks & Peterson 1988). A further limitation of existing studies is that it is difficult to study the correlation with luminosity and/or redshift for weaker lines, in particular the narrow-line region (NLR). The spectra used in such analyses are typically `survey' quality, i.e. relatively low signal-tonoise (S/N) ratio (S/N 5­10) and thus narrow emission lines can be difficult to detect in individual spectra. Composite QSO spectra have been generated from most large QSO surveys over the past decade (Boyle 1990; Francis et al. 1991), providing a detailed picture of the ensemble average spectral properties of the QSO sample. Typical S/N ratios in these spectra approach or even exceed 100, with even relatively weak emission lines (e.g. [Ne V] 3426) easily detectable. However, previous surveys have been too small (comprising 1000 QSOs or less) to generate composite spectra as a function of both luminosity and redshift with which to examine correlations. With the recent advent of much larger QSO surveys such as the 2dF QSO Redshift Survey (2QZ, Croom et al. 2001) and Sloan Digital Sky Survey (SDSS, Vanden Berk et al. 2001; Schneider et al. 2002) we may now use composite, rather than individual spectra, to investigate the correlation of QSO spectral properties with luminosity and redshift in much greater detail that has hitherto been possible. In this paper we describe the result of an analysis of composite QSO spectra based on the almost 22 000 QSOs observed to date (2002 January) in the 2QZ. The bulk of these objects lie around the break in the luminosity function (LF), thus providing a better sampling in luminosity at any given redshift than QSO surveys at the bright end of the LF (e.g. the Large Bright Quasar Survey; Hewett, Foltz & Chaffee 1995). Moreover, we have also included a few hundred brighter QSOs observed with the new 6 field (6dF) multiobject spectrographic facility on the UK Schmidt Telescope (Croom et al., in preparation) to increase the luminosity range studied at any given redshift to typically 3­4 mag. As well as providing a wide baseline over which to study correlations such as the Baldwin effect, this sampling of the QSO ( L , z ) plane provides an opportunity to disentangle the effects of luminosity and redshift. In Section 2 we describe the data used in our analysis, while in Section 3 we discuss the methods used to generate the composite spectra and measure the spectral line equivalent widths. In Section 4 we present the results of our analysis, we then discuss these in the context of theoretical models in Section 5.

The data used in our analysis is taken from the 2dF and 6dF QSO Redshift Surveys (Croom et al. 2001; 6QZ Croom et al., in preparation). QSO candidates were selected for observation based on their stellar appearance and blue colours found from automated plate measurements (APM) of UK Schmidt Telescope (UKST) photographic plates and films in the u, bJ and r bands. The 2QZ/6QZ area comprises 30 UKST fields arranged in two 75 â 5deg2 declination strips centred on =-30 and 0 . The =-30 strip extends from = 21h 40m to 3h 15m in the South Galactic Cap and the equatorial strip from = 9h 50m to 14h 50m in the North Galactic Cap. The 2QZ and 6QZ sources were selected from the same photometric data, the only difference being their ranges in apparent magnitude: 18.25 < bJ < 20.85 (2QZ) and 16.0 < bJ 18.25 (6QZ). The combined data sets thus produce a uniform QSO sample over a wide range in luminosity. Details of the candidate selection can be found in Smith et al. (2002). The 2QZ objects were observed over the period 1997 October to 2002 January using the 2dF instrument at the Anglo-Australian Telescope. Observations were made with the low-dispersion 300B ° ° grating, providing a dispersion of 178.8 A mm-1 (4.3 A pixel-1 ) ° ° and a resolution of 8.6 A over the range 3700­7900 A. Typical integration times were 55 min, in a range of observing conditions (1­2.5 arcsec seeing) resulting in median S/N 5 pixel-1 . The brighter 6QZ objects used in the present paper were observed in 2001 September using the 6dF facility at the UKST. A low° dispersion 250B grating was used to provide a dispersion of 286 A ° ° mm-1 (3.6 A pixel-1 ) and a resolution of 11.3 A over the range ° 3900­7600 A. Exposure times were typically 100 min resulting in median S/N 15 pixel-1 . Data from both 2dF and 6dF were reduced using the pipeline data reduction system 2DFDR (Bailey et al. 2002). Identification of spectra and the determination of redshifts was carried out by a automated program, AUTOZ (Croom et al. 2001; Miller et al., in preparation). Each spectrum was checked by eye by two members of the team. In our analysis below we only include quality Class 1 identifications (96 per cent reliable identification), these being the best quality spectra. We also only take the best spectrum (based on quality class and then the S/N ratio) of each object in the case where there is more than one spectrum available. The combined 2QZ/6QZ data set provides us with 22 041 independent QSO spectra. Typical redshift errors are z = 0.003 and photometric errors in the bJ band are 0.1 mag. Absolute magnitudes were computed from the observed photographic bJ magnitude, after correction for Galactic extinction (Schlegel, Finkbeiner & Davis 1998), using the K-corrections found by Cristiani & Vio (1990). Throughout we assume a flat cosmological world model with 0 = 0.3, 0 = 0.7 and H0 = 70 km s-1 Mpc-1 . 3 METHOD

We have generated composite QSO spectra in discrete absolute magnitude ( M B = 0.5 mag) and redshift ( z = 0.25) bins. The bin widths were chosen to give good resolution in luminosity and redshift, whilst typically retaining over 100 QSOs in at least 5 M B bins (a factor of 10 in luminosity) at each redshift (see Table 1). Once QSOs identified as broad absorption line (BAL) QSOs had been removed, there remained a total of 21 102 QSOs with which to

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QSO line strength versus luminosity and redshift
Table 1. The number of QSOs in each of our absolute magnitude­redshift ( M B ­z) bins. For each bin the central redshift and absolute magnitude is displayed. The last column shows the total number of QSOs in each magnitude interval over all redshifts. In some M B ­z intervals there are only a small number of QSOs. In these cases the spectra in adjacent M B intervals were combined together, an or indicates where this has been done. For example, in the z = 0.375 interval, QSOs in the M B = -24.75, -24.25 and -23.75 bins were combined together. Redshift 0.125 0.375 0.625 0.875 1.125 1.375 1.625 1.875 2.125 2.375 2.625 2.875 ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ 2 ­ 2 8 15 22 22 16 11 4 ­ 1 ­ ­ ­ ­ ­ ­ ­ ­ ­ 2 7 14 66 101 158 220 239 117 27 7 ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ 3 4 27 85 217 334 410 528 274 38 ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ 1 3 12 77 178 360 546 692 420 51 ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ 1 5 13 76 218 441 703 778 359 2 ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ 3 10 80 194 434 766 974 456 ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ 2 5 54 183 370 667 956 779 11 ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ 1 23 100 259 517 788 942 92 ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ 1 8 48 152 316 545 791 341 ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ 1 ­ 1 13 48 116 289 439 446 25 ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ 1 2 15 37 101 211 277 99 ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ 3 4 13 37 71 50 ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­

277

M

B

All 1 1 7 43 180 585 1432 2483 3524 3678 3000 2022 1453 933 739 502 292 139 49 23 11 4 ­ 1

-29.25 -28.75 -28.25 -27.75 -27.25 -26.75 -26.25 -25.75 -25.25 -24.75 -24.25 -23.75 -23.25 -22.75 -22.25 -21.75 -21.25 -20.75 -20.25 -19.75 -19.25 -18.75 -18.25 -17.75

generate the composite spectra. The most important issue relating to the construction of the composites was that the spectra were not flux calibrated. The effects of differential atmospheric refraction, corrector chromatic aberration and fibre positioning errors makes obtaining even a relative flux calibration for sources extremely challenging. We therefore chose not to attempt flux calibration of our spectra. We did, however, correct for absorption owing to the atmospheric telluric bands (the optical fibres also provide some absorption in these same bands). We summed all the spectra in a single observation in order to obtain a mean absorption correction, which was then applied to the data. Also, pixels which had anomalously high variance owing to residuals of night sky emission lines were flagged as bad and discarded from our analysis. As the spectra were not flux calibrated we decided to normalize each spectrum to a continuum level as a function of wavelength. This allows us to measure equivalent widths, linewidths and line centres, however, we lose any information concerning continuum shape and absolute line strengths. Fitting the continuum relies on defining linefree parts of the spectrum. This is not always possible, particularly in regions of the spectrum dominated by weak Fe II emission. Our approach, therefore, was to remove all strong emission-line features, interpolating linearly between pseudo-continuum bands defined on each side of the line. The strong features removed, and the continuum bands defined are listed in Table 2. After removing these strong lines, a fourth-order polynomial was fitted to each spectrum, which was then used to divide the spectra, providing an approximate continuum normalization. In a second step to remove residual large-scale features in the spectrum, each spectrum was divided by a median filtered version using a wide box-car filter of width 201 pixels (each spectrum containing 1024 pixels or 1032 pixels for 2dF
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Table 2. List of strong spectral features removed before continuum fitting. A simple linear interpolation is made between two `continuum' bands defined on either side of the feature. Feature Ly +N V Si IV+O IV] C IV+He II C III]+Al III Mg II+Fe II [O II] [Ne III] H H Fe II H +[O III] Fe II He I H Blue cont. ° band (A ) 1130 1350 1445 1800 2650 3675 3845 4020 4220 4430 4710 5080 5740 6320 ­1155 ­1360 ­1470 ­1830 ­2685 ­3705 ­3855 ­4050 ­4270 ­4460 ­4760 ­5105 ­5790 ­6380 Red cont. ° band (A) 1280 1445 1685 1985 3025 3745 3905 4165 4430 4710 5080 5450 5940 6745 ­1290 ­1470 ­1705 ­2020 ­3065 ­3785 ­3920 ­4200 ­4460 ­4760 ­5105 ­5500 ­5980 ­6805

and 6dF data, respectively). At the edges of the spectrum the filter was reduced in size to a minimum half-width of 5 pixels. The above processing was all carried out in the observed frame. After continuum normalization the spectra were shifted to the rest ° frame, interpolating linearly on to a uniform scale of 1 A pixel-1 . Finally, the composite spectra were produced by taking the median value of each pixel. For each pixel the median z and M B of the contributing QSOs was also determined. We can then determine

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Figure 1. Composite QSO spectra. Top: all spectra combined into one composite. Bottom: composites computed in absolute magnitude intervals ( M B = 0.5) with no redshift binning. The brightest and faintest bins have been made wider to include a sufficient number of spectra. All the spectra have a continuum level of one, but have been offset for clarity.

appropriate values for each feature, and not just each composite. The values of z and M B assigned to each feature are the average, over the wavelength range of the feature, of the pixel median z and M B values. We derived errors for each composite by looking at the distribution of values to be medianed for each pixel. The 1 errors were taken to be the 68 per cent semi-interquartile range of the pixel values divided by the square root of the number of objects contributing. We have constructed composites in z­ M B and also composites binned in absolute magnitude only. One final composite was made from all

the spectra (see Fig. 1). The resulting composites are normalized to the pseudo-continuum over most parts of the spectrum, except ° for the 2000­3500 A region where our procedure treats the Fe II emission bands as though they were a continuum. Therefore, in our subsequent analysis of these spectra we are unable to deduce any results concerning these broad Fe II features. The composites in Fig. 1 (and subsequent figures) are plotted when at least 10 individual QSOs contribute to the spectrum. It can be seen that as the number of QSOs is reduced the S/N
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QSO line strength versus luminosity and redshift

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Figure 2. The luminosity-segregated composite spectra, as shown in Fig. 1, divided by the average composite (top). From this apparent correlations can be seen between luminosity and line strength in a number of lines, including [O II], [Ne V], Mg II,C III] and C IV. These correlations are discussed in the text. Again, the mean flux ratio in each spectrum is one, but the spectra have been offset for clarity.

ratio declines. From this plot a number of trends can already be seen, with the narrow [Ne V], [O II] and [Ne III] showing an anticorrelation of line strength with luminosity. The broad emission lines of C IV,C III] and Mg II also show a similar correlation, appearing to confirm previous detections of the Baldwin effect. A further graphical representation of these (and other) correlations is shown in Fig. 2, which shows the luminosity-segregated composites divided by the mean composite. This confirms that anticorrelations with luminosity are seen for a wide variety of emission lines. An anticorrelation
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is also seen between the strength of the Ca II H and K absorption lines and QSO luminosity, consistent with a picture where the host galaxy luminosity of QSOs is only weakly correlated with QSO luminosity. Finally, we note that the Balmer series (in particular H and H ) appears to show a positive correlation with luminosity, in contrast to the other emission lines. We will analyse these apparent correlations in a quantitative manner below. In Fig. 3 we show examples of the composites divided into absolute magnitude and redshift bins. These allow us to decouple the

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Figure 3. Examples of the QSO composites generated in absolute magnitude­redshift intervals. Top: constant luminosity examples (-25.5 < M B < -25.0 and -23.5 < M B < -23.0) over a range of redshifts. Bottom: constant redshift intervals as a function of luminosity for 1.5 < z < 1.75 and 0.25 < z < 0.5.

effects of redshift and luminosity. Figs 3(a) and (b) show composite spectra with a fixed luminosity over a range of redshifts. There is no obvious evidence for emission features varying with redshift in these plots. Figs 3(c) and (d) show composites in a fixed redshift interval over a range in luminosity. In this case we do see an apparent correlation between luminosity and some lines (C IV, [Ne V], [O II], [Ne III], Ca II K), with the lines is question becoming weaker with increasing luminosity. To investigate the nature of these correlations, in particular whether they are primarily a function of luminosity or redshift, we will carry out detailed fitting of the spectral features, followed by a correlation analysis. 3.1 Line fitting procedure

The composite spectra exhibit a number of spectral features, both in emission and absorption, which their high S/N ratio allow us to fit. Twelve of these features, including three narrow (forbidden) lines, seven broad (permitted) emission lines, one semiforbidden line (C III]) and one absorption feature (Ca II K), were selected for

detailed study. These features were chosen because they exhibit large equivalent widths (e.g. Ly , C IV) and, in the case of the narrow emission lines, are relatively free from contamination by other emission lines. The local pseudo-continuum on either side of each spectral feature was fitted with a straight line, using a linear least-squares method, and subtracted from the spectrum. This continuum was by no means the `true' continuum as the emission lines in QSOs often lie on top of other emission lines, in particular broad Fe II features. It was, however, relatively flat and close to the feature of interest. The majority of the strong emission lines in QSO spectra are blended with other, weaker, emission lines, usually from different elements. Additionally, permitted emission lines such as the Balmer series often exhibit both a broad and a narrow component, which are emitted from physically distinct regions. It is therefore necessary to model and remove the contribution from these different lines to obtain an accurate measurement of the linewidths and equivalent widths. The overlapping lines contributing to each spectral feature were modelled using multicomponent Gaussian fits as listed in Table 3.
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QSO line strength versus luminosity and redshift
Table 3. Spectral features studied. The first column gives the principal emission line in each feature for which line equivalent widths were measured. Columns 2 and 3 give the regions of the spectrum used in the continuum fit. Columns 4 to 10 give the properties of the individual fitted components. Column 4 lists the component number, column 5 the element/elements causing the emission, column 6 the laboratory (vacuum) wavelengths of the components and column 7 indicates whether the emission is narrow or broad. Columns 8, 9 and 10 list the fitted parameters, showing which parameters were tied together. Principal line Ly Blue cont. ° (A) 1135­1155 Red cont. ° (A ) 1320­1340 Component number 1 2 3 4 1 2 3 1 2 3 4 1 2 3 4 5 1 2 3 1 2 1 1 2 1 2 3 1 2 1 2 3 1 2 3 4 Emission source Ly Ly NV NV Si IV1 Si IV1 Si IV1 C IV1 C IV1 C IV1 He II2 C III] C III] C III] Al III Si III] Mg II1 Mg II1 Fe II blend [Ne V] Fe II? [O II]1 [Ne III] He I Ca II K Ca II H [Ne III]3 H H H H [O III]+[Fe II] H H [O III] [O III] lab ° (A ) 1215.67 1215.67 1240.14 1240.14 1396.76 1396.76 1396.76 1549.06 1549.06 1549.06 1640.42 1908.73 1908.73 1908.73 1857.40 1892.03 2798.75 2798.75 2965 3426.84 3415 3728.48 3869.85 3889.74 3934.78 3969.59 3968.58 4102.89 4102.89 4341.68 4341.68 4361.62 4862.68 4862.68 4960.30 5008.24 Emission type Broad Broad Broad Broad Narrow Broad Broad Narrow Broad Broad Broad Narrow Broad Broad Broad Broad Broad Broad Broad Narrow Narrow Narrow Narrow Broad Broad Broad Narrow Narrow Broad Narrow Broad Narrow Narrow Broad Narrow Narrow
c

281

Amp. a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a

1 2 1 2 1 2 3 1 2 3 4 1 2 3 2 2 1 2 3 1 2 1 1 2 1 1 3 1 2 4 1 2 4 1 1 2 1 1

Si IV+O IV]

1350­1365

1440­1455

C

IV

1440­1460

1690­1710

C III]

1800­1820

1975­1995

Mg

II

2640­2660

3030­3050

[Ne V] [O II] [Ne III] Ca II K

3360­3380 3700­3710 3845­3850 3900­3910

3450­3470 3742­3752 3910­3915 4010­4020

H H H

4000­4020 4200­4220

4200­4220 4440­4460

4740­4760

5070­5090

1 2 1 1 1 2 2 1 2 2 4 1 2 2 2 2 1 2 3 1 1 1 1 2 1 1 3 1 2 1 2 2 1 2 1 1

1 2 3 4 1 2 3 1 2 3 4 1 2 3 4 5 1 2 3 1 1 1 1 2 1 1 3 1 2 1 2 3 1 2 3 4

Notes: 1. Unresolved doublets or multiplets, mean wavelength quoted. 2. Although this feature is identified here as He II it is actually a blend of several lines including Fe II and O III] and is therefore relatively broad. 3. The [Ne III] 3968 feature is also contaminated by the H 3970 which may be present in emission or absorption. 4. When both H and H were present in the spectrum, the velocity width of these components were fixed to that measured for the [O III] 5007 emission line.

We note, however, that assuming a Gaussian form for the features in our spectra may be a gross oversimplification, and future work will endeavour to define non-parametric measurements of line properties as well as these Gaussian fits. Each component was fitted with a Gaussian of the form F () = a exp - (c - ) 2
2

,

(1)

where a is the peak emission, c is the wavelength of the peak emission and is the width of the line. When possible, the number of independent parameters in the model was reduced by linking some of them together. For example, since the [O III] 5007, 4959 and narrow H emission arises from the same region of the QSO (the narrow-line region) it is reasonable to assume that the emitting
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gas will have similar velocity shifts and dispersions. The central wavelengths and linewidths of the [O III] 4959 and narrow H emission were therefore tied to those of the [O III] 5007. Columns 8­10 in Table 3 show how features were tied together. For example, all the components of the broad H line are free, while the line centres (c ) and widths ( ) for the two [O III] lines and the narrow H line are tied together. The narrow emission lines were modelled as single Gaussians and were restricted to velocity widths < 1500 km s-1 . Adequate fits to the Ca II absorption feature and the broad Balmer emission lines (H , H and H ) were also obtained using a single Gaussian, although there is some evidence (see Fig. 4) from these high S/N ratio spectra that the broad H has an asymmetric non-Gaussian profile. The broad ultraviolet (UV) lines, i.e. from Mg II 2798 blueward,

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Figure 4. Example line fits. We plot each line or complex of lines fitted in our analysis for the case of the total composite spectrum. Shown is the data (solid line), the individual Gaussian components (dot-dashed lines), the sum of the Gaussian components (dashed line) and the residuals after subtracting the fit (solid line). In most cases the dashed line denoting the total fit is hardly visible over the data. The vertical lines indicate the wavelengths of the primary component (solid line) and secondary contaminating components (dashed lines).

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display emission-line profiles with very broad bases, which cannot be adequately modelled by a single Gaussian. They were therefore fitted with two components; a very broad Gaussian (FWHM 10000 km s-1 ) and a narrower component (FWHM 2000­4000 km s-1 ). This narrower component is not believed to be emission from the narrow-line region since its velocity dispersion is much larger than that measured in the narrow lines (e.g. [O II] 3727 and [O III] 5007) which is typically 800 km s-1 . When two broad components were fitted to a broad emission line, the central wavelengths of the Gaussians were tied together as we found no evidence for a velocity shift between the components. Systematic shifts between different components, have been seen by other authors (Brotherton et al. 1994b), and potential line shifts will be investigated in detail by Corbett et al., in preparation. The only line in which the broad components were not tied was Ly , because absorption to the blue side of the line resulted in an asymmetric profile and it was necessary to allow a velocity shift between the two components to fit the line profile. Previous studies (Wills et al. 1993; Brotherton et al. 1994a,b) have highlighted the fact that the broad-line region can be well described by two components, often described as the intermediate line region and the very broad-line region. It is clear that the broad UV lines in our composite spectra show these two components, however, we reserve a detailed discussion of line shapes for the forthcoming paper, Corbett et al. In all cases the best fit to the spectral feature was found using 2 minimization techniques. The broad Balmer emission line H proved difficult to de-blend as it is contaminated by emission from both [Fe II] 4358 and [O III] 4363 as well as narrow H emission. Since the [Fe II] and [O III] ° emission are within 6 A of each other they are not resolved in the 2dF spectra and were therefore modelled as single narrow component centred between the two lines. The fit was further constrained by fixing the velocity width of the narrow H and the combined [Fe II] and [O III] lines to that obtained for the [O III] 5007 emission. It was not possible to de-blend the O IV] 1402 multiplet emission from the Si IV 1393, 1402 emission and hence the equivalent width calculated for Si IV also contains emission from O IV]. Once the spectral feature had been modelled, the fits to the contaminating line emission were subtracted, leaving only the line of interest. The total flux in the line was measured by integrating the flux over a wavelength range defined as c ± 1.5 â FWHM, where c is the central wavelength and the FWHM is that of the broadest Gaussian component fitted to the line. The equivalent width of the emission (or absorption) was defined as W = Fline ° A, Fcont (2)

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the line parameters and redshift and luminosity. In this paper we report the results for W . Discussion of linewidths and centres will be reported elsewhere. We have carried out non-parametric rank correlation analysis, deriving the Spearman rank-order correlation coefficient, . We select a priori 99 per cent to be the confidence level at which we will claim significant correlations. Specifically, we will test for an W ­z correlation by correlating log W with log(1 + z ), as evolutionary parameters for QSOs are generally an approximate power law in (1 + z ), in particular, QSO luminosity evolution (Boyle et al. 2000). In testing for W ­ M B correlations we will correlate log W with M B . A particularly important issue is to deduce whether z or M B is the primary parameter with which W correlates. We approach this problem in two ways: the first is to carry out correlations in separate z or M B intervals, removing any possible spurious correlations with the second independent variable. The second approach is to use partial Spearman rank correlation (e.g. Macklin 1982) to derive the correlation coefficient while holding one independent variable constant: AX - XY AY AX ,Y = , (3) 2 1 - XY 1 - 2 AY where X and Y are two independent variables (e.g. z and M B ) and A is the dependent variable (e.g. W ). AX , AY and XY are the Spearman correlation coefficients for the separate correlations between two variables. The significance of AX ,Y is given by N -4 1 + AX ,Y ln D AX ,Y = , (4) 2 1 - AX ,Y which is distributed normally about zero with unit variance (Macklin 1982), where N is the size of the sample. In using this partial rank correlation approach we are testing the null hypotheses that: (i) the W ­z correlation arises entirely from the W ­ M B and M B ­z correlations and (ii) the W ­ M B correlation arises entirely from the W ­z and M B ­z correlations. If the coefficients for the W ­z