SDSS-IV/SPIDERS: A Catalogue of X-Ray Selected AGN Properties; Spectral Properties and Black Hole Mass Estimates for SPIDERS SDSS DR14 Type 1 AGN

This work presents the catalogue of optical spectral properties for all X-ray selected SPIDERS active galactic nuclei (AGN) up to SDSS DR14. SPIDERS (SPectroscopic IDentification of eROSITA Sources) is an SDSS-IV programme that is currently conducting optical spectroscopy of the counterparts to the X-ray selected sources detected in the ROSAT all-sky survey and the XMM-Newton slew survey in the footprint of the Extended Baryon Oscillation Spectroscopic Survey (eBOSS). The SPIDERS DR14 sample is the largest sample of X-ray selected AGN with optical spectroscopic follow-up to date. The catalogue presented here is based on a clean sample of 7344 2RXS ($\rm \bar{z}$ = 0.5) and 1157 XMM-Newton slew survey ($\rm \bar{z}$ = 0.4) type 1 AGN with spectroscopic coverage of the H$\rm \beta$ and/or MgII emission lines. Visual inspection results for each object in this sample are available from a combination of literature sources and the SPIDERS group, which provide both reliable redshifts and source classifications. The spectral regions around the H$\rm \beta$ and MgII emission lines have been fit in order to measure both line and continuum properties, estimate bolometric luminosities, and provide black hole mass estimates using the single-epoch (or photoionisation) method. The use of both H$\rm \beta$ and MgII allows black hole masses to be estimated up to z $\rm \simeq$ 2.5. A comparison is made between the spectral properties and black hole mass estimates derived from H$\rm \beta$ and MgII using the subsample of objects which have coverage of both lines in their spectrum. These results have been made publicly available as an SDSS-IV DR14 value added catalogue.


Introduction
A crucial requirement for understanding AGN evolution and demographics is the ability to select a sample for study in a complete and unbiased way. X-ray emission has been frequently used for AGN selection, and can distinguish the high energy emission associated with mass accretion by a black hole (BH) from inactive galaxies and stars. Combining wide-area X-ray surveys with the ability to classify large numbers of objects spectroscopically via the Sloan Digital Sky Survey (SDSS; York et al. 2000;Gunn et al. 2006) provides a powerful tool for the study of AGN.
SPIDERS (SPectroscopic IDentification of eROSITA Sources; PIs Merloni and Nandra) is an SDSS-IV (Blanton et al. 2017) eBOSS (Dawson et al. 2016) subprogramme that is currently conducting optical spectroscopy of extragalactic X-ray detections in wide-area ROSAT and XMM-Newton surveys (Dwelly et al. 2017). Lying at the bright end of the X-ray source population, these sources will also be detected by eROSITA (Merloni et al. 2012;Predehl et al. 2016). The current SDSS DR14 (Abolfathi et al. 2018) SPIDERS sample is a powerful resource for the multiwavelength analysis of AGN. This work aims to capitalise on the wealth of information already available by providing detailed optical spectral measurements, as well as estimates of BH masses and Eddington ratios.
An accurate measurement of the central supermassive black hole (SMBH) mass is necessary for the study of AGN and their coevolution with their host galaxies. BH mass has been found to scale with a number of host galaxy spheroid properties; stellar velocity dispersion (the M BH −σ relation, e.g. Gebhardt et al. 2000;Merritt & Ferrarese 2001;Tremaine et al. 2002), stellar mass (e.g. Magorrian et al. 1998), and luminosity (e.g. Kormendy & Richstone 1995). These correlations suggest a symbiotic evolution of SMBHs and their host galaxies.
Reverberation mapping (RM) has been used to measure the approximate radius of the broad-line region (BLR) in AGN (e.g. Bahcall et al. 1972;Capriotti et al. 1982;Blandford & McKee 1982;Peterson 1993;Bentz & Katz 2015;Shen et al. 2015). This technique involves measuring the time delay between variations in the continuum emission, which is expected to arise from the accretion disk, and the induced variations in the broad emission lines. It was found that different emission lines have different time delays, which is expected if the BLR is stratified, with lines of lower ionisation being emitted further from the central ionising source (e.g. Gaskell & Sparke 1986). For example, the high ionisation line CIVλ1549 has a shorter time delay than Hβ (Peterson & Wandel 2000).
The RM effort has also revealed a tight relationship between the continuum luminosity and the radius of the BLR (Kaspi et al. 2000;Bentz et al. 2006Bentz et al. , 2009a. Therefore, by using the measured luminosity as a proxy for the BLR radius, and measuring the BLR line-of-sight velocity from the width of the broad emission lines, BH masses can be estimated from a single spectrum (Vestergaard 2002;McLure & Jarvis 2002;Assef et al. 2011;Shen & Liu 2012;Shen 2013). This approach is known as the single-epoch, or photoionisation, method.
Since Hβ is the most widely studied RM emission line it is therefore considered to be the most reliable line to use for single-epoch mass estimation. In addition, AGN Hβ emission lines typically exhibit a clear inflection point between the broad and narrow line components, making the virial full width at half maximum (FWHM) measurement relatively straightforward (see Sect. 3.3). The MgII line width correlates well with that of Hβ (see Sect. 7.2), and therefore MgII has also been used for single-epoch mass estimation (e.g. McLure & Jarvis 2002). For SDSS spectra, either Hβ or MgII is visible in the redshift range 0 ≤ z 2.5.
At higher redshifts, the broad, high-ionisation line CIVλ1549 is available. The CIV line width does not correlate strongly with that of low ionisation lines (e.g. Baskin & Laor 2005;Trakhtenbrot & Netzer 2012) and this, along with the presence of a large blueshifted component (e.g. Richards et al. 2002) makes it difficult to employ CIV for mass estimation. A number of calibrations have been developed which aim to improve the mass estimates derived from CIV (Denney 2012;Runnoe et al. 2013;Park et al. 2013;Coatman et al. 2017), however, whether CIV can provide reliable mass estimates when compared with low ionisation lines is still a subject of debate (see Mejía-Restrepo et al. 2018). This paper is organised as follows: the selection of a reliable subsample of sources to be used for optical spectral fitting is discussed in Sect. 2. Section 3 describes the method used to fit the Hβ and MgII emission line regions. The methods for estimating BH mass and bolometric luminosity are discussed in Sect. 4. The X-ray flux measurements used in this work are discussed in Sect. 5. Section 6 describes where the catalogue containing the results of this work can be accessed. A comparison between the UV and optical spectral fitting results is given in Sect. 7. Section 8 provides a discussion of the sample properties, and finally, Sect. 9 includes a discussion of the reliability and limitations of the fitting procedure. In order to facilitate a direct comparison with previous studies based on X-ray surveys, a concordance flat ΛCDM cosmology was adopted where Ω M = 0.3, Ω Λ = 1 − Ω M , and H 0 = 70 km s −1 Mpc −1 .

X-ray data
The ROSAT sample used in this work is part of the second ROSAT all-sky survey (2RXS) catalogue (Boller et al. 2016), which has a limiting flux of ∼10 −13 erg cm −2 s −1 , which corresponds to a luminosity of ∼10 43 erg s −1 at z = 0.5. Compared to the first ROSAT data release (Voges et al. 1999), the 2RXS catalogue is the result of an improved detection algorithm, which uses a more detailed background determination relative to the original ROSAT pipeline. A full visual inspection of the 2RXS catalogue has been performed, which provides a reliable estimate of its spurious source content (see Boller et al. 2016). The first XMM-Newton slew survey catalogue release 1.6 (XMMSL1; Saxton et al. 2008) was also used in this work. This catalogue includes observations made by the European Photon Imaging Camera (EPIC) pn detectors while slewing between targets, and has a limiting flux of 6 × 10 −13 erg cm −2 s −1 in the soft band, which corresponds to a luminosity of 5.8 × 10 44 erg s −1 at z = 0.5.

The SPIDERS programme
The SPIDERS programme has been providing SDSS spectroscopic observations of 2RXS and XMMSL1 sources 1 in the eBOSS footprint. Before the start of the eBOSS survey in 2014, the SPIDERS team compiled a sample of X-ray selected spectroscopic targets and submitted this sample for spectroscopic follow-up using the BOSS spectrograph as part of the eBOSS/SPIDERS subprogramme (see Dwelly et al. 2017, for further details on the SPIDERS programme). As of the end of eBOSS in February 2019, the eBOSS/SPIDERS survey has covered a sky area of 5321 deg 2 . The SDSS DR14 SPIDERS sample presented in this work covers an area of ∼2200 deg 2 (∼40% of the final eBOSS/SPIDERS area).
The spectroscopic completeness achieved by the SPIDERS survey as of SDSS DR14 in the eBOSS area is ∼53% for the sample as a whole, ∼63% considering only high-confidence X-ray detections (see Sect. 2.5), and ∼87% considering sources with high-confidence X-ray detections and optical counterparts with magnitudes in the nominal survey limits (17 ≤ m Fiber2,i ≤ 22.5). Outside the eBOSS area, the spectroscopic completeness of this sample is lower: ∼28% for the sample as a whole, ∼39% considering only high-confidence X-ray detections, and ∼57% considering sources with high-confidence X-ray detections and optical counterparts with magnitudes in the nominal survey limits. The spectroscopic completeness of the SDSS DR16 SPIDERS sample inside and outside the eBOSS area is expected to be similar to that of the sample presented here.
In addition to those targeted during eBOSS/SPIDERS, a large number of 2RXS and XMMSL1 sources received spectra during the SDSS-I/II York et al. 2000) and the SDSS-III (Eisenstein et al. 2011) BOSS (2009-2014Dawson et al. 2013) surveys. This paper includes spectra obtained by eBOSS/ SPIDERS up to DR14 (2014DR14 ( -2016 as well as spectra from SDSS-I/II/III.

Identifying IR counterparts
To identify SPIDERS spectroscopic targets, the Bayesian crossmatching algorithm "NWAY" (Salvato et al. 2018) was used to select AllWISE (Cutri et al. 2013) infrared (IR) counterparts for the 2RXS and XMMSL1 X-ray selected sources in the BOSS footprint. The AllWISE catalogue consists of data obtained during the two main survey phases of the Wide-field Infrared Survey Explorer mission (WISE; Wright et al. 2010) which conducted an all-sky survey in the 3.4, 4.6, 12, and 22 µm bands (magnitudes Dwelly et al. 2017) which, at the depth of the 2RXS and XMMSL1 surveys, can distinguish between the correct counterparts and chance associations. These colours would not be efficient if the 2RXS survey was much deeper (see Salvato et al. 2018, for a complete discussion). The  (Marchesi et al. 2016a,b;Civano et al. 2016), AEGIS-X (Nandra et al. 2015), and the Lockman Hole deep field (LHDF; Brunner et al. 2008;Fotopoulou et al. 2012). For each sample, the 0.5-2 keV luminosities are shown, except for the 2RXS sample, where the 0.1-2.4 keV luminosities are shown, and the XMMSL1 sample, where the 0.2-2 keV luminosities from Saxton et al. (2008) are shown. The detection limit for the 2RXS and XMMSL1 samples are shown by the solid and dashed grey lines respectively. The X-ray luminosities for the 2RXS sample are derived from the classical flux estimates described in Sect. 5, however it is noted here that some low count rate 2RXS sources do not have flux estimates. For sources that were detected in both 2RXS and XMMSL1, only the XMMSL1 luminosities are shown. Sources classified as stars have not been included in this figure.
resulting 2RXS and XMMSL1 catalogues with AllWISE counterparts contained 53455 and 4431 sources respectively. All-WISE positions were then matched to photometric counterparts, where available, in SDSS. Figure 1 displays the sources in the 2RXS and XMMSL1 samples which have spectroscopic redshifts and measurements of the soft X-ray flux. For comparison, a series of previously published X-ray selected samples that have optical spectroscopic redshifts are also shown. The large number of sources present in the 2RXS and XMMSL1 samples motivated the optical spectroscopic analysis discussed in the following sections.

Selecting a reliable subsample
The selection of SPIDERS spectroscopic targets was discussed in detail by Dwelly et al. (2017). This section summarises the selection steps discussed in detail by Dwelly et al. (2017) and describes the additional cuts made in this work to select a sample for spectral analysis. The sequence of selection criteria used and the resulting sample size are shown in Fig. 2.
2RXS sources with an X-ray detection likelihood (EXI_ML) ≤ 10 were excluded since these detections are considered highly uncertain with a spurious fraction ≥20% (see Boller et al. 2016). XMMSL1 sources with an X-ray detection likelihood (XMMSL_DET_ML_B0) ≤ 10 were also excluded. Salvato et al. (2018;Fig. 1) show the distribution of flux with detection likelihood for both samples. These cuts returned 23245/53455 2RXS and 3803/4431 XMMSL1 sources.
The following cuts, which were described in detail in Dwelly et al. (2017), have also been applied to the sample: -For each X-ray source, Salvato et al. (2018) give the probability, p_any, that a reliable counterpart exists among the possible AllWISE associations. Sources with p_any < 0.  Fig. 2. As shown above, sources with match_flag=1 were targeted; however, for 14% of the 2RXS sample and 10% of the XMMSL1 sample, more than one counterpart was highly likely. This implies that either the counterpart association was not reliable, or that the X-ray detection was the result of emission from multiple sources. These sources were not included in the discussion of optical spectral properties as a function of X-ray properties in Sect. 8.3. After selecting the brightest SDSS-DR13 (Albareti et al. 2017)  15 cases where two unique 2RXS sources were matched to the same AllWISE/SDSS counterpart and 3 cases where two unique XMMSL1 sources were matched to the same AllWISE/SDSS counterpart. These sources were also removed.
Of these samples with reliable SDSS photometric counterparts, 8777 2RXS and 1315 XMMSL1 sources have received spectra during SDSS-I/II/III while 1122 2RXS and 221 XMMSL1 sources have received spectra during the SPIDERS programme (including SEQUELS), resulting in a sample of 9899 2RXS and 1536 XMMSL1 sources with spectra as of DR14. The distribution of SDSS i band fiber2 magnitudes for this sample (showing the different spectroscopic programmes) is presented in Fig. 3. Due to targeting constraints (as discussed in Sect. 2.2), the sample completeness is much lower outside of the nominal magnitude limits for the survey (17 ≤ m Fiber2,i ≤ 22.5 for eBOSS).

Source classification
Visual inspection results for each object in this sample are available from a combination of literature sources (Anderson et al. 2007;Plotkin et al. 2010;Schneider et al. 2010;Pâris et al. 2017) and the SPIDERS group. The SPIDERS visual inspection (see Dwelly et al. 2017, for further details) provides a visual confirmation of the SDSS pipeline redshift and object classification. The results of this inspection include a flag indicating the confidence of the redshift, "CONF_BEST", which can take the values 3 (highly secure), 2 (uncertain), 1 (poor/unusable), 0 (insufficient data). A confirmation of the source classification was also added during the visual inspection, which uses the categories QSO, broad absorption line QSO (BALQSO), blazar, galaxy, star, and none. Anderson et al. (2007)   The coloured curves represent all of the sources with spectra, and the survey from which the spectra were taken. The grey histogram displays the X-ray sources with a reliable SDSS photometric counterpart, including stars which cannot be targets for spectroscopy due to their brightness. classifications, which are defined based on the presence or absence of broad (FWHM > 1000 km s −1 ) permitted emission lines.
The main goal of this work is to analyse the type 1 AGN in the SPIDERS sample, and therefore only sources that have been classified via their optical spectra as either "BLAGN" or "QSO" were selected for spectroscopic analysis. This returned 7805/9899 2RXS and 1192/1536 XMMSL1 sources. Since the categories "BLAGN" and "QSO" are based on different classification criteria, there will be some overlap between the two sets of sources. Therefore, no distinction will be made between the two categories; instead, both sets of objects will be considered type 1 AGN in this work.

Contamination from starburst galaxies
Although our sample probes luminosity ranges typically associated with AGN emission, starburst galaxies are also powerful X-ray sources and may be present as contaminants in our AGN sample. The X-ray emission from starburst galaxies is expected to originate from a number of energetic phenomena including supernova explosions and X-ray binaries (e.g. Persic & Rephaeli 2002). Therefore, the X-ray emission from starburst galaxies can be expected to be correlated with the star formation rate (SFR). Using their sample of luminous infrared galaxies, and a sample of nearby galaxies from Ranalli et al. (2003), Pereira-Santaella et al. (2011) found that the total SFR is related to the soft X-ray luminosity as follows: (1) Ilbert et al. (2015), Fig. 3, show the specific SFR for the COSMOS (Scoville et al. 2007) and GOODS (Giavalisco et al. 2004) surveys for a series of redshift bins in the range 0.2 < z < 1.4. The peak of the redshift distribution of the 2RXS/XMMSL1 samples presented in this work is ∼0.25. Therefore, assuming that the COSMOS/GOODS sample in the redshift bin 0.2-0.4 is a good representative of the 2RXS/XMMSL1 samples, the upper limit on the SFR that can be expected for galaxies in our sample is ∼50 M yr −1 . According to Eq. (1), this corresponds to a soft X-ray luminosity of ∼10 41 erg s −1 , which is below the lower range probed by our samples (∼10 42 erg s −1 , see Fig. 1).

Redshift constraints
Using the "CONF_BEST" flag, sources with uncertain redshift or spectral classification (identified during the visual inspection of the sample) were also removed. This process resulted in a sample of 7795/7805 2RXS sources and 1190/1192 XMMSL1 sources. In the spectral fitting procedure (described in Sect . 3), the Hβ and MgII lines were fit independently. Sources with Hβ and MgII present in their optical spectrum were selected using the following logic: Different redshift ranges have been used because the BOSS spectrograph has a larger wavelength coverage than the SDSS spectrograph. In some cases, parts of the fitting region will have been redshifted out of the SDSS/BOSS spectrograph range (Smee et al. 2013), and therefore will not be fit. However, the redshift limits where chosen so that both samples contain the broad lines used for estimating BH mass. Sources with a median signal-to-noise ratio (S/N) less than or equal to five per resolution element were excluded from the spectral analysis since for these sources the broad line decomposition and resulting BH mass estimates may be unreliable (see Denney et al. 2009;Shen et al. 2011). Table 1 lists the numbers of sources with spectral coverage of either Hβ or MgII, while Fig. 4 shows the redshift distribution of these sources. There are 711 cases where the same optical counterpart was detected by both 2RXS and XMMSL1. The final combined (2RXS and XMMSL1) sample for spectral analysis contains 7790 unique type 1 sources.

Spectral analysis
A series of scripts have been written to perform spectral fits using the MPFIT least-squares curve fitting routine (Markwardt 2009). Each spectrum was corrected for Milky Way extinction using the A123, page 5 of 20 Notes. There are 711 sources which were detected in both the 2RXS and XMMSL1 surveys. The "total" row lists the total number of unique sources obtained from combining the 2RXS and XMMSL1 samples. extinction curve from Cardelli et al. (1989), and the dust map from Schlegel et al. (1998), with an R V = 3.1. No attempt has been made to estimate and correct for the intrinsic (host) extinction of each source 2 . Measured line widths were corrected for the resolution of the SDSS/BOSS spectrographs. The Hβ and MgII emission line regions were fit independently using similar methods described in the following sections 3 .

Iron emission template
AGN typically exhibit FeII emission consisting of a large number of individual lines across the optical and UV regions of the spectrum. These lines appear to be blended, probably due to the motion of the gas from which they are emitted, and the magnitude of this broadening varies significantly from source to source. The presence of FeII emission in the optical and UV portions of the spectrum can be a significant complication when attempting to accurately measure line profiles. Therefore it is crucial that the model used to derive line widths for BH mass measurements also accounts for the nearby FeII emission. Figure 5 shows the two FeII templates used in this work; the Vestergaard & Wilkes (2001) and Boroson & Green (1992) templates used for the UV and optical regions of the spectrum, respectively. Both of these templates have been derived from the narrow line Seyfert 1 galaxy I Zwicky 1 which, due to its bright 2 Also note that extinction laws (e.g. Calzetti and Prevot) are based on samples of nearby SB and irregular type galaxies. Due to the lack of nearby passive galaxies, an extinction law for these galaxy types is not yet available. 3 For each model parameter, the 1-sigma uncertainties from MPFIT were adopted. FeII emission and narrow emission lines, is an ideal candidate for generating the FeII template. In order to model the observed blending of the FeII emission, the templates were convolved with a Gaussian whose width was included as a free parameter in the fitting procedure.

Hβ
The region from 4420-5500 Å was fit for each spectrum. The continuum model consisted of a power law, a galaxy template, and the Boroson & Green (1992) FeII emission template. The FeII template was convolved with a Gaussian while fitting, and the width of this Gaussian, along with the normalisation of the template were included as free parameters in the fit (see Sect. 3.1). Previous spectral analyses of AGN spectra have assumed an early-type galaxy component in the model (Calderone et al. 2017). Following this method, we use an earlytype SDSS galaxy template 4 in the fit, and the normalisation of this template as well as the normalisation and slope of the power law were also free parameters. The use of a single, early-type galaxy template is an approximation, however, it is considered to be justified since AGN are typically found to reside in bulge dominated galaxies (e.g. Grogin et al. 2005;Pierce et al. 2007), and the spectroscopic fiber collects emission mostly from the bulge (which is characterised by an old stellar population) and the active nucleus.
The [OIII]λ4959 and [OIII]λ5007 narrow lines were each fit with two Gaussians, one used to fit the narrow core, and an additional Gaussian to account for the presence of blue-shifted wings which are often detected (Boroson 2005). A single Gaussian was used to fit the HeIIλ4686 emission line. To avoid overfitting the Hβ line, the fitting process was run four times, with one, two, three, and four 5 Gaussian components used to fit the Hβ line. For each fit, the velocity width and peak wavelength of one of the Gaussian components was fixed to that of [OIII]λ4959 and [OIII]λ5007 in order to aid the identification of the narrow Hβ component. The normalisation ratio of the [OIII]λ4959 and [OIII]λ5007 lines was fixed to the expected value of 1:3 (e.g. Storey & Zeippen 2000). The best-fit model was then selected using the Bayesian information criterion (BIC; Schwarz 1978), which can be written as where n is the number of data points, k is the number of model parameters, and χ 2 is the chi-square of the fit. The preferred model is that with the lowest BIC. An example of a fit to the Hβ spectral region is shown in the left panel of Fig. 6.

Broad line decomposition
The narrow Hβ and [OIII] components are required to have widths ≤800 km s −1 . Any of the additional Gaussians used to fit MgII and Hβ with FWHM > 800 km s −1 are considered 5 Three broad Gaussians are used in addition to a single narrow component to account for the three distinct broad components that are expected to be present (see Sect. 8.1) in at least some sources (Marziani et al. 2010).
"broad". This threshold of 800 km s −1 is taken from the approximate division between broad and narrow FWHM distributions in the lower panels of Fig. 12. The virial FWHM used for BH mass estimation is the FWHM of the line profile defined by the sum of these broad Gaussian components (see Fig. 7). A major challenge with using the single-epoch method for estimating BH mass is decomposing the broad and narrow components of the line in order to measure the virial FWHM. Figure 7 presents an example of the decomposition of a broad Hβ line. In this case, the narrow Hβ core can be easily distinguished and removed before measuring the virial FWHM. However, there are many cases where the broad and narrow components are blended, making it difficult to successfully identify the appropriate virial FWHM. There are also cases where there is a clear distinction between two broad line components that are shifted in wavelength relative to each other (known as "double-peaked emitters"). How one should interpret the single-epoch BH mass estimates for these unusual objects is uncertain (also see Sect. 9.2).

MgII
The region from 2450-3050 Å was fit for each spectrum. As in the case of the Hβ fits, a power law, an early-type galaxy template (5 Gyr old elliptical galaxy; Silva et al. 1998;Polletta et al. 2007), and the Vestergaard & Wilkes (2001) FeII emission template were used to fit the continuum. Again, the FeII template normalisation, and width of the Gaussian smoothing applied to the template, were included as free parameters in the fit. The MgII line is a doublet; however, due to the close spacing and virial broadening of the lines, it usually appears as a single broad component in AGN spectra. The narrow MgII line cores are usually not observed in AGN spectra, therefore the MgII profile was fit using three broad Gaussians. An example of a fit to the MgII spectral region is presented in the right panel of Fig. 6. These bolometric corrections have been derived using mean AGN SEDs; however, Richards et al. (2006) note that using a bolometric correction resulting from a single mean SED can result in bolometric luminosities with inaccuracies up to 50%.
Under the assumption that the BLR gas is virialised, the single-epoch method can be used to estimate BH mass as follows: where L λ is the monochromatic luminosity at wavelength λ, and FWHM is the full width at half maximum of the broad component of the emission line. A, B, and C are constants that are calibrated using RM results and vary depending on which line is used.
Over the years, many groups have provided calibrations of Eq. (2) for MgII and Hβ. In this work, the calibrations from  and Assef et al. (2011) are used for Hβ.  based their work on an updated study of the R BLR −L relationship (Kaspi et al. 2005;Bentz et al. 2006) and a reanalysis of the RM mass estimates (Peterson et al. 2004) and therefore presented an improved mass calibration relative to previous studies.   and Assef et al. (2011). These calibrations agree reasonably well, with the standard deviation σ 0.3 in both cases, which is likely due to the fact that these BH mass estimates were derived using two different emission lines. A list of the three BH mass calibrations used in this work is given in Table 2.
BH masses were computed for each of these calibrations and are included in the catalogue (see Appendix A). BH masses were only estimated for sources with a detected broad line component (see Sect. 3.3). These BH mass estimates were then used to estimate the Eddington luminosity and the Eddington ratio where c is the speed of light, G is the gravitational constant, M BH is the BH mass, m p is the proton mass, and σ T is the Thomson scattering cross-section.

X-ray flux estimates
Since X-ray detections are available for all objects in this sample, X-ray flux estimates have also been included in the catalogue. XMMSL1 fluxes in the 0.2-12 keV range from Saxton et al. (2008) are included. Saxton et al. (2008) convert the XMMSL1 count rates to fluxes using a spectral model consisting of an absorbed power law with a photon index of 1.7 and N H = 3 × 10 20 cm −2 .
Many of the sources in the 2RXS sample have flux measurements close to the ROSAT flux limit (∼10 −13 erg cm −2 s −1 ). Therefore, when estimating fluxes for this sample, it was necessary to correct for the Eddington bias. This was done by adopting a Bayesian method to derive a probability distribution of fluxes based on the known distribution of AGN as a function of flux. Following Kraft et al. (1991), Laird et al. (2009), andNandra (2011), the probability of a source having flux f X , given an observed number of counts C, is where C is the total number of observed source and background counts, T is the mean expected total counts in the detection cell for a given flux, and π( f X ) is the prior, which is the distribution of AGN per unit X-ray flux interval. The exact expression for the prior was taken from Georgakakis et al. (2008), Eq. (1). Source and background counts were taken from the 2RXS catalogue (Boller et al. 2016). A flux-count rate conversion factor, which was required to estimate T in Eq. (3), was derived using XSPEC (Arnaud 1996)  The fluxes resulting from the method described above with and without applying the prior (termed "Bayesian" and "classical", respectively) are compared in Fig. 9. The disagreement between the two flux estimates increases with decreasing flux, which is expected since, without the prior, the classical method fails to account for the Eddington bias. Low count rate sources in this sample would be assigned unrealistically low Bayesian fluxes. To avoid this, the flux was left as undetermined when the Bayesian flux estimate was more than a factor of ten smaller than the classical flux estimate.

Accessing the data
The results from the spectral analysis discussed above, along with X-ray flux measurements and visual inspection results, have been made available in an SDSS DR14 value added catalogue 6 . Additionally, an extended version of the catalogue will be maintained at http://www.mpe.mpg.de/ XraySurveys/SPIDERS/SPIDERS_AGN/. The column description for the catalogue is given in Appendix A.

Comparing the UV and optical fitting results
A subsample of sources have spectral measurements available from both the MgII and Hβ spectral regions. In order to test the consistency of the independent fits to these two regions, properties measured from both were compared.
Of this sample, 1718 sources had reliable measurements of both L 2500 Å and L 5100 Å . The L 2500 Å −L 5100 Å relation was fit using the LINMIX (Kelly 2007) package. LINMIX is a Bayesian linear regression algorithm that accounts for uncertainties in both dependent and independent variables, as well as non-detections. The upper left panel of Fig. 10 shows the L 2500 Å −L 5100 Å distribution and the best-fit relation Log 10 (L 5100 Å ) = (0.841 ± 0.007) Log 10 (L 2500 Å ) − (6.0 ± 0.3) (4) with a regression intrinsic scatter of 0.0151. The comparison between the estimated bolometric luminosities derived from the 3000 Å and 5100 Å monochromatic fluxes is shown in the upper right panel of Fig. 10. Equation (4) can be used to estimate L 2500 Å from L 5100 Å , which allows low redshift sources to be included in the α OX analysis discussed in Sect. 8.3.

Comparing MgII and Hβ FWHM measurements
A subsample of AGN whose spectra cover the broad Hβ and MgII emission lines was selected using the following criteria with a regression intrinsic scatter of 0.005. This deviation from the one-to-one relation has also been observed by Wang et al. (2009), who reported a slope of 0.81 ± 0.02, and Shen & Liu (2012), who found a slope of 0.57 ± 0.09. The single-epoch BH mass relations (Eq. (2)) account for the FWHM MgII − FWHM Hβ slope; when the correct BH mass calibration is used, the Hβ and MgII virial FWHM measurements yield BH masses that are in close agreement (see the lower right panel of Fig. 10). Figure 11 presents the comparison between this sample and the full sample of SDSS DR7 AGN with optical spectral properties measured by Shen et al. (2011) in the bolometric luminosity-redshift and bolometric luminosity-BH mass planes. As discussed in Sect. 1, H β -derived BH masses are used where available (shown in blue), while MgII-derived masses are used for the remaining higher-redshift sources (shown in green). The left panel of Fig. 11 shows that this sample populates the lowredshift, high-luminosity region of the parameter space, which is partially due to the high flux threshold of the X-ray selection. From the right panel of Fig. 11 it can be seen that the sample presented in this work appears to be well bounded by the Eddington limit at least up to M BH 10 9.5 M .

Hβ line components
Section 3.2 described how the Hβ line profile was fit with either one, two, three, or four Gaussian components. Figure 12 displays the resulting distribution of Hβ FWHM measurements (the panels are split based on the number of Gaussian components required to fit the line). There is a clear peak in the distribution at low FWHM associated with the narrow Hβ core typically measured at a few hundred km s −1 . Above ∼1000 km s −1 the distribution is bimodal (in the two lower panels) with a large number of sources showing evidence for the "very broad component" (VBC) of Hβ at FWHM ≥ 10 000 km s −1 also discussed in Marziani et al. (2010). It has been suggested that the VBC is emitted from a distinct physical region, and is possibly the result of line emission from the accretion disk (e.g. Bon et al. 2009). If the VBC represents emission from the accretion disk, then a strong VBC may result in a bias towards a higher BH mass estimate, since the single-epoch method assumes a calibration that is based on  the luminosity-BLR radius relation. However, since the kinematics and physical origin of the VBC remains uncertain, detected VBCs have not been excluded from the broad line profiles used to measure the virial FWHM in this analysis (as discussed in Sect. 3.3).

This sample in the 4D eigenvector 1 context
The 4D Eigenvector 1 (4DE1) system (Boroson & Green 1992;Sulentic et al. 2000Sulentic et al. , 2011 aims to define a set of parameters that uniquely account for AGN diversity. Two main 4DE1 parameters are the FWHM of the broad component of Hβ (FWHM H BC β ) and the strength of the FeII emission relative to that of Hβ, defined as R FeII = F FeII /F Hβ where F FeII and F Hβ are the fluxes of the FeII emission in the 4434-4684 Å range and broad Hβ line, respectively. A sample of 2098 sources with measurements of these parameters and reli-able spectral fits (0 ≤ χ 2 ν,Hβ ≤ 1.2) was selected. The left panel of Fig. 13 shows the distribution of this sample in the 4DE1 parameter space (grey). It is expected that a reliable measurement of the FeII component will be difficult for many of the lower S/N sources (see Marziani et al. 2003). For this reason, the subset of sources in Fig. 13 with a median S/N greater than or equal to 20 per resolution element is also shown (blue). The right panel of Fig. 13 presents the higher S/N sources, colour-coded as a function of Eddington ratio. The expected trend of increasing Eddington ratio towards smaller FWHM H BC β and larger R FeII is observed for this sample of high-S/N sources. Typically, sources with both high R FeII and high FWHM H BC β are not observed. If these sources exist, they may be difficult to detect since strong FeII emission might conceal a faint H β broad component. The potential bias in the 4DE1 plane source distribution due to model limitations and spectral S/N is discussed in Sects. 9.1.2 and 9.1.3.
The grey dashed line in the right panel of Fig. 13 indicates the division between population A (FWHM H BC β ≤ 4000 km s −1 ) and population B (FWHM H BC β ≥ 4000 km s −1 ) sources in the 4DE1 context (see Sulentic et al. 2011). Population A sources often possess Lorentzian broad line profiles, and it has been suggested that Gaussian fits to population A broad lines will result in an underestimation of the BH mass (see Sulentic et al. 2014).

Relationship between AGN X-ray and optical emission
Quasars exhibit a non-linear relationship between their X-ray and UV emission, usually represented by the α OX parameter α OX = Log(L 2 keV /L 2500 Å ) Log(ν 2 keV /ν 2500 Å ) where L 2 keV , L 2500 Å , ν 2 keV , and ν 2500 AA are the monochromatic luminosities and frequencies at 2 keV and 2500 Å, respectively (Vignali et al. 2003;Strateva et al. 2005;Steffen et al. 2006;Just et al. 2007;Kelly et al. 2008;Green et al. 2009;Young et al. 2009;Lusso et al. 2010). The α OX parameter is considered to be a proxy for the relative contribution of the UV accretion disk emission and the X-ray emission from the surrounding corona to the total luminosity. In order to study this relationship, a sample of sources with measurements of the 2 keV, A123, page 11 of 20 2500 Å, and 5100 Å luminosities was selected. For lower redshift sources without spectral coverage of 2500 Å, Eq. (4) was used to estimate the 2500 Å luminosity from the 5100 Å luminosity. Extended sources were removed in order to prevent additional scatter in the relationship due to the contribution of the host galaxy. This was done by requiring that the SDSS g band "stellarity" 7 (defined as S(g) = cModelMag_g − psfMag_g) lies between ±0.1. This sample does not contain X-ray sources with more than one potential AllWISE counterpart and therefore avoids cases where the X-ray detection includes emission from more than one object. This selection process resulted in a sample of 4777 sources. Figure 14 shows the α OX parameter versus the monochromatic luminosity at 2500 Å. The α OX − L 2500 Å relation was fit using LINMIX, which gave the following best-fit result α OX = 2.39 ± 0.16 − (0.124 ± 0.005) Log(L 2500 Å ) with a regression intrinsic scatter of 0.0034. This slope is consistent with previous results from the literature (e.g. Kelly et al. 2008).

Interpreting the data and limitations
In this section, the reliability and limitations of the sample will be discussed.

Measuring the FeII emission
Distinguishing the FeII component from the continuum emission becomes more difficult when using low S/N spectra. In addition, for a given S/N, it may also be more difficult to detect FeII emission if the intrinsic broadening of the FeII lines is large, since broader, blended FeII emission lines are more likely to be fit by the model as continuum emission (see Marziani et al. 2003). Using simulated AGN spectra, Marziani et al. (2003) estimate the minimum detectable optical FeII emission as a function of Hβ width for different bins of S/N. 7 For a description of how cModelMag_g and psfMag_g are measured see https://www.sdss.org/dr12/algorithms/magnitudes/. A poor fit to the FeII emission may affect the accuracy of the BH mass estimates, since FeII emission can influence measurements of both the broad line width (see Sect. 9.1.1) and the continuum luminosity. FeII emission may also conceal a broad Hβ component thus biasing a source's position in the 4DE1 plane (Fig. 13). These potential issues are tested in the following three sections. widths measured by these two models should be the upper limit on what can be expected for cases where the FeII fit is inadequate. Figure 15 shows that the line width dispersion induced by ignoring the presence of FeII emission is 640 km s −1 .

Model limitations in detecting sources in the 4DE1 plane
Sources with both large R FeII and large FWHM H BC β are typically not observed, however, this absence may be due to model limitations; at high R FeII the broad Hβ component may be concealed beneath the FeII emission, and therefore may not be detected. The experiment outlined in this section was carried out in order to determine whether the spectral fitting code used in this work would return accurate measurements for sources with high R FeII and FWHM H BC β values. A parameter space defined by 0.1 ≤ R FeII < 5 and 1000 km s −1 ≤ FWHM H BC β < 15 000 km s −1 was divided into a 12 × 12 grid. 10 S/N bins between 5 and 50 (a representative range for the samples presented in this work) were selected for each point on the grid, and 10 spectra were simulated for each R FeII − FWHM H BC β − S /N combination, resulting in 14 400 simulated spectra. For the parameters that were fixed in this experiment, the interquartile mean of the best-fit values for the type 1 AGN in this sample were used. The Hβ line profile was modelled with one narrow and one broad Gaussian. The wavelength range was set to 4420−5500 Å (as in Sect. 3.2) and the logarithmic wavelength spacing 8 was set to be equal to that of SDSS spectra; Log 10 λ i+1 − Log 10 λ i = 0.0001. These spectra were fit using a version of the Hβ fitting script which used one narrow and one broad Gaussian component to fit Hβ. The minimum S/N required for the fitting script to return the correct R FeII and FWHM H BC β combinations was then determined. In order to consider an R FeII and FWHM H BC β combination detectable at a given S/N, at least 7/10 spectra were required to have best fit R FeII and FWHM H BC β values that agreed with the input values. Figure 16 shows the detectable R FeII and FWHM H BC β combinations for each point on the grid, along with the minimum 8 https://www.sdss.org/dr12/spectro/spectro_basics/ Points on the grid that do not have a minimum S/N indicator represent R FeII and FWHM H BC β combinations that are not detectable even at the highest S/N used in this experiment. Sources detected at these R FeII and FWHM H BC β combinations are likely to be spurious (see Fig. 17).
S/N required to detect that combination. It is clear from Fig. 16 that at the S/N levels available in this sample, a large region of the 4DE1 parameter space would not be detected.
9.1.3. Bias in the R FeII and FWHM H β BC distribution due to model limitations Figure 17 shows the comparison between the simulated and measured R FeII and FWHM H BC β values for the highest and lowest S/N bins used in Sect. 9.1.2. The left panel of Fig. 17 shows that at low S/N the results are clearly biased against high R FeII and FWHM H BC β values. At higher S/N (Fig. 17, right panel), the accuracy of the lower left quadrant measurements is significantly improved. However, even at S /N = 45.5 (which is approximately the upper end of the S/N distribution of the samples presented in this work) the high R FeII − FWHM H BC β measurements deviate significantly from the corresponding "true" values. This may suggest that the L-shaped distribution of sources in the 4DE1 plane (e.g. Fig. 13) is at least in part due to model limitations.

Reliability of the single-epoch method for mass estimation
Assuming that AGN broad emission lines are produced by gas whose motion is dominated by the gravitational potential of the central SMBH, the single-epoch method is expected to produce reliable mass estimates when compared to RM (see , with a systematic uncertainty of 0.3-0.4 dex. However, it is not clear how to measure the virial FWHM of lines that deviate from this norm. The spectrum shown in the left panel of Fig. 18 is an example of a source which exhibits a double-peaked Hβ line profile, where a clear inflection point is visible between two velocityshifted broad line components. Double-peaked broad line profiles in AGN are expected to be the result of emission from the accretion disk (Perez et al. 1988;Chen et al. 1989;Eracleous & Halpern 1994Strateva et al. 2003). Zhang et al. (2007) have found that single-epoch BH mass estimates obtained from doublepeaked line profiles are significantly larger than BH mass A123, page 13 of 20 A&A 625, A123 (2019) Fig. 17. Comparison between the measured and simulated R FeII and FWHM H BC β values for the highest and lowest S/N bins used in Sect. 9.1.2. For clarity, each figure displays only one of the ten sets of spectra for that S/N. The values used to simulate the spectra (grey points) are connected to the corresponding best fit measurements (except for cases where either the broad Hβ or FeII components were not detected). For clarity, the figures do not show a small number of unphysically high R FeII measurements. estimates derived from stellar velocity dispersion measurements. Zhang et al. (2007) suggest that this discrepancy is the result of an overestimation of the BLR radius by the single-epoch mass calibrations for these objects. Therefore, the BH mass estimates provided in this work for sources which exhibit double-peaked broad emission lines should be treated with caution.
The right panel of Fig. 18 shows an example of narrow absorption in the UV portion of the spectrum caused by intervening absorbing material along the line of sight to the AGN. Sources identified during the visual inspection as having narrow absorption lines have been flagged in the catalogue (column 189; flag_abs). These sources were fit using the model described in Sect. 3.4 with the absorption line regions masked. However, in many cases, the absorption features distort the broad MgII line, and therefore the resulting BH mass estimates may not be reliable.

Conclusions
This work presents a catalogue of spectral properties for all SPIDERS type 1 AGN up to SDSS DR14. Visual inspection results were used to select a reliable subsample for spectral analysis, and the spectral regions around Hβ and MgII were fit with a multicomponent model. Using the single-epoch method, BH masses, bolometric luminosities, Eddington ratios, along with additional spectral parameters were measured. A catalogue containing these results has been made available as part of a set of SDSS DR14 value added catalogues. This catalogue also includes the results of a visual inspection of the sample 9 .