# OzDES Reverberation Mapping Program: Stacking analysis with H$\beta$, Mg ii
and C iv

U. Malik1, R. Sharp1, A. Penton2, Z. Yu3, P. Martini3,4, B. E. Tucker1,5,6, T.
M. Davis2, G. F. Lewis7, C. Lidman1,8, M. Aguena9, O. Alves10, J. Annis11, J.
Asorey12, D. Bacon13, D. Brooks14, A. Carnero Rosell9,15,16, J. Carretero17,
T.-Y. Cheng18, L. N. da Costa9, M. E. S. Pereira19, J. De Vicente20, P.
Doel14, I. Ferrero21, J. Frieman11,22, G. Giannini17, D. Gruen23, R. A.
Gruendl24,25, S. R. Hinton2, D. L. Hollowood26, D. J. James27, K. Kuehn28,29,
J. L. Marshall30, J. Mena-Fernández20, F. Menanteau24,25, R. Miquel17,31, R.
L. C. Ogando32, A. Palmese33, A. Pieres9,32, A. A. Plazas Malagón34,35, K.
Reil35, A. K. Romer36, E. Sanchez20, M. Schubnell10, M. Smith37, E. Suchyta38,
M. E. C. Swanson14, G. Tarle10, C. To4, N. Weaverdyck10,39, P. Wiseman37
(Affiliations listed at the end of the paper)
umang.malik<EMAIL_ADDRESS>
(Accepted 2024 April 25. Received 2024 April 21; in original form 2023 July
31)

###### Abstract

Reverberation mapping is the leading technique used to measure direct black
hole masses outside of the local Universe. Additionally, reverberation
measurements calibrate secondary mass-scaling relations used to estimate
single-epoch virial black hole masses. The Australian Dark Energy Survey
(OzDES) conducted one of the first multi-object reverberation mapping surveys,
monitoring 735 AGN up to $z\sim 4$, over 6 years. The limited temporal
coverage of the OzDES data has hindered recovery of individual measurements
for some classes of sources, particularly those with shorter reverberation
lags or lags that fall within campaign season gaps. To alleviate this
limitation, we perform a stacking analysis of the cross-correlation functions
of sources with similar intrinsic properties to recover average composite
reverberation lags. This analysis leads to the recovery of average lags in
each redshift-luminosity bin across our sample. We present the average lags
recovered for the H$\beta$, Mg ii and C iv samples, as well as multi-line
measurements for redshift bins where two lines are accessible. The stacking
analysis is consistent with the Radius-Luminosity relations for each line. Our
results for the H$\beta$ sample demonstrate that stacking has the potential to
improve upon constraints on the $R-L$ relation, which have been derived only
from individual source measurements until now.

###### keywords:

galaxies: nuclei – galaxies: active – (galaxies:) quasars: supermassive black
holes – (galaxies:) quasars: emission lines – quasars: general

††pubyear: 2024††pagerange: OzDES Reverberation Mapping Program: Stacking
analysis with H$\beta$, Mg ii and C iv–Affiliations

##  1 Introduction

Reverberation mapping is a powerful technique that can resolve the cores of
active galactic nuclei (AGN) in the time domain. The accretion disk around the
central supermassive black hole (SMBH) produces intrinsically variable
emission at UV-optical wavelengths. The surrounding broad-line region (BLR) is
ionised by this continuum emission, which drives a reverberation response in
the emission-line flux from the BLR on time-scales of weeks to months
(Blandford & McKee, 1982; Peterson, 1993). Multi-epoch photometric and
spectroscopic observations can be used to trace the variability of the
continuum and the emission-line response, respectively.

The size difference between the accretion disk (light-days to weeks) and the
BLR (light-weeks to months) introduces a delay in the response of the BLR to
the variation in the ionising flux. The delay, i.e. reverberation lag, $\tau$,
can be recovered by cross-correlating the two light curves, in order to
measure the radius of the BLR ($R_{\rm BLR}=c\tau$). The velocity dispersion
of the BLR ($\Delta V$) can be estimated from the width of the broadened
emission lines. The mass of the central black hole ($M_{\textrm{BH}}$) can
then be measured using the virial theorem:

$M_{\textrm{BH}}=f\frac{R_{\textrm{BLR}}\Delta V^{2}}{G},$ (1)

where $f$ is the virial coefficient; a dimensionless scale factor that
accounts for the geometry, orientation, and kinematics of the BLR (Woo et al.,
2015).

Reverberation mapping (RM) is presently the only method that can be used to
directly measure SMBH masses beyond the local Universe, as other techniques
are reliant on resolving the gravitational sphere-of-influence of the black
hole, which remains challenging even with high angular resolution instruments
(e.g., Gebhardt et al., 2000, 2011; Kuo et al., 2011; Event Horizon Telescope
Collaboration et al., 2019). However, RM is by nature observationally
intensive. It requires repeated observation over the relevant variability
time-scales of AGN in order to ensure the light-curve variability and
reverberation lag are resolved (Horne et al., 2004). Early surveys monitored
AGN on a source-by-source basis, making observations over several months to
years. Lag measurements were made for dozens of sources, using the H$\beta$
line (e.g., Peterson et al., 1998; Kaspi et al., 2000; Peterson & Horne, 2004;
Bentz et al., 2009). From these measurements, a tight correlation was found
between the AGN luminosity and the radius of the BLR ($R-L$ relation; e.g.,
Bentz et al., 2009, 2013). Lags recovered using higher ionisation emission
lines (e.g., C iv) were found to be shorter than lags recovered using lower
ionisation emission lines (e.g., H$\beta$), demonstrating the ionisation
stratification of the BLR (Gaskell & Sparke, 1986; Dietrich et al., 1993). The
$R-L$ relation is importantly used to calibrate secondary mass-scaling
relations to estimate single-epoch virial BH masses (e.g., Shen et al., 2011),
and has also been proposed as a way to standardise AGN for use as a
cosmological distance indicators (Watson et al., 2011; Martínez-Aldama et al.,
2019).

Through the advent of wide-field photometric surveys such as the Dark Energy
Survey, (DES, Dark Energy Survey Collaboration et al., 2016), multi-epoch
photometric data for large samples of AGN has become readily available.
Concurrent observations can be made with multi-object spectrographs, however
the demand for these instruments is high and therefore limits the number of
epochs which can be feasibly acquired. The Australian Dark Energy Survey
(OzDES) and Sloan Digital Sky Survey Reverberation Mapping (SDSS-RM) Project
have conducted the first multi-object RM surveys, observing hundreds of AGN
probing a wide range of AGN luminosities and redshifts (King et al., 2015;
Shen et al., 2015). These programs have delivered over one hundred new lag
measurements (Grier et al., 2017; Hoormann et al., 2019; Grier et al., 2019;
Homayouni et al., 2020; Yu et al., 2021, 2023; Malik et al., 2023, Penton et
al. in prep). This allowed the Mg ii and C iv $R-L$ relations to be
constrained for the first time using statistically significant samples,
however there is significant scatter in the measurements. This is mostly due
to challenges with data quality (low signal-to-noise, limited sampling; see
Malik et al., 2022) and lag recovery reliability (Li et al., 2019; Penton et
al., 2022). These factors have limited the lag recovery efficacy of each
survey to about 10-25%.

Stacking can be used to combine the cross-correlation signals of physically
similar AGN to recover average lags for these objects. The technique was first
applied by Fine et al. (2012, 2013) using only two spectroscopic epochs, which
yielded a marginal result. After demonstrating the success of the technique
with the Bentz et al. (2013) H$\beta$ sample, Li et al. (2017) measured
composite lags with H$\alpha$, H$\beta$, He ii and Mg ii using a subset of the
SDSS-RM sample. Stacked averages are not swayed by the systematic errors from
individual sources. Their consistency (or not) with the measurements made for
individual sources is therefore important. Additionally, with the wide
redshift range covered by our sample, the gaps in the observational window
function can be filled in to some extent. Therefore, stacking leverages the
data in a way that cannot be done with traditional individual measurements.

We present a stacked lag analysis of the entire OzDES sample, for the
H$\beta$, Mg ii and C iv lines. Section 2 details the observations obtained by
OzDES and the data calibration procedures. In Section 3 we describe the
technique used to recover stacked lags. In Section 4 we present our average
lag measurements, and comparisons with individual measurements on the
respective $R-L$ relationships for each emission line. We summarize our
results and the discuss the outlook to the future in Section 5.

Throughout this work we adopt a flat $\Lambda$CDM cosmology, with
$\Omega_{\Lambda}=0.7$, $\Omega_{M}=0.3$, and $H_{0}=70$ km s-1 Mpc-1.

##  2 Data

Our photometric data were obtained as part of the Dark Energy Survey (DES)
Supernova Program, which observed 10 deep fields covering 27 deg2, comprising
the ELAIS, XMM-LSS, Chandra deep-field South, and SDSS Stripe 82 fields
(Kessler et al., 2015; Morganson et al., 2018). These fields were observed in
the $griz$ filters, with the Dark Energy Camera (DECam) on the 4m Blanco
telescope at Cerro Tololo Inter-American Observatory (CTIO) (Flaugher et al.,
2015). The fields were observed with $\sim$6 day cadence over a 5-6 month
season (August to January) from 2013 to 2018, with additional science
verification data taken in 2012. The OzDES project (Yuan et al., 2015;
Childress et al., 2017; Lidman et al., 2020) conducted follow-up spectroscopic
observations with the 2dF multi-object fibre positioning system and the
AAOmega spectrograph (3700-8800 Å, Sharp et al., 2006) on the 3.9m Anglo-
Australian Telescope (AAT), taken with approximately monthly cadence over the
same seasons, from 2013 to 2019. After the conclusion of the Supernova
Program, additional DECam observations were taken monthly in the 2018-19
season, taking the baseline of our photometric light curves to 7 years.

Figure 1: Distribution of redshifts and monochromatic luminosity at 5100 Å for
the 690 AGN in the OzDES RM sample. The H$\beta$ sample extends to $z=0.75$,
with 13 sources overlapping with our Mg ii sample. The Mg ii sample extends to
$z=1.92$, with 106 sources overlapping with our C iv sample.

The OzDES Reverberation Mapping sample comprises 735 AGN, ranging from
$0.1<z<4.0$, with apparent magnitudes 17.2 $<$ $r_{\rm{AB}}$ $<$ 22.3 (Tie et
al., 2017). Of these 735 AGN, we removed 9 of the 78 AGN from the H$\beta$
sample due to broad-absorption lines (BALs) or incorrect classification as a
Type 1 AGN, 3 of the 453 AGN from the Mg ii sample for the same reason (these
sources overlapped with the H$\beta$ sample), and 88 of the 378 AGN from the C
iv sample due to BALs. These sources were included in the initial survey
selection to improve the source density on the sky and study BAL variability,
but have proven challenging for reverberation analysis. The final sample we
use in this analysis comprises 69 H$\beta$ sources, 450 Mg ii sources, and 290
C iv sources (690 AGN in total). The redshift and luminosity distribution of
these targets is shown in Figure 1.

As done for the individual lag measurements made by Yu et al. (2023) and Malik
et al. (2023), for the H$\beta$ and Mg ii samples we measure the emission-line
flux from spectra obtained on different nights as separate epochs in order to
maximise the cadence of our sampling for our emission-line light curves. As we
have lower signal-to-noise for the C iv sample, we co-add the spectra over
each observing run (typically 4-7 nights during dark time each month), as done
by Hoormann et al. (2019).

We do not measure the continuum luminosity directly from the spectra due to
fibre aperture effects from variable atmospheric seeing and fibre placement
uncertainties. From the average $r$-band magnitude and redshift of the AGN, we
estimated the monochromatic continuum flux at rest frame 5100 Å, 3000 Å and
1350 Å using the DECam $r$-band filter transmission curve and the SDSS quasar
template (Vanden Berk et al., 2001). The template is scaled to the magnitude
of the source, assuming $L_{\rm bol}=9\,\lambda L_{\lambda}$ (5100 Å) (Kaspi
et al., 2000). The source properties for the OzDES sample used in this work
are provided in §A and complete sample characteristics for the final OzDES RM
sample will be provided in a future OzDES RM Program paper.

The DES photometry is calibrated using the DES data reduction pipeline
(Morganson et al., 2018; Burke et al., 2018). We perform a spectrophotometric
flux calibration following Hoormann et al. (2019). For the H$\beta$ and C iv
samples, we measure the line fluxes as done by Hoormann et al. (2019). For the
continuum subtraction, the local continuum windows we use for H$\beta$ are
4760 to 4790 Å and 5100 to 5130 Å, and for C iv are 1450 to 1460 Å and 1780 to
1790 Å. For the Mg ii sample, the iron subtraction and line flux measurement
is performed as detailed in Yu et al. (2023). The calibration uncertainties of
the line flux for each line are measured using the F-star warping function
method as detailed in Yu et al. (2021).

##  3 Lag recovery method

As reverberation lags should be dependent on the intrinsic AGN luminosity
alone (at least to first order), we bin the sources by their continuum
luminosity. Further details are provided for each emission-line subsample in
§4.

For each source in a redshift-luminosity bin, we covert the observation dates
to the rest frame of the source by dividing by (1+$z$). We use the PyCCF code
to perform the interpolated cross-correlation function method for each
individual source (ICCF; Gaskell & Peterson, 1987; Sun et al., 2018). The
continuum and emission-line light curves of each source are linearly
interpolated to a grid spacing of 3 days. The interpolated light curves are
cross-correlated as a function of time-lag. We then average the cross-
correlation functions (CCF) of each source in the bin to obtain the stacked
CCF. We search for lags over a (rest-frame) lag range of $[-100,300]$ days for
H$\beta$ and C iv, and $[-100,500]$ days for Mg ii as it has a longer expected
lag for our sample.

We measure the average lag and its uncertainties by bootstrapping the sample
in each bin. We perform the above procedure to calculate the stacked CCF’s for
each bootstrapped re-sample of the original binned sample. We repeat this 1000
times, and record the centroid of each CCF ($r_{\rm max}$) to build the
bootstrap distribution, from which we adopt the median and 16th and 84th
percentiles of this distribution as the recovered average stacked lag, $\tau$,
and lower and upper uncertainties, $\sigma_{\tau}$, for the bin.

Following Li et al. (2017), we shuffle the spectroscopic epochs and repeat the
stacking for 100 Monte Carlo realisations, and compare the stacked CCF
produced by these uncorrelated light curves to the original stacked CCF. This
is similar to the null hypothesis test used by Malik et al. (2023) to check
that the lag recovery is not simply a product of the interaction of the window
function with underlying red-noise correlation in the photometric light
curves, considering the relatively low sampling density and modest signal-to-
noise of our light curves.

##  4 Results

We present the results of our stacking analysis for each emission line sample
in the OzDES RM sample, and a multi-line analysis of the subsamples for which
two emission-lines are present. With the basic assumption that the lag of a
source is dependent on the intrinsic AGN luminosity alone, by using the
stacking method we are assuming the lags of each source within a bin are
similar (in the rest-frame) so that we recover a representative average lag
for these AGN. Since the binned sources are at different redshifts, when the
light curve data is converted to the rest-frame, different variability and
reverberation time-scales are probed by each source through their unique rest-
frame observational window function. By stacking we can partially circumvent
the usual impact of the sparse sampling (particularly the 7-month seasonal
gaps) in the light curves of any one source, as we are combining the CCF’s for
all sources in a bin. We compare the average lag measurements to the sample of
existing individual lag measurements on the respective $R-L$ relations for
each line.

###  4.1 H$\beta$

Figure 2: The luminosity bins for the H$\beta$ sample, labelled with the
number of binned sources. Within each bin, the standard deviation of the
expected lags for the individual sources (measured using the source luminosity
and the Bentz et al. (2013) $R-L$ relation for H$\beta$) is $\sim$10% of the
expected mean lag for the binned sample (measured as the mean of the expected
lags for the individual sources).  Figure 3: Left column: The coloured solid
lines are the stacked cross correlation functions (CCF) for each of the five
luminosity bins for the H$\beta$ sample. The colours correspond to the
respective bins in Figure 2. The 1$\sigma$ scatter of the bootstrapped CCF’s
is shown by the coloured shaded region. The vertical dashed and dotted lines
indicate the recovered average lag and its uncertainty, as measured from the
bootstrap distribution (coloured histogram). The black solid line and grey
shaded area show the mean and 1$\sigma$ scatter of the CCF’s generated using
the randomised spectroscopic light curves following the procedure described in
§3. Right column: The number of overlapping spectroscopic and photometric
epochs as a function of time lag, in total for each source in the
corresponding bin. The expected mean lag for the bin is indicated by the black
dashed line.  Figure 4: The Radius-Luminosity relation for H$\beta$ (dotted
lines), including the stacked average lag measurements made using the OzDES
H$\beta$ sample, and existing individual lag measurements from Bentz et al.
(2013, and references therein); SDSS-RM (Grier et al., 2017, quality 4 and 5);
SEAMBH (Du et al., 2014; Wang et al., 2014; Du et al., 2015, 2016, 2018; Hu et
al., 2021); Lick AGN Monitoring Project (LAMP, U et al., 2022); and other
measurements from Bentz et al. (2009); Barth et al. (2013); Bentz et al.
(2014); Pei et al. (2014); Lu et al. (2016); Bentz et al. (2016a, b);
Fausnaugh et al. (2017); Zhang et al. (2019); Rakshit et al. (2019); Li et al.
(2021), of which measurements published before 2019 are compiled by Martínez-
Aldama et al. (2019). The multi-line average lag measurement is presented in
§4.4.

We divide our sample into five luminosity bins of equal size, as shown in
Figure 2. The size of the bins were chosen as to maximise the number of
sources in each bin while avoiding introducing a broad underlying distribution
in the expected lags. The highest luminosity source was excluded from the
analysis for this reason. Although there are a relatively small number of
sources stacked in each bin, particularly when compared to stacking done by
Fine et al. (2012, 2013), the signal-to-noise of our stacked CCF’s are
sufficiently high as we have much more light curve data.

The stacked CCF’s for each bin of the H$\beta$ sample are shown in Figure 3,
alongside the total number of overlapping light curve epochs as a function of
time-lag for all sources stacked within the bin. As the observation dates of
each source in a bin are converted to the rest-frame of the source, and there
is a distribution of source redshifts within each bin, the total light curve
sampling of the stacked sample begins to in-fill the rest frame observational
gap imposed by the observed frame 7-month seasonal gap present in the
individual observed light curves.

Comparing the stacked CCF, and its scatter measured from bootstrapping, to the
stacked CCF’s after light curve randomisation, we see significant correlation
signal present. This implies that the signal is not dominated by the
correlation of any individual source. In all cases there is one major peak
present, however, the lowest luminosity bin (blue) has a flatter CCF. There is
limited but non-zero data overlap around the expected mean lags for the two
highest luminosity bins, as they coincide with the first seasonal gap in our
light curves. However, we recover significant average lags in each of these
bins. This demonstrates the ability of stacking to overcome the limitations
imposed by sparse sampling, which impede lag recovery for individual sources.

We plot the recovered average lags from each luminosity bin on the $R-L$
relation, as shown in Figure 4. Our stacked measurements are consistent with
the Bentz et al. (2013) slope, which agrees with the physically motivated
slope of $\sim$0.5. The uncertainty in the average lags are consistent to the
uncertainties in the eight lags recovered for individual sources (Malik et
al., 2023), and are inconsistent with the distribution of the SDSS-RM
measurements (Grier et al., 2017; Li et al., 2017), for which shorter lags are
recovered. Given the similarities of our programs and sample selection, the
reason for this discrepancy is unclear. Although the main difference between
the surveys is the baseline and cadence of the data, simulations by Fonseca
Alvarez et al. (2020) and Malik et al. (2022) find that this does not bias the
lag recovery of SDSS-RM to shorter lags, or OzDES to longer lags. For our
composite lags we bin across our entire H$\beta$ sample, and do not reject any
sources based on light curve signal-to-noise, or any other criteria.

As a test, we repeated the stacking after excluding all the objects with
individual recovered lags (Malik et al., 2023). We show the results of this
test in §B. Although the average lag uncertainties increase after the
exclusion, the lags remain in close agreement with those from the original
analysis.

###  4.2 Mg ii

Figure 5: The luminosity bins for the Mg ii sample, labelled with the number
of binned sources. Within each bin, the standard deviation of the expected
lags for the individual sources (measured using the source luminosity and the
Trakhtenbrot & Netzer (2012) $R-L$ relation for Mg ii) is $\sim$20% of the
expected mean lag for the binned sample. Figure 6: Left column: The coloured
solid lines are the stacked cross correlation functions (CCF) for each of the
three luminosity bins for the Mg ii sample. The colours correspond to the
respective bins in Figure 5. The 1$\sigma$ scatter of the bootstrapped CCF’s
is shown by the coloured shaded region. The vertical dashed and dotted lines
indicate the recovered average lag and its uncertainty, as measured from the
bootstrap distribution (coloured histogram). The black solid line and grey
shaded area show the mean and 1$\sigma$ scatter of the CCF’s generated using
the randomised spectroscopic light curves following the procedure described in
the text. Right column: The number of overlapping spectroscopic and
photometric epochs as a function of time lag, in total for each source in the
corresponding bin. The expected mean lag for the bin is indicated by the black
dashed line. Figure 7: Radius-Luminosity relation for Mg ii, with existing
individual lag measurements from Metzroth et al. (2006); Lira et al. (2018);
Czerny et al. (2019); Zajaček et al. (2020, 2021) and SDSS-RM (Homayouni et
al., 2020, gold sample), along with the OzDES individual measurements (Yu et
al., 2023), and our stacked average lag measurements. The multi-line average
lag measurements are presented in §4.4.

The three luminosity bins used for the Mg ii sample are shown in Figure 5. The
lowest and highest luminosity bins are slightly wider to include sources close
to the edge of the bin. Ten sources were excluded from the analysis to
optimise the bin densities and reduced smoothing of the stacked CCF’s. Larger
luminosity bins were required to achieve adequate signal-to-noise in the
stacked CCF’s for this sample.

We present the stacked CCF’s in Figure 6. The strength of the correlation
signals in each bin are lower than for the H$\beta$ sample, however, comparing
to the CCF’s produced using randomised light curves we can see there is
significant signal present. The signal-to-noise of the Mg ii light-curve input
data is lower than for the H$\beta$ sample, as the Mg ii sample is fainter and
requires subtraction of Fe ii from the emission-line (Yu et al., 2021, 2023).
However, we have 450 AGN in the Mg ii sample, and are therefore stacking many
more sources in each bin. Since sample size is not the limiting factor in this
case, the lower signal-to-noise of the Mg ii line light curves must be
producing weaker stacked cross correlation signals. In the lowest luminosity
bin, the signal is flat and no clear peak is present. For the other two bins a
dominant peak is present, and the bootstrap distributions are adequately
constrained to recover average lags.

We plot the recovered average lags from each luminosity bin on the Mg ii $R-L$
relation in Figure 7, along with the 25 individual measurements made with this
sample by Yu et al. (2023). The average lags are in agreement with the recent
individual measurements from Homayouni et al. (2020) and Yu et al. (2023).
There is no clear progression to longer lags with higher luminosities given
that the average lags for the lowest and intermediate luminosity bins are not
particularly well constrained. As shown in Figure 6, there is limited data
coverage over the expected mean lags for the lowest luminosity bin (blue),
which coincides with the first seasonal gap in our light curves. The time-
dilation distribution over the binned sample is not sufficient to ‘fill in’
the short timescales, but it is able to sufficiently bridge the second
seasonal gap. This could explain why the uncertainty on the recovered average
lag for the lowest luminosity bin is larger than the uncertainties for the
intermediate and highest luminosity bins. The average lags for the three
luminosity bins are formally consistent with both the steeper $R-L$ relation
measured by Trakhtenbrot & Netzer (2012), and the shallower relation recently
constrained by Yu et al. (2023), however, the better constrained mean lag for
the highest luminosity bin is only consistent with the shallower relation.

###  4.3 C iv

Figure 8: The luminosity bins for the C iv sample, labelled with the number of
binned sources. Within each bin, the standard deviation of the expected lags
for the individual sources (measured using the source luminosity and the
Hoormann et al. (2019) $R-L$ relation for C iv) is $\sim$15% of the expected
mean lag for the binned sample. Figure 9: Left column: The coloured solid
lines are the stacked cross correlation functions (CCF) for each of the three
luminosity bins for the C iv sample. The colours correspond to the respective
bins in Figure 8. The 1$\sigma$ scatter of the bootstrapped CCF’s is shown by
the coloured shaded region. The vertical dashed and dotted lines indicate the
recovered average lag and its uncertainty, as measured from the bootstrap
distribution (coloured histogram). The black solid line and grey shaded area
show the mean and 1$\sigma$ scatter of the CCF’s generated using the
randomised spectroscopic light curves following the procedure described in the
text. Right column: The number of overlapping spectroscopic and photometric
epochs as a function of time lag, in total for each source in the
corresponding bin. The expected mean lag for the bin is indicated by the black
dashed line. Figure 10: Radius-Luminosity relation for C iv, with our stacked
average lags and existing individual lag measurements from Peterson et al.
(2005, and references therein); Kaspi et al. (2007); Trevese et al. (2014);
Lira et al. (2018), and SDSS-RM (Grier et al., 2019; Shen et al., 2019, gold
sample), Kaspi et al. (2021), along with the OzDES individual measurements
(Hoormann et al., 2019). The multi-line average lag measurement is presented
in §4.4.

As for the previous samples, we present the luminosity bins for the C iv
sample in Figure 8, and the stacked CCF results in Figure 9. As required for
Mg ii, larger luminosity bins were necessary to achieve sufficient signal-to-
noise after stacking, and nine sources were excluded from the analysis to
avoid overly wide bins in luminosity. The OzDES C iv sample has lower signal-
to-noise than the H$\beta$ and Mg ii samples, as the AGN are faint. The
bootstrap distributions are not well constrained for the lowest or highest
luminosity bins. However, Li et al. (2017) found that the mean recovered lag
remains stable when the light curve signal-to-noise is degraded, although the
uncertainty increases proportionally with the decline. Therefore we continue
to recover the average lags and compare with individual source measurements.

We plot the stacked average lags from the C iv sample alongside existing
measurements from the literature in Figure 10. The average lags for the
intermediate and highest luminosity bins are in agreement with the $R-L$
relations constrained by Hoormann et al. (2019) and Grier et al. (2019),
although the uncertainty on the average lag for the highest luminosity bin is
large. As discussed for the Mg ii sample, the time dilation over the binned
samples does not sufficiently bridge the first of the 7-month seasonal gaps in
our light curves. With the shorter expected lags for C iv, the average lags
for the lowest and intermediate luminosity bins coincides with this gap. In
addition to the lower signal-to-noise of the light curves, this may be
contributing to the poorer quality of the stacked CCF’s. It is unclear why the
average lag recovered for the lowest luminosity bin is much longer than
expected.

###  4.4 Multi-line measurements

Both the H$\beta$ and Mg ii lines are visible for 13 AGN, and Mg ii and C iv
for 106 AGN (see Figure 1). We attempt to recover average lags independently
with each line, in order to compare the lag ratios to investigate the
ionisation stratification of the BLR.

We repeated the stacking procedure for the sample of 13 AGN with the H$\beta$
and Mg ii light curves. As there are few sources we do not bin them by
luminosity. We present the stacked CCF’s for each line in Figure 11. We
measure an average lag of 75${}^{+14}_{-16}$ days for the H$\beta$ sample, and
an average lag of 79${}^{+22}_{-53}$ days for the Mg ii sample. We formally
recover a Mg ii to H$\beta$ lag ratio of 1.05$\pm 0.54$, however the inherent
uncertainty is significant due to the large uncertainty of the Mg ii average
lag. This result is broadly consistent with the expectation that these two
BLRs are approximately cospatial. This ratio is consistent with previous
multi-line measurements made by Homayouni et al. (2020), who found that Mg ii
is emitted from a similar or slightly larger region than H$\beta$ in several
individual sources, as well as Clavel et al. (1991) and Czerny et al. (2019).

We repeated this for the sample of 106 AGN with Mg ii and C iv, and present
the stacked CCF’s in Figure 12. The signal-to-noise was insufficient to divide
the sample into two luminosity bins. We measure an average Mg ii lag of
182${}^{+128}_{-37}$ days, and an average C iv lag of 64${}^{+165}_{-45}$
days. We formally recover a Mg ii to C iv lag ratio of 2.84$\pm 4.84$, however
this is poorly (if at all) constrained given that the average lags are not
well constrained (particularly for the CIV sample). The average lags are
broadly consistent with the BLR stratification model, and the multi-line
comparison made for a single source by Homayouni et al. (2020).

We include the average lags recovered from the multi-line samples on the
respective $R-L$ plots presented in Figure 4, Figure 7 and Figure 10. We also
provide all average lags recovered in this work from each multi-line and
emission line sample in Table 1.

Figure 11: The stacked cross correlation functions (CCF) for the multi-line
sample with both H$\beta$ and Mg ii, comprising 13 AGN.  Figure 12: The
stacked cross correlation functions (CCF) for the multi-line sample with both
Mg ii and C iv, comprising 106 AGN.  Table 1: The average lags for each
luminosity bin or multi-line sample, for each emission-line sample from the
OzDES RM Program. Luminosities are given in erg s-1, and average lags are in
the rest frame. H$\beta$
---
Binned sample | Average lag (days)
43.45$<$log($\lambda L_{\lambda})<$43.77 | $16^{+44}_{-9}$
43.77$<$log($\lambda L_{\lambda})<$44.09 | $56^{+16}_{-16}$
44.09$<$log($\lambda L_{\lambda})<$44.41 | $65^{+15}_{-13}$
44.41$<$log($\lambda L_{\lambda})<$44.73 | $63^{+13}_{-13}$
44.73$<$log($\lambda L_{\lambda})<$45.05 | $93^{+14}_{-21}$
multi-line H$\beta$ \+ Mg ii | $75^{+14}_{-16}$
Mg ii
Binned sample | Average lag (days)
44.40$<$log($\lambda L_{\lambda})<$45.00 | $157^{+30}_{-71}$
45.00$<$log($\lambda L_{\lambda})<$45.50 | $143^{+38}_{-34}$
45.50$<$log($\lambda L_{\lambda})<$46.10 | $191^{+14}_{-29}$
multi-line Mg ii \+ H$\beta$ | $79^{+22}_{-53}$
multi-line Mg ii \+ C iv | $182^{+128}_{-37}$
C iv
Binned sample | Average lag (days)
44.90$<$log($\lambda L_{\lambda})<$45.50 | $124^{+11}_{-25}$
45.50$<$log($\lambda L_{\lambda})<$46.00 | $43^{+12}_{-13}$
46.00$<$log($\lambda L_{\lambda})<$46.60 | $71^{+196}_{-23}$
multi-line C iv \+ Mg ii | $64^{+165}_{-45}$

##  5 Summary

We use the stacking technique developed by Fine et al. (2012, 2013) to measure
average lags in luminosity bins for the H$\beta$, Mg ii and C iv samples from
the OzDES Reverberation Mapping Program. By utilising the bulk of our sample
to recover composite lags, we avoid the potential selection biases in the lag
recovery for individual sources. We successfully recover significant cross-
correlation signals for each emission-line sample:

  * •

The average lags from each luminosity bin of the H$\beta$ sample are
consistent with the $R-L$ relation constrained by Bentz et al. (2013), and the
size of the uncertainties on the average lags are on par with that of
individual measurements, despite the relatively small number of sources
stacked in each bin. This provides confidence in the individual measurements,
and demonstrates the potential for stacked RM analyses to improve upon
constraints which have thus far been made with individual source measurements
alone.

  * •

For Mg ii and C iv, the stacked cross-correlations are weaker, but still
present above the correlation signal generated using randomised light curves.
Further data or larger samples are required to recover significant average
lags for these samples across each luminosity bin.

  * •

From our multi-line analysis, we measure a Mg ii to H$\beta$ lag ratio that is
consistent with earlier findings that the size of each of these line-emitting
regions is similar. Our average lags for the Mg ii and C iv multi-line sample
are not well-constrained due to the limited sample size, however, the lag
ratio we recover is largely consistent with the BLR ionisation stratification
model.

Stacking can be applied beyond RM-specific surveys. It can be done with just a
few spectroscopic epochs, using large AGN samples, provided the continuum
behaviour is well sampled. With LSST forthcoming, high cadence photometry of
the deep-drilling fields will yield quality continuum light curves for tens of
thousands of AGN. The SDSS-V Black Hole Mapper (BHM) will be spectroscopically
following these fields. In addition to their dedicated RM survey of $\sim
1,000$ AGN, SDSS-V BHM will monitor 25,000 AGN over multiple epochs, which
will be combined with earlier SDSS spectra (Kollmeier et al., 2017). The Time
Domain Extragalactic Survey (TiDES) will also be following up these fields to
conduct an RM survey of $\sim 700$ AGN up to $z\sim 2.5$ (Swann et al., 2019).
Stacking analyses of these future, large samples has promise to significantly
extend the reverberation mapping results from these projects. Although the
improved signal-to-noise and survey sampling of these future programs are
expected to yield an increased number of higher quality individual lag
measurements than the first generation of multi-object RM surveys, these
datasets can benefit from the ability of stacking to alleviate the impact of
the unavoidable seasonal gaps on lag recovery (Malik et al., 2022). Stacking
also presents an opportunity to combine all large time-domain datasets to
recover average lags that are potentially more robust than individual lags,
which remain challenging to recover reliably, particularly at high redshift.

## Acknowledgements

We thank the anonymous referee for their comments that improved the paper. UM
and AP are supported by the Australian Government Research Training Program
(RTP) Scholarship. PM and ZY are supported in part by the United States
National Science Foundation under Grant No. 161553 to PM. PM also acknowledges
support from the United States Department of Energy, Office of High Energy
Physics under Award Number DE-SC-0011726. TMD is supported by an Australian
Research Council Laureate Fellowship (project number FL180100168).

We acknowledge parts of this research were carried out on the traditional
lands of the Ngunnawal and Ngambri peoples. This work makes use of data
acquired at the Anglo-Australian Telescope, under program A/2013B/012. We
acknowledge the Gamilaraay people as the traditional owners of the land on
which the AAT stands. We pay our respects to their elders past and present.

This analysis used NumPy (Harris et al., 2020), Astropy (Astropy Collaboration
et al., 2013, 2018), and SciPy (Virtanen et al., 2020). Plots were made using
Matplotlib (Hunter, 2007). This work has made use of the SAO/NASA Astrophysics
Data System Bibliographic Services.

This paper has gone through internal review by the DES collaboration. Funding
for the DES Projects has been provided by the U.S. Department of Energy, the
U.S. National Science Foundation, the Ministry of Science and Education of
Spain, the Science and Technology Facilities Council of the United Kingdom,
the Higher Education Funding Council for England, the National Center for
Supercomputing Applications at the University of Illinois at Urbana-Champaign,
the Kavli Institute of Cosmological Physics at the University of Chicago, the
Center for Cosmology and Astro-Particle Physics at the Ohio State University,
the Mitchell Institute for Fundamental Physics and Astronomy at Texas A&M
University, Financiadora de Estudos e Projetos, Fundação Carlos Chagas Filho
de Amparo à Pesquisa do Estado do Rio de Janeiro, Conselho Nacional de
Desenvolvimento Científico e Tecnológico and the Ministério da Ciência,
Tecnologia e Inovação, the Deutsche Forschungsgemeinschaft and the
Collaborating Institutions in the Dark Energy Survey.

The Collaborating Institutions are Argonne National Laboratory, the University
of California at Santa Cruz, the University of Cambridge, Centro de
Investigaciones Energéticas, Medioambientales y Tecnológicas-Madrid, the
University of Chicago, University College London, the DES-Brazil Consortium,
the University of Edinburgh, the Eidgenössische Technische Hochschule (ETH)
Zürich, Fermi National Accelerator Laboratory, the University of Illinois at
Urbana-Champaign, the Institut de Ciències de l’Espai (IEEC/CSIC), the
Institut de Física d’Altes Energies, Lawrence Berkeley National Laboratory,
the Ludwig-Maximilians Universität München and the associated Excellence
Cluster Universe, the University of Michigan, NSF’s NOIRLab, the University of
Nottingham, The Ohio State University, the University of Pennsylvania, the
University of Portsmouth, SLAC National Accelerator Laboratory, Stanford
University, the University of Sussex, Texas A&M University, and the OzDES
Membership Consortium.

Based in part on observations at Cerro Tololo Inter-American Observatory at
NSF’s NOIRLab (NOIRLab Prop. ID 2012B-0001; PI: J. Frieman), which is managed
by the Association of Universities for Research in Astronomy (AURA) under a
cooperative agreement with the National Science Foundation.

The DES data management system is supported by the National Science Foundation
under Grant Numbers AST-1138766 and AST-1536171. The DES participants from
Spanish institutions are partially supported by MICINN under grants
ESP2017-89838, PGC2018-094773, PGC2018-102021, SEV-2016-0588, SEV-2016-0597,
and MDM-2015-0509, some of which include ERDF funds from the European Union.
IFAE is partially funded by the CERCA program of the Generalitat de Catalunya.
Research leading to these results has received funding from the European
Research Council under the European Union’s Seventh Framework Program
(FP7/2007-2013) including ERC grant agreements 240672, 291329, and 306478. We
acknowledge support from the Brazilian Instituto Nacional de Ciência e
Tecnologia (INCT) do e-Universo (CNPq grant 465376/2014-2).

This manuscript has been authored by Fermi Research Alliance, LLC under
Contract No. DE-AC02-07CH11359 with the U.S. Department of Energy, Office of
Science, Office of High Energy Physics.

## Data Availability

The underlying DES and OzDES data are available in Abbott et al. (2021) and
Lidman et al. (2020). The final light curve data for the full OzDES RM data
set will be made available in a future OzDES paper.

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##  Appendix A Source properties

The source properties are given for the H$\beta$ sample of 69 AGN in Table 2,
the Mg ii sample of 450 AGN in Table 4, and the C iv sample of 290 AGN in
Table 12.

Table 2: Properties for our OzDES H$\beta$ stacking sample. Columns left to right: DES name (J2000), redshift, $r$-band apparent AB magnitude, monochromatic luminosity at 5100Å. The superscript $a$ flags sources which also have Mg ii data.  DES ID | $z$ | $m_{r}$ |  $\log({\lambda}L_{5100})$ (erg s-1)
---|---|---|---
DES J002802.42-424913.52 | 0.127 | 17.88 | 43.67
DES J033633.16-284027.18 | 0.129 | 17.73 | 43.74
DES J022024.92-061731.51 | 0.139 | 18.04 | 43.69
DES J003515.60-433357.64 | 0.145 | 17.75 | 43.84
DES J003245.59-421441.67 | 0.183 | 18.85 | 43.62
DES J025007.02+002525.49 | 0.198 | 18.02 | 44.03
DES J024347.34-005354.84 | 0.237 | 19.19 | 43.73
DES J024340.97-002601.16 | 0.268 | 19.16 | 43.86
DES J025021.72-005413.02 | 0.271 | 19.87 | 43.59
DES J025211.61-003629.35 | 0.294 | 20.10 | 43.58
DES J034028.46-292902.41 | 0.310 | 18.09 | 44.43
DES J022249.67-051453.01 | 0.314 | 19.03 | 44.07
DES J025240.59-002117.04 | 0.315 | 20.37 | 43.53
DES J022851.50-051223.00 | 0.317 | 18.01 | 44.48
DES J003954.13-440509.97 | 0.332 | 19.53 | 43.92
DES J022330.16-054758.06 | 0.354 | 19.87 | 43.85
DES J024325.53-000412.67 | 0.356 | 20.47 | 43.62
DES J024902.03-004322.43 | 0.360 | 20.75 | 43.52
DES J024320.36-001825.41 | 0.373 | 19.47 | 44.07
DES J024519.82-010245.63 | 0.381 | 20.46 | 43.69
DES J024225.86-004142.50 | 0.383 | 20.74 | 43.59
DES J003622.82-424759.11 | 0.390 | 21.02 | 43.49
DES J004009.06-431255.29 | 0.434 | 19.04 | 44.40
DES J003834.47-433807.12 | 0.453 | 20.61 | 43.82
DES J025042.90-004138.74 | 0.457 | 20.54 | 43.86
DES J022258.90-045852.28 | 0.466 | 19.77 | 44.20
DES J024712.89-011106.21 | 0.486 | 20.56 | 43.92
DES J024211.93-010959.69 | 0.488 | 20.18 | 44.08
DES J024538.29-004705.32 | 0.488 | 20.49 | 43.96
DES J003017.47-422446.39 | 0.491 | 18.48 | 44.77
DES J022133.82-054842.69 | 0.501 | 18.77 | 44.67
DES J024643.04-013149.55 | 0.502 | 19.32 | 44.45
DES J033002.93-273248.31 | 0.527 | 20.33 | 44.10
DES J003552.21-423352.14 | 0.530 | 21.29 | 43.72
DES J022019.61-060729.77 | 0.541 | 20.07 | 44.23
DES J021910.57-055114.76 | 0.558 | 19.49 | 44.49
DES J025119.79-004831.62 | 0.559 | 19.98 | 44.30
DES J033758.00-294618.46 | 0.561 | 19.27 | 44.58
DES J024939.57+000700.39 | 0.564 | 20.90 | 43.94
DES J024646.73-001220.60 | 0.564 | 19.73 | 44.41
DES J022717.88-051623.78 | 0.566 | 20.87 | 43.95
DES J033946.12-295030.94 | 0.582 | 20.33 | 44.20
DES J003114.43-424227.81 | 0.591 | 20.53 | 44.13
DES J033905.07-292134.36 | 0.600 | 18.66 | 44.89
DES J022329.27-045451.85 | 0.604 | 20.78 | 44.05
DES J033738.50-272306.75 | 0.613 | 18.60 | 44.94
DES J022246.23-041450.67 | 0.614 | 19.94 | 44.40
DES J024651.86-010732.56 | 0.622 | 20.36 | 44.25
DES J033910.13-264311.77 | 0.622 | 21.39 | 43.84
DES J024442.77-004223.14 | 0.628 | 19.92 | 44.43
DES J021923.29-045148.69 | 0.630 | 19.36 | 44.66
DES J033051.45-271254.90 | 0.633 | 20.24 | 44.31
DES J032718.70-281857.85 | 0.634 | 19.52 | 44.60
DES J002904.43-425243.04 | 0.644 | 19.54 | 44.61
Table 3: continued

H$\beta$ sample  DES ID $z$ $m_{r}$ $\log({\lambda}L_{5100})$ (erg s-1) DES
J021820.49-050426.42 0.650 19.59 44.60 DES J034056.37-293339.67 0.652 20.44
44.26 DES J003013.70-425733.44 a 0.654 20.31 44.32 DES J024533.65-000744.91 a
0.655 19.66 44.58 DES J003010.25-423356.22 a 0.667 20.14 44.40 DES
J003231.39-433511.71 a 0.679 20.39 44.32 DES J004334.89-440546.53 a 0.681
19.62 44.63 DES J021952.14-040919.86 a 0.692 20.30 44.37 DES
J022452.19-040519.38 a 0.695 19.85 44.55 DES J002906.71-423904.49 a 0.703
18.69 45.03 DES J021514.27-053321.33 a 0.703 20.01 44.50 DES
J033819.34-274346.33 a 0.706 18.81 44.98 DES J022617.85-043108.99 a 0.708
19.52 44.70 DES J021524.99-045353.83 a 0.714 20.51 44.31 DES
J021808.24-045845.20 a 0.716 18.18 45.25

Table 4: Properties for our OzDES Mg ii stacking sample. Columns left to right: DES name (J2000), redshift, $r$-band apparent AB magnitude, monochromatic luminosity at 3000Å. The superscript $a$ flags sources which also have H$\beta$ data, and $b$ flags sources which also have C iv data.  DES ID | $z$ | $m_{r}$ |  $\log({\lambda}L_{3000})$ (erg s-1)
---|---|---|---
DES J003013.70-425733.44 a | 0.654 | 20.31 | 44.47
DES J024533.65-000744.91 a | 0.655 | 19.66 | 44.73
DES J003010.25-423356.22 a | 0.667 | 20.14 | 44.56
DES J003231.39-433511.71 a | 0.679 | 20.39 | 44.47
DES J004334.89-440546.53 a | 0.681 | 19.62 | 44.78
DES J021952.14-040919.86 a | 0.692 | 20.30 | 44.53
DES J022452.19-040519.38 a | 0.695 | 19.85 | 44.71
DES J002906.71-423904.49 a | 0.703 | 18.69 | 45.18
DES J021514.27-053321.33 a | 0.703 | 20.01 | 44.66
DES J033819.34-274346.33 a | 0.706 | 18.81 | 45.14
DES J022617.85-043108.99 a | 0.708 | 19.52 | 44.86
DES J021524.99-045353.83 a | 0.714 | 20.51 | 44.47
DES J021808.24-045845.20 a | 0.716 | 18.18 | 45.40
DES J033545.58-293216.49 | 0.724 | 20.30 | 44.56
DES J024126.71-004526.12 | 0.727 | 18.92 | 45.12
DES J033227.00-274105.28 | 0.730 | 19.81 | 44.77
DES J024727.97-013008.97 | 0.741 | 20.26 | 44.60
DES J022421.67-064613.71 | 0.755 | 20.48 | 44.53
DES J032724.94-274202.77 | 0.756 | 19.78 | 44.81
DES J021902.96-062107.22 | 0.758 | 20.42 | 44.55
DES J022244.40-043346.88 | 0.761 | 19.23 | 45.03
DES J025048.65+000207.62 | 0.766 | 19.12 | 45.08
DES J003155.93-434225.34 | 0.768 | 19.30 | 45.01
DES J021705.51-042253.46 | 0.788 | 20.24 | 44.66
DES J033459.10-293317.41 | 0.801 | 19.99 | 44.77
DES J032850.20-271207.84 | 0.802 | 19.42 | 45.00
DES J003350.95-435606.17 | 0.806 | 19.61 | 44.93
DES J022155.25-064916.59 | 0.807 | 18.06 | 45.55
DES J024801.09-004015.63 | 0.811 | 20.05 | 44.76
DES J025146.78-004035.49 | 0.813 | 19.63 | 44.93
DES J022326.46-045705.99 | 0.825 | 20.72 | 44.50
DES J025100.99+004802.99 | 0.829 | 20.03 | 44.78
DES J021628.43-040147.11 | 0.831 | 19.52 | 44.99
DES J033246.02-282232.12 | 0.839 | 20.07 | 44.78
DES J033328.93-275641.20 | 0.839 | 20.29 | 44.69
DES J022255.89-051351.61 | 0.849 | 19.01 | 45.21
DES J004042.70-440341.05 | 0.851 | 19.78 | 44.91
DES J033332.81-282220.34 | 0.858 | 19.14 | 45.17
DES J024637.94-004105.24 | 0.859 | 20.10 | 44.79
DES J033137.70-284808.03 | 0.862 | 21.68 | 44.16
DES J033230.63-284750.36 | 0.862 | 20.70 | 44.55
Table 5: continued

Mg ii sample  DES ID $z$ $m_{r}$ $\log({\lambda}L_{3000})$ (erg s-1) DES
J033235.64-290202.05 0.866 19.33 45.10 DES J003527.80-443411.36 0.869 19.90
44.88 DES J002831.10-421538.06 0.871 18.98 45.25 DES J033523.52-280723.67
0.871 17.25 45.94 DES J003331.34-441039.28 0.878 19.64 44.99 DES
J004020.36-432053.98 0.880 19.49 45.05 DES J002641.26-424900.31 0.882 19.95
44.87 DES J021557.63-045009.52 0.884 18.73 45.36 DES J003301.72-440750.87
0.886 19.86 44.91 DES J024831.08-005025.58 0.887 20.42 44.69 DES
J002951.05-433629.34 0.892 20.66 44.60 DES J002702.17-431755.99 0.900 20.15
44.81 DES J021413.01-042930.02 0.901 19.08 45.24 DES J024159.74-010512.38
0.904 20.16 44.81 DES J024357.90-011330.42 0.905 20.22 44.79 DES
J022440.72-043657.71 0.907 20.14 44.82 DES J025217.48-005249.30 0.912 20.52
44.67 DES J002930.76-432724.34 0.914 18.35 45.54 DES J003437.73-424318.36
0.915 19.09 45.25 DES J033520.08-284258.52 0.931 20.14 44.84 DES
J003435.26-441127.90 0.933 19.40 45.14 DES J024425.38-004652.99 0.937 18.90
45.34 DES J003809.48-435241.29 0.937 19.40 45.14 DES J033435.50-282812.24
0.940 19.88 44.95 DES J002926.51-431250.54 0.944 18.96 45.33 DES
J002917.61-433759.92 0.951 18.58 45.48 DES J024237.79-012354.10 0.957 19.65
45.06 DES J033435.49-283631.56 0.963 20.09 44.89 DES J022049.53-053731.08
0.974 20.00 44.94 DES J022344.57-064039.01 0.983 20.83 44.61 DES
J022712.98-044636.25 0.983 18.13 45.69 DES J033945.79-275333.88 0.984 21.29
44.43 DES J033404.10-275629.92 0.984 20.75 44.65 DES J033339.36-281724.26
0.987 20.02 44.94 DES J033509.98-283255.27 0.993 18.03 45.74 DES
J002933.85-435240.66 0.995 18.06 45.73 DES J022114.78-050832.95 0.996 20.60
44.72 DES J032853.99-281706.94 1.000 20.29 44.84 DES J024514.00-003535.43
1.005 19.41 45.20 DES J025237.80-004627.79 1.008 19.49 45.17 DES
J021500.22-043007.46 1.012 19.76 45.06 DES J024300.44-003030.10 1.018 20.52
44.76 DES J022449.86-043025.80 1.024 20.44 44.80 DES J024924.67+002536.38
1.025 19.93 45.00 DES J033531.95-271825.19 1.029 19.14 45.32 DES
J033408.25-274337.81 1.029 20.69 44.70 DES J003914.17-443844.22 1.033 19.62
45.13 DES J033854.56-291001.97 1.049 20.21 44.91 DES J032831.40-285249.79
1.050 20.47 44.80 DES J022104.63-044239.89 1.052 20.25 44.89 DES
J002826.18-433829.09 1.063 20.90 44.64 DES J003710.86-444048.06 1.067 18.53
45.59 DES J033810.75-275153.11 1.077 19.45 45.23 DES J033948.28-275438.98
1.077 17.51 46.01 DES J021817.44-045112.40 1.083 19.25 45.32 DES
J002949.39-434806.73 1.088 19.29 45.31 DES J025228.55+003109.14 1.110 18.81
45.52 DES J025128.38+001144.60 1.117 20.17 44.98 DES J033045.54-284150.29
1.119 19.57 45.22 DES J003145.76-421747.61 1.129 19.38 45.30 DES
J003834.04-432457.69 1.133 20.29 44.94 DES J034020.28-291750.48 1.135 18.28
45.75 DES J003536.95-443104.40 1.136 20.06 45.04 DES J002639.87-432307.71
1.139 19.58 45.23

Table 6: continued

Mg ii sample  DES ID $z$ $m_{r}$ $\log({\lambda}L_{3000})$ (erg s-1) DES
J024617.07-000602.60 1.143 18.42 45.70 DES J003452.22-434613.99 1.146 20.77
44.76 DES J024854.80+001054.04 1.146 19.57 45.24 DES J033836.19-295113.53
1.148 20.95 44.69 DES J003444.53-433749.06 1.153 20.12 45.03 DES
J021631.35-043207.93 1.155 19.74 45.18 DES J022501.68-040754.18 1.157 19.67
45.21 DES J003332.28-430526.16 1.159 18.53 45.67 DES J022718.54-053124.86
1.159 21.06 44.66 DES J033350.23-284244.42 1.161 21.12 44.63 DES
J021849.86-035835.29 1.162 19.18 45.41 DES J033612.01-290152.96 1.164 19.58
45.25 DES J033353.02-283022.38 1.165 18.51 45.68 DES J033429.54-293904.49
1.167 20.57 44.86 DES J033416.89-274504.73 1.168 20.12 45.04 DES
J033719.99-262418.84 1.169 19.56 45.27 DES J003725.23-431710.85 1.173 19.94
45.12 DES J022556.83-045853.05 1.180 21.09 44.66 DES J022823.19-041223.67
1.181 17.57 46.07 DES J022533.79-050801.95 1.183 18.40 45.74 DES
J033744.23-262559.74 1.187 18.85 45.56 DES J025036.99-002408.04 1.195 20.68
44.84 DES J033335.92-264915.24 1.199 19.99 45.12 DES J024840.98-001228.80
1.199 19.11 45.47 DES J003848.77-434518.55 1.200 21.03 44.70 DES
J003549.87-424526.29 1.208 20.26 45.02 DES J033627.43-294149.95 1.218 18.59
45.69 DES J022212.40-061246.20 1.220 20.71 44.85 DES J022108.60-061753.21
1.225 20.00 45.13 DES J033534.69-283149.26 1.225 19.71 45.25 DES
J022134.35-062941.64 1.228 20.71 44.85 DES J024544.78-004415.24 1.229 19.82
45.21 DES J022423.52-065001.40 1.229 20.15 45.08 DES J022023.48-064959.19
1.232 20.35 45.00 DES J033525.23-270200.72 1.233 19.31 45.42 DES
J022055.16-060136.43 1.234 20.55 44.92 DES J003703.65-434759.50 1.236 19.87
45.20 DES J004111.46-441014.38 1.237 20.20 45.06 DES J033211.42-284323.98
1.237 21.86 44.40 DES J033928.30-291714.73 1.241 20.08 45.12 DES
J003125.94-434743.50 1.243 20.25 45.05 DES J024918.24-001731.03 1.244 19.82
45.22 DES J021906.15-063000.89 1.250 20.12 45.10 DES J002743.35-425258.79
1.252 19.94 45.18 DES J033635.40-273427.02 1.254 20.17 45.09 DES
J003322.53-442412.38 1.257 19.47 45.37 DES J022445.39-065556.80 1.261 21.11
44.72 DES J022115.87-062217.45 1.273 18.82 45.64 DES J024306.66-002531.29
1.279 20.36 45.03 DES J022245.85-041932.10 1.283 20.61 44.93 DES
J034106.19-291410.86 1.287 21.20 44.70 DES J022529.40-050946.39 1.288 20.93
44.81 DES J024939.57-001157.73 1.295 20.97 44.80 DES J024621.09-000152.02
1.296 18.64 45.73 DES J021957.86-060534.66 1.296 20.74 44.89 DES
J025323.64+000446.97 1.297 20.18 45.12 DES J022024.34-061401.95 1.297 21.31
44.66 DES J033911.64-290601.76 1.298 20.06 45.16 DES J025224.97+001308.30
1.300 20.68 44.92 DES J003819.73-443134.02 1.305 18.80 45.67 DES
J024455.17-002501.41 1.308 19.29 45.48 DES J034032.74-270521.33 1.310 20.91
44.83 DES J024811.51-012609.51 1.313 19.29 45.48 DES J003639.49-430400.30
1.317 20.20 45.12

Table 7: continued

Mg ii sample  DES ID $z$ $m_{r}$ $\log({\lambda}L_{3000})$ (erg s-1) DES
J033308.48-285832.12 1.318 19.72 45.31 DES J025005.69-004054.86 1.320 20.41
45.04 DES J033030.59-282135.43 1.322 18.89 45.65 DES J022024.93-053744.40
1.322 21.14 44.75 DES J003245.16-440451.51 1.323 20.84 44.87 DES
J033216.20-273930.61 1.324 20.60 44.96 DES J033525.44-265531.09 1.325 17.55
46.19 DES J033939.33-272454.08 1.325 19.19 45.53 DES J033303.99-271531.43
1.329 20.13 45.16 DES J033533.91-264847.02 1.330 20.25 45.11 DES
J002855.47-434210.06 1.331 20.14 45.15 DES J024214.97-003131.71 1.332 19.93
45.24 DES J033057.32-284737.42 1.335 20.99 44.81 DES J033635.49-263735.76
1.336 19.99 45.22 DES J033824.55-263527.10 1.340 19.65 45.35 DES
J024652.16-011242.95 1.340 19.44 45.44 DES J024326.61-002056.06 1.345 20.51
45.01 DES J022351.09-053750.25 1.347 18.61 45.77 DES J033723.98-294917.22
1.351 19.00 45.62 DES J022446.16-050827.57 1.357 18.85 45.69 DES
J022436.17-065912.26 1.360 20.78 44.91 DES J022419.74-062142.31 1.361 18.52
45.82 DES J025324.69-002655.67 1.364 19.41 45.47 DES J003922.97-430230.45
1.369 19.71 45.35 DES J024234.93-010351.83 1.371 19.46 45.45 DES
J025252.02-002211.61 1.371 20.68 44.96 DES J025318.92+001559.61 1.374 20.92
44.87 DES J002857.80-424644.03 1.377 18.74 45.74 DES J033923.53-265229.48
1.379 20.57 45.01 DES J034027.16-285641.30 1.379 18.74 45.74 DES
J004055.63-441249.41 1.383 20.42 45.08 DES J033444.13-264215.40 1.384 19.57
45.42 DES J003738.22-443838.25 1.385 20.13 45.19 DES J025145.09-004639.64
1.386 19.81 45.32 DES J021749.09-041215.57 1.386 20.13 45.19 DES
J022815.08-041942.59 1.387 20.10 45.21 DES J024746.99-011334.42 1.389 20.63
44.99 DES J003814.08-433314.92 1.390 18.27 45.94 DES J022032.25-044217.60
1.401 20.25 45.16 DES J021451.07-044236.60 1.401 20.97 44.87 DES
J022446.95-055739.13 1.409 20.88 44.91 DES J022402.07-062943.14 1.412 20.17
45.20 DES J022124.53-050205.23 1.415 19.02 45.66 DES J032942.54-272012.09
1.415 19.94 45.29 DES J003827.69-433518.19 1.419 19.96 45.28 DES
J022436.64-063255.90 1.423 20.95 44.89 DES J024935.55-001336.76 1.423 19.99
45.28 DES J024606.20-005531.75 1.426 20.38 45.12 DES J003052.76-430301.10
1.428 19.39 45.52 DES J024929.19-002104.15 1.428 19.00 45.67 DES
J022216.72-041719.73 1.432 19.89 45.32 DES J033918.13-293008.14 1.436 21.12
44.83 DES J024340.09-001749.37 1.436 19.68 45.41 DES J024753.20-002137.75
1.437 20.16 45.22 DES J024212.65-010339.46 1.438 20.77 44.97 DES
J033435.10-262635.67 1.441 19.45 45.50 DES J021939.92-061407.00 1.446 20.60
45.05 DES J022041.19-055039.80 1.454 20.27 45.19 DES J022006.60-061936.36
1.460 19.83 45.37 DES J033630.87-291753.39 1.462 19.63 45.45 DES
J024820.90-002546.67 1.463 19.98 45.31 DES J025030.77-000801.72 1.466 18.31
45.98 DES J002940.83-424308.05 1.472 19.66 45.44 DES J025024.52-001419.03
1.472 19.98 45.31

Table 8: continued

Mg ii sample  DES ID $z$ $m_{r}$ $\log({\lambda}L_{3000})$ (erg s-1) DES
J033310.16-282433.18 1.476 20.99 44.91 DES J003253.01-435626.33 1.476 20.01
45.30 DES J022644.23-040720.13 1.479 19.76 45.41 DES J003035.42-433249.60
1.480 18.77 45.80 DES J024944.09+003317.50 1.480 19.71 45.43 DES
J003053.45-432344.99 1.490 20.58 45.09 DES J033213.36-283621.03 1.492 20.36
45.18 DES J003232.61-433303.00 1.492 19.77 45.41 DES J032604.02-275629.36
1.494 18.53 45.91 DES J022429.11-045807.69 1.498 20.30 45.20 DES
J003621.41-435139.13 1.501 20.21 45.24 DES J034101.59-293056.44 1.504 20.49
45.13 DES J022350.77-043158.10 1.504 19.90 45.37 DES J021620.91-053417.45
1.508 20.11 45.29 DES J033253.86-283139.33 1.509 20.61 45.09 DES
J024959.77-000104.11 1.512 20.09 45.30 DES J024920.97+004206.39 1.524 20.66
45.08 DES J021630.87-042051.45 1.528 19.90 45.39 DES J024455.45-011500.42
1.529 20.51 45.15 DES J033951.49-291713.89 1.530 20.83 45.02 DES
J032643.99-280657.07 1.532 19.73 45.46 DES J004232.48-440757.18 1.532 18.38
46.00 DES J003207.44-433049.00 1.533 19.65 45.50 DES J033400.71-271540.89
1.538 20.04 45.35 DES J003254.85-420236.96 1.541 20.28 45.25 DES
J022338.53-063246.90 1.546 21.24 44.88 DES J025311.70-004241.62 1.547 20.36
45.23 DES J022059.48-044917.03 1.547 18.51 45.97 DES J033355.67-282651.58
1.551 20.39 45.22 DES J033853.03-271735.34 1.553 21.16 44.91 DES
J022509.54-040838.19 1.553 20.43 45.21 DES J003006.53-435107.85 1.555 20.46
45.20 DES J022520.75-041246.56 1.559 20.38 45.23 DES J022154.21-061941.56
1.559 20.13 45.33 DES J021612.83-044634.12 1.560 19.86 45.44 DES
J003433.01-423342.34 1.561 20.28 45.27 DES J033410.83-280949.16 1.562 21.54
44.77 DES J033058.53-275148.31 1.562 20.90 45.03 DES J025318.76+000414.19
1.563 20.15 45.33 DES J033101.15-275125.44 1.563 19.12 45.74 DES
J004016.88-442556.16 1.565 20.24 45.29 DES J003829.91-434454.27 1.567 17.83
46.26 DES J003858.70-443045.51 1.569 19.95 45.41 DES J003653.08-435441.53
1.572 19.32 45.67 DES J033211.64-273726.16 1.574 19.22 45.71 DES
J033325.92-290142.07 1.574 20.77 45.09 DES J022422.63-061943.20 1.575 21.53
44.78 DES J002939.03-431253.68 1.577 20.70 45.12 DES J033553.51-275044.68
1.578 18.99 45.80 DES J025148.53-004637.61 1.579 19.50 45.60 DES
J003413.73-432600.36 1.588 21.23 44.91 DES J022733.98-042523.34 1.590 20.57
45.18 DES J032801.84-273815.71 1.590 20.14 45.35 DES J003952.64-442753.23
1.591 20.03 45.40 DES J003254.79-423926.69 1.597 19.28 45.70 DES
J003307.13-424912.19 1.598 20.49 45.22 DES J024603.67-003211.73 b 1.601 18.99
45.82 DES J033304.62-291230.05 b 1.603 20.19 45.34 DES J024823.76-010002.36
1.603 20.48 45.23 DES J022152.62-062834.38 b 1.604 20.96 45.03 DES
J033617.72-300224.76 b 1.605 19.88 45.47 DES J033604.07-292659.88 b 1.610
20.07 45.39 DES J021505.09-045855.98 1.610 19.33 45.69 DES
J033721.40-292323.42 b 1.612 19.99 45.43

Table 9: continued

Mg ii sample  DES ID $z$ $m_{r}$ $\log({\lambda}L_{3000})$ (erg s-1) DES
J033918.18-293142.92 b 1.612 21.04 45.01 DES J033407.62-291607.55 b 1.615
19.59 45.59 DES J002950.78-423801.20 b 1.616 20.69 45.15 DES
J003723.59-442258.09 b 1.618 19.98 45.44 DES J033139.43-284939.85 1.619 20.93
45.06 DES J003426.66-422807.96 1.622 21.07 45.00 DES J022016.53-043209.15
1.624 21.22 44.94 DES J025225.52+003405.92 1.624 19.97 45.44 DES
J021600.36-043829.30 b 1.624 20.33 45.30 DES J033220.31-280214.82 1.625 21.11
44.99 DES J021947.13-043754.70 b 1.626 20.63 45.18 DES J033835.80-274224.52 b
1.629 20.00 45.44 DES J003501.58-425344.26 b 1.632 19.98 45.45 DES
J003454.09-425716.21 b 1.633 20.62 45.19 DES J022247.88-043330.04 b 1.635
20.24 45.34 DES J003234.33-431937.83 b 1.641 19.40 45.68 DES
J022224.82-062626.69 b 1.641 20.16 45.38 DES J025254.18-001119.67 b 1.641
21.25 44.94 DES J022716.52-050008.33 b 1.642 20.50 45.24 DES
J022337.73-062354.60 1.646 20.91 45.08 DES J034044.75-270720.15 1.647 21.14
44.99 DES J024207.50-004423.41 1.647 22.32 44.52 DES J033437.58-275826.84 b
1.648 18.69 45.97 DES J022008.73-045905.31 b 1.649 20.52 45.24 DES
J033657.91-274244.39 b 1.649 20.14 45.39 DES J003015.00-430333.45 b 1.650
19.97 45.46 DES J022029.60-051022.59 b 1.652 20.68 45.18 DES
J024422.20-011247.11 1.654 20.14 45.40 DES J022228.25-060547.60 1.658 20.34
45.32 DES J022319.01-070927.36 1.659 21.32 44.93 DES J003143.64-425420.21 b
1.662 20.03 45.44 DES J022208.15-065550.48 1.662 21.12 45.01 DES
J003245.74-431453.18 1.671 20.78 45.15 DES J003548.43-431444.38 b 1.673 20.47
45.27 DES J022424.16-043229.83 b 1.674 20.32 45.34 DES J025340.94+001110.20 b
1.675 18.31 46.14 DES J024906.74+000823.79 1.677 20.68 45.19 DES
J003956.32-442047.73 b 1.680 20.08 45.44 DES J021439.12-051355.34 1.683 20.96
45.08 DES J033903.66-293326.48 b 1.684 21.85 44.73 DES J003948.24-445323.16 b
1.684 19.59 45.63 DES J025429.12-000404.45 1.685 21.98 44.68 DES
J003635.93-434636.05 b 1.689 19.90 45.51 DES J025220.53+002735.19 b 1.690
19.86 45.53 DES J033341.61-284603.55 1.693 21.02 45.07 DES
J021902.58-044628.33 b 1.694 19.92 45.51 DES J025356.07+001057.54 b 1.695
19.47 45.69 DES J003325.69-434826.13 b 1.696 20.26 45.37 DES
J024527.72-010602.84 b 1.696 20.05 45.46 DES J003030.66-420243.68 1.696 20.65
45.22 DES J033457.77-274956.61 1.700 21.58 44.85 DES J022445.77-061149.99 b
1.701 20.19 45.40 DES J003213.12-434553.39 1.706 17.34 46.55 DES
J003256.53-441451.15 1.708 19.89 45.53 DES J022907.98-045102.02 1.714 20.91
45.12 DES J022014.98-062253.15 b 1.716 19.91 45.52 DES J024207.18-002818.79
1.716 19.83 45.56 DES J003721.82-443051.40 1.716 20.33 45.36 DES
J003221.43-423908.40 1.719 21.21 45.01 DES J024632.55-003439.14 b 1.724 19.87
45.55 DES J022134.97-070831.84 b 1.728 20.70 45.22 DES J032940.47-275143.61 b
1.730 19.87 45.55 DES J022602.20-061626.10 b 1.736 19.97 45.51 DES
J003734.68-441539.48 1.738 20.15 45.44

Table 10: continued

Mg ii sample  DES ID $z$ $m_{r}$ $\log({\lambda}L_{3000})$ (erg s-1) DES
J024611.20-003134.33 1.738 20.52 45.29 DES J021647.25-044029.81 1.746 21.58
44.87 DES J003206.50-425325.23 b 1.750 19.84 45.57 DES J033814.33-294213.78 b
1.750 19.94 45.53 DES J002920.73-420425.08 1.750 19.66 45.64 DES
J033453.60-264121.34 b 1.751 20.14 45.45 DES J033817.74-290324.90 b 1.753
19.61 45.67 DES J021732.31-052950.95 1.755 21.84 44.77 DES
J033211.80-284257.07 1.755 20.26 45.41 DES J022115.04-043155.51 b 1.757 21.33
44.98 DES J033452.89-265215.54 b 1.757 19.10 45.87 DES J033451.51-280041.23
1.758 21.49 44.92 DES J022117.44-063856.45 b 1.763 19.83 45.58 DES
J024140.99-012712.41 1.768 20.33 45.39 DES J024257.19-004549.41 b 1.770 21.08
45.09 DES J022119.91-045948.62 b 1.770 20.76 45.22 DES J003120.86-425145.98 b
1.771 20.14 45.47 DES J002859.58-423239.47 1.776 19.43 45.75 DES
J022024.08-045709.48 1.776 19.84 45.59 DES J033912.33-293043.57 1.778 21.35
44.98 DES J004029.04-441704.97 b 1.783 20.04 45.51 DES J003255.12-435757.56 b
1.784 20.07 45.50 DES J022533.36-065917.56 1.784 18.95 45.95 DES
J032759.97-271921.90 b 1.785 20.37 45.38 DES J024222.95-011527.57 b 1.785
20.24 45.43 DES J032914.81-290130.69 1.787 20.50 45.33 DES
J033328.60-290314.66 b 1.787 19.58 45.70 DES J022027.32-045115.53 b 1.788
21.14 45.08 DES J033922.52-292857.78 1.789 21.27 45.02 DES
J022002.08-050101.91 b 1.791 19.69 45.66 DES J022751.50-044252.66 b 1.795
20.60 45.30 DES J003939.41-444612.90 b 1.797 20.17 45.47 DES
J022503.11-065258.79 b 1.798 20.09 45.50 DES J032835.62-274406.09 b 1.800
19.94 45.56 DES J033722.89-274020.85 b 1.804 19.93 45.57 DES
J003921.57-441844.65 1.813 19.91 45.58 DES J003920.50-440441.16 b 1.814 19.79
45.63 DES J003739.59-432521.40 b 1.815 20.40 45.39 DES J022231.63-043256.29
1.816 19.67 45.68 DES J033047.84-281521.39 1.818 21.53 44.94 DES
J034001.87-270136.24 1.819 21.05 45.13 DES J004156.96-435856.50 1.821 20.36
45.41 DES J024635.61-000850.46 b 1.822 19.26 45.85 DES J033002.51-274858.28 b
1.823 20.70 45.27 DES J033017.79-280231.25 1.823 20.61 45.31 DES
J033548.18-290943.65 b 1.826 20.33 45.42 DES J022352.09-064029.96 b 1.827
20.50 45.35 DES J022409.89-044718.00 b 1.832 20.11 45.51 DES
J033319.58-290431.65 b 1.833 20.73 45.27 DES J024716.32-010401.36 b 1.834
21.10 45.12 DES J021958.13-041707.68 1.837 21.09 45.12 DES
J033222.47-285935.09 b 1.837 20.68 45.29 DES J033301.69-275818.80 b 1.840
20.94 45.19 DES J004014.18-431716.29 b 1.842 19.87 45.62 DES
J021643.70-052236.21 1.844 20.57 45.34 DES J021903.49-043935.00 b 1.845 20.48
45.37 DES J033539.94-265025.37 1.846 19.68 45.69 DES J024737.50-000458.97 b
1.847 19.88 45.62 DES J024608.67-013933.97 b 1.848 19.68 45.70 DES
J022515.35-044008.91 b 1.850 19.82 45.64 DES J025038.68-004739.06 b 1.856
18.67 46.10 DES J002729.28-431501.02 b 1.863 19.67 45.71 DES
J024723.54-002536.48 b 1.864 19.42 45.81 DES J022845.57-043350.18 b 1.864
17.41 46.61

Table 11: continued

Mg ii sample  DES ID $z$ $m_{r}$ $\log({\lambda}L_{3000})$ (erg s-1) DES
J024748.87-000147.41 b 1.868 19.58 45.75 DES J024133.65-010724.20 b 1.874
20.86 45.24 DES J003940.80-443718.32 b 1.875 19.49 45.79 DES
J024838.93-000325.87 1.876 20.61 45.34 DES J022047.63-051835.83 b 1.878 19.55
45.77 DES J021544.02-053607.56 1.885 21.31 45.06 DES J025513.03+000639.59
1.885 19.78 45.68 DES J021707.96-055152.07 b 1.885 19.70 45.71 DES
J033145.20-275435.75 b 1.891 21.19 45.12 DES J033225.90-282208.45 1.894 21.55
44.97 DES J022213.31-041030.05 1.903 20.14 45.54 DES J024242.50-002212.87 b
1.904 20.57 45.37 DES J022828.19-040044.25 b 1.905 18.31 46.28 DES
J003626.44-430820.66 b 1.907 19.80 45.68 DES J022050.39-061748.80 b 1.908
21.89 44.85 DES J021953.45-061123.39 b 1.910 19.90 45.64 DES
J003150.13-432726.88 b 1.912 18.68 46.13 DES J022328.88-040134.71 b 1.915
19.82 45.68 DES J033739.88-272045.97 b 1.916 19.21 45.92 DES
J033924.44-271250.15 b 1.918 20.52 45.40 DES J025428.31+002418.43 b 1.918
20.42 45.44 DES J033415.37-265535.62 b 1.922 19.85 45.67 DES
J033011.77-283636.65 b 1.922 20.99 45.21 DES J022327.85-040119.16 b 1.922
20.81 45.29 DES J024639.22-012731.85 b 1.923 20.34 45.47

Table 12: Properties for our OzDES C iv stacking sample. Columns left to right: DES name (J2000), redshift, $r$-band apparent AB magnitude, monochromatic luminosity at 1350Å. The superscript $b$ flags sources which also have Mg ii data.  DES ID | $z$ | $m_{r}$ |  $\log({\lambda}L_{1350})$ (erg s-1)
---|---|---|---
DES J024603.67-003211.73 a | 1.601 | 18.99 | 45.93
DES J033304.62-291230.05 a | 1.603 | 20.19 | 45.45
DES J022152.62-062834.38 a | 1.604 | 20.96 | 45.14
DES J033617.72-300224.76 a | 1.605 | 19.88 | 45.57
DES J033604.07-292659.88 a | 1.610 | 20.07 | 45.50
DES J033721.40-292323.42 a | 1.612 | 19.99 | 45.53
DES J033918.18-293142.92 a | 1.612 | 21.04 | 45.11
DES J033407.62-291607.55 a | 1.615 | 19.59 | 45.70
DES J002950.78-423801.20 a | 1.616 | 20.69 | 45.26
DES J003723.59-442258.09 a | 1.618 | 19.98 | 45.54
DES J021600.36-043829.30 a | 1.624 | 20.33 | 45.41
DES J021947.13-043754.70 a | 1.626 | 20.63 | 45.29
DES J033835.80-274224.52 a | 1.629 | 20.00 | 45.54
DES J003501.58-425344.26 a | 1.632 | 19.98 | 45.55
DES J003454.09-425716.21 a | 1.633 | 20.62 | 45.30
DES J022247.88-043330.04 a | 1.635 | 20.24 | 45.45
DES J003234.33-431937.83 a | 1.641 | 19.40 | 45.79
DES J022224.82-062626.69 a | 1.641 | 20.16 | 45.48
DES J025254.18-001119.67 a | 1.641 | 21.25 | 45.05
DES J022716.52-050008.33 a | 1.642 | 20.50 | 45.35
DES J033437.58-275826.84 a | 1.648 | 18.69 | 46.08
DES J022008.73-045905.31 a | 1.649 | 20.52 | 45.35
DES J033657.91-274244.39 a | 1.649 | 20.14 | 45.50
DES J003015.00-430333.45 a | 1.650 | 19.97 | 45.57
DES J022029.60-051022.59 a | 1.652 | 20.68 | 45.28
DES J003143.64-425420.21 a | 1.662 | 20.03 | 45.55
DES J003548.43-431444.38 a | 1.673 | 20.47 | 45.38
DES J022424.16-043229.83 a | 1.674 | 20.32 | 45.44
DES J025340.94+001110.20 a | 1.675 | 18.31 | 46.25
DES J003956.32-442047.73 a | 1.680 | 20.08 | 45.54
DES J033903.66-293326.48 a | 1.684 | 21.85 | 44.84
Table 13: continued

C iv sample  DES ID $z$ $m_{r}$ $\log({\lambda}L_{1350})$ (erg s-1) DES
J003948.24-445323.16 a 1.684 19.59 45.74 DES J003635.93-434636.05 a 1.689
19.90 45.62 DES J025220.53+002735.19 a 1.690 19.86 45.63 DES
J021902.58-044628.33 a 1.694 19.92 45.61 DES J025356.07+001057.54 a 1.695
19.47 45.79 DES J003325.69-434826.13 a 1.696 20.26 45.48 DES
J024527.72-010602.84 a 1.696 20.05 45.56 DES J022445.77-061149.99 a 1.701
20.19 45.51 DES J022014.98-062253.15 a 1.716 19.91 45.63 DES
J024632.55-003439.14 a 1.724 19.87 45.65 DES J022134.97-070831.84 a 1.728
20.70 45.32 DES J032940.47-275143.61 a 1.730 19.87 45.66 DES
J022602.20-061626.10 a 1.736 19.97 45.62 DES J003206.50-425325.23 a 1.750
19.84 45.68 DES J033814.33-294213.78 a 1.750 19.94 45.64 DES
J033453.60-264121.34 a 1.751 20.14 45.56 DES J033817.74-290324.90 a 1.753
19.61 45.77 DES J022115.04-043155.51 a 1.757 21.33 45.09 DES
J033452.89-265215.54 a 1.757 19.10 45.98 DES J022117.44-063856.45 a 1.763
19.83 45.69 DES J024257.19-004549.41 a 1.770 21.08 45.20 DES
J022119.91-045948.62 a 1.770 20.76 45.32 DES J003120.86-425145.98 a 1.771
20.14 45.57 DES J004029.04-441704.97 a 1.783 20.04 45.62 DES
J003255.12-435757.56 a 1.784 20.07 45.61 DES J032759.97-271921.90 a 1.785
20.37 45.49 DES J024222.95-011527.57 a 1.785 20.24 45.54 DES
J033328.60-290314.66 a 1.787 19.58 45.80 DES J022027.32-045115.53 a 1.788
21.14 45.18 DES J022002.08-050101.91 a 1.791 19.69 45.76 DES
J022751.50-044252.66 a 1.795 20.60 45.40 DES J003939.41-444612.90 a 1.797
20.17 45.58 DES J022503.11-065258.79 a 1.798 20.09 45.61 DES
J032835.62-274406.09 a 1.800 19.94 45.67 DES J033722.89-274020.85 a 1.804
19.93 45.67 DES J003920.50-440441.16 a 1.814 19.79 45.74 DES
J003739.59-432521.40 a 1.815 20.40 45.49 DES J024635.61-000850.46 a 1.822
19.26 45.95 DES J033002.51-274858.28 a 1.823 20.70 45.38 DES
J033548.18-290943.65 a 1.826 20.33 45.53 DES J022352.09-064029.96 a 1.827
20.50 45.46 DES J022409.89-044718.00 a 1.832 20.11 45.62 DES
J033319.58-290431.65 a 1.833 20.73 45.37 DES J024716.32-010401.36 a 1.834
21.10 45.23 DES J033222.47-285935.09 a 1.837 20.68 45.40 DES
J033301.69-275818.80 a 1.840 20.94 45.29 DES J004014.18-431716.29 a 1.842
19.87 45.72 DES J021903.49-043935.00 a 1.845 20.48 45.48 DES
J024737.50-000458.97 a 1.847 19.88 45.72 DES J024608.67-013933.97 a 1.848
19.68 45.80 DES J022515.35-044008.91 a 1.850 19.82 45.75 DES
J025038.68-004739.06 a 1.856 18.67 46.21 DES J002729.28-431501.02 a 1.863
19.67 45.81 DES J024723.54-002536.48 a 1.864 19.42 45.92 DES
J022845.57-043350.18 a 1.864 17.41 46.72 DES J024748.87-000147.41 a 1.868
19.58 45.85 DES J024133.65-010724.20 a 1.874 20.86 45.34 DES
J003940.80-443718.32 a 1.875 19.49 45.89 DES J022047.63-051835.83 a 1.878
19.55 45.87 DES J021707.96-055152.07 a 1.885 19.70 45.82 DES
J033145.20-275435.75 a 1.891 21.19 45.22 DES J024242.50-002212.87 a 1.904
20.57 45.48 DES J022828.19-040044.25 a 1.905 18.31 46.38 DES
J003626.44-430820.66 a 1.907 19.80 45.79

Table 14: continued

C iv sample  DES ID $z$ $m_{r}$ $\log({\lambda}L_{1350})$ (erg s-1) DES
J022050.39-061748.80 a 1.908 21.89 44.95 DES J021953.45-061123.39 a 1.910
19.90 45.75 DES J003150.13-432726.88 a 1.912 18.68 46.24 DES
J022328.88-040134.71 a 1.915 19.82 45.78 DES J033739.88-272045.97 a 1.916
19.21 46.03 DES J033924.44-271250.15 a 1.918 20.52 45.51 DES
J025428.31+002418.43 a 1.918 20.42 45.55 DES J033415.37-265535.62 a 1.922
19.85 45.78 DES J033011.77-283636.65 a 1.922 20.99 45.32 DES
J022327.85-040119.16 a 1.922 20.81 45.39 DES J024639.22-012731.85 a 1.923
20.34 45.58 DES J022250.47-060104.89 1.925 21.54 45.10 DES
J022206.47-060746.70 1.927 20.89 45.36 DES J022514.39-044700.14 1.928 18.83
46.19 DES J034005.69-292312.82 1.928 19.04 46.10 DES J033701.63-282753.94
1.933 20.20 45.64 DES J034016.06-270925.57 1.935 19.72 45.84 DES
J033832.50-291215.65 1.935 20.77 45.41 DES J022537.03-050109.34 1.936 20.03
45.71 DES J033316.17-292917.48 1.947 19.95 45.75 DES J033607.36-263207.88
1.948 20.02 45.72 DES J033401.79-265054.28 1.952 19.72 45.84 DES
J033232.00-280309.98 1.954 19.98 45.74 DES J025233.79+004340.74 1.954 20.60
45.49 DES J033646.40-291617.17 1.956 20.47 45.54 DES J033052.19-274926.84
1.958 21.49 45.14 DES J033559.60-280324.41 1.965 20.60 45.49 DES
J024918.63+000548.34 1.966 20.66 45.47 DES J033650.66-293142.07 1.972 21.68
45.06 DES J032926.49-271844.01 1.978 20.33 45.61 DES J021949.99-064208.13
1.984 19.93 45.77 DES J033839.06-292351.17 1.987 20.33 45.61 DES
J025159.70-005159.89 1.988 21.84 45.01 DES J022812.23-043227.58 1.992 21.04
45.33 DES J004016.18-435116.09 1.995 19.98 45.75 DES J033912.95-273516.85
2.006 20.08 45.72 DES J032821.07-282055.17 2.011 19.50 45.95 DES
J022352.19-043031.68 2.012 19.75 45.85 DES J033040.28-274203.95 2.013 19.96
45.77 DES J022657.24-035944.42 2.018 20.17 45.68 DES J025019.26+003100.81
2.018 20.26 45.65 DES J022530.19-065458.19 2.030 19.49 45.96 DES
J032703.62-274425.27 2.031 19.45 45.98 DES J022034.93-052956.02 2.036 18.20
46.48 DES J034036.10-284811.29 2.039 20.13 45.71 DES J022629.26-043057.07
2.040 20.18 45.69 DES J002959.21-434835.24 2.041 17.77 46.65 DES
J022045.50-045121.91 2.045 19.92 45.80 DES J021935.78-064227.17 2.060 21.83
45.04 DES J003146.74-423601.03 2.061 19.54 45.95 DES J033635.40-280828.78
2.067 20.28 45.66 DES J021905.63-055958.78 2.069 20.11 45.73 DES
J003549.05-440236.08 2.072 19.23 46.08 DES J021957.25-043952.46 2.077 18.90
46.22 DES J004143.04-440234.42 2.081 20.32 45.65 DES J024453.25-011256.33
2.083 20.73 45.49 DES J024344.30-000201.08 2.083 20.04 45.77 DES
J032602.35-281031.00 2.085 20.01 45.78 DES J021850.07-050954.10 2.091 19.52
45.98 DES J021921.81-043642.21 2.092 20.04 45.77 DES J021941.16-044100.36
2.096 21.15 45.33 DES J033015.97-280219.79 2.097 20.18 45.72 DES
J004022.52-442820.25 2.100 19.42 46.02 DES J022431.59-052818.78 2.102 17.53
46.78

Table 15: continued

C iv sample  DES ID $z$ $m_{r}$ $\log({\lambda}L_{1350})$ (erg s-1) DES
J024628.49-004457.13 2.104 19.94 45.81 DES J003848.52-440202.07 2.105 19.72
45.90 DES J024357.91-005447.75 2.105 21.03 45.38 DES J022044.45-050905.95
2.108 21.19 45.32 DES J025209.79+000549.21 2.108 19.95 45.81 DES
J024756.35-001555.92 2.119 18.70 46.32 DES J022813.61-042251.65 2.121 19.63
45.95 DES J033640.29-284423.00 2.124 20.80 45.48 DES J024739.11-005221.01
2.124 20.50 45.60 DES J022411.52-060915.92 2.128 19.82 45.87 DES
J024550.79-004328.13 2.131 20.52 45.59 DES J003816.16-434647.44 2.141 19.54
45.99 DES J003936.81-443439.72 2.144 19.97 45.82 DES J022219.46-062539.66
2.146 19.04 46.19 DES J032829.96-274212.23 2.150 20.12 45.76 DES
J024632.44-003214.12 2.152 18.89 46.25 DES J021441.86-043709.03 2.152 22.17
44.94 DES J022028.95-045802.58 2.153 20.53 45.60 DES J033326.24-275829.85
2.161 20.53 45.60 DES J022351.07-044729.93 2.163 20.93 45.44 DES
J033217.15-271956.41 2.169 19.24 46.12 DES J032923.16-280022.78 2.175 19.77
45.91 DES J002913.21-433044.56 2.180 20.11 45.78 DES J025335.12-003039.26
2.184 20.41 45.66 DES J032939.97-284952.40 2.188 20.22 45.73 DES
J024557.22-000823.36 2.199 20.05 45.81 DES J022001.63-052216.92 2.219 20.17
45.77 DES J003320.08-430428.45 2.231 20.19 45.76 DES J024840.78-003548.15
2.235 18.89 46.28 DES J022358.64-045351.63 2.235 20.29 45.72 DES
J003448.83-442519.26 2.237 20.13 45.79 DES J033852.79-282256.93 2.246 19.78
45.93 DES J022402.32-061740.34 2.246 19.91 45.88 DES J002907.77-420916.39
2.247 20.77 45.54 DES J024907.29-000649.35 2.251 20.31 45.72 DES
J003743.89-434715.68 2.257 19.60 46.01 DES J022725.81-033837.75 2.257 18.20
46.57 DES J021757.52-045059.15 2.257 20.73 45.56 DES J003516.08-432451.82
2.260 19.47 46.06 DES J022557.62-045005.32 2.271 19.55 46.03 DES
J022229.62-044941.93 2.275 21.22 45.37 DES J033604.00-274203.95 2.277 21.41
45.29 DES J022729.22-043227.66 2.280 19.75 45.96 DES J033655.83-290218.23
2.283 19.41 46.09 DES J024204.58-003835.64 2.287 20.21 45.77 DES
J022451.98-041210.79 2.294 20.14 45.80 DES J022612.64-043401.32 2.306 21.08
45.43 DES J022748.85-042820.90 2.311 20.08 45.84 DES J022410.96-050653.95
2.315 20.66 45.60 DES J024950.74-004224.16 2.317 20.45 45.69 DES
J024520.05-004534.45 2.321 20.79 45.55 DES J021730.92-041823.54 2.322 19.75
45.97 DES J033843.76-294922.54 2.328 20.67 45.60 DES J022824.68-041545.71
2.328 19.63 46.02 DES J003436.78-440043.41 2.330 19.58 46.04 DES
J025128.73-002650.64 2.330 19.95 45.89 DES J022055.10-061842.21 2.340 21.09
45.44 DES J024337.15-002340.17 2.347 19.36 46.14 DES J033822.77-275910.73
2.349 19.64 46.02 DES J024505.03-003441.97 2.350 20.60 45.64 DES
J025033.20+003829.22 2.364 19.96 45.90 DES J004056.56-431446.40 2.384 19.56
46.07 DES J033734.80-294213.92 2.390 19.84 45.96 DES J033953.34-270053.36
2.410 18.53 46.49

Table 16: continued

C iv sample  DES ID $z$ $m_{r}$ $\log({\lambda}L_{1350})$ (erg s-1) DES
J003430.47-433311.36 2.415 20.75 45.60 DES J025102.06-004142.78 2.425 22.15
45.05 DES J032942.28-281906.69 2.436 20.42 45.74 DES J033605.57-290354.17
2.450 20.17 45.85 DES J022354.81-044814.94 2.452 18.74 46.42 DES
J022014.33-042917.10 2.458 19.30 46.20 DES J024511.94-011317.50 2.462 20.46
45.74 DES J024757.67+001542.65 2.467 20.87 45.57 DES J033430.30-275958.91
2.472 21.32 45.40 DES J022540.58-043825.15 2.477 20.27 45.82 DES
J032640.93-283206.80 2.492 20.28 45.82 DES J024717.40-000052.27 2.497 20.30
45.81 DES J003017.36-423144.34 2.497 20.00 45.93 DES J003957.42-434107.92
2.500 20.14 45.88 DES J033237.62-271448.07 2.519 20.30 45.82 DES
J033608.10-285245.81 2.522 20.30 45.82 DES J003145.23-424618.45 2.523 20.70
45.66 DES J033545.52-275451.69 2.540 20.28 45.83 DES J003341.34-420811.51
2.541 19.80 46.02 DES J033216.69-272411.37 2.547 19.77 46.04 DES
J022259.87-063326.65 2.563 20.60 45.71 DES J003547.38-430558.81 2.565 20.03
45.94 DES J022434.33-043200.27 2.568 20.06 45.93 DES J033518.30-275304.01
2.576 19.33 46.22 DES J003530.07-444539.88 2.587 20.06 45.93 DES
J003352.72-425452.55 2.593 19.10 46.32 DES J033331.37-275634.38 2.602 20.37
45.81 DES J024719.59-003313.11 2.607 20.48 45.77 DES J032739.71-281934.84
2.616 20.18 45.89 DES J034121.52-265901.04 2.621 19.44 46.19 DES
J021457.21-043011.44 2.636 18.34 46.63 DES J022104.88-060728.52 2.648 20.05
45.95 DES J022631.82-045127.47 2.655 20.77 45.66 DES J022330.15-043004.09
2.677 20.78 45.66 DES J021719.45-052305.27 2.695 19.36 46.23 DES
J022034.52-045132.47 2.732 20.40 45.83 DES J033944.09-284604.07 2.744 19.33
46.27 DES J022620.86-045946.48 2.745 21.30 45.48 DES J025223.48-003623.57
2.769 20.20 45.93 DES J033526.38-285747.93 2.770 18.08 46.78 DES
J033938.51-291019.54 2.778 21.16 45.55 DES J021921.22-044315.03 2.794 20.17
45.95 DES J022636.07-043428.92 2.801 19.88 46.07 DES J022354.85-054839.89
2.814 19.31 46.30 DES J021659.87-053203.49 2.818 17.60 46.99 DES
J022305.97-054015.26 2.823 20.04 46.01 DES J022321.26-055600.27 2.846 21.55
45.42 DES J022255.51-044410.32 2.871 20.31 45.92 DES J033720.58-272434.70
2.896 20.16 45.99 DES J003255.24-430948.41 3.010 19.57 46.26 DES
J022423.43-070627.92 3.030 21.48 45.50 DES J003318.29-434301.10 3.082 19.31
46.38 DES J033246.76-280846.78 3.180 19.17 46.47 DES J021438.15-052024.38
3.214 20.93 45.77 DES J025250.10+000830.68 3.237 20.27 46.04 DES
J003133.50-422953.97 3.248 20.62 45.90 DES J021906.24-041933.94 3.330 21.60
45.54 DES J033712.16-285146.74 3.364 20.33 46.06 DES J003411.44-424329.48
3.373 20.83 45.86 DES J002926.44-420752.35 3.403 19.71 46.32 DES
J022543.53-042834.48 3.411 20.64 45.95 DES J024325.96-003145.11 3.435 19.63
46.36 DES J022133.35-065713.47 3.440 20.16 46.15 DES J034122.60-291302.04
3.470 20.33 46.09

Table 17: continued

C iv sample  DES ID $z$ $m_{r}$ $\log({\lambda}L_{1350})$ (erg s-1) DES
J033512.61-292351.14 3.712 19.98 46.27 DES J024509.76-010001.28 3.807 20.58
46.05 DES J022144.21-062745.18 3.856 20.14 46.24

##  Appendix B H$\beta$ excluding objects with individual lags

The luminosity bins for the H$\beta$ sample excluding sources with individual
lags are shown in Figure 13, and the stacked CCF’s and average lags for this
reduced sample are given in Figure 14 and Figure 15. Only the two lowest (blue
and orange) and second highest (red) luminosity bins had objects excluded. The
stacked CCF peaks remain intact for each of these bins, although the signal-
to-noise degrades slightly, which is to expected as the size of the stacked
sample decreased by $\sim$one sixth. The average lags are in close agreement
to those recovered in the original analysis in §4. This test indicates that
the results from stacking are not dominated by objects with high quality
individual lags, although their addition does considerably improve the lag
uncertainties for the final result.

Figure 13: The same as Figure 2 after excluding sources with individual lag
recoveries.  Figure 14: The same as Figure 3 after excluding sources with
individual lag recoveries from the stacked sample.  Figure 15: The Radius-
Luminosity relation for H$\beta$ (dotted lines), including the stacked average
lag measurements made using the OzDES H$\beta$ sample after excluding sources
with individual lag recoveries, and existing individual lag measurements (same
as in Figure 4).

## Affiliations

1Research School of Astronomy and Astrophysics, Australian National
University, Canberra, ACT 2611, Australia
2School of Mathematics and Physics, The University of Queensland, St Lucia,
QLD 4101, Australia
3Department of Astronomy, The Ohio State University, Columbus, Ohio 43210, USA
4Center of Cosmology and Astro-Particle Physics, The Ohio State University,
Columbus, Ohio 43210, USA
5National Centre for the Public Awareness of Science, Australian National
University, Canberra, ACT 2601, Australia
6The Australian Research Council Centre of Excellence for All-Sky Astrophysics
in 3 Dimension (ASTRO 3D), Australia
7Sydney Institute for Astronomy, School of Physics, The University of Sydney,
NSW 2006, Australia
8Centre for Gravitational Astrophysics, College of Science, The Australian
National University, ACT 2601, Australia
9Laboratório Interinstitucional de e-Astronomia - LIneA, Rua Gal. José
Cristino 77, Rio de Janeiro, RJ - 20921-400, Brazil
10Department of Physics, University of Michigan, Ann Arbor, MI 48109, USA
11Fermi National Accelerator Laboratory, P. O. Box 500, Batavia, IL 60510, USA
12Departamento de Física Teórica and Instituto de Física de Partículas y del
Cosmos (IPARCOS-UCM), Universidad Complutense de Madrid, 28040 Madrid, Spain
13Institute of Cosmology and Gravitation, University of Portsmouth,
Portsmouth, PO1 3FX, UK 14Department of Physics & Astronomy, University
College London, Gower Street, London, WC1E 6BT, UK
15Instituto de Astrofisica de Canarias, E-38205 La Laguna, Tenerife, Spain
16Universidad de La Laguna, Dpto. AstrofÃsica, E-38206 La Laguna, Tenerife,
Spain
17Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of
Science and Technology, Campus UAB, 08193 Bellaterra (Barcelona) Spain
18Centre for Extragalactic Astronomy, Durham University, South Road, Durham,
DH1 3LE, UK
19Hamburger Sternwarte, Universität Hamburg, Gojenbergsweg 112, 21029 Hamburg,
Germany
20Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas
(CIEMAT), Madrid, Spain
21Institute of Theoretical Astrophysics, University of Oslo. P.O. Box 1029
Blindern, NO-0315 Oslo, Norway
22Kavli Institute for Cosmological Physics, University of Chicago, Chicago, IL
60637, USA
23University Observatory, Faculty of Physics, Ludwig-Maximilians-Universität,
Scheinerstr. 1, 81679 Munich, Germany
24Center for Astrophysical Surveys, National Center for Supercomputing
Applications, 1205 West Clark St., Urbana, IL 61801, USA
25Department of Astronomy, University of Illinois at Urbana-Champaign, 1002 W.
Green Street, Urbana, IL 61801, USA
26Santa Cruz Institute for Particle Physics, Santa Cruz, CA 95064, USA
27Center for Astrophysics $|$ Harvard & Smithsonian, 60 Garden Street,
Cambridge, MA 02138, USA
28Australian Astronomical Optics, Macquarie University, North Ryde, NSW 2113,
Australia
29Lowell Observatory, 1400 Mars Hill Rd, Flagstaff, AZ 86001, USA
30George P. and Cynthia Woods Mitchell Institute for Fundamental Physics and
Astronomy, and Department of Physics and Astronomy, Texas A&M University,
College Station, TX 77843, USA
31Institució Catalana de Recerca i Estudis Avançats, E-08010 Barcelona, Spain
32Observatório Nacional, Rua Gal. José Cristino 77, Rio de Janeiro, RJ -
20921-400, Brazil
33Department of Physics, Carnegie Mellon University, Pittsburgh, Pennsylvania
15312, USA
34Kavli Institute for Particle Astrophysics & Cosmology, P. O. Box 2450,
Stanford University, Stanford, CA 94305, USA
35SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA
36Department of Physics and Astronomy, Pevensey Building, University of
Sussex, Brighton, BN1 9QH, UK
37School of Physics and Astronomy, University of Southampton, Southampton,
SO17 1BJ, UK
38Computer Science and Mathematics Division, Oak Ridge National Laboratory,
Oak Ridge, TN 37831
39Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA 94720,
USA