2. Data and sample selection

Over the course of five years, DES imaged ten fields with approximately weekly cadence in the g, r, i, z bands, which OzDES followed up with spectroscopy at monthly cadence for six years (Lidman et al. Reference Lidman2020). DES imaging was performed on the CTIO Blanco 4-metre Telescope in Chile, while OzDES spectroscopy used the Anglo-Australian Telescope’s AAOmega spectrograph fed by the 2dF fibre positioner (for details see Lidman et al. Reference Lidman2020). While DES and OzDES were designed to discover supernovae and measure redshifts of their host galaxies, the program also had very good cadence for gathering AGN continuum light curves and spectroscopic response light curves needed for RM measurements. However, the seasonal observational window was not ideal for RM, with observations lasting roughly six months of the year for DES and five months for OzDES; this leaves large seasonal gaps in the RM light curves.

The 2dF instrument enables 400 spectra to be taken simutaneously, and about a quarter of its fibres were placed on AGN in each exposure. OzDES monitored a total of 771 AGN over six years (2013–2019) with redshifts between $0.127 \lt z \lt 3.451$ , gathering between 18 and 25 epochs on each AGN with a spectral resolution of $1\,400\lt R\lt 1\,700$ and a wavelength range of 3 700 to 8 800 $\unicode{x00C5}$ . The images and catalogues from the whole DES survey are available at https://des.ncsa.illinois.edu/releases/dr2. The OzDES spectra are available from https://docs.datacentral.org.au/ozdes/overview/dr2/.

We use the calibration procedures outlined in Hoormann et al. (Reference Hoormann2019) for spectroscopic measurements. We take DES photometry in the g, r and i bands (discarding any of low quality, lacking adequate calibration, or outliers), and then average measurements that were taken on the same night. These are used to calibrate the OzDES spectra for each source, correcting for wavelength-dependent losses due the finite size of the fibres, and these calibrated spectra are then used to identify reverberating emission lines, their variations in strength for RM, and their velocity dispersions for SMBH mass estimates; see Hoormann et al. (Reference Hoormann2019) for more detail. The OZDES spectra of all 29 AGN with measured CIV lags are shown in Figure 1.

Figure 1.

Mean spectra for all successfully recovered Civ sources. Note that the OzDES spectrum spans the wavelength range 3 800–8 800 Å, however, for visibility the plotting range has been restricted to 3 800–7 500 Å. The Civ line appears at $\sim$ 4 537 Å in the lowest redshift source and progresses towards the right as redshift increases (darker red indicates higher redshift). Some spectra show absorption features in the Civ line, which were severe enough in four sources to prevent an accurate linewidth measurement (see Table A1).

Figure 1. Long description

A line graph displays the flux in arbitrary units on the vertical axis and wavelength in angstroms on the horizontal axis. Multiple lines represent different sources, each labeled with a unique identifier. The lines vary in color from purple to yellow, indicating different redshift values, with darker red representing higher redshifts. The flux values range from 0 to over 300 arbitrary units, and the wavelength ranges from 4000 to 7000 angstroms. Each line shows distinct peaks and troughs, indicating the presence of spectral features such as emission and absorption lines. The graph illustrates how the spectral features shift with increasing redshift.

3. Civ lag recovery statistics

In total, there are 305 Civ sources in the DES/OzDES sample, although we expect only a fraction of them to provide recoverable lags. Based on projections made at the beginning of the OzDES campaign by King et al. (Reference King2015), we should expect between $\sim$ 20% and 30% successful recoveries from the Civ sample due to a number of limiting factors. Firstly, only a fraction of the AGN are likely to vary significantly during the time of our observations. Secondly, the expected low signal-to-noise ratio in the OzDES data leads to large uncertainties in the individual measurements. Finally, the seasonal gaps in our observing cadence make some time delays difficult to recover accurately, particularly those at half yearly intervals, e.g. 180 days, 540 days, etc. (Malik et al. Reference Malik2022), where there tend to be more false-positives unless strict selection cuts are made.

Using the quality cuts introduced in Penton et al. (Reference Penton2022), we ensure that we only select high-quality lag recoveries. In Table 1 we show the number of sources that pass each cut independently and cumulatively. Detailed descriptions of the cuts can be found in Penton et al. (Reference Penton2022), but in summary:

1. 1. Consistent with 0 at 3 $\sigma$ : The first cut removes the sources that either have broad and/or noisy posterior distributions that give them large uncertainties consistent with zero lag; this removes 50 sources (from 305 to 255).

2. 2. $|$ JAV. $-$ ICCF $| \lt $ 100 days: The second cut is based on the disparity between measurements made using ICCF and JAVELIN. This is not a cut that is often made in the literature, however, simulations by Penton et al. (Reference Penton2022) showed it to be important; it removes another 145 sources (from 255 to 110).

3. 3. The final pair of cuts splits the sample into bronze, silver, and gold. To make it into each sample both of the following criteria have to be passed to the appropriate level (as listed in Table 1).

   1. a. median $-$ peak ( $\lt x$ days): Do the median and peak of the JAVELIN lag distributions agree to within a certain number (x) of days?

   2. b. % in peak ( $\gt y$ %): Is there more than a certain percentage (y%) of the probability distribution in the JAVELIN primary peak?

These latter criteria penalise sources that have significant likelihood outside the primary (highest) peak.Footnote ^b We show three examples of recoveries, one each for gold, silver, and bronze, in Figures 2–4. These cuts result in 6 gold-standard sources, 6 silver, and 17 bronze. The simulations in Penton et al. (Reference Penton2022) show that gold, silver, and bronze all represent high-quality lags – the mean offset from the true lag ranges from 13 (gold) to 18 days (bronze) and the false detection percentage ranges from 12% (gold) to 19% (bronze).

Table 1.

Number of sources that remain after each quality cut, both independently and cumulatively. For example, the $|$ JAV $-$ ICCF $|$ cut removes 174 sources (305–131) if applied independently of the first cut, but only 145 sources (255–110) when applied after the first cut. Note that the pairs of cuts for gold, silver and bronze indicate the number that pass, firstly, only the cut on the difference between median and peak lag (median $-$ peak), and secondly, both the median $-$ peak and the peak proportion cuts for that rating.

Table 1. Long description

The table shows the number of sources that pass each quality cut both independently and cumulatively. It has 8 rows and 4 columns. The columns are labeled as follows: Categories, # Pass each cut indep., and # Pass each cut cumul. The row labels are: All, Consistent with 0 at 3, JAV.ICCF 100 days, Bronze median-peak (<110 days), Bronze % in peak (<33%), Silver median-peak (<80 days), Silver % in peak (<45%), Gold median-peak (<65 days), and Gold % in peak (<60%). The values in the table are as follows: Row 1: All, 305, 305. Row 2: Consistent with 0 at 3, 255, 255. Row 3: JAV.ICCF 100 days, 131, 110. Row 4: Bronze median-peak (<110 days), 146, 65. Row 5: Bronze % in peak (<33%), 85, 29. Row 6: Silver median-peak (<80 days), 127, 57. Row 7: Silver % in peak (<45%), 26, 12. Row 8: Gold median-peak (<65 days), 113, 52. Row 9: Gold % in peak (<60%), 13, 6.

The cut that has the biggest impact on the final number of recovered sources is the cut on the proportion of the lag posterior contained within the peak of the posterior (only 85 of the 305 AGN pass this criterion at the Bronze level). Given that we find that sources observed at higher redshifts often have lower signal-to-noise due to observational limitations, it is not surprising that a high-redshift sample would contain a significant number of low SNR posterior lag distributions.

When measuring high-quality black hole masses, a strict cut on this parameter is necessary, though it may be possible to instead use this information on a sliding scale.

4. Recovering black hole masses

Having collated a set of 29 time lags, we can now use them to measure the masses of their associated black holes. To compute a black hole mass, we use the virial equation:

(1) \begin{equation} M_{\textrm{BH}} = f\frac{c\,t_{\textrm{lag}} \Delta V^2}{G}, \end{equation}

where $t_{\textrm {lag}}$ denotes the time lag between the central SMBH and the BLR, so that $c t_{\textrm {lag}}$ is an estimate of the BLR radius; $\Delta V$ denotes the BLR velocity dispersion as measured from the reverberating emission line; and f represents the ‘virial factor,’ an empirical correction factor that accounts for the mean kinematic properties of all AGN including unknown inclination, internal kinematics, and other undetermined properties of the internal regions of the AGN. Multiple estimates for the virial factor are discussed in the literature, based on different data sets and different methodologies. In this work, we use the virial factor of $f=4.47\pm1.1$ based on the work by Woo et al. (Reference Woo, Yoon, Park, Park and Kim2015), as it is the most widely used – however, it is important to note that this was derived based on measurements for H $\beta$ . The uncertainty on this measurement is quite large, often being the dominant source of uncertainty in the mass measurements.

To measure the BLR velocity dispersion for each source we measure the linewidth of the Civ line. This is done by measuring the linewidth of the mean spectrum; however, this does come with limitations. There is some evidence showing that there are non-negligible contributions from outflows in the line profile of some Civ sources. Denney (Reference Denney2012) showed that high velocity outflows from the central region of AGN may cause widening on the blue side of the Civ line. This widening would make linewidth measurements using the mean spectrum possibly inaccurate since these outflows are not part of the orbital motion of the BLR clouds. This could be mitigated by using the RMS of the spectrum, thus showing only the parts of the line profile that are changing with time. Unfortunately, the signal-to-noise ratio of the OzDES spectra are insufficient to reliably measure linewidths of the RMS spectrum. However, for single epoch mass measurements, the majority of the outflows that have been observed cause shifts of less than $1\sigma$ in the velocity measurement. Therefore, this effect would be sub-dominant to the uncertainties in the virial factor and the lag uncertainty.

Figure 2.

An example of gold rated source, DES J022620.86-045946.48. In the photometric and spectroscopic lightcurves, we can see that there is a long term smooth variation that is present in both lightcurves. This is an important feature in most high quality lag measurements. This leads to a posterior for the lag (top right) with a sharp peak in both JAVELIN and ICCF. The smaller broader peaks at $\sim$ 180 days and $\sim$ 540 days correspond to seasonal gaps and are likely caused by aliasing.

Figure 2. Long description

Panel A: A line graph shows continuum flux over time, with the x-axis labeled MJD (days) and the y-axis labeled Continuum flux. The data points are plotted in blue, showing variations over the observed period. Panel B: Another line graph displays C IV line flux over time, with the x-axis labeled MJD (days) and the y-axis labeled C IV line flux. The data points are plotted in yellow, showing variations over the same period. Panel C: A histogram compares the normalized units of time lag using two methods, JAVELIN and ICCF. The x-axis is labeled Time lag (days), and the y-axis is labeled Normalized units (arbitrary). The JAVELIN data is shown in blue, and the ICCF data is shown in yellow, with a sharp peak around 300 days and smaller peaks at 180 days and 540 days. Panel D: A combined line graph shows flux over time, with photometry data in blue and spectroscopy data in yellow, which is shifted and scaled. The x-axis is labeled MJD (days), and the y-axis is labeled Flux (Arbitrary units). The graph illustrates the long-term smooth variation present in both photometric and spectroscopic light curves.

Figure 3.

An example of silver rated source, DES J002959.21-434835.24. In the original photometric and spectroscopic lightcurves we can see that there is a long term variation present in the photometric lightcurve, however in this case there is a less obvious signal in the spectroscopic lightcurve. This leads to a posterior for the lag with a sharp peak in both JAVELIN and ICCF accompanied by many smaller peaks. These smaller peaks are likely caused by aliasing given their location, however, since there is much more of the probability contained within them, this example is rated as having a lower quality lag measurement than the example shown in Figure 2.

Figure 4.

An example of bronze rated source, DES J032703.62-274425.27. In the photometric and spectroscopic lightcurves we can see that there is a variation in both lightcurves, however, with a generally lower signal-to-noise than seen in Figures 2 and 3, and very little temporal overlap due to seasonal gaps. This leads to a posterior for the lag with multiple sharp peaks in both JAVELIN and ICCF, however, the most prominent peak in both are the same, giving credibility to this measurement, albeit at lower confidence than the silver and gold samples.

Four of our 29 sources had successful lag measurements but their Civ line suffered from significant absorption features, preventing an accurate measure of line dispersion (see the first, second, fourth, and tenth spectra from the topFootnote ^c in Figure 1). As a result, we are left with 25 black hole mass measurements, which are presented in Appendix Table A1. Our stringent selection criteria mean that this sample is very robust. We find an intrinsic scatter in our radius-luminosity relation 2.5 times smaller than that in the SDSS sample ( $\sim0.2$ dex vs $\sim0.5$ dex); see Figure 7 of McDougall et al. (Reference McDougall2026a).

To assess how supermassive black holes have evolved over cosmic time we will require many more sources. To achieve this, McDougall et al. (in preparation) will leverage the results presented here to measure black hole masses of a larger sample. While we have only a limited number of reverberation mapped sources, there are thousands of AGN in the OzDES catalogue for which we have photometry and spectroscopy, just not over as long a time period. All of these represent a possible black hole mass measurement using the $R-L$ relation combined with a single-epoch spectroscopic velocity measurement. Future analyses will be able to apply these $R-L$ relations to even larger samples, such as those from SDSS, the Dark Energy Spectroscopic Instrument (DESI), and 4MOST (Swann et al. Reference Swann2019).

5. Selection effects, demographics, and the $R-L$ relation

In order to infer properties of the population of AGN as a function of redshift, one needs to consider the selection effects that impact the sample. The selection effects occur at two stages. First, did OzDES observe a representative sample of AGN? Second, of the observed AGN, which had successfully measured lags?

As a means of contrasting our mass measurements with a priori estimates, we use an $R-L$ relation from the literature (Grier et al. Reference Grier2019) to predict time lags for our entire sample, and combine that with the measured velocity dispersion, to give an estimate of the black hole mass. This allows us to estimate the distribution of lags and SMBH masses that are expected for the OzDES sample.Footnote ^d In Figure 5 we compare the 29 measured lags with the predicted lags inferred from the $R-L$ relation (Grier et al. Reference Grier2019),

(2) \begin{equation} \log R_{\rm BLR} ({\rm light-days}) = \beta + \alpha \log_{\rm 10}\frac{\lambda L_{\lambda}(1\,350\,\unicode{x00C5})}{10^{44}{\rm erg}^{-1}} \pm \epsilon,\end{equation}

where $R_{\rm BLR}$ is the radius of the broad line region in light-days, $\beta=1.15\pm0.008$ , $\alpha=0.51\pm0.05$ , and the intrinsic scatter is $\epsilon=0.15\pm0.03$ . Our results are consistent with the predictions, given the large uncertainties in the predictions.Footnote ^e

Figure 6 shows the distribution of our black hole mass measurements, compared to the masses one would expect based on the $R-L$ relation from Equations (2) to (1) with $f=4.47\pm1.1$ (Woo et al. Reference Woo, Yoon, Park, Park and Kim2015).

Figure 5.

The distribution of recovered rest frame lags and redshifts compared to the expected distribution of the OzDES sample based on the previous $R-L$ relation estimate of Grier et al. (Reference Grier2019).

We see the bulk of our successful black hole mass recoveries lie at relatively low redshift and that our success rate is better for lower black hole masses. There are several reasons for this:

• • Cadence and Seasonal Gaps: Short lags are difficult to constrain reliably given the monthly cadence of our observations, and the 6–8 month gaps between seasons. As discussed in Malik et al. (Reference Malik2022), filling in the seasonal gaps increases the chances of successfully measuring lags.

• • Survey duration: Time dilation lengthens the observer-frame duration of lags, which makes it difficult to observe very long lags at high redshift, as observed lags can become longer than the maximum duration of the survey. This has an important impact on the $R-L$ relation (see Section 5.1).

• • Variability time scale: Sources with longer lags indicate a larger BLR, which is generally correlated with longer-term variability (Lu et al. Reference Lu2019; Tarrant et al. Reference Tarrant2025), meaning they can be constrained even when there are large gaps in the data.

• • Variability amplitude: Smaller black holes, contained within lower luminosity AGN, tend to be more variable sources (MacLeod et al. Reference MacLeod2012). These sources will have lightcurves with higher variability and would therefore be more likely to be recovered.

• • Signal-to-noise: High-redshift targets tend to have lower signal-to-noise than low-redshift targets.

These selection effects can be seen in our black hole mass distribution. In the right panels of Figure 6, we show histograms of the black hole masses that we have measured through RM compared to those predicted by the $R-L$ relation. This comparison shows that, on average, OzDES successfully recovered lags more efficiently for the sources with lower black hole masses. This is primarily due to the smaller black holes having higher variability, and larger black holes hitting the duration limit of the survey (see Section 5.1).

Figure 6.

A comparison of the distribution of predicted black hole (BH) masses for the whole OzDES sample with the distribution of successfully measured black hole masses (in units of solar mass). The prediction uses the Grier et al. (Reference Grier2019) $R-L$ relation with $f=4.47\pm1.1$ from Woo et al. (Reference Woo, Yoon, Park, Park and Kim2015). The left panel shows the black hole masses plotted vs redshift, with the measured data coloured by its quality. The central panel shows a histogram of predicted masses compared to the successfully measured (observed) masses. The right panel shows the fraction of successful lags as a function of mass, showing the generally smaller masses of the black holes that had successful measurements relative to the input sample. Note also that we find a low recovery rate above a redshift $z=2.8$ , with no recoveries out of a possible $\sim$ 30, and no gold measurements above $z=2.35$ . This is likely due to low intrinsic variability of high-luminosity sources, the low signal-to-noise of high-redshift measurements, and time limit due to the maximum survey duration.

Both of these reasons are selection effects and are likely not indicative of individual black holes being less massive than expected. However, this does indicate that it is difficult to measure the very large black hole masses above $10^{10}\,{\rm M}_{\odot}$ with the survey structure and length of OzDES. A longer baseline and/or deeper spectroscopy would be required to measure these gargantuan black holes.

One final feature of importance is that many of the Civ observer-frame lags are expected to be in seasonal gaps, because at $2\lesssim z\lesssim 3$ time dilation shifts a rest-frame lag of 50 days to $\sim$ 150 to 200 days in the observer frame. We found that current lag recovery methods may be overly sensitive to aliasing effects due to seasonal gaps in the light curves. In future work, we aim to use the new LITMUS program to do AGN reverberation mapping (McDougall et al. Reference McDougall, Pope and Davis2026b), as this significantly improves on JAVELIN’s method of exploring the parameter space, reducing the impact of aliasing.

5.1 Selection effects’ impact on the Radius-Luminosity Relation

Measuring black hole masses is only one of the applications of this data set. In addition, we can construct a scaling relation based on the measured radius of the broad line region and the luminosity of the AGN. In McDougall et al. (Reference McDougall2026a) we re-derive the $R-L$ relation for all emission lines used by OzDES, so we defer to that paper for the new Civ $R-L$ relation both from OzDES and in combination with existing surveys.Footnote ^f

Here, we look at one important feature of the Civ sample that impacts the $R-L$ relation, namely the selection effect that arises due to survey duration. The observed duration of events is time-dilated by a factor of $1+z$ relative to the duration at emission (recent measurements from quasars and DES supernovae respectively include Lewis & Brewer Reference Lewis and Brewer2023; White et al. Reference White2024). Therefore, a lag of one year in the rest frame would appear as three years for a $z=2$ object. Due to the high redshift of the Civ sample, it is more affected by time-dilation than H $\beta$ or Mgii.

While exploring the $R-L$ relation in Penton (Reference Penton2023), we discovered a discrepancy between the $R-L$ relation constructed using the literature data points and that using only the data from this work. At first glance it appears that the high-luminosity sample of OzDES has a shallower slope than the literature data that extend to lower luminosities. There are multiple possible reasons for this distinction between low and high luminosity regimes. The first possibility is that there is an intrinsic difference between the sources in the different regimes. If there were an evolutionary difference between the populations, this could cause the disparity in the relations. On the other hand, there are possible observational biases that would prevent recoveries in certain parts of the $R-L$ relation. For example, if time lags on certain time scales are less likely to be successfully recovered, this could skew the $R-L$ relation. It is this selection effect we believe to be at play in the OzDES data.

In Figure 7 we plot lag vs redshift, colour coding the points by their luminosity. For this plot we include high-quality data from the literature as compiled in our companion paper (McDougall et al. Reference McDougall2026a), including data from H $\beta$ and Mgii lines (Peterson et al. Reference Peterson2005; Rosa et al. Reference Rosa2015; Grier et al. Reference Grier2019; Kaspi et al. Reference Kaspi, Brandt, Maoz, Netzer, Schneider, Shemmer and Grier2021a; Shen et al. Reference Shen2024). It is clear that higher luminosities tend to come from sources at higher redshifts.

A ramification of this can also be seen in Figure 7, where we draw contours of the approximate rest-frame lags that can be measured as a function of redshift. One cannot recover a lag longer than the survey duration, and ideally one wants the observing window to be significantly longer than the lag. So these contours (at 1 000 and 1 500 days in the observer frame) act as approximate upper limits to the lags we could detect (OzDES spanned approximately 2 150 days from the first to last observation).

Figure 7.

Compilation of data from the literature and this paper, showing rest-frame lags as a function of redshift, and coloured by the luminosity of the AGN. Blue shading shows the approximate upper limit of possible lag recoveries given typical survey durations (observer-frame lags of 1 000 and 1 500 days). Grey shading shows the approximate position of seasonal gaps. There is a decrease in the highest measurable rest-frame lag as redshift increases. This impacts Civ measurements the most and is an important selection effect for the Civ $R-L$ relation (see Figure 8). Data are from the compilation in McDougall et al. (Reference McDougall2026a), which includes Peterson et al. (Reference Peterson2005), Rosa et al. (Reference Rosa2015), Grier et al. (Reference Grier2019), Kaspi et al. (Reference Kaspi, Brandt, Maoz, Netzer, Schneider, Shemmer and Grier2021a), Shen et al. (Reference Shen2024) in addition to the OzDES measurements.

Figure 7. Long description

Panel A: A scatter plot showing the relationship between rest frame lag in days and redshift, colored by the luminosity of the AGN. The horizontal axis represents redshift, ranging from 0 to 3.5. The vertical axis represents rest frame lag in days, ranging from 10^0 to 10^3. The data points are color-coded according to the log luminosity of the AGN, with a color bar on the right indicating the luminosity values. The plot includes data from various surveys, with different markers for OzDES and other surveys. Blue shading indicates the approximate upper limit of possible lag recoveries given typical survey durations of 1000 and 1500 days. Grey shading shows the approximate position of seasonal gaps. There is a noticeable decrease in the highest measurable rest-frame lag as redshift increases.

This is compounded at high redshift by the fact that high-luminosity sources also have intrinsically longer lags (as seen in the $R-L$ relation). The cut-offs in Figure 7 can therefore be translated into cut-offs that could adversely affect the $R-L$ relation. Since there is not a direct correlation between luminosity and redshift, we have binned the data into seven luminosity bins, calculating the average ‘maximum lag’ measurable for the AGN in each of those bins. The result of this can be seen in Figure 8, which includes the same data sets as Figure 7.

Figure 8.

Compilation of data from the literature and this paper, showing rest frame lag vs luminosity. Shaded regions show the estimated upper limit of possible recoveries given the duration of typical large-scale surveys (averaging the limit shown in Figure 7 in luminosity bins). Note that at higher luminosities ( $L\gtrsim 10^{46}$ erg s $^{-1}$ ) the areas that are excluded due to survey duration start to impact regions where we expect data. Thus, there may be a bias towards points on the lower side of the $R-L$ relation at higher luminosities.

There is a clear ceiling where one would expect to see longer duration lags, but they are not detectable because the duration of the survey was insufficient to see the very delayed spectral response to the continuum variation. This is an important selection effect we need to correct for when deriving the $R-L$ relationship for Civ (see McDougall et al. Reference McDougall2026a).

Moving into the future, this bias will need to be carefully parameterised if we are to accurately derive the $R-L$ relation using even larger samples of high-redshift data. One can mitigate this effect by extending RM surveys to longer observational baselines, enabling them to recover longer rest-frame lags successfully. Such data will be necessary to conclusively rule out a flattening of the slope of the Civ $R-L$ relation. Notably, the DES supernova fields we used this AGN monitoring campaign continue to be monitored with the same instrument as DES (DECam) by the High-quality Extragalactic Legacy-field Monitoring (HELM) program (Zhuang et al. Reference Zhuang2024), resulting in a photometric sequence that spans more than a decade.