The Sloan Digital Sky Survey Reverberation Mapping Project: Initial C iv Lag Results from Four Years of Data

The parent sample of quasars consists of the 849 quasars monitored in the SDSS-RM field; details of this sample are provided by Shen et al. (2019b). We first restrict our sample to the 492 quasars with z > 1.3, i.e., quasars with observed-frame wavelength coverage of the C iv emission line in the BOSS spectra.

In many sources, however, the C iv emission line was not sufficiently variable to obtain RM measurements. Before performing our analysis, we thus first excluded sources whose C iv emission lines did not show significant variability over the span of our observations. To characterize the variability, we measured the C iv light curve variability signal-to-noise ratio (S/N) using the quantity S/N2, which is an output from the PrepSpec software (see Section 2.2 for a discussion of PrepSpec). S/N2 is defined as $\sqrt{{\chi }^{2}-\mathrm{DOF}}$, where χ² is calculated against the average of the light curve flux (using the measurement uncertainties of the light curves σ_i), and DOF is the degrees of freedom, which is equal to the number of points in the light curve −1. Larger values of S/N2 indicate that the null-hypothesis model of no variability is a poor description of the emission-line light curve, while smaller values indicate that the light curve is consistent with zero variability. We require that the S/N2 of the C iv emission line is greater than 20 for a quasar to be included in our sample (this number was chosen based on visual inspection of the PrepSpec fits, light curves, and rms residual line profiles). This criterion produced a final sample of 348 quasars, with redshifts ranging from 1.35 to 4.32. Basic information on these quasars is provided in Table 1, and Figure 1 displays the distributions of redshift, i-mag, and luminosity of the quasars in our final sample.

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We obtained the spectra used in this study during the first four years of observations for the SDSS-RM campaign (e.g., Shen et al. 2015a), which monitors 849 quasars with i < 21.7 at redshifts ranging from 0.1 to 4.5. The spectra were acquired with the BOSS spectrograph (Dawson et al. 2013; Smee et al. 2013), which covers a wavelength range of ∼3560–10400 Å. The spectrograph has a spectral resolution of R ∼ 2000 and the data are binned to 69 km s⁻¹ per pixel. We obtained a total of 68 epochs between 2014 January and 2017 July, with observations taken between January and July in each year only, leaving a gap of six months between observing seasons. The first year of SDSS-RM monitoring yielded 32 spectroscopic epochs and the additional three years of monitoring yielded 12 epochs each. Figure 2 displays the observing cadence for the observations.

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The 2014 spectra were processed using the standard SDSS-III pipeline (version 5_7_1); data from the subsequent years were processed using the updated SDSS-IV eBOSS reduction pipeline (version 5_10_1). We then further processed all spectra using a custom flux-calibration scheme described by Shen et al. (2015a), which improves the spectrophotometric calibrations by using additional standard stars observed on the plate.

To further enhance the relative flux calibration of the data, we employed a custom procedure using software referred to as PrepSpec²⁹ (this code is described in detail by Shen et al. (2015a, 2016) and Horne et al. (2019, in preparation)). PrepSpec models the spectra using a variety of different components, and applies a time-dependent flux correction that is calculated by using the narrow emission lines (when present) as a calibrator. The correction assumes that there is no intrinsic variability in the fluxes of the narrow emission lines over the course of the campaign—some observations of long-term changes in narrow-line flux in local, low-luminosity sources have been reported (e.g., NGC 5548; Peterson et al. 2013), but simple luminosity scaling from NGC 5548 predicts narrow-line variability timescales of >30 rest-frame years in our quasars.

The PrepSpec model includes intrinsic variations in the continuum and broad emission lines, and the model is optimized to simultaneously fit all of the spectra of an object. In addition to the intrinsic variability of the continuum and emission lines, PrepSpec also accounts for variations in seeing and small shifts in the wavelength solution. Various spectral measurements from PrepSpec using the first year of data only are presented by Shen et al. (2019b).

We use PrepSpec to improve our flux calibrations and subsequently to produce measurements of line fluxes, line widths, mean/rms profiles, and light curves for each emission line (and various continuum regions, depending on the wavelength ranges accessible for each object). We convolve our PrepSpec-corrected spectra with the SDSS filter response curves (Fukugita et al. 1996; Doi et al. 2010) to produce g- and i-band synthetic photometry for each quasar. To estimate the uncertainties in the synthetic photometric fluxes, we sum in quadrature the spectral uncertainties and the errors in the flux-correction factors reported by PrepSpec.

Before further analysis, we first removed any suspect epochs and outliers from our spectroscopic light curves. The seventh epoch is a significant outlier in a large fraction of the light curves; following Grier et al. (2017), we remove this epoch from all of our spectroscopic light curves. In addition, there are occasional spectra (roughly 4% of epochs) that have zero flux or are significant low-flux outliers in the light curves (these are cases where the BOSS spectrograph fibers were not plugged in correctly or the SDSS pipeline failed to extract a proper spectrum). We excluded all points with zero flux, as well as those that were offset from the median flux by more than five times the normalized median absolute deviation (NMAD) of the light curve (Maronna et al. 2006).

To improve the cadence of our continuum light curves, we also monitored the SDSS-RM field in the g and i bands with the Steward Observatory Bok 2.3 m telescope on Kitt Peak from 2014 to 2017, and the 3.6 m CFHT on Maunakea from 2014 to 2016. We used the Bok/90Prime instrument (Williams et al. 2004) for our observations; it has a 1° × 1° field of view, mapping the observations onto a 4k × 4k CCD with a plate scale of 045 pixel⁻¹. On the CFHT, we used the MegaCam instrument (Aune et al. 2003), which has a similar 1° × 1° field of view and a pixel scale of 0187. The observing cadence of the photometric observations is provided in Figure 2.

Following Grier et al. (2017), we adopted the image subtraction method as implemented in the software package ISIS (Alard & Lupton 1998; Alard 2000) to produce the photometric light curves. The basic steps are as follows: (1) the images are aligned; (2) the images with the best seeing, transparency, and sky background are used to create a reference image; (3) for each epoch, the reference image point-spread function (PSF) is altered to match that of the epoch, and a flux-calibration scale factor is applied to the target image; (4) the epoch and the reference image are subtracted, yielding a "difference" image that has the same flux calibration as the reference image; (5) a residual-flux light curve is produced by placing a PSF-weighted aperture over each source to measure the flux in the subtracted image.

We performed the image subtraction separately for each individual telescope, field, filter, and CCD, to obtain g- and i-band light curves for each quasar. Before further analysis, we removed problematic epochs from the light curves, such as epochs where the source fell on or near the edge of the detector, epochs where the sources were saturated or too close to a nearby saturated star, or epochs affected by cirrus clouds. As with our spectroscopy, epochs were identified as outliers in the light curves that deviated from the median flux by >5 times the NMAD of the light curve within each individual observing season (i.e., the NMAD was calculated using only data taken within a specific observing season, and outliers excluded from that season based on that NMAD alone, rather than the entire four-year light curve). We visually inspected all of the resulting light curves to confirm that this procedure was effective.

To improve the precision of our continuum light curves, we placed all of the light curves from different instruments, telescopes, fields, and in different bands onto the same flux scale—we hereafter refer to this as light-curve "intercalibration." This approach accounts for differences in detector properties, telescope throughputs, and properties specific to the individual telescopes. We combine both g- and i-band light curves together to increase the number of data points, assuming that the time lag between these two bands is negligible. Interband continuum lags have been measured for some of the SDSS-RM sample by Homayouni et al. (2019), but the measured lags are generally on the order of a week or less, which is smaller than the uncertainties for our lag measurements.

To combine our light curves, we use the Continuum REprocessing AGN MCMC (CREAM) software recently developed by Starkey et al. (2016). A brief overview of this technique is provided here; see Starkey et al. (2016) for details. CREAM models the light curves using Markov chain Monte Carlo (MCMC). The model assumes that the observed continuum emission is first emitted from a central "lamp post" and later reprocessed by more distant gas. Each telescope/field/CCD light curve is fit to a model that includes an additive offset, scaling parameter, and transfer function (for intercalibration purposes, we set the parameters within CREAM such that it has a delta function response at zero lag). After optimization via the MCMC fitting process, the rescaled g and i light curves are placed on the same scale as the reference light curve, and the resulting light curves are treated as a single light curve for all further analysis purposes. Figure 3 provides a demonstration of this procedure.

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The final step in our light-curve preparation considers the uncertainties in our data. The ISIS image subtraction software reports only local Poisson error contributions and neglects additional systematic uncertainties; our photometric/continuum light-curve uncertainties are thus generally underestimated by a factor of a few. Similarly, PrepSpec includes only spectral uncertainties in its emission-line flux calculations. To address this, we use an additional feature of the CREAM software that allows it to adjust the nominal error bars of the light curves. We used CREAM to search for extra variance within the light curves and apply a multiplicative correction to the uncertainties when they are underestimated. For our quasar sample, CREAM applied a median scale factor of 3.5 to correct the uncertainties in the continuum light curves and 2.6 for the emission-line light curves. We adopt the CREAM-scaled light curves and their adjusted uncertainties for all further analysis. Table 2 provides the final, intercalibrated light curves for each source with adjusted uncertainties.

Because we are using photometric light curves (including synthetic photometry produced from spectra) to represent the continuum light curves, we also investigate the emission lines that fall within the wavelength range covered by the g- and i-band filters. The broad emission lines are expected to be variable, and strongly variable emission lines falling within the wavelength range of the filters could have a significant impact on the photometric/continuum light curve. Significant variability contamination from the BLR would result in underestimated lag measurements, effectively making it more difficult to detect a lag.

Because the lag measurements depend on the observed variability, we need to know how much of that observed variability is due to the broad emission lines instead of the continuum. To estimate this, we use the PrepSpec measurements of intrinsic rms variability for the broad emission lines and continuum within the wavelength range covered by the g and i filters. The "variability contamination fraction" (hereafter f_var,BLR) is the sum of the variability contributions from each emission line within the FWHM of the filter: f_var,BLR = $\sum \left(\tfrac{{\mathrm{rms}}_{\mathrm{line}}}{{\mathrm{rms}}_{\mathrm{cont}}}\right)\left(\tfrac{{\mathrm{EW}}_{\mathrm{line}}}{\mathrm{FWHM}}\right)$. Here, rms_line and rms_cont are the PrepSpec-measured fractional rms variability of each broad emission line and the continuum nearest the filter effective wavelength, and EW_line is the observed-frame equivalent width of the emission line measured by Shen et al. (2019b). In our sources, this quantity is generally small, matching the expectation that the continuum is more variable than the emission lines (e.g., Sun et al. 2015). We find a median variability contamination fraction of 9.1% in the g band and 1.4% in the i band in our quasar sample. In other words, the BLR contamination is negligible for most of our sources, and will generally be smaller than the measured lag uncertainties.

We follow Grier et al. (2017), hereafter G17, and employ three lag detection methods to analyze our sample: The JAVELIN software (Zu et al. 2011), traditional cross-correlation functions (CCF; e.g., Peterson et al. 2004), and the CREAM software (Starkey et al. 2016). Details of each of these methods are provided in each of these works as listed; we provide only a brief synopsis of each method here.

Our primary method for time-lag detection is the JAVELIN code (Zu et al. 2011, 2013). We model the light curves as autoregressive processes using a damped random walk (DRW) model, which has been demonstrated to be a good description of quasar behavior on the timescales relevant to our study (e.g., Kelly et al. 2009; Kozłowski et al. 2010; MacLeod et al. 2010, 2012; Kozłowski 2016). JAVELIN accounts for all of the likely behavior of the light curves during gaps in the light curve, and applies uncertainties to the model accordingly. JAVELIN builds a model of both the continuum and emission-line light curves while simultaneously fitting a transfer function using Markov Chain Monte Carlo techniques. We assume that the emission-line light curves are smoothed, lagged versions of the continuum light curve, and adopt a top-hat transfer function that is parameterized by a scaling factor, width, and time delay. We allow JAVELIN to explore a range of observed lags from −750 to 750 days, which is about 60% of the total length of our campaign. We then determine τ_JAV, the best-fit time delay, from the posterior distribution of lags produced by the MCMC chain, after some modifications that are described below (Section 3.2).

Accurately modeling the light curves requires a well-constrained damping timescale (τ_DRW), and for the time baseline covered by our data, this quantity is not fit well by JAVELIN—for example, using simulated light curves, Kozłowski (2017) found that the light curves must span at least 10 times τ_DRW in order to obtain a reliable measurement. Prior RM studies using JAVELIN have fixed the value to be longer than the length of the observing campaign (e.g., Fausnaugh et al. 2016; Grier et al. 2017), which effectively negates the impact of this on the time-lag measurements. Because the time baseline of the data in this work is longer than the expected damping timescales, however, we here allow this parameter to vary in JAVELIN, but place a strong constraint on the τ_DRW parameter. For each source, we calculate the expected τ_DRW value based on Table 1 and Equation (7) of MacLeod et al. (2010), which relates the damping timescale to the luminosity of the quasar; this expected value (typically on the order of ∼400–600 days for our sample) is fed into JAVELIN as a starting point, with small allowable uncertainties, for the MCMC step. This prevents the software from fitting unphysically small damping timescales to the data. However, the lag measurements are quite insensitive to the τ_DRW value fit by JAVELIN; lag measurements obtained with and without setting this constraint are almost always consistent with one another. In addition, we also fixed the width of the top-hat transfer function to 20 observed-frame days; this helps keep JAVELIN from fitting unphysical values when the top-hat width cannot be constrained by our data. We tested several different top-hat widths (ranging from 10 to 40 days), and the lag results came out consistent with one another regardless of the width chosen: Fixing the top-hat width produces more clean posterior lag distributions than when it is allowed to vary, but the exact value of the chosen width has a negligible effect on our results.

Historically, CCF methods have been used most frequently to measure RM lags, so we include these measurements for completeness and ease of comparison with prior results. However, we note that these methods have been reported to perform less well on data sets with quality similar to ours (e.g., G17; Li et al. 2019); these data have more sparse time sampling and noisy light curves, compared to much of the RM data for local AGNs. This class of methods includes the interpolated cross correlation function (ICCF; e.g., Peterson et al. 1998), the discrete correlation function (DCF; Edelson & Krolik 1988) and z-transformed DCF (zDCF; Alexander 1997). We adopted the ICCF method, as it has been used most often in previous studies and has also been shown to perform better than the DCF in cases of low sampling (White & Peterson 1994). The ICCF linearly interpolates between data points on a user-specified grid, and the CCF is constructed by calculating the Pearson coefficient r between the two light curves at each possible lag. The centroid of the CCF (τ_cent) is measured using points surrounding the maximum correlation coefficient r_max of the CCF. We used the PyCCF code³⁰ (Peterson et al. 1998; Sun et al. 2018) to perform our ICCF calculations with an interpolation grid spacing of two days, and again restricted our lag search to lags between −750 and 750 days. We calculate the best lag measurement and its uncertainties via the flux randomization/random subset sampling method, using Monte Carlo simulations, as discussed by Peterson et al. (2004). We perform 5000 realizations to obtain the cross correlation centroid distribution (CCCD) and adopt the median of the distribution; the uncertainties in either direction are set to the 68th percentile of the distribution.

As an additional check, we report the lags measured by CREAM, which also measures time delays while performing the intercalibration of the light curves discussed above. CREAM is similar to JAVELIN in many ways, but it assumes a random walk model (where the Fourier transform of the time series is inversely proportional to the square of the frequency) instead of a DRW model to interpolate the light curves (Starkey et al. 2016). During the intercalibration process, CREAM fits a top-hat transfer function to the emission lines and reports the posterior probability distribution of lag values, from which we measure the best-fit lag (τ_CREAM).

One of the hazards of obtaining RM data with regular seasonal gaps is the potential for lag-detection algorithms to prefer lags that result in the light curves being shifted into the seasonal gaps in the data; i.e., because RM lag detection algorithms interpolate or model within these gaps, they often end up associating features in the real continuum light curves with "fake" (i.e., model or interpolated) data in the shifted emission-line light curves. Inopportune features in the light curves can cause various lag-detection methods to latch onto incorrect lags (e.g., Grier et al. 2008). In addition, these data (and single-season data) often possess multiple significant peaks in their lag posterior distributions that can easily be identified as aliases of a primary lag solution; including the entire posterior distribution in the lag calculation in these cases often results in a skewed lag measurement and/or uncertainties that are unreasonably large.

To remedy these issues, we require additional procedures beyond simply measuring the lags from the entire posterior distributions for each method. We adopt a procedure similar to that used by G17 (see their Section 3.2), but modified to take into account the effects of seasonal gaps on the data. We apply a weight on the distribution of τ measurements in the posterior probability distributions—this weight is used to search for the primary peak of the distribution and establish a range of lags within the posterior distribution that are included in the final lag and uncertainty calculations. Our weighting procedure has two components:

• 1.  
  The first component takes into account the number of overlapping spectral epochs at each time delay. Applying a time lag τ to the emission-line light curve will shift the data such that fewer "real" points will overlap. If the time lag is such that the shift results in little or no overlap between the two data sets (for example, a τ of 180 days in data sets with regular seasonal gaps of six months), detecting that lag will be very difficult. Any potential detection of such a lag in our data has a relatively high probability of being spurious, therefore we downweight such lags in the posterior distribution. We calculate the function P(τ) = [N(τ)/N(0)]², where N(τ) is the number of real emission-line data points that overlap in date ranges with the continuum data and N(0) is the number of overlapping points at τ = 0. Thus, the weight on a lag measurement is 1 at τ = 0 and decreases each time a data point moves outside the data overlap regions. Because our data have regular annual gaps of six months, P(τ) rises and falls as each segment of the light curve is shifted into and out of the overlapping ranges of each year of data.
• 2.  
  The second component accounts for the effect our seasonal gaps will have on our ability to detect certain lags. To characterize this phenomenon, we compute the autocorrelation function (ACF) of the continuum variations. If the ACF declines rapidly, the annual gaps will have a significant effect on our sensitivity because we are less likely to account correctly for the light-curve behavior during the gaps. In cases where the ACF declines slowly away from zero lag, it is straightforward to interpolate across the seasonal gaps, and the gaps are thus less likely to have an effect on our lag measurements.

The final weight that we apply to the posterior distributions is thus a convolution of the continuum ACF and the P(τ) function, with one small adjustment: if the ACF drops below zero within our lag range, we set its value at that lag to zero before the convolution. Figure 4 shows two examples of these functions (one with a rapidly declining ACF and one with a slowly declining ACF). We smooth the weighted posterior lag distributions (for JAVELIN and CREAM, this is the posterior lag distribution, and in the case of the cross-correlation function, this is the CCCD) by a Gaussian kernel with a width of 15 days, and identify the tallest peak within this smoothed distribution as the "primary" peak. We identify local minima in the distribution to either side of the peak and adopt these minima as the minimum and maximum lags to be included in our final lag calculation. We then return to the unweighted posteriors, reject all lag samples that lie outside the determined range, and use the remaining samples to calculate the final lag and its uncertainties.

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The best lag is taken to be the median of the distribution, with the uncertainty in either direction calculated using samples within the 68th percentile of the distribution. Figure 5 provides a demonstration of this procedure for one of the quasars in our sample. We tested this alias removal approach with mock light curves (with known lags) that mimic the SDSS-RM data, and found that this approach is very efficient in removing alias lags (Li et al. 2019).

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While our alias-removal procedure above mitigates the problem of lag aliases and seasonal gaps, these methods are not foolproof. The fact remains that, in some cases, the lags are just not well-measured, despite the models reporting their best solutions. Following G17, we thus impose a number of additional criteria on our measurements for a lag to be considered a significant detection:

• 1.  
  The lag can be positive or negative, but must be inconsistent with zero at 1σ significance.
• 2.  
  Less than half of the posterior lag samples can be removed by our alias-removal procedure described in Section 3.2. If this procedure eliminates a larger fraction of samples, it indicates that most of the samples lie outside of the primary peak that we identified, suggesting that we lack a solid measurement of τ.
• 3.  
  The behavior of the light curves must be well-correlated at or near the measured lag, as characterized by the Pearson correlation coefficient r measured by the ICCF. We include only measurements of quasars for which r reaches a value greater than 0.5 within ±1σ of the reported lag (see below for a discussion of how this threshold was chosen).
• 4.  
  When selecting our quasar sample, we required that the emission-line light curves showed some variability (see Section 2.1). However, after merging the light curves and adjusting the uncertainties of the light curves, some sources are no longer significantly variable. We thus require that both the continuum and emission lines are still considered significantly variable after the intercalibration process. To quantify this variability, we follow G17 and measure the rms variability S/Ns in the merged/adjusted light curves. We require that the continuum and emission-line rms variability S/N (S/N_con and S/N_line) are greater than 6.5 and 2.0, respectively. This criterion effectively eliminates cases where the light curves are consistent with little-to-no real variability, which can result in the lag detection methods latching onto monotonic trends or spurious correlations between noisy light curves. Roughly 20% of the 348 quasars do not meet this criterion for S/N_line. However, all but two of those sources also fail additional criteria, and would thus not have been selected as significant lags regardless.

Detailed simulations addressing the quality of lag detections yielded by our procedures are presented by Li et al. (2019). To determine the thresholds for r_max, S/N_con, and S/N_line, we utilize a positive/negative false-positive test as implemented by Shen et al. (2016), G17, and Li et al. (2019). We assume that there is no physical reason to measure a negative lag; if all lag measurements were due to spurious correlations rather than physical processes, we would expect to measure equal numbers of positive and negative lags in our sample (the nonuniform temporal sampling pattern in our data does not bias our results toward either positive or negative lags³¹ ). We can thus use the number of negative lag measurements to estimate the rate of false-positive detections at positive lags in our sample. We define the "false-positive rate" as the ratio of negative lags to positive lags. Even including all of our lowest-quality measurements, we see a strong preference for positive lags: without imposing any selection criteria at all, we have 253 positive measurements and 95 negative measurements (see Figure 6), which indicates a false-positive rate of 37%. We provide all 348 measurements, as well as the quantities via which we measure their significance, in the Appendix in Table 5.

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We choose the thresholds for our selection criteria described above in order to lower our false-positive rate to an acceptable level while maximizing the number of positive lag detections. We choose a maximum acceptable false-positive rate of 10%. Figure 6 shows the resulting distribution of lags for both those deemed "insignificant" and those passing our selection criteria. By downselecting the sample to a false-positive rate of 10%, we exclude many true lags: based on the false-positive rate without imposing our additional constraints, we expect that our sample has on the order of ∼100 additional measurable lags. Such lags may be recoverable with additional years of data.

We adopt JAVELIN as our primary lag-detection method and therefore require that all of our significance criteria are satisfied specifically for the JAVELIN measurements. This results in 48 positive lag detections and five negative measurements in our full "primary" sample of lag detections.

For comparison purposes, we apply these selection criteria separately to the lags measured with all three methods. In about 2/3 of our lag measurements, the resulting lags from all three methods are consistent with one another (see Figure 7). As reported by G17 and others (e.g., Li et al. 2019), the ICCF generally produces larger uncertainties than JAVELIN and CREAM, and the ICCF is less sensitive than JAVELIN to lag detection with light-curve qualities similar to SDSS-RM (Li et al. 2019). There has been some discussion in the literature (e.g., Edelson et al. 2019) regarding the uncertainties reported by JAVELIN; i.e., it has been suggested that JAVELIN uncertainties are underestimated. However, recent work by two independent groups suggests that the JAVELIN lag uncertainties are actually more representative of the true uncertainties than those reported by the ICCF method, provided that the JAVELIN assumption of Gaussian light-curve uncertainties is satisfied (Li et al. 2019; Yu et al. 2019). In addition, we note that 41 out of 48 of our significant lags were also formally detected by the ICCF method, which has been found to overestimate the lag uncertainties, and while we chose 1σ as our detection threshold, all but four of them are >2σ detections. Our detections are thus robust against the possibility that the uncertainties reported by JAVELIN are underestimated to within a reasonable extent.

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For about a third of our measurements, the ICCF or CREAM software reported different alias lags than JAVELIN; in these cases, a different primary peak was identified, resulting in lag disagreements. In all of these cases, we see the same peaks present for all three methods, but their strengths vary, causing different lags to be preferred by different methods. In these cases, the different lags are frequently one-year aliases of one another. We have visually inspected all of the cases where the three measurement methods disagree, and can confirm that the peaks identified by JAVELIN are reliable in most cases. Those cases where the JAVELIN lags appear to be incorrect are taken into account with our lag measurement quality ratings (discussed in Section 3.4).

3.4.1. Quality Ratings

Though our false-positive test (Figure 6) indicates that the majority of our lag measurements are robust, because our lag-selection procedure uses statistical arguments and we apply our criteria to achieve a false-positive rate of 10%, it is statistically likely that the lag sample presented here contains false detections. A subset of our lag detections have characteristics indicating that they are more likely to be real than others. Thus, we follow G17 and assign quality ratings to each of our measurements, in order to help readers assess the results. We use a scale of 1–5, with 1 representing the lowest-quality measurements and 5 representing the highest-quality measurements. We took into account a variety of criteria when assigning these quality ratings:

• 1.  
  There are variability features visible in the continuum light curve that also appear in the emission-line light curve; i.e., it is possible to pick out a "lag" between the two light curves by eye.
• 2.  
  There is clearly defined structure corresponding to the C iv emission line in the rms line profile (see Figure 12 in the Appendix).
• 3.  
  The model fits from JAVELIN and CREAM match the light-curve data well, and there is general agreement in the models between the two methods.
• 4.  
  The ICCF has a clear, well-defined peak on or around the measured lag.
• 5.  
  There is general agreement between the three different methods used.
• 6.  
  Unimodality of the posterior lag distribution: If there are several other peaks with strengths comparable to that of the peak that was determined to be the primary one, this reduces our confidence in a lag measurement.

We include these quality ratings, assigned by the first author of this work, in Table 3. In addition, we place all of the measurements with quality ratings of 4 and 5 into a "gold sample" of lag measurements that represent our highest-confidence individual measurements. Our gold sample includes 16 sources. We note that the criteria used to rate the lag measurements are subjective and based primarily on our prior experience with RM measurements. Thus, our gold sample is not statistically meaningful and should not be interpreted as such.

Table 3.  SDSS-RM Observed-frame Lag Detections

		τJAV	τCCF	τCREAM	Qualitya
RMID	z	(days)	(days)	(days)	Rating
000	1.463	${322.8}_{-90.1}^{+105.6}$	${463.9}_{-163.4}^{+33.7}$	$-{675.2}_{-22.6}^{+48.4}$	2
032	1.720	${62.0}_{-9.8}^{+9.5}$	${57.5}_{-34.8}^{+61.7}$	${67.4}_{-22.8}^{+2.1}$	5
036	2.213	${605.2}_{-93.1}^{+50.1}$	${416.4}_{-162.5}^{+104.2}$	${601.1}_{-31.9}^{+30.8}$	1
052	2.311	${187.1}_{-19.4}^{+10.4}$	${107.9}_{-21.7}^{+22.8}$	${100.3}_{-14.4}^{+21.7}$	4
057	1.930	${610.4}_{-16.5}^{+31.2}$	${137.6}_{-14.8}^{+150.0}$	${187.1}_{-19.2}^{+16.8}$	1
058	2.299	${614.0}_{-24.4}^{+19.5}$	${84.8}_{-41.8}^{+62.5}$	${177.4}_{-53.0}^{+43.9}$	1
130	1.960	${663.8}_{-112.1}^{+36.8}$	${631.8}_{-55.6}^{+59.7}$	${178.9}_{-29.4}^{+10.9}$	2
144	2.295	${591.2}_{-139.3}^{+102.9}$	${256.9}_{-189.2}^{+156.3}$	${573.6}_{-115.7}^{+96.1}$	2
145	2.138	${567.8}_{-14.9}^{+14.7}$	${306.9}_{-79.5}^{+109.4}$	${200.0}_{-28.4}^{+28.5}$	3
158	1.477	${91.0}_{-64.6}^{+46.0}$	${145.1}_{-102.1}^{+83.4}$	${127.0}_{-66.3}^{+46.0}$	3
161	2.071	${553.0}_{-19.5}^{+17.2}$	$-{193.4}_{-126.7}^{+346.4}$	$-{190.0}_{-17.4}^{+55.0}$	2
181	1.678	${274.9}_{-27.1}^{+13.3}$	${273.3}_{-81.6}^{+71.8}$	${272.6}_{-19.7}^{+13.5}$	4
201	1.797	${115.5}_{-54.4}^{+89.6}$	${90.8}_{-131.3}^{+99.6}$	${76.4}_{-101.7}^{+98.9}$	3
231	1.646	${212.8}_{-20.0}^{+16.6}$	$-{668.1}_{-84.1}^{+90.1}$	${208.2}_{-26.9}^{+15.8}$	3
237	2.394	${169.4}_{-15.0}^{+22.4}$	$-{534.1}_{-22.9}^{+22.9}$	${165.0}_{-14.5}^{+20.7}$	2
245	1.677	${286.6}_{-76.6}^{+61.4}$	${60.1}_{-78.3}^{+64.9}$	${284.6}_{-58.2}^{+39.4}$	2
249	1.721	${67.8}_{-8.3}^{+26.5}$	${62.0}_{-36.8}^{+85.3}$	${64.3}_{-5.5}^{+34.3}$	4
256	2.247	${139.5}_{-38.7}^{+52.9}$	${140.0}_{-84.7}^{+159.0}$	${151.6}_{-34.7}^{+34.7}$	5
269	2.400	${670.3}_{-42.8}^{+8.0}$	${100.0}_{-47.9}^{+34.0}$	${160.1}_{-12.5}^{+15.2}$	1
275	1.580	${209.1}_{-63.0}^{+21.0}$	${198.0}_{-24.5}^{+25.8}$	${156.6}_{-43.0}^{+4.9}$	5
295	2.351	${549.0}_{-17.9}^{+27.4}$	${549.7}_{-62.7}^{+72.5}$	${186.4}_{-21.9}^{+8.9}$	3
298	1.633	${279.5}_{-83.5}^{+49.3}$	${216.6}_{-80.9}^{+169.9}$	${299.9}_{-95.1}^{+27.4}$	4
312	1.929	${166.7}_{-19.5}^{+33.4}$	${207.6}_{-22.4}^{+28.1}$	${196.4}_{-29.1}^{+43.4}$	4
332	2.580	${292.1}_{-40.9}^{+20.0}$	${299.9}_{-69.5}^{+83.3}$	${292.8}_{-35.3}^{+12.3}$	4
346	1.592	${186.2}_{-29.3}^{+61.6}$	${67.1}_{-111.9}^{+225.9}$	${181.1}_{-30.2}^{+56.5}$	3
362	1.857	${224.9}_{-27.2}^{+17.9}$	${227.9}_{-30.8}^{+36.8}$	${218.6}_{-34.1}^{+16.9}$	2B
386	1.862	${109.4}_{-55.2}^{+37.7}$	${103.1}_{-55.5}^{+32.9}$	${104.5}_{-55.2}^{+40.8}$	2
387	2.427	${104.0}_{-11.7}^{+67.3}$	${165.9}_{-118.1}^{+118.8}$	${97.5}_{-15.8}^{+12.0}$	4
389	1.851	${639.5}_{-51.4}^{+20.3}$	${99.1}_{-19.7}^{+21.8}$	${149.6}_{-36.6}^{+31.9}$	2
401	1.823	${133.8}_{-25.0}^{+43.0}$	${171.1}_{-41.5}^{+103.7}$	${138.1}_{-29.8}^{+35.7}$	4
408	1.742	${487.9}_{-20.5}^{+32.7}$	${460.8}_{-73.0}^{+62.4}$	$-{564.7}_{-4.4}^{+3.7}$	3B
411	1.734	${678.8}_{-106.6}^{+57.7}$	${677.9}_{-111.0}^{+53.2}$	${144.7}_{-19.4}^{+34.7}$	2
418	1.419	${199.6}_{-40.9}^{+66.9}$	${141.8}_{-32.9}^{+124.9}$	${203.1}_{-43.5}^{+28.9}$	4
470	1.883	${57.5}_{-11.4}^{+124.6}$	${79.1}_{-50.8}^{+183.2}$	${58.4}_{-7.1}^{+5.2}$	4
485	2.557	${474.3}_{-18.5}^{+80.5}$	${494.0}_{-78.2}^{+39.0}$	${476.3}_{-23.2}^{+83.3}$	3
496	2.079	${609.4}_{-20.2}^{+29.9}$	${217.9}_{-76.0}^{+223.9}$	${275.4}_{-103.1}^{+32.4}$	1
499	2.327	${560.8}_{-119.5}^{+67.8}$	${544.1}_{-86.9}^{+123.1}$	${289.6}_{-163.6}^{+106.4}$	2
506	1.753	${637.6}_{-30.6}^{+36.5}$	${60.1}_{-21.7}^{+19.7}$	${142.2}_{-27.0}^{+25.3}$	1
527	1.651	${138.6}_{-32.3}^{+40.1}$	${125.4}_{-71.7}^{+35.3}$	${123.7}_{-64.7}^{+17.2}$	5
549	2.277	${228.9}_{-23.6}^{+17.4}$	${225.7}_{-29.0}^{+103.6}$	${229.2}_{-21.3}^{+25.5}$	4
554	1.707	${525.1}_{-33.0}^{+55.2}$	${517.0}_{-69.3}^{+91.7}$	${556.2}_{-44.1}^{+58.7}$	3
562	2.773	${597.9}_{-129.2}^{+68.7}$	${642.0}_{-103.0}^{+37.9}$	${45.2}_{-212.5}^{+150.2}$	2
686	2.130	${202.6}_{-19.8}^{+39.4}$	${163.3}_{-153.5}^{+180.0}$	${200.2}_{-20.2}^{+21.6}$	2
689	2.007	${474.0}_{-126.9}^{+68.7}$	${317.1}_{-178.2}^{+131.7}$	${120.8}_{-12.5}^{+27.5}$	2
722	2.541	${148.7}_{-46.6}^{+46.4}$	$-{711.1}_{-15.8}^{+43.6}$	${193.5}_{-23.4}^{+34.1}$	1B
734	2.324	${289.9}_{-36.5}^{+46.1}$	${225.9}_{-76.8}^{+127.1}$	${288.0}_{-55.6}^{+47.3}$	5
809	1.670	${290.1}_{-135.3}^{+73.9}$	${52.7}_{-161.3}^{+95.3}$	$-{2.9}_{-13.6}^{+13.9}$	1
827	1.966	${408.4}_{-57.6}^{+54.4}$	${38.3}_{-72.8}^{+73.2}$	${81.8}_{-17.6}^{+3.8}$	3

Note.

^aLag quality rating (see Section 3.4). Quasars with significant BAL presence that affected our line width measurements (see Section 3.4.2) are identified with a "B" following their numerical rating.

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3.4.2. Broad Absorption-line Contamination

We identify significant positive lags in 48 quasars in our primary sample. Of these, 16 are deemed to be high-confidence lags that constitute our "gold sample" of lag detections. All 48 positive lag measurements that constitute our sample are listed in Table 3. Light curves, model fits, and posterior lag distributions are shown for all of our positive lag detections in Figure 8.

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To place our measurements on the C iv R_BLR−L relationship, we measure logλL_λ1350, the luminosity at 1350 Å, from the PrepSpec model fits. In our 10 lowest-redshift sources, 1350 Å was not covered by the spectrum; in these sources, we measure the luminosity at 1700 Å and convert the values to logλL_λ1350 by multiplying L_λ1700 by factor of 1.09, which was computed from the mean quasar luminosities reported in Table 3 of Richards et al. (2006). The uncertainties on the luminosity measurements provided in Table 1 include only statistical uncertainties; due to the variability of the quasars, the actual uncertainties in the average quasar luminosities are somewhat higher. To quantify this additional source of uncertainty, we calculate the standard deviation in the flux at 1350 Å for our targets and add it to the statistical uncertainties.

Figure 9 shows the location of our sources on the R_BLR−L relation. Previous recent measurements of the relation included only ∼15 sources (Lira et al. 2018; Hoormann et al. 2019); our measurements raise this number to 63. In addition, our measurements span two orders of magnitude in luminosity in a region that was previously unpopulated on the C iv R_BLR−L relation. In general, our measurements lie fairly close to the locations expected based on previously measured R_BLR−L relations.

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We use the LINMIX procedure described by Kelly (2007) to fit a new relationship including our new measurements, which includes a measurement of the intrinsic scatter of the relation. We fit the relation in the form

$$\begin{eqnarray}&&\mathrm{log}\ \displaystyle \frac{{R}_{\mathrm{BLR}}}{(\mathrm{light} \mbox{-} \mathrm{days})}=a+b\times \mathrm{log}\displaystyle \frac{\lambda {L}_{\lambda }(1350\,\mathring{\rm A} )}{{10}^{44}\,\mathrm{erg}\,{{\rm{s}}}^{-1}}+\epsilon ,\end{eqnarray} \tag{ 2 }$$

where is the intrinsic random scatter of the relation. The resulting line fits are shown in Figure 9. Including our entire sample of significant lags, we measure a slope of b = 0.51 ± 0.05, an intercept of a = 1.15 ± 0.08, and an rms intrinsic scatter ${\left\langle {\epsilon }^{2}\right\rangle }^{1/2}=0.15\pm 0.03$. Our measured slope is consistent with the most recent measurements by Lira et al. (2018) and Hoormann et al. (2019), though somewhat shallower than earlier measurements by Peterson et al. (2005) and Kaspi et al. (2007). In addition, our measured intercept is larger than that measured by Hoormann et al. (2019). Previous studies used a variety of methods to measure the line fit; for comparison purposes, we also fit our relation using the Bivariate Correlated Errors and Intrinsic Scatter (BCES) method (Akritas & Bershady 1996), implemented with the publicly available code of Nemmen et al. (2012). Results from the BCES method are consistent with those using LINMIX.³²

Because our full sample likely includes some false-positive measurements, we also fit the relation while including only the measurements in our gold sample (see Section 3.4) and the previously reported measurements. We measure a slope of b = 0.52 ± 0.04, an intercept of a = 0.92 ± 0.08, and ${\left\langle {\epsilon }^{2}\right\rangle }^{1/2}=0.11\pm 0.04.$ The slope is consistent with that measured using our full sample, as well as with that measured by Hoormann et al. (2019) and Lira et al. (2018).

We caution that the fit of the R_BLR−L relation here (and in earlier work) does not take into account selection effects in the sample, which have several effects on the appearance of the R_BLR−L relation. For example, visual inspection suggests that there is some tension between our results and those at higher luminosities from Lira et al. (2018) and Hoormann et al. (2019); our measurements, when separated from the others, would indicate a steeper slope of the relation. This tension is due to a selection effect: none of these studies is capable of measuring rest-frame lags in the 800–1000 days range within their quasar sample. Thus, the highest-luminosity end of this relation cannot currently include measurements above the measured relation and must be composed only of measurements that scatter below the relation. To fully address this issue, we require additional data for such high-luminosity sources from campaigns with extended time baselines.

Similarly, our study is unable to detect lags longer than ∼750 observed-frame days. At the luminosities of most of our sources, this is long enough for us to detect lags. However, at the high-luminosity end of our sample (logλ_Lλ > 45.5), the expected rest-frame time lags based on the R_BLR−L relation are on par with the rest-frame time lag threshold for the range of redshifts of our sample. It is thus likely that we are missing some of the lags at the high-luminosity end of our sample range, due to their likely scatter above the relation (and thus above our detection threshold; this causes the apparent "flattening" effect that is visible when considering only our measurements). However, the finite observation baseline is unlikely to be affecting the detected lag measurements themselves; Figure 9 shows that the majority of our measurements fall well below the rest-frame equivalent of our 750 days detection threshold (for example, 750 observed-frame days translates to 250 rest-frame days for a quasar at a redshift of 2). This suggests that our lag measurements themselves are unlikely to be biased low due to the observed-frame lag detection limit of 750 days; if this were the case, we would expect many of our measurements to lie close to the upper detection limit. While a more detailed treatment/investigation of these issues is beyond the scope of this work, Li et al. (2019) and Fonseca Alvarez et al. (2019) have investigated this issue for the Hβ-detected lag sample using simulations, and both studies come to similar conclusions regarding selection effects for Hβ lag measurements.

Future high-luminosity measurements from data spanning long timescales will continue to shed light on the slope and scatter of the relation; however, the lack of measurements at the low-luminosity end is also problematic. The only two measurements in sources with luminosities below 10⁴³ erg s⁻¹ lie below our measured relation. It could be that these measurements are consistent with the relation to within the expected intrinsic scatter; additionally, there may be an intrinsic difference in the accretion and/or line-emission region between low-luminosity sources and the high-luminosity quasars that populate much of the relation. Future RM experiments in the UV focused on local, low-luminosity AGNs would be greatly beneficial in determining whether this is the case, as well as in more concretely constraining the slope of this relation.

A more detailed quantification of the selection effects on the measured R_BLR−L relation is beyond the scope of this paper, and will be investigated with future SDSS-RM work that specifically focuses on the R_BLR−L relation using simulations similar to those performed by Li et al. (2019) and Fonseca Alvarez et al. (2019). For this reason, the preliminary C iv R_BLR−L relation presented here is primarily used as a sanity check on the bulk reliability of our C iv lags, and we do not recommend its usage for other applications (e.g., SE masses).

For each quasar, we measure M_BH with Equation (1) using our adopted rest-frame time lags from JAVELIN and line widths measured by PrepSpec during the fitting process. We adopt σ_line,rms as our line width measurement to compute the virial product, as past studies (e.g., Peterson 2011) have suggested that σ_line,rms is a less biased estimator for M_BH than the FWHM, for a number of reasons. For example, the relationship between FWHM and σ_line is not linear, which can cause the underestimation of low masses and the overestimation of high masses when FWHM is used. In addition, FWHM measurements can often be significantly affected by narrow line components; see, e.g., Wang et al. (2019) for a recent discussion on this topic. However, this issue is still in contention, so we include several different characterizations of line width in Table 4. We again note that some of our objects have significant BAL contamination that has affected the PrepSpec fits (see Section 3.4.2); we flag such cases in Table 4 and caution that M_BH measurements for these sources may be inaccurate.

Table 4.  Line Width, Virial Product, and M_BH Measurements

		τfinalb	σline,mean	σline,rms	FWHMmean	FWHMrms	VP	MBHc
RMIDa	z	(days)	(km s−1)	(km s−1)	(km s−1)	(km s−1)	(107 M⊙)	(107 M⊙)
000	1.463	${131.1}_{-36.6}^{+42.9}$	1807 ± 106	2144 ± 46	3509 ± 74	4380 ± 87	${11.8}_{-5.4}^{+5.8}$	${52.6}_{-24.3}^{+25.9}$
032	1.720	${22.8}_{-3.6}^{+3.5}$	1805 ± 15	2017 ± 10	2768 ± 22	5010 ± 20	${1.8}_{-0.7}^{+0.7}$	${8.1}_{-3.2}^{+3.2}$
036	2.213	${188.4}_{-29.0}^{+15.6}$	2905 ± 19	3900 ± 34	4906 ± 18	7975 ± 129	${55.9}_{-22.3}^{+21.1}$	${249.9}_{-99.8}^{+94.4}$
052	2.311	${56.5}_{-5.9}^{+3.1}$	1397 ± 7	1322 ± 22	3258 ± 11	3354 ± 67	${1.9}_{-0.7}^{+0.7}$	${8.6}_{-3.3}^{+3.2}$
057	1.930	${208.3}_{-5.6}^{+10.6}$	1592 ± 7	1682 ± 12	2652 ± 8	3944 ± 25	${11.5}_{-4.2}^{+4.3}$	${51.4}_{-19.0}^{+19.1}$
058	2.299	${186.1}_{-7.4}^{+5.9}$	2695 ± 24	3412 ± 30	3564 ± 95	7512 ± 121	${42.3}_{-15.7}^{+15.6}$	${189.0}_{-70.0}^{+69.9}$
130	1.960	${224.3}_{-37.9}^{+12.4}$	4084 ± 18	4324 ± 36	5986 ± 25	7923 ± 44	${81.8}_{-33.2}^{+30.5}$	${365.8}_{-148.2}^{+136.3}$
144	2.295	${179.4}_{-42.3}^{+31.2}$	2830 ± 14	2792 ± 19	4419 ± 39	7222 ± 74	${27.3}_{-11.9}^{+11.1}$	${122.0}_{-53.4}^{+49.7}$
145	2.138	${180.9}_{-4.7}^{+4.7}$	3321 ± 25	3408 ± 16	5220 ± 65	7976 ± 41	${41.0}_{-15.1}^{+15.1}$	${183.3}_{-67.7}^{+67.7}$
158	1.477	${36.7}_{-26.1}^{+18.6}$	2043 ± 74	2136 ± 31	3621 ± 80	4888 ± 40	${3.3}_{-2.6}^{+2.0}$	${14.6}_{-11.7}^{+9.1}$
161	2.071	${180.1}_{-6.4}^{+5.6}$	2342 ± 16	2524 ± 20	2938 ± 17	4950 ± 38	${22.4}_{-8.3}^{+8.3}$	${100.1}_{-37.0}^{+37.0}$
181	1.678	${102.6}_{-10.1}^{+5.0}$	2116 ± 49	2721 ± 34	3024 ± 32	4533 ± 49	${14.8}_{-5.7}^{+5.5}$	${66.3}_{-25.3}^{+24.6}$
201	1.797	${41.3}_{-19.5}^{+32.0}$	1861 ± 6	2408 ± 117	5413 ± 39	4061 ± 44	${4.7}_{-2.8}^{+4.0}$	${20.9}_{-12.5}^{+17.9}$
231	1.646	${80.4}_{-7.5}^{+6.3}$	3326 ± 49	3803 ± 18	6496 ± 56	11792 ± 35	${22.7}_{-8.6}^{+8.5}$	${101.5}_{-38.6}^{+38.2}$
237	2.394	${49.9}_{-4.4}^{+6.6}$	2711 ± 13	2779 ± 23	5428 ± 34	6442 ± 30	${7.5}_{-2.8}^{+2.9}$	${33.6}_{-12.7}^{+13.2}$
245	1.677	${107.1}_{-28.6}^{+22.9}$	3910 ± 61	3953 ± 86	6847 ± 64	7031 ± 64	${32.6}_{-14.9}^{+13.9}$	${145.9}_{-66.4}^{+62.2}$
249	1.721	${24.9}_{-3.1}^{+9.7}$	1461 ± 10	1640 ± 15	2388 ± 14	2601 ± 29	${1.3}_{-0.5}^{+0.7}$	${5.8}_{-2.3}^{+3.1}$
256	2.247	${43.0}_{-11.9}^{+16.3}$	1720 ± 22	1802 ± 24	2440 ± 39	3565 ± 49	${2.7}_{-1.3}^{+1.4}$	${12.2}_{-5.6}^{+6.4}$
269	2.400	${197.2}_{-12.6}^{+2.4}$	2671 ± 27	3547 ± 30	3575 ± 25	6937 ± 99	${48.4}_{-18.1}^{+17.8}$	${216.4}_{-80.9}^{+79.8}$
275	1.580	${81.0}_{-24.4}^{+8.2}$	2027 ± 7	2406 ± 5	2992 ± 12	6943 ± 22	${9.2}_{-4.4}^{+3.5}$	${40.9}_{-19.5}^{+15.6}$
295	2.351	${163.8}_{-5.3}^{+8.2}$	2434 ± 20	2446 ± 19	4139 ± 32	6402 ± 41	${19.1}_{-7.1}^{+7.1}$	${85.5}_{-31.6}^{+31.8}$
298	1.633	${106.1}_{-31.7}^{+18.7}$	2045 ± 20	2549 ± 35	3176 ± 22	5177 ± 51	${13.5}_{-6.4}^{+5.5}$	${60.2}_{-28.5}^{+24.6}$
312	1.929	${56.9}_{-6.7}^{+11.4}$	4289 ± 33	4291 ± 30	8553 ± 89	10248 ± 53	${20.5}_{-7.9}^{+8.6}$	${91.4}_{-35.3}^{+38.3}$
332	2.580	${81.6}_{-11.4}^{+5.6}$	2945 ± 100	4277 ± 33	3813 ± 290	7828 ± 32	${29.1}_{-11.5}^{+10.9}$	${130.2}_{-51.3}^{+48.8}$
346	1.592	${71.9}_{-11.3}^{+23.8}$	2183 ± 33	3055 ± 29	3385 ± 54	5864 ± 57	${13.1}_{-5.2}^{+6.5}$	${58.5}_{-23.4}^{+29.0}$
362*	1.857	${78.7}_{-9.5}^{+6.3}$	3541 ± 39	4326 ± 44	5829 ± 42	12041 ± 151	${28.7}_{-11.1}^{+10.8}$	${128.5}_{-49.8}^{+48.4}$
386	1.862	${38.2}_{-19.3}^{+13.2}$	1839 ± 26	2187 ± 41	2935 ± 31	3756 ± 70	${3.6}_{-2.2}^{+1.8}$	${15.9}_{-10.0}^{+8.0}$
387	2.427	${30.3}_{-3.4}^{+19.6}$	2181 ± 11	2451 ± 23	3733 ± 18	4797 ± 30	${3.6}_{-1.4}^{+2.6}$	${15.9}_{-6.1}^{+11.8}$
389	1.851	${224.3}_{-18.0}^{+7.1}$	3790 ± 12	4064 ± 15	5014 ± 49	7740 ± 27	${72.3}_{-27.3}^{+26.7}$	${323.2}_{-121.9}^{+119.5}$
401	1.823	${47.4}_{-8.9}^{+15.2}$	2517 ± 9	3321 ± 12	3754 ± 19	10120 ± 497	${10.2}_{-4.2}^{+5.0}$	${45.6}_{-18.8}^{+22.3}$
408*	1.742	${177.9}_{-7.5}^{+11.9}$	2519 ± 22	3872 ± 29	4130 ± 159	9227 ± 536	${52.1}_{-19.3}^{+19.5}$	${232.7}_{-86.3}^{+87.1}$
411	1.734	${248.3}_{-39.0}^{+21.1}$	2375 ± 36	2490 ± 39	3535 ± 35	6024 ± 70	${30.0}_{-12.0}^{+11.4}$	${134.3}_{-53.8}^{+50.8}$
418	1.419	${82.5}_{-16.9}^{+27.6}$	2542 ± 23	3110 ± 23	2952 ± 22	6159 ± 44	${15.6}_{-6.6}^{+7.8}$	${69.6}_{-29.3}^{+34.7}$
470	1.883	${19.9}_{-4.0}^{+43.2}$	2401 ± 31	2317 ± 60	3957 ± 46	5028 ± 70	${2.1}_{-0.9}^{+4.6}$	${9.3}_{-3.9}^{+20.5}$
485	2.557	${133.4}_{-5.2}^{+22.6}$	2919 ± 26	3961 ± 41	5422 ± 37	8535 ± 82	${40.8}_{-15.1}^{+16.6}$	${182.5}_{-67.6}^{+74.0}$
496	2.079	${197.9}_{-6.6}^{+9.7}$	2076 ± 29	2409 ± 45	2477 ± 38	5620 ± 73	${22.4}_{-8.3}^{+8.3}$	${100.2}_{-37.1}^{+37.2}$
499	2.327	${168.5}_{-35.9}^{+20.4}$	3007 ± 32	3085 ± 26	3233 ± 33	6371 ± 49	${31.3}_{-13.3}^{+12.1}$	${139.9}_{-59.5}^{+54.3}$
506	1.753	${231.6}_{-11.1}^{+13.3}$	3378 ± 24	3510 ± 24	4174 ± 21	9354 ± 35	${55.7}_{-20.7}^{+20.8}$	${248.9}_{-92.5}^{+92.8}$
527	1.651	${52.3}_{-12.2}^{+15.1}$	3380 ± 55	3587 ± 34	5263 ± 106	8306 ± 53	${13.1}_{-5.7}^{+6.1}$	${58.7}_{-25.6}^{+27.5}$
549	2.277	${69.8}_{-7.2}^{+5.3}$	1840 ± 64	2176 ± 21	4081 ± 54	4995 ± 53	${6.5}_{-2.5}^{+2.4}$	${28.8}_{-11.0}^{+10.9}$
554	1.707	${194.0}_{-12.2}^{+20.4}$	2286 ± 29	2229 ± 35	3636 ± 37	5609 ± 52	${18.8}_{-7.0}^{+7.2}$	${84.1}_{-31.4}^{+32.2}$
562	2.773	${158.5}_{-34.2}^{+18.2}$	2034 ± 21	2078 ± 27	4544 ± 47	5189 ± 37	${13.4}_{-5.7}^{+5.2}$	${59.7}_{-25.5}^{+23.0}$
686	2.130	${64.7}_{-6.3}^{+12.6}$	2126 ± 20	2203 ± 27	3839 ± 26	4847 ± 37	${6.1}_{-2.3}^{+2.6}$	${27.4}_{-10.4}^{+11.4}$
689	2.007	${157.6}_{-42.2}^{+22.9}$	1281 ± 7	1407 ± 5	2253 ± 17	2791 ± 17	${6.1}_{-2.8}^{+2.4}$	${27.2}_{-12.4}^{+10.8}$
722*	2.541	${42.0}_{-13.2}^{+13.1}$	3560 ± 108	8571 ± 122	6892 ± 62	17233 ± 4743	${60.2}_{-29.1}^{+29.1}$	${269.1}_{-130.1}^{+130.0}$
734	2.324	${87.2}_{-11.0}^{+13.9}$	2978 ± 50	3405 ± 40	6296 ± 103	7042 ± 65	${19.7}_{-7.7}^{+7.9}$	${88.2}_{-34.4}^{+35.4}$
809	1.670	${108.6}_{-50.7}^{+27.7}$	4748 ± 42	4749 ± 96	11172 ± 92	11743 ± 700	${47.8}_{-28.4}^{+21.4}$	${213.7}_{-127.0}^{+95.7}$
827	1.966	${137.7}_{-19.4}^{+18.3}$	995 ± 9	1443 ± 13	2772 ± 19	2393 ± 134	${5.6}_{-2.2}^{+2.2}$	${25.0}_{-9.9}^{+9.8}$

Notes.

^aQuasars with significant BAL inference on the C iv emission line (see Section 3.4.2) are flagged with an asterisk. These sources may have incorrect line width measurements. ^bMeasurements are in the quasar rest frame. ^cVirial products were converted to M_BH using f = 4.47, as measured by Woo et al. (2015).

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When calculating the uncertainties in the virial products, we follow G17 and add a 0.16 dex uncertainty in quadrature to the statistical uncertainties (which are calculated via standard propagation) to account for systematic uncertainties that have not been taken into account, following the 0.16 dex standard deviation among the many different mass determinations of NGC 5548 (Fausnaugh et al. 2017). To convert the virial products into M_BH, we adopt f = 4.47 (Woo et al. 2015). All virial products and M_BH measurements are provided in Table 4. Our M_BH measurements range from about 10⁸ to 10¹⁰ solar masses, and are among the most massive SMBHs to have RM mass measurements (see Figure 10).

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Figure 11 compares our RM M_BH measurements with SE M_BH estimates from Shen et al. (2019b). We add systematic uncertainties of 0.4 dex to the SE measurements to the measurement uncertainties in the Shen et al. (2019b) values (e.g., Vestergaard & Peterson 2006; Shen 2013). The SE and RM measurements are largely consistent within their (large) uncertainties for many quasars; however, there is noticeable scatter around a one-to-one relation. Our C iv lags are consistent with the previously measured R_BLR−L relation from which the SE estimators are derived, so we are unsurprised to see so many that are consistent; however, given the uncertainties around C iv SE M_BH estimates (see Section 1), we are also unsurprised to see cases with inconsistencies. A detailed analysis of the reliability of SE mass measurements is beyond the scope of this work, but will be addressed thoroughly in future work dedicated to improving SE mass estimators.

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