Space Telescope and Optical Reverberation Mapping Project. V. Optical Spectroscopic Campaign and Emission-line Analysis for NGC 5548

To place the instrumental fluxes on an absolute flux scale, we measured the narrow [O iii] λ5007 line flux from spectra taken under photometric conditions and scaled all other nightly spectra to have the same [O iii] flux. There were 21 epochs identified as having been observed under photometric conditions by the MDM observers. We determined the flux of the [O iii] line (λ_observed = 5093 Å) by first subtracting a linear fit to continuum windows on either side of the line and then integrating over a fixed wavelength range. We used the rest-frame wavelength ranges 4976.5–4948.0 Å and 5027.7–5031.6 Å to fit the continuum and integrated over the range 4980.5–5026.7 Å for the line flux. The 2σ outliers from this set of [O iii] flux measurements were discarded, the mean was recomputed, and this process was repeated until there were no more 2σ outliers, which resulted in a total of 16 final photometric spectra. The mean spectrum of these 16 epochs has an [O iii] λ5007 line flux of (5.01 ± 0.11) × 10⁻¹³ erg s⁻¹ cm⁻², which represents our best estimate of the true [O iii] flux for NGC 5548 during this campaign and is not expected to vary over a 6-month period. For comparison, Peterson et al. (2013) found the [O iii] flux in NGC 5548 to be (4.77 ± 0.14) × 10⁻¹³ erg s⁻¹ cm⁻² in their 2012 monitoring campaign, and the difference is within the range of total [O iii] variability observed for NGC 5548 over the course of 21 yr (see Peterson et al. 2013).

In addition to the intrinsic variability of the AGN, many other factors contribute to nightly variations in the spectra. These include changes in transparency due to clouds, changes in seeing conditions, inconsistent instrument focus, and miscentering of the AGN in the slit during observations. We used the flux-scaling method described by van Groningen & Wanders (1992) to align the nightly spectra and place them on a consistent flux scale. For each spectrum in the data set, the algorithm looks for a combination of wavelength shift, multiplicative scale factor, and Gaussian kernel convolution that minimizes the residual between each individual spectrum and a reference spectrum over a region containing the narrow [O iii] line.

We constructed a separate reference spectrum for each telescope by averaging the highest-S/N spectra in each data set and then broadened the reference spectrum so that the [O iii] line width matches the broadest [O iii] line width in the data set. This extra broadening of the reference spectrum helps to reduce the [O iii] residuals from spectral scaling (Fausnaugh 2016). We then scaled each spectrum to have the same [O iii] flux as the photometrically calibrated mean MDM spectrum. This brings all spectra to a common flux scale after spectral scaling.

To assess the accuracy of spectral scaling, we estimated the intrinsic fractional variability of the residual [O iii] λ5007 light curve after correcting for random measurement errors,

$$\begin{eqnarray}&&{F}_{\mathrm{var}}=\displaystyle \frac{\sqrt{{\sigma }^{2}-\langle {\delta }^{2}\rangle }}{\langle f\rangle },\end{eqnarray} \tag{ 3 }$$

where σ² is the [O iii] flux variance, $\langle {\delta }^{2}\rangle$ is the mean-square value of the measurement uncertainties determined from the nightly error spectra produced by the data reduction pipeline, and $\langle f\rangle$ is the unweighted mean flux. The F_var for the [O iii] λ5007 light curve gives a good estimate of the residual flux-scaling errors (Barth & Bentz 2016), and the value for each telescope is listed in the last column of Table 1. We found F_var to be between 0.27% and 0.62% for all telescopes, which means that there is an additional scatter of less than 1% in the [O iii] light curve above the measurement errors. These F_var values are consistent with or better than the best values typically obtained in ground-based campaigns. For example, Barth et al. (2015) found F_var values ranging from 0.5% to 3.3% for individual AGNs in the 2011 Lick AGN Monitoring Project.

Figure 2 shows (in black) the mean and rms residual spectra for the MDM data set. The rms spectrum indicates the degree of variability at each wavelength over the course of the campaign. Both the broad Hβ and He ii λ4686 emission lines exhibit strong variations, and the Hβ rms profile appears to have multiple peaks. Traditionally, the rms spectrum is constructed such that the value at each wavelength is taken to be the standard deviation of fluxes from all epochs, but this does not take into account Poisson or detector noise, which may bias the rms profile by a small amount (Barth et al. 2015). Park et al. (2012b) suggest using the S/N for each spectrum as the weight for that spectrum in calculating the rms, or using a maximum-likelihood method to obtain the rms. We adopt a simpler approach that uses the excess variance as a way to exclude variations that are not intrinsic to the AGN. This "excess rms" value at each wavelength is defined as

$$\begin{eqnarray}&&{\rm{e}}-{\mathrm{rms}}_{\lambda }=\sqrt{\displaystyle \frac{1}{N-1}\displaystyle \sum _{i=1}^{N}[{({F}_{\lambda ,i}-\langle {F}_{\lambda }\rangle )}^{2}-{\delta }_{\lambda ,i}^{2}]},\end{eqnarray} \tag{ 4 }$$

where N is the total number of spectra in the data set, $\langle {F}_{\lambda }\rangle$ is the mean flux at each wavelength, and F_λ,i and δ_λ,i are the wavelength-specific fluxes and associated measurement uncertainties from individual epochs, respectively. This method estimates the degree of variability above what is expected given the measurement uncertainties and pixel-to-pixel noise.

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To more accurately remove the continuum underlying the emission lines and to deblend the broad emission features from each other, we employed the spectral decomposition algorithm described by Barth et al. (2015). The components fitted in this procedure include narrow [O iii], broad and narrow Hβ, broad and narrow He ii, Fe ii emission blends, the stellar continuum, and the AGN continuum. The host-galaxy starlight was modeled with an 11 Gyr, solar-metallicity, single-burst spectrum from Bruzual & Charlot (2003). For the Fe ii model component, we tested three different templates from Boroson & Green (1992), Véron-Cetty et al. (2004), and Kovačević et al. (2010). The Fe ii templates were broadened by convolution with a Gaussian kernel in velocity. The free fit parameters for Fe ii include the velocity shift relative to broad Hβ, the broadening kernel width, and the flux normalization of the broadened template spectrum. The Boroson & Green (1992) and Véron-Cetty et al. (2004) templates are monolithic and require only one flux normalization parameter, whereas the Kovačević et al. (2010) template has five components that can vary independently in flux. The Kovačević et al. (2010) template achieves the best fit to the nightly spectra, presumably a result of the larger number of free fit parameters due to the multicomponent Kovačević et al. (2010) template.

We made several modifications to the spectral fitting procedures used by Barth et al. (2015). First, because of the complex line profiles, we used sixth-order Gauss–Hermite functions (van der Marel & Franx 1993) to fit the broad and narrow Hβ and narrow [O iii] lines instead of fourth-order functions. Second, there is significant degeneracy between the weak Fe ii blend and the continuum flux in the nightly fits. Since the Fe ii fit is poorly constrained and sometimes varied drastically from night to night, the continuum model flux also varied significantly as a result, which in turn introduced noise to the broad Hβ fit component. To address this issue, we constrained the Fe ii flux to lie within 10% of the value from the fit to the mean spectrum (Barth et al. 2013). We also fixed the Fe ii redshift to that of the mean spectrum and constrained the Fe ii broadening kernel to be within 5% of its value from the mean spectrum fit. The He i λ4922 and λ5016 lines are very weak and are heavily blended with broad Hβ, making it impossible to constrain their fit parameters. We therefore do not fit for these components in our model.

The broad He ii λ4686 component has very low amplitude compared to the other fit components, and it is blended with the blue wing of broad Hβ. It is also highly variable, as demonstrated by the broad bump in the rms spectrum. This made it difficult to fit the He ii broad-line profile accurately, and the width varied significantly from night to night when fitted as a free parameter. Since the He ii λλ1640 and 4868 lines are expected to form under the same physical conditions and should thus have similar widths, we used fits to the λ1640 line in concurrent HST spectra to constrain the λ4686 line width.

The He ii λ1640 line was modeled with five Gaussian components (G. De Rosa et al. 2017, in preparation), and we took the three broadest components to represent the broad He ii λ1640 line profile. For each MDM spectrum, the He ii λ4686 broad-line FWHM was allowed to vary within 3 Å of the He ii λ1640 FWHM measured from the closest HST epoch. The first 23 epochs from the MDM campaign do not have corresponding HST spectra, so for each of these "pre-HST" epochs, we found the three epochs from later in the campaign with the closest matching 5100 Å continuum flux density. We then used the weighted mean of the broad He ii λ1640 widths from these three nights as the width constraint for the pre-HST epoch, where the weights were determined by how closely the 5100 Å fluxes of the later epochs matched that of the pre-HST epoch. The He ii λ1640 line width was highly variable during the HST campaign, and the model FWHM widths used to constrain the spectral decomposition have a mean of 48 Å, with a minimum of 28 Å and maximum of 59 Å.

We applied spectral decomposition to the data from all telescopes, but since the MDM data set is the largest and has the highest data quality and consistency, we use this data set for all subsequent analysis. Figure 4 shows the fit components for the mean MDM spectrum, where the black spectrum is the data and the red spectrum is the sum of all the model components. The model does not fit the detailed structure of the broad Hβ line well, especially in the line core. To prevent this from impacting our measured Hβ fluxes, we subtracted all the other well-modeled fit components except the broad and narrow Hβ components from the full spectrum and then obtained the Hβ line flux by integrating over the same wavelength range used to measure the flux without spectral decomposition. The He ii λ4686 flux was taken to be the total flux in the broad- and narrow-line models for each night. The narrow Hβ and He ii λ4686 line fluxes from fits to the mean spectrum are 48.4 × 10⁻¹⁵ erg s⁻¹ cm⁻² and 8.5 × 10⁻¹⁵ erg s⁻¹ cm⁻² (respectively), with uncertainties of ∼2% from the overall photometric scale of the data. The ratio of the narrow Hβ flux to the [O iii] λ5007 flux is F_Hβ/F_{[O III]} = 0.099 ± 0.002, which is in good agreement with the value of F_Hβ/F_{[O III]} = 0.110 ± 0.010 found by Peterson et al. (2004).

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The red spectrum in Figure 2 shows the rms of the MDM spectra after subtracting the AGN continuum and stellar continuum models from individual spectra so that only the emission-line components remain. This rms spectrum is expected to be a more accurate representation of the emission-line variability than the rms of the full spectra (Barth et al. 2015). We show the rms here and not the excess rms defined by Equation (4) because, for parts of the spectra dominated by continuum emission, the continuum-subtracted flux could be lower than the total flux uncertainties and the e-rms would be undefined. Thus, we use the excess rms only for the full spectrum and not for individual fit components.

Panels (a) and (c) of Figure 5 show the Hβ mean and rms fluxes as a function of line-of-sight velocity (v_r) after spectral decomposition, and panel (b) shows the difference between the T1 and T2 mean fluxes. The rms flux has a statistical uncertainty of ∼12% and the [O iii] residuals are much lower compared to the case with no spectral decomposition (Figure 2). The rms profile still has jagged features, which likely reflect real variability across the broad emission line.

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Figure 6 shows the 1158 Å UV continuum light curve from Paper I, the MDM optical 5100 Å continuum light curve, the V-band photometric light curve from Paper III, and the MDM Hβ and He ii λ4686 emission-line light curves. The He ii light curve reaches a flat-bottomed minimum near THJD = 6720. This is because the He ii flux includes contributions from the broad- and narrow-line components, so when the broad-line flux is near zero, the total He ii line flux stays at a minimum value equal to the narrow-line flux. Light-curve statistics that quantify the variability of NGC 5548 during the monitoring period are given in Table 3. F_var is as defined in Equation (3), and R_max is the ratio between the maximum and minimum fluxes.

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We measured the host-galaxy contribution to the continuum using an "AGN-free" image of NGC 5548 generated by Bentz et al. (2013) after performing two-dimensional surface brightness decomposition on HST images of the galaxy. We found that the amount of starlight expected through a 5'' × 15'' aperture with a slit position angle of 0° is F_5100,gal = (4.52 ± 0.45) × 10⁻¹⁵ erg s⁻¹ cm⁻² Å⁻¹. Subtracting this from the mean continuum flux density of F₅₁₀₀ = (11.96 ± 0.07) × 10⁻¹⁵ erg s⁻¹ cm⁻² Å⁻¹ gives a mean AGN flux of F_5100,AGN = (7.44 ± 0.50) × 10⁻¹⁵ erg s⁻¹ cm⁻² Å⁻¹, which is consistent with the value of F_5100,AGN = (7.82 ± 0.02) × 10⁻¹⁵ erg s⁻¹ cm⁻² Å⁻¹ measured from the power-law component of the spectral decomposition for the mean MDM spectrum.

RM analyses typically assume that the emission-line light curve responds linearly to continuum variations and is a lagged, scaled, and smoothed version of the continuum light curve. However, this does not appear to be the case for a portion of our campaign. As described in Papers I and IV, there are significant differences between the UV continuum and emission-line light curves after THJD = 6780. The continuum flux increased while the emission-line fluxes either decreased or remained roughly constant in a suppressed state for the remainder of the campaign.

The Hβ emission line shows similar behavior to that of Lyα and C iv, in that there is a marked difference in the line response between the first and second halves of the campaign. This "decorrelation" phenomenon is illustrated in Figure 7(a), where the Hβ and UV continuum light curves trace each other well in the first half of the campaign, but the continuum flux continues to trend upward beyond THJD = 6740, while the Hβ flux begins to fall. For the remainder of the campaign, the Hβ flux remains in a suppressed state and the light curve does not follow the continuum light curve well in that prominent features in the continuum light curves (e.g., THJD ≈ 6770, 6785) are not present in the emission-line light curve. The He ii λ4686 light curve behaves similarly and decorrelates from the continuum at around THJD = 6760 (Figure 7(b)). This phenomenon is also apparent when comparing the Hβ light curve to the 5100 Å continuum, as shown in Figure 7(c). Though there are small differences between the light curves in T1 (such as around THJD 6685), the overall correlation in T1 is significantly better than in T2.

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Owing to this change in the emission-line response, we followed the procedures presented in Paper I for determining the UV emission line lags and divided the 5100 Å continuum and optical emission-line light curves into two subsets, labeled T1 and T2, to examine the lag of each segment separately. The subsets are divided at THJD = 6747, and each has 67 epochs. The 1158 Å and V-band continuum light curves were also separated into two segments at THJD = 6747. Note that this is a different dividing epoch from the one used in Paper I. The characteristics of the half-campaign light curves are given in the bottom portion of Table 3. Figure 5 shows the MDM mean and rms spectra for T1 and T2 in gray and orange, respectively. While the three mean spectra look almost identical, the T1 and T2 rms spectra are significantly different, which indicates changes in the amount of variability between the two campaign halves.

We measured the Hβ and He ii λ4686 lags relative to both the 5100 Å continuum and the 1158 Å continuum. All light curves were detrended by subtracting a linear least-squares fit to the data to remove long-term trends that may bias lag calculations (Welsh 1999). In this case, we found very weak trends for all the light curves, and detrending has a very small effect (∼0.01 days) on the measured lags. We computed the cross-correlation coefficient r for lags between −20 and 40 days in increments of 0.25 days using the interpolated cross-correlation function (ICCF; White & Peterson 1994). Two lag estimates were made for each light-curve pair—the value corresponding to r_max (τ_peak) and the centroid of all values with r > 0.8 r_max (τ_cen). Estimates for the final τ_peak and τ_cen values and their uncertainties were obtained using Monte Carlo bootstrapping analysis (Peterson et al. 2004), where many realizations of the continuum and emission-line light curves were created by randomly choosing n data points with replacement from the observed light curves, where n is the total number of points in the data set. If a data point is picked m times, then the uncertainty on that point is decreased by a factor of m^1/2. Each value is then varied by a random Gaussian deviate scaled by the measured flux uncertainty. We constructed 10³ realizations of each light curve and computed the cross-correlation function (CCF) for each pair of line and continuum light-curve realizations to create a distribution of τ_peak and τ_cen values. The median value from each distribution and the central 68% interval are then taken to be the final lag and its uncertainty.

Table 4 lists the ICCF lags for Hβ and He ii λ4686 measured against the 1158 Å, 5100 Å, and V-band continua. The lag between the 5100 Å and 1158 Å continua is also given. For comparison with Paper I, which presents the UV emission-line lags against the 1367 Å continuum, we also include Hβ and He ii lags measured against this continuum. Distributions of τ_cen values from the Monte Carlo bootstrap analysis using the 1158 Å continuum are shown in the top panels of Figure 8.

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Table 4.  Rest-frame Emission-line Lags

Light Curves	τpeak	τcen	τcen,T1	τcen,T2	τJAVELIN	τJAVELIN,T1	τJAVELIN,T2
Hβ versus Fλ(1158 Å)	${6.14}_{-0.98}^{+0.74}$	${6.23}_{-0.44}^{+0.39}$	${7.62}_{-0.49}^{+0.49}$	${5.99}_{-0.75}^{+0.71}$	${6.56}_{-0.49}^{+0.48}$	${6.91}_{-0.63}^{+0.64}$	${7.42}_{-1.07}^{+0.97}$
Hβ versus Fλ(1367 Å)	${5.90}_{-0.74}^{+0.25}$	${5.89}_{-0.37}^{+0.37}$	${7.24}_{-0.48}^{+0.49}$	${5.99}_{-0.82}^{+0.76}$	${6.12}_{-0.47}^{+0.46}$	${6.52}_{-0.57}^{+0.60}$	${7.11}_{-1.06}^{+1.03}$
Hβ versus Fλ(5100 Å)	${4.42}_{-0.25}^{+0.98}$	${4.17}_{-0.36}^{+0.36}$	${4.99}_{-0.47}^{+0.40}$	${3.10}_{-0.80}^{+0.77}$	${3.84}_{-0.59}^{+0.57}$	${5.15}_{-0.69}^{+0.68}$	${4.78}_{-1.17}^{+1.13}$
Hβ versus V band	${3.93}_{-0.98}^{+0.98}$	${3.79}_{-0.34}^{+0.37}$	${3.82}_{-0.47}^{+0.57}$	${4.13}_{-0.58}^{+0.55}$	${3.54}_{-0.46}^{+0.45}$	${4.89}_{-0.71}^{+0.66}$	${4.05}_{-0.78}^{+0.93}$
He ii versus Fλ(1158 Å)	${2.46}_{-0.25}^{+0.49}$	${2.69}_{-0.25}^{+0.24}$	${3.71}_{-0.38}^{+0.39}$	${3.19}_{-0.35}^{+0.36}$	${2.65}_{-0.27}^{+0.27}$	${3.27}_{-0.35}^{+0.35}$	${2.99}_{-0.26}^{+0.25}$
He ii versus Fλ(1367 Å)	${2.21}_{-0.25}^{+0.25}$	${2.45}_{-0.24}^{+0.25}$	${3.43}_{-0.43}^{+0.36}$	${3.16}_{-0.33}^{+0.29}$	${2.41}_{-0.26}^{+0.25}$	${3.04}_{-0.36}^{+0.35}$	${2.79}_{-0.25}^{+0.25}$
He ii versus Fλ(5100 Å)	${0.49}_{-0.25}^{+0.25}$	${0.79}_{-0.34}^{+0.35}$	${1.21}_{-0.36}^{+0.28}$	${0.85}_{-0.36}^{+0.36}$	${0.16}_{-0.37}^{+0.37}$	${1.13}_{-0.48}^{+0.51}$	${0.85}_{-0.35}^{+0.38}$
He ii versus V band	${0.49}_{-0.49}^{+0.25}$	${0.50}_{-0.26}^{+0.34}$	${0.40}_{-0.39}^{+0.43}$	${1.46}_{-0.27}^{+0.34}$	${0.44}_{-0.23}^{+0.23}$	${0.63}_{-0.36}^{+0.37}$	${0.91}_{-0.21}^{+0.23}$
Fλ(5100 Å) versus Fλ(1158 Å)	${1.97}_{-0.49}^{+0.25}$	${2.23}_{-0.26}^{+0.31}$	${2.55}_{-0.33}^{+0.28}$	${2.77}_{-0.45}^{+0.41}$	⋯	⋯	⋯
Hβfull,MDM versus Fλ(1158 Å)	${5.90}_{-0.49}^{+0.74}$	${6.26}_{-0.37}^{+0.38}$	⋯	⋯	⋯	⋯	⋯
Hβfull,allsites versus Fλ(1158 Å)	${5.65}_{-0.25}^{+0.74}$	${6.49}_{-0.37}^{+0.37}$	⋯	⋯	⋯	⋯	⋯

Note. Rest-frame Hβ and He ii λ4686 lags (days) for the full campaign and for the T1 (THJD < 6747) and T2 (THJD > 6747) subsets, measured using both ICCF and JAVELIN. The last two lines show the Hβ lags measured using the light curve derived without spectral decomposition up to THJD = 6828.75.

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We also computed Hβ and He ii λ4686 lags for time periods T1 and T2 and found the T1 lags to be consistently longer by about 2σ. For Hβ, the T1 and T2 lags bracket the full-campaign lag, while for He ii λ4686, the full-campaign lag is shorter than both T1 and T2 lags. For comparison, Paper I found the Lyα, Si iv, C iv, and He ii λ1640 lags to be longer for T2 than for T1, which is the opposite of what we find for Hβ.

To illustrate the effects of spectral decomposition, we also include in Table 4 the ICCF lags for the Hβ light curve where the fluxes were measured using the straight-line continuum-subtraction method and without spectral decomposition. We calculated lags for both the MDM-only and the multisite Hβ light curves, which were truncated at THJD = 6828.75 to exclude the last 10 epochs of MDM data (see Section 2). The lags measured with and without using spectral decomposition are consistent to within 1σ.

In addition to the ICCF method, we computed the emission-line lags using the JAVELIN suite of Python codes (Zu et al. 2011). We used JAVELIN to linearly detrend the light curves and model the AGN continuum variability as a damped random walk process (DRW; Kelly et al. 2009; Zu et al. 2013). JAVELIN explicitly models the emission-line light curves as smoothed, scaled, and lagged versions of the continuum light curve. Since the decorrelation of the line and continuum light curves during the latter half of the campaign clearly violates these assumptions, it is of interest to examine the consequences for the JAVELIN models. For these models, we simultaneously fit the Hβ and He ii light curves using either the 1158 Å, 5100 Å, or V-band continuum light curve. The AGN STORM light curves are too short to accurately determine the DRW damping timescale, so this value was fixed to τ_DRW ≈ 164 days as derived by Zu et al. (2011) from fits to the 13 yr light curve of NGC 5548 (Peterson et al. 2002). The precise value of τ_DRW is not critical for the algorithm to work provided that it is approximately correct.

The top three panels of Figure 9 show the results of using JAVELIN directly on the observed data. Despite the long DRW timescale, the light-curve models show rapid fluctuations. The algorithm tries to match the suppressed flux in the line light curve to the continuum light curve, and because of the small uncertainties, it strongly prefers lag times for which the continuum and line light curves have minimal temporal overlap. This caused the posterior lag distribution to have multiple narrow peaks corresponding to lags that best desynchronize the light curves.

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We can attempt to compensate for this problem by increasing the uncertainties to encompass the amplitude of the decorrelation. This requires scaling up the full-campaign light-curve uncertainties by factors of 5 and 3 for the continuum and line light curves, respectively. The lower panels in Figure 9 show the JAVELIN results from fitting to the light curves with scaled errors, where the broader uncertainties allow the algorithm to construct smooth light-curve models. Since there is more statistical weight from fitting both lines simultaneously, the models track the line light curves best and show a smooth systematic offset for the continuum where the line and continuum light curves are decorrelated. When computing the half-campaign lags, JAVELIN favors a smaller line flux scale factor for T2 to account for the suppressed line fluxes, which begins near the epoch separating T1 and T2. We therefore did not need to scale the flux errors by as much as for the full campaign to account for the decorrelation, and we used an error scaling factor of 3 for both continuum and line light curves. The resulting JAVELIN lags, shown in Table 4, are consistent with those measured using the ICCF method. Similar to the ICCF lags, the JAVELIN lags for the full-campaign light curves are also shorter than those for T1 and T2. However, since the JAVELIN assumptions of the relationship between the line and continuum light curves are not valid for this campaign and the flux errors were scaled for the sole purpose of producing convergent solutions, we do not use the JAVELIN lags for subsequent analysis.

We examined the velocity-resolved emission-line response by dividing the Hβ line profile into bins with velocity width of 500 km s⁻¹ and set zero velocity using the peak of the narrow Hβ component in the mean spectrum. We constructed light curves for each velocity bin separately, and Figure 10 shows the light curves for 1500 km s⁻¹ velocity bins across the Hβ line profile (black), with the velocity at the center of each bin shown in the top left of each panel. There were six epochs of spectra⁹⁴ that produced outlying Hβ fluxes and significantly higher than average flux uncertainties for individual velocity bins, so we removed them from the velocity-resolved light curves in order to improve the lag measurements.

We determined the ICCF lag for each of these binned light curves with respect to both the UV and optical continua, and we show these lags as a function of line-of-sight velocity in the top left panel of Figure 11. The middle left panel shows the velocity-resolved Hβ–UV lag for T1 and T2, and the maximum cross-correlation coefficients (r_max) are shown in the right panels. The bottom panel of Figure 11 shows the MDM full-campaign mean spectrum for reference, and Table 5 lists the velocity-resolved lags. Emission-line variations have lower amplitudes during T2 compared with T1, which led to poorly constrained ICCF lags with large uncertainties for velocity bins with low line flux. We therefore reduced the upper limit of the CCF lag range from 40 to 20 days when computing the T2 lags.

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Table 5.  Rest-frame Hβ Velocity-resolved Lags

Wavelength	vr	τFull	rmax,Full	τT1	rmax,T1	τT2	rmax,T2
(Å)	(km s−1)	(days)		(days)		(days)
4743.82−4751.92	7000	${1.74}_{-0.60}^{+0.59}$	0.61	${2.05}_{-0.94}^{+1.04}$	0.79	${2.13}_{-0.66}^{+0.59}$	0.42
4751.92−4760.03	6500	${2.34}_{-0.49}^{+0.49}$	0.72	${2.57}_{-0.71}^{+0.60}$	0.88	${3.08}_{-0.77}^{+0.98}$	0.52
4760.03−4768.13	6000	${2.94}_{-0.48}^{+0.45}$	0.73	${3.41}_{-0.70}^{+0.63}$	0.88	${3.48}_{-0.66}^{+0.71}$	0.62
4768.13−4776.23	5500	${3.18}_{-0.46}^{+0.38}$	0.75	${3.25}_{-0.54}^{+0.57}$	0.83	${3.46}_{-0.62}^{+0.72}$	0.62
4776.23−4784.33	5000	${3.92}_{-0.47}^{+0.50}$	0.73	${3.12}_{-0.53}^{+0.57}$	0.85	${4.95}_{-0.94}^{+1.04}$	0.56
4784.33−4792.43	4500	${4.69}_{-0.49}^{+0.56}$	0.73	${3.94}_{-0.49}^{+0.63}$	0.85	${5.88}_{-0.70}^{+0.63}$	0.65
4792.43−4800.53	4000	${6.19}_{-0.68}^{+0.63}$	0.63	${7.00}_{-0.85}^{+0.74}$	0.83	${6.26}_{-1.29}^{+1.34}$	0.53
4800.53−4808.63	3500	${7.26}_{-0.61}^{+0.62}$	0.68	${8.45}_{-0.87}^{+0.94}$	0.79	${6.93}_{-1.57}^{+2.34}$	0.51
4808.63−4816.73	3000	${8.69}_{-0.67}^{+0.64}$	0.63	${10.90}_{-0.89}^{+0.89}$	0.81	${6.40}_{-1.48}^{+2.71}$	0.42
4816.73−4824.84	2500	${8.70}_{-1.13}^{+1.29}$	0.53	${10.54}_{-0.96}^{+1.55}$	0.77	${4.92}_{-0.86}^{+1.65}$	0.42
4824.84−4832.94	2000	${7.63}_{-1.01}^{+0.87}$	0.58	${10.46}_{-1.07}^{+1.24}$	0.77	${4.31}_{-0.50}^{+0.62}$	0.66
4832.94−4841.05	1500	${5.91}_{-0.53}^{+0.58}$	0.68	${8.71}_{-0.87}^{+0.78}$	0.80	${5.36}_{-0.74}^{+0.62}$	0.70
4841.05−4849.15	1000	${4.65}_{-0.45}^{+0.48}$	0.71	${5.79}_{-0.53}^{+0.63}$	0.89	${5.36}_{-0.60}^{+0.55}$	0.74
4849.15−4857.25	500	${5.27}_{-0.49}^{+0.38}$	0.74	${5.80}_{-0.65}^{+0.61}$	0.90	${6.11}_{-0.67}^{+0.51}$	0.76
4857.25−4865.35	0	${6.01}_{-0.49}^{+0.37}$	0.79	${6.50}_{-0.60}^{+0.52}$	0.90	${6.59}_{-0.76}^{+0.57}$	0.71
4865.35−4873.45	500	${6.40}_{-0.39}^{+0.47}$	0.75	${8.06}_{-0.70}^{+0.67}$	0.84	${6.43}_{-0.71}^{+0.64}$	0.67
4873.45−4881.56	1000	${6.99}_{-0.46}^{+0.38}$	0.77	${8.86}_{-0.39}^{+0.55}$	0.90	${6.87}_{-0.59}^{+0.53}$	0.74
4881.56−4889.66	1500	${7.77}_{-0.37}^{+0.44}$	0.80	${9.80}_{-0.46}^{+0.41}$	0.92	${7.05}_{-0.52}^{+0.57}$	0.73
4889.66−4897.76	2000	${8.59}_{-0.39}^{+0.40}$	0.81	${10.65}_{-0.55}^{+0.53}$	0.90	${6.38}_{-0.68}^{+0.75}$	0.65
4897.76−4905.86	2500	${10.18}_{-0.67}^{+0.66}$	0.74	${11.13}_{-0.68}^{+0.67}$	0.87	${6.47}_{-2.38}^{+2.01}$	0.27
4905.86−4913.96	3000	${10.19}_{-0.92}^{+0.98}$	0.67	${11.18}_{-0.61}^{+0.71}$	0.86	${2.58}_{-0.98}^{+1.21}$	0.21
4913.96−4922.06	3500	${8.23}_{-0.96}^{+1.03}$	0.66	${9.82}_{-0.96}^{+0.86}$	0.81	${3.78}_{-1.46}^{+2.74}$	0.27
4922.06−4930.16	4000	${7.25}_{-0.91}^{+0.87}$	0.65	${8.80}_{-0.70}^{+0.71}$	0.87	${4.06}_{-0.97}^{+1.57}$	0.50
4930.16−4938.27	4500	${6.01}_{-0.59}^{+0.55}$	0.62	${7.01}_{-0.72}^{+0.81}$	0.88	${5.52}_{-0.70}^{+0.64}$	0.62
4938.27−4946.38	5000	${5.04}_{-0.53}^{+0.59}$	0.47	${6.63}_{-0.56}^{+0.61}$	0.88	${4.85}_{-0.68}^{+0.69}$	0.58
4946.38−4954.48	5500	${4.00}_{-0.57}^{+0.56}$	0.40	${5.22}_{-0.83}^{+0.84}$	0.80	${4.55}_{-0.64}^{+0.72}$	0.59
4954.48−4962.58	6000	${3.41}_{-0.60}^{+0.63}$	0.43	${3.16}_{-1.30}^{+1.05}$	0.83	${4.89}_{-0.70}^{+0.65}$	0.62
4962.58−4970.68	6500	${3.20}_{-0.53}^{+0.61}$	0.53	${3.46}_{-0.72}^{+0.74}$	0.85	${4.30}_{-0.96}^{+0.87}$	0.53

Note. ICCF Hβ lags (τ_cen) for the full campaign and for the T1 (THJD < 6747) and T2 (THJD > 6747) segments. The first column gives the rest-frame wavelength range for each bin, and the second column gives the line-of-sight velocity at the center of each bin. The r_max values give the maxima of the cross-correlation functions between the light curve for each velocity bin and the UV continuum.

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The velocity-resolved Hβ–UV lag for the full campaign is shortest (τ_cen ≈ 2 days) in the line wings where v_r ≈ ±7000 km s⁻¹. The lag increases as v_r approaches zero from both sides of the lag profile, reaches local maxima of τ_cen ≈ 10 days at about v_r ≈ ±3000 km s⁻¹, and then steadily decreases until it reaches a local minimum of τ_cen ≈ 4 days near the line profile center. The lag profile measured against the optical continuum has a similar shape, but with all lags ∼2–3 days shorter, as we would expect from the ∼2-day lag between the two continua (Table 4). A similar double-peaked lag profile is also observed for Lyα (see Paper I). The T1 lag profile closely resembles that of the full campaign, but the T2 lag profile shows a slightly different structure. The bins where the T1 and T2 lags are most discrepant are also where the T2 light curves are least correlated with the continuum (r_max < 0.4). However, even excluding these outliers, there are still discernible differences between the T1 and T2 lag profiles. Additionally, the T2 r_max values are lower than those of T1 in every velocity bin, which clearly demonstrates that the line and continuum light curves are less correlated in T2 than in T1.

The shape of the velocity-resolved lag profile can provide qualitative information about the kinematics of the line-emitting gas (e.g., Kollatschny 2003; Bentz et al. 2009b; Denney et al. 2010; Barth et al. 2011; Du et al. 2016a). In simple models of the BLR (Ulrich et al. 1984; Gaskell 1988; Welsh & Horne 1991; Horne et al. 2004; Goad et al. 2012; Gaskell & Goosmann 2013; Grier et al. 2013), pure infall motion would lead to longer lags on the blue side of the line profile, and for outflow, the most redshifted gas would have the longest lag. For gas in Keplerian orbits, the shortest lags would be in the line wings, since gas with higher v_r is closer to the central BH. Gas with very low v_r could have a wide range of lags, and a spherical or flat disk distribution of BLR clouds in Keplerian motion could lead to a double-peaked velocity-resolved lag profile if the ionizing source is emitting anisotropically (Welsh & Horne 1991; Goad & Wanders 1996; Horne et al. 2004).

Previous studies of the UV and optical lines in NGC 5548 have inferred either Keplerian orbits (Horne et al. 1991; Wanders et al. 1995; Denney et al. 2009; Bentz et al. 2010b) or infalling motion (Crenshaw & Blackwell 1990; Done & Krolik 1996; Welsh et al. 2007; Pancoast et al. 2014; Gaskell & Goosmann 2016) for the BLR gas. From our data, the shape of the Hβ velocity-resolved lag profile suggests a BLR dominated by Keplerian motion. The discrepancy between the T1 and T2 lag profiles may suggest a change in the distribution or dynamics of the BLR gas, though such changes typically occur on timescales much longer than our campaign. More detailed interpretation requires comparison with transfer functions generated for various dynamical models of the BLR, which will be the subject of future work in this series (A. Pancoast et al. 2017, in preparation).

Figure 10 also shows modified versions of the 1158 Å continuum light curve in red. These light curves were shifted in time by the average T1 lag of the bins incorporated in each Hβ light curve, which are shown in the bottom right of each panel. The fluxes were roughly scaled and shifted to match the first half of the Hβ light curves. Comparing the line and continuum light curves, it is evident that the Hβ response in T2 is heavily dependent on the line-of-sight velocity.

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Our data show that previous assumptions about the relationship between the continuum and emission-line light curves—namely, that the emission-line light curves are smoothed, scaled, and time-shifted versions of the continuum light curve—are not always valid, as we observed all the UV and optical emission-line light curves decorrelating from the UV continuum about halfway through the monitoring period. Paper IV examined this effect for the UV emission lines by measuring changes in the emission-line equivalent width (EW),

$$\begin{eqnarray}&&\mathrm{EW}=\displaystyle \frac{{F}_{\mathrm{line}}}{{F}_{\mathrm{cont}}},\end{eqnarray} \tag{ 7 }$$

and the responsivity (η_eff), which is the power-law index that relates the driving continuum flux to the responding emission-line fluxes,

$$\begin{eqnarray}&&\mathrm{log}\,{F}_{\mathrm{line}}=A+{\eta }_{\mathrm{eff}}[\mathrm{log}\,{F}_{\mathrm{cont}}].\end{eqnarray} \tag{ 8 }$$

In the case of no line response, η_eff = 0, and if the line responds linearly to continuum variations (i.e., the transfer function is a δ function), then η_eff = 1. The emission-line EW and the continuum flux are related via the Baldwin relation (Baldwin 1977), which is described by

$$\begin{eqnarray}&&\mathrm{log}\,{\mathrm{EW}}_{\mathrm{line}}=B+\beta [\mathrm{log}\,{F}_{\mathrm{cont}}],\end{eqnarray} \tag{ 9 }$$

where the choice for F_cont is assumed to be a reasonable proxy for the ionizing continuum. Thus, β is also known as the slope of the Baldwin relation.

Following the same procedures as in Paper IV, we compute the responsivity η_eff and EW for the portion of the Hβ light curve that correlates with the UV continuum and then examine how these values change in different segments of the light curves. The values F_cont and F_line refer to the continuum and emission-line fluxes after removing nonvariable components such as host-galaxy and narrow-line flux contributions, and after correcting for the mean time delay between the continuum and line light curves (Pogge & Peterson 1992; Gilbert & Peterson 2003; Goad et al. 2004). There is very little host-galaxy flux in the 1158 Å continuum, which is dominated by the variable AGN. For the line fluxes, we took Hβ fluxes measured after linear continuum removal (without spectral decomposition) and subtracted a constant narrow Hβ flux measured from the MDM mean spectrum fit to remove the nonvariable line component. To correct for the emission-line time delay, we shifted the Hβ light curve by 8 days, which corresponds to the lag for the portion of the line light curve closely correlated with the UV continuum. Figure 12(a) shows the 1158 Å continuum light curve (black) with the time-shifted and flux-scaled Hβ light curve, which has been truncated at the beginning to match the first epoch of continuum observations. To show the Hβ light curve's general behavior toward the end of the campaign, we have shown here the full 143 epochs of Hβ flux measurements instead of the 133-epoch light curve we used in the Hβ lag analysis. However, since the last 10 epochs of spectra suffer from inconsistent spectral flux calibration (see Section 2), we do not use these points in calculating η_eff or β.

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We divided the Hβ light curve into five segments. The first segment corresponds to the period when the line light curve closely follows the continuum light curve (blue points); the second and third segments correspond to periods when the line light curve decouples from the continuum (cyan points) and remains in a state of depressed flux (red points); the last two segments correspond to the line light curve recovering from the depressed state (magenta points) and correlating once again with the continuum light curve (green points). The epochs that divide these segments are THJD = [6743, 6772, 6812, 6827].

Figures 12(d) and (e) show the Hβ broad-line flux and EW as a function of the 1158 Å continuum flux density determined from the HST epoch closest to each MDM epoch. The red lines represent linear least-squares fits to Equations (8) and (9) using only the blue points. We found that the cyan, red, and magenta points—corresponding to when the light curves are not well correlated—lie well below the best fits of Equations (8) and (9) to the blue points. Furthermore, the epochs during the anomaly (red points) are characterized by an η_eff value consistent with zero (η_eff = 0.02 ± 0.03; black dotted line in Figure 12(d)), which shows that the emission-line strength remained constant independent of continuum strength. Similar results were found for the C iv, Lyα, He ii(+O iii]), and Si iv(+O iv]) emission lines in Paper IV. Table 6 summarizes the η_eff and β values for all broad emission lines measured during this campaign. Note that the values from Paper IV were computed using epochs both before and after the anomaly (blue and green points), whereas our values were calculated using only epochs before the anomaly (blue points).

We measured the amplitude of the anomaly by comparing the observed Hβ light curve with a simulated light curve that represents what the line response would have been without the anomaly. The simulated line fluxes (F_sim) were calculated using the observed continuum fluxes and Equation (8), where η_eff and A are chosen to be the best-fit values for the period when the light curves are well correlated (blue points). This simulated light curve is shown in Figure 12(b) with gray dots, and comparing it with the observed data (colored points) shows that the Hβ line had lower-than-expected variability amplitude and mean flux during T2. If we define the fractional flux loss as F_lost = (F_sim − F_obs)/F_sim (Figure 12(c)), then this implies an Hβ flux deficit of ∼6% during the anomaly (red points), which is close to the deficit for Lyα but much smaller than that of the other UV emission lines, as shown in Table 6.

Table 7 summarizes the Hβ responsivities and AGN optical continuum flux densities measured by Goad et al. (2004) for every year of the 13 yr monitoring campaign carried out by the AGN Watch consortium (Peterson et al. 2002),⁹⁵ along with the values of η_eff = 0.59 ± 0.01 and $\langle {F}_{5100,\mathrm{AGN}}\rangle =(7.44\pm 0.50)\,\times {10}^{-15}\,\mathrm{erg}\,{{\rm{s}}}^{-1}\,{\mathrm{cm}}^{-2}\,{\mathring{\rm A} }^{-1}$ calculated from this data set. Both the responsivity and optical continuum flux density for this campaign are close to those measured from the 1998 data. Using the mean Hβ flux without narrow-line contributions of $\langle {F}_{{\rm{H}}\beta }\rangle =(690\pm 2.40)\times {10}^{-15}\,\mathrm{erg}\,{{\rm{s}}}^{-1}\,{\mathrm{cm}}^{-2}$, we find a mean EW for this campaign of 92.75 ± 2.45 Å, which is lower than values measured by Goad & Korista (2014) for previous campaigns.

The Hβ light curve appears to decorrelate from the UV continuum light curve at a somewhat earlier time (THJD ≈ 6742) than C iv (THJD ≈ 6765 as found in Paper IV). If we assume that the Hβ light curve decorrelates and recorrelates with the continuum light curve at the same times as C iv and use the same dividing epochs as those used in Paper IV (THJD = [6766, 6777, 6814, 6830]), then η_eff = 0.13 ± 0.01 and β = −0.88 ± 0.01 for the blue points.

While He ii λ4686 also shows anomalous behavior during the T2 period (Figure 7), its broad-line component is very weak and the fitted profile is poorly constrained in the spectral decomposition process. The He ii light curve is thus noisier than that of Hβ, and the F_line and EW values are poorly correlated with F_cont. We therefore do not perform a detailed analysis of the responsivity for He ii.

The BH mass in NGC 5548 has been estimated for several previous RM campaigns, including the AGN Watch consortium (Peterson et al. 2002), Bentz et al. (2007, 2009b), and Denney et al. (2010). The AGN Watch group determined the BH mass using data from each of the program's monitoring years, and subsequent campaigns each produced an independent BH mass value. Here we compute the BH mass using data from this campaign and compare it with previous results.

We measured the line widths from the Hβ mean and rms spectra as shown in Figure 5. The narrow Hβ line essentially disappears in the rms spectrum but is still present in the mean spectrum. We removed this emission component by subtracting a Gaussian fit to the Hβ narrow line in the mean MDM spectrum, and then linearly interpolated over the narrow Hβ residuals and the [O iii] λλ4959 and 5007 residuals.

Two emission-line width values are typically measured in RM: the FWHM and the line dispersion, defined by

$$\begin{eqnarray}&&{\sigma }_{\mathrm{line}}^{2}={\left(\displaystyle \frac{c}{{\lambda }_{0}}\right)}^{2}\left(\displaystyle \frac{\sum \,{\lambda }_{i}^{2}{S}_{i}}{\sum \,{S}_{i}}-{\lambda }_{0}^{2}\right),\end{eqnarray} \tag{ 10 }$$

where S_i is the flux density at wavelength bin λ_i and λ₀ is the flux-weighted centroid wavelength of the line profile. We measured σ_line and FWHM for the mean and rms spectra using the line profile within the rest-frame wavelength range 4669.8–5063.0 Å. We treated the mean profile as double peaked and followed the procedures described by Peterson et al. (2004) to measure its FWHM. From each of the two peaks at 4827.1 and 4886.1 Å, we traced the line profile outward until the flux reached 0.5F_max, and then traced the line profile inward from the continuum until the flux again reached 0.5F_max. The two wavelengths at 0.5F_max—which generally agree well for a smooth line profile—are then averaged to obtain the wavelength at half-maximum on each side of the profile. The rms profile is more complicated because it has more than two peaks and the troughs between them can reach well below half of the peak fluxes. We therefore identified a single maximum flux F_max and traced the profile from the continuum toward the center on both sides until the flux reached 0.5F_max. The separation between the two wavelengths at 0.5F_max is taken to be the FWHM of the rms spectrum.

The Hβ line widths and their uncertainties were determined using Monte Carlo bootstrap analysis. With n total spectra, we randomly selected n spectra from the data set with replacement, constructed mean and rms line profiles, and measured the line dispersion and FWHM. The median and standard deviation of 10⁴ bootstrap realizations are used for the σ_line and FWHM and their estimated uncertainties.

There are additional systematic uncertainties in the line widths from using different Fe ii templates in the spectral decomposition. We repeated the bootstrap analysis after performing spectral decompositions using each of the Boroson & Green (1992), Véron-Cetty et al. (2004), and Kovačević et al. (2010) Fe ii templates, and then took the standard deviation of the Hβ widths from using the different templates as the systematic uncertainty for the line width. This systematic error dominates the error budget for all σ_line measurements and the FWHM of the mean spectrum, but is comparable to the uncertainty from bootstrapping analysis for the FWHM of the rms spectrum. We added this systematic uncertainty in quadrature to the statistical uncertainty from the Kovačević et al. (2010) line width to obtain the final Hβ line width uncertainty.

The line widths are also affected by instrumental broadening due to the use of a wide slit. The observed line width is the quadratic sum of the intrinsic and instrumental line widths (${\sigma }_{\mathrm{observed}}^{2}={\sigma }_{\mathrm{intrinsic}}^{2}+{\sigma }_{\mathrm{instrumental}}^{2}$ or similarly for FWHM). To calculate the instrumental broadening for a 5'' slit, we followed the methods described by Bentz et al. (2009b) and compare the [O iii] λ5007 line width measured from our observations with the width measured from a higher-resolution observation taken using a narrow (∼2'') slit, which represents the intrinsic line width. The FWHM of the [O iii] λ5007 model from the MDM rest-frame mean spectrum is 9.79 Å (572 km s⁻¹), while Whittle (1992) found an FWHM of 410 km s⁻¹ using a 2'' slit. This implies an instrumental broadening of FWHM_instrument = 399 km s⁻¹, corresponding to σ_instrument = 170 km s⁻¹ for a Gaussian model of the [O iii] line profile. We subtract this instrumental width in quadrature from the Hβ line width measurements to obtain the intrinsic Hβ line widths, which are listed in Table 8. The large uncertainties on the FWHM measurements from the rms spectrum are a result of the jagged shape of the rms profile.

We use the Hβ line dispersion measured from the rms spectrum as the velocity dispersion ΔV, as is common practice in RM (Peterson et al. 2004; but also see Collin et al. 2006; Mejía-Restrepo et al. 2016, for comparison of FWHM and sigma as indicators of BLR virial velocity for BH mass estimation), and calculate the virial product, defined as VP = cτΔV²/G. The f factor in Equation (2), which incorporates the geometry and kinematics of the BLR, is generally unknown for any individual AGN, so a single value $\langle f\rangle$ is often used to represent the average normalization for all AGNs. This value is usually taken to be the scale factor that puts the sample of RM virial products onto the same M_BH–σ_⋆ relation as nearby inactive galaxies (see Kormendy & Ho 2013, for a discussion of the uncertainties in the M_BH–σ_⋆ relation), and can vary depending on the sample of AGNs used in the fit, as well as the fitting method (Onken et al. 2004; Watson et al. 2007; Woo et al. 2010; Graham et al. 2011; Park et al. 2012a; Grier et al. 2013; Ho & Kim 2015). We adopt a value of $\langle f\rangle =4.47$ as calculated by Woo et al. (2015). Since $\langle f\rangle$ is calibrated using Hβ lags measured against the optical continuum, we used the Hβ–5100 Å lag to calculate the VP and BH mass.

Table 9 lists the virial products and the inferred BH masses for the full, T1, and T2 segments. Our M_BH uncertainties do not include uncertainties in $\langle f\rangle$ (Woo et al. 2015) or scatter in the distribution of f for different AGNs (e.g., Ho & Kim 2015). The T1 and T2 M_BH estimates are consistent even though the two lags are different by more than 1σ. Compared to recent measurements, the full-campaign virial product (${1.49}_{-0.49}^{+0.49}\times {10}^{7}\,{M}_{\odot }$) is entirely consistent with the values of ${1.50}_{-0.51}^{+0.37}\times {10}^{7}\,{M}_{\odot }$ and ${1.38}_{-0.41}^{+0.51}\times {10}^{7}\,{M}_{\odot }$ obtained by Bentz et al. (2009b) and Lu et al. (2016), respectively. Our BH mass measurement (${6.66}_{-2.17}^{+2.17}\times {10}^{7}\,{M}_{\odot }$) is also consistent to 1σ with the dynamical mass of ${3.24}_{-0.90}^{+2.26}\times {10}^{7}\,{M}_{\odot }$ as determined by Pancoast et al. (2014), who use the V-band continuum as the ionizing source but do not use the f factor, which compensates for the difference in lag between using the UV and optical continua (see next section). This will lead to an underestimate of R_BLR and hence a proportional underestimate of the BH mass (Equation (2)). If we scale the Pancoast et al. (2014) mass by the ratio between the Hβ–1158 Å and the Hβ–V-band lags from Table 4 (τ_Hβ–UV/τ_Hβ–V = 1.64 ± 0.12), then the two M_BH measurements become much more congruent.

Table 9.  Hβ Line Measurements, M_BH Estimates, and Continuum Flux Densities

Segment	σline	τHβ–opt	Virial Product	MBH	F5100,total	F5100,AGN
	(km s−1)	(days)	(107 M⊙)	(107 M⊙)	(10−15 erg s−1 cm−2 Å−1)
Full	4278 ± 671	${4.17}_{-0.36}^{+0.36}$	${1.49}_{-0.49}^{+0.49}$	${6.66}_{-2.17}^{+2.17}$	11.96 ± 0.07	7.44 ± 0.50
T1	4155 ± 513	${4.99}_{-0.47}^{+0.40}$	${1.68}_{-0.45}^{+0.44}$	${7.53}_{-1.99}^{+1.96}$	11.31 ± 0.08	6.79 ± 0.46
T2	4856 ± 731	${3.10}_{-0.80}^{+0.77}$	${1.43}_{-0.56}^{+0.55}$	${6.38}_{-2.53}^{+2.49}$	12.51 ± 0.04	7.99 ± 0.45

Note. τ_Hβ–opt is the rest-frame ICCF τ_cen value measured against the 5100 Å continuum.

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Ground-based RM campaigns have traditionally used the optical continuum light curve—by necessity—to determine emission-line lags, even though the far-UV continuum is a better proxy for the ionizing source. Lags relative to the UV continuum (τ_Hβ–UV) thus should yield more accurate estimates of the BLR characteristic radius than lags measured relative to the optical continuum. Our Hβ–UV lag (${\tau }_{{\rm{H}}\beta -\mathrm{UV}}={6.23}_{-0.44}^{+0.39}\,\mathrm{days}$) is ∼2 days longer than the Hβ–optical lag (${\tau }_{{\rm{H}}\beta -\mathrm{opt}}={4.17}_{-0.36}^{+0.36}\,\mathrm{days}$). Given that past measurements of the Hβ–optical lag for this object range from ∼4 to ∼25 days (Bentz et al. 2013, and references therein), and assuming that τ_Hβ–opt is always ∼2 days longer than τ_Hβ–UV, the BLR characteristic radius estimated from previous campaigns using only optical data is biased low by 10%–50%. The difference in these Hβ lags is also consistent with the optical-to-UV continuum lag of ${2.24}_{-0.24}^{+0.24}\,\mathrm{days}$ found in Paper III.

Since virial estimates of M_BH scale with R_BLR, it may seem that this difference between τ_Hβ–UV and τ_Hβ–opt will change the BH mass estimate for NGC 5548 and other reverberation-mapped AGNs. However, the virial product—not the BH mass—is the quantity that is directly affected, and the normalization factor f is still needed to scale the virial product to a calibrated BH mass (Equation (2)). If the ratio of τ_Hβ–UV/τ_Hβ–opt is the same for all AGNs, then all RM virial products would be scaled up by a constant value, so simply changing the value of f would remove this bias and leave the RM BH masses unchanged. Even if the lag ratio is not constant for all AGNs, its effect on the BH mass scale is still small because the largest source of M_BH uncertainty in RM is the calibration uncertainty for f at ∼0.12 dex (Woo et al. 2015). Furthermore, for NGC 5548, the Hβ lag measured during this campaign is relatively short compared to its historical values (see Section 5.3). If the lag had been longer, the ratio of τ_Hβ–UV/τ_Hβ–opt would be closer to unity and the bias in the BLR characteristic size and BH mass estimate would be much smaller.

While the discrepancy between τ_Hβ–UV and τ_Hβ–opt may not change M_BH measurements that use the f factor, dynamical models that directly infer M_BH and BLR characteristics (e.g., Pancoast et al. 2011; Li et al. 2013) using only optical continuum data are affected since they do not depend on this virial normalization. The BLR characteristic size for each AGN inferred using optical data alone would thus be biased by a factor that depends on the value of τ_Hβ–UV/τ_Hβ–opt for that particular object. Changes in the inferred R_BLR could also impact single-epoch M_BH estimates, which rely on the empirical relation between the BLR characteristic radius and the AGN continuum luminosity (${R}_{\mathrm{BLR}}\propto {L}_{\mathrm{AGN}}^{\alpha }$ with $\alpha \approx 1/2$; e.g., Laor 1998; Wandel et al. 1999; Kaspi et al. 2000, 2005; McLure & Jarvis 2002; Bentz et al. 2006, 2009a, 2013; Vestergaard & Peterson 2006). If τ_Hβ–UV/τ_Hβ–opt correlates with AGN luminosity, then the expected value of α would change, and if this ratio is different for all AGNs but is uncorrelated with any other AGN properties, then this would introduce additional scatter to the scaling relation.

We can examine the expected scaling of τ_Hβ–UV/τ_Hβ–opt with respect to M_BH and L_AGN by using simple disk and BLR ionization models. Assuming that τ_Hβ–UV is the sum of τ_Hβ–opt and the optical–UV interband continuum lag τ_opt–UV, then

$$\begin{eqnarray}&&\displaystyle \frac{{\tau }_{{\rm{H}}\beta -\mathrm{opt}}}{{\tau }_{{\rm{H}}\beta -\mathrm{UV}}}=1-\displaystyle \frac{{\tau }_{\mathrm{opt}-\mathrm{UV}}}{{\tau }_{{\rm{H}}\beta -\mathrm{UV}}}.\end{eqnarray} \tag{ 11 }$$

For a standard thin disk, the characteristic size scale of the disk region emitting at wavelength λ scales as

$$\begin{eqnarray}&&{R}_{\lambda }\propto {M}_{\mathrm{BH}}^{2/3}{l}^{1/3}{\lambda }^{4/3},\end{eqnarray} \tag{ 12 }$$

where l = L/L_Edd. For a simple photoionization equilibrium model, the BLR characteristic radius scales as

$$\begin{eqnarray}&&{R}_{\mathrm{BLR}}\propto {M}_{\mathrm{BH}}^{1/2}{l}^{1/2}.\end{eqnarray} \tag{ 13 }$$

If the interband continuum lags are due to light-travel time across the accretion disk, then

$$\begin{eqnarray}&&\displaystyle \frac{{\tau }_{\mathrm{opt}-\mathrm{UV}}}{{\tau }_{{\rm{H}}\beta -\mathrm{UV}}}\propto {M}_{\mathrm{BH}}^{1/6}{l}^{-1/6}{\lambda }^{4/3}.\end{eqnarray} \tag{ 14 }$$

The lag ratio is thus weakly dependent on both M_BH and accretion rate, where even a factor of 10³ increase in the BH mass or accretion rate will change the ratio by only a factor of three. Empirically, Bentz et al. (2013) found a low scatter of 0.13 dex around the R_BLR–L_AGN relation for 41 AGNs over four orders of magnitude in luminosity, which suggests that this effect is indeed small for most AGNs. However, it is important to directly examine the potential consequences of this effect by obtaining more simultaneous observations of the UV/optical continua and the broad emission lines for AGNs over a wide range of luminosities.

Despite apparent differences in the C iv and Hβ decorrelation start times and flux deficits during T2, it is likely that the cause of the anomalous light-curve behavior is the same for the UV and optical emission lines. The line response during the anomaly is also heavily dependent on the line-of-sight velocity for Hβ (Figure 10) and the UV emission lines (M. Goad et al. 2017, in preparation). Paper IV suggests two scenarios that could produce the anomaly: (1) a temporary obscuration of the ionizing source from parts of the BLR by a moving veil of gas between the accretion disk and BLR, or (2) a temporary change in spectral energy distribution of the ionizing source. Future papers will investigate in detail the timing and magnitude of the anomaly for all UV and optical lines using the full multiwavelength data set from this campaign.

The bottom panel of Figure 7 shows that the Hβ light-curve decorrelation was also clearly detected using only the optical data. If our campaign had lasted for only the duration of T2, we still would have been able to measure the Hβ lags with fairly high precision (${\tau }_{{\rm{H}}\beta -\mathrm{UV}}={5.99}_{-0.75}^{+0.71}\,\mathrm{days}$ and ${\tau }_{{\rm{H}}\beta -\mathrm{opt}}\,={3.10}_{-0.80}^{+0.77}\,\mathrm{days}$), but the lag signal would be contaminated by other unknown factors and would lead to a somewhat biased estimate of the BLR characteristic radius. Depending on how common this decorrelation behavior is for Hβ, this effect could contribute to additional scatter in the single-object R_BLR–L_AGN relations for NGC 5548 and other AGNs, which can account for about half of the observed scatter in the global R_BLR–L_AGN relation for the entire sample of reverberation-mapped AGNs (Kilerci Eser et al. 2015).

The high cadence and long duration of this campaign have both been crucial in detecting this decorrelation phenomenon. Horne et al. (2004) found that a campaign duration of at least three times the maximum BLR light-crossing time is needed to recover high-fidelity velocity-delay maps from reverberation mapping data. Given the Hβ–UV lag of ∼6 days for NGC 5548 during our monitoring period, the BLR characteristic light-crossing time is ∼12 days, and the minimum campaign length needed to recover velocity-delay maps would correspond to ∼40 days, which would not have allowed us to see this decorrelation. In order to detect and characterize these anomalous behaviors in the emission-line light curves, RM campaigns must be much longer than the minimum requirement for obtaining velocity-delay maps.

Finally, while there are no previously published results documenting similar emission-line light-curve behavior, it is possible that this decorrelation phenomenon was indeed observed in other AGNs in previous RM campaigns, but was not recognized as such because the campaign had relatively low cadence and/or short duration. RM programs designed to study large numbers of sources with lower cadence would also not be able to detect these decorrelations. This further highlights the importance of high-cadence, long-duration, and high-S/N multiwavelength reverberation data sets in order to determine the prevalence of this phenomenon.

We compare the NGC 5548 Hβ–optical lags and optical continuum luminosity (L₅₁₀₀) from this campaign with those from previous RM campaigns targeting this object, as compiled by Kilerci Eser et al. (2015). The total 5100 Å flux and the AGN continuum flux densities for the full, T1, and T2 segments are listed in the sixth and seventh columns of Table 9, respectively. We applied a Galactic extinction correction of E(B − V) = 0.017 mag (Schlegel et al. 1998; Schlafly & Finkbeiner 2011) and used a luminosity distance of 75 Mpc in converting fluxes to luminosities. Figure 13 shows the R_BLR–L_AGN relation for NGC 5548, where the uncertainties are from absolute photometric calibration using [O iii] λ5007 and do not include the luminosity distance uncertainty. The lags from this campaign have smaller uncertainties, due to the high cadence and long duration of the ground-based monitoring. Denney et al. (2010) monitored NGC 5548 as part of a multiobject RM campaign and found ${\tau }_{{\rm{H}}\beta -\mathrm{opt}}={12.40}_{-3.85}^{+2.74}\,\mathrm{days}$. However, the light curves were dominated by a large, long-term trend, and after detrending the light curves with a third-order polynomial, the Hβ lag becomes ${5.07}_{-2.37}^{+2.46}\,\mathrm{days}$ (open circle in Figure 13).

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The surprising result is that, given the AGN luminosity during this campaign, the Hβ lags are nearly five times shorter than expected based on past measurements. NGC 5548 was also monitored in 2012 (G. De Rosa et al. 2017, in preparation) and had an Hβ lag of 4.1 ± 0.9 days and a luminosity of log(λ L₅₁₀₀) = 43.22 ± 0.1, whereas Lu et al. (2016) found the Hβ lag to be ${7.2}_{-0.35}^{+1.33}\,\mathrm{days}$ and the AGN luminosity to be log(λ L₅₁₀₀) = 43.21 ± 0.1 during their 2015 campaign, as shown in Figure 13. Both of these lags are also shorter than expected based on past results, though the point from Lu et al. (2016) suggests that the AGN may be returning to its previously measured R_BLR–L_AGN relation.

In numerical simulations of the emission-line response to continuum variations for a model BLR with fixed radial extent, Goad & Korista (2014) found that if the characteristic continuum variability timescale (τ_char) is smaller than the BLR light-crossing time, then there exists a strong correlation between τ_char, the line responsivity (η_eff), and measured lag, such that both η_eff and the lag decrease as τ_char decreases (their Figure 9). This is because short-timescale continuum variations only probe the inner parts of the BLR, so the measured lag and responsivity would be biased low. If we use the FWHM of the continuum light-curve autocorrelation function as a crude proxy for the characteristic variability timescale, then τ_char ∼ 10 days, which is significantly shorter than the values measured for this source for the 1989 IUE campaign and the 1993 HST campaign and could explain the shorter-than-expected Hβ lags.

Regardless of the physical causes of the short lags, these results suggest that the R_BLR–L_AGN relation is more complex than previously realized. Bentz et al. (2013) found a tight correlation between R_BLR and L_AGN for a sample of ∼40 reverberation-mapped AGNs, but recent studies by Du et al. (2015, 2016b) have shown that many AGNs with very high accretion rates tend to have considerably shorter Hβ lags compared to low-accretion AGNs with similar luminosities. Now, we have shown that even for a single AGN with low accretion rate (λ_Edd = 0.021 for NGC 5548; Vasudevan et al. 2010), the R_BLR–L_AGN relation does not always follow a tight power law, and that more complex physical processes may contribute significantly to the scatter. In order to further investigate the single-object R_BLR–L_AGN relation, repeated monitoring campaigns for individual AGNs are needed to track the behavior of each object over a range of timescales and luminosity states. This will, in turn, help improve our understanding of the global R_BLR–L_AGN relation.