Variability and the Size–Luminosity Relation of the Intermediate-mass AGN in NGC 4395

In the optical range, we mainly used the V-band and narrow Hα-band filters, while the B- and R-band filters were occasionally used for flux calibration. As the time lag of the Hα emission line with respect to the optical continuum is expected to be $\lesssim 1\,\mathrm{hr}$, a relatively short time cadence was required. For the continuum monitoring with the V-band filter, we mainly used 1 m class telescopes, while for the narrow Hα-band monitoring we used ∼2 m class telescopes to increase the signal-to-noise ratio (S/N) per exposure.

Examples of the images of NGC 4395 taken from different telescopes and bands are shown in Figure 1. To ensure better than 1%–2% flux measurement errors, we determined the optimal exposure time for each telescope based on the imaging data, which were obtained before the start of the monitoring campaign. For example, we used 180 s exposure time for the V-band imaging with the MDM 2.4 m telescope, while in general we used 300 s exposure time for both the V band and Hα. Thus, we maintained ∼5-minute time resolution at each telescope.

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For the narrow Hα-band observations, we used the MDM 1.3 m, BOAO 1.8 m, and MDM 2.4 m telescopes in 2017. The weather at the MDM Observatory was relatively good, while the data from BOAO suffered large uncertainties due to bad weather and low sensitivity; hence, these data were not used in the cross-correlation analysis. In 2018, we used the MDM 2.4 m telescope for the narrow Hα-band observations. Since we only used the Hα-band data from the MDM 2.4 m telescope for the time-lag analysis, we present the response function of the narrow Hα filter in Figure 2, which covers a spectral range of 6470–6560 Å, including the broad Hα emission line along with the narrow [N ii] and Hα lines. Note that while the flux from emission lines is dominant in the narrow Hα band, there is a significant contribution from the continuum, which has to be taken into account to obtain a reliable lag for the Hα emission line (see Section 3.3).

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Standard data reduction was performed including bias subtraction and flat-fielding using IRAF²⁴ procedures and cosmic-ray rejection using the L.A.Cosmic algorithm (van Dokkum 2001). If necessary, two to four consecutive exposures were combined to construct a single-epoch image to decrease the photometric uncertainty to <5%, while the time resolution between epochs was kept at a maximum of 10 minutes. After that, data quality was assessed based on visual inspection, and any epoch with quality issues (e.g., failed tracking or performance trouble reported in the observing log) was rejected from further photometric analysis.

We observed NGC 4395 using the Swift UVOT to monitor the variability of the UV continuum and to investigate the time lag between continuum bands. The UVOT data were taken from 2017 April 28 to May 2 using the UVM2 filter, which is centered at 2231 Å. Note that one orbital period of Swift is 96 minutes, of which NGC 4395 was visible for ∼2000 s. We performed the data reduction with HEASOFT v6.22²⁵ (Blackburn et al. 1999), including background subtraction, correction for anomalous zero exposures, and correction for the degradation of the UVOT sensitivity.

We monitored NGC 4395 using J, H, and K/K_s filters at the Caucasus Mountain Observatory (CMO) 2.5 m telescope (the ASTRONIRCAM instrument; Nadjip et al. 2017) and Okayama Astrophysical Observatory (OAO) 0.91 m telescope (OAO/WFC; Yanagisawa et al. 2019). At the CMO 2.5 m, we used the K-band filter of the Maunakea Observatory (MKO) system for three nights in 2017. In addition, J and H filters were occasionally used during the monitoring. In the case of OAO observations, we used the K_s filter, but the image quality was too poor to perform further analysis.

In addition to the photometric observations, we performed spectroscopic observations for ∼3.5 hr, using the Gemini Multi-Object Spectrograph (GMOS) on the Gemini North telescope on 2017 April 29. Initially, we planned to observe NGC 4395 for two consecutive nights in 2017 (GN-2017A-Q2, PI: Woo) and three nights in 2018 (GN-2018-Q102, PI: Woo), but all scheduled nights were lost as a result of snowstorms. Nevertheless, we were able to monitor the target for ∼3.5 hr under varying cloudy conditions on 2017 April 29.

We used a long slit with a 075 width and the R831 grating, obtaining a spectral resolution of R = 2931, good enough to resolve the broad and narrow components of Hα and the wing and core components of the narrow lines, [N ii] and [S ii], as presented by Woo et al. (2019). The instrument setup covered the spectral range 4606–6954 Å with a 0.374 Å pixel⁻¹ scale. We set the position angle to be 502 east from north. We used 2-pixel binning along the spatial direction, resulting in a scale of 016 pixel⁻¹. Each exposure was 300 s long, and we obtained a high-quality spectrum every 6 minutes, including 1 minute of overhead per exposure. A total of 36 exposures was obtained during the 3.5 hr run, but three epochs were discarded owing to strong cosmic rays that hit the Hα line. Additionally, we observed G191-B2B for flux calibration purposes (Massey et al. 1988; Massey & Gronwall 1990; Bohlin et al. 1995).

We performed standard data reduction with the Gemini IRAF package, including bias subtraction, flat-fielding, wavelength calibration, and flux calibration. Cosmic rays were rejected using the L.A.Cosmic routine (van Dokkum 2001). From each exposure, we extracted a one-dimensional spectrum using an aperture size that was three times the seeing FWHM, in order to compensate for varying seeing during the observing run. Out of the 33 epochs, two consecutive spectra showed relatively low S/N, so we averaged these two epochs. Thus, we finalized a total of 32 spectra.

To obtain the flux of the broad Hα emission line, we performed decomposition analysis as outlined by Woo et al. (2019). In brief, we modeled the [S ii] λλ6717, 6731 doublet using two Gaussian components for each line since both [S ii] lines exhibit a broad wing component and a narrow core component. For the continuum subtraction, we adopted a straight line using the continuum flux around the 6660–6700 Å and 6760–6800 Å ranges. By assuming that the line profile and flux of [S ii] were constant during the night, we performed a calibration for the flux, spectral resolution, and wavelength shift, so that the [S ii] λλ6717, 6731 model profile of each epoch remains constant. Also, we constructed mean and rms spectra using the calibrated spectra.

We then modeled the Hα and [N ii] region by assuming that the narrow Hα line and the [N ii] λλ6548, 6583 doublet have the same profile as that of [S ii] λλ6717, 6731. For each epoch, we modeled the broad Hα line with a single Gaussian profile and the narrow lines (Hα and [N ii]) with the same profile as obtained for [S ii]. In addition, we used a linear continuum. We simultaneously fitted emission lines and continuum in the spectral range 6450–6670 Å. We obtained the light curve of the broad Hα line flux as shown in the second panel of Figure 3. Note that the ∼3.5 hr baseline is too short to reliably measure the time lag between the continuum and the broad emission line (see Section 3.4).

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To measure the flux variability of the AGN continuum and Hα emission line, we first performed aperture photometry, using the photutils package (Bradley et al. 2017). Since the majority of images showed seeing variations during the night, we matched the point-spread function (PSF) before performing aperture photometry. The PSF was constructed based on isolated, bright, and unsaturated stars in each image, which were subsequently convolved so that all images have the same matched PSF, which was obtained from the worst-seeing image of the night, typically 15–4''. Using the PSF-matched images, we then performed aperture photometry for the target AGN and comparison stars in the field of view. A global background image was constructed using the SExtractorBackground estimator of the photutils package, which was subtracted from each image.

In addition, we determined the residual background for individual sources using annuli with an outer radius of 3–5 times the seeing FWHM and an inner radius of 2–3 times the seeing FWHM. The calculated residual background value was then subtracted from the median value measured within the aperture. We note that the residual background flux is insignificant and the additional background subtraction did not change the flux of most of the comparison stars. In contrast, this process was required for NGC 4395, since the host galaxy contribution at the galactic center was significant. Consequently, the additional subtraction decreased the AGN flux.

We determined the aperture size to include more than 99% of the point-source flux and performed differential photometry for a number of nearby comparison stars. Depending on the field of view of each camera at each telescope, we selected various numbers of bright stars (three to eight stars for each set of observations) that were nonvarying and unsaturated with photometric uncertainty <2%. To identify variable stars, we used the table from Thim et al. (2004).

In Figure 1, we present an example of the V-band and Hα-band images along with the selected comparison stars. We calculated the difference between the instrumental magnitude and the known magnitude of each comparison star and adopted the mean difference as the relative normalization value (δV) for each epoch. We assumed the standard deviation of the δV from individual comparison stars as a systematic error of the normalization, which was added to the uncertainties of the instrumental magnitude and the background flux for calculating a total uncertainty.

Based on the aperture photometry and calibration, we constructed light curves by combining measurements from different telescopes. In this process, we intercalibrated the light curves in order to avoid a systematic offset between light curves obtained from different telescopes due to differences in the response function of the filters, detector efficiency, etc. We matched each light curve with a reference light curve by adding a linear shift in magnitude. In other words, the mean magnitude within the overlapped time interval in a light curve was forced to be the same as that of the reference light curve.

3.1.1. Detailed Intercalibration Information

3.1.2. Light Curves

In Table 2 and Figures 3 and 4, we present the calibrated light curves of the V band and Hα band, after excluding the data obtained during bad weather since the error bars are too large to provide any meaningful measurements. Overall, the two curves show similar trends, demonstrating correlated variability. However, most segments of the V-band light curve are not suitable for reverberation mapping analysis owing to (1) the lack of corresponding Hα observations, (2) the weak variability in the Hα-band light curve, and (3) the large uncertainty of the Hα photometry. Among the monitoring data obtained in 2017 and 2018, we identified only two nights, 2017 May 2 and 2018 April 8, from which we were able to achieve reliable time-lag measurements. We will focus on these two nights for further reverberation mapping analysis in Section 3.3.1.

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Table 2.  Photometry Data

MJD –50,000.0	Band	Magnitude	Uncertainty	Telescope Identifier
(1)	(2)	(3)	(4)	(5)
7869.90099	J	15.412	0.005	CMO 2.5m
7869.90569	K	14.064	0.010	CMO 2.5m
7869.91038	J	15.426	0.011	CMO 2.5m
7869.91508	K	14.065	0.012	CMO 2.5m
7869.91931	J	15.429	0.021	CMO 2.5m

Note. Columns are (1) Modified Julian Date, (2) filter, (3) magnitude, (4) 1σ uncertainty in magnitude, and (5) telescope identifier (see Table 1).

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

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For the data obtained with the Swift UVM2 filter, we binned event files into 300 s exposures and measured the count rate from circular apertures of 3'' radii in order to maximize the S/N. Photon count rates, $\dot{\gamma }$, were then corrected for the large-scale sensitivity gradient and converted into AB magnitudes as ${m}_{\mathrm{UVM}2}=-2.5{\mathrm{log}}_{10}\dot{\gamma }+18.54$ (Breeveld et al. 2011). Finally, aperture correction to the standard UVOT aperture of 5'' was applied using on-field stars in each temporal bin in order to convert aperture magnitude into PSF magnitude.

For the J, H, and K images, AGN magnitudes were obtained for each exposure by performing photometry with circular apertures of 22 diameter, with respect to the comparison star 2MASS J12255090+3333100, whose magnitude in each band is J = 14.362, H = 13.939, and K = 13.786 when converted to the MKO system.

We quantified the variability of NGC 4395 using the light curves presented in Figures 3 and 4. We calculated the rms variability in magnitude (σ_m), the ratio between the maximum flux and minimum flux (R_max), and the fractional variability (${F}_{\mathrm{var}}$), using the 2017 and 2018 light curves. The fractional variability ${F}_{\mathrm{var}}$ is defined as

$$\begin{eqnarray}&&{F}_{\mathrm{var}}=\displaystyle \frac{1}{\langle f\rangle }\sqrt{\langle {f}^{2}\rangle -\langle f{\rangle }^{2}-\left\langle {{\epsilon }_{f}}^{2}\right\rangle }\end{eqnarray} \tag{ 1 }$$

(Vaughan et al. 2003), where f is the flux at each epoch, $\langle f\rangle$ is the mean flux, and _f is the flux uncertainty. The error of the fractional variability is given by

$$\begin{eqnarray}&&\varepsilon ({F}_{\mathrm{var}})=\sqrt{{\left(\sqrt{\displaystyle \frac{1}{2N}}\displaystyle \frac{\left\langle {{\epsilon }_{f}}^{2}\right\rangle }{{\left\langle f\right\rangle }^{2}{F}_{\mathrm{var}}}\right)}^{2}+{\left(\sqrt{\displaystyle \frac{\left\langle {{\epsilon }_{f}}^{2}\right\rangle }{N}\displaystyle \frac{1}{\left\langle f\right\rangle }}\right)}^{2},}\end{eqnarray} \tag{ 2 }$$

where N is the number of epochs.

Table 3 summarizes the variability measurements. Using the light curves obtained in 2017, we find rms variability from 0.02 to 0.13 mag in the continuum, and the 2018 data show a similar range. R_max of the continuum band ranges from 1.08 to 1.87 in 2017 and has similar values in 2018. Accounting for the measurement errors in the light curves from 2017, we find that the fractional rms variability ranges from 1% to 8%, showing a decreasing trend with increasing continuum wavelength. The exception is the UVM2 band, which has a similar fractional variability compared to the V band, due to the larger uncertainty of the UV photometry. In general, we find similar trends in the light curves obtained in 2018.

Table 3.  Variability Statistics

Band	Central Wavelength	σm	Rmax	${F}_{\mathrm{var}}$
	(μm)	(mag)		(%)
2017
UVM2	0.225	0.13	1.87	8.1 ± 1.2
V	0.551	0.10	1.70	8.2 ± 0.1
J	1.22	0.03	1.15	2.7 ± 0.2
H	1.63	0.02	1.08	1.6 ± 0.3
K	2.19	0.12	1.37	1.1 ± 0.1
Hαa	0.66	0.01	1.07	0.6 ± 0.1
2018
V	0.551	0.05	1.23	4.7 ± 0.1
Hαb	0.66	0.02	1.08	1.2 ± 0.1
2017 Apr 28
J	1.22	0.03	1.12	2.4 ± 0.2
H	1.63	0.02	1.08	1.6 ± 0.3
K	2.19	0.02	1.07	1.2 ± 0.6
2017 May 2
V	0.551	0.03	1.11	2.5 ± 0.1
Hαb	0.657	0.01	1.04	0.1 ± 0.4
2018 Apr 8
V	0.551	0.02	1.10	1.7 ± 0.1
Hαb	0.657	0.01	1.03	0.6 ± 0.1

Notes.

^aLight curves from MDM 1.3 m and MDM 2.4 m. ^bLight curves from MDM 2.4 m.

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To compare the variability with the consistent length of the time baseline, we calculated the variability statistics of the near-IR bands using the light curves obtained on 2017 April 28. The rms deviation, R_max variability, and fractional variability show a clear decreasing trend with increasing wavelength.

We also used the data from 2017 May 2 and 2018 April 8 to measure the variability in the V band and the Hα narrow band for comparison. We obtained rms variability of 0.01 mag, R_max of 1.1, and fractional rms variability of 1%–2%. Note that since the narrow band contains nonvariable narrow lines ([N ii] and narrow Hα emission) that account for 49% of the total flux observed in the Hα narrow band (see Section 3.3), the actual variability amplitude is a factor of 3 higher than these measurements. We also measured the variability of the entire Hα light curves of 2017 and 2018 and obtained ${\sigma }_{m,{\rm{H}}\alpha }=0.012$, ${R}_{\max ,{\rm{H}}\alpha }=1.07$, and ${{F}_{\mathrm{var}}}_{,{\rm{H}}\alpha }=0.006$ in 2017 and ${\sigma }_{m,{\rm{H}}\alpha }=0.015$, ${R}_{\max ,{\rm{H}}\alpha }=1.08$, and ${{F}_{\mathrm{var}}}_{,{\rm{H}}\alpha }=0.012$ in 2018, which are broadly consistent with single-night values with continuum correction.

Ideally, spectroscopic monitoring can provide better data to measure the Hα emission-line flux by separating the emission line from the continuum based on the spectral decomposition, leading to less uncertainty in the cross-correlation analysis between AGN continuum and Hα emission line. The main uncertainty of photometric reverberation mapping comes from the fact that the contribution from the AGN continuum to the total flux obtained with a broad filter has to be properly determined (Desroches et al. 2006). Compared to a broadband filter, the narrow Hα-band filter contains less AGN continuum and can be effectively used for the Hα emission-line flux monitoring. If the continuum contribution in the narrowband Hα filter can be properly removed, narrowband photometry can lead to successful measurements of the Hα emission-line flux. In this section, we investigate the effect of the variability of the continuum in the Hα band.

3.3.1. Test of Continuum Variability for Hα Photometry

The total flux measured with a narrowband Hα filter is composed of the flux from the broad Hα line, narrow emission lines, and the continuum emission from the AGN and its host galaxy. Thus, we model the narrowband Hα flux ${F}_{\mathrm{nH}\alpha }(t)$ as

$$\begin{eqnarray}&&{F}_{\mathrm{nH}\alpha }(t)={f}_{\mathrm{BH}\alpha }(t)+{f}_{\mathrm{cont}}(t)+{f}_{\mathrm{NL}},\end{eqnarray} \tag{ 3 }$$

where ${f}_{\mathrm{BH}\alpha }(t)$ is the variable flux of the broad Hα emission, ${f}_{\mathrm{cont}}(t)$ is the variable flux of the continuum from both AGNs and nonvarying stars, and f_NL is the nonvarying flux from narrow emission lines. While the variability of ${f}_{\mathrm{BH}\alpha }(t)$ is delayed with respect to the V-band continuum, the variability of ${f}_{\mathrm{cont}}(t)$ is similar to that of V. If we ignore the difference of the wavelength between V and Hα, the flux variability of f_cont(t) is to be coherent with that of the V band. This assumption is reasonable if there is no color variability in this relatively short wavelength range covered by the V and Hα bands. Furthermore, if there is no significant contribution from nonvarying stars to the Hα filter, then the variability amplitude of the continuum will be similar between the V-band and Hα-band spectral ranges.

A key for the proper continuum correction is to have a high-quality spectrum with which the AGN continuum fraction can be reliably determined. We used the mean spectrum obtained with the Gemini GMOS during our 3.5 hr observing run for measuring the flux contribution of each component based on the spectral decomposition. We modeled the GMOS spectrum with multiple components: the narrow Hα emission line and [N ii] λλ6548, 6583 doublet, the broad Hα emission line, and the continuum. We used double-Gaussian models for the narrow emission line to account for the core and wing components, a single-Gaussian component for the broad Hα emission line, and a first-order polynomial for the continuum (see Figure 2). After convolving each component with the response function of the KP1468 Hα filter, we determined that the continuum is 18.3% ± 0.3% of the total flux in the narrowband Hα filter, while the narrow line and broad line contribute 49% and 32% of the flux, respectively.

On the other hand, the variability amplitude of the continuum in the narrowband Hα filter can differ from that of the V band if the variability amplitude depends on the continuum wavelength, while it is reasonable to assume the same amplitude, considering the small difference of the wavelengths between two filters. We model the continuum in the Hα filter by quantifying the dimensionless variability amplitude K as

$$\begin{eqnarray}&&{f}_{\mathrm{cont}}(t)=\left[(1-K)+K\displaystyle \frac{{f}_{{\rm{V}}}(t)}{\left\langle {f}_{{\rm{V}}}\right\rangle }\right]\left\langle {f}_{\mathrm{cont}}\right\rangle ,\end{eqnarray} \tag{ 4 }$$

where $\left\langle {f}_{\mathrm{cont}}\right\rangle$ is the mean continuum flux in the Hα filter, $\left\langle {f}_{{\rm{V}}}\right\rangle$ is the mean flux of the V-band filter, and f_V (t) is the V-band flux at each epoch. For example, if K = 1, then the variability amplitude of the continuum is the same between the V band and Hα, while the continuum in the Hα band has no variability for K = 0. Thus, by parameterizing the variability amplitude by K, we can test the effect of the continuum contribution to the Hα light curve. Different assumptions on variability amplitude would affect the recovered Hα light curve as shown in Figure 5, where we present the change of the narrowband Hα filter light curve using K = 0, 0.5, and 1.

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To quantify the effect of the continuum contribution in the Hα band on the time-lag analysis, we used five Hα light curves, which were corrected for the continuum contribution with an assumed variability amplitude (K in Equation (4)).

For measuring a time lag from a pair of light curves (V and Hα), we computed the interpolated cross-correlation function (ICCF; White & Peterson 1994). We adopted the flux randomization/random subset selection method (FR/RSS; Peterson et al. 1998; see also Peterson et al. 2004) to estimate its uncertainty. The ICCF r(τ) was computed over $-4\,\mathrm{hr}\lt \tau \lt 4\,\mathrm{hr}$ with 0.01 hr interval. We obtained two ICCFs by interpolating either the V-band light curve or the Hα light curve and then adopted the average of the two ICCFs. We simulated 2000 realizations with the FR/RSS. For each realization, we resampled each light curve by allowing any epoch to be drawn multiple times. Then, the flux at each epoch was randomized with a lognormal distribution corresponding to the measured flux, flux uncertainty, and the number of times that epoch was drawn in the resampling step. The centroid of the ICCF, defined as the ICCF-weighted mean of τ where $r(\tau )\gt 0.8\,{r}_{\max }$, was calculated for each realization. Finally, the median and the lower/upper bounds of the 68% central confidence interval of the centroid distribution were taken as the time lag and its lower/upper uncertainty. In addition, we used the z-transformed discrete correlate function (zDCF; Alexander 1997) and the JAVELIN method (Zu et al. 2011) to measure the time lag between V-band and Hα-band light curves, in order to compare with the ICCF results. Our measurements of continuum-to-Hα time lag are summarized in Table 4.

Table 4.  Time Lags for Broad Hα Line from Photometric Light Curves

Date	Continuum Correction	τICCF	τzDCF	τJAV
(UT)		(minutes)	(minutes)	(minutes)
(1)	(2)	(3)	(4)	(5)
2017 May 2	no correction	${55}_{-31}^{+27}$	${67}_{-32}^{+22}$	${59}_{-14}^{+14}$
	25% of V-band variability	${72}_{-33}^{+25}$	${67}_{-21}^{+36}$	${74}_{-14}^{+18}$
	50% of V-band variability	${88}_{-44}^{+27}$	${119}_{-37}^{+27}$	${98}_{-22}^{+17}$
	75% of V-band variability	${104}_{-55}^{+31}$	${119}_{-20}^{+30}$	${120}_{-22}^{+14}$
	100% of V-band variability	${122}_{-67}^{+33}$	${147}_{-32}^{+20}$	${135}_{-52}^{+7}$
2018 Apr 8	no correction	${49}_{-14}^{+15}$	${33}_{-27}^{+24}$	${68}_{-22}^{+11}$
	25% of V-band variability	${56}_{-13}^{+13}$	${67}_{-32}^{+4}$	${76}_{-11}^{+36}$
	50% of V-band variability	${64}_{-14}^{+14}$	${67}_{-28}^{+23}$	${84}_{-13}^{+28}$
	75% of V-band variability	${73}_{-14}^{+14}$	${67}_{-23}^{+30}$	${94}_{-13}^{+29}$
	100% of V-band variability	${83}_{-14}^{+13}$	${99}_{-35}^{+9}$	${100}_{-11}^{+18}$
2017 Apr 29	no correction	${79}_{-25}^{+30}$	${70}_{-16}^{+11}$	⋯
2017 Apr 30	no correction	${84}_{-66}^{+86}$	${131}_{-80}^{+29}$	⋯
2017 May 1	no correction	${2}_{-14}^{+19}$	${8}_{-16}^{+21}$	⋯

Note. Rest-frame time-lag measurements after subtracting the continuum contribution from the Hα narrowband flux. The continuum flux is on average 18.3% but varies as in the V-band variability. The time lag represents the median of the distribution for ICCF and JAVELIN, and the maximum likelihood lags for zDCF. Central 68% intervals are taken as their uncertainties.

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First, we present the ICCF, zDCF, and JAVELIN measurements using the best light curves from 2018 April 8 in Figure 6. We also used the light curves from 2017 May 2 for a consistency check. Without correcting for the continuum contribution to the Hα band, we obtained the ICCF time lag of ${55}_{-31}^{+27}$ minutes from the 2017 May 2 data and ${49}_{-14}^{+15}$ minutes from the 2018 April 8 data. These results are consistent with those of zDCF and JAVELIN measurements, where ${67}_{-32}^{+22}$ minutes (zDCF) and ${59}_{-14}^{+14}$ minutes (JAVELIN) were measured for the 2017 May 2 data and ${33}_{-27}^{+24}$ minutes (zDCF) and ${68}_{-22}^{+11}$ minutes (JAVELIN) were measured for the 2018 April 8 data.

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Although the quality of the light curves is much lower, we also tried to measure the time lag using the light curves from other dates, including 2017 April 29, April 30, and May 1. As summarized in Table 4, the obtained time lag from these dates suffers large uncertainty owing to the poor data quality, the limited time baseline, and the lack of strong variable features. Nevertheless, we find that the lag measurements are broadly consistent with that of the best light curves from 2018 April 8.

Second, we used the light curves from the best two dates to test the effect of the continuum variability in the Hα band on the time-lag measurement. Assuming that the variability amplitude of the continuum in the Hα band is 25%, 50%, 75%, and 100% of that of V, we subtracted the continuum contribution from the total flux observed with the Hα filter, which was on average 18.3%, but slightly varied as the V-band light curve. The continuum flux observed through the Hα filter generally decreases the time lag between the V-band continuum and Hα line since the continuum in the V band and that in the Hα band have the same variability pattern. Thus, if we assume a smaller variability amplitude of the continuum, the continuum variability signal is less subtracted from the Hα-band light curve, weakening the variability pattern of the Hα emission-line flux. For example, we can obtain a lower limit of the lag if we do not correct for the continuum variability (i.e., assuming 0% variability amplitude) in the Hα-band light curve.

As shown in Figure 7, the time lag increases by almost a factor of two with the maximum correction (K = 1). While the three analysis methods (ICCF, zDCF, and JAVELIN) provided somewhat different lag measurements, they are mostly consistent within the uncertainties. Using the light curves from 2017 May 2, we obtained consistent results, with an increasing time lag with the higher variability amplitude. Table 4 summarizes the time-lag measurements, depending on the used light curves and the analysis method.

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Assuming that the variability amplitude is the same between V and Hα, we compensated for 18.3% continuum contribution in the Hα light curve, and we found the ICCF Hα time lag to be τ_ICCF = ${122}_{-67}^{+33}$ minutes on 2017 May 2 and τ_ICCF = 83 ± 14 minutes on 2018 April 8, which are consistent within 1σ uncertainties. We also conducted ICCF measurements with Hα light curves compensating for 18.0% and 18.6% continuum, which are the 1σ bounds for the continuum fraction in the narrowband Hα filter. We found that the difference in time lag is not larger than 1 minutes; thus, the uncertainty arising from the error in the continuum contamination measurement can be ignored.

On the other hand, we did find a difference in the time-lag measurement if the variability amplitude of the continuum in the Hα filter is different from that of the V-band filter, as shown in Figure 7. We also checked the consistency between ICCF and zDCF or JAVELIN time lags. We found that zDCF time lags are consistent with ICCF lags within 1σ. JAVELIN time lags seem to be systematically larger than those of ICCF and zDCF, although the difference is within 1σ.

As a consistency check for the Hα time lag, we also used the light curves from three nights: 2017 April 29, April 30, and May 1. Since these light curves showed relatively large flux uncertainties due to bad weather, we did not correct for the continuum contribution and measured the time lag of the Hα-band light curve with respect to the V-band light curve as shown in Figure 8. For these measurements, we only used the Hα-band data from the MDM 1.3 m by excluding the low-quality data with large uncertainties from the BOAO 1.8 m. The measured time lags from 2017 April 29 and 30 have large uncertainties as expected and are roughly consistent with the best lag measurement from 2018 April 8 within the error. In the case of 2017 May 1, we obtained a time lag consistent with zero, presumably due to the lack of a strong pattern in the light curves.

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During the campaign on 2017 April 29, we obtained spectroscopic monitoring data with the Gemini GMOS for ∼3.5 hr and constructed a light curve of the Hα emission line. By cross-correlating with the V-band light curve, we measured the time lag as shown in Figure 9. Note that the flux calibration has large uncertainties since the sky conditions were quickly changing during the campaign, which had to be ended after ∼3.5 hr. We calibrated the flux of the broad Hα emission line, by assuming that the [S ii] emission-line flux is constant. Then, we converted the line flux to magnitude units for consistency with the Hα-band light curves. We could not obtain meaningful results since the overlap between the V band and the Hα light curves was limited, as was the sampling.

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We investigated the time lag between continuum bands using the UV, optical, and near-IR light curves. While all continuum light curves showed consistent variability patterns, we were not able to detect any reliable lag between two continuum bands, as summarized in Table 5.

Table 5.  Time Lags between Continuum Light Curves

Date	Telescopes	Light Curve 1	Light Curve 2	τ	Method
(UT)				(minutes)
(1)	(2)	(3)	(4)	(5)	(6)
2017 Apr 30	UVOT, BOAO, DOAO, LOAO,	UVM2	V	${66}_{-146}^{+277}$	ICCF
	MDM 1.3 m, MLO, Nickel, WMO			$-{136}_{-11}^{+157}$	zDCF
2017 May 1	UVOT, BOAO, DOAO, Hiroshima,	UVM2	V	${135}_{-126}^{+134}$	ICCF
	LOAO, MDM 1.3 m, MLO, Nickel			${228}_{-259}^{+15}$	zDCF
2017 Apr 26	CMO 2.5 m	J	K	${0}_{-119}^{+95}$	ICCF
				$-{7}_{-7}^{+24}$	zDCF
2017 Apr 28	CMO 2.5 m	J	H	$-{7}_{-92}^{+91}$	ICCF
				$-{33}_{-15}^{+47}$	zDCF
2017 Apr 28	CMO 2.5 m	J	K	${2}_{-145}^{+129}$	ICCF
				${34}_{-13}^{+16}$	zDCF
2017 Apr 28	CMO 2.5 m	H	K	${24}_{-158}^{+122}$	ICCF
				${47}_{-20}^{+177}$	zDCF

Note. Rest-frame time-lag values are chosen from the medians of the distributions for ICCF and from the maximum likelihood lags for zDCF. Central 68% intervals are taken as their uncertainties.

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First, we performed a cross-correlation analysis using the UV and V-band light curves. However, these light curves have several limitations. The UV light curve has gaps of approximately an hour between epochs owing to the invisibility of the target in each orbit of Swift. Thus, a relatively short lag of ∼1 hr is challenging to measure. In addition, the flux uncertainties of the UVM2 band are relatively high, Δm ≈ 0.05–0.1, comparable to the fractional variability of the UVM2 light curve.

Second, we investigated the lag of the near-IR continuum. Unfortunately, there was no time baseline when the optical and near-IR monitoring observations were performed simultaneously. Thus, we only compared among J-, H-, and K-band light curves. We obtained no meaningful time-lag measurements among the J, H, and K light curves, as their temporal baselines were relatively short, and the sampling and time resolution were limited (see Figure 3).

In this section, we investigate the size–luminosity relation by measuring the monochromatic luminosity at 5100 Å. First, we calculate the mean V-band magnitude of the AGN from the light curve on 2018 April 8 and obtain V_AGN = 16.1. Second, we rescale the mean spectrum constructed from the 3.5 hr GMOS observations on 2017 April 29 by multiplying by a scale factor of 0.507, in order to match the synthetic V-band magnitude measured from the mean spectrum with the photometry result V_AGN = 16.1 mag. Here we assume that the spectral shape changed insignificantly during 2017 and 2018. Then, we measure the monochromatic luminosity at 5100 Å from the rescaled mean spectrum and obtain $\lambda {L}_{\lambda }(5100\,\mathring{\rm A} )=1.02\times {10}^{40}\,\mathrm{erg}\,{{\rm{s}}}^{-1}$, after Galactic extinction correction, which was adopted as 0.05 mag from Carson et al. (2015).

Note that the determined $\lambda {L}_{\lambda }(5100\,\mathring{\rm A} )$ is an upper limit of the AGN luminosity since there is a contribution from the host galaxy stellar component. To investigate the effect of host galaxy contribution, we model the radial surface brightness profile of the central source using two components: a point source and an exponential disk. For this analysis, we construct an average image using the high-quality V-band image data (i.e., 16 × 180 s exposure), which were obtained with the MDM 2.4 m telescope on 2018 April 8. Note that we use the images from the same date, from which we measured the time lag of the Hα emission line, in order to secure consistent measurements of the luminosity and the lag. Using the same aperture size as for the aperture photometry, we calculate the flux from a point source to be 84% of the total flux in the aperture. If we remove the 16% contribution from the host galaxy disk, then the AGN luminosity becomes $\lambda {L}_{\lambda }(5100\,\mathring{\rm A} )=8.52\times {10}^{39}\,\mathrm{erg}\,{{\rm{s}}}^{-1}$.

However, a more serious issue in measuring AGN monochromatic luminosity is the presence of a nuclear star cluster (NSC), which is a point-like source with an effective radius <03 (Carson et al. 2015). Since we cannot separate the NSC and the AGN in our images with a large seeing disk, we instead adopt the estimated luminosity of the NSC based on the modeling of the SED from Carson et al. (2015), which is $-{9.78}_{-0.04}^{+0.03}$ mag in the F438W band and $-{10.48}_{-0.09}^{+0.06}$ in the F547M band after Galactic extinction correction, and determine the luminosity at 5100 Å. After correcting the luminosity for the distance to NGC 4395 that we adopted in this work, we obtain $\lambda {L}_{\lambda ;\mathrm{NSC}}(5100\,\mathring{\rm A} )=3.59\times {10}^{39}\,\mathrm{erg}\,{{\rm{s}}}^{-1}$. By subtracting the flux from the NSC, we determine the AGN luminosity to be $\lambda {L}_{\lambda ;\mathrm{AGN}}(5100\,\mathring{\rm A} )=5.75\times {10}^{39}\,\mathrm{erg}\,{{\rm{s}}}^{-1}$.

To estimate the uncertainty of the AGN luminosity, we include several sources of error: (1) the flux measurement uncertainty at 5100 Å is 1.54%, (2) the systematic uncertainty due to the conversion of the SDSS magnitudes of comparison stars to the V band magnitudes is 0.01 mag (Jester et al. 2005), (3) the standard deviation of the mean magnitude from the V-band light curve is 0.015 mag, and (4) the flux measurement uncertainty of the NSC is 0.075 mag (Carson et al. 2015). Combining these errors, we determine $\mathrm{log}\lambda {L}_{\lambda ;{5100}_{\mathrm{AGN}}}(5100\,\mathring{\rm A} )=39.76\pm 0.03$, or $\lambda {L}_{\lambda ;{5100}_{\mathrm{AGN}}}(5100\,\mathring{\rm A} )=\left(5.75\pm 0.40\right)\times {10}^{39}\,\mathrm{erg}\,{{\rm{s}}}^{-1}$.

By combining the monochromatic luminosity at 5100 Å and the best measurement of the Hα lag, τ = 83 ± 14 minutes, we compare NGC 4395 with other reverberation-mapped AGNs in the size–luminosity relation (Figure 10). NGC 4395 is offset by 0.48 dex from the size–luminosity relation defined by more luminous AGNs (Bentz et al. 2013, case for Clean+ExtCorr in Table 14). If we consider the intrinsic scatter (i.e., ≲0.19 dex) of the relation reported by Bentz et al. (2013), the offset is significant (≥2.5σ). On the other hand, the systematic uncertainty of the AGN luminosity of NGC 4395 can be very large owing to the difficulty of separating the AGN from the NCS. Note that recent reverberation studies showed that more luminous AGNs are scattered below the best-fit relation given by Bentz et al. (2013); see Section 4.3 for more details.

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There have been several previous studies of the emission-line time lag in NGC 4395, and our time-lag measurement is broadly consistent with these results. For example, Desroches et al. (2006) measured the Hα line lag to be ${0.06}_{-0.030}^{+0.034}$ days (${86}_{-43}^{+49}$ minutes) by integrating continuum-subtracted line spectra, consistent with our measurement, while Edri et al. (2012) measured a lag of 3.6 ± 0.8 hr (216 ± 48 minutes) based on photometric light curves with broadband filters (SDSS g', r', and i'). In the case of the broadband photometry light curves, they measured autocorrelations for each light curve, as well as cross-correlations for each combination of two light curves, and then subtracted autocorrelations from cross-correlations to determine the lag between the continuum and emission line. However, this method is less reliable since the continuum flux is dominant (>75%) in the total flux measured with the broadband filters, leading to the difficulty that the flux measurement is more prone to photometric errors. Lastly, Peterson et al. (2005) reported the lag between the continuum at 1350 Å and the C iv λ1549 broad emission line as ∼1 hr based on two different sets of light curves. The C iv lag is shorter than our Hα lag, indicating that these measurements are consistent with the stratification of the BLR.

In the case of AGN luminosity, Filippenko & Ho (2003) reported ${L}_{5100}=6.6\times {10}^{39}\,\mathrm{erg}\,{{\rm{s}}}^{-1}$, which is close to our estimate. Other studies determined the bolometric luminosity of NGC 4395 by integrating the SED as $1.2\times {10}^{41}\,\mathrm{erg}\,{{\rm{s}}}^{-1}$ (Lira et al. 1999), $1.9\times {10}^{40}\,\mathrm{erg}\,{{\rm{s}}}^{-1}$ (Moran et al. 1999), and $9.9\times {10}^{40}\,\mathrm{erg}\,{{\rm{s}}}^{-1}$ (Brum et al. 2019). If we adopt the bolometric correction of 10 (Woo & Urry 2002) for the reported measurements, L₅₁₀₀ ranges from $1.9\times {10}^{39}$ ergs⁻¹ to 1.2 × 10⁴⁰ erg s⁻¹, which are similar to our estimate.

The current investigation, along with prior studies reporting estimates of the AGN luminosity, is affected by various sources of systematic uncertainties. Note that the AGN PSF decomposition using high-quality imaging data has been applied to many of the reverberation-mapped AGNs (Bentz et al. 2013). However, even the best spatial resolution of Hubble Space Telescope (HST) imaging may not be enough to reliably separate the AGN from the NSC with an effective radius of <03.

Although the luminosity of the AGN in NGC 4395 is two orders of magnitude lower than in typical Seyfert 1 galaxies, the AGN seems to broadly follow the size–luminosity relation, indicating that the same photoionization assumption is valid at the low-luminosity end. Based on the black hole mass measurement from the Hα reverberation mapping (9000 ${M}_{\odot }$; Woo et al. 2019) and the bolometric luminosity log L_bol = 42.06, we determined the Eddington ratio to be ∼5%. These results indicate that NGC 4395 is a scaled-down version of a typical Seyfert 1 galaxy with an intermediate-mass black hole and ∼5% of the Eddington accretion.

We measured the variability of the AGN continuum in the V band as ${F}_{\mathrm{var}}\approx 0.02$ and ${R}_{\max }\approx 1.1$ based on 1-day baseline light curves. The amplitude of the variability slightly increases as ${F}_{\mathrm{var}}\approx 0.04\mbox{--}0.08$ and ${R}_{\max }\approx 1.2\mbox{--}1.7$ with a longer baseline of several days. These results are consistent with those of Desroches et al. (2006), who reported the variability in V-band photometry ${F}_{\mathrm{var}}=0.019\mbox{--}0.042$ and R_max = 1.08–1.20 based on single-night light curves. The variability of NGC 4395 is similar to those of other Seyfert 1 galaxies (e.g., Walsh et al. 2009). For example, the 15 AGNs with relatively low luminosity, which were monitored by the Lick AGN Monitoring Project 2011 over several-month timescales, showed ∼0.1 mag variability, ${F}_{\mathrm{var}}$ ranges of 0.02–0.13, and R_max ranges of 1.13–1.68 (Pancoast et al. 2019). These results imply that the variability characteristics of NGC 4395 are similar to those of other Seyfert 1 galaxies.

We investigated the size–luminosity relation at the low-luminosity end by including our lag and luminosity measurements of NGC 4395. While the size–luminosity relation has been defined based on the Hβ lag measurements, we only obtained an Hα lag measurement. Thus, the systematic difference between Hβ and Hα lags may introduce additional uncertainty.

It is not clear whether the Hα time lag is longer than the more commonly used Hβ lag for a given object. Kaspi et al. (2000) found no significant difference between continuum-to-Hα and continuum-to-Hβ time-lag measurements in their reverberation sample. In contrast, Hα is expected to show a longer time lag than Hβ owing to optical depth effects, which are manifested as the radial stratification within the BLR (Netzer 1975; Rees et al. 1989; Korista & Goad 2004). Bentz et al. (2010) provided a detailed discussion, reporting that the Hα lag is a factor of 1.54 longer on average than the Hβ lag based on the reverberation mapping results of low-redshift AGNs. If we assume that the Hβ lag is shorter than the Hα lag, the offset of NGC 4395 from the size–luminosity relation becomes larger.

On the other hand, we need to consider the uncertainty of the measured AGN luminosity. The main systematic uncertainty comes from the correction for the flux from the NCS, which is not easily decomposed from the AGN. We adopted the luminosity of the NSC measured by Carson et al. (2015), which suffers large uncertainty due to the limited spatial resolution. Note that the AGN and the NSC have comparable effective radii, and even with the spatial resolution provided by HST, the two sources were not clearly decomposed in the two-dimensional imaging analysis. Carson et al. (2015) argued that the degeneracy between the NSC and the AGN introduced a systematic uncertainty of 0.2 mag for the luminosity of the NSC. We note that, based on our high-quality GMOS spectrum, we were not able to decompose the AGN power-law component and stellar component. Considering the degeneracy of the AGN and the NSC in the imaging and spectroscopy and the dependence of the flux ratio on wavelength, the overall uncertainty of the AGN luminosity seems considerable. Thus, we find no strong evidence that NGC 4395 is offset from the size–luminosity relation defined by more luminous AGNs.

Given the measured luminosity and size of the BLR, the offset of NGC 4395 from the size–luminosity relation is not significantly large when compared to more recent reverberation mapping results. For example, AGNs from the studies by Du et al. (2016, 2018), Grier et al. (2017), and Ilić et al. (2017) exhibit large scatter, and some of them are more offset than NGC 4395. Note that the AGNs in Du et al. (2016, 2018) have a high accretion rate (e.g., super-Eddington), which may be the reason for the offset from the relation. In contrast, NGC 4395 has a much lower Eddington ratio (∼5%). On the other hand, the AGNs studied by Grier et al. (2017) are higher-redshift objects with Eddington ratio larger than 0.1, and their luminosity may suffer systematic uncertainties due to the contribution from the host galaxies. To constrain the size–luminosity relation at the low-luminosity end, it is necessary to obtain better measurements of the AGN luminosity of NGC 4395 and to investigate the scatter of the relation caused by systematic effects and Eddington ratios.