# More Evidence for the Intermediate Broad Line Region of the Mapped AGN PG
0052+251

Xue-Guang Zhang1,2
1Purple Mountain Observatory, Chinese Academy of Sciences, 2 Beijing XiLu,
NanJing, JiangSu, 210008, P. R. China
2Chinese Center for Antarctic Astronomy, NanJing, JiangSu, 210008, P. R. China

###### Abstract

In the manuscript, the properties of the proposed intermediate BLR are checked
for the mapped AGN PG 0052+251. With the considerations of the apparent
effects of the broad He ii line on the observed broad H$\beta$ profile, the
line parameters (especially the line width and the line flux) of the observed
broad H$\alpha$ and the broad H$\beta$ are carefully determined. Based on the
measured line parameters, the model with two broad components applied for each
observed broad balmer line is preferred, and then confirmed by the calculated
much different time lags for the inner/intermediate broad components and the
corresponding virial BH masses ratio determined by the properties of the inner
and the intermediate broad components. Then, the correlation between the broad
line width and the broad line flux is checked for the two broad components:
one clearly strong negative correlation for the inner broad component, but one
positive correlation for the intermediate broad component. The different
correlations for the two broad components strongly support the intermediate
BLR of PG0052+251.

###### keywords:

Galaxies:Active – Galaxies:nuclei – Galaxies:quasars:Emission lines –
Galaxies: Individual: PG 0052+251

††pagerange: More Evidence for the Intermediate Broad Line Region of the
Mapped AGN PG 0052+251–LABEL:lastpage

##  1 Introduction

PG 0052+251 is one well studied mapped blue quasar (Bentz et al. 2009,
Chelouche & Daniel 2012, Collin et al. 2006, Kaspi et al. 2000, 2005, Peterson
et al. 2004, Zu et al. 2011, Zhang 2011b). Based on the measured size of the
BLR (Broad emission Line Region) and the line width of the broad $H\alpha$ and
the broad H$\beta$ in the literature, we (Zhang 2011b, Paper I) have shown
that the blue quasar PG 0052+251 is one special object in the plane of
$(\frac{\sigma(H\beta)}{\sigma(H\alpha)})^{2}$ versus
$\frac{R_{BLR,H\alpha}}{R_{BLR,H\beta}}$, where $\sigma$ and $R_{BLR}$ mean
the measured broad line width based on the mean/rms spectra and the size of
the BLR determined by the reverberation mapping technique (Blandford & Mckee
1992, Peterson 1993, Peterson & Horne 2004), because of the much different
virial black hole masses determined by the parameters of the broad H$\beta$
and the broad H$\alpha$. So that, in the Paper I, we have reported that it is
more appropriate for PG 0052+251 to describe the observed broad H$\alpha$ by
two broad components rather than by one broad component, and then reported the
strong evidence for the intermediate BLR with the size about 700 light-days,
besides the common BLR with the size about 100-200 light-days as discussed in
Kaspi et al. (2000, 2005), Peterson et al. (2004) etc.. The method in Paper I
to determine the intermediate BLR of PG 0052+251 is much different from the
other methods by emission line fitted results, such as in Bon et al. (2009),
Hu et al. (2012), Shapovalova et al. (2012), Zhu et al. (2009) etc. As the
first reported mapped AGN with the reliable intermediate BLR with measured
size by the mapping technique, we will further discuss whether there are
different intrinsic properties for the common inner BLR and the intermediate
BLR of PG 0052+251.

In Paper I, we have discussed that the intermediate BLR is not the extended
part of the common inner BLR, i.e, there is enough physical geometrical
distance between the common inner BLR and the intermediate BLR. Therefore, it
will be interesting to check whether the common inner BLR and the proposed
intermediate BLR have much different kinematic properties (such as much
different properties of kepler velocities of the line clouds in the two
regions), which is the main objective of the manuscript. In other words, we
should check the properties of the line parameters (line width tracing
properties of kepler velocity, and line flux tracing distance between the line
region and the central black hole) of the broad optical balmer lines from the
inner BLR and from the intermediate BLR for PG 0052+251.

It is very difficult to clearly reconstruct the detailed kinematic structures
of the inner BLR and the intermediate BLR, through the sparse and incomplete
observational data series of PG 0052+251. Therefore, in the manuscript, we
only check the simple correlations between the line width and the line flux of
the broad lines from the two line regions. Surely, the correlation should be
strongly negative, under the Virialization assumption (Bennert et al. 2011,
Collin et al. 2006, Down et al. 2010, Greene & Ho 2004, 2005, Kelly & Bechtold
2007, Marziani et al. 2003, Netzer & Marziani 2010, Onken et al. 2004, Park et
al. 2012, Peterson et al. 2004, Peterson 2010, Rafiee & Hall 2011, Shen & Liu
2012, Sluse et al. 2011, Sulentic et al., 2000, Vestergaard 2002):

$M_{BH}\propto R_{BLR}\times\sigma^{2}\propto L^{0.5}\times\sigma^{2}$ (1)

However, besides the commonly expected negative correlation, we (Zhang 2013a)
have recently reported that for the well-known mapped double-peaked emitter
(AGN with double-peaked broad low-ionization emission lines) 3C390.3 (Dietrich
et al. 1998, 2012, Eracleous et al. 1995, 1997, Flohic & Eracleous 2008,
Popovic et al. 2011, Sergeev et al. 2011, Shapovalova et al. 2001, Zhang
2011a, 2013b), the correlation is positive for the broad optical balmer lines,
which should further indicates the accretion disk origination for the observed
broad lines. Therefore, if the correlations are much different for the broad
lines from the inner BLR and from the intermediate BLR for PG 0052+251, we
should confirm that the kinematic properties are intrinsically different for
the two line regions, and should give some further structure information about
the intermediate BLR.

This manuscript is organized as follows. Section 2 shows the main results,
including our procedure to measure the line parameters of the broad balmer
lines, and the line parameters correlations of the broad lines. Section 3
gives the discussions and conclusion. Moreover, the redshift $z=0.155$ has
been accepted for the PG 0052+251 in the manuscript.

##  2 Main Results

In Paper I (Zhang 2011b), we have shown that it is much preferred to describe
the broad observed H$\alpha$ by two broad components. Then, PG 0052+251 will
have the reasonable location in the plane of
$(\frac{\sigma(H\beta)}{\sigma(H\alpha)})^{2}$ versus
$\frac{R_{BLR,H\alpha}}{R_{BLR,H\beta}}$. However, in Paper I, only the mean
values and the statistical results are discussed about the line parameters of
the inner broad H$\alpha$ and the intermediate broad H$\alpha$ of PG 0052+251.
Here, we will show some more detailed results and further discussions about
the line parameters of both the broad H$\alpha$ and the broad H$\beta$.

In the manuscript, we consider the observational data and the spectra of PG
0052+251 collected from Kaspi et al. (2000) (http://wise-
obs.tau.ac.il/~shai/PG/). The 53 spectra have both apparent broad H$\alpha$
and apparent broad H$\beta$ observed from 16th Oct. 1991 to 27th Sep. 1998,
and have been well binned into 1$\AA$ per pixel. Then, the line properties of
the broad H$\alpha$ and the broad H$\beta$ have been checked for PG 0052+251,
with $S/N=10$ having been accepted for the collected spectra as discussed in
Kaspi et al. (2000).

###  2.1 Effects of the broad He ii$\lambda 4687\AA$ on the properties of the
Observed Broad H$\beta$ of PG 0052+251

As what have been done in Kaspi et al. (2000), Peterson et al. (2004) and
Zhang (2011b), effects of the optical Fe ii lines and He ii$\lambda 4686\AA$
line have been totally ignored. However, we can find that the apparent He ii
lines have strong effects on the line profile of the observed broad H$\beta$.
Certainly, we will find that there are much weak optical Fe ii lines in the
spectra of PG 0052+251. And moreover, the weak Fe ii lines can be well
described and removed by our following procedure. Thus, besides the effects of
the He ii line in the manuscript, there are no further discussions for the
effects of the Fe ii lines.

In Kaspi et al. (2000), Peterson et al. (2004) and in Zhang (2011b), the AGN
continuum emission underneath the observed H$\beta$ is determined by the two
continuum windows with the rest-wavelength from 4690Åto 4750Åand from 5115Åto
5175Å, without the considerations of the effects of the weak Fe ii and He ii
lines. It is clear that the blue window used to determine the continuum is on
the shoulder of the broad He ii line, which will lead to much steeper
determined AGN continuum, and lead to much weak broad wings of the broad
H$\beta$. Figure 1 shows the effects of the broad He ii line on the the
determined AGN continuum, and then the effects on the line parameters of the
H$\beta$. In the figure, the spectrum of PG 0052+251 observed on 14th, Nov.
1993 is shown, because of the more apparent He ii and optical Fe ii lines in
the spectrum. The spectral properties are discussed twice as follows. On the
one hand, the spectral lines are fitted within the wavelength range from
4690Åto 5175Åwithout the consideration of the He ii line, as what have been
done in the literature. On the other hand, the spectral lines are fitted
within the wavelength range from 4400Åto 5500Åwith the consideration of the He
ii line and the weak optical Fe ii lines. It is clear that there are strong
effects of the He ii line on the determined AGN continuum (the dashed and the
dot-dashed lines in the Figure 1).

Then, the line profile of the broad H$\beta$ is roughly checked. More detailed
discussions about the fitting procedure for the emission lines could be found
in the following subsection. If the spectral lines are considered within the
narrower wavelength range from 4690Åto 5175Å, the broad H$\beta$ can be well
described by one broad gaussian function (the dashed line near the bottom in
the Figure 1). However, the broad H$\beta$ can be well described by two broad
gaussian functions ( the solid lines near the bottom in the Figure 1), if the
spectral lines are considered within the wider wavelength range from 4400Åto
5500Å. Actually, the more recent optical Fe ii template discussed in the
Kovacevic et al. (2010) has been included in our procedure, in order to
clearly remove the probable effects of the optical Fe ii lines (the shadow
areas near the bottom in the Figure 1). Based on the results in the Figure 1,
we can find that the Fe ii lines are much weak and have few effects on our
results about the line parameters of the broad H$\beta$.

It is clear that there are apparent and strong effects of the He ii line on
the final results, especially on the AGN continuum and on the wings of the
broad H$\beta$. Thus, the effects of the He ii line should be well considered.
And therefore, in the following procedure to fit the spectral lines around the
H$\beta$, the wider wavelength range from 4400Åto 5500Åis accepted, rather
than the narrower wavelength range from 4690Åto 5175Å.

###  2.2 Line Parameters of the broad H$\beta$ and the broad H$\alpha$

In the manuscript, in order to obtain more reliable line parameters, the lines
around the H$\alpha$ (the broad and the narrow H$\alpha$ and the [N
ii]$\lambda 6548,6583$Ådoublet) and around the H$\beta$ (the broad and the
narrow H$\beta$, the broad He ii line, the [O iii]$\lambda 4959,5007$Ådoublet
and the optical Fe ii line) are fitted simultaneously within the wavelength
ranges from 4400Åto 5500Åfor the lines around the H$\beta$ and the ranges from
6300Åto 6900Åfor the lines around the H$\alpha$.

In the manuscript, two different models are considered to describe the
observed broad balmer lines: the model with two broad gaussian functions
applied for each observed broad balmer line, and the other model with one
broad gaussian function applied for each observed broad balmer line. Besides
the two models for the broad balmer lines, the narrow lines are described by
narrow gaussian functions with similar line profiles, i.e., they have the same
emission line redshifts, the same line width. And moreover, the [O iii] ([N
ii]) doublet has the fixed theoretical intensity ratio. Furthermore, one broad
gaussian function is applied for the He ii line. Then, two power law functions
are applied for the continuum under the H$\beta$ and the continuum under the
H$\alpha$ ($f_{\lambda}\propto\lambda^{\alpha}$).

Moreover, when two broad gaussian functions are applied for each observed
broad balmer line, the following restrictions are set:

$\begin{split}\frac{\sigma(H\alpha_{1})}{\sigma(H\alpha_{2})}&=\frac{\sigma(H\beta_{1})}{\sigma(H\beta_{2})}\\\
z(H\beta_{1})&=z(H\alpha_{1})\\\ z(H\beta_{2})&=z(H\alpha_{2})\end{split}$ (2)

where $\sigma$ and $z$ mean the broad line width (the second moment as
discussed in Peterson et al. 2004) and the broad emission line redshift of the
corresponding broad component, the suffixes ’1’ and ’2’ represent the broad
components from the corresponding broad line regions (’1’ for the inner broad
component and ’2’ for the intermediate broad component). The restrictions can
be reasonably accepted under the following considerations.

If the two broad components were physically true for the broad H$\alpha$ and
the broad H$\beta$, the result could be expected under the virialization
assumption that

$\frac{R_{BLR}(H\alpha_{1})\times\sigma(H\alpha_{1})}{R_{BLR}(H\alpha_{2})\times\sigma(H\alpha_{2})}=\frac{R_{BLR}(H\beta_{1})\times\sigma(H\beta_{1})}{R_{BLR}(H\beta_{2})\times\sigma(H\beta_{2})}$
(3)

where $R_{BLR}$ means the distance between the broad line region and the
central black hole. Once the results $R_{BLR}(H\alpha)\sim R_{BLR}(H\beta)$
are accepted, we can find the restriction for the line width ratio in the
equation (2). And moreover, once we accepted that the inner (intermediate)
broad components of the H$\alpha$ and the H$\beta$ from the same physical
emission region, the restriction on the broad line redshift in equation (2)
can be naturally accepted.

According to the models above and the corresponding restrictions, the spectral
lines can be well fitted through the Levenberg-Marquardt method. Then, the
results are firstly checked under the model with one broad gaussian function
applied for each observed broad balmer line. Here, we do not show the best
fitted results for all the 53 observed spectra, but two simple examples with
the maximum and the minimum line widths of the broad H$\beta$ in the Figure 2.
The basic correlations of the line parameters of the broad H$\alpha$ and the
broad H$\beta$ are checked and shown in Figure 3. It is clear that there is no
clear broad line width correlation: the spearman correlation coefficient is
0.14 with $P_{null}=30\%$, and no clear broad line flux correlation: the
coefficient is 0.29 with $P_{null}\sim 3\%$. If the broad H$\alpha$ and the
broad H$\beta$ are from the unique region, strong broad line flux and broad
line width correlations should be expected. The much weak correlations shown
in the Figure 3 indicate single broad component applied for each broad balmer
line is not so reasonable, and further considerations should be checked.

Then, the model with two broad components applied for each observed broad
balmer line is considered, with the restrictions in the equation (2). And
moreover, by the following three steps, the model can be checked and further
confirmed. The broad line parameters of the broad balmer lines are firstly
checked under the model. Then, the F-test technique is applied to check which
model is preferred for the broad balmer lines. Finally, the time-lagged
correlations are checked.

The best fitted results for the spectral lines are shown in the Figure 4 under
the model with two broad components applied for each observed broad balmer
line. The measured line parameters are listed in the Table 1. Then, we check
the correlations of the line parameters of the broad components of the balmer
lines in the Figure 5. The corresponding correlations of the line parameters
are apparent and strong (coefficient not less than 0.7 with $P_{null}$ less
than $10^{-8}$, the corresponding coefficients and $P_{null}$ are marked in
each panel of the figure),

$\begin{split}\sigma(H\alpha_{1})&=0.95\times\sigma(H\beta_{1})\\\
flux(H\alpha_{1})&=3.1\times flux(H\beta_{1})\\\
\sigma(H\alpha_{2})&=0.93\times\sigma(H\beta_{2})\\\
flux(H\alpha_{2})&=3.1\times flux(H\beta_{2})\end{split}$ (4)

It is clear that the broad line width ratios and the broad line flux ratios
for the inner/intermediate broad components are more reasonable.

Moreover, the properties about the relative shifted velocities of the two
broad components are checked and shown as the open circles in the Figure 6. It
is clear that the time dependent relative shift velocities are strongly linear
decreasing (the coefficient is 0.61 with $P_{null}\sim 10^{-6}$), and the best
fitted result (the solid line in the figure) can be written as,

$\frac{W_{0}(1)-W_{0}(2)}{\rm km/s}\propto(-0.76\pm
0.04)\times(Julian-2448837)$ (5)

Furthermore, the Figure 6 shows the properties of the relative shift
velocities of the intermediate broad component relative to the narrow [O
iii]$\lambda 5007$Å(solid circles in the figure). We can find that the
intermediate broad components have tiny relative shift velocities to the
narrow [O iii]. The time dependent rather than one randomly distributed
relative shift velocities between the inner broad and the intermediate broad
components strongly indicate the two components have physical meanings: one
line region having no radial components and the other component having
apparent radial moving contributions. Here, we should note the inner BLR
including different contributions from different components DOES NOT have the
similar meaning as the multiple BLRs. in the manuscript and in the literature,
we accept and define that the inner BLR and the intermediate BLR mean they are
two physical separated line emission regions with apparent physical space
between the two regions. In other words, the observed complicated spectral
broad lines do not indicate there are two or multiple BLRs, because the
different line components were perhaps included in the same line region.
Meanwhile, the current quality of the spectra can not provide further
information to discuss whether the radial components are from the other line
region which has apparent physical space from the inner BLR and/or the
intermediate BLR. Thus, no further discussions about the radial motions are
shown in the manuscript.

Then, the F-test technique is applied to determine which model is preferred
for the observed broad balmer lines. Based on the best fitted results by the
two models above, the F values firstly are calculated as

$F=\frac{(SSE_{1}-SSE_{2})/(DoF_{1}-DoF_{2})}{SSE_{2}/(DoF_{2})}$ (6)

where $SSE$ represents the sum of squared residual for one model, the suffix
’1’ is for the model with one broad component applied for each observed broad
balmer line, and the suffix ’2’ is for the model with two broad components
applied for each observed broad balmer line, $DoF$ represents the degree of
freedom for one model. Through the comparison between the calculated value $F$
by the equation (6) and the F-value estimated by the F-distribution with the
numerator degrees of freedom of $DoF_{1}-DoF_{2}$ and the denominator degrees
of freedom of $DoF_{2}$, we can conclude our preferred model. Based on the
selected wavelength range for the lines around the H$\alpha$ and around the
H$\beta$ and the model parameters, the values of the degrees of freedom for
the two models are: $DoF_{1}=1829$, $DoF_{2}=1826$. It is clear that the
F-value by the F-distribution with $p=0.05$ is 2.6 (the IDL function
$f\\_cvf(0.05,3,DoF_{2}-1)$) based on the numerator and denominator degrees of
freedom. However, the calculated values $F$ listed in the Figure 4 by the
equation (6) are much larger than 2.6, which strongly indicates that it is
more preferred to describe each observed broad balmer line by two broad
components.

Furthermore, the time-lagged correlations are checked for the two broad
components. If the inner and the intermediate broad components were physically
true and from two independent line regions, there should be much different
time lags between the variabilities of the AGN continuum and the two broad
components. And then, based on the time-lagged results, we can confirm whether
the model dependent line parameters are physically reliable or only the
mathematical model results. Before proceeding further, one point we should
note. Because of the effects of the He ii lines and the narrow lines around
the H$\alpha$, it should be not so appropriate to directly use the scaled
light curves of the H$\alpha$ and the H$\beta$ shown in the Kaspi et al.
(2000), as what we have done in Paper I. Therefore, the light curves of the
two broad components of the H$\beta$ (the H$\alpha$) are determined with the
assumption that the [O iii]$\lambda 5007$Åflux is constant,

$flux=flux(obs)\times\frac{710\times 10^{-16}{\rm
erg/s/cm^{2}}}{flux([OIII]\lambda 5007\AA)}$ (7)

where $710\times 10^{-16}{\rm erg/s/cm^{2}}$ is the mean flux of the [O
iii]$\lambda 5007$Å, $flux(obs)$ is the line flux for the corresponding broad
component directly measured through the observed spectrum, $flux$ means the
corrected line flux. It is clear that there is no time-dependent trend for the
[O iii], and the rms variation about the mean is around 10%, which indicates
the flux normalization to the [O iii] flux is necessary. Moreover, we can find
that the center wavelengths of the [O iii]$\lambda 5007$Åhave tiny shifts,
which is perhaps due to the large dispersions and spectral resolutions of the
original spectra of PG 0052+251 (Kaspi et al. 2000). Meanwhile, the center
wavelength shifts of the [O iii] have few effects on our final results about
the broad line parameter correlations. Thus, there are no further discussions
about the shifts in the manuscript.

Once the observational light curves of the broad components are determined,
the commonly accepted ICCF technique (Interpolated Cross Correlation Function,
Gaskell & Peterson 1987, Koratkar & Gaskell 1989, Koptelova et al. 2006,
Peterson 1993) and the more recent SPEAR technique (Stochastic Process
Estimation for AGN Reverberation based on the damped random walk model for AGN
variability, Kelly et al. 2009, Kozlowski et al. 2010, MacLeod et al. 2010, Zu
et al. 2011) are applied to check the time lags between the variabilities of
the continuum and the inner/intermediate broad components. Here, the light
curve of the continuum is the one collected from Kaspi et al. (2000).
Moreover, when the commonly used ICCF method is applied, the direct
interpolating method is not only applied to the measured observational light
curves (the open circles in the right panels of Figure 7 and Figure 8) of the
broad components and the continuum emission, but also applied to the best
descriptions of the light curves determined by the damped random walk method
(the shadow areas in the right panels of Figure 7 and Figure 8), in order to
reduce the effects of the large time gaps of the observational light curves.
Moreover, the two different method (ICCF and SPEAR) should lead to more
reliable results, if there were similar ICCF and SPEAR results.

The time-lagged correlations are shown in the Figure 7 for the broad
components of the H$\beta$ and in the Figure 8 for the broad components of the
H$\alpha$. It is clear that there are apparent ans different time lags between
the broad components and the AGN continuum based on the ICCF and SPEAR
results,

$\begin{split}R_{BLR}(H\beta_{1},ICCF)&\simeq R_{BLR}(H\alpha_{1},ICCF)\\\
&\sim 270\pm 80\hskip 7.11317pt{\rm light-days}\\\
R_{BLR}(H\beta_{1},SPEAR)&\simeq R_{BLR}(H\alpha_{1},SPEAR)\\\ &\sim 211\pm
50\hskip 7.11317pt{\rm light-days}\\\ R_{BLR}(H\beta_{2},ICCF)&\simeq
R_{BLR}(H\alpha_{2},ICCF)\\\ &\sim 1200\pm 300\hskip 7.11317pt{\rm light-
days}\\\ R_{BLR}(H\beta_{2},SPEAR)&\simeq R_{BLR}(H\alpha_{2},SPEAR)\\\ &\sim
1056\pm 160\hskip 7.11317pt{\rm light-days}\\\ \end{split}$ (8)

where the uncertainties with $3\sigma$ confidence levels of the time lags are
determined by the bootstrap method as what we have done in Paper I, and the
ICCF results are the mean values based on the observational light curves and
the light curves determined through the random walk method. The results
strongly support that the two model dependent broad components are both
mathematically and physically true, and have much different structures, and it
is more preferred to describe the observed broad balmer line by two broad
components for PG 0052+251.

###  2.3 On the Correlation between the Line Width and the Line Flux

Now, based on the reliable measured line parameters and the corresponding
uncertainties, the correlations of the broad line parameters of the two broad
components of the balmer lines can be checked. The linear correlation
coefficients are about -0.63 with $P_{null}\sim 9\times 10^{-7}$, 0.72 with
$P_{null}\sim 5\times 10^{-9}$, -0.48 with $P_{null}\sim 4\times 10^{-4}$ and
0.69 with $P_{null}\sim 9\times 10^{-8}$ for the correlations between the line
width and the line flux for the inner broad H$\alpha$, for the intermediate
broad H$\alpha$, for the inner broad H$\beta$ and for the intermediate broad
H$\beta$ respectively. The strong correlations are shown in Figure 9. It is
clear that there are much different properties for the inner and the
intermediate broad components of PG 0052+251: one clear positive correlation
for the intermediate broad component, but one clear negative correlation for
the inner broad component. The best fitted results for the correlations with
the considerations about the uncertainties in both the coordinates can be
written as,

$\begin{split}\log(\frac{flux(H\alpha_{1})}{10^{-16}{\rm
ergs/s/cm^{2}}})&=(7.89\pm 0.21)\\\ &-(1.27\pm
0.06)\times\log(\frac{\sigma(H\alpha_{1})}{\rm km/s})\\\
\log(\frac{flux(H\alpha_{2})}{10^{-16}{\rm ergs/s/cm^{2}}})&=(-2.16\pm
0.33)\\\ &+(1.81\pm 0.11)\times\log(\frac{\sigma(H\alpha_{2})}{\rm km/s})\\\
\log(\frac{flux(H\beta_{1})}{10^{-16}{\rm ergs/s/cm^{2}}})&=(8.69\pm 0.39)\\\
&-(1.65\pm 0.12)\times\log(\frac{\sigma(H\beta_{1})}{\rm km/s})\\\
\log(\frac{flux(H\beta_{2})}{10^{-16}{\rm ergs/s/cm^{2}}})&=(-2.85\pm 0.41)\\\
&+(1.85\pm 0.13)\times\log(\frac{\sigma(H\beta_{2})}{\rm km/s})\end{split}$
(9)

Meanwhile, the corresponding 99.95% confidence bands for the best fitted
results above are also shown in Figure 9.

Before the end of the subsection, one point we should mote. Based on the
fitted results shown in the Figure 4 and the listed line parameters in the
Table 1, we can find that there are five spectra of which the narrow H$\alpha$
(and/or [N ii]$\lambda 6583\AA$) are much stronger, while the narrow H$\beta$
are much weaker: JD-2448837, JD-2449219, JD-2449249, JD-2449279 and
JD-2450459. We do not know the clear reason why the narrow balmer lines are
much different from the lines in the other spectra. However, we can find that
the results have few effects on our final results about the broad line
parameters correlations, because no different re-calculated broad line
parameters correlations can be found without the considerations of the five
spectra with the different narrow lines. Without the considerations of the
five cases, the corresponding correlation coefficients are about -0.62 with
$P_{null}\sim 6\times 10^{-6}$, 0.74 with $P_{null}\sim 3\times 10^{-9}$,
-0.49 with $P_{null}\sim 7\times 10^{-3}$ and 0.72 with $P_{null}\sim 2\times
10^{-8}$ for the correlations between the broad line width and the broad line
flux for the inner broad H$\alpha$, for the intermediate broad H$\alpha$, for
the inner broad H$\beta$ and for the intermediate broad H$\beta$ respectively.
Therefore, no apparent effects of the narrow lines in the several special
cases can be found for our final results. Thus, there are no further
discussions about the cases with special narrow lines in the manuscript.

As we commonly know that the properties of the broad line flux can be used to
trace the distance between the broad line clouds and the central black hole,
and the properties of the line width can be used to trace the kepler
velocities of the broad line clouds. The different correlations between the
line width and the line flux for the inner and the intermediate broad
components strongly indicate there are much different properties of the two
broad line regions of PG 0052+251.

##  3 Discussions and Conclusions

It is clear that based on the widely accepted Virialization assumption for the
broad line AGN, the negative correlation between the line width and the line
flux can be expected for individual object. Such negative correlation has been
found and confirmed for several mapped objects, such as NGC5548 (Bentz et al.
2006, Denney et al. 2010, Peterson et al. 2004, Zhang 2011a) and some other
mapped objects discussed in Peterson et al. (2004). Then based on the
empirical relation to estimate the size of the BLR $R_{BLR}\propto L^{\alpha}$
(Bentz et al. 2006, 2009, Denney et al. 2010, Kaspi et al. 2005, Greene et al.
2010, Wang & Zhang 2003), one strongly negative correlation between the broad
line flux and the broad line width can be expected for individual object.
Meanwhile, the common viewpoint about gravity dominated BLR can be used to
naturally explain the negative correlation (Kollatschny & Zetzl1 2011, Krause
et al. 2011, Netzer & Marziani 2010, Peterson & Wandel 1999, and references
therein).

Moreover, we should note that if the common value $\alpha\sim 0.5$ was
accepted for the empirical relation to estimate the BLR size of AGN, we should
expect the slope of the correlation for the inner broad component is about
$-4$, which is smaller than the reported slope, $\sim-1.5$ shown in Figure 9
for PG 0052+251. The difference can be well and naturally explained by the
following reason: the shape of the continuum changes as AGNs vary, i.e.,
variability amplitudes are different for UV and optical bands. And moreover,
UV flux rather than optical flux is a better measure for ionizing flux which
is one much better indicator for the size of BLR. So that, the different
variability amplitudes in UV and optical bands lead to some different slope
from $-4$ for the correlations of the inner broad components of PG 0052+251,
and smaller variability amplitudes in optical bands lead to the slope larger
than $-4$.

Besides the negative correlation for the inner broad H$\alpha$, there is one
clear positive correlation between the line width and the line flux for the
intermediate broad components of PG 0052+251, which is against the
virialization assumption. However, we (Zhang 2013a) have recently reported
that there is one positive correlation between the line width and the line
flux of the broad double-peaked H$\alpha$ of the well-known mapped object
3C390.3. Furthermore, we have discussed that the positive correlation of broad
line parameters could be used as one indicator for the accretion disk
origination of the broad lines. So that, if the accretion disk origination was
accepted for the intermediate broad components of PG 0052+251, the positive
correlation could be naturally explained, as we have explained the positive
correlation for the double-peaked emitter of 3C390.3.

Although there are different dependent modes of the size of BLR on the line
flux for the two components, the correlation between the measured size of the
BLR (not the line flux) and the line width can be checked under the
virialization assumption: similar black hole masses determined by the
properties of the inner BLR and the intermediate BLR

$\begin{split}\frac{R_{BLR}(H\alpha_{1})\times\sigma^{2}(H\alpha_{1})}{R_{BLR}(H\alpha_{2})\times\sigma^{2}(H\alpha_{2})}\sim\frac{\frac{226}{{\rm
light-days}}\times(\frac{3100}{{\rm km/s}})^{2}}{\frac{1090}{{\rm light-
days}}\times(\frac{1400}{{\rm km/s}})^{2}}=1.01\\\ \end{split}$ (10)

where $\sigma(H\alpha_{1})\sim 3100{\rm km/s}$ and $\sigma(H\alpha_{2})\sim
1400{\rm km/s}$ are the mean line widths of the inner broad and the
intermediate broad components of the H$\alpha$, and $R_{BLR}$ is the weighted
mean value from the ICCF and SPEAR results (Equation (8)). Similar result can
be confirmed for the two broad components of the H$\beta$. The results
indicate the measured time lags for the inner/intermediate broad components
are reliable, and the two model-calculated components are not fake.

Before the end of the manuscript, there are two points we should note. On the
one hand, the main objective of the manuscript is to provide further evidence
for the intermediate BLR of PG 0052+251. The much different and reliable
correlations for the two components in the Figure 9 provide enough evidence to
support our objective. Therefore, no further discussions are shown for the
detailed structure information on the two broad components. The apparent time-
dependent shifted velocities of the inner broad component (Figure 6) indicates
probable radial contributions for the component. The positive correlation
provides the possibility for the accretion disk origination of the
intermediate broad components. So far only two individual AGNs, 3C390.3 in our
previous paper and PG 0052+251 in the manuscript, have shown the positive
correlation between the line width and the line flux. Meanwhile, the accretion
disk origination for the double-peaked broad lines have been widely accepted
for the 3C390.3. Therefore, we naturally presume but not confirm that the
intermediate broad balmer lines of PG 0052 have the similar characters as the
lines of 3C390.3. Surely, more efforts should be done to give the final
confirmed conclusions about the structures of the two components, which is
beyond the scope of the manuscript. On the other hand, more reasonable
continuum windows are selected to determine the AGN continuum especially under
the H$\beta$ in the manuscript, which leads to some different BLR size based
on the H$\beta$ variabilities. If the contributions of the narrow lines are
subtracted, the measured size of the BLR is around $R\sim 200$ light-days
based on the H$\beta$ variabilities, similar with the values determined by the
H$\alpha$ variabilities. Therefore, the position of PG 0052+251 is reasonable
in the plane of $(\frac{\sigma(H\beta)}{\sigma(H\alpha)})^{2}$ versus
$\frac{R_{BLR,H\alpha}}{R_{BLR,H\beta}}$. The selected narrower wavelength
range to determine the continuum lead the inner broad H$\beta$ being much
weakened. Yet, in other ways, it is effective to select the objects with
probable intermediate BLR through the properties of objects in the plane of
$(\frac{\sigma(H\beta)}{\sigma(H\alpha)})^{2}$ versus
$\frac{R_{BLR,H\alpha}}{R_{BLR,H\beta}}$.

Our final main conclusions are as follows.

  * •

The observed broad balmer lines are being fitted by two models. If the model
with only one simple broad component was applied for each observed broad
balmer line, the corresponding broad line parameters correlations between the
broad H$\alpha$ and the broad H$\beta$ are much weak (Figure 3). However,
Under model with two broad components applied for each observed broad balmer
line, the broad line width and the broad line flux correlations are much
strong and more reasonable for the corresponding broad components of the
H$\alpha$ and the H$\beta$ (Figure 5). Moreover, the F-test technique has been
applied to check the two models, and indicates two broad components for the
broad balmer line (Figure 4) are preferred. Then, the time-lagged correlations
have been checked for the two components (Figure 7 and Figure 8). The much
different time lags between the two broad components and the continuum ensure
that the two components are not mathematical model dependent components but
have physical meanings for different geometric structures.

  * •

Based on the measured line parameters, one positive correlation between the
line width and the line flux can be found for the intermediate broad
component, but one negative correlation can be found for the inner broad
component, of the balmer lines of PG 0052+251. The different correlations
strongly support the intermediate BLR of PG 0052+251, and clearly indicate the
inner BLR and the intermediate BLR have much different dynamic/geometric
structures.

## Acknowledgements

ZXG very gratefully acknowledge the anonymous referee for giving us
constructive comments and suggestions to greatly improve our paper. ZXG
gratefully acknowledges the support from NSFC-11003043 and NSFC-11178003, and
gratefully thanks Dr. Kaspi S. to provide public observed spectra of PG
0052+251 (http://wise-obs.tau.ac.il/~shai/PG/).

## References

  * [Bentz et al.2006] Bentz M. C., Peterson B. M., Pogge R. W., Vestergaard M., Onken C. A., 2006, ApJ, 644, 133
  * [Bentz et al.2009] Bentz M. C., Walsh J. L., Barth A. J., Baliber N., Bennert V. N., et al., 2009, ApJ, 705, 199
  * [Bennert et al.2011] Bennert N., Auger M. W., Treu T., Woo J.-H., Malkan M. A., 2011, ApJ, 726, 59
  * [Blandford & Mckee1982] Blandford R. D., & Mckee C. F., 1982, ApJ, 255, 419
  * [Bon et al.2009] Bon E., Popovic L. C., Gavrilovic N., Mura G. L., Mediavilla E., 2009, MNRAS, 400, 924
  * [Brotherton et al.1994] Brotherton M. S., Wills B. J., Francis P. J., Steidel C. C., 1994, ApJ, 430, 495
  * [Chelouche & Daniel2012] Chelouche D. & Daniel E., 2012, ApJ, 747, 62
  * [Collin et al.2006] Collin S., Kawaguchi T., Peterson B. M., Vestergaard M., 2006, A&A, 456, 75
  * [Denney et al.2010] Denney K. D., Peterson B. M., Pogge R. W., Adair A., Atlee D. W., et al., 2010, ApJ, 721, 715
  * [Dietrich et al.1998] Dietrich M., Peterson B. M., Albrecht P., Altmann M., Barth A. J., et al., 1998, ApJS, 115, 185
  * [Dietrich et al.2012] Dietrich M., Peterson B. M., Grier C. J., Bentz M .C., Eastman J., et al., 2012, ApJ, 757, 53D
  * [Down et al.2010] Down E. J., Rawlings S., Sivia D. S., Baker J. C., 2010, MNRAS, 401, 633
  * [Eracleous et al.1995] Eracleous M., Livio M., Halpern J. P., Storchi-Bergmann T., 1995, ApJ, 438, 610
  * [Eracleous et al.1997] Eracleous M., Halpern J. P., Gilbert A. M., Newman J. A., Filippenko A. V., 1997, ApJ, 490, 216
  * [Flohic & Eracleous2008] Flohic H. M. L. G. & Eracleous M., 2008, ApJ, 686, 138
  * [Francis et al.1992] Francis P. J., Hewett P. C., Foltz C. B., Chaffee F. H., 1992, ApJ, 398, 476
  * [Gaskell & Peterson1987] Gaskell C. M. & Peterson B. ., 1987, ApJS, 65, 1
  * [Greene & Ho2004] Greene J. E. & Ho L. C., 2004, ApJ, 610, 722
  * [Green & Ho2005a] Greene J. E., & Ho L. C., 2005a, ApJ, 627, 721
  * [Greene & Ho2005] Greene J. E. & Ho L. C., 2005, ApJ, 630, 122
  * [Greene et al.2010] Greene J. E., Hood C. E., Barth A. J., Bennert V. N., Bentz M. C., et al., 2010, ApJ, 723, 409
  * [Hu et al.2012] Hu C., Wang J. M., Ho L. C., Ferland G. J., Baldwin J. A., Wang Y., 2012, ApJ, 760, 126
  * [Kaspi et al.2000] Kaspi S., Smith P. S., Netzer H., Maoz D., Jannuzi B. T., Giveon U., 2000, ApJ, 533, 631
  * [Kaspi et al.2005] Kaspi S., Maoz D., Netzer H., Peterson B. M., Vestergaard M., Jannuzi B. T., 2005, ApJ, 629, 61
  * [Kelly & Bechtold2007] Kelly B. C. & Bechtold J., 2007, ApJS, 168, 1
  * [Kelly et al.2009] Kelly B. C., Bechtold J., Siemiginowska A. 2009, ApJ, 698, 895
  * [Kollatschny & Zetzl12011] Kollatschny W. & Zetzl1 M., 2011, Nature, 470, 366
  * [Koptelova et al.2006] Koptelova E. A., Oknyanskij V. L., Shimanovskaya E. W., 2006, A&A, 452, 37
  * [Koratkar & Gaskell1989] Koratkar A. P. & Gaskell C. M., 1989, ApJ, 345, 637
  * [Kovacevic et al.2010] Kovacevic J., Popovic L. C., Dimitrijevic M. S., 2010, ApJS, 189, 15
  * [Kozlowski et al.2010] Kozlowski S., Kochanek C. S., Udalski A., Wyrzykowski L., Soszynski I., et al., 2010, ApJ, 708, 927
  * [Krause et al.2011] Krause M., Burkert A., Schartmann M., 2011, MNRAS, 411, 550
  * [MacLeod et al.2010] MacLeod C. L., Ivezic Z., Kochanek C. S., KozLowski S., Kelly B., et al., 2010, ApJ, 721, 1014
  * [Marziani et al.2003] Marziani P., Sulentic J. W., Zamanov R., Calvani M., Dultzin-Hacyan D., Bachev R., Zwitter T., 2003, ApJS, 145, 199
  * [Netzer & Marziani2010] Netzer H. & Marziani P., 2010, ApJ, 724, 318
  * [Onken et al.2004] Onken C. A., Ferrarese L., Merritt D., Peterson B. M., Pogge R. W., Vestergaard M., Wandel A., 2004, ApJ, 615, 645
  * [Park et al.2012] Park D., Woo J. H., Treu T., Barth A. J., Bentz M. C., et al., 2012, ApJ, 747, 30
  * [Peterson1993] Peterson B. M., 1993, PASP, 105, 247
  * [Peterson & Wandel1999] Peterson B. M. & Wandel A., 1999, ApJ, 521, L95
  * [Peterson et al.2004] Peterson B. M., Ferrarese L., Gilbert K. M., Kaspi S., et al., 2004, ApJ, 613, 682
  * [Peterson & Horne2004] Peterson B. M. & Horne K., 2004, Astronomische Nachrichten, 325, 248
  * [Peterson2010] Peterson B. M., 2010, Co-Evolution of Central Black Holes and Galaxies, Proceedings of the International Astronomical Union, IAU Symposium, Volume 267, p. 151-160
  * [Popovic et al.2011] Popovic L. C., Shapovalova A. I., Ilic D., Kovacevic A., Kollatschny W., Burenkov A. N., Chavushyan V. H., Bochkarev N. G., Leon-Tavares J., 2011, A&A, 528, 130
  * [Rafiee & Hall2011] Rafiee A., & Hall P. B., 2011, ApJS, 194, 42
  * [Sergeev et al.2011] Sergeev S. G., Kilmanov S. A., Doroshenko V. T., Efimov Y. S., Nazarov S. V., Pronik V. I., 2011, MNRAS, 410, 1877
  * [Shapovalova et al.2001] Shapovalova A. I., Burenkov A. N., Carrasco L., Chavushyan V. H., Doroshenko V. T., et al., 2001, A&A, 376, 775
  * [Shapovalova et al.2012] Shapovalova A. I., Popovic L. C., Burenkov A. N., Chavushyan V. H., Ilic D., et al., 2012, ApJS, 202, 10
  * [Shen & Liu2012] Shen Y. & Liu X., 2012, ApJ, 753, 125
  * [Sluse et al.2011] Sluse D., Schmidt R., Courbin F., Hutsemekers D., Meylan G., Eigenbrod A., Anguita T., Agol E., Wambsganss J., 2011, A&A, 528, 100
  * [Sulentic et al.2000] Sulentic J. W., Marziani P., Dultzin-Hacyan D., 2000, ARA&A, 38, 521
  * [Turler & Courvoisier1998] Turler M. & Courvoisier T. J. L., 1998, A&A, 329, 863
  * [Vestergaard2002] Vestergaard M., 2002, ApJ, 571, 733
  * [Wang & Zhang2003] Wang T. G., & Zhang X. G., 2003, MNRAS, 340, 793
  * [Zhang2011a] Zhang X. G., 2011a, MNRAS, 416, 2857, arXiv:1107.0455
  * [Zhang2011b] Zhang X. G., 2011b, ApJ, 741, 104, Paper I
  * [Zhang2013a] Zhang X. G., 2013a, MNRAS, 429, 2274
  * [Zhang2013b] Zhang X. G., 2013b, MNRAS Letter, 431, L112
  * [Zhu et al.2009] Zhu L., Zhang S.-N., Tang S., 2009, ApJ, 700, 1173
  * [Zu et al.2011] Zu Y., Kochanek C. S., Peterson B. M., 2011, ApJ, 735, 80

Table 1: Line Parameters of PG 0052+251

JD | Inner Broad | Intermediate Broad | [O iii] | ’ ’
---|---|---|---|---
| $W_{0}$ | $\sigma$ | flux | $W_{0}$ | $\sigma$ | flux | $W_{0}$ | $\sigma$ | flux | flux(H$\beta_{N}$) | flux(H$\alpha_{N}$) | flux([N ii])
48837 | 4858.9$\pm$5.0 | 3967$\pm$469 | 8.81$\pm$4.88 | 4868.6$\pm$1.7 | 2568$\pm$234 | 14.68$\pm$4.74 | 5012.0$\pm$0.3 | 660$\pm$17 | 9.53$\pm$0.28 | 0.13$\pm$0.40 | 10.05$\pm$1.17 |
| 6554.4$\pm$6.6 | 2965$\pm$349 | 20.29$\pm$11.21 | 6567.5$\pm$2.3 | 1920$\pm$234 | 33.86$\pm$6.41 |  |  |  |  |  |
48885 | 4900.7$\pm$18.2 | 4249$\pm$640 | 5.46$\pm$2.41 | 4853.4$\pm$1.7 | 2591$\pm$177 | 13.95$\pm$2.06 | 5007.6$\pm$0.2 | 389$\pm$13 | 6.74$\pm$0.24 | 1.13$\pm$0.25 | 5.07$\pm$0.58 |
| 6619.1$\pm$24.1 | 2828$\pm$640 | 13.98$\pm$3.25 | 6555.3$\pm$1.3 | 1724$\pm$95.7 | 35.75$\pm$5.73 |  |  |  |  |  |
48989 | 4893.5$\pm$5.5 | 5253$\pm$365 | 5.51$\pm$0.74 | 4864.7$\pm$1.4 | 2406$\pm$107 | 15.45$\pm$0.78 | 5008.0$\pm$0.2 | 383$\pm$14 | 6.81$\pm$0.24 | 0.67$\pm$0.27 | 3.22$\pm$0.62 |
| 6600.8$\pm$7.2 | 3972$\pm$227 | 17.48$\pm$2.28 | 6561.9$\pm$1.9 | 1819$\pm$107 | 49.05$\pm$1.06 |  |  |  |  |  |
49004 | 4899.3$\pm$3.2 | 4925$\pm$338 | 9.71$\pm$0.88 | 4869.0$\pm$1.7 | 2117$\pm$142 | 12.03$\pm$0.77 | 5010.7$\pm$0.4 | 611$\pm$22 | 7.45$\pm$0.29 | 0.69$\pm$0.46 | 4.14$\pm$0.95 | 7.73$\pm$1.04
| 6587.8$\pm$3.6 | 3852$\pm$115 | 28.82$\pm$1.87 | 6547.1$\pm$2.3 | 1656$\pm$142 | 35.74$\pm$1.04 |  |  |  |  |  |
49011 | 4895.3$\pm$11.1 | 3187$\pm$328 | 3.85$\pm$1.31 | 4861.8$\pm$1.9 | 1955$\pm$153 | 11.34$\pm$1.49 | 5008.2$\pm$0.2 | 424$\pm$16 | 6.53$\pm$0.24 | 0.49$\pm$0.32 | 4.14$\pm$0.61 |
| 6603.8$\pm$16.1 | 3363$\pm$328 | 16.35$\pm$1.77 | 6558.6$\pm$1.4 | 2062$\pm$90 | 48.13$\pm$5.21 |  |  |  |  |  |
49219 | 4875.3$\pm$1.5 | 4012$\pm$219 | 16.38$\pm$0.76 | 4863.2$\pm$1.4 | 1398$\pm$136 | 6.286$\pm$0.61 | 5006.9$\pm$0.2 | 407$\pm$12 | 6.52$\pm$0.24 | 1.18$\pm$0.34 | 14.31$\pm$0.93 |
| 6550.1$\pm$1.2 | 2297$\pm$48 | 34.81$\pm$1.19 | 6533.8$\pm$1.8 | 801$\pm$136 | 13.35$\pm$0.81 |  |  |  |  |  |
49220 | 4892.2$\pm$17.1 | 5728$\pm$1002 | 1.53$\pm$0.58 | 4861.8$\pm$1.3 | 2570$\pm$110 | 17.01$\pm$0.71 | 5007.6$\pm$0.3 | 629$\pm$18 | 8.18$\pm$0.24 | 1.72$\pm$0.38 |  |
| 6608.3$\pm$23.2 | 4027$\pm$1002 | 4.63$\pm$0.79 | 6567.3$\pm$0.7 | 1806$\pm$38 | 51.64$\pm$1.81 |  |  |  |  |  |
49249 | 4893.0$\pm$2.3 | 7634$\pm$388 | 15.89$\pm$0.82 | 4865.5$\pm$1.8 | 2252$\pm$159 | 8.91$\pm$0.54 | 5008.3$\pm$0.3 | 569$\pm$19 | 6.86$\pm$0.26 | 1.54$\pm$0.34 | 13.45$\pm$1.07 | 6.71$\pm$0.62
| 6565.7$\pm$1.7 | 3341$\pm$80 | 32.45$\pm$1.14 | 6528.9$\pm$2.4 | 985$\pm$159 | 18.18$\pm$0.72 |  |  |  |  |  |
49250 | 4871.8$\pm$2.6 | 3916$\pm$338 | 7.39$\pm$1.43 | 4865.6$\pm$1.2 | 2022$\pm$130 | 11.88$\pm$1.38 | 5006.1$\pm$0.3 | 594$\pm$18 | 8.15$\pm$0.25 | 1.13$\pm$0.41 | 1.01$\pm$0.91 |
| 6567.5$\pm$3.1 | 3223$\pm$237 | 20.71$\pm$3.98 | 6559.1$\pm$1.7 | 1664$\pm$130 | 33.28$\pm$1.86 |  |  |  |  |  |
49279 | 4874.1$\pm$2.2 | 4327$\pm$286 | 10.79$\pm$0.95 | 4861.2$\pm$1.1 | 1930$\pm$109 | 13.51$\pm$0.92 | 5007.7$\pm$0.3 | 584$\pm$19 | 6.73$\pm$0.24 | 0.43$\pm$0.47 | 12.22$\pm$1.05 |
| 6560.6$\pm$2.4 | 3512$\pm$139 | 28.55$\pm$2.25 | 6543.3$\pm$1.5 | 1566$\pm$109 | 35.73$\pm$1.25 |  |  |  |  |  |
49282 | 4881.5$\pm$2.3 | 5581$\pm$288 | 6.41$\pm$0.41 | 4865.9$\pm$1.2 | 2198$\pm$92 | 11.85$\pm$0.46 | 5010.4$\pm$0.2 | 409$\pm$13 | 5.96$\pm$0.19 | 0.63$\pm$0.23 | 0.62$\pm$0.53 |
| 6582.7$\pm$2.6 | 4183$\pm$143 | 22.01$\pm$1.29 | 6561.6$\pm$1.6 | 1648$\pm$91 | 40.74$\pm$0.62 |  |  |  |  |  |
49303 | 4884.6$\pm$2.9 | 4903$\pm$316 | 8.85$\pm$0.77 | 4862.6$\pm$1.5 | 2292$\pm$132 | 11.25$\pm$0.71 | 5008.6$\pm$0.3 | 615$\pm$20 | 7.49$\pm$0.26 | 0.85$\pm$0.37 | 4.11$\pm$0.91 |
| 6585.9$\pm$3.3 | 3485$\pm$113 | 25.24$\pm$2.01 | 6556.1$\pm$2.1 | 1629$\pm$132 | 32.10$\pm$0.96 |  |  |  |  |  |
49306 | 4875.7$\pm$3.3 | 4845$\pm$370 | 6.87$\pm$0.96 | 4863.1$\pm$1.3 | 2321$\pm$126 | 13.93$\pm$0.95 | 5007.6$\pm$0.3 | 595$\pm$18 | 8.37$\pm$0.26 | 0.85$\pm$0.39 | 0.63$\pm$0.96 | 0.92$\pm$0.91
| 6577.9$\pm$3.8 | 3611$\pm$208 | 21.88$\pm$2.99 | 6561.0$\pm$1.8 | 1730$\pm$126 | 44.34$\pm$1.28 |  |  |  |  |  |
49325 | 4876.6$\pm$2.2 | 6137$\pm$328 | 18.36$\pm$1.25 | 4859.4$\pm$1.9 | 2324$\pm$202 | 8.91$\pm$0.92 | 5007.7$\pm$0.3 | 575$\pm$22 | 6.94$\pm$0.31 | 1.75$\pm$0.37 | 8.33$\pm$1.21 | 4.34$\pm$0.65
| 6553.6$\pm$1.4 | 2726$\pm$75 | 36.73$\pm$1.91 | 6530.5$\pm$2.6 | 1032$\pm$202 | 17.81$\pm$1.24 |  |  |  |  |  |
49366 | 4876.6$\pm$2.6 | 5219$\pm$397 | 8.08$\pm$1.38 | 4875.6$\pm$1.5 | 2590$\pm$135 | 13.70$\pm$1.36 | 5007.3$\pm$0.2 | 499$\pm$16 | 7.03$\pm$0.25 | 1.16$\pm$0.28 | 5.67$\pm$0.89 | 3.69$\pm$0.74
| 6549.6$\pm$2.4 | 3207$\pm$218 | 24.77$\pm$4.02 | 6548.2$\pm$2.0 | 1591$\pm$135 | 42.04$\pm$1.84 |  |  |  |  |  |
49386 | 4883.7$\pm$4.8 | 4328$\pm$330 | 5.42$\pm$1.02 | 4864.6$\pm$1.4 | 2269$\pm$115 | 13.17$\pm$1.01 | 5007.3$\pm$0.2 | 393$\pm$12 | 7.01$\pm$0.23 | 0.85$\pm$0.26 | 5.26$\pm$0.68 | 2.21$\pm$0.61
| 6590.4$\pm$6.1 | 3533$\pm$219 | 18.31$\pm$3.43 | 6564.6$\pm$1.9 | 1852$\pm$115 | 44.54$\pm$1.36 |  |  |  |  |  |
49542 | 4864.7$\pm$1.4 | 2175$\pm$78 | 14.58$\pm$0.54 | 4789.8$\pm$8.5 | 1771$\pm$368 | 1.11$\pm$0.36 | 5005.6$\pm$0.1 | 370$\pm$11 | 7.42$\pm$0.22 | 1.01$\pm$0.22 | 5.53$\pm$0.48 |
| 6557.0$\pm$1.5 | 1980$\pm$51 | 43.17$\pm$1.24 | 6456.1$\pm$11.1 | 1612$\pm$368 | 3.27$\pm$0.49 |  |  |  |  |  |
49569 | 4869.0$\pm$1.8 | 4559$\pm$251 | 7.59$\pm$0.65 | 4864.7$\pm$1.2 | 2040$\pm$97 | 9.47$\pm$0.65 | 5007.0$\pm$0.1 | 347$\pm$9 | 7.08$\pm$0.22 | 0.74$\pm$0.22 | 2.44$\pm$0.65 | 0.12$\pm$0.54
| 6567.6$\pm$1.7 | 3369$\pm$141 | 27.27$\pm$2.32 | 6561.8$\pm$1.6 | 1508$\pm$97 | 34.04$\pm$0.87 |  |  |  |  |  |
49571 | 4869.1$\pm$1.5 | 3193$\pm$160 | 10.55$\pm$0.97 | 4861.5$\pm$1.3 | 1656$\pm$136 | 5.39$\pm$0.94 | 5007.7$\pm$0.1 | 346$\pm$9 | 7.12$\pm$0.21 | 0.88$\pm$0.21 | 1.91$\pm$0.57 |
| 6566.0$\pm$1.3 | 2476$\pm$81 | 38.67$\pm$3.44 | 6555.8$\pm$1.8 | 1284$\pm$136 | 19.78$\pm$1.27 |  |  |  |  |  |

Notice: The first column gives the observational dates (JD-2400000), the
second to forth columns show the line parameters of the inner broad component:
center wavelength $W_{0}$ in unit of $\AA$, line width $\sigma$ in unit of
${\rm km/s}$ and line flux in unit of $10^{-14}{\rm erg/s/cm^{2}}$, the fifth
to seventh columns show the line parameters of the intermediate broad
component, the eighth to tenth columns show the line parameters of the narrow
[O iii], the last three columns show the line fluxes (in unit of $10^{-14}{\rm
erg/s/cm^{2}}$) of the narrow H$\beta$, narrow H$\alpha$ and [N ii]$\lambda
6583\AA$. Because the narrow lines have the same line redshift and the same
line width (${\rm km/s}$), thus we do not list the center wavelengths and the
line widths of the narrow H$\beta$, the narrow H$\alpha$ and the [N ii] line
in the table. The first line of every two rows lists the parameters for the
two components of the H$\beta$ (second to seventh columns), and the second
line lists the parameters for the H$\alpha$ (second to seventh columns).

Table 1: continued JD | Inner Broad | Intermediate Broad | [O iii] | ’ ’
---|---|---|---|---
| $W_{0}$ | $\sigma$ | flux | $W_{0}$ | $\sigma$ | flux | $W_{0}$ | $\sigma$ | flux | flux(H$\beta_{N}$) | flux(H$\alpha_{N}$) | flux([N ii])
49596 | 4869.7$\pm$1.7 | 3929$\pm$221 | 7.02$\pm$0.76 | 4863.8$\pm$1.2 | 1903$\pm$95 | 8.78$\pm$0.75 | 5008.1$\pm$0.1 | 353$\pm$8 | 7.29$\pm$0.19 | 0.65$\pm$0.19 | 2.69$\pm$0.55 |
| 6566.5$\pm$1.7 | 3093$\pm$141 | 25.95$\pm$2.74 | 6558.5$\pm$1.4 | 1498$\pm$95 | 32.46$\pm$1.01 |  |  |  |  |  |
49597 | 4877.4$\pm$1.9 | 4464$\pm$209 | 6.29$\pm$0.54 | 4865.5$\pm$1.3 | 2097$\pm$78 | 10.77$\pm$0.55 | 5009.4$\pm$0.1 | 361$\pm$8 | 6.83$\pm$0.18 | 0.81$\pm$0.19 | 1.81$\pm$0.54 |
| 6577.9$\pm$2.1 | 3393$\pm$124 | 24.25$\pm$2.04 | 6561.8$\pm$1.3 | 1594$\pm$77 | 41.51$\pm$0.75 |  |  |  |  |  |
49598 | 4878.5$\pm$2.2 | 4476$\pm$209 | 6.43$\pm$0.54 | 4861.8$\pm$1.0 | 2105$\pm$75 | 11.62$\pm$0.55 | 5006.7$\pm$0.1 | 356$\pm$8 | 6.94$\pm$0.18 | 0.75$\pm$0.19 | 2.33$\pm$0.59 | 1.01$\pm$0.52
| 6579.9$\pm$2.6 | 3450$\pm$119 | 23.97$\pm$1.94 | 6557.4$\pm$1.3 | 1622$\pm$75 | 43.37$\pm$0.75 |  |  |  |  |  |
49661 | 4868.5$\pm$1.3 | 3446$\pm$173 | 6.69$\pm$0.66 | 4870.1$\pm$1.2 | 1736$\pm$101 | 5.91$\pm$0.64 | 5013.0$\pm$0.1 | 351$\pm$8 | 6.93$\pm$0.17 | 0.67$\pm$0.16 | 0.39$\pm$0.57 |
| 6565.0$\pm$1.2 | 2703$\pm$100 | 32.13$\pm$3.11 | 6567.1$\pm$1.4 | 1362$\pm$101 | 28.40$\pm$0.87 |  |  |  |  |  |
49681 | 4877.5$\pm$1.9 | 4561$\pm$215 | 5.38$\pm$0.41 | 4864.1$\pm$1.1 | 2102$\pm$87 | 7.85$\pm$0.41 | 5010.1$\pm$0.1 | 364$\pm$8 | 6.67$\pm$0.17 | 0.78$\pm$0.16 | 2.13$\pm$0.51 |
| 6580.0$\pm$2.0 | 3357$\pm$108 | 23.83$\pm$1.71 | 6562.0$\pm$1.5 | 1547$\pm$87 | 34.75$\pm$0.56 |  |  |  |  |  |
49688 | 4883.9$\pm$2.0 | 5483$\pm$255 | 7.57$\pm$0.51 | 4873.8$\pm$1.6 | 2417$\pm$115 | 7.05$\pm$0.47 | 5009.5$\pm$0.1 | 318$\pm$7 | 6.86$\pm$0.19 | 0.98$\pm$0.14 | 2.04$\pm$0.46 |
| 6574.1$\pm$1.5 | 3204$\pm$95 | 28.98$\pm$1.73 | 6560.5$\pm$2.2 | 1412$\pm$115 | 26.97$\pm$0.63 |  |  |  |  |  |
49719 | 4875.3$\pm$1.8 | 3949$\pm$212 | 8.19$\pm$0.52 | 4864.9$\pm$1.5 | 1771$\pm$119 | 4.73$\pm$0.48 | 5011.3$\pm$0.1 | 321$\pm$8 | 6.87$\pm$0.19 | 0.78$\pm$0.16 | 2.08$\pm$0.46 |
| 6571.7$\pm$1.3 | 2855$\pm$77 | 33.72$\pm$1.89 | 6557.6$\pm$2.1 | 1280$\pm$119 | 19.48$\pm$0.64 |  |  |  |  |  |
49921 | 4870.8$\pm$1.9 | 4081$\pm$263 | 10.03$\pm$1.08 | 4863.6$\pm$1.4 | 1978$\pm$133 | 8.719$\pm$1.05 | 5008.4$\pm$0.1 | 314$\pm$9 | 6.96$\pm$0.23 | 0.77$\pm$0.22 | 0.94$\pm$0.51 |
| 6568.8$\pm$1.8 | 2903$\pm$130 | 31.05$\pm$3.20 | 6559.1$\pm$1.9 | 1408$\pm$133 | 26.99$\pm$1.42 |  |  |  |  |  |
49962 | 4880.3$\pm$2.7 | 4182$\pm$327 | 9.91$\pm$0.79 | 4860.8$\pm$1.8 | 1856$\pm$139 | 8.21$\pm$0.73 | 5007.9$\pm$0.2 | 349$\pm$12 | 6.62$\pm$0.24 | 0.76$\pm$0.26 | 1.79$\pm$0.59 | 2.94$\pm$0.56
| 6580.8$\pm$2.4 | 3349$\pm$97 | 33.65$\pm$2.03 | 6554.4$\pm$2.5 | 1487$\pm$139 | 27.91$\pm$0.98 |  |  |  |  |  |
49963 | 4862.9$\pm$2.4 | 4208$\pm$416 | 7.92$\pm$2.11 | 4864.8$\pm$1.5 | 2320$\pm$176 | 10.92$\pm$2.10 | 5007.1$\pm$0.2 | 341$\pm$11 | 6.79$\pm$0.23 | 0.89$\pm$0.24 | 2.84$\pm$0.58 |
| 6559.3$\pm$2.4 | 2961$\pm$271 | 24.03$\pm$6.37 | 6561.9$\pm$2.1 | 1633$\pm$176 | 33.14$\pm$2.84 |  |  |  |  |  |
49983 | 4892.1$\pm$3.2 | 4272$\pm$280 | 8.38$\pm$0.61 | 4858.8$\pm$1.5 | 1871$\pm$113 | 10.24$\pm$0.57 | 5007.3$\pm$0.2 | 325$\pm$11 | 6.47$\pm$0.24 | 0.56$\pm$0.25 | 3.72$\pm$0.51 |
| 6594.7$\pm$3.8 | 3468$\pm$91 | 26.81$\pm$1.65 | 6549.9$\pm$2.2 | 1519$\pm$113 | 32.76$\pm$0.77 |  |  |  |  |  |
49990 | 4875.9$\pm$2.6 | 4628$\pm$301 | 7.65$\pm$0.77 | 4862.7$\pm$1.4 | 2146$\pm$113 | 11.48$\pm$0.78 | 5009.0$\pm$0.2 | 370$\pm$13 | 6.47$\pm$0.23 | 0.71$\pm$0.26 | 2.39$\pm$0.71 | 0.01$\pm$0.59
| 6580.0$\pm$2.8 | 3352$\pm$145 | 26.42$\pm$2.56 | 6562.3$\pm$1.9 | 1555$\pm$113 | 39.66$\pm$1.05 |  |  |  |  |  |
50049 | 4874.9$\pm$2.3 | 4666$\pm$298 | 9.72$\pm$1.06 | 4864.2$\pm$1.6 | 2240$\pm$132 | 10.19$\pm$1.04 | 5007.2$\pm$0.2 | 348$\pm$11 | 6.59$\pm$0.23 | 0.82$\pm$0.23 | 2.08$\pm$0.72 | 0.08$\pm$0.57
| 6572.2$\pm$2.3 | 3001$\pm$136 | 29.72$\pm$3.05 | 6557.8$\pm$2.1 | 1441$\pm$132 | 31.16$\pm$1.40 |  |  |  |  |  |
50052 | 4884.3$\pm$4.1 | 4710$\pm$315 | 6.07$\pm$0.78 | 4863.5$\pm$1.2 | 2214$\pm$96 | 15.64$\pm$0.83 | 5008.3$\pm$0.2 | 407$\pm$13 | 7.84$\pm$0.26 | 0.75$\pm$0.31 | 2.29$\pm$0.75 | 2.44$\pm$0.73
| 6590.2$\pm$5.2 | 3618$\pm$196 | 19.59$\pm$2.51 | 6562.1$\pm$1.7 | 1701$\pm$96 | 50.55$\pm$1.13 |  |  |  |  |  |
50079 | 4879.9$\pm$2.8 | 4642$\pm$296 | 6.93$\pm$0.74 | 4865.8$\pm$1.3 | 2118$\pm$98 | 12.33$\pm$0.77 | 5009.3$\pm$0.1 | 343$\pm$11 | 6.94$\pm$0.22 | 0.68$\pm$0.24 | 1.83$\pm$0.63 | 0.05$\pm$0.51
| 6580.2$\pm$3.3 | 3606$\pm$180 | 24.17$\pm$2.50 | 6561.2$\pm$1.7 | 1645$\pm$98 | 43.01$\pm$1.04 |  |  |  |  |  |
50094 | 4881.0$\pm$2.5 | 4778$\pm$286 | 7.66$\pm$0.68 | 4865.7$\pm$1.3 | 2165$\pm$104 | 11.87$\pm$0.69 | 5009.8$\pm$0.2 | 405$\pm$13 | 6.76$\pm$0.23 | 0.79$\pm$0.26 | 1.54$\pm$0.69 | 0.44$\pm$0.60
| 6582.3$\pm$2.7 | 3453$\pm$133 | 26.09$\pm$2.15 | 6561.7$\pm$1.8 | 1565$\pm$104 | 40.47$\pm$0.93 |  |  |  |  |  |
50097 | 4880.6$\pm$2.7 | 5178$\pm$292 | 6.67$\pm$0.58 | 4863.5$\pm$1.2 | 2226$\pm$96 | 13.32$\pm$0.62 | 5008.3$\pm$0.2 | 387$\pm$13 | 6.75$\pm$0.22 | 0.79$\pm$0.26 | 0.81$\pm$0.61 |
| 6584.9$\pm$3.2 | 3633$\pm$153 | 22.28$\pm$1.83 | 6561.8$\pm$1.7 | 1562$\pm$96 | 44.52$\pm$0.84 |  |  |  |  |  |
50110 | 4874.8$\pm$2.4 | 4758$\pm$304 | 9.18$\pm$0.67 | 4860.7$\pm$1.5 | 1949$\pm$113 | 9.94$\pm$0.66 | 5009.4$\pm$0.2 | 398$\pm$13 | 7.08$\pm$0.24 | 0.95$\pm$0.29 | 1.46$\pm$0.73 | 3.21$\pm$0.67
| 6578.2$\pm$2.4 | 3680$\pm$129 | 31.26$\pm$1.94 | 6559.2$\pm$2.2 | 1508$\pm$113 | 33.83$\pm$0.89 |  |  |  |  |  |

Table 1: continued JD | Inner Broad | Intermediate Broad | [O iii] | ’ ’
---|---|---|---|---
| $W_{0}$ | $\sigma$ | flux | $W_{0}$ | $\sigma$ | flux | $W_{0}$ | $\sigma$ | flux | flux(H$\beta_{N}$) | flux(H$\alpha_{N}$) | flux([N ii])
50333 | 4880.6$\pm$3.4 | 4200$\pm$282 | 6.32$\pm$0.73 | 4861.7$\pm$1.3 | 1984$\pm$99 | 12.32$\pm$0.77 | 5008.1$\pm$0.2 | 392$\pm$15 | 6.14$\pm$0.23 | 0.57$\pm$0.29 | 2.69$\pm$0.72 | 1.92$\pm$0.64
| 6585.6$\pm$4.1 | 3457$\pm$166 | 22.51$\pm$2.52 | 6560.1$\pm$1.7 | 1633$\pm$99 | 43.89$\pm$1.04 |  |  |  |  |  |
50371 | 4864.0$\pm$2.1 | 3451$\pm$382 | 8.31$\pm$2.59 | 4862.8$\pm$1.2 | 1923$\pm$148 | 12.89$\pm$2.59 | 5007.1$\pm$0.2 | 340$\pm$11 | 7.59$\pm$0.26 | 0.69$\pm$0.31 | 2.06$\pm$0.68 |
| 6564.1$\pm$2.4 | 2710$\pm$285 | 24.94$\pm$7.76 | 6562.5$\pm$1.6 | 1510$\pm$148 | 38.73$\pm$3.50 |  |  |  |  |  |
50391 | 4878.3$\pm$3.1 | 4352$\pm$307 | 6.66$\pm$0.81 | 4862.8$\pm$1.3 | 2030$\pm$107 | 13.21$\pm$0.83 | 5009.3$\pm$0.2 | 396$\pm$15.1 | 6.19$\pm$0.23 | 0.68$\pm$0.31 | 3.65$\pm$0.71 |
| 6583.1$\pm$3.8 | 3430$\pm$178 | 21.50$\pm$2.52 | 6562.2$\pm$1.7 | 1600$\pm$107 | 42.65$\pm$1.13 |  |  |  |  |  |
50400 | 4863.3$\pm$1.6 | 3072$\pm$202 | 16.67$\pm$2.01 | 4867.3$\pm$1.6 | 1633$\pm$195 | 6.68$\pm$1.97 | 5008.9$\pm$0.2 | 381$\pm$13 | 7.93$\pm$0.27 | 0.75$\pm$0.34 |  |
| 6562.2$\pm$1.2 | 2570$\pm$109 | 51.71$\pm$6.01 | 6567.6$\pm$2.2 | 1366$\pm$195 | 20.72$\pm$2.66 |  |  |  |  |  |
50401 | 4868.5$\pm$1.7 | 3959$\pm$255 | 12.45$\pm$0.96 | 4864.0$\pm$1.3 | 1696$\pm$113 | 9.99$\pm$0.93 | 5008.7$\pm$0.2 | 317$\pm$12 | 6.75$\pm$0.25 | 0.68$\pm$0.32 | 1.49$\pm$0.66 |
| 6564.7$\pm$1.5 | 2892$\pm$112 | 36.73$\pm$2.64 | 6558.6$\pm$1.7 | 1238$\pm$113 | 29.47$\pm$1.25 |  |  |  |  |  |
50459 | 4880.7$\pm$1.9 | 4019$\pm$205 | 15.68$\pm$0.77 | 4857.6$\pm$1.3 | 1391$\pm$101 | 8.06$\pm$0.63 | 5010.9$\pm$0.1 | 322$\pm$10 | 6.42$\pm$0.25 | 0.57$\pm$0.28 | 6.89$\pm$0.72 | 7.31$\pm$0.49
| 6570.8$\pm$1.8 | 2722$\pm$68 | 32.96$\pm$1.29 | 6539.7$\pm$1.8 | 942$\pm$101 | 16.95$\pm$0.85 |  |  |  |  |  |
50716 | 4868.0$\pm$1.4 | 3258$\pm$182 | 13.59$\pm$1.03 | 4863.5$\pm$1.1 | 1517$\pm$115 | 7.71$\pm$0.97 | 5009.3$\pm$0.1 | 320$\pm$11 | 6.25$\pm$0.22 | 0.62$\pm$0.28 | 3.43$\pm$0.73 |
| 6571.2$\pm$1.1 | 2660$\pm$86 | 45.12$\pm$3.23 | 6565.1$\pm$1.6 | 1238$\pm$115 | 25.58$\pm$1.31 |  |  |  |  |  |
50717 | 4863.0$\pm$2.1 | 3559$\pm$283 | 7.51$\pm$1.46 | 4867.2$\pm$1.3 | 1928$\pm$126 | 9.74$\pm$1.47 | 5004.2$\pm$0.1 | 322$\pm$9 | 7.79$\pm$0.24 | 1.06$\pm$0.24 |  | 0.08$\pm$0.51
| 6557.3$\pm$2.8 | 2936$\pm$283 | 29.94$\pm$1.98 | 6563.0$\pm$1.2 | 1591$\pm$91 | 38.82$\pm$5.82 |  |  |  |  |  |
50747 | 4867.9$\pm$1.4 | 4157$\pm$224 | 13.93$\pm$0.91 | 4867.6$\pm$1.1 | 1778$\pm$106 | 9.77$\pm$0.88 | 5008.5$\pm$0.1 | 347$\pm$11 | 7.14$\pm$0.23 | 0.94$\pm$0.27 |  | 0.88$\pm$0.60
| 6567.3$\pm$1.1 | 2819$\pm$88 | 40.16$\pm$2.34 | 6566.9$\pm$1.6 | 1205$\pm$106 | 28.16$\pm$1.19 |  |  |  |  |  |
50771 | 4861.4$\pm$1.2 | 3315$\pm$180 | 16.79$\pm$0.61 | 4857.3$\pm$1.4 | 1017$\pm$101 | 3.69$\pm$0.63 | 5006.0$\pm$0.2 | 439$\pm$13 | 7.56$\pm$0.24 | 0.27$\pm$0.40 | 2.01$\pm$1.73 |
| 6560.4$\pm$0.6 | 2182$\pm$39 | 48.98$\pm$1.23 | 6554.9$\pm$1.9 | 669$\pm$101 | 10.78$\pm$0.85 |  |  |  |  |  |
50773 | 4863.1$\pm$1.2 | 3232$\pm$139 | 17.14$\pm$0.64 | 4870.2$\pm$1.2 | 861$\pm$123 | 3.27$\pm$0.45 | 5011.7$\pm$0.1 | 298$\pm$8 | 8.07$\pm$0.25 | 0.78$\pm$0.28 |  | 5.46$\pm$0.81
| 6560.1$\pm$0.7 | 2242$\pm$36 | 48.95$\pm$1.03 | 6569.6$\pm$1.6 | 597$\pm$123 | 9.35$\pm$0.60 |  |  |  |  |  |
50806 | 4866.6$\pm$1.5 | 3543$\pm$214 | 11.04$\pm$1.12 | 4868.4$\pm$1.2 | 1720$\pm$115 | 8.82$\pm$1.09 | 5010.2$\pm$0.1 | 340$\pm$11 | 6.89$\pm$0.23 | 0.75$\pm$0.26 |  |
| 6565.1$\pm$1.2 | 2782$\pm$115 | 39.52$\pm$3.77 | 6567.5$\pm$1.6 | 1350$\pm$115 | 31.55$\pm$1.47 |  |  |  |  |  |
50831 | 4860.8$\pm$2.9 | 4669$\pm$419 | 5.902$\pm$1.20 | 4868.0$\pm$1.3 | 2380$\pm$115 | 14.53$\pm$1.23 | 5011.1$\pm$0.2 | 381$\pm$11 | 7.41$\pm$0.23 | 1.41$\pm$0.27 |  |
| 6560.3$\pm$3.4 | 3178$\pm$260 | 19.91$\pm$3.98 | 6569.9$\pm$1.8 | 1620$\pm$115 | 49.00$\pm$1.67 |  |  |  |  |  |
51051 | 4871.9$\pm$1.5 | 3641$\pm$214 | 13.83$\pm$0.83 | 4864.7$\pm$1.2 | 1418$\pm$108 | 7.45$\pm$0.79 | 5007.8$\pm$0.2 | 368$\pm$12 | 6.81$\pm$0.22 | 0.43$\pm$0.30 | 2.49$\pm$1.01 | 0.56$\pm$0.82
| 6564.5$\pm$1.0 | 2708$\pm$65 | 41.72$\pm$1.72 | 6554.7$\pm$1.7 | 1055$\pm$108 | 22.48$\pm$1.07 |  |  |  |  |  |
51074 | 4862.5$\pm$2.4 | 3658$\pm$421 | 5.43$\pm$1.91 | 4864.7$\pm$1.1 | 2092$\pm$117 | 13.19$\pm$1.92 | 5004.1$\pm$0.2 | 414$\pm$12 | 7.56$\pm$0.22 | 0.82$\pm$0.27 |  |
| 6557.7$\pm$3.3 | 2946$\pm$421 | 19.73$\pm$2.57 | 6560.6$\pm$0.8 | 1685$\pm$81 | 48.01$\pm$7.02 |  |  |  |  |  |
51084 | 4861.4$\pm$1.3 | 2797$\pm$108 | 13.12$\pm$0.42 | 4865.2$\pm$0.9 | 797$\pm$51 | 3.52$\pm$0.27 | 5008.1$\pm$0.1 | 345$\pm$10 | 7.35$\pm$0.22 |  |  |
| 6561.4$\pm$1.3 | 2259$\pm$108 | 57.19$\pm$0.56 | 6566.5$\pm$0.7 | 644$\pm$35 | 15.34$\pm$1.12 |  |  |  |  |  |

Figure 1: Effects of the broad He ii line on the line profile of the H$\beta$.
The observed spectrum is shown in thin dotted line, the best fitted result is
shown in the thick solid line, the dot-dashed line and the thick dashed line
under the spectrum are for the power law components with and without the
considerations of the broad He ii line. The shadow area near the bottom shows
the weak Fe ii components, the dashed line near the bottom shows the gaussian
broad component for the observed broad H$\beta$ without the consideration of
the broad He ii, the two solid lines near the bottom show the two gaussian
broad components for the observed broad H$\beta$ with the consideration of the
broad He ii, the dotted line near the bottom shows the broad He ii component.
Figure 2: Two examples for the best fitted results for the lines around the
H$\beta$ (left panels) and the H$\alpha$ (right panels), under the model with
one broad component applied for each observed broad balmer line. The thin
dotted lines are for the observed spectra, the thick solid lines are for the
best fitted results. Near the bottom, the solid line and the dashed line are
for the broad components and the other narrow lines. In the left panels, the
dotted line around the 4680Ånear the bottom shows the probable He ii line.
Then, in each panel, the MJD and the line width of the broad line are marked.
Figure 3: The broad line width and broad line flux correlations between the
broad H$\alpha$ and the broad H$\beta$ under the model with one broad
component applied for each observed broad balmer line. The line in the left
panel is $\sigma(H\alpha)=0.97\sigma(H\beta)$, the line in the right panel is
$flux(H\alpha)=3.1\times flux(H\beta)$.  Figure 4: Best fitted results for the
lines around the H$\beta$ and around the H$\alpha$ under the model with two
broad components applied for each observed broad balmer line. The dotted lines
are for the observed spectra, the thick solid lines are for the best fitted
results, the AGN continuum is shown in the dotted line under the spectrum. The
thick and the thin solid lines near the bottom represent the two broad
components for each observed broad balmer line, the shadow areas near the
bottom show the narrow lines, the dotted line near the bottom shows the He ii
line. In each panel, the information of the MJD (seven characters) and the F
value (starting with F:) calculated by the equation (6) are marked.  Figure 4:
–continued.  Figure 4: –continued.  Figure 5: The broad line width correlation
(the left panels) and the broad line flux correlation (the right panels)
between the two broad components of the H$\alpha$ and the H$\beta$. The solid
lines are the best fitted results for the correlations. The coefficient and
the corresponding $P_{null}$ are marked in each panel for the correlation.
Figure 6:  The properties of the relative shifted velocities of the inner
broad component to the intermediate broad component (the open circles), and
the relative shifted velocities of the intermediate broad component to the
narrow [O iii]$\lambda 5007$Å(the solid circles). The solid line shows the
time dependence of the relative shifted velocities of the inner broad
component to the intermediate broad component.  Figure 7: The ICCF and SPEAR
results for the inner and the intermediate broad components of the H$\beta$ of
PG 0052+251. Top left panel shows the ICCF results for the inner broad
H$\beta$ (dotted line for the result through the observational light curves,
dashed line for the result through the light curves determined by the random
walk model) and the intermediate broad H$\beta$ (solid line for the result
through the observational light curves, dot-dashed line for the result through
the light curves determined by the random walk model), and bottom left panel
shows the distributions of the time lags determined by the SPEAR method (thin
solid line for H$\beta_{1}$ and thick dotted line for H$\beta_{2}$). The right
panels from top to bottom shows the observational light curves (open circles)
of the inner broad H$\beta$, the intermediate broad H$\beta$ and the continuum
emission, and the corresponding best descriptions for the observational light
curves by the damped random walk model for AGN variability.  Figure 8: The
ICCF and SPEAR results for the H$\alpha$, symbols and lines have the same
meanings as those in the Figure 7, but for the H$\alpha$.  Figure 9: On the
correlations between the broad line flux and the broad line width for the
inner broad component, the intermediate broad component of the H$\alpha$ (the
left panel) and the H$\beta$ (the right panel). The open circles are for the
inner broad components, the solid circles are for the intermediate broad
components. The thick solid line, the thin solid line, the dotted lines and
the dashed lines show the best fitted results for the correlations for the
inner broad components, for the intermediate broad components, and the
corresponding 99.95% confidence bands for the best fitted results.