text:
\section{Introduction}
The mass of super-massive black holes (SMBHs) is of fundamental importance for
understanding active galactic nuclei (AGN) which are powered by mass accretion
onto a SMBH.
Analysis of AGN variability by applying the technique of reverberation
mapping (RM) has been established as a powerful tool to determine the size of
the broad emission-line region (BLR) of AGN (Blandford \& McKee 1982;
Horne et al.\,2004; Netzer \& Peterson 1997; Peterson 2003) and, under the
assumption of virial gas motion, consequently the SMBH mass
(e.g., Peterson et al.\,2004).

Large observational efforts are required to obtain data of sufficient quality
and temporal coverage to study AGN variability and to employ RM methods.
Currently, about 50 AGN have been monitored for periods of at least a few
months, usually as part of international collaborations.
The entire available database of reverberation observations obtained through
2003 was uniformly re-analyzed with improved methods of time series analysis to
minimize systematic errors (Peterson et al.\,2004).
Some of these results have been superseded by more recent experiments
(Bentz et al.\,2006b,\,2007a; Denney et al.\,2006,\,2009a; Grier et al.\,2008;
Woo et al.\,2010) and
additional reverberation results steadily increase the size and quality of the
database (e.g., Bentz et al.\,2009b,\,2010a; Denney et al.\,2009b,\,2010).

It has been shown that AGN and non-active galaxies follow the same relation
between the black hole mass, M$_{bh}$, and stellar velocity dispersion,
$\sigma_\ast$, of the central spheroidal component of the host galaxy
(Ferrarese et al.\,2001; Gebhardt et al.\,2000; G\"{u}ltekin et al.\,2009;
Merritt \& Ferrarese 2001; Tremaine et al.\,2002) and that the masses based on
RM studies are consistent with the masses derived from the
M$_{bh}$ - $\sigma_\ast$ relation (Nelson et al.\,2004; Onken et al.\,2004;
Woo et al.\,2010).
The close relations of the black hole mass with physical properties of the host
galaxy, e.g. stellar velocity dispersion, bulge mass and bulge luminosity,
indicate a coupled growth of the black hole and the formation and evolution
of the host galaxy (e.g., Silk \& Rees 1998; Haiman \& Loeb 1998,2001;
Bromm \& Loeb 2003; Di\,Matteo et al.\,2004; Yoo \& Miralda-Escud\'e 2004;
Volonteri \& Rees 2006; Volonteri \& Begelman 2010).

The broad-line radio galaxy (BLRG) 3C\,390.3 is a bright and nearby
($m_v = 15.0$, $z=0.056$; Osterbrock, Koski, \& Phillips 1976) FR\,II radio
galaxy with extended double-lobed radio emission (Leahy \& Perley 1995).
After the identification as optical counterpart of the radio source 3C\,390.3
(Wyndham 1966), it was classified as a N-type galaxy by Sandage (1966).
Soon, it was discovered that 3C\,390.3 shows very broad Balmer emission-lines
(Lynds 1968) which were later recognized as prominent double-peaked
emission-line profiles (Burbidge \& Burbidge 1971). These double-peaked
profiles are generally regarded as a characteristic signature of accretion
disk emission (e.g., Eracleous \& Halpern 1994,2003; Gezari, Halpern, \&
Eracleous 2007).

So far almost all AGN variability studies have focused on radio-quiet AGN.
However, 3C\,390.3 has a well-known variability history (e.g.,
Cannon, Penston, \& Penston 1968; Selmes, Tritton, \& Wordsworth 1975;
Barr et al.\,1980; Penston \& Perez 1984; Veilleux \& Zheng 1991; Zheng 1996;
Wamsteker et al.\,1997; O'Brien et al.\,1998; Dietrich et al.\,1998;
Sergeev et al.\,2002; Tao et al.\,2008), with photometric measurements
going back to 1968 (Yee \& Oke 1981). Using the Harvard plate collection Shen,
Usher, \& Barrett (1972) traced back brightness variations to 1895.
Thus, 3C\,390.3 was a prime target of a multiwavelength monitoring campaign
in 1994/95 especially because of
previous reports of dramatic changes in the Balmer line profile shape and
strength and to perform coordinated X-ray/UV/optical monitoring of a radio-loud
AGN for the first time.
Currently, 3C\,120 and 3C\,390.3 are the only radio-loud AGN which have been
monitored in detail.
The multiwavelength study of 3C\,390.3 in 1994/95 (Leighly et al.\,1997;
O'Brien et al.\,1998; Dietrich et al.\,1998) shows significant variations in
the X-ray, UV, and optical domain over a period of one year.
However, the light curves of the UV and optical variations show a nearly
monotonic increase of the continuum and emission-line flux with only moderately
strong substructures.
The measured delays of several broad emission-lines relative to the observed
continuum variations are about $\tau \simeq 20\pm6$\,days for H$\beta $
and H$\alpha$ (Dietrich et al.\,1998) and $\tau \simeq 36$ to 60\,days
($\pm 18$\,days) for \ifmmode {\rm C}\,{\sc iv} \else C\,{\sc iv}\fi\ and Ly$\alpha$ (O'Brien et al.\,1998).
More recently, Sergeev et al.\,(2002) studied the variability characteristics
of 3C\,390.3 for a period of nearly one decade. They found a longer delay of
the response of the  H$\beta $ emission with respect to continuum variations
compared to the result of the 1994/95 study. They concluded that the difference
might be caused by different continuum variability characteristics which
manifest in different continuum auto-correlation functions.
Recently, Shapovalova et al.\,(2010), Jovanovic et al.\,(2010),
Popovic et al.\,(2011), and Sergeev et al.\,(2011) discussed profile variations
over periods from a few years up to about 15 years.

In the following work, we present the results of a monitoring campaign
undertaken at MDM Observatory in late 2005.
Based on imaging and spectroscopic data, we find that 3C\,390.3 clearly showed
broad band variations, delayed variations of the broad Balmer
emission-lines H$\alpha$, H$\beta $, and H$\gamma $, and of the helium
line He\,{\sc ii} $\lambda 4686$.
Using the time delays and the peak separation in the rms spectra of these
emission lines, we estimate a virial black hole mass of
M$_{bh}^{vir} = 1.77^{+0.29}_{-0.31}\,\times\,10^8 M_\odot$ for 3C\,390.3
and using $\sigma_{line}$ of the rms spectra
M$_{bh}^{vir} = 2.60^{+0.23}_{-0.31}\,\times\,10^8 M_\odot$, respectively.
The detection of superluminal motion for 3C\,390.3 indicates an inclination
angle of $i = 27^o \pm 2^o$ which allows to correct the observed velocity for
the tilt of the line emitting region relative to the observer.
Taking this into account, we derive a black hole mass of
M$_{bh} = 0.86^{+0.19}_{-0.18}\times 10^9 M_\odot$ (peak separation) and
M$_{bh} = 1.26^{+0.21}_{-0.16}\times 10^9 M_\odot$ ($\sigma_{line}$) for
3C\,390.3, respectively,
which is, within the uncertainties, consistent with recent results based on the
Ca\,{\sc ii} $\lambda \lambda 8494, 8542,8662$ stellar absorption triplet and the
$M_{bh} - \sigma_\ast$ relation
(Lewis \& Eracleous 2006; Nelson et al.\,2004).

\section{Observations}
\noindent
We revisited 3C\,390.3 to determine the size of the BLR with improved accuracy.
In 2005 from September until December we used the 2.4-m Hiltner telescope at
MDM Observatory to obtain spectroscopic and imaging data (Table\,1).

The instrumental setup of the Boller \& Chivens CCD Spectrograph (CCDS) and
imaging camera RetroCam (Morgan et al.\,2005) was kept unchanged for the
entire observing campaign to achieve a homogeneous data set, i.e., avoiding the
impact of different instrumental settings.
The spectrograph was equipped with a Loral 1200\,x\,800 pixel CCD, with a
projected pixel size that corresponds to $0\farcs4$/pixel.
To cover the entire optical wavelength range, a 150 grooves/mm grating was used
with a fixed grating tilt for the entire observing season. The slit
width was set to a uniform value of $3\arcsec$ and a position angle of
PA\,$= 90^\circ$.
To allow for correction of cosmic ray event contamination, at each epoch two
spectra were recorded for 3C\,390.3 with an integration time of
t$_{\rm int}$\,=\,900\,s each.
In contrast to previous campaigns we observed HD\,217086 (BD$+61^\circ 2373$,
O7Vn) for the entire campaign for flux calibration
to minimize the uncertainty which is introduced by flux calibrations that are
based on different standard stars.
In addition, HD\,217086 was employed to correct for strong atmospheric
absorption bands, i.e., the O$_2$ C-band ($\sim 6275 - 6300$\,\AA ),
                 O$_2$ B-band ($\sim 6850 - 6950$\,\AA ), and
                 broad H$_2$O absorption ($\sim 7160 - 7320$\,\AA ).
This is especially important for the broad H$\alpha$ emission line profile
which is severely affected by the B-band absorption.
In total, optical spectra were recorded for 28 epochs (Table\,1).

In addition, 3C\,390.3 was simultaneously observed for 25 epochs in SDSS
{\it g}-band (Fu\-ku\-gi\-ta et al.\,1996) using RetroCam at the 2.4-m
telescope (Table\,1).
RetroCam was equipped with a E2V CCD\,55-20 (1152\,x\,770 pixel) with a pixel
size of $22.5\mu$m, which corresponds to $0\farcs 259$/pixel.
The optical design of RetroCam provides the valuable option to switch between
spectroscopic and imaging mode in less than 2 minutes.
Thus, the {\it g}-band measurements were taken no more than a few minutes
before the spectroscopic observations. The exposure time was uniformly set to
t$_{\rm int}$\,=\,120 sec and generally one exposure was recorded.

The spectra of 3C\,390.3 and the standard star HD\,217086, as well as the
{\it g}-band imaging data were processed using MIDAS\footnote{Munich Image
Data Analysis System, trade-mark of the European Southern Observatory}
software. Standard dark and flat-field corrections were applied to the spectra
and {\it g}-band imaging data of 3C\,390.3 and the HD\,217086 spectra.
We subtracted the night sky intensity for each spectrum individually.
The night sky fit was based on two regions, $\sim 100\arcsec$ to $130\arcsec$
wide on average, which were separated by $\sim 60\arcsec$ relative to the
spectrum of 3C\,390.3 and HD\,217086, respectively. A $3^{rd}$ order
polynomial fit was used for each wavelength element to fit the spatial
intensity distribution of the night sky emission.

Argon\,--\,xenon comparison spectra were recorded for each spectrum of
3C\,390.3 for wavelength calibration, which is based on $\sim 15$ to 20
individual lines. The wavelength calibration yields a sampling of
$(3.07\pm 0.05)$\,\AA /pxl. The spectral resolution, measuring the full width
at half maximum (FWHM) of isolated lines in the argon\,--\,xenon spectra,
amounts to $R \simeq 280$ at $\lambda \simeq 5600$\,\AA .
The spectra of 3C\,390.3 were corrected for galactic reddening using
$E_{B-V} = 0.072$ (Schlegel et al.\,1998).

To transform the observed spectra into the rest-frame of 3C\,390.3, we measured
a redshift of z =$\,0.056 \pm 0.001$ which is based on the narrow emission
lines of H$\alpha$, H$\beta $, [O\,{\sc i} ]$\lambda 6300$,
[O\,{\sc iii} ]$\lambda \lambda 4959,5007$, and [O\,{\sc iii} ]$\lambda 4363$.
In the following, we present the analysis of the rest-frame spectra of
3C\,390.3 and discuss the results based on this spectra.

\section{Data Analysis}
\subsection{{\it g}-Band Imaging}
We used the flat-field corrected images to measure the {\it g}-band flux of
3C\,390.3
relative to comparison stars in the field. The approach of relative photometry
has the advantage of being quite insensitive to weather conditions, i.e.,
photometric conditions are not required.
The BLRG 3C\,390.3 is among a sample of 34 AGN which were carefully studied by
Penston, Penston, \& Sandage (1971).
They provide Johnson U,\,B,\,V magnitudes for three non-variable stars in the
field of 3C\,390.3. RetroCam which has a field of view of
$5\farcm0 \times 3\farcm3$,
allows us to observe stars A and B together with 3C\,390.3 (Fig.\,1). However,
with an apparent brightness of $m_V = 11.^m71$, star A is usually saturated in
the observed {\it g}-band frames.
Star B has a magnitude ($m_V = 14.^m28$) comparable to that of 3C\,390.3. This
star was already successfully employed in a prior monitoring campaign of
3C\,390.3 as a flux standard (Dietrich et al.\,1998). Hence, we used star B to
determine the relative broad-band flux changes of 3C\,390.3.

To measure the {\it g}-band flux of 3C\,390.3 and of star B, we applied a
square aperture with a size of of $13\arcsec \times 13\arcsec $ (Fig.\,1). By
using such a large aperture for the comparison star and particularly for
3C\,390.3 we ensured that the total flux is recorded independently of the
seeing, which varied from $1\farcs1$ to $2\farcs7$ with an average of
$(1\farcs7 \pm 0\farcs4)$ during this monitoring campaign.
To correct for the night sky flux, the object aperture was separated by a
2\arcsec\ wide region (so-called no-man's-land) from a 2\arcsec\ wide region
that enclosed the square aperture (Fig.\,1). This outer region provided an
average sky brightness which was used to correct the observed flux of the
object for the night sky contribution.

\subsection{Optical Spectroscopy}
\subsubsection{Intercalibration of the 3C\,390.3 Spectra}
To study broad emission-line flux variations, it is necessary to calibrate the
spectra to a uniform flux level. This can be achieved using the flux of
forbidden narrow emission-lines from the narrow-line region (NLR).
Due to the large spatial extension of the NLR (of the order of 100\,pc in
Seyfert galaxies) and the long recombination time scales which are due to the
low gas density of the NLR
($\tau_{\rm rec} \approx 100$\,years for $n_e \approx 10^3$\,cm$^{-3}$),
light travel-time effects and long recombination time scales
will damp out short time-scale variability.
Thus, it can be assumed that the flux of narrow emission lines can be treated
as constant, at least on time scales of years to decades
(e.g., Peterson 1993,\,2000).

However, 3C\,390.3 needs careful additional attention. The NLR of 3C\,390.3
seems to be very compact (Baum et al.\,1988; Sergeev et al.\,2002) and the
small emission-line flux ratio of F([O\,{\sc iii} ]$\lambda\lambda 4959,5007$) to
F([O\,{\sc iii} ]$\lambda 4363$) indicates the presence of high density gas
($n_e \simeq 10^5$\,cm$^{-3}$).
Furthermore, narrow-line variability has been reported for this object.
Clavel \& Wamsteker (1987) analyzed the strength of the narrow Ly$\alpha$
and \ifmmode {\rm C}\,{\sc iv} \else C\,{\sc iv}\fi $\lambda 1549$ emission lines. They found that the strength of these
two narrow lines decreased by a factor of about 2 to 3 from 1978 to 1986.
On the basis of optical spectra obtained between 1974 and 1990,
Zheng et al.\,(1995) presented evidence that the fluxes of
[O\,{\sc iii}]\,$\lambda\lambda 4959,5007$ follow continuum variations, although on a
longer time scale than the broad emission-lines.
During the period of decreasing or increasing [O\,{\sc iii}] flux there might also
be periods of several months or years of nearly constant [O\,{\sc iii}] flux.
Hence, we examined the data closely to test for variability of the
[O\,{\sc iii}] emission lines before we used them for flux calibration.

To test the reliability of the narrow [O\,{\sc iii} ] emission lines as an internal
calibrator, the {\it g}-band imaging data are of great value.
As noted earlier, these broad band flux measurements were taken nearly
simultaneously with the spectra, i.e., within minutes of the spectral
observations (Table\,1) and the {\it g}-band brightness of 3C\,390.3 was
measured with high precision (see \S 4.2, $\sim 0.1$\% ).
To compare the {\it g}-band variations to those which can be derived from the
spectral data, the spectra were convolved with the transmission curve of the
SDSS {\it g}-band filter. The fluxes of the convolved spectra were measured for
the transmission wavelength range of the {\it g}-band filter curve
($\lambda = 4000$\,\AA\ to 6000\,\AA ).
To adjust the flux level of the spectra to the {\it g}-band measurements, the
spectra were rescaled. These scaling factors are on average $(1.10 \pm 0.07)$.

We used these adjusted spectra, based on the observed {\it g}-band flux
variations, to test whether the [O\,{\sc iii}]$\lambda 5007$ emission line flux was
constant during this monitoring campaign.
Although the broad-band flux measurements include the broad and narrow H$\beta$
emission-line flux, as well as the [O\,{\sc iii} ]$\lambda \lambda 4959,5007$ line
emission, the contribution of emission line variability to photometric
variations can be neglected (Walsh et al.\,2009) if it amounts to less than
$\sim10$\,\%\ of the broad band flux. For 3C\,390.3 we find that the H$\beta$
flux amounts to less than 5\,\%\ of the g-band flux.
To test the assumption that the [O\,{\sc iii} ]$\lambda 5007$ emission line flux was
constant for the duration of this monitoring campaign, these adjusted spectra
were internally flux calibrated by scaling each individual spectrum to a
uniform flux of the [O\,{\sc iii} ]$\lambda 5007$ emission line.
First, we calculated a mean spectrum which was used as a reference spectrum.
Next, we applied a modified version of the scaling algorithm of van Groningen
\& Wanders (1992) to adjust the flux of the [O\,{\sc iii} ]$\lambda 5007$ in the
individual spectra to the reference spectrum.
This routine minimizes the residuals of the [O\,{\sc iii} ]$\lambda 5007$ in a
difference spectrum which is calculated for each spectrum with the reference
spectrum.
The intercalibration to a uniform flux level was achieved by allowing different
flux scales, small wavelength shifts, and different spectral resolutions. The
average scaling factor amounts to $(0.99 \pm 0.02)$. This result indicates that
the [O\,{\sc iii} ]$\lambda 5007$ flux was constant in the adjusted spectra with a
flux of
F([O\,{\sc iii} ]$\lambda 5007$) = $(189\pm4)\times10^{-15}$\,erg\,s$^{-1}$\,cm$^{-2}$
(Table 2).
It is interesting to note that during the monitoring campaign of 3C\,390.3 in
1995 (Dietrich et al.\,1998) the [O\,{\sc iii} ]$\lambda 5007$ emission line flux was
measured to be
F([O\,{\sc iii} ]$\lambda 5007$) = $(161\pm4)\times10^{-15}$\,erg\,s$^{-1}$\,cm$^{-2}$
(rest frame flux) which is about $\sim 15$\,\%\ lower. This indicates that the
[O\,{\sc iii} ]$\lambda 5007$ emission line flux was lower in 1995 compared to 2005
when 3C\,390.3 was in a less luminous state.
Based on the average scaling factor and the small scatter, it is justified to
assume that the F([O\,{\sc iii} ]$\lambda\lambda 4959,5007$) emission-line flux was
constant during this monitoring campaign.

While the H$\beta $ -- [O\,{\sc iii} ]$\lambda \lambda 4959,5007$ region is scaled
with respect to the narrow [O\,{\sc iii} ]$\lambda 5007$ line, we investigated whether
this internal calibration holds for the H$\alpha$ region at longer wavelengths
and the H$\gamma $ -- [O\,{\sc iii} ]$\lambda 4363$ region at shorter wavelengths.
We intercalibrated the spectra for the H$\alpha$ region with respect to the
fluxes of the relatively strong [O\,{\sc i} ]$\lambda 6300$ emission line and the
H$\gamma $ -- [O\,{\sc iii} ]$\lambda 4363$ region using the narrow
[O\,{\sc iii} ]$\lambda 4363$ emission line.
We found that the H$\alpha$ region required small adjustments to achieve a
constant [O\,{\sc i} ]$\lambda 6300$ flux. The average scaling factor for the
H$\alpha$ region amounts to $(1.014 \pm 0.021)$.
For the H$\gamma $ -- [O\,{\sc iii} ]$\lambda 4363$ region, minor rescaling of the
spectra was also necessary. These scaling factors are on average
$(1.014\pm0.004)$.

\subsubsection{Accounting for Host Galaxy and Optical Fe\,{\sc ii}\ Emission}
A spectrum of an active galactic nucleus is the superposition of various
sources, including the host galaxy, thermal and non-thermal continuum emission
from the AGN, which can be described by a power-law continuum, Balmer continuum
emission, Fe\,{\sc ii}\ line emission, and emission from other metal line transitions,
e.g., carbon, nitrogen, oxygen, magnesium, neon, sulfur. These contributions
need to be accounted for in order to obtain reliable line measurements and the
strength of the AGN continuum that most of our study relies on.
We adopted a multi-component fit approach (e.g., Wills et al.\,1985) that we
have successfully applied in prior studies of high-$z$ quasars and Narrow Line
Seyfert\,1 (NLS1)
galaxies (for more details see Dietrich et al.\,2002a,\,2003b,\,2005,\,2009).
We assume that the spectrum of 3C\,390.3 can be described as a superposition of
three components,
      (i) a power law continuum (F$_\nu \sim \nu ^{\alpha}$),
     (ii) a host galaxy spectrum (Kinney et al.\,1996),
and (iii) a pseudo-continuum due to merging Fe\,{\sc ii}\ emission blends.
Neither a Balmer nor a Paschen continuum emission were taken into account
because the Balmer edge at $\lambda = 3645$\,\AA\ is close to the short
wavelength end of our spectra of 3C\,390.3 and the strength of the Paschen
continuum is only weakly constrained (Korista \& Goad 2001).

As demonstrated by Bentz et al.\,(2006a,\,2009a) it is crucial to correct for
the host galaxy contribution to measure the strength of the AGN continuum flux
density.
Based on ACS/HST images which were obtained for 14 AGN of the AGN-watch sample
(Peterson et al.\,2004), Bentz et al.\,(2009a) estimated the host galaxy
contribution to the continuum flux density at $\lambda =$\,5100\,\AA\ for those
AGN, including 3C\,390.3. For the large aperture of
($3\arcsec \times 9\farcs4$) which we used, the galaxy contribution amounts to
$F_{gal}(5100{\rm \AA}) = (0.87\pm0.09)\,\times\,10^{-15}$
 erg\,s$^{-1}$\,cm$^{-2}$\,\AA $^{-1}$, based on ACS/HST imaging data
(Bentz priv.comm.).
The average host galaxy contribution which we
determined, based on the multi-component fits, is $F_{gal}^{obs}(5100{\rm \AA})
= (0.77\pm0.10)\,\times 10^{-15}$ erg\,s$^{-1}$\,cm$^{-2}$\,\AA $^{-1}$, i.e.,
within the errors consistent with the measurements based on the ACS image.
To construct representative host galaxy template spectra we combined several
individual spectra of various Hubble types. These galaxy spectra were
retrieved from the publicly available sample published by Kinney
et al.\,(1996). The spectral resolution of these galaxy spectra amounts to
$R\simeq 8$ \AA\ which is comparable to the spectral resolution of our spectra.

To account for Fe\,{\sc ii}\ emission, we used the rest-frame optical Fe\,{\sc ii}\ template
that is based on observations of I\,Zw1 by Boroson \& Green (1992) which covers
the wavelength range from 4250\,\AA\ to 7000\,\AA .
An alternative optical Fe\,{\sc ii}\ emission line template was presented by
V\'eron-Cetty et al.\,(2004) which in addition takes into account
NLR contributions to the Fe\,{\sc ii}\ emission. In general, these two templates are
similar but in detail they differ at around $\lambda \simeq 5000$\,\AA\ and
$\lambda \raisebox{-.5ex}{$\;\stackrel{>}{\sim}\;$} 6400$\,\AA .
The optical Fe\,{\sc ii}\ emission in the spectrum of 3C\,390.3 is weak, however, and
the width of the Fe\,{\sc ii}\ emission is expected to be quite broad, as is seen for
other permitted emission lines. Therefore, the choice of the Fe\,{\sc ii}\ emission
template has no impact on the results of this study.

The components (i), (ii), and (iii) were simultaneously fitted to the
spectra of 3C\,390.3 that were intercalibrated with respect to the
[O\,{\sc iii} ]$\lambda\lambda 4959,5007$ emission-line flux, to determine the minimum
$\chi^2$ of the fit.
Various host galaxy templates were employed and the best results were obtained
using an appropriately scaled spectrum of the E0 galaxy NGC\,1407, which is
consistent with the morphological type of the host galaxy of 3C\,390.3. The
width of the Fe\,{\sc ii}\ emission template was allowed to vary from
FWHM\,=\,3000 km\,s$^{-1}$ up to 9000 km\,s$^{-1}$ in steps of
$\Delta$FWHM\,=\,500 km\,s$^{-1}$.
The best fit results were achieved for Fe\,{\sc ii}\ emission templates whose width
was on average FWHM\,=\,$(6000 \pm 1000)$ km\,s$^{-1}$, ranging from
FWHM\,=\,5000 km\,s$^{-1}$ to FWHM\,=\,8500 km\,s$^{-1}$.
In Fig.\,2 we show the fit for a typical spectrum of 3C\,390.3 from this study,
to illustrate the method to determine the different components.

The uncertainty of the fit was estimated based on the distribution of $\chi^2$
around the minimum. The spectral slope $\alpha$ of the continuum fit has an
average error of $\Delta \alpha \simeq 0.01$, while the uncertainties in the
continuum flux density at $\lambda = 5100$ and the Fe\,{\sc ii}\ emission flux are of
the order of $\sim 5$\,\% .
The best fit of the components (i) to (iii) were subtracted before we continued
to analyze the emission-line profiles of interest.

\subsection{Narrow-Line Region Emission Lines}
The spectrum of 3C\,390.3 shows strong narrow-line emission (Fig.\,2).
Hence, it is necessary to correct the broad emission-lines for NLR
contributions before line flux and profile parameters are measured.
In addition, the study of the narrow emission-lines provide information about
the ionizing continuum strength. Under the assumption that the NLR emission is
constant during the observing period in 2005 (September to December), we
measured the line strength of the narrow emission-lines in the individual
spectra of the entire campaign.
This is an additional test for the quality of the intercalibration of the
spectral region of the broad emission-lines, studied for variability.

We used a strong NLR emission line as a template profile to fit the narrow-line
spectrum and determine its flux (e.g., Whittle 1985c; Dietrich et al.\,2005).
Using high-quality, high-resolution spectra, Whittle (1985a,b)
showed that NLR emission-line profiles are similar and in particular that the
Balmer emission-line profiles are identical to the [O\,{\sc iii}]\,$\lambda 5007$
line profile within the uncertainties, even in the case of strong profile
asymmetries. Therefore, we used the strong emission-line profile of
[O\,{\sc iii}]\,$\lambda 5007$ to obtain a representative NLR line profile template.
To obtain such a profile template we made use of a spectrum of 3C\,390.3 which
we observed with the 2.2\,m telescope at Calar Alto Observatory/Spain
(Aug.\,30, 1994).
At this time 3C\,390.3 was at a lower intensity level than in 2005, i.e., the
narrow emission-lines are more pronounced (Fig.\,3).
This spectrum which covers a wavelength range comparable to this study, has
the advantage of a higher spectral resolution (R\,$\simeq 700$ at $\lambda
\simeq 6500$\,\AA ).

To isolate the [O\,{\sc iii} ] emission lines which are located in the extended red
wing of the double-peaked H$\beta $ line profile we used an appropriately
scaled H$\alpha $ profile to recover the red wing of H$\beta  $. This scaled
H$\alpha$ profile was subtracted and the residual was used to fit the
[O\,{\sc iii} ]$\lambda \lambda 4959,5007$ line profiles (Fig.\,4).
The [O\,{\sc iii} ] line profiles are well described using a dominant narrow
Gaussian component (FWHM\,=\,$11.0\,{\rm \AA}\pm0.1\,{\rm \AA}$) and a
broader Gaussian component (FWHM\,=\,$26.0\,{\rm \AA}\pm1.5\,{\rm \AA}$)
which is slightly blue-shifted by $v_{shift}\simeq100$\,km\,s$^{-1}$, to
account for the
base of the line profile (Fig.\,5). We find that the narrow component carries
$\sim 75$\,\%\ of the [O\,{\sc iii} ]$\lambda 5007$ emission-line flux. The individual
Gaussian components have a priori no physical meaning by themselves, but are
just used to obtain a NLR line profile template.

\section{Results}
\subsection{The Narrow-Line Region Spectrum}
The [O\,{\sc iii} ]$\lambda 5007$ emission-line profile fit (\S\,3.3) was used to
measure the NLR emission-line flux of the narrow lines in the spectra of
3C\,390.3.
While the NLR emission-line profile was kept fixed, we allowed the strength of
the profile template to vary and also allowed variations of the profile width
and the location in wavelength space.
For measurable emission-line doublets,
we assumed that the line ratios are
F([O\,{\sc iii} ]$\lambda 5007$)/F([O\,{\sc iii} ]$\lambda 4959$) = 2.94,
F([O\,{\sc i} ]$\lambda 6300$)/F([O\,{\sc iii} ]$\lambda 6364$) = 3.05, and
F([N\,{\sc ii} ]$\lambda 6583$)/F([N\,{\sc ii} ]$\lambda 6548$) = 3.06
(Osterbrock \& Ferland 2005) in order to fit the weaker line of each doublet.

Applying this approach we measured the strength of the emission lines and
listed them in Table 2.
The measurement uncertainty for an individual spectrum is of the order of
$\sim$\,5\,\%\ for strong narrow emission-lines like
[O\,{\sc iii} ]$\lambda\lambda 4959,5007$. In the case of moderately strong lines like
the [O\,{\sc i} ]$\lambda 6300$, [O\,{\sc ii} ]$\lambda 3727$, [Ne\,{\sc iii} ]$\lambda 3869$, and
blended lines like [N\,{\sc ii}]$\lambda \lambda 6548,6583$ the error is of the order
of $\sim$\,10\,\%\ or less, while for the weakest lines it is $\sim$\,25\,\% ,
e.g., [Fe\,{\sc x} ]$\lambda 6374$, [S\,{\sc ii} ]$\lambda \lambda 6716,6731$. In Table 2 we
present the mean narrow emission-line fluxes as measured for all epochs and the
scatter of the distribution.

We corrected the observed line fluxes for internal reddening before the
emission-line flux ratios were analyzed.
Generally, it is assumed that the observed Balmer decrement, i.e.
F(H$\alpha$)/F(H$\beta$)$_{obs}$, can be used to estimate the internal
reddening (e.g., Davidson \& Netzer 1979; Netzer 1982).
However, there are strong indications that the intrinsic Balmer decrement of
the emission-line gas of AGN is about $F(H\alpha)/F(H\beta) = 3.1$ instead of
the classical case B value for the BLR
due to collisional enhancement in the higher density partially ionized zone
(e.g., Gaskell \& Ferland 1984; Halpern \& Steiner 1983; Netzer 1982).

For the NLR gas the strength of the [O\,{\sc ii} ]\,$\lambda 3727$ emission
indicates the presence of a large fraction of low density gas
($n_e^{crit}(O^+) = 3.1 \times 10^3$ cm$^{-3}$ for $2D_{5/2}$ and
$n_e^{crit}(O^+) = 1.6 \times 10^4$ cm$^{-3}$ for $2D_{3/2}$;
Osterbrock \& Ferland 2005). Thus, additional collisional enhancement,
particularly of H$\alpha$ emission, is expected to be weak.
Therefore, we used the classical value of the Balmer decrement of
$F(H\alpha)/F(H\beta) _{int} = 2.85$, for pure recombination case\,B
(e.g., Osterbrock \& Ferland 2005) to correct
the narrow emission-lines for reddening (e.g., Crenshaw et al.\,2001).
We determine an E$_{B-V} = 0.205\pm 0.004$ for the NLR of 3C\,390.3.
Together with a Galactic reddening curve (Seaton 1979), we corrected the
observed emission line ratios relative to $F(H\beta)$, applying

\begin{equation}
{F(line) \over F(H\beta)}_{int} =
  {F(line) \over F(H\beta)}_{obs} \times
   10^{\,0.4\,\,E_{B-V}\,\,(R_\lambda - 3.68)}
\end{equation}

\noindent
with $R_\lambda$ as the Galactic extinction coefficient at the wavelength of
the corresponding emission line (Seaton 1979).
We also investigated the impact of a larger Balmer decrement,
$F(H\alpha)/F(H\beta) = 3.1$ which has been suggested to be more typical for
emission line ratios of the BLR, i.e., it takes into account collisional
excitation and radiative transfer effects - (Osterbrock \& Ferland 2005).
We find that it results in reddening-corrected
line ratios that are less than $\sim 8$\,\%\ larger for line ratios shortward
of H$\beta$ and less $\sim 8$\,\%\ smaller for line ratios longward of
H$\beta$. The reddening-corrected narrow emission-line measurements
(flux$_{cor}$), are given in Table 2.

\subsection{Continuum Variability}

We measured the relative broad-band flux variations of 3C\,390.3 relative to
the calibrated comparison star\,B in the field of 3C\,390.3 (Fig.\,1). The
Johnson $V$ magnitude of this star is given as $m_V = 14.28$ (Penston, Penston,
\& Sandage 1971). During the monitoring campaign, star\,B and 3C\,390.3 showed
comparable {\it g}-band brightness. This already indicates that 3C\,390.3 was
in a brighter state during this monitoring campaign in late 2005 than in 1995
(Dietrich et al.\,1998).

Based on the measured {\it g}-band flux ratios, we calculate the {\it g}-band
magnitude variations of 3C\,390.3. To do this we utilized the known $V$-band
magnitude of the comparison star\,B.
Fukugita et al.\,(1996) and Smith et al.\,(2002) give the transformation of a
$g'$\,-band into $V$-band magnitude, which involves in addition the ($B-V$)
color.
Applying these relations we find a $g'$\,-band magnitude of $m_{g'} = 14.59$
(Fukugita et al.\,1996) and $m_{g'} = 14.62$ (Smith et al.\,2002) for star\,B,
respectively.
However, we used the {\it g}-band filter of RetroCam (Morgan et al.\,2005) at
the MDM 2.4\,m telescope to measure the broad-band flux of 3C\,390.3. It has
been pointed out that there are small differences between the $g'$\,band
magnitudes (used at the 0.5\,m telescope of the SDSS) and the {\it g}-band
filter (used at the 2.5\,m telescope of the SDSS; Tucker et al.\,2006;
Davenport et al.\,2007; Smith et al.\,2007).

Thus, we had to transform the $g'$\,-band magnitude of the comparison star\,B
into a {\it g}-band magnitude.
We employed the transformation given by Tucker et al.\,(2006) with
$g = g' + 0.060 \times ((g' -r') - 0.53)$. To get an estimate of the color
$g' - r'$ we used the color of the star L107-S97 in Bilir et at.\,(2008) which
has a very similar ($B-V$) color to comparison star\,B. This results in a
correction of $\Delta (g-g') = -0.0014$, which can be neglected. Therefore,
for comparison star\,B the {\it g}-band and the {\it g'}-,band magnitudes can
be treated as identical.
In Figure 6 (top panel), we show the broad {\it g}-band flux density variations
of 3C\,390.3.

The errors of the {\it g}-band magnitudes of 3C\,390.3 and comparison star\,B
are estimates using the uncertainties of the flux measurements. These
uncertainties are combined in quadrature to obtain the error of the flux ratio
and hence of the flux density of 3C\,390.3. Due to the high integrated count
rates of comparison star\,B and of 3C\,390.3, in the range of several $10^6$
counts, the errors of the flux ratios are of the order of $\sim 0.1$\,\% .

Next, we measured the continuum flux density variations at
$\lambda = 5100$\,\AA\ directly from the power law continuum fit for each
spectrum (Table 3).
In Figure 6, the variations of $F_\lambda$(5100 \AA ) are displayed. It can be
seen that the AGN continuum and the {\it g}-band variations follow the same
pattern and have comparable amplitudes.

\subsection{Broad Emission-Line Flux Variations}
\subsubsection{H$\alpha \,\lambda $\,6563}
In the spectral region of the broad and double-peaked H$\alpha$ emission line
some of the corrected spectra still exhibit a weak residual continuum flux
level. To adjust for the residual continua, we fit a linear local
pseudo-continuum. The H$\alpha$ emission-line flux was measured within
the wavelength range of 6200\,\AA\ to 6800\,\AA.
This spectral range contains contributions of several narrow emission lines,
including H$\alpha _{nar}$. To correct for narrow line flux contamination the
average intensities of the narrow emission-lines of
[O\,{\sc i} ]$\lambda \lambda 6300,6364$, [Fe\,{\sc x} ]$\lambda 6374$,
[N\,{\sc ii} ]$\lambda \lambda 6548,6583$, [S\,{\sc ii} ]$\lambda \lambda 6716,6731$, and
H$\alpha _{nar}$ were subtracted (Table\,2) and the resulting broad H$\alpha$
emission line flux is given in Table 3.

To estimate the uncertainties of the broad H$\alpha$ flux measurements, first
the uncertainties of the multi-component fit were taken into account.
As noted earlier, we assumed
that the strength of the power law continuum fit, the host galaxy
contribution, and the optical Fe\,{\sc ii} \,emission can be determined within 1\,\%.
The next source of error is given by the uncertainties of the narrow
emission-line intensities (Table\,2). The largest source of error is the level
of the pseudo-continuum. The strength of the linear pseudo-continuum fit is
based on two windows which are located at 6135\,\AA\ - 6160\,\AA\
and 6875\,\AA\ - 6895\,\AA , respectively. Using the scatter of the
continuum level of these two windows, the error introduced by the
pseudo-continuum fit was determined.
The individual errors were combined in quadrature to obtain the uncertainty of
the individual broad H$\alpha$ emission-line flux measurements (Table\,3).
In Figure 6, we present the light curve of the broad H$\alpha$ emission line
flux.
Although the scatter is larger than for the {\it g}-band and
$F_\lambda$(5100 \AA ) variations, the broad H$\alpha$ flux shows a similar
variation pattern which is shifted to later epochs.

\subsubsection{H$\beta \,\lambda$\,4861 and He\,{\sc ii} \,$\lambda 4686$}
As in the case of the H$\alpha $ emission line, it was necessary to correct for
a residual continuum level of the H$\beta \,\lambda 4861$ --
He\,{\sc ii} $\lambda 4686$ wavelength range. The linear local pseudo-continuum fits
are based on two 20\,\AA\ wide continuum regions centered at
$\lambda = 4520$\,\AA\ and $\lambda = 5240$\,\AA , respectively. The corrected
spectra were used to measure the broad H$\beta \,\lambda 4861$ and
He\,{\sc ii} $\lambda 4686$ emission-line fluxes.
Because the emission-line profiles of 3C\,390.3 are so broad (Fig.\,2) it is
necessary to evaluate and to correct for the mutual blending of the
H$\beta \,\lambda 4861$ and He\,{\sc ii} $\lambda 4686$ emission, i.e., to identify
the contributions of the H$\beta \,\lambda 4861$ and He\,{\sc ii} $\lambda 4686$
emission in the overlapping region.

We used the broad H$\alpha \,\lambda 6563$ emission-line profile as a
template to estimate the shape and strength of the broad He\,{\sc ii} $\lambda 4686$
emission. To extract the broad H$\alpha \,\lambda 6563$ emission-line profile,
the mean spectrum of the campaign was used (\S 4.4) and the mean H$\alpha$
profile was corrected for the narrow emission-line contributions
([O\,{\sc i} ]$\lambda \lambda 6300,6364$, [Fe\,{\sc x}]$\lambda 6374$,
[N\,{\sc ii}]$\lambda \lambda 6548,6583$, H$\alpha _{nar}$, and
[S\,{\sc ii} ]$\lambda \lambda 6716,6731$). The width of the double-peaked broad
emission-line profile of H$\alpha \,\lambda 6563$ was scaled to have the same
width in velocity space at the location of the H$\beta \,\lambda 4861$ emission
line and the strength was rescaled to fit the central part and red wing of
the H$\beta \,\lambda 4861$ profile. In Figure 7 we show the
H$\beta \,\lambda 4861$ -- He\,{\sc ii} $\lambda 4686$ range corrected for narrow
emission of He\,{\sc ii} $\lambda 4686$, H$\beta \,\lambda 4861$, and
[O\,{\sc iii}]$\lambda\lambda 4959,5007$. The scaled double-peaked H$\alpha$
emission-line profile describes the broad H$\beta \,\lambda 4861$ emission
profile well, except the blue hump which is less prominent in the H$\beta$
profile compared to the H$\alpha \,\lambda 6563$ emission-line profile. This
results in an absorption line-like feature in the residual spectrum (Fig.\,7,
bottom panel) which indicates a steeper Balmer decrement for the blue peak
in the double-peaked profiles.
To measure the He\,{\sc ii} $\lambda 4686$ emission-line flux, the residual emission
at the location of the He\,{\sc ii} $\lambda 4686$ line was fit with a rescaled broad
H$\alpha \,\lambda 6563$ double-peaked profile and also with a single broad
Gaussian profile.
The profile in the residual spectrum of the mean spectrum is better represented
by a Gaussian profile than using an appropriately scaled double-peaked
H$\alpha$ profile (Fig.\,7).
To determine an appropriate Gaussian profile for the broad He\,{\sc ii} $\lambda 4686$
emission, the blue wing of the He\,{\sc ii}\ line in the residuum was extracted and
assuming that the broad He\,{\sc ii}\ profile is symmetric the blue wing was mirrored
to represent the red wing of the He\,{\sc ii} $\lambda 4686$ line profile (Fig.\,8).
The resulting profile can be described with a single Gaussian profile at
$\lambda _c = 4686.14\,{\rm \AA}\pm0.04$\,\AA\ and a profile width of
FWHM\,=\,$242.3\,{\rm \AA}\pm1.4$\,\AA\
($15500\,{\rm km\,s}^{-1}\pm100$ km\,s$^{-1}$).
To measure the He\,{\sc ii} $\lambda 4686$ emission-line light curve (Fig.\,6) a
Gaussian profile of fixed width (FWHM = 15500 km\,s$^{-1}$) was fit to the
blue wing of the He\,{\sc ii} $\lambda 4686$ profile in the spectra of 3C\,390.3
(Fig.\,8).
The flux of the He\,{\sc ii} $\lambda 4686$ emission was measured from this Gaussian
fit for a wavelength range of $\lambda = 4472$\,\AA\ to $\lambda = 4900$\,\AA.
This Gaussian profile fit was subtracted from the spectrum to measure the broad
H$\beta \,\lambda 4861$ emission flux in the range from $\lambda = 4680$\,\AA\
to $\lambda = 5000$\,\AA\ (Table\,3). The resulting light curves for the broad
H$\beta \,\lambda 4861$ emission line flux, corrected for narrow H$\beta$
emission, and the He\,{\sc ii} $\lambda 4686$ emission line, are displayed in Fig.\,6.

To estimate the total error of these flux measurements, we assumed that the
uncertainties of the multi-component fit are of the order of 1\,\% .
The errors introduced by the correction of the narrow emission lines are taken
from Table 2. The uncertainty due to the broad He\,{\sc ii} $\lambda 4686$ emission is
of the same order as the total error that is caused by the narrow emission
lines.
As in the case of H$\alpha \,\lambda 6563$, the dominant source of error is the
level of the pseudo-continuum fit. The level of the pseudo continuum fit was
varied within the scatter given by the two ranges centered at
$\lambda_c = 4520$\,\AA\ and $\lambda _c = 5240$\,\AA\ that are 20\,\AA\ wide.
The individual contributions to the uncertainty were combined in quadrature to
obtain the total uncertainties of the individual broad H$\beta$ and
He\,{\sc ii} $\lambda 4686$ emission-line flux measurements (Table\,3).

\subsubsection{H$\gamma \,\lambda $\,4340}
In the case of the H$\gamma $ emission line profile region, we correct for a
residual continuum level as well. The linear local pseudo-continuum fits are
based on two 20\,\AA\ wide continuum regions centered at
$\lambda _c = 4160$\,\AA\ and $\lambda _c = 4530$\,\AA , respectively. The
corrected spectra were used to measure the H$\gamma \,\lambda 4340$
emission-line flux (4220\,\AA\ to 4500\,\AA ).
These flux measurements were corrected for the emission line contributions of
the narrow H$\gamma \,\lambda 4340$ emission and of the [O\,{\sc iii} ]$\lambda 4363$
emission, using the average narrow line fluxes as given in Table 2. The
resulting light curve of the variable broad H$\gamma \,\lambda 4340$ emission
line is shown in Fig.\,6. The variability pattern is very similar to the broad
H$\beta$ variations.

To estimate the total error of the broad H$\gamma$ flux measurements
(Table\,3), we assumed that the uncertainties of the multi-component fit are
of the order of 1\,\%. The errors introduced by the correction of the narrow
emission lines are taken from Table 2.
The dominant source of error is the level of the pseudo-continuum fit. The
level of the pseudo-continuum fit was varied within the scatter given by the
two 20\,\AA\ wide ranges ($\lambda_c = 4160$\,\AA\ and
$\lambda _c = 4530$\,\AA ).
The contributions of the individual error sources were combined in quadrature
to estimate the total uncertainty of the broad H$\gamma \,\lambda 4340$
emission line flux.

\subsection{Mean and rms Spectra}
\subsubsection{H$\alpha \,\lambda 6563$, H$\beta \,\lambda 4861$, and
               H$\gamma \,\lambda 4340$}
Based on the calibrated spectra of 3C\,390.3, we calculated mean and residual
(hereafter simply {\it rms}) spectra
of the broad emission profiles of Balmer lines H$\alpha$, H$\beta$, and
H$\gamma$ which are shown in Figure 9.
These mean and rms spectra are based on the entire set of MDM spectra, except
the spectrum that was recorded at the epoch JD\,=\,244\,3696. The
signal-to-noise (S/N) ratio for this spectrum is significantly lower than for
all the other spectra of 3C\,390.3 on account of bad weather conditions
(S/N$_{2443696} \simeq 10$, compared to an average signal-to-noise ratio for
the sample of S/N\,=\,$35\pm7$).

The mean spectra of the Balmer emission lines show a characteristic
double-peaked emission-line profile with a strong blue hump while the red
hump is very weak.
The rms spectra of the Balmer lines show a similar shape.
The blue hump is the dominant feature for the H$\alpha $ and H$\beta$
rms spectra while it is less pronounced for H$\gamma$.
Only weak residuals of narrow emission-lines can be seen in the Balmer
rms spectra of H$\alpha$, H$\beta$, and H$\gamma$.
The rms spectra of the Balmer emission lines also display extended red wings.

The line width can be characterized by its full width at half maximum
(FWHM) and by the line dispersion $\sigma _{line}$ (the second moment of the
line profile; e.g., Peterson et al.\,2004). In order to
characterize the uncertainties in each of these parameters we employed a
procedure described by Peterson et al.\,(2004). For a set of {\it N} spectra,
{\it N} spectra are randomly selected, in particular without regard whether the
spectrum has been previously selected or not. These {\it N} randomly selected
spectra are used to construct mean and rms spectra from which the line width
measurements are made. This process yields one Monte Carlo realization, and a
large number ($N\simeq 10\,000$) of these realizations yield a mean and
standard deviation for each of the measurements of the line width.
The results of the line profile measurements and the corresponding errors are
presented in Table 4.

We find that the mean spectra of the Balmer emission lines show a similar
profile width of FWHM = 11900 km\,s$^{-1}$ to 13200 km\,s$^{-1}$ and the
second moment of the line profiles $\sigma_{line}$ ranges from
4000 km\,s$^{-1}$ to 5400 km\,s$^{-1}$, respectively.
The comparison of the rms spectrum profile widths show basically the same
result. The Balmer emission line rms spectra have an average profile width
of FWHM = $(11430 \pm 790)$\,km\,s$^{-1}$ and an average second moment of
the line profiles of
$\sigma_{line}$\,= $(5160 \pm 310)$\,km\,s$^{-1}$, respectively.

\subsubsection{He\,{\sc ii} $\lambda 4686$}
The mean and rms profiles are a Gaussian due to our approach to measure the
He\,{\sc ii} $\lambda 4686$ emission line flux and hence also the rms spectrum
(\S 4.3.2).
However, the rms spectrum of the He\,{\sc ii} $\lambda 4686$ variations is contained
in the rms spectrum of the broad H$\beta$ emission line (Fig.\,9). To recover
the He\,{\sc ii} $\lambda 4686$ rms spectrum we examined two approaches.

First, the fit of the He\,{\sc ii} $\lambda 4686$ emission-line was subtracted from
each spectrum of the H$\beta $-[O\,{\sc iii} ]$\lambda \lambda 4959,5007$ emission
line region. This results in an uncontaminated broad H$\beta$ profile. These
spectra are used to calculate a mean and rms spectrum which represent the
H$\beta$ variation alone. In Figure 10 the mean spectrum of the
H$\beta $-[O\,{\sc iii} ]$\lambda \lambda 4959,5007$ emission-line region with and
without correction for the broad He\,{\sc ii} $\lambda 4686$ emission is displayed,
as well as the comparison of the rms spectra. The difference of these rms
spectra can be associated with the He\,{\sc ii} $\lambda 4686$ rms spectrum
(Fig.\,10).

As an alternative approach to recover the He\,{\sc ii} $\lambda 4686$ rms spectrum, we
assumed that the rms spectrum of the broad  H$\alpha $ emission-line can be
used as a template for the rms spectrum of the H$\beta$ emission line.
The H$\alpha$ rms spectrum was re-binned that the width is unchanged in
velocity space at the location of the H$\beta$ emission-line. In Figure 11 the
rms spectra of the broad H$\beta$ and H$\alpha$ emission lines are shown.
Next, the re-binned H$\alpha $ rms spectrum was rescaled by dividing by 3.50
to fit the red wing of the H$\beta$ rms spectrum. The difference between the
H$\beta $ rms spectrum and the scaled, re-binned H$\alpha$ rms spectrum can be
associated with the He\,{\sc ii} $\lambda 4686$ rms spectrum as well. This difference
is displayed in the bottom panel of Fig.\,11. It can be seen that this
representation of the He\,{\sc ii} $\lambda 4686$ rms spectrum is nearly identical
to the rms spectrum which is obtained by comparison of the rms spectra of the
H$\beta$-[O\,{\sc iii} ]$\lambda \lambda 4959,5007$ spectral region, corrected and
uncorrected for He\,{\sc ii} $\lambda 4686$ emission, as described above.

The comparison of the He\,{\sc ii}$\lambda 4686$ rms spectrum with the mean Gaussian
profile fits to the He\,{\sc ii} $\lambda 4686$ line profile indicates that the
recovered rms spectrum of the broad He\,{\sc ii} $\lambda 4686$ emission line tends to
show less variability in the far blue wing than the mean spectrum and thus the
FWHM is smaller.
This result is consistent with the properties of the mean and rms spectra of
the Balmer emission lines which also show narrower profiles in the rms spectra
compared with the corresponding mean spectra (Table\,4).
We used both He\,{\sc ii} $\lambda 4686$ rms spectra to measure their FWHM. While the
overall shapes of the rms spectra are very similar, the signal-to-noise ratio
is different. Hence, we used the average of the FWHM, as well as the second
moment $\sigma _{line}$ of the profile. The results are given in Table 4.

\subsection{Variability Characteristics}
We calculated basic variability parameters to characterize the statistical
properties of the observed emission-line and continuum variations (Fig.\,6).
The results are presented in Table 5. Column (1) gives the spectral feature.
The mean flux and the standard deviation are presented in column (2) and (3).
The excess variance, $F_{var}$, in column (4) is computed as

\begin{equation}
F_{var} = {1 \over {\overline{F}}} \, \sqrt{\sigma_F^2 - \Delta^2}
\end{equation}

\noindent
with
$\overline{F}$ as the mean flux (column 2), $\sigma_F$ as the rms of the flux
variations and $\Delta^2$ as the mean square value of the measurement errors
(Rodriguez-Pascual et al.\,1997). Finally, in columns (5) and (6) the minimum
and maximum fluxes are given for each light curve.
The relative variations of the AGN continua (F$_\lambda$(5100\AA) and
{\it g}-band) and of the emission lines of H$\alpha$, H$\beta$, and H$\gamma $
are of the order of $\sim 5$\,\% . The weak He\,{\sc ii} $\lambda 4686$ emission line,
however, shows a relative variation of about $\sim 15$\,\% .
In spite of the larger uncertainties of the emission-line flux measurements of
He\,{\sc ii} $\lambda 4686$ these uncertainties are accounted for by the parameter
$\Delta $ in eq.\,2 to calculate the relative variability.
There is a trend for stronger relative variations of emission lines with a
higher ionization potential of the involved atom. The larger relative
variability is also consistent with the results of former variability studies
which find that F$_{var}$ of high-ionization lines like He\,{\sc ii} $\lambda 1640$ or
He\,{\sc ii} $\lambda 4686$ are always larger by a factor of about $\sim 2$ to 3 times
than F$_{var}$ for low ionization lines like H$\beta$ or H$\alpha$ (e.g.
Clavel et al.\,1991; Collier et al.\,1998; Dietrich et al.\,1993,\,1998;
Korista et al.\,1995; O'Brien et al.\,1998; Peterson et al.\,1991;
Reichert et al.\,1994; Rodriguez-Pascual et al.\,1997;
Santos-Lle\'o et al.\,1997; Stirpe et al.\,1994; Wanders et al.\,1997).

\subsection{Time Series Analysis}
Generally, AGN monitoring campaigns have focused on the H$\beta$ --
[O\,{\sc iii} ]$\lambda \lambda 4959,5007$ spectral range
because the strong forbidden [O\,{\sc iii} ]$\lambda \lambda 4959,5007$ emission
lines can be used to establish a robust calibration of the individual spectra.
With the large wavelength coverage of this campaign for 3C\,390.3 we are able
to study the delayed response of not only H$\beta$ but H$\alpha$, H$\gamma$,
and He\,{\sc ii} $\lambda 4686$ as well.

To measure the time delay between AGN continuum variations and variable broad
line emission, the continuum light curve is used as the driving light curve
with the line emission in response to these variations. To calculate the time
delay between the observed variations, we use the interpolation correlation
function (ICCF) method (Gaskell \& Peterson 1987; White \& Peterson 1994;
Peterson et al.\,1998,\,2004).
For this monitoring campaign we derived an AGN continuum light curve from the
power-law continuum fits at $\lambda =5100$\,\AA , as well as the {\it g}-band
light curve.

First, we selected an appropriate continuum light curve. Since the {\it g}-band
flux contains variable broad H$\beta $ emission in addition to the AGN
continuum, we studied the impact of the broad H$\beta $ line emission on the
{\it g}-band variations.
The contribution of the host galaxy can be assumed to be constant.
The {\it g}-band light curve and the F$_\lambda$(5100\AA) light curve (Fig.\,6)
are cross correlated using the ICCF method with F$_\lambda$(5100\AA) as the
driving light curve. The resulting CCF is shown in Figure 12.
Close inspection of this CCF shows that the {\it g}-band light curve is delayed
with respect to the F$_\lambda$(5100\AA) variations by
$\tau _{cent} = (0.2 \pm 1.1$) days and
$\tau _{peak} = (0.6 \pm 1.2$) days, respectively (Table\,6).
Within the uncertainties, the F$_\lambda$(5100\AA) variations and the
{\it g}-band variations are simultaneous and the detected small delay can be
neglected. It is reasonable to attribute this hint of a delay to the variable
broad H$\beta$ emission which is part of the {\it g}-band flux.
Since the scatter in the {\it g}-band fluxes is much smaller than in the
F$_\lambda$(5100\AA) continuum light curve, we selected the {\it g}-band
variations as the driving continuum in the subsequent cross-correlation
analysis.
For comparison, we also provide the cross-correlation results using
F$_\lambda$(5100\AA) as the driving continuum light curve (Table\,6).
The cross-correlation functions (ICCFs) for the broad emission lines are
displayed in Figure 13. The ICCFs show some asymmetric shape and the region
around the peak has some structure as well.

To quantify the uncertainties in the time delay measurements, we employ
the model-independent Monte Carlo FR/RSS method (Peterson et al.\,1998),
including modifications described by Peterson et al.\,(2004). For each single
realization of the method, random subset sampling (RSS) is applied in which a
light curve with N data points is randomly sampled N times without regard to
the previous selection of each point.
Flux randomization (FR), in which a random Gaussian deviation, based on the
associated error, is then applied to each of the selected N points.
This FR/RSS-altered subset of data points is then cross-correlated as though it
were real data. The peak of the cross-correlation function, r$_{max}$, which
occurs at a time lag $\tau _{peak}$, is determined, as is the centroid,
$\tau _{cent}$.
A cross-correlation peak distribution (CCPD) for $\tau _{peak}$ and
a cross-correlation centroid distribution (CCCD) for $\tau _{cent}$ are built
with a large number (N\,$\simeq$\,10,000) of Monte Carlo realizations.
We take the average value of the CCPD to be $\tau _{peak}$
and the average of the CCCD to be $\tau _{cent}$.
To calculate the uncertainties $\Delta \tau _{up}$ and $\Delta \tau _{low}$
we assume that 15.87\,\%\ of the cross-correlation centroid realizations
have values $\tau > \tau _{cent} + \Delta \tau _{up}$ and
15.87\,\%\ have values $\tau < \tau _{cent} - \Delta \tau _{low}$, with analog
estimated uncertainties for $\tau _{peak}$.
These definitions of the uncertainty correspond to $\pm1\,\sigma$ for a
Gaussian distribution.

\subsubsection{Velocity-Dependent Broad Emission-Line Variations}
While the variability characteristics of the integrated broad-line flux can be
used to infer the size of the BLR, the analysis of the response of different
parts of the broad emission-line profile, e.g., the line core, and the profile
wings, yield information on the dominant gas motion, i.e., the kinematics of
the broad emission-line gas (e.g., Blandford \& McKee 1982;
Horne et al.\,2004).
Previous investigations of 3C\,390.3 have found that the profile wings vary in
phase (Dietrich et al.\,1998; Popovic et al.\,2011; Sergeev et al.\,2002;
Shapovalova et al.\,2010) which strongly favors orbital motion, i.e., virial
motion dominates the gas kinematics. This is also supported by accretion disk
models to describe the double-peaked  Balmer emission line profiles
(e.g., Eracleous \& Halpern 1994; Flohic \& Eracleous 2008).
Recently, results for several AGN have been presented (Denney et al.\,2009b;
Bentz at al.\,2009b) which indicate a more complex picture with signatures for
orbital motion, as well as for radial motions.
In addition, for Arp\,151 the analysis of spectroscopically resolved broad
emission-lines results into velocity-delay maps which indicate the presence of
substructures like orbiting hot spots (Bentz et al.\,2010b).

As in former studies of 3C\,390.3, we extracted light curves for different
parts of the broad emission-line profile. For better comparison with prior
studies (e.g., Dietrich et al.\,1998; Gezari et al.\,2007;
Shapovalova et al.\,2010) the width and placement of those regions are
motivated by the location and the widths of the blue and red peak in the
double-peaked line profile.

In Table 7 the location of the blue peak and red peak for the H$\alpha$,
H$\beta $, and H$\gamma $ emission-line profiles are given. Within
$\sim 100$ km\,s$^{-1}$ both peaks are at similar velocities. Based on the mean
line profiles (Fig.\,9) the width of the peaks amounts to
FWHM\,$\simeq$\,50\,\AA\ and FWHM\,$\simeq$\,70\,\AA\ for H$\beta$ and
H$\alpha$, respectively.
We investigated the profiles of the H$\alpha$ and H$\beta$ emission lines only
because the H$\gamma $ emission line is too weak and He\,{\sc ii} $\lambda 4686$ is
best represented by a single Gaussian profile.
We extracted the light curves of the blue and red peak for a 3000 km\,s$^{-1}$
wide region. In Figure 14 the boundaries of the blue and red wings, the blue
and red peaks, and the line center are shown. For comparison the location of
those profile sections are given in Table 8 which were used by
Gezari et al.\,(2007).
The errors for the extracted light curves were determined following the same
approach as for the integrated emission line fluxes.

Next, the H$\alpha$ and H$\beta$ line profile section variations are
cross-correlated with the {\it g}-band light curve, as well as with the AGN
continuum F$_\lambda$(5100\,\AA).
In Figure 15 the corresponding ICCF($\tau$) are shown. While
for H$\alpha$ the light curves of the blue wings, the blue and red peak and of
the line center result into ICCFs with well defined structures, the light curve
of the red wing of the broad H$\alpha$ line profile results into a ICCF which
provides merely an indication for a possible delay (Fig.\,15). For the H$\beta$
line profile the ICCFs are broad and in the case of the red wing for H$\beta$
there is only a weak indication for a marginally defined peak (Fig.\,15).

The location of the centroid, the peak and the uncertainties in the ICCFs for
the wings, the peaks, and the line center of the H$\alpha$ and H$\beta$
emission lines are determined using the technique described above (\S 4.3) and
the results are given in Table 9. As can be seen already in Figure 15, the blue
and red peak of the H$\alpha$ line and of the H$\beta$ line vary basically with
the same time delay relative to the continuum variations, consistent with the
model that the hydrogen Balmer line emission originates in a rotating disk
(e.g., Eracleous \& Halpern 1994; Flohic \& Eracleous 2008). Within the
uncertainties there is also no delay of the profile wings with respect to the
peaks or the center of the line profile.
To test this result we also applied the time series analysis to the variations
of the blue and red wings and the blue and red peaks to eliminate uncertainties
which are introduced by the continuum light curves. The corresponding ICCFs for
the H$\alpha $ and H$\beta$ lines are displayed in Figures 16.
Within the uncertainties we detect no time delay between the variations of the
blue and red peaks and wings (Table\,9).

\subsection{Stochastic Process Estimation for AGN Reverberation}

Generally, the time delay between continuum and broad emission line flux
variations is determined by calculating cross-correlation functions. However,
for a better specification of the possible impact of gaps in the temporal
coverage of the light curves, recently an alternative approach has been
suggested by Zu et al.\,(2011) and applied by Grier et al.\,(2012) to the
measured variability of the NLS1 galaxy Mkn\,335.
This method to analyze irregularly sampled light curves with a more statistical
approach was developed by Press et al.\,(1992) and Rybicki \& Press (1992).
They assumed that an irregularly sampled light curve can be treated as a damped
random walk process with a specific amplitude $\hat{\sigma}$ and an exponential
damping time scale $\tau_d$.
In recent years it has been shown that quasar light curves can be, indeed, well
described with this approach (Kelly et al.\,2009; Zu et al.\,2012) and
furthermore that the amplitude $\hat{\sigma}$ and damping time scale $\tau_d$
for quasar variability are found in a well defined region of the $\hat{\sigma}$
-- $\tau_d$ space (Koz\l owski et al.\,2010; MacLeod et al.\,2010).
Recently, Mushotzky et al.\,(2011), however, have shown using Kepler data for
four AGN, that the variability of all AGN cannot be described with the random
walk approach but that individual AGN have intrinsically different variability
characteristics.

To investigate also AGN variability data and in particular the impact of gaps
in the temporal sampling in AGN light curves Zu et al.\,(2011) have modified
this statistical approach.
We used their method of Stochastic Process Estimation for AGN Reverberation
(SPEAR) as presented by Zu et al.\,(2011) to investigate the variations of
3C\,390.3 (Fig.\,6).
First, we used the {\it g}-band variation and the F$_\lambda$(5100\AA)
variability to test whether the SPEAR results are consistent with our
cross-correlation results (Table\,6). We started with an amplitude of
$\hat{\sigma}=0.05$ and an damping time scale of $\tau_d = 60$\,days. With the
{\it g}-band variations as a driver light curve (because of its much smaller
errors than the F$_\lambda$(5100\AA) light curve), we find using SPEAR a delay
of $\tau = 0.55 ^{+1.56}_{-0.45}$\,days which is consistent with the
cross-correlation result.

Next, we used the {\it g}-band light curve as the driver to recover the time
delays of the H$\alpha$, H$\beta$, H$\gamma$, and He\,{\sc ii} $\lambda 4686$
variations. Using SPEAR we computed time delays for the strong Balmer lines
H$\alpha$ and  H$\beta$ which are basically identical within the errors to the
cross-correlation based delays.
In the case of the H$\gamma$ and He\,{\sc ii} $\lambda 4686$ emission lines, however,
the delays determined with SPEAR and based on the cross-correlation analysis
show some differences. The time delays of the Balmer lines H$\alpha$, H$\beta$,
and H$\gamma$ derived with {\it SPEAR} are consistent with those of the ICCF
analysis using F$_\lambda$(5100\AA ) as the driving continuum. However, for
the He\,{\sc ii} $\lambda 4686$ emission lines the delays are just consistent within
the 1-$\sigma$ errors. The time delay of the H$\gamma$ variations based on the
g-band light curve as the driver continuum and the {\it SPEAR} result differ
by nearly a factor of 2 (Table 6).
Furthermore, due to the larger uncertainties of the flux measurements for the
H$\gamma$ and He\,{\sc ii} $\lambda 4686$ emission lines, {\it SPEAR} needed to be
restricted to a narrow range of allowed time delays to avoid spurious delays
at $\tau \simeq 120$ days, which is longer than the period covered by the
experiment.

SPEAR treats large gaps in the temporal coverage of a light curve in a
statistically based approach and also follows the impact on the uncertainty of
the time delay. However, in the case of the study of 3C\,390.3 with no large
gaps in the light curve, we applied SPEAR predominantly to compare the results
with those of the ICCF analysis and the results of both methods do well agree.
Hence, we used the results of the ICCF analysis in the following for
consistency with former variability investigations which allows an easier
comparison with those results.

\subsection{Black Hole Mass and Eddington Ratio}
\subsubsection{Black Hole Mass Estimates}

To determine the mass of the black hole in the center of 3C\,390.3, we assumed
that the line-emitting gas is bound, i.e., that the virial theorem can be
applied. This approach is well-motivated by the results of the fitting of the
double-peaked emission line profiles of 3C\,390.3 with an elliptical disk model
(Flohic \& Eracleous 2008). In addition, for several AGN it has been possible
to measure the time delay of additional broad emission line flux variations.
These studies consistently show that emission-lines with higher ionization
energies show shorter time delays, in keeping with the observed ionization
stratification of the BLR and their closer locations to the central continuum
source (Bentz et al.\,2009a; Kollatschny 2003; Onken \& Peterson 2002;
Peterson \& Wandel 1999,\,2000).
Together with broader emission line profile widths, these results provide
strong support that the gas is in gravitational bound motion.
The virial mass of the black hole is given by

\begin{equation}
M_{bh}^{vir} = f\,{{c\,\tau \,\,\Delta v^2} \over G}
\end{equation}

\noindent
with $c\,\tau$ as the size of the broad emission line region, $\Delta v$ which
is associated with the line profile width, and $G$ as the gravitational
constant. The factor $f$ depends of the geometry, kinematics, and the
orientation of the line emitting region. It has been shown by
Onken et al.\,(2004) that the average of $f$ amounts to $<f> = 5.5$ when the
virial black hole mass, based on a rms spectrum profile width, is calibrated to
the $M_{bh} - \sigma_\ast$ relation for quiescent galaxies
(e.g., Tremaine et al.\,2002; G\"{u}ltekin et al.\,2009, 2011).
In the following we calculate the pure virial product, i.e., we will assume
$f = 1.0$ because in the case of 3C\,390.3 and the successful accretion disk
models $v_{obs} = v_{intr}\times {\rm sin}\,i$ can be used to derive the
intrinsic velocity, $v_{intr}$, of the gas.

\begin{equation}
M_{bh}^{vir} = 1.951\times 10^5\,\left({\tau \over days}\right)
               \left({\sigma_{line} \over {1000\,km/s}}\right)^2 \,\,M_\odot
\end{equation}

Using the second moment of the emission-line profiles $\sigma_{line}$
(cf.\,Peterson et al.\,2004) for the mean and rms spectra (Table 4) and the
measured time delay of the broad
emission-line flux response to continuum variations, given by $\tau _{cent}$
(Table 6), derived from a threshold of 80\,\%\ of the maximum of the ICCF, we
calculated the virial black hole mass using eq.(4). The results are presented
in Table 10. For comparison we estimated black hole masses for the individual
emission lines using $\sigma_{line}$ from the the mean and the rms spectra
and the time delay which we derived using the AGN continuum variations of
F$_\lambda$(5100\AA) and of the {\it g}-band, as well (Table 6).
We find that within the uncertainties the virial mass, M$_{bh}^{vir}$, of the
black hole of 3C\,390.3, based on the mean emission line profiles, is in the
range of
$1.0\times10^8 M_\odot$ to $2.6\times10^8 M_\odot$
based on the properties of the mean profiles of the Balmer lines and the
He\,{\sc ii} $\lambda 4686$ emission line, independent of the continuum used
(Fig.\,17, Table\,10).
However, if only the strong Balmer emission lines H$\alpha$ and H$\beta$ are
considered because the uncertainties for the H$\gamma$ and He\,{\sc ii} $\lambda 4686$
emission lines are larger, the virial products are in better agreement,
$2.3\times10^8 M_\odot$ to $2.6\times10^8 M_\odot$.
The rms spectra yield results which are consistent with the mean-spectrum
with virial black hole masses of
$1.1\times10^8 M_\odot$ to $3.0\times10^8 M_\odot$ (Table\,10) and the strong
Balmer emission lines H$\alpha$ and H$\beta$ yield black hole
mass estimates of about $\sim 2.6\times10^8 M_\odot$.
Since, the rms spectrum represents the actually variable part of the emission
line profile, we conclude that the virial product of the black hole of
3C\,390.3, based on the strong Balmer emission lines H$\alpha$ and H$\beta$ is
M$_{bh}^{vir}(3C390.3) = (2.60^{+0.23}_{-0.31})\times 10^8\,M_\odot$.

To estimate the black hole mass M$_{bh}$ using reverberation mapping studies,
it is still necessary to specify the factor $f$ in eq.\,(3) which depends on
the not well-constrained geometry and kinematics of the gas, as well as on the
orientation of the line emitting region. While it is generally assumed that
this factor $f$ is of the order of unity, it has been pointed out that a small
inclination of the line emitting region can result in a significant
underestimation of the black hole mass (e.g., Collin et al.\,2006)
if the gas motions are almost entirely in the disk plane with little motion in
the polar direction.
In contrast to almost all AGN monitored so far, the BLRG 3C\,390.3 is unique
since it is the only radio loud AGN with extended double-lobed radio emission
(Leahy \& Perley 1995) whose variability has been studied in detail.
This allows us to estimate the impact of the inclination $i$ of the line
emitting region on the black hole mass measurement and hence the factor $f$,
assuming pure disk motion of the gas.
Based on VLBI observations, Alef et al.\,(1988) reported indications for
super-luminal motion for 3C\,390.3. Further radio observations and a detailed
analysis provided information on the inclination $i$ of the axis of the radio
emission in 3C\,390.3 (Alef et al.\,1994,\,1998), which was found to be
$i = 28^o$\,$^{+5^o}_{-9^o}$.
The inclination of the radio axis of 3C\,390.3 has been also estimated based on
X-ray observations (Eracleous et al.\,1996).
They successfully modeled the resolved Fe K$\alpha$ line emission with X-ray
reprocessing in a cool, dense disk of gas at an inclination of $i \simeq 26^o$.
A third way to estimated the inclination of the disk-like line-emitting region
is provided by fitting the double-peaked profile. Using a relativistic
Keplerian disk Eracleous \& Halpern (1994) derived an inclination angle of
$i = 26^o$\,$^{+4^o}_{-2^o}$. Recently, Flohic \& Eracleous (2008) analyzed
the variations of the double-peaked profile shape of H$\alpha$ for Arp\,102B
and 3C\,390.3. They found that the best disk models for 3C\,390.3 strongly
indicate an inclination angle of $i = 27^o \pm 2^o$.

In a simple model of an accretion disk as the dominant source of the observed
double-peaked emission-line profile, the observed velocity is actually
$v_{obs} = v_{intr}\times {\rm sin}\,i$.
Assuming an inclination angle of $i=27^o \pm 2^o$ this implies a correction
factor of $f = 4.85^{+0.75}_{-0.60}$. Within the  uncertainties, this factor is
consistent with $<f> = 5.5$, determined by Onken et al.\,(2004)
and $<f> = 5.25$ by G\"{u}ltekin et al.\,(2009)
which were determined by comparing the reverberation-based black hole masses
with the masses determined using the M\,--\,$\sigma$ relation, with the
stellar velocity dispersion $\sigma$ based on stellar or gas dynamics of the
host galaxy's bulge.
Applying the correction due to the measured inclination of the accretion disk,
the black hole mass of 3C\,390.3 based on the H$\alpha$ and H$\beta$ rms
spectrum profile properties and $\tau_{cent}$ yields
M$_{bh}({\rm 3C\,390.3}) = (1.26^{+0.21}_{-0.16})\times 10^9\,M_\odot$.

Accretion disk models have been shown to be successful in explaining the
observed profiles and even profile variations over longer time scales for
3C\,390.3, Thus, the typical velocity of the line emitting gas can be
associated with the location of the blue and red peak of the double-peaked
emission-line profile, i.e., the location in velocity space of the dominant
part of the line emitting gas. Using the separation of the blue and red peak
of the Balmer emission-line profiles as $\Delta v$, we estimated the virial
product using eq.(4) and $\tau_{cent}$ (80\,\%\ threshold level). The derived
black hole masses are given in Table 10.
Based on the Balmer emission lines H$\alpha$, H$\beta$, and H$\gamma$ we find
virial black hole masses in the range of
$1.1\times10^8 \raisebox{-.5ex}{$\;\stackrel{<}{\sim}\;$} M_{bh} \raisebox{-.5ex}{$\;\stackrel{<}{\sim}\;$} 2.0\times10^8 M_\odot$ using the mean
emission-line profiles and
$0.9\times10^8 \raisebox{-.5ex}{$\;\stackrel{<}{\sim}\;$} M_{bh} \raisebox{-.5ex}{$\;\stackrel{<}{\sim}\;$} 1.9\times10^8 M_\odot$ based on
the rms spectra (Fig.\,17, Table\,10).
However, this wide range is caused by the H$\gamma$ based results which have a
larger uncertainty than the black hole mass estimates obtained from the strong
H$\alpha$ and H$\beta$ emission lines which are consistent within the errors.
Since the rms spectrum represents the actual variable part of the emission line
gas, we calculated the average virial black hole mass which is based on the rms
spectra of the Balmer emission lines H$\alpha$, H$\beta$, and H$\gamma$. We
find a virial black hole mass of
M$_{bh}^{vir} = (1.77^{+0.29}_{-0.31})\times10^8 M_\odot$.
Together with the correction factor $f = 4.85^{+0.75}_{-0.60}$ which is given
by the inclination of the accretion disk, we find for the black hole mass for
3C\,390.3 a value of $M_{bh} = 0.86^{+0.19}_{-0.18}\,\times\,10^9\,M_\odot$.

\subsubsection{Eddington Ratio}
Using the black hole mass estimates based on the broad Balmer and emission-line
profiles in the rms spectrum and the optical continuum luminosity of
3C\,390.3 at $\lambda = 5100$\,\AA , we computed the Eddington ratio
${\rm L}_{bol} / {\rm L}_{edd}$. The value of the conversion factor $f_L$
between the monochromatic luminosity and the bolometric luminosity
(${\rm L}_{bol} = f_L \times \lambda \, {\rm F}_\lambda (5100)$), is still
debated in the literature (e.g., Elvis et al.\,1994; Laor 2000; Netzer 2003;
Richards et al.\,2006). Recently, Marconi et al.\,(2008) suggested even a
luminosity-dependent correction factor $f_L$, due to radiation pressure
effects. We assumed that the bolometric luminosity is given by
$L_{bol} = 9.74\times \lambda \,L_\lambda (5100\,{\rm \AA })$
(Vestergaard 2004). We find $L_{bol} = 2.22\times10^{45}$ erg\,s$^{-1}$.
To calculate the Eddington luminosity ${\rm L}_{edd}$, we assumed that the gas
is a mixture of hydrogen and helium ($\mu = 1.15$), i.e.,
${\rm L}_{edd} =
             1.45\times 10^{38}\,{\rm M}_{bh}\,/\,{\rm M}_\odot$ erg\,s$^{-1}$.
The derived Eddington ratio $L_{bol} / L_{edd}$ for 3C\,390.3, based on this
monitoring campaign, amounts to $L_{bol} / L_{edd} = 0.018^{+0.006}_{-0.005}$.
This low Eddington ratio is typical for radio-loud AGN like 3C\,390.3 (e.g.,
Boroson \& Green 1992; Boroson 2002).

\section{Discussion}

\subsection{Times Series Analysis and the Size of the BLR}
Recently, results of studies on the long-term variability properties of
3C\,390.3 have been presented by Sergeev et al.\,(2002,\,2011) and Shapovalova
et al.\,(2010). In two studies Sergeev et al.\,(2002,\,2011) investigated the
correlated variations of the optical continuum and the response of the broad
H$\beta$ emission-line flux for the years 1992 to 2000 and 2000 to 2007,
respectively.
In both studies they found that the H$\beta$ variations are delayed by
$\tau (H\beta) = 82^{+12}_{-10}$\,days ($1992 - 2000$) and
$\tau (H\beta) = 94\pm6$\,days ($2000 - 2007$) and for H$\alpha$ delays of
$\tau (H\alpha) = 162^{+32}_{-15}$\,days ($1992 - 2000$) and
$\tau (H\alpha) = 174\pm16$\,days ($2000 - 2007$) were determined.
A comparable result was found by Shapovalova et al.\,(2010) who studied the
optical variations for 3C\,390.3 from 1995 to 2007. They report that the
variations of the broad H$\beta$ and H$\alpha$ emission-line flux are delayed
by $\tau (H\beta) = 96^{+28}_{-47}$\,days and
   $\tau (H\alpha) = 127\pm18$\,days,
both too long to be measurable from our data.
However, due to the lower sampling rate of the H$\alpha$ light curve the ICCF
analysis displays two possible peaks also at $\tau (H\alpha) \simeq 24$\,days
and $\tau (H\alpha) \simeq 151$\,days, respectively.

Those results are inconsistent with the delays which were reported by Dietrich
et al.\,(1998) using the data of the X-ray\,--\,UV\,--\,optical
monitoring campaign in 1994/95 (Leighly et al.\,1997; O'Brien et al.\,1998;
Dietrich et al.\,1998), i.e.,
$\tau (H\beta) = 23\pm4$\,days and $\tau (H\alpha) = 19\pm9$\,days
and also with the results of this study (Table 6).
However, the time delays which we determined for 3C\,390.3 in 1995 are
consistent with the delays we find for H$\alpha$ and H$\beta$ in this study.
In 1995 the strength of the optical continuum corrected for host-galaxy
contributions was F$_\lambda$(5100\AA )\,$=
1.16\times10^{-15}$ erg\,s$^{-1}$\,cm$^{-2}$\,\AA $^{-1}$.
During the 2005 monitoring campaign the continuum was about $\sim 6\times$
stronger (Table 5).
Using the radius\,--\,luminosity relation for AGN (Bentz et al.\,2009a) it can
be expected that the derived delays of the H$\alpha$ and H$\beta$
emission-lines should be about $\sim 2.5\times$ as long than those of 1995.
This is in good agreement with the delays which we have measured (Table 6).

To investigate the cause of the discrepancy between the results based on the
analysis of the variations over about 10 years compared with those covering
about three months up to one year, we re-analyzed the data published
by Sergeev et al.\,(2002,2011) and Shapovalova et al.\,(2010).
Using the data of the Sergeev et al. study,
we compiled H$\beta$ and F$_\lambda$(5100\AA ) continuum light curves which
cover about 15 years with 413 epochs for the continuum and 131 epochs for
H$\beta$. We applied the same ICCF analysis to these light curves as we did for
the measurements for this study.
We found $\tau (H\beta) = 81.6^{+16.4}_{-22.5}$\,days which is consistent with
the results of Sergeev et al. and due to the large uncertainties, within
1-$\sigma$ it is even in the range with the result of this study. Next, we
studied parts of the light curve
which covered approximately 1000 days to study the impact of the luminosity
state of 3C\,390.3 on the delay. We found delays of the broad H$\beta$
variations ranging from $\tau (H\beta) = 13^{+34}_{-30}$\,days to
             $\tau (H\beta) = 102^{+11}_{-16}$\,days with no clear relation
between the continuum state and the delay. However, the mean spacing,
especially for the H$\beta$ emission-line flux measurements, is only
$\sim20$\,days to $\sim160$\,days, i.e., probably not sufficient. Only for the
last three years of the light curve the temporal sampling is about
$\sim$$6$\,days for
the continuum and $\sim$$20$\,days for the H$\beta$ emission-line flux.
For this period we find a delay of $\tau (H\beta) = 102^{+6}_{-6}$\,days.
The H$\beta$ emission line flux measurements by Sergeev et al.\,(2011) and by
Shapovalova et al.\,(2010) do overlap with our monitoring campaign. Therefore,
we can compare those with our H$\beta$ emission line light curve (Fig.\,18).
It can be seen that the continuum light curve follows the variations we
measured while the coverage in H$\beta$ is not as high.

In the same way, we re-analyzed the continuum and H$\beta$ emission-line light
curves given by Shapovalova et al.\,(2010). For the entire data set which
covers about 12.5 years we find $\tau (H\beta) = 96.2^{+35.4}_{-35.2}$\,days,
consistent with the results of Sergeev et al.
Similar to the Sergeev et al. data the light curves were split up into
periods of about 1000 days duration with temporal sampling of about 40 days.
We found delays of the broad H$\beta$ variations
ranging from $\tau (H\beta) = 16^{+39}_{-41}$\,days to
             $\tau (H\beta) = 210^{+55}_{-140}$\,days with no clear relation
between the continuum state and the delay.

In a study on the reliability of cross-correlation function time delay
determinations Welsh (1999) has pointed out that variations on longer time
scales, e.g., on the dynamical time scale of the BLR which is of the order of
years, will shift the response time to longer delays.
Long term variations are different from direct reverberation signals which
measure the instantaneous response of the emission-line gas to continuum
variations, while long term variations trace a more gradual response to an
overall increase or decrease of the continuum strength.
To correct for this effect it is necessary to detrend light curves from those
gradual changes. To detrend the continuum and H$\beta$ emission-line
variations, we fit a low order polynomial to the light curves.
Next, we applied the analog time series analysis to the detrended light curves
of the Sergeev et al.\,(2002,2011) and Shapovalova et al.\,(2010) studies. We
derived time delays of the H$\beta$ variations of
$\tau (H\beta) = 90.4^{+8.9}_{-9.2}$\,days (Sergeev et al.) and
$\tau (H\beta) = 82.7^{+13.9}_{-12.9}$\,days (Shapovalova et al.).
Within the uncertainties (1-$\sigma$\,errors) these delays are consistent with
those obtained with the original light curves. However, the uncertainties of
the time delays using the detrented light curves are about a factor 2 to 3
smaller than those for the light curves including gradual long term variations.

Furthermore, the properties of continuum strength variations have a significant
effect on the time delay measured from cross-correlation functions. This issue
can be responsible for the different delays measured in our study and those
using variations of the continuum and the broad emission lines over more than
10 years, in particular, the auto-correlation function of the continuum,
ACF$_{cont}$.
It has been already noted by Sergeev et al.\,(2002,2011) that the width of the
ACF$_{cont}$ of the continuum light curve which is covering several years up to
more than a decade is much broader than the ACF$_{cont}$ of a shorter campaign
like the one in 1994/95 and that this will result in a longer time delay
(see also the Appendix for a more detailed discussion).

In addition, our campaign covered only a little more than 80 days and hence we
are not able to measure time delays of about 100 days and more.
We think that the different time delays are caused by the long time period of
about a decade to cover the variation of 3C\,390.3 and the wider temporal
sampling of the measurements.
Furthermore, the significantly different widths of the ACF$_{cont}$ and the
fact that in addition to reverberation signals, i.e., the direct response of
line emitting gas to continuum variations, also variations of the emission-line
flux are included. These are associated with changes of the physical conditions
and the distribution of the gas which happen on dynamical time scales and
which are uncorrelated with continuum variability also contributes {\bf to} the
different time delays.
Therefore, a long duration campaign for 3C\,390.3 with densely sampled
measurements will be necessary to find a definitive result.

\subsection{Black Hole Mass Estimates}
A wide range of mass estimates for the super-massive black hole of 3C\,390.3
have been reported, ranging from
$\sim 1.3\times10^8\,M_\odot$ up to $\sim 7\times10^9\,M_\odot$ using emission
line profile properties and estimates of the size of the BLR
(e.g., Barr et al.\,1980; Bentz et al.\,2009b; Clavel \& Wamsteker 1987;
       Gaskell 1996; Peterson et al.\,2004; Sergeev et al.\,2002,2011;
       Wamsteker et al.\,1997),
as well as using the Ca\,{\sc ii}\ triplet in the near infrared employing the
M\,--\,$\sigma_\ast$ relation yielding about M$_{bh}\simeq 4$ to $5\times$
$10^8\,M_\odot$ (Nelson et al.\,2004).
Most of these studies favor a black hole mass for 3C\,390.3 of the order of
5 to $10\times$ $10^8\,M_\odot$. Our measurement of the mass of the black hole
of 3C\,390.3 with
$M_{bh} = 0.86^{+0.19}_{-0.18}\,\times\,10^9\,M_\odot$
(based on the separation of the blue and red peak in the rms spectrum)
and
$M_{bh} = 1.26^{+0.21}_{-0.16}\,\times\,10^9\,M_\odot$
(using $\sigma_{line}$) is consistent with the black hole mass based on the
$M - \sigma_\ast $ relation.
Using the M-$\sigma_\ast$ relation from G\"{u}ltekin et al.\,(2009), we
calculated the stellar velocity dispersion $\sigma_\ast$ which is expected for
the host galaxy of 3C\,390.3 based on our estimated black hole mass. We find
$\sigma_\ast = 257^{+90}_{-70}$\,km\,s$^{-1}$ for 3C\,390.3 which is consistent
with $\sigma_\ast = 273\pm16 $\,km\,s$^{-1}$ as measured by
Nelson et al.\,(2004).
Furthermore, simple disk models which we applied to describe the overall
structure of the broad double-peaked hydrogen Balmer emission lines yield a
mass estimate of $M_{bh}\simeq 10^9\,M_\odot$.

An additional test for the reliability of the derived black hole mass for
3C\,390.3 is given by the comparison of our measured values for the size and
continuum luminosity of 3C\,390.3 with the expected values derived from the
radius\,--\,luminosity relation.
Guided by simple photoionization models, a relation between the continuum
luminosity of an AGN and the radius of the BLR is expected and
Kaspi et al.\,(2000) provided the first convincing evidence for such a
relation. Careful re-analysis and additional observations
(e.g., Peterson et al.\,2004; Bentz et al.\,2006b,2007a,2009b;
Denney et al.\,2006,2009a,2010; Grier et al.\,2008; Onken et al.\,2003)
have reduced the uncertainty of the slope of the relation. It turned out that
the correction for host galaxy contamination has a profound impact on the
R\,--\,L relation (Bentz et al.\,2006a,2009a). With a slope of
$\alpha =0.52\pm0.04$ (Bentz et al.\,2009a), we estimated the black hole mass
of 3C\,390.3.
For the continuum flux at $\lambda = 5100$\,\AA\ we used the average continuum
flux of the AGN continuum (Table 5), corrected for host galaxy contributions,
with
$\lambda\,L_\lambda(5100{\rm \AA}) = 2.28\times10^{44}$ erg\,s$^{-1}$
and the measured delay for the H$\beta$ emission line is
$\tau _{cent} \simeq 44$ days. Using the radius\,--\,luminosity relation as
given in Bentz et al.\,(2009a)

\begin{equation}
\log\,R_{BLR} = K + \alpha \,\log\,(\lambda\,F_\lambda (5100{\rm \AA}))
\end{equation}

\noindent
with K\,=\,$-21.3^{+2.9}_{-2.8}$ and $\alpha = 0.519^{+0.063}_{-0.066}$ the
H$\beta$ BLR radius amounts to $\tau = 52.7^{+2.9}_{-2.8}$ days,
which given the intrinsic scatter in the relationship, is consistent with the
measured $\tau _{cent}(H\beta) = 44.3^{+3.0}_{-3.3}$\,days or the
$\tau _{cent}(H\beta) = 47.9^{+2.4}_{-4.2}$\,days using SPEAR.

\section{Summary}
We present results of a ground-based monitoring campaign on the broad-line
radio galaxy 3C\,390.3.
Optical spectra and {\it g}-band imaging were obtained in late 2005 for three
months using the 2.4-m telescope at MDM Observatory.
Integrated emission-line flux variations were measured for the Balmer lines
H$\alpha$, H$\beta$, H$\gamma$, and for the helium line He\,{\sc ii} $\lambda 4686$,
as well as {\it g}-band fluxes and the optical AGN continuum at 5100\,\AA.
The {\it g}-band fluxes and the optical AGN continuum are varying
simultaneously within the uncertainties ($\tau _{cent} = -0.2\pm1.1$ days).
We measure time delays for the emission-line variations with respect to the
variable {\it g}-band continuum of
$\tau (H\alpha)    = 56.3^{+2.4}_{-6.6}$\,days,
$\tau (H\beta)     = 44.3^{+3.0}_{-3.3}$\,days,
$\tau (H\gamma)    = 58.1^{+4.3}_{-6.1}$\,days, and
$\tau ($He\,{\sc ii} \,4686$) = 22.3^{+6.5}_{-3.8}$\,days.
The blue and red peak in the double peaked line profiles, as well as the
blue and red outer profile wings vary simultaneously within $\pm3$ days. This
provides strong support for gravitationally bound orbital motion for the
dominant part of the line emitting gas.
Using the separation of the blue and red peak in the broad double-peaked
profiles in the rms spectra of the Balmer emission lines
and the corresponding time delays we determine a virial black hole mass of
M$_{bh}^{vir} = 1.77^{+0.29}_{-0.31}\,\times\,10^8 M_\odot$ for the black hole
of 3C\,390.3. Using the inclination angle $i = 27^o\pm2^o$ of the line emitting
region the intrinsic velocity, $v_{intr}$, can be recovered from the measured
$v_{obs} = v_{intr}\sin\,i$. This results in a black hole mass of
M$_{bh} = (0.86^{+0.19}_{-0.18})\,\times10^9 M_\odot$ for 3C\,390.3
and M$_{bh} = (1.26^{+0.21}_{-0.16})\,\times10^9 M_\odot$ based on
$\sigma_{line}$ of the rms-spectrum.
This mass estimate is consistent with the mass indicated by simple accretion
disk models to describe the observed double-peaked profiles, as well as with
black hole masses derived from studies on the stellar dynamics of 3C\,390.3.
Furthermore, the mean continuum luminosity and the measured time delay for the
broad emission-line flux variations of H$\beta$ is consistent with the most
recent AGN radius\,--\,luminosity relation. Thus 3C\,390.3 as a radio-loud AGN
with a low Eddington ratio of only L$_{edd}$/L$_{bol}$ = 0.02 follows the same
AGN radius\,--\,luminosity relation as radio-quiet AGN.

\begin{acknowledgements}
      We thank J.\,Halpern, S.\,Tyagi, and all the observers at MDM Observatory
      who conducted the observations in Fall 2005, for the first time in
      service mode at MDM.
      We also acknowledge financial support from NSF grants AST-0604066 and
      AST-1008882 to OSU.
\end{acknowledgements}


text:
King and Emperor by Harry Harrison. Chapter 31, 32, 33, 34
"Move," he shouted. "Or I'll have you back in a collar like you were before." His old comrade spat blood, pulled loose another tooth, gaped at it incredulously. Turned to obey the order.
"All masters are the same in the end," remarked one of his mates, hacking at the ropes to make the dart-thrower at least temporarily useless. Cwicca did not reply. In the darkness Tolman and the three boys with him hesitated over their bundles of cloth and canes and rope. Light enough for boys to carry, but a burden just the same. Cwicca seized two bundles from them, slung one over each shoulder.
"I'll carry thothe," he said, lisping badly. Tolman eyed the tears rolling down his face, said nothing.
Hours later the weary column struggled up the aqueduct to the walls of the Eternal City itself. They had run through the night like travelers chased by wolves. Their long thin column had been attacked again and again by men coming in from either side, men who had ridden ahead of them and then swerved in to a line which could not be missed. The crossbows had taken heavy toll of the attackers, but several times the column had been cut in two and there had been fierce work with blades in the dark before it could be reunited. Every time men had been left behind, lost or crippled or unconscious. Their comrades threw the dead into the running water, and as time went on threw in those they were not sure of as well. Few of the wounded were being carried now. In the hot night death by drowning seemed a delight to the sweating and exhausted men who were left. Shef was aware several times of Hund raging and struggling in the darkness as his charges were abandoned or given the warrior's death. He had no time or strength to intervene.
The light was beginning to show in the east as Shef led the rearguard up the final gentle slope to the lodgement that the advance guard had made on the walls of Rome itself, on the very slopes of the Aventine Hill. Light, he thought. And shelter. A chance to see what was happening. To seize the initiative, control the battle instead of reacting to it. He yearned for time more than for food or rest or water. He needed it as an outmatched wrestler needs a foothold.
As he reached the wall, saw the remains of his command spread out along the inner, undefended battlements, he turned and looked out, stepped on to the parapet to feel the dawn wind on his sweat-soaked tunic.
Two hundred yards away Erkenbert said with vindictive relish to his catapult captain, "Launch." The short arm dropped, the long arm shot up, the sling dragged along the ground and then whipped round in its vicious swing. Its load shot into the sky, not neatly but in a confusion of twisted limbs.
Shef, on the parapet, saw nothing except a momentary glimpse of movement coming towards him. He threw up an arm, felt a body-shaking thud, found himself sprawled on the ground, a weight on top of him. He tried to thrust it off, found his hands caught in something tough and sticky, clawed at it in desperation. It was off him and men were lifting him to his feet. He realized his hands were caught in human entrails, from a burst-open body at his feet. It was Trimma the cross-bowman, his dead face set in a rictus of torment.
"They're shooting our own dead at us," explained Brand. "They must have known where we were headed and brought the big catapults round to meet us. These are men who were killed in the night."
Ahead of us again, thought Shef. Ahead of us again. I do not know what to do next.
"They're all round us," Brand added. "I doubt there's more than half of us left."
"The worship of Loki has brought us little good, then," said Thorvin. His tone was bitter, his white clothing torn and blood-stained. He had fought with his hammer in the night. He had not been able to save Skaldfinn, cut down by the aqueduct. Solomon the Jew had vanished, no-one knew how. Of Shef's immediate council only six remained: he and Thorvin, Brand and Hagbarth. Hund was there, his face cast down. Svandis too. He should have given her a thought at least during the night, Shef reflected, but he had not. The blood of Ragnar could usually look after itself. But she had within her now the blood of himself and of Rig. Why had he not stayed by her? He had had other duties.
Page: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
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redpajama_set_name: RedPajamaCommonCrawl


Anna Norton's life with diabetes began the summer between high school graduation and college.
Norton, who lived in south Florida at the time, was working as a camp counselor, drinking lots of water and visiting the bathroom, as you'd expect. She also was losing weight – 30 pounds in less than three months. And after a favorite dinner with her family at home, she became very sick.
After trips to the doctor and the emergency room, Norton finally got her diagnosis on a summer day in 1993: Type 1 diabetes. About 5 percent to 10 percent of people with diabetes have this form. Scientists don't know what causes the autoimmune disease, but they think genetic and environmental factors, even viruses, could be involved.
And that journey to understood the diagnosis and figure out how she could live with it brought her to Diabetes Sisters, a Durham-based nonprofit that has followers from around the world. It aims to connect women with diabetes – either Type 1 or Type 2 – so they can share information, seek advice and find support.
Norton's understanding of the disease and acceptance of it took some wrong turns. She left the hospital in 1993 ill-prepared for what lay ahead.
"One doctor said, 'I just want to let you know, you'll never have kids,'" Norton remembers.
She made it through college, but was in a funk by the time she got to graduate school. For 18 months, she didn't take her insulin shots regularly and landed in the hospital. There, a doctor told her she had a decision to make – whether she wanted to live or die.
Norton got back on track. She's started using an insulin pump and now also uses a continuous glucose monitor.
And in 2007, she and her husband welcome their son, now a healthy, happy preschooler. Norton enjoyed a complication-free pregnancy.
Norton hooked up with Diabetes Sisters in 2011 after seeing a pamphlet for the group at her doctor's office a year before. She attended the group's conference and never looked back. Last year, Brandi Barnes, another local mom and Diabetes Sisters founder, who I featured last year, offered her the job of operations manager. She took it.
Diabetes Sisters offers online forums, regular meet-ups and more across the country. Norton finds both support and an opportunity to help other women with diabetes.
"It's nice to be able to ask, but it's really nice to be able to answer," she said.
Now, the group is gearing up for its fourth annual conference at the downtown Raleigh Sheraton from May 3 to May 5. The weekend includes a variety of workshops and discussions about living with diabetes – everything from food and exercise tips to emotional issues to a discussion about eating disorders and diabetes. There's also plenty of time for women to socialize.
In parallel to the conference, there are programs for husbands, boyfriends and partners of women with diabetes where they talk about marriage and relationships, how to support their spouses and other topics.
As part of the conference, Diabetes Sisters will host the 2013 orange:will Diabetes Awareness Walk on May 4. Wear orange for the one-mile walk through downtown Raleigh, which will raise money for Diabetes programs and services.
Watch my video interview to hear more from Norton.
"Life is better," she said.
Go Ask Mom features local moms every Monday.
This entry was posted in Diabetes and tagged diabetes, Diabetes Sisters, Go Ask Mom, insulin, life by david. Bookmark the permalink.


A small flying gurnard (Dactylopterus volitans). We figure this was a younger one due to its smaller "wings". It also jumped and started every time the strobe went off. This one showed up in the beginning and again at the end of our dive.
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License. Please attribute Kristaps, the photographer, with a link to kristaps.bsd.lv/photo0013.html.