# Exploring possible relations between optical variability time scales and
broad emission line shapes in AGN

E. Bon 1,∗, P. Jovanović1,∗, P. Marziani 2, N. Bon 1, and A. Otašević

###### Abstract

Here we investigate the connection of broad emission line shapes and continuum
light curve variability time scales of type-1 Active Galactic Nuclei (AGN). We
developed a new model to describe optical broad emission lines as an accretion
disk model of a line profile with additional ring emission. We connect ring
radii with orbital time scales derived from optical light curves, and using
Kepler’s third law, we calculate mass of central supermassive black hole
(SMBH). The obtained results for central black hole masses are in a good
agreement with other methods. This indicates that the variability time scales
of AGN may not be stochastic, but rather connected to the orbital time scales
which depend on the central SMBH mass.

## 1

##  2 Keywords:

galaxies:active-galaxies, quasar:supermassive black holes, quasar:emission
lines, line:profiles

##  3 Introduction

Type-1 Active Galactic Nuclei (AGN) are very powerful and variable emitters.
The continuum emission in radio-quiet AGN is assumed to originate mainly from
an accretion disk (AD) around a central supermassive black hole (SMBH)
(Lynden-Bell, 1969; Shakura and Sunyaev, 1973). There is consensus that the
accretion disk can be represented as virialized (rotating) gas in a flattened
distribution following a Keplerian velocity field.

The optical broad emission lines (BELs) are assumed to be produced with
photoionization processes (Netzer, 2013), as they respond to the variations of
UV continuum. The accretion disk itself may be a low-ionization line emitter
(see, e. g. Chen and Halpern, 1989; Chen et al., 1989; Eracleous and Halpern,
1994; Popović et al., 2004; Bon et al., 2006; Gavrilović et al., 2007; Bon,
2008; Bon et al., 2009a, b, 2015), if part of the continuum radiation is
scattered toward it. The optical broad line light curves (like for e. g.
H$\alpha$) are highly correlated with the optical continuum light curves (e.
g., Kaspi et al., 2000). The time lags between correlated patterns in the
continuum and H$\alpha$ flux are of the order of days, up to months, defining
the size of broad line region (BLR). Reverberation mapping campaigns are based
on this fact, and they measure time lags of correlated light curves in order
to determine the sizes of reverberating region (which are after used for
determination of central BH masses) in AGN (see e. g. Peterson et al., 2002;
Denney et al., 2009; Kaspi et al., 2000; Peterson, 1997). The correlation of
light curves might indicate that the signature of the main driver of the
variability could be detected in the shape of the broad emission line
profiles. This could give us the velocity resolved information about processes
that drive the variability.

The shape of Balmer emission lines, particularly H$\alpha$ and H$\beta$ line
profile, in many AGN could be described as similar to the shape of an AD line
profile expected to originate from flattened distribution of rotating emitting
gas. Characteristic double peaked very broad profile, are usually seen in
simulated emission line profiles (see for e. g. Chen and Halpern, 1989; Chen
et al., 1989; Čadež et al., 1998; Eracleous and Halpern, 1994; Newman et al.,
1997; Popović et al., 2003, 2004; Bon et al., 2006; Bon, 2008; Bon et al.,
2009b, a; Jovanović et al., 2010) but are observed only in one percent of AGN
(Eracleous and Halpern, 1994; Strateva et al., 2003; Netzer, 2013). In
typical, single peaked BEL profiles, the AD contributions could be blended by
surrounding isotropic velocity component in the BLR (Popović et al., 2004; Bon
et al., 2006; Bon, 2008; Bon et al., 2009b; Gavrilović et al., 2007; Collin et
al., 2006; Popović et al., 2003). In some cases, broad H$\alpha$ and H$\beta$
line profiles show a red side more broadened and extended further into the red
part of the spectrum, that could be associated with gravitational redshift
(see, e. g., Bon et al., 2015, and references therein). In case the blue side
of a line is more extended, the contribution is usually assumed to be from the
winds or outflows (see, Czerny, 2006; Collin et al., 2006; Marziani et al.,
1996; Sulentic et al., 2007).

Even though long term monitoring campaigns of AGN may still not be long enough
to search for periodic variability (Bon et al., 2017), there are some highly
monitored cases for which some claims of detecting significant periodicity
have been made (see for example Bon et al., 2012; Graham et al., 2015a, b;
Charisi et al., 2016; Bon et al., 2016, 2017; Bhatta et al., 2016). Currently,
there are some ongoing campaigns of extensive monitoring programs (see e. g.
Gezari et al., 2007; Sergeev et al., 2007; Peterson et al., 2002; Ilić et al.,
2017) that may provide valuable light curves for the future variability
investigations.

Here we explore a possibility that ripples in the observed broad optical
emission line profiles may be in connection with variability time scales
observed in optical continuum light curves. We present a case study of Arp
102B, using spectra and light curves from Shapovalova et al. (2013). Our
hypothesis is that the variability patterns in the light curves may be induced
by the orbiting of perturbers ”perturbation” (a hot spot, a spiral arm, a
compact body such as a stellar mass object or even up to intermediate mass
black hole) within the accretion disk (see more i, for e. g. Chakrabarti and
Wiita, 1994; Lin and Papaloizou, 1996; Newman et al., 1997; Flohic and
Eracleous, 2008; Gezari et al., 2007; Jovanović et al., 2010; McKernan et al.,
2012). Using the AD model with additional emitting rings (separated with
gaps), developed specially for this purpose, we match the synthetic broad
emission line profiles to the observed H$\alpha$ line, in order to measure the
ring radii. We connect variability time scales, with radii, and calculate the
central BH mass.

The paper is organized as follows: first, we present the method (section 4) of
measuring the radii that could be paired with variability time scales from
light curves. For that purpose we developed a model of an AD emission with
additional enhanced thin rings (section 4.1). We used data (spectra and light
curves) available in Shapovalova et al. (2013). We match the AD model to the
observed H$\alpha$ broad emission line and measure the ring radii that we
connect to optical variability time scales. We analyze optical light curves,
find variability time scales that we match with measure ring radii, and
calculate the mass of the SMBH as a test of our hypothesis (section 5). We
discuss possible mechanisms in section 6. In the last section 7, we point out
the main conclusions of our investigation.

##  4 Method

Light curves of an optical continuum and broad emission line flux are highly
correlated (Kaspi et al., 2000). This may indicate the same origin of their
variability source. Therefore, one could expect that the source of variability
could leave a trace in the shapes of their broad line profile shape. Analysis
of variation time scales may give us valuable information about why they vary
the way they do, while the line profiles could provide us with the information
about the kinematic parameters of the variability drive (like the radii where
the source of variation is located).

In order to investigate the variability time scales of optical continuum light
curves, we use standard methods like Lomb-Scargle Lomb (1976); Scargle (1982),
and sine function fitting, that we use here to determine variability time
scales. Here we assume that the variability time scales corresponds to the
orbital time scales within the region of AD where the optical light could be
originating from (see e. g., Bon et al., 2012, 2016). Ripples in the broad
emission line profiles could be produced by the effects of the same phenomena
that drives the variability Eracleous and Halpern (1994); McKernan et al.
(2013). If we detect them, we would then be able to determine some dynamical
properties (see for e. g. Newman et al., 1997; Gezari et al., 2007). In case
we could identify more then one variability time scale period in the light
curves that could be linked to the radius of an emitting ring in the broad
emission line profile, then for each ring-radius pair we should expect to
obtain the same mass (or at least very close value) of the central SMBH using
Kepler’s laws.

In order to test these assumptions, as a first step we model synthetic line
emission of an orbiting gas in the flat, disk like gas distribution, assuming
that photo ionization process produces the emission line from that region,
that we could approximate with the accretion disk emission model (Chen and
Halpern, 1989; Chen et al., 1989; Čadež et al., 1998; Eracleous and Halpern,
1994; Jovanović and Popović, 2008; Jovanović et al., 2010; Bon et al., 2015).

By matching the AD model to the Hα broad emission line profile, we determine
the inclination, inner and outer radii and additional ring radii. The inner
radius is defined by matching the far red and blue wings of the observed line
profile to the red wing of AD model line shape. The red wing part is most
sensitive to the and gravitational redshift effect (see, e. g. Bon et al.,
2015), and therefore the extension of the red side of the line wing determines
how close to the BH the gas is emitting the optical Balmer lines. We note that
we determine the inner radius of an AD of the H$\alpha$ broad line from the
fit of the model, and that the inner radius in gravitational units is usually
$\gtrsim$ 100, much larger than the inner radius derived from X-ray lines
(like Fe Kα), usually close to the innermost stable circular orbit, 1 to 6
gravitational radii (for AD size of the optical emission lines, see for e. g.
Chen and Halpern, 1989; Chen et al., 1989; Eracleous and Halpern, 1994;
Popović et al., 2004; Bon et al., 2006; Gavrilović et al., 2007; Bon, 2008;
Bon et al., 2009a, b, 2015). The part of the disk that contributes to the
thermal continuum emission is the one of highest temperature, also close to
the the innermost stable circular orbit (Lynden-Bell, 1969; Shakura and
Sunyaev, 1973). This region is expected to be much closer to the black hole
than the AD region suitable for the optical emission line emission. From the
fit of the model to the observed broad line we determine inner and outer
radius of the AD and each ring as well as the inclination and emissivity law
that is common parameter for the complete model.

Simulated profiles of AD emission usually have characteristic two peaks in the
core of the line, are broadened due to virial motion and made asymmetric by
relativistic effects. The two peaks are usually blended by the isotropic
emission component in the core of the line profile, originated further away
from the AD, which is observed in majority of AGN spectra (Bon et al., 2006;
Bon, 2008; Bon et al., 2009b; Popović et al., 2003, 2004; Popovic et al.,
2008). Only in a very small number (less then 1%) of objects the two peaks are
clearly recognized (see e. g. Strateva et al., 2003)).

Small bump-like features can be found on the BEL profiles. They cannot be
immediately modeled by smooth AD profiles.

###  4.1 Model of AD with additional ring emission or AD with ring gaps

The AD model is an idealization of emission with assumption of an homogeneous
AD. This may not be the case, and therefore the AD profile may not sufficient
to describe all features in observed profiles like e. g., small bumps on the
wings which are often present.

Assuming that the time scale of perturbed disk (cooling time, shock wave
progression, or anything that produced additional emission from that ring) is
significantly longer then the orbital time scale, then we could approximate
that the time scale of variations measured in optical light curves correspond
to the orbiting of some features within the AD at radii that could be
associated to narrow rings that we located in AD by matching the observed
emission lines with synthetic modeled profiles. Their radii are measured in
units of gravitational radii Rg, since from the AD model we cannot obtain the
information about the central mass. By connecting each variability time scale
to some radii in the AD, with an assumption that the shorter variability time
scale corresponds to a closer ring, while the outer radii correspond to a
longer variability time scale, we could be able to calculate the mass of the
central SMBH 111This is similar as in the case of planetary system where all
orbiting objects radii and periods correspond to the same mass of the central
body using the Kepler’s third law for a circular orbit:

$P=2\pi\sqrt{r^{3}\over{GM}}={{2\pi GM\xi^{3/2}}\over{c^{3}}},$ (1)

where $r=\xi(r_{g})$ is the ring radius in gravitational radii and $P$ is the
circular orbital period of the orbiting region at such radii (as prposed in
Newman et al., 1997; Gezari et al., 2007). We note here that regardless of the
formula, our method is different then the method of Newman et al. (1997).
These authors used monitoring spectra to determine the radius of a hot spot,
which they then connected to the orbiting period. Here we use single epoch
spectra and variability time scales measured from photometric data.

We use different AD model than in previous papers (Chen and Halpern, 1989;
Chen et al., 1989; Gezari et al., 2007; Newman et al., 1997; Antonucci et al.,
1996), even though we obtain similar values of parameters for the inclinations
and the inner and outer radius. Here we use the relativistic ray tracing AD
model222We tested several different AD models Čadež et al. (1998); Jovanović
and Popović (2008); Fanton et al. (1997); Jovanović (2012); Bon et al. (2015)
for a line fit, and find that obtained inclinations were practically the same
regardless of the model used and also if we adopt more complex model, assuming
the additional rings with the same AD parameters (inclination and emissivity
law). We propose that the origin of the variability patterns, could be traced
to the ripples in the shape of broad line profiles. Making a connection of
variability time scales and radii, Eq. 1 can be used to determine dynamical
properties of AGN.

We construct our model assuming the emission of an AD and each ring
contributions to the line profiles with the same inclination and emissivity
law as in the parent AD, which is preserved in ring models. The code includes
both special relativistic and general relativistic effects on radiation from
the accretion disk around SMBH (see e.g. Jovanović, 2012). This AD model is
based on ray-tracing method in the Kerr metric (Fanton et al., 1997; Čadež et
al., 1998), for different values of inner and outer radii and inclinations of
rings in AD. The emissivity index was kept to be close as possible to the
value q=-2, assuming the emissivity law to be $\sim r^{q}$, as expected for
the case of photo-ionization mechanism. The model is then constructed using a
previous match of the AD profile to the emission line, as a starting point.
The scaled contributions of the ring profiles are added to the AD profile
until bumpy features in observed spectra are described with the synthetic
spectrum. Beside the fact that the shape of the line is fitted more realistic
then with a simple AD model, we are also obtaining a valuable information
about the radii in the disk plane where the emission is emitted from.

We considered our model as analogy to AD in which the emission is not
continuous from $R_{min}$ to $R_{max}$, but instead is restricted to emission
emission annuli. The physical justification of disk gaps can reside on the
removal of the gas disk in systems in which the the emission is not
contributing to the emission line shape due to obscuration by dust in the
outscirt of BLR Bon et al. (2016) or by voids produced due to accreting
secondary object within the AD plane Lin and Papaloizou (1996); Lin (1997), or
in case where gas was originally counterrotating with respect to the black
hole spin (Vorobyov et al. 2016), or by an accreting object in the disk plane
(Artymovicz and Lin 1993). In this case, the disk profile is modeled by the
addition of several emission annuli (assuming the same AD model and one
inclination value). The analysis of the line profile is otherwise analogous to
the excess ring emission model.

##  5 Results

In order to test this our model interpretation of the BEL profiles, we
performed a case study of Arp 102B because it is well known for its broad
emission lines with double peaked shape that was already proposed to
correspond to the AD emission profile (Chen and Halpern, 1989; Chen et al.,
1989; Eracleous and Halpern, 1994; Gezari et al., 2007; Jovanović et al.,
2010; Newman et al., 1997; Popović et al., 2014; Sergeev et al., 2000;
Antonucci et al., 1996; Sulentic et al., 1990).

Using the line profile matching to the model, we measure the ring radii that
we connect to the variability time scales.

Assuming that the orbital time scale is the only match to time scale of
variability patterns seen in these light curves, we combine measured radii
$\xi$ and variability scale periods, and derive mass assuming circular
Keplerian orbit of this variable region positioned within the AD.333It is
important to stress that emission lines do respond to continuum changes on a
timescale that is $\tau\ll P$ (months vs. 10 years), but this should not
invalidate our argument right because the reverberation response $\tau$ is
much smaller than $P$, which is the orbital period at radius $\xi$.

We measured $\xi$ radii with an AD model in units of gravitational radii (Rg)
from the broad emission line profiles. If two or more significant periods were
detected, assuming a low cut taken to be at 400 days period (in order to avoid
effects of Earth’s orbital period of 1 year), then we try to pair the to the
parts of an AD which could be perturbed, like inner and outer radius of a ring
or a main part of AD, where the interaction with different state medium could
be expected.444We note that the expected orbital periods in optical part of
the AD for typical AGN of M $\sim 10^{8}$ M⊙ should be about 1 year (see for
e. g. Gaskell, 2008), but this should not be a problem since also longer
periods are detected. We test the assumption by calculating the mass of the
central BH following Eq. 1, with expectation that the obtained results for
masses, for each pair of variability time scale and the ring radius, should be
equal, or at least to be of similar values.

The example of the model matched to the observed spectrum of the object Arp
102B is presented in Fig. 2. The inclination is 32 degrees, and the AD is
truncated in the following rings: 370-1050 Rg, 1430-1540 Rg and 3500-3800 Rg,
with the emissivity parameter q=-2.1 over the whole model. We note that the
result is very similar to other fits of this object Chen and Halpern (1989);
Chen et al. (1989); Newman et al. (1997), who obtained the same inclination
while the complete disk was assumed to correspond to main part of AD in our
model, with Rinn = 350 Rg, and Rout = 1000 Rg555We note that at about the same
radius was obtained as outer radius of AD in previous disk models Chen and
Halpern (1989); Chen et al. (1989); Newman et al. (1997). The measurement of
variability time scales of light curves is shown in the Fig. 3. We find the
longer time scale to be about 14 years period (intrinsically 5250 days, after
correction for the systematic redshift), while the shorter time scale is taken
from earlier variability analysis Newman et al. (1997); Sergeev et al. (2000);
Shapovalova et al. (2013), where the variability time scale was found to be of
about 700 days (in the interval 650-750 days, here taken as 680 after scaling
for the redshift).

We assume that the variability is produced sharp edges of gaps and emitting
rings. By matching the inner radius of AD to the corresponding variability
time scale (370 Rg with 680 days), and 1500 Rg with 5255 days variability time
scale), we obtain the mass of about 2.7 $\cdot 10^{8}$ M$\odot$ (as an average
of these two values: 2.68 $\cdot 10^{8}$ and 2.71 $\cdot 10^{8}$ M$\odot$).
This value is very close to the value of with 2.1 $\cdot 10^{8}$ M$\odot$ in
Newman et al. (1997, obtained from the orbiting hotspot assumption) and not so
different from 3.5 $\cdot 10^{8}$ M$\odot$ suggested in Sergeev et al. (2000,
obtained with the model of thousands randum orbiting clouds, mached to the
radial velocity maps of broad line variability), and about 2 times higher then
the mass value of 1.1 $\cdot 10^{8}$ M$\odot$ as suggested in Shapovalova et
al. (2013).

The virial product $r\delta{v_{r}}^{2}/G$ can then be obtained from the 20 day
lag of line flux to continuum Shapovalova et al. (2013), and following the
formula form Collin et al. (2006) for radial velocity dispersion in case of
rectangular shape666line $FWHM/\sigma=2\times\sqrt{3}=3.46$ line profile
$\delta{v_{r}}$ = 14500 / 3.46 $\approx$ 4190 km s-1. The virial factor $f$
can then be estimated by computing $r\delta{v_{r}}^{2}/G/M_{BH,P}$ = $1/f$,
where $M_{BH,P}$ is the black hole mass computed from the $P$ following Eq. 1.
Using these values we derive $1/f$ = $7.36\cdot 10^{7}/(2.7\cdot
10^{8})\approx 0.287.$. The $1/f$ should be equal to ratio of virial product
and the mass777$f=((\sin(i))^{2}+(H/R)^{2})^{-1}$ as suggested in Netzer
(2013), were H/R represents the contribution of isotropic velocity component
as a ratio between the width of a disk and the radius of AD. Assuming H/R
$\approx$ 0 the formula transforms into $f=(sin(i))^{-2}$. obtained from the
period by definition, and $f$ depends on inclination as
$f\approx(sin(i))^{-2}$, resulting the inclination of 32∘, which is consistent
with the value from the AD model fitted to the H$\alpha$ broad emission line
(with our model and earlier fits as well). Therefore, not only that the model
gives the consistent mass with the three different period-radii pairs, but
also the retrieved inclination from the virial product gives a consistent
value of inclination as the AD model fit to the H$\alpha$ broad emission line.

Admittedly, our model follow from a very strong assumption: the use of
variability time scale $P$ (derived from the continuum variation) for
estimating the black hole mass and the use of $\xi$ derived from the profile
ring should be consistent. The assumption may not be correct in principle,
since the $P$ obtained from the continuum may not refer to the same $\xi$ of
the profile rings. It requires in-situ emission at the $\xi$ deduced from the
ring.

##  6 Possible interpretations

Here we do not consider any details about what produces the hot ring regions
or the dips in the AD, and we are fully aware that the measured periods are
significant above the white noise levels, but may not appear significant
compared to the red noise AR curves (Vaughan and Uttley, 2006; Vaughan et al.,
2016). We were mainly interested in measuring time scales of orbital periods
assuming that the variability patterns Marziani et al. (2017a, b) in the light
curves could be induced by the orbital time scales. Some interpretations of
possible periodicities are discussed in many works (Bon et al., 2016; Charisi
et al., 2016; Chakrabarti and Wiita, 1994; Eracleous and Halpern, 1994; Graham
et al., 2015b; Gezari et al., 2007; Graham et al., 2015a; Liu et al., 2016; Li
et al., 2016; Newman et al., 1997; Bon et al., 2017; Popović, 2012). Assuming
circular orbits in the disk as we did here, we suggest that possible source of
optical variability should be located in the AD, amplifying emission at that
radius. We are aware that at such radii, the standard models of thermal
emission of AD (Shakura and Sunyaev, 1973) shows that the temperature of the
disk is relatively low, under 1000 K (according to the standard disk model,
Shakura and Sunyaev, 1973), which is not sufficient enough for the photo
ionization mechanism to produce optical broad emission lines, or to
significantly contribute to the optical continuum flux, without additional
emission mechanism, like shocks (Chakrabarti and Wiita, 1994; Eracleous and
Halpern, 1994; Gezari et al., 2007), hot spot Jovanović et al. (2010); Newman
et al. (1997); Flohic and Eracleous (2008), secondary orbiting object on a
circular orbit around the central SMBH with additional accretion mechanism
that is sufficient to produce significant contribution to the continuum and
the line emission (see e. g. McKernan et al., 2014; Lin and Papaloizou, 1996;
Lin, 1997, where they show a fast forming of intermediate mass BH’s in AD with
circular orbits arround the cetral SMBH)). It is expected that in such cases
the voids or gaps would be formed (see, for e. g., McKernan et al., 2012,
2013, 2014) in the AD (similar to the planet formation in the stellar disks),
with piling up of matter at the outer border of the gap ring (see, McKernan et
al., 2013, and the references therein), that may represent the region that
could be associated with the ring emission that we modeled here.

##  7 Conclusions

We simulated an AD emission profiles with additional ring regions and compared
them with the observed profiles of the broad H$\alpha$ emission lines. We
measured variability time scales from available optical light curves. We pair
each ring profile with the variability time scale. Using Kepler’s third law,
we then calculate central SMBH masses.

Our results show that:

1) The model of an AD with additional emitting rings or by a sequence of
emission annuli separated by gaps could well describe the observed H$\alpha$
emission line profiles in the case of Arp 102B.

2) Masses calculated from each pair of variability time scale and narrow ring
with enhanced emission, result with very similar values providing support for
the model and initial hypothesis, indicating that the features fitted in the
line profiles are probably emitted in an AD (virial velocity field).

3) We also test our model prediction from the fact that the virial factor
depends on the inclination. Since, from the ratio of VP and the mass obtained
with our model using Keplerian velocity, we obtain practically identical value
of inclination as from the AD fit to the line profile. Therefore this gives
another justification of our model.

This result may indicate that the variability time scales of AGN may be
connected to the orbiting time scales which depend on the central SMBH mass.

In near future, we plan to extend the sample (Bon et al. 2018, in
preparation), selecting more AGN with long term monitoring data.

## Conflict of Interest Statement

The authors declare that the research was conducted in the absence of any
commercial or financial relationships that could be construed as a potential
conflict of interest.

## Author Contributions

EB is responsible for developing the idea and writing the text of the
manuscript. PJ developed the code for the model. EB, NB, PJ, PM and OA worked
on analyses and discussions

## Funding

This research is part of projects 176003 “Gravitation and the large scale
structure of the Universe” and 176001 “Astrophysical spectroscopy of
extragalactic objects” supported by the Ministry of Education and Science of
the Republic of Serbia.

## Acknowledgments

This research is part of projects 176003 “Gravitation and the large scale
structure of the Universe” and 176001 “Astrophysical spectroscopy of
extragalactic objects” supported by the Ministry of Education and Science of
the Republic of Serbia.

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## Figure captions

Figure 1: An examples of AD + 2 outer rings (left panel) with corresponding
shape of broad line profile, matched to H$\alpha$ line of Arp 102B in 2.
Figure 2: An example of AD + rings model matching the observed broad
H${\alpha}$ emission line profiles. Here is presented the case of Arp 102B
Figure 3: Long term variability analysis of Arp 102B light curve after trend
removal correction fitted with the sine function with the period of about 14
years.