The Supermassive Black Hole in the Gamma-ray Loud Blazar PKS 1510$-$089
G. Z. Xie \inst{1,2}
Z. J. Jiang \inst{2}
D. C. Mei \inst{2}
This paper has been withdrawn by the author(s), due crucial errors in 'Introduction' and "Discussion and Conclusion". We present the optical light curve for the $\gamma$-ray blazar PKS 1510$-$089 with a significant variability of 2.0 mag within about 41 minutes in the R band which is the most violently rapid variability detected in our optical monitoring campaign operating since 1982. In the framework of the relativistic beaming model, the central supermassive black hole mass of PKS 1510$-$089 is of $(1.16-1.98)\times10^8M_\odot$. This is larger than some previous estimates for the central mass in blazars that have been based on models for nonthermal emission, but is consistent with the estimated result of the $M_\bullet-\sigma_\star$ correlation. Some other physical parameters, including the emission region size, Doppler factor $\delta$, the efficiency $\eta$ for conversion of accreted matter into energy and luminosity are calculated. The value of $\eta$ = 62.2 strongly implies that the relativistic beaming is responsible for the rapid variability of the $\gamma$-ray loud blazar PKS 1510$-$089. \keywords{galaxies: active --- galaxies: fundamental parameters --- quasars: individual (PKS 1510$-$089)---radiation mechanisms: non-thermal }
astro-ph0205482.tex
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\begin{document}
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   \title{The Supermassive Black Hole in the Gamma-ray Loud Blazar PKS 1510$-$089}

%   \subtitle{}
   \author{B. Z. Dai
          \inst{1,2}\thanks{email:bzdai@public.km.yn.cn}
          \and
          G. Z. Xie
          \inst{1,2}
          \and
          Z. J. Jiang
          \inst{2}
          \and
          D. C. Mei
          \inst{2}
          }

   \offprints{B. Z. Dai}

   \institute{Department of Physics, Yunnan University, Kunming 650091, PR China
            \and
              Yunnan Astronomical Observatory, National Astronomical Observatories, The Chinese Academy of
              Science, P.O. Box 110, Kunming 650011, PR China
             }

   \date{Received: 5 Feburary 2002; accepted }
%%%%%%%%%%%%%%
   \authorrunning{Dai et al.}
   \titlerunning{The Supermassive Black Hole in the Gamma-ray Loud Blazar}
%%%%%%%%%%%%%%

   \abstract{
   This paper has been withdrawn by the author(s),
due crucial errors in 'Introduction' and "Discussion and
Conclusion". We present the optical light curve for the
$\gamma$-ray blazar PKS 1510$-$089 with a significant variability
of 2.0 mag within about 41 minutes in the R band which is the most
violently rapid variability detected in our optical monitoring
campaign operating since 1982. In the framework of the
relativistic beaming model, the central supermassive black hole
mass of PKS 1510$-$089 is of $(1.16-1.98)\times10^8M_\odot$. This
is larger than some previous estimates for the central mass in
blazars that have been based on models for nonthermal emission,
but is consistent with the estimated result of the
$M_\bullet-\sigma_\star$ correlation. Some other physical
parameters, including the emission region size, Doppler factor
$\delta$, the efficiency $\eta$ for conversion of accreted matter
into energy and luminosity are calculated. The value of $\eta$ =
62.2 strongly implies that the relativistic beaming is responsible
for the rapid variability of the $\gamma$-ray loud blazar PKS
1510$-$089.
   \keywords{galaxies: active --- galaxies: fundamental parameters
--- quasars: individual (PKS 1510$-$089)---radiation mechanisms: non-thermal
               }
   }

   \maketitle
%
%________________________________________________________________

\section{Introduction}
One of the most important quantities in theoretical models of
active galactic nuclei (AGNs) is the black hole mass (M$_\bullet$)
that, together with the total luminosity, defines the fraction of
the Eddington luminosity at which the AGN is emitting. Since the
earliest days of research on quasars and AGNs, supermassive black
holes (SMBHs) have been considered to be the most likely driving
power of the activity in these sources (Richstone et al. 1998;
Kormendy \& Gebhardt 2001; Merritt \& Ferrarese 2001). Indeed,
compact dark masses, probably SMBHs, have been detected in the
cores of many normal galaxies using stellar dynamics (Kormendy \&
Richstone 1995). In the case of AGNs, however, direct detection of
nuclear SMBHs through stellar-dynamical methods has not been
achieved on account of technical difficulties arising from the
large surface brightness contrast between the stellar component of
the galaxy and the AGN itself on arcsecond and smaller angular
scales. The strongest evidence to date has been the detection of
Keplerian motions of megamaser sources in the Seyfert galaxy
NGC~4258 (Miyoshi et al. 1995).


Variability is one of the important properties of AGNs and a
powerful constraint on models of these sources. Observations show
that AGNs are characterized by rapid and large amplitude continuum
variations over the entire electromagnetic spectrum. CCD-based
differential photometric observations of rapid variability over
timescales of significantly less than a day in the optical
emission of AGNs are powerful tools for probing the innermost
regions of these objects. The original models based on a central
black hole surrounded by an accretion disk (Rees 1984) were based
on the constraints on the source size and energy density provided
by the early single-band variability studies. PKS 1510$-$089 is
one of the $\gamma$-ray loud blazars (a subclass of AGNs) which
characterized by their powerful featureless continuum radiation
spanning from radio to gamma-ray bands. It is generally believed
that synchrotron self-Compton (SSC) emission of high energy
electrons in a relativistic jet is responsible for the
multiwaveband continuum of the BL Lacs (Urry \& Padovani 1995).
The emission is highly beamed. The featureless continuum of the
blazars permits us to use timescale of variability to estimate
black hole mass. It has been pointed out that the masses of black
holes in all the radio-loud quasars of low redshift PG sample
should exceed $10^9M_\odot$ (Laor 2000). This suggests the black
hole mass controls the radio-loudness $R$, defined as the ratio of
radio to optical fluxes. The relativistic jet is generally thought
to originate from the innermost vicinity of black hole (Blandford
2001). The emission from the jet may reflect the black hole
parameters in a more direct way. In addition, the black hole model
and accretion disk theory suggest that the observed minimal
timescale of variation and the bolometric luminosity should obey
the Abramowicz -- Nobili relation.

In this paper, we present the optical light of the $\gamma$-ray
loud blazar PKS 1510$-$089 with the 1-m telescope at the Yunnan
Astronomical Observatory in 2000. Using this result, we derive an
estimate of the center black hole mass in PKS 1510$-$089.
Throughout this paper, the $q_{0}$=0.5, and $H_{0}=75 \rm{km
s}^{-1}\rm{Mpc}^{-1}$ are adopted.

%__________________________________________________________________

\section{The observational light curve and central SMBH's mass}
The optical observations were carried out at the Yunnan
Astronomical Observatory, with the 1-m telescope equipped with a
direct CCD (1024 $\times$ 1024 pixels) camera at the Cassegrain
focus. The data reduction and observational errors are discussed
in detail in previous works (Dai et al. 2001).

This quasar presents a pronounced UV excess, a very flat X-ray
spectrum, and a steep $\gamma$-ray spectrum. Up to now, the
maximum brightness variation of 5.4 mag in the B band has been
obtained by Liller et el. (1975). A bright state in 1987 was
followed by a rapid dimming (Villata et al., 1997 and references
therein). Small amplitude oscillations on short time scales have
also been observed by Villata et al. (1997), who found a variation
of 0.63 mags in the R and B bands. This object has been included
in our monitoring program since 1999. In our previous observations
in 1999, it exhibited a high level of activity each night. It
brightened from 17.21 mag to 16.65 mag in 40 minutes in the B
band. A rapid decline of 0.55 mag in 22 minutes, and a flare of
0.51 mag in 26 minutes were observed on May 15, on June 15, 1999
in the R band respectively (Xie et al. 2001). Our recent
observations on May 29, 2000 are displayed in Fig. 1. The source
was still in a very active state during our observation period. An
apparent variation of about 2 mag in the R band within 41 minutes
was observed. The source faded from 16.02 to 17.74 in 27 minutes
and then brightened to 15.74 in about 13 minutes. This is the most
extremely rapid variability in our optical monitoring program
since 1982. Fig. (1a) shows that the differential magnitudes of
two comparison stars are less than 0.02 mag during the night and
Fig (1b) shows the light curve about this maximum variation of PKS
1510$-$089. According to the definition of the variability
parameter (Romero et al. 1999, Fan et al.2001), the value of this
dramatic variability is C=59.6. We examine the contribution of the
host galaxy to the variability and find there is no correlation
between intranight brightness variations and seeing conditions,
which means that seeing in no way has affected the computed
magnitudes of PKS 1510$-$089. So, we conclude that the observed
apparent variation of PKS 1510$-$089 is intrinsic to the source,
as determined by a rigorous check for correlations between
variability and seeing conditions.

%%%%%%%%%%%%%%%%%%%%%%%%
If we view the dramatic variability as a single event, the
observed variability by 2.0 mag within 41 minutes in PKS
1510$-$089 can be used to compute the efficiency ($\eta$) for
conversion of accreted matter into energy. If $\Delta L$ is the
change in luminosity within the variability time scale $\Delta
t_{\rm{obs}}$(defined as $\Delta t_{\rm{obs}}=\frac{F}{|\Delta
F/\Delta t|}$, Wagner \& Witzel 1995), then $\eta$ can be written
as (Cavallo \& Rees, 1978; Xie et al. 1989)
\begin{equation}
\eta \ge 5.0\times 10^{-43}\frac{\Delta L}{\Delta t_{\rm{obs}}}
\end{equation}
where $\Delta L$ is in erg~s$^{-1}$ and $\Delta t_{\rm{obs}}$ in
seconds. The value of $\Delta L$ of the variability in our
observation is $7.3\times 10^{47}\rm{erg~s}^{-1}$. Using equation
(2), the value of $\Delta L$, and $\Delta t_{\rm{obs}}$ which is
equal to 2700 s, we find $\eta \ge 62.2$. This value of $\eta$
strongly suggests the presence of relativistic beaming in PKS
1510$-$089 (Guilbert et al. 1983; relativistic beaming is inferred
if $\eta >0.1$). In our previous paper (Xie et al. 1991), we have
obtained a formula to estimate the Doppler factor $\delta$,
\begin{equation}
 \delta \ge [{\frac{\eta_{\rm{obs}}}{\eta_{\rm{in}}}}]^{1/(4+\alpha)}
\end{equation}
where $\eta_{\rm{obs}}$ and $\eta_{\rm{in}}$ are the conversion
efficiency of the observed and intrinsic values respectively, and
$\alpha$ is the spectral index in the form
$f_{\nu}\propto\nu^{-\alpha}$. In the optical band, we assume
$\alpha=1.0$ (Stocke et al. 1991). It is known that the efficiency
of conversion for nuclei reactions is $\eta_{\rm{in}}$=0.007, and
that for pure accretion is $\eta_{\rm{in}}<$ 0.1. The median value
of 0.05 is almost equal to the value 0.057 in the thick accretion
disk theory for the Schwazschild metric (Paczynski \& Witta,
1980). Thus we obtained the value of $\delta$ in the range of
$3.62-6.16$. This value of the Doppler factor, $\delta$, can be
used to compute the size of the emission region, $R$, using the
light travel time argument, namely
\begin{equation}
 R\le \frac{c\delta \Delta t_{\rm{obs}}}{1+z}
\end{equation}
where $c$ is the light velocity, $z$ is the cosmological redshift,
$\delta$ is the Doppler factor. The resulting value of $R$ from
equation (3) is $(2.15-3.67)\times 10^{14}$ cm. Note that $R$ need
not be the linear dimension of a massive black hole, it could be
the thickness of a thin plane shock at some distance out along a
jet or the thickness of the optically thin boundary of an
optical-thick emission region (Marsher \& Gear 1985).

If the blazar's luminosity is produced from accretion of its
central black hole, the luminosity L should be significantly
correlated with the mass of the central black hole, M$_\bullet$,
\begin{equation}
L \sim \frac{GM_\bullet \dot{M}}r
\end{equation}
where \.{M} is mass accretion rate, and r is the radius of the
marginally bound orbit. The luminosity L is expressed as $\nu
L_\nu $ (Peterson 1997). The M$_\bullet$ and the minimal timescale
of AGN variability, $\Delta t_{\min }$, are related with
\begin{equation}
\Delta t_{\min }=\tau \frac{r_s}c=0.98\times 10^{-5}\tau (\frac
{M_\bullet} {M_{\odot }})s
\end{equation}

where $r_s=\frac{2\rm{G M_\bullet}}{c^2}$ is the radius of the
black-hole event horizon (i.e., the boundary at which the escape
velocity equals the speed of light), $G$ is the gravitational
constant, $M_\bullet$ is the mass of the black hole, and $c$ is
the speed of light,  $\tau $ is the dimensionless parameter $\tau
=\pi (r_{*}^{3/2}+a)$ and it must obey $\tau >\tau _{\min }=2\pi $
for a=1; the hole rotates at the maximum possible rate. If $\tau
_{\max }<2\pi $, observations exclude the possibility of the black
hole model(Abramowicz \& Nobili 1982). Adopting $\tau =\tau _{\min
}=2\pi $ and considering the relativistic beaming effect, the
intrinsic minimal timescale of AGN variability is $\Delta t_{\min
}(\rm in)$=$\frac \delta {1+z}\Delta t_{\min }(\rm obs)$, and
\begin{equation}
M_\bullet\leq1.62\times 10^4\frac \delta {1+z}\Delta t_{\min }(\rm
obs)(M_{\odot })
\end{equation}
A similar formula was obtained by Miller et al. 1989. We obtain
the central supermassive black hole of
$(1.16-1.98)\times10^8M_\odot$ in PKS 1510$-$089. Baganoff et al.
(2001) also obtained consistent results with the X-ray variability
of a few handred second rise/fall timescales and the 10-ks
duration which provide compelling evidence that the X-ray emission
is coming from accretion onto a supermassive black hole of $2.6
\times 10^{6}M_\odot$ at the Galactic Centre. Barth et al. (2002)
assume the blazar Mrk 501 follows the $M_\bullet-\sigma_\star$
relation defined for nearby galaxies(Ferrarese, \& Merritt, D.
2000; Gebhardt et al. 2000), and found the center supermassive
black hole mass of $(0.9-3.4)\times10^9\rm (M_\odot)$.


\section{Conclusions and discussions}

In the framework of the EC models, Tavecchio et al. (2000)
suggested that the quasar-like blazar environment is rich in soft
photons, produced by the accretion disk and/or by the broad line
region (BLR). They estimated the physical quantities in the jet
emitting region and shed light on the energy transport mechanisms
in jets using the BeppoSAX X-ray observation results. They found
that the central black hole masses of three quasar-like balzars,
0836+710, 1510-089, 2230+114, are in the range of
$10^7-10^9M_\odot$.

To explain the observed rapid variability, there are some
mechanisms, like eclipsing of hot spots by the accretion disk or
microflares in the accretion disk (Wiita, 1996). It has been
suggested that the turbulent magnetic field with a relativistic
jet may produce the rapidly oscillating variation seen in some
blazars (Massaro et al. 1998; Nesci et al. 1998). Among these
models, the relativistic model appears to be the most promising to
explain the observed rapid variability in $\gamma$-ray loud
blazars. The nature of the variations provides strong constraints
on the astrophysical processes near the event horizon of the black
hole. This makes PKS 1510$-$089 a valuable source for testing the
theory of accretion onto supermassive black holes in $\gamma$-ray
loud balzars.

\begin{acknowledgements}
The authors are grateful to Dr. J. H. Fan and the anonymous
referee for the significant suggestions and comments and of Dr. L.
Zhang for his reading of the manuscript and suggestions. This work
is supported by the National Natural Scientific Foundation of
China (NSFC) and Natural Science Foundation of Yunnan Province
(2000A004M).
\end{acknowledgements}

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\end{document}

astro-ph0205482.extracted_bib
\begin{thebibliography}{}
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\bibitem{}Blandford, R., 2001, astro-ph/0110394
\bibitem{}Blandford, R.D., \& McKee, C.F. 1982, ApJ, 255, 419
\bibitem{}Cavallo, G., \& Rees, M. J., 1978, MNRAS, 183, 359
\bibitem{}Dai, B.Z., Xie, G.Z., Li, K.H. et al., 2001, AJ, 122, 2901
\bibitem{}Fan J. H., Qian, B. C., Tao, J. 2001, A\&A, 369, 758
\bibitem{}Fan, J. H., Xie, G. Z., \& Bacon, R. 1999, A\&AS, 136, 13
\bibitem{}Ferrarese, L., \& Merritt, D. 2000, ApJ, 539, L9
\bibitem{}Ferrarese, L., Ford, H. C., \& Jaffe, W. 1996, ApJ, 470, 444
\bibitem{}Gebhardt, K., et al. 2000, ApJ, 539, L13
\bibitem{}Guilbert, P. W., Fabian, A. C., \& Rees, M. J., 1983, MNRAS, 205, 593
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\bibitem{}Kormendy, J., \& Richstone, D.  1995, ARA\&A, 33, 581
\bibitem{}Kormendy, J., \& Gebhardt, K. 2001, astro-ph/0105230
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\bibitem{}Laor, A., 2000, ApJ, 543, L111
\bibitem{}Marscher , A. P. \& Gear, W. K., 1985, ApJ, 298,114
\bibitem{}Massaro, E., Nesci, R., Maesano, M., et al., 1998, MNRAS, 299, 47
\bibitem{}Merritt, D., \& Ferrarese, L., 2001, MNRAS, 320, L30
\bibitem{}Miyoshi, M., Moran, J., Herrnstein, J., Greenhill, L., Nakai, N., Diamond, P., \& Inoue, E. 1995, Nature, 373, 127
\bibitem{}Nesci, R.; Maesano, M.; Massaro, E. et al., 1998, A\&A, 332, L1
\bibitem{}Paczynski, B. \& Wiita, P. J., 1980, A\&A, 88, 23
\bibitem{}Peterson B. M., 1997, An Introduction to Active Galactic Nuclei, Cambridge University press, p.34
\bibitem{}Rees, M. 1984, ARA\&A, 22, 741
\bibitem{}Richstone, D., et al.\ 1998, Nature, 395, A14
\bibitem{}Rieger, F. M., \& Mannheim, K. 2000, A\&A, 359, 948
\bibitem{}Romero G. E., Cellone S. A., \& Combi J. A. 1999, A\&AS,135, 477
\bibitem{}Stocke J. T., Morris, S. L., Gioia, I. M. et al., 1991, ApJS, 76,813
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\bibitem{}Villata, M., Raiteri, C. M., Ghisellini, G., et al., 1997, A\&AS, 121,119
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\bibitem{}Wandel, A. 1999, ApJ, 519, L39
\bibitem{}Wandel, A., Peterson, B.M., \& Malkan, M.A. 1999, ApJ, 526, 579
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