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\def\be{\begin{equation}}
\def\ee{\end{equation}}
\def\mdot{\dot{m}}
\def\msun{M_{\odot}}
\def\ergscc{\rm \  \ erg \ cm^{-3} \ s^{-1}}
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\date{}
\title{Possible evidence for the disk origin for the powering of jets in 
Sgr A$^*$ and nearby elliptical galaxies}
\author{Feng Yuan$^{1,2,3}$}
\institute{
$^1$ Department of Astronomy, Nanjing University, Nanjing 210093,
China. Email: fyuan@nju.edu.cn\\
$^2$ Beijing Astrophysical Center, Beijing, 10080, China\\
$^3$ Korea Institute for Advanced Study, Seoul, 130-012, Korea}

\date{Accepted .
      Received ;
     in original form }

\pagerange{\pageref{firstpage}-- \pageref{lastpage}}
\pubyear{2000}

\begin{document}

\maketitle

\label{firstpage}

\begin{abstract}
Recent VLBA observation indicates the existence 
of an elongated (jet) structure in the compact radio source Sgr A$^*$.
This is hard to explain in the context of advection-dominated accretion 
flow (ADAF) model for this source. On the other hand, 
the mass accretion rate favored by ADAF
is 10-20 times smaller than that favored by the hydrodynamical 
simulation based on Bondi capture. 
If the latter were adopted, the predicted 
radio flux would significantly exceed the observation by about two orders of 
magnitude. 
%While the X-ray luminosity produced by bremsstrahlung 
%can be naturally deduced after seriously considering the outer 
%boundary condition of the accretion flow, 
%the overprediction of radio flux 
%remains a serious problem. 
A similar situation exists in the case of nearby giant ellipticals, 
where the canonical ADAF model -- the widely assumed 
standard model for these sources -- also significantly overpredict
the radio flux.
Based on these facts,
in this paper we propose a truncated ADAF model for Sgr A$^*$ and 
three ellipticals M87, NGC 4649 and NGC 4636.
We assume that the accretion disk is truncated at a certain radius
$R_{\rm tr}$ within which the jet forms by extracting the energy of the disk. 
The radio flux is greatly suppressed due to the radiative 
truncation of the disk and the fits to the observational data are excellent. 
For example, for Sgr A$^*$, the model 
fits the observational spectrum very well from
radio including the ``excess'' below the break frequency 
to hard X-ray under a high accretion rate near the simulation value,
and the predicted  
size-frequency relationship is also in excellent agreement with 
the observation; for M87, the predicted upper limit of the jet location
is $24 R_{\rm g}$, in excellent agreement with the observational result 
that the jet is formed on scales smaller than $30 R_{\rm g}$, 
and the $\approx 20 \%$ variability at $\sim$ 1 Kev -- which is hard to 
explain in another model trying to 
explain the low radio flux of M87 -- is also marginally interpreted. 
The success of the model supplies a possible piece of evidence for the 
disk rather than the hole origin for the powering of jets. 
\end{abstract}


\begin{keywords}
accretion, accretion disks -- black hole physics -- 
galaxies: active  -- galaxies: individual 
(M87, NGC 4649, NGC 4636) -- galaxies: jets -- Galaxy: centre -- hydrodynamics
\end{keywords}

\section{Introduction}
The energetic radio source Sgr A$^*$ located
at the centre of our Galaxy is widely believed to be a black hole
with mass $M = 2.5 \times 10^6 \msun$ (Mezger, Duschl \& Zylka 1996). 
Due to its proximity, the observational data are abundant, which makes it an 
ideal laboratory to test our accretion theories. Any successful model needs 
to explain its relative low-luminosity, 
the emergent spectrum from radio to X-ray wavelength, 
and the frequency-size relationship.

Several models have been put forward for Sgr A$^*$. They include
Bondi accretion (Melia 1992; 1994), emission from mono-energetic 
electrons (Duschl \& Lesch 1994), jet model 
(Falcke, Mannheim \& Biermann 1993; Falcke \& Biermann 1999), 
and the most recent two temperature 
advection-dominated accretion flows (ADAFs; 
Narayan, Yi \& Mahadevan 1995; Manmoto, Mineshige, \& Kusunose 1997; 
Narayan et al. 1998). 
Among them, ADAF model is the most dynamically 
self-consistent. However, two puzzles still remain in this model. First, 
as pointed out by Quataert \& Narayan (1999), 
the mass accretion rate required in this model ($ \approx 6.8 \times 
10^{-5} \dot{M}_{\rm Edd}$, here $\dot{M}_{\rm Edd}
=2.2 \times 10^{-8} {\rm M}\,{\rm yr}^{-1}$ 
denotes the Eddington accretion rate and $M$ is the mass of the central hole) 
is more than 10 
times smaller than that favored by three-dimensional hydrodynamical 
simulation based on the Bondi capture ($ \approx 9 \times 10^{-4} 
\dot{M}_{\rm Edd}$; Coker \& Melia 1997), 
otherwise the bremsstrahlung and synchrotron radiations would yield an X-ray 
and a radio fluxes well above the observational 
limits, as shown by the dotted line in Figure 1.
Yuan (1999) found that the outer boundary condition 
of the accretion flow plays an important role in
the dynamics and radiation of an optically thin accretion flow therefore
should be seriously considered.
This point was neglected in previous ADAF models in the literature.
After considering this effect, it was found 
that the accretion in Sgr A$^*$ should belong to Bondi-like (not Bondi type),
characterized by a much larger sonic radius and a low 
surface density compared with the conventional disk-like ADAF.
The bremsstrahlung radiation therefore is 
greatly suppressed (Yuan et al. 2000). However,  
the synchrotron radiation would still produce  
too much radio flux were the mass accretion rate favored by 
the simulation adopted.
In fact, even though an accretion rate as low as 
that in Quataert \& Narayan (1999) were chosen, a magnetic 
field strength substantially lower than the equilibrium  
value has to be used in order to accommodate the radio limit.

The second puzzle is that the ADAF model strongly 
underpredicts the radio flux in the radio spectrum below a ``break'' 
frequency around $\sim $ 50 GHz (Narayan et al. 1998). 
Mahadevan (1998) argued that the charged pion produced by the energetic
proton collisions in the ADAF will subsequently decay into $e^-$$e^+$,
which will further produce synchrotron emission
and could serve as the origin of the radio excess below the break.
However, the result depends on the power-law index 
of the proton energy spectrum, which we are not clear.
In fact, due to the existence of the threshold energy
needed for pion production, these extra photons should be principally 
produced in the innermost region of the disk. 
This is in serious conflict with the observed intrinsic size 
of $\sim 72 R_{\rm g}$ at 43 GHz (Lo et al. 1998; see also Figure 2),
here $R_{\rm g}= 2GM/c^2$ is the Schwarzschild radius of the black hole.

More importantly, recent excellent near-simultaneous VLBA measurements
showed that the intrinsic source structure at 43 GHz is 
elongated along an essentially north-south direction, with an
axial ratio of less than 0.3 (Lo et al. 1998). 
This is hard to explain in an ADAF model, while 
it provides a convincing piece of evidence for the existence of the jet
in the jet-nozzle model by Falcke et al. (1993). 
In this model the radio spectrum below the break is produced by
a jet while those above the break is assumed to be produced by a 
``nozzle'' located at the lower base of the jet. 
The question is, however, this model can not account for the entire 
spectral energy distribution from radio to X-ray, and we lack
any detailed understanding to the ``nozzle'' which is crucial to the 
fit of the spectrum above the break.

A similar situation exists in the case of
nearby elliptical galaxies. The existence of a massive black hole 
and the hot gas pervading the galactic centre is in sharp contrast 
to their low luminosity. Recently it was suggested that ADAF 
could serve as a feasible explanation for the quiescence of the 
galaxies (Fabian \& Rees 1995). Recent observation, however, showed that 
the canonical ADAF model overpredicts the radio flux by more than two 
orders of magnitude (Di Matteo et al. 1999). The current explanation is 
to drive a wind from the accretion disk, assuming 
the accretion rate $\dot{M}=(R/R_{\rm out})^p\dot{M}_{\rm out}$ 
(Di Matteo et al. 2000),
where $R_{\rm out}$ is the radius from which the 
wind starts to play an important role and $\dot{M}_{\rm out}$ is 
the mass accretion rate there.
Since the electron is basically adiabatic, its temperature is determined 
by the compression work. When a strong wind is introduced, 
the density profile would become flatter which results in a 
significant decrease of the temperature and further the synchrotron radiation. 
The presence of a strong wind is based on the assumption that 
the Bernoulli parameter of an ADAF is positive therefore the flow
is in some sense unstable (Blandford \& Begelman 1999).
As shown by Nakamura (1998) and Abramowicz, Lasota, \& Igumenshchev 
(2000), however, the Bernoulli parameter is negative in most 
of the reasonable cases. Numerous numerical simulations also confirm the 
absence of winds from the disks (but jets do present in the 
innermost region of the disk in some cases) (Eggum, Coroniti, \& Katz 1988; 
Molteni, Lanzafame, \& Chakrabarti 1994; Igumenshchev \& Abramowicz 1998;
Stone, Pringle, \& Begelman 1999; Koide et al. 2000). 
Thus the scenario of strong winds from ADAFs
might be questionable.
%Even though we assume the existence of a strong wind 
%from ADAF, we must further assume that the wind stars well inside 
%the outer boundary of the accretion flow ($\sim 10^6 R_{\rm g}$), 
%typically several hundreds of $R_{\rm g}$, otherwise the amount 
%of mass loss needed to satisfied the X-ray to radio flux 
%and/or the observed X-ray slope would give rise to a cut-off
%in the bremsstrahlung emission at energies $\la 10$ keV, which is apparently
%inconsistent with the ASCA data (Di Matteo et al. 2000). 
Even so, the fit is not satisfactory, as illustrated below.
On the other hand, it is interesting to note that 
all the sources in Di Matteo et al. (2000)'s sample have the extended 
and often highly collimated radio structures
which are again the evidence for the existence
of jets (e.g. Stanger \& Warwick 1986).
%Any valid model for Sgr A$^*$ and nearby ellipticals 
%must take into account the existence 
%of jets.

Based on the above facts, in this paper, we propose an ADAF-jet model for
Sgr A$^*$ and nearby elliptical galaxies.

\section{Truncated ADAF by a jet}

Jets are observed in many classes of astrophysical objects
involving an accretion flow, ranging from AGNs and quasars,
to old compact stars in binaries, and to young stellar objects.
%Unfortunately, our understanding of the jet formation from the disk
%is rather primitive after many years' efforts 
%(see recent reviews by Lovelace, Ustyugova \& Koldota 1999 and Livio 1999).
There are currently two main energetic mechanisms for jets
(see recent reviews by Lovelace, Ustyugova \& Koldota 1999 and Livio 1999).
The first one is the Blandford-Znajek mechanism (Blandford \& Znajek 1977).
The rotation of the black hole drags the inertial
frame near it and twists the magnetic field line supported
by the surrounding disk. The resulted magnetic stress is then released
as a Poynting flux away from the hole. In this mechanism,
the powering of jets is provided by the rotating hole.
The second is the 
electromagnetic output from the inner region of the 
accretion disk (Blandford 1976; Lovelace 1976;
Blandford \& Payne 1982; see Spruit 1996 for more references). 
The twisting of the field caused by
the rotation of a Keplerian accretion disk results 
in outflows out of the disk,
or the material in the disk is accelerated by the
centrifugal force and magnetic pressure gradient force. In these models,
the powering of jets is the energy output from the disk.
We are not clear at present which mechanism plays the dominated role even
after so many years' efforts.

But we are sure at this point that the jet must originates
from the inner region of the disk. This conclusion is based on
numerous observations. One piece of evidence is that
the jet velocity is always of the order of the escape velocity from the 
central objects in any case involving jets. 
Another good example comes from the observation 
of the jet in M87, as to be stated
in this paper (for more evidence, see Livio 1999). Numerical simulations
also obtain the same result (e.g., Koide et al. 2000).

For our purpose, in this paper we adopt the ``disk'' origin of jets.
We assume the jet forms within a certain radius $R_{\rm tr}$ by 
extracting the energy of the ADAF. Since the jet power is generally comparable
with the total accretion power of the disk (Rawlings \& Saunders 1991), 
we further assume
the ``disk'' within $R_{\rm tr}$ (if it still exists) does not 
emit any radiation, i.e. ADAF is radiatively truncated by the jet. 
We treat $r_{tr}$ as a free parameter.

The resulted spectrum of the truncated ADAF can be qualitatively understood 
by the following simple estimate. The synchrotron photons 
emitted at a radius $R$ in an ADAF,
which are responsible for the radio spectrum, are highly self-absorbed and
give a blackbody spectrum, up to a critical frequency $\nu_c(R)$ above
which the radiation becomes optically thin.
The emergent spectrum of the ring at radius $R$ 
is peaked at this frequency and the total radio spectrum is the superposition
of each ring of ADAF. Therefore each point along the radio spectrum
corresponds to a certain radius in an ADAF (Mahadevan 1997), 
\be
\nu_c(r) \approx 30 m_9^{-1/2}\dot{m}_{-4}^{1/2}T_{e9}^2 r^{-5/4} {\rm GHz}.
\ee
Here, $m_9=M/(10^9\msun)$, $\dot{m}_{-4}=\dot{M}/(10^{-4}\dot{M}_{\rm Edd})$,
$T_{e9}=T_e/10^9{\rm K}$, and $r=R/R_{\rm g}$.
Therefore, the high-frequency part of the radio spectrum 
from $\nu(R_{\rm tr}/R_{\rm g})$ up to the previous
radio peak $\nu(r=1)$ will be taken away due to the
the truncation of ADAF at $R_{\rm tr}$, as illustrated by Figure 1. 
Thus the radio flux is strongly suppressed.

The detailed numerical procedure for the calculation of the spectrum of ADAF
is presented in Yuan et al. (2000). 
Bremsstrahlung and synchrotron radiations amplified by Comptonization
are taken into account and the two-temperature plasma assumption is adopted.
For Sgr A$^*$, we set the outer boundary at the radius 
where the accretion begins, $\sim 1.5 \times 10^5 R_{\rm g}$,
and adopt the flow's temperature and angular momentum
there as the outer boundary condition (for details, see Yuan et al. 2000).
But for ellipticals, for simplicity we set the outer boundary 
at $10^4 R_{\rm g}$ and
the temperatures of electrons and ions 
at $R_{\rm out}$ are set as $T_{\rm i,out} \approx
T_{\rm e,out} \approx 7 \times 10^7 {\rm K}$. 
Strictly saying, we should set the outer boundary at the radius 
where the accretion begins, and adopt the flow's 
temperature and angular momentum there as the outer boundary condition,
like in the case of Sgr A$^*$.
Our previous calculation to Sgr A$^*$ shows
that if only we set the outer boundary far enough from the hole, 
say $\ga 10^4 r_g$ in the present case,
the effects due to different $T_{\rm out}$ are not large.
However, the angular momentum of the accretion flow
in ellipticals is very small,
we therefore set $\Omega_{\rm out} \la 0.2\Omega_{\rm Kepler}$ in 
all the cases thus the accretion mode is 
of Bondi-like.
Other parameters we set are $\alpha=0.1$ and 
$\beta=0.9$ for Sgr A$^*$ (for consistency with 
previous papers) or $\beta=0.5$ for ellipticals. Here $\alpha$
is the viscosity parameter and $\beta$ denotes the ratio of 
the gas pressure to the sum of the magnetic and gas pressures. 
Note since we assume a strict equipartition between the magnetic pressure
and the gas pressure for ellipticals, the truncation radii we obtain below 
are all upper limits.
We self-consistently solve the set of equations describing the 
radiation hydrodynamics of accretion flows and obtain their 
emergent spectrum by integrating from the outer boundary 
to the assumed truncation radius $R_{\rm tr}$.

For completeness, for some sources we calculate the radiation of the jet
as well. However, compared with ADAF, there are 
much more free parameters in 
the general jet model developed especially for BL Lac 
objects (e.g. Ghisellini, 
Maraschi, \& Treves 1985). Here 
we follow Falcke \& Biermann (1999) to calculate the radiation of the jet.
The formula are derived from the Blandford \& Konigl (1979) model which 
calculate the synchrotron emission of a freely expanding, pressure 
driven jet as a function of jet power.
The free parameters include the jet power $Q_{\rm jet}$, 
the characteristic electron Lolentz factor
$\gamma_e$, and the angle between the sight line and the jet axis
$i$. We set the scale height
of the acceleration zone $Z_{\rm nozz}$ -- a free parameter in 
Falcke \& Biermann (1999)'s model-- to equal to the 
scale height of the disk at $R_{\rm tr}$. 
We should note that the formula we adopt is somewhat simplified.
For example, it assumes the electron energy distribution is
quasi-monoenergetic rather than the more realistic 
power law. Since in almost all practical cases, the synchrotron radiation 
is highly self-absorbed, the final spectrum results from the superposition
of the radiation from different radii. 
Therefore, even though the energy distribution were
power law, the result should be roughly the same if only the maximum 
Lolentz factor is not too large, which is reasonable if the radiative
zone is not too far away from the base of the jet hence the electrons have
not been accelerated to a power law by, e.g. a shock. 
%This model, initially developed for Sgr A$^*$, has been successfully applied 
%to other sources with jet such as M81, NGC 4258 and black hole X-ray 
%binary. So in the present paper, we assume it can be applied 
%to describe the jet in ellipticals (except M87).
We sum the radiations of the disk and the jet to obtain the total spectrum.

\section{Applications to individual sources}
\subsection{Sgr A$^*$}

\begin{figure}
\psfig{file=fig1.ps,width=0.45\textwidth,angle=270}
\caption{The predicted spectrum of the ADAF-jet model for 
Sgr A$^*$ together with the observation.  The dotted 
line is for the ``not-truncated''  
ADAF with the mass accretion rate 
$4 \times 10^{-4} \dot{M}_{\rm Edd}$.
The thin-solid line is
for the truncated ADAF with the same accretion rate, the truncation radius
is $R_{\rm tr}=10 R_{\rm g}$.
The dashed line is for the jet and the thick-solid line 
is their sum. Other parameters are $M=2.5 \times 10^6 \msun,
\gamma_e=125, i=45^{\circ}$, and $Q_{\rm jet}=10^{38.4} \ergsec$.}
\end{figure}

Figure 1 shows the calculated spectrum for Sgr A$^*$ together with 
the observational data taken from Narayan et al. (1998). The dotted 
line is for the ``not-truncated''  
ADAF with the mass accretion rate 
$4 \times 10^{-4} \dot{M}_{\rm Edd}$.
The predicted spectrum is in obvious conflict with the observation. 
The thin solid
line is for the truncated disk with the same accretion rate,
the dashed line is for
the jet, and the thick-solid line denotes the total 
spectrum of the ADAF-jet system. The truncation radius 
$R_{\rm tr}= 10R_{\rm g}$. Compared with the ``not-truncated''
ADAF, the radio flux is significantly suppressed in the truncated ADAF.
>From the figure we find that the spectrum below $\sim 50$ GHz is mainly
contributed by the jet while those above is principally
produced by the disk and the fit to the observation 
is good. Figure 2 shows the
predicted size-frequency relationship of our ADAF-jet model together
with the observational data taken from Lo et al. (1998) (for 43 GHz) and
Krichbaum et al. (1998) (for 86 and 215 GHz) 
\footnote{Because of the existence of two components, 
jet and disk, and the reason stated in Krichbaum et al. 1998,
their ``case 2'' result is more reasonable and is adopted here.
See Krichbaum et al (1998) for details}. 
The solid one is the result of our ADAF-jet model, with the line
below and above the break frequency at around 
$\sim 50$ GHz resulted by the jet and
the truncated ADAF respectively.
For comparison, we also show by the dashed line 
the prediction of the most latest 
version of the ``not-truncated'' ADAF model with
$\dot{M}=6 \times 10^{-5} \dot{M}_{\rm Edd}$ and 
$\beta=0.9$ (Quataert \& Narayan 1999) 
\footnote{The different 
prediction of the ``not-truncated'' ADAF between 
the present result (dashed line) and that in Narayan et al. (1998) is
due to the difference of the adopted electron adiabatic index $\gamma_e$. 
We take it to be that of a monatomic ideal gas, as in 
Quataert \& Narayan (1999), while 
in Narayan et al. (1998) $\gamma_e$ includes the 
contribution of the magnetic density as well. Compared with ours, 
the choice in Narayan et al. (1998) results in 
a lower electron temperature therefore
a larger radio source size is needed
to produce the observed flux at a given frequency.
Due to the same reason, in Quataert \& Narayan (1999) and the present paper,
a noticeably smaller mass accretion rate
and weaker magnetic field than Narayan et al. (1998)
is required to fit the observation.
However, as argued by Quataert \& Narayan (1999),
$\gamma_e$ should not include the contribution of the magnetic density.}.
Although two models are both compatible with the data at 86 and 215 GHz, 
our ADAF-jet one seems to give a somewhat better fit to the observation,
and the prediction at 43 GHz by ADAF model is in obvious conflict with
observation. In this context,
we note that although it would be possible for the 
``ADAF+wind'' model of Quataert \& Narayan (1999) 
to interpret the spectrum even if  
the high accretion rate favored by simulation were
adopted, the predicted size-frequency relationship may be in conflict
with the observation, since that model should produce a
similar frequency-size relationship with the ``not-truncated'' ADAF model. 

\begin{figure}
\psfig{file=fig2.ps,width=0.45\textwidth,angle=270}
\caption{The predicted size-frequency relationship together with 
the observation for Sgr A$^*$. 
The thick solid line is the 
result of our ADAF-jet model with the line above the vertical dotted line  
being for the jet and the line below for the truncated ADAF. The
long-dashed line is for the ``not-truncated'' ADAF.}
\end{figure}

\subsection{Nearby Elliptical galaxies}

Encouraged by the above success, 
we further apply our model to the six ellipticals presented 
in Di Matteo et al. (2000), where jets also exist.
Due to the successful applications
of Falcke's jet model to other sources like M81, GRS 1915+105,
and NGC 4258 (Falcke \& Biermann 1999), 
we assume here that for our purpose 
this model can give an enough 
description to the weak jets (excluding M87) in ellipticals as well.
We find that due to the suppression of the radio flux 
by the truncation of the disk, 
the predicted spectra are in good agreement with the observations.
We present below three sources as illustrations. The observational 
data are taken from Reynold et al. (1996) (for M87) and 
Di Matteo et al.(1999) (for NGC 4649 and NGC 4636). 

\subsubsection{NGC 4649}

\begin{figure}
\psfig{file=fig3.ps,width=0.45\textwidth,angle=270}
\caption{The predicted spectrum of the ADAF-jet 
model for  NGC 4649 together with the observation. The long-dashed 
line is the result of the truncated ADAF, the short-dashed 
line is for the jet, and the solid line shows the sum. 
The parameters are $M=4 \times 10^9 \msun, \dot{M}
=8 \times 10^{-3} \dot{M}_{\rm Edd}, Q_{\rm jet}=
10^{40.7} {\ergsec}, i=20^{\circ},
R_{tr}=40 R_g$, and $\gamma_e=200$.}
\end{figure}

We first model NGC 4649 because it has the best 
observational constraints in 
Di Matteo et al. (2000)'s sample. 
Figure 3 shows the predicted spectrum of this source 
together with the observation. The long-dashed 
line is the result of the truncated ADAF, the short-dashed 
line is for the jet, and the solid line shows the sum. 
As clearly shown, this source, which can be matched  
well by the ADAF with winds, also can be matched quite well by a truncated ADAF.
However, in the wind model,
if we assume the wind were to start at the outer 
boundary $10^4R_{\rm g}$, the radius
where the accretion starts, a fairly strong suppression
of the X-ray emission above $\sim$ 5keV
is introduced, which is in conflict with the ASCA data (Di Matteo et al. 2000).
As stated by Di Matteo et al. (2000), this is because 
the introduction of winds at $10^4R_{\rm g}$
strongly decreases the bremsstrahlung emissivity at $10^3 \sim 10^4R_{\rm g}$,
where the X-ray emission $\ga 10$ keV mainly originates from.
Therefore, in their model, they have to assume the winds to start
at a certain radius much smaller than $10^4R_{\rm g}$, which
is not easy to understand. \footnote{Although they argue that if the 
specific angular momentum of the flows at the accretion radius
$\sim 10^4R_{\rm g}$ is a small fraction($\xi$) of the corresponding Keplerian
value, then the angular momentum will start to dominate the flow at 
$r \sim \xi^2 10^4R_{\rm g}$, where the winds start to play an
important role. However, according to our numerical calculation 
(Yuan et al. 2000), when the specific angular momentum at the 
accretion radius is rather low, it will remain highly sub-Keplerian
throughout the way to the hole rather than dominate the flow at a certain small
radius. This is the so-called Bondi-like type accretion. 
See also Abramowicz (1998).}
In our model, the X-ray emission above $\sim 5$keV doesn't show any suppression,
in agreement with ASCA observation. This is because out of the (small)
truncation radius  $R_{\rm tr}$, ADAF is the canonical one in the sense 
that no winds are introduced.
In addition, due to the introduction 
of the jet, the radio flux near 1 GHz, which 
ADAF with winds model underpredicts it greatly, can be interpreted
as the contribution from the jet, as in the case of Sgr A$^*$.


\subsubsection{NGC 4486 (M87)}

\begin{figure}
\psfig{file=fig4.ps,width=0.45\textwidth,angle=270}
\caption{The predicted spectrum of the truncated ADAF for 
NGC 4486 (M87) together with the observation. 
The parameters are $\dot{M}
=3 \times 10^{-2} \dot{M}_{\rm Edd}$ and $M=3 \times 10^9 \msun$. 
The truncation radius $R_{\rm tr}$ equals $24 R_g$.}
\end{figure}

For this source we have 
convincing observational evidence
for the existences of a strong jet and a disk. Its jet is famous, while HST 
spectroscopy of its nucleus has given
strong evidence for a rapidly rotating ionized gas disk
at its centre (e.g., Ford et al. 1994). 
Although its high frequency radio data is consistent
with the canonical ``not-truncated'' ADAF model, the 
X-ray emission in this case 
would be dominated by Comptonization of the synchrotron photons thus
the slope would be too soft to be consistent with the ASCA data.
Therefore, the radio flux must also be significantly smaller than 
that emitted by a canonical ADAF (Di Matteo et al. 2000).
Figure 4 shows the predicted radio spectrum of 
this source by the truncated ADAF
together with the observation. 
Three points need to be emphasized. 
First, compared with the wind model, the truncated ADAF 
can  fit the 100GHz VLBI data much better.
Although the 5 GHz VLBI data is still strongly underpredicted, 
the excess may again be due to the contribution of
the jet, like in the cases of Sgr A$^*$ and NGC 4649.
Second, both winds and the truncated 
ADAF models can give a good match to the spectrum of this source (and others),
but they are intrinsically different. 
One point reflecting the difference is that, 
in the former, the wind starts at a much larger radius, 
typically several hundreds of $R_{\rm g}$,
while in the latter, the theoretically predicted truncation radius at which 
the jet forms is much smaller.
For M87, this radius equals $24 R_{\rm g}$. Were it larger, the ADAF would
predict a radio flux well below the observed one. On the other hand,
as a triumph of 
precision astronomy, the excellent 43GHz observation for this source by 
Junor, Biretta \& Livio (1999) indicates that the jet  
is formed on scales smaller
than $\sim 30 R_{\rm g}$ from the black hole, 
in excellent agreement with our prediction. 

The last point we want to emphasize concerns the variability of M87.
In addition to that mentioned in the last paragraph, 
another intrinsic difference between the wind model and ADAF-jet model
is that the density of the disk at moderate radius differs greatly 
under a same accretion rate.
Due to the large mass loss through the wind, the surface density
of the disk in the wind model is much smaller than the latter.
As a result, the bremsstrahlung emissivity within the wind-starting 
radius is strongly reduced. Therefore, the radius near which most of the 
bremsstrahlung emission flux at frequency $\nu$ can be produced -- $r_{\nu}$ 
-- increases and the dynamical time scale relevant to the bremsstrahlung 
variability at $r_{\nu}$ -- $t_d(r_{\nu})$ -- increases. 
Since for variability we have,
\be
\frac{\delta L_{\nu}(\delta t)}{L_{\nu}} \sim A \, {\rm Min} \left(
1,\left[ \frac{\delta t}{t_d(r_{\nu})}\right]^{3/2} \right),
\ee
thus, on timescale of $\approx$ 6 months to a year
only $\la 1\%$ variability is expected, therefore, the $\approx 20\%$ 
variability observed  by the ROSAT HRI ($\sim 1$ keV) of the core of M87
is hard to reconcile in the wind model (Di Matteo et al. 2000),
while it can be marginally interpreted if
the jet originates at $\sim$
$30 R_{\rm g}$. This is the very case of our truncated ADAF model. 

\subsubsection{NGC 4636}
\begin{figure}
\psfig{file=fig5.ps,width=0.45\textwidth,angle=270}
\caption{The predicted spectrum of the ADAF-jet model for 
NGC 4636 together with the observation. The long-dashed line is the 
spectrum of the truncated ADAF, the short-dashed line is for the jet, and the 
solid line is their sum. The parameters are $\dot{M}
=3 \times 10^{-2} \dot{M}_{\rm Edd}, M=3 \times 10^8 \msun, Q_{\rm jet}=
10^{41.3} {\ergsec}, i=15^{\circ},
R_{tr}=100 R_g$, and $\gamma_e=300$.}
\end{figure}

We can imagine that there may exist such a case that the jet originates
at a moderate large radius so that the radio peak decreases a lot 
according to eq. (1) and it is the jet   
rather than the disk dominates the radio spectrum. This might be the case
for NGC 4636, as Figure 5 illustrates. 
For this source, the wind model predicts a synchrotron peak with 
a much higher frequency than expected by the radio and 
sub-mm measurements (Di Matteo et al. 2000).
In that model 
to correctly fit the peak, a black hole with a much larger 
mass -- $10^9 \msun$ -- than the observational value -- 
$3 \times 10^8 \msun$ -- 
must be used. Figure 5 shows that this puzzle can be solved 
in the truncated ADAF model if
the truncation radius is as large as $100 R_{\rm g}$. 
If this interpretation is correct, polarization should be 
observed,
and the low-frequency radio spectrum should 
not exhibit ``excess'' as in Sgr A$^*$, NGC 4649, and M87.  
%We believe that the radio measurements at 8 GHz and 22 GHz are both come from 
%a weak jet. 

\section{Summary and Discussion}
The predicted radio flux for nearby ellipticals by the canonical 
ADAF model is well
above the observations. If the mass accretion rate favored by the numerical
simulation were adopted, the ADAF model would also overpredict the 
radio flux by about two orders of magnitude in 
the case of Sgr A$^*$. On the observational side,
strong evidence for the existence of jets in Sgr A$^*$ and 
these ellipticals has been observed. Based on these facts, 
in this paper we propose an ADAF-jet model for Sgr A$^*$ 
and the nearby giant elliptical galaxies. 
We assume that  the advection-dominated 
accretion disk is truncated by a 
jet at a certain radius $R_{tr}$ within which 
most of the energy of the disk (if it still exists) is 
extracted for the powering of the jet therefore its radiation 
is completely suppressed. 
We calculate the spectrum of the ADAF-jet system for 
Sgr A$^*$ and three ellipticals and find that the radio overpredictions 
are solved and the fits to the observation are
excellent. For example, for Sgr A$^*$, we can reproduce 
the spectrum from radio to X-ray under a high accretion rate near the
numerical simulation value, including
the break around the 50 GHz point in the radio wavelength, and 
the predicted size-frequency relationship is in good consistency
with the observation. For M87, the truncation radius favored
by our model, $R_{\rm tr} \approx 24 R_{\rm g}$,
agrees with the most recent joint 
observation by VLBI, VLA and other instruments which shows
the jet should originate from within
$\sim 30 R_{\rm g}$ to the central black hole.

In our model we assume that the disk is radiatively truncated at 
a radius $R_{tr}$ by the jet. It is interesting to note 
that this idea has been invented in the study of the black hole
X-ray binary GRS 1915 +105 where we have much better observational
constrains. Radio-infrared oscillation with 
periods of 10-60 min has been found to follow X-ray dips (Mirabel et al. 1998).
The oscillation has been found to be due to synchrotron emission
from repeated small ejections, i.e., jet, possibly resulted from suffering  
strong adiabatic expansion losses (Fender et al. 1997; 
Eikenberry et al. 1998), while the X-ray dips have 
been interpreted as the repeated {\em disappearance} of the inner accretion
disk (Belloni et al. 1997). 

The suppression of the radio flux also can be accessed by 
ADAF with strong winds (Blandford \& Begelman 
1999; Quataert \& Narayan 1999; Di Matteo et al. 2000). Our
truncated ADAF model is different with their wind model.
The wind model is based on the assumption that the Bernoulli parameter
of ADAF is positive therefore strong winds are inevitable. 
%Numerous mass loss from the ADAF makes the density profile of the disk
%flatter and the electrons temperature is decreased, which further
%deduces the radio emission of ADAF.  
The validity of this assumption
is at least in debate at present. On the other hand, our model is based on the 
observation that jets really exist in the inner region of these sources
therefore has much more reliable physical base. The predictions of these
two models are also different. Comparisons between the
prediction and observation on the emergent spectra in the 
sources in our sample, 
the location of the jet origin in M87, 
the $\approx 20\%$ variability at $\sim 1$ keV of M87, and the frequency-size
relationship of Sgr A$^*$, all
incline to support our model.

Noting that in nearby ellipticals and Sgr A$^*$, 
two kinds of sources where ADAFs
are assumed to exist, jets are observed.
In NGC 4258, another source where ADAF is assumed to exist (Gammie, Narayan,
\& Blandford 1999), a jet also exists (e.g., Herrnstein et al. 1998).
Moreover,  in black hole X-ray binary a steady jet is usually 
present at the hard/low state, 
while this state is typically interpreted 
as an inner advection-dominated accretion disk 
plus an outer standard thin disk (Fender 1999; 
Esin, McClintock, \& Narayan 1997). Thus, it seems that a jet 
always be present in an ADAF. If it is the case, we should  
check some result obtained under the frame of a canonical ADAF. 
An example is the radio/X-ray luminosity relation 
obtained by Yi \& Boughn (1998). 
Since the radio spectrum below a possibly 
existed break frequency $\nu_{\rm break}$ (as in the sources 
presented in this paper)
may be dominated by the jet while that above a frequency the spectrum
may disappear due to the truncation of the disk at $r_{\rm tr}$, 
their conclusion holds only if the radio frequency 
$\nu$ satisfies,
\be
\nu_{\rm break} \la \nu \la 20 m_7^{-1/2}\dot{m}_{-3}^{1/2}T_{e9}^2 
\left( \frac{r_{\rm tr}}{20}\right)^{-5/4} {\rm GHz}.
\ee
Here $r_{\rm tr}=R_{\rm tr}/R_{\rm g}$.

The crucial factor in our model is to assume that the
powering of the jet is the energy output from the disk 
rather than from the hole.
The excellent agreement between the predictions of our model
and the observations for both Sgr A$^*$ and 
elliptical galaxies in turn confirms the correctness of our assumption, and 
supports the ``disk'' origin of jets. 
In this context we note that Livio, Ogilvie \& Pringle (1999) 
recently argue that since there is no reason 
to suppose that the magnetic field threading the central
spinning black hole differs significantly in strength from that 
threading the central regions of the disk, and the hole is a very 
poor conductor compared to the surrounding disk material, 
the electromagnetic output from the inner disk
region is expected to dominate over B-Z 
process. We want to note that this conclusion doesn't contradict
the possibility that the rotation of the hole may play a role
in the powering of jets.
This is because  a strong magnetic field may be created
due to the frame dragging in the ergo-sphere of a Kerr black hole, 
therefore the energy
extraction from the disk will be more efficient compared with 
the Schwarzschild black hole case (Koide et al. 2000). 


\section*{Acknowledgments}
I thank Insu Yi for the comments on this
paper and many helpful discussions with me.
This work is partially supported
by China Postdoctoral Science Foundation.

%\end{multicols}

\begin{thebibliography}{}
%\begin{references}
%\twocolumn
%\vfill\eject
%\references
\def\refpar{\hangindent=3em\hangafter=1}
%\def\reference{\refpar\noindent}
\def\reference{\bibitem{}}
\def\apj{ApJ}
\def\apjs{ApJS}
\def\mn{MNRAS}
\def\aa{A\&A}
\def\aas{A\&A Suppl. Ser.}
\def\aj{AJ}
\def\araa{ARA\&A}
\def\nat{Nature}
\def\pasj{PASJ}

\reference Abramowicz, M.A. 1998, in ``The Theory of Black Hole Accretion
Discs'', eds. M.A. Abramowicz, G. Bjornsson, 
and J.E. Pringle (Cambridge University Press)

\reference Abramowicz, M.A., Lasota, J.-P., \& Igumenshchev, I.V. 2000,
\mn, in press (astro-ph/0001479)

\reference Belloni, T., Mendez, M., King, A.R., van der Klis, M., van 
Paradijs, J. 1997, \apj, 488, L109

\reference Blandford, R.D. \& Begelman M.C. 1999, \mn, 303, L1

\reference Blandford, R.D. \& Konigl, A. 1979, \mn, 232, 34

\reference Blandford, R.D. \& Payne 1982, \mn, 199, 883

\reference Blandford, R.D. \& Znajek, R.L. 1977, \mn, 179, 433

\reference Coker, R. \& Melia, F. 1997, \apj, 488, L149

%\reference Coppi, P. 1999, preprint (astro-ph/9903162)

\reference Di Matteo, T., Fabian, A.C., Rees, M.J., Carilli, C.L., \& 
Ivison, R.J. 1999, \mn, 305, 492 

\reference Di Matteo, Quataert, E., Allen, S.W., Narayan, R., \& Fabian, A.C.
2000, \mn, 311, 507

\reference Duschl, W.J., \& Lesch, H. 1994, \aa, 286, 431

\reference Eggum, G. E.; Coroniti, F. V.;
\& Katz, J.I. 1988, \apj, 330, 142

\reference Eikenberry, S.S., Matthews, K., Morgan, E.H., Remillard, R.A.,
Nelson, R.W. 1998, \apj, 494, L61

\reference Esin, A.A., McClintock, J.E., \& Narayan, R. 1997, \apj, 489, 865

\reference Fabian, A.C. \& Rees M.J. 1995, \mn, 277, L55

\reference Falcke, H. \& Biermann, P.L. 1999, \aa, 342, 49

\reference Falcke, H., Mannheim, K., \& Biermann, P.L. 1993, \aa, 278, L1

\reference Fender, R.P. 1999, in ``Black Hole in 
binaries and galactic nuclei'' (astro-ph/9911176)

\reference Fender, R.P. Pooley, G.G., Brocksopp, C., Newell, S.J. 1997, \mn,
290, L65

\reference Ford, H.C. et al. 1994, \apj, 435, L27

\reference Gammie, C.F., Narayan, R., \& Blandford, R. 1999, \apj, 516, 177

\reference Ghisellini, G., Maraschi, L., \& Treves, A. 1985, \aa, 146, 204

\reference Herrnstein, J.R., et al. 1998, \apj, 497, L69

%\reference Junor, W., \& Biretta, J.A., 1995, \aj, 109, 500
\reference Igumenshchev, I.V. \& Abramowicz, M.A. 1999, \mn, 303, 309

\reference Junor, W., Biretta, J.A., \& Livio, M. 1999, \nat, 401, 891

\reference Krichbaum, T.P., et al. 1998, \aa, 335, L106

\reference Koide, S., Meier, D.L., Shibata, K., \& Kudoh, T. 2000, \apj, in
press (astro-ph/9907434)

%\reference Koide, S., Shibata, K. \& Kudoh, T. 1998, \apj, 495, L63

\reference Livio, M. 1999, Phys. Rep. 311, 225

\reference Livio, M., Ogilvie, G.I., \& Pringle, J.E. 1999, \apj, 512, 100

\reference Lo, K.L., Shen, Z.Q., Zhao, J.H., \& Ho, P.T.P. 1998, 
\apj, 508, L61

\reference Lovelace, R.V.E. 1976, \nat, 262, 649

\reference Lovelace, R.V.E., Ustyugova, G.V., \& Koldoba, A.V. 1999, 
in Proceedings of IAU Symp. 194, {\em Activity in 
Galaxies and Related Phenomena}.

\reference Mahadevan, R. 1997, \apj, 477, 585

\reference Mahadevan, R. 1998, \nat, 394, 651

\reference Manmoto, T., Mineshige, S., Kusunose, M. 1997, \apj, 489, 791

\reference Melia, F. 1992, \apj, 387, L25

\reference Melia, F. 1994, \apj, 426, 577

\reference Mezger, P.G., Duschl, W.J., \& Zylka, R. 1996, A\&AR, 7, 289

\reference Mirabel, I.F. et al. 1998, \aa, 330, L9

\reference Molteni, D., Lanzafame, G., \& Chakrabarti, S.K. 1994, \apj, 425, 161

\reference Nakamura, K.E. 1998, \pasj, 50, L11

\reference Narayan, R., Mahadevan, R., Grindly, J.E., Popham, R., \& Gammie, C.
1998, \apj, 492, 554

\reference Narayan, R., Yi, I., \& Mahadevan, R., 1995, \nat, 374, 623

\reference Quataert, E., \& Narayan, R. 1999, \apj, 520, 298

\reference Rawlings, S. \& Saunders, R. 1991, \nat, 349, 138

\reference Reynolds, C.S. et al. 1996, \mn, 283, L111

\reference Spruit, H.C. 1996, in `Physical Processes in Binary Stars', 
eds. R.A.M.J. Wijers, M.B. Davies and C.A. Tout, Kluwer Dordrecht, p249

\reference Stanger, V.J. \& Warwick, R.S. 1986, \mn, 220, 363

\reference Stone J.M., Pringle J.E., \& Begelman M.C. 1999, \mn,
310, 1002

\reference Yi, I. \& Boughn, S.P. 1998, \apj, 499, 198

%\reference Yi, I. \& Boughn, S.P. 1999, \apj, 515, 576

\reference Yuan, F. 1999, \apj, 521, L55

\reference Yuan, F., Peng, Q., Lu, J.F., \& Wang, J.M. 2000, \apj, in press
(astro-ph/0002068)

\end{thebibliography}

\end{document}
\end


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