\documentstyle[epsf,psfig]{mn}

\newcommand{\abs}[1]{\mbox{$\left|{#1}\right|$}}

\newcommand{\ranktwo}[3]{\mbox{${#1}{#2}{#3}$}}
\newcommand{\rankfour}[5]{\mbox{${#1}{#2}{#3}{#4}{#5}$}}
\newcommand{\fracd}[2]{\frac{\displaystyle{#1}}{\displaystyle{#2}}}
\newcommand{\mh}{m_{\rm H}}
\newcommand{\dd}{{\rm d}}

\newcommand{\civ}{C\,{\sc IV}}
\newcommand{\civa}{C\,{\sc IV}\,1550\aa}
\newcommand{\ha}{H$\alpha$}
\newcommand{\hb}{H$\beta$}
\newcommand{\hg}{H$\gamma$}
\newcommand{\heii}{He\,{\sc II}}
\newcommand{\heiia}{He\,{\sc II}\,4686\aa}
\newcommand{\hei}{He\,{\sc I}}
\newcommand{\heia}{He\,{\sc I}\,5876\aa}
\newcommand{\taumax}{\tau_{\rm max}}

\newcommand{\het}{{\em HET}}
\newcommand{\hst}{{\em HST}}
\newcommand{\iue}{{\em IUE}}
\newcommand{\kronos}{{\em Kronos}}

\newcommand{\kms}{km~s$^{-1}$}
\newcommand{\dv}{\Delta V}
\newcommand{\vrms}{V_{\sc RMS}}
\newcommand{\memecho}{{\sc MEMECHO}}


\begin{document}

\title[ Echo Maps of Mrk~110]
{ Velocity-Delay Maps of Broad Emission Lines in Mrk 110}

\author[Horne]
{
Keith Horne$^{1}$, Kollatschny, W.$^{2}$, (Welsh, W.F.?)
\\ $^{1}$Physics and Astronomy,
	University of St.~Andrews,
	KY16 9SS, Scotland, UK
\\ ( \verb"kdh1@st-and.ac.uk")
\\ $^{2}$Universit\"{a}ts-Sternwarte G\"{o}ttingen,
	Greismarlandstra$\beta$e 11,
	D-37083 G\"{o}ttingen, Germany
\\ ( \verb"wkollat@uni-sw.dwdg.de")
}

\date{Accepted . Received ; 
in original form }

\maketitle

\begin{abstract} 


We present velocity-delay maps for
Balmer, \hei, and \heii\ emission
from the active nucleus of the Seyfert~1 galaxy Mrk 110
based on spectral variations observed with the
9.2~m \het\ at Mc~Donald Observatory.

\end{abstract} 

\begin{keywords}
( ?? )
\end{keywords}

\section{Introduction}
\label{sec:intro}
\typeout{ introduction }

The correlation between black hole mass and the properties
of the bulge stellar population in nearby galaxies
(macgorian,ferrarese)
indicates that nuclear black holes are intimately
connected with the formation and evolving structure
of their host galaxies.
Masses for black holes in nearby galactic nuclei can be
estimated from observations of stellar velocity distributions 
at small angular separations from the nucleus
(refs).
This technique works well for nearby galaxies, but
becomes difficult for more distant galaxies and 
for galaxies with active nuclei (AGN).

In Seyfert~1 galaxies
exhibiting Broad Emission-line Regions (BLR),
black hole masses can be estimated from measurments of
the emission-line velocity dispersion,
and time delays from monitoring continuum and
emission line flux variations (refs).
The emission line variations lag behind those seen in
the continuum, the lines being driven by photo-ionisation,
and the delays arising from light travel time.
These reverberation masses are generally in good agreement,
(ferrarese)
and enable the method to be extended to much greater
distances.
Indeed, by using reverberation masses to calibrate
secondary mass estimators (Peterson,Wandel,..),
a method analogous to distance ladder techniques,
the black hole masses can be estimated at large redshifts
to assist in population studies of the growth and evolution
of black holes and their host galaxies (ref).

While substantial evidence for the presence
of virial motions validates the use of this assumption
in deriving black hole masses (petererson),
the results are still relatively crude because
the detailed geometry and kinematics of the BLR gas
is not well understood (krolik).
One set of models envisions the gas arising from an
accretion disk wind,
driven either magnetically \cite{bp82,b+97}
or by radiation pressure \cite{cm96,psk00}.
Alternatively, galactic centres are often the sites
of bursts of star formation,
and the nuclear black holes thereby attract 
tight star clusters that interact dynamically with the black hole.
Our own galactic centre is a good example (ref).
The BLR gas may have a more isotropic velocity
distribution if it arises from debris stripped
or evaporated from the obiting stars.
The reverberation masses are uncertain by factors
of order 3 due to the uncertain geometry.

The geometry and kinematics of the BLR can be probed
by using the observed spectral variations to
construct velocity-delay maps of the emission-line gas
(refs).
The velocity-delay distribution is strongly dependent
on the nature of the flow \cite{wh91,prf92}.
This technique achieves micro-arcsecond resolution,
and may help to discriminate among various models
currently under consideration.
The method has been used to construct velocity-delay maps
of \civa\ emission based on
\iue\ observations of NGC~4151 \cite{uh96},
and \hst\ observations of NGC~5548 \cite{dk96}.
The maps are generally consistent with virial motion,
and rule out BLR models with purely radial motion.
The delay resolution of these maps is of order 5-10 days,
limited by the number of spectra (typically $\sim 50$)
and systematic errors in the
\iue\ and early \hst\ spectrophotometry ($\approx 2-3$\%).
This is typical of most of the AGN monitoring campaigns
undertaken to date.
As a consequence, the velocity-delay maps are not yet sharp
enough to cleanly discriminate among several competing BLR models.

With the advent of robotic and queue-scheduled spectroscopy on
ground-based telescopes, sustained monitoring
of AGNs may soon become more routine.
There is also some possibility that as the \hst\ 
approaches the climax of its active life it will be
used in a relatively low-cost observing mode for
sustained monitoring of selected targets,
as was the case with \iue.
These opportunities may enable substantially improve
resolution of velocity-delay maps of AGNs.
The delay resolution improves roughly in proportion to the
duration and signal-to-noise ratio of the observations,
up to a limit set by the time resolution.
Assuming that post-calibration systematic errors
can be kept at or below 1/%, 1-day time resolution by daily
monitoring sustained for 200 days.
Ground-based monitoring will be limited to optical lines, but
parallel /hst/ observations could provide ultraviolet lines
needed for 5-dimensional mapping \cite{hkg03}.
The proposed \kronos\ mission would routinely deliver
micro-arcsecond velocity-delay maps for a variety of ultraviolet
and optical lines, with time-lapse mapping capabilities
to track fine structures such as spiral wave patterns on AGN
disks or debris trails behind individual stars.

In this paper we construct velocity-delay maps for
the optical emission lines in Mrk~110 based on 
a 26-epoch campaign of spectroscopic \het\ observations.
Section~\ref{sec:obs} summarises the \het\ observations,
data reduction, and previous cross-correlation analysis.
Section~\ref{sec:maps} fits a reverberation model to the 
observed spectral variations to derive velocity-delay maps
for the emission lines.
Section~\ref{sec:maps} discusses the results,
and Section~\ref{sec:maps} summarises the main conclusions.

\section{Observations and Cross-Correlation Analysis}
\typeout{Observations}
\label{sec:obs}

The observations taken with the \het\
are described elsewhere \cite{k+01}.
Briefly, these consist of 26 spectra taken 
with the LRS spectrograph at the prime focus of the \het\,
obtained on 26 nights during the 183-day interval
1999~Nov~13 to 2000~May~14.
The mean and median time sampling are 7.3
and 3.0 days, respectively.
The spectra cover 4200\aa\ to 6900\aa\ with
a velocity resolution of 460~\kms\ at 5000~\aa.

The data reduction is also described elsewhere \cite{k03}.
The observed spectra were corrected for small instrumental
and seeing-induced pixel shifts and blurring, 
and then renormalized to make the fluxes of narrow emission
lines constant in time.
After transformation to the emitted frame,
a pseudo-continuum was fitted to each spectrum,
and lightcurves were extracted by summing over selected
wavelength intervals to sample the continuum at several
wavelengths, and emission lines in velocity bins.
A common velocity grid with a velocity of
either $\dv=200$~\kms\ or $\dv=400$\kms\
was used for the \ha, \hb, \heia, and \heiia,
emission lines.

A cross-correlation analysis of these lightcurves \cite{k03}
has already revealed evidence for virial motions,
estimates for the black hole mass, 
$M\sin{i} \approx 2\times10^7M_\odot$,
and longer delays in the red wing of the line
suggesting that the broad emission lines
arise from an accretion disc wind.
The velocity-resolved cross-correlation function between
emission-line and continuum lightcurves is
\begin{equation}
	CCF(V, \tau)
	=
	\int\ \eta_c( t - \tau )\ \eta_\ell( V, t )\ \dd t
\ ,
\end{equation}
where $\eta_c(t)$ and $\eta_\ell$
are normalized versions of the continuum
and velocity-resolved emission-line lightcurves, respectively,
e.g., interpolated from the observations.
The average time delay, or `lag', is defined by
\begin{equation}
	\left< \tau \right>
	= \int_{\tau_1}^{\tau_2} \tau\ \dd \tau\
	\int \dd V\
	CCF( V, \tau )
\ ,
\end{equation}
averaging over a delay range $\tau_1$ to $\tau_2$
bracketing the peak of the cross-correlation peak.
Assuming that the time delays arise principally from light-travel time,
the measurement of $\left< \tau \right>$ estimates the size of the 
emission-line region, 
\begin{equation}
        \left< R \right> = c
        \left< \tau \right>
\ ,
\end{equation}
with $c$ the speed of light.
The measured delays correlate inversely with the velocity dispersion
of the variable component of the emission-line flux,
$\left<\tau\right> \propto 1/\left<V^2\right>$,
consistent with and providing evidence for virial motions.
The black hole mass is then estimated via
\begin{equation}
 M =   \fracd{f\,c}{G} \left<V^2\right> \left< \tau \right>
\ ,
\end{equation}
with $G$ the gravitational constant and $f$ a fudge factor
depending on the uncertain geometry of the virial flow,
e.g., $f\propto\sin{i}$ for a Keplerian disk at inclination angle $i$.

\section{Velocity-Delay Maps}
\typeout{Velocity-Delay Maps}
\label{sec:maps}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}
\begin{tabular}{c}
\psfig{file=hbfit.ps,angle=0,width=7.5cm}
\end{tabular}
\caption[] {\small
\memecho\ fit to continuum measurements (bottom)
and velocity-resolved emission-line measurements
(top right) deterine delay maps for each velocity bin
(top left).
This fit to the \hb\ emission line achieves $\chi^2/N=1$.
}
\label{fig:1}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



The velocity-delay maps $\Psi(V,\tau)$ describe
spectral variations $f(\lambda,t)$
in terms of delayed responses to variations in a `driving'
lightcurve $X(t)$.
\begin{equation}
	f(V,t)
	= b(\lambda)
	+ \int_0^{\taumax}
	\Psi( V,\tau)\ X(t-\tau)\ \dd\tau
\ .
\end{equation}
In this reverberation model, 
the time-independent `background' spectrum, 
$b(\lambda)$ accounts for steady light sources,
such as starlight and emission from regions
too large to reverberate on the monitoring timescale.
For the maximum time delay, $\taumax$, we adopt 50 days,
about $1/3$ of the duration of the monitoring observations.
For the `driving lightcurve', $X(t)$, we adopt a fit to
the observed variations in the continuum at 5130\aa\,
\begin{equation}
	X(t) = f_c(t) - f_0
\ ,
\end{equation}
where we subtract a constant $f_0$, taken to be flux
exceeded by 95\% of the continuum measurements.


We have used the \memecho\ code \cite{hwp91,h94,uh96}
to fit the above reverberation model to the observed spectral variations.
The fit adjusts the driving lightcurve
$X(t)$, the background spectrum $b(\lambda)$,
and the velocity-delay map $\Psi(V,\tau)$.
The fit attempts to minimize $\chi^2$, but is regularized
by a maximum entropy criterion designed to deliver,
roughly speaking, the `smoothest' functions
that fit the data at specified levels of $\chi^2$.
Fig.~\ref{fig:1} shows a representative fit to
the observed lightcurves
in selected velocity bins across the \hb\ profile.


We have constructed maps $\Psi(V,\tau)$ for 5 emission lines,
\ha, \hb, \hb, \heia, and \heiia.
Fig.~\ref{fig:2} shows one map for each line, while
Figs.~\ref{fig:3} thru \ref{fig:7} show 9
maps for each line, to illustrate the trade-off between
noise and resolution, and between smearing in $v$ vs $\tau$.




For each line we have constructed 18 maps,
considering two different velocity binnings,
$\dv=200$~\kms\ and $\dv=400$~\kms,
3 different $\chi^2$ levels, $\chi^2/N=1$, 1.5, and 2,
and 3 different values of a control parameter,
$A=0$, 0.1, and 1.
When the control parameter $A$ is 0, there is no connection
between adjacent velocity bins, and the entropy makes $\Psi(V,\tau)$
`as smooth as possible' in the $\tau$ direction.
For $a=0.1$ there is a mild connection between adjacent
velocity bins, and for $a=1$ the connection is stronger,
causing the maps to become smoother in $v$ and less smooth in $\tau$.


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure*}
\begin{tabular}{cc}
\ha & \heia \\
\psfig{file=ha200c1.0a0.0.ps,angle=-90,width=8cm}
&
\psfig{file=hei200c1.0a0.0.ps,angle=-90,width=8cm}
\\
\hb & \heiia \\
\psfig{file=hb200c1.0a0.0.ps,angle=-90,width=8cm}
&
\psfig{file=heii200c1.0a0.0.ps,angle=-90,width=8cm}
\\
\hg & \\
\psfig{file=hg200c1.0a0.0.ps,angle=-90,width=8cm}
\\
\end{tabular}
\caption[] {\small
Velocity-delay maps $\Psi(V,\tau)$ for optical
emission lines in Mrk~110.
The velocity and delay resolution
are $\Delta v=200$~km~s$^{-1}$ and $\Delta\tau=1$~d,
and the maps are for $\chi^2/N=1$ and $A=0$.
}
\label{fig:2}
\end{figure*}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure*}
\begin{tabular}{cc}
\ha & \heia \\
\psfig{file=ha200eta.ps,angle=-90,width=8cm}
&
\psfig{file=hei200eta.ps,angle=-90,width=8cm}
\\
\hb & \heiia \\
\psfig{file=hb200eta.ps,angle=-90,width=8cm}
&
\psfig{file=heii200eta.ps,angle=-90,width=8cm}
\\
\hg & \\
\psfig{file=hg200eta.ps,angle=-90,width=8cm}
\\
\end{tabular}
\caption[] {\small
Normalized residuals of the \memecho\ fit 
as a function of velocity and time for each of
the emission lines in Fig.~\ref{fig:2}.
}
\label{fig:2a}
\end{figure*}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure*}
\begin{tabular}{ccc}
\ha $A=0$ $\chi^2/N=1$ 
& $A=0.1$ $\chi^2/N=1$ 
& $A=1$ $\chi^2/N=1$ \\
\psfig{file=ha200c1.0a0.0.ps,angle=-90,width=4cm}
&
\psfig{file=ha200c1.0a0.1.ps,angle=-90,width=4cm}
&
\psfig{file=ha200c1.0a1.0.ps,angle=-90,width=4cm}
\\
\ha  $A=0$ $\chi^2/N=1.5$ 
& $A=0.1$ $\chi^2/N=1.5$ 
& $A=1$ $\chi^2/N=1.5$ \\
\psfig{file=ha200c1.5a0.0.ps,angle=-90,width=4cm}
&
\psfig{file=ha200c1.5a0.1.ps,angle=-90,width=4cm}
&
\psfig{file=ha200c1.5a1.0.ps,angle=-90,width=4cm}
\\
\ha $A=0$ $\chi^2/N=2$ 
& $A=0.1$ $\chi^2/N=2$ 
& $A=1$ $\chi^2/N=2$ \\
\psfig{file=ha200c2.0a0.0.ps,angle=-90,width=4cm}
&
\psfig{file=ha200c2.0a0.1.ps,angle=-90,width=4cm}
&
\psfig{file=ha200c2.0a1.0.ps,angle=-90,width=4cm}
\\
\end{tabular}
\caption[] {\small
\ha\  velocity-delay maps $\Psi(V,\tau)$
with $\Delta v=200$~km~s$^{-1}$ $\Delta \tau=1$~d.
Columns vary $\chi^2/N=1,1.5,2$ and rows vary $A=0,0.1,1$.
}
\label{fig:3}
\end{figure*}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure*}
\begin{tabular}{ccc}
\hb $A=0$ $\chi^2/N=1$ 
& $A=0.1$ $\chi^2/N=1$ 
& $A=1$ $\chi^2/N=1$ \\
\psfig{file=hb200c1.0a0.0.ps,angle=-90,width=4cm}
&
\psfig{file=hb200c1.0a0.1.ps,angle=-90,width=4cm}
&
\psfig{file=hb200c1.0a1.0.ps,angle=-90,width=4cm}
\\
\hb $A=0$ $\chi^2/N=1.5$ 
& $A=0.1$ $\chi^2/N=1.5$ 
& $A=1$ $\chi^2/N=1.5$ \\
\psfig{file=hb200c1.5a0.0.ps,angle=-90,width=4cm}
&
\psfig{file=hb200c1.5a0.1.ps,angle=-90,width=4cm}
&
\psfig{file=hb200c1.5a1.0.ps,angle=-90,width=4cm}
\\
\hb $A=0$ $\chi^2/N=2$ 
& $A=0.1$ $\chi^2/N=2$ 
& $A=1$ $\chi^2/N=2$ \\
\psfig{file=hb200c2.0a0.0.ps,angle=-90,width=4cm}
&
\psfig{file=hb200c2.0a0.1.ps,angle=-90,width=4cm}
&
\psfig{file=hb200c2.0a1.0.ps,angle=-90,width=4cm}
\\
\end{tabular}
\caption[] {\small
\hb\ velocity-delay maps $\Psi(V,\tau)$
with $\Delta v=200$~km~s$^{-1}$ $\Delta \tau=1$~d.
Columns vary $\chi^2/N=1,1.5,2$ and rows vary $A=0,0.1,1$.
}
\label{fig:4}
\end{figure*}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\begin{figure*}
%\begin{tabular}{ccc}
%\hg\ $A=0$ $\chi^2/N=1$ 
%& $A=0.1$ $\chi^2/N=1$ 
%& $A=1$ $\chi^2/N=1$ \\
%\psfig{file=hg200c1.0a0.0.ps,angle=-90,width=4cm}
%&
%\psfig{file=hg200c1.0a0.1.ps,angle=-90,width=4cm}
%&
%\psfig{file=hg200c1.0a1.0.ps,angle=-90,width=4cm}
%\\
%H$\gamma$ $A=0$ $\chi^2/N=1.5$ 
%& $A=0.1$ $\chi^2/N=1.5$ 
%& $A=1$ $\chi^2/N=1.5$ \\
%\psfig{file=hg200c1.5a0.0.ps,angle=-90,width=4cm}
%&
%\psfig{file=hg200c1.5a0.1.ps,angle=-90,width=4cm}
%&
%\psfig{file=hg200c1.5a1.0.ps,angle=-90,width=4cm}
%\\
%H$\gamma$ $A=0$ $\chi^2/N=2$ 
%& $A=0.1$ $\chi^2/N=2$ 
%& $A=1$ $\chi^2/N=2$ \\
%\psfig{file=hg200c2.0a0.0.ps,angle=-90,width=4cm}
%&
%\psfig{file=hg200c2.0a0.1.ps,angle=-90,width=4cm}
%&
%\psfig{file=hg200c2.0a1.0.ps,angle=-90,width=4cm}
%\\
%\end{tabular}
%\caption[] {\small
%\hg\  velocity-delay maps $\Psi(V,\tau)$
%with $\Delta v=200$~km~s$^{-1}$ $\Delta \tau=1$~d.
%Columns vary $\chi^2/N=1,1.5,2$ and rows vary $A=0,0.1,1$.
%}
%\label{fig:5}
%\end{figure*}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure*}
\begin{tabular}{ccc}
\heia\ $A=0$ $\chi^2/N=1$ 
& $A=0.1$ $\chi^2/N=1$ 
& $A=1$ $\chi^2/N=1$ \\
\psfig{file=hei200c1.0a0.0.ps,angle=-90,width=4cm}
&
\psfig{file=hei200c1.0a0.1.ps,angle=-90,width=4cm}
&
\psfig{file=hei200c1.0a1.0.ps,angle=-90,width=4cm}
\\
\heia\ $A=0$ $\chi^2/N=1.5$ 
& $A=0.1$ $\chi^2/N=1.5$ 
& $A=1$ $\chi^2/N=1.5$ \\
\psfig{file=hei200c1.5a0.0.ps,angle=-90,width=4cm}
&
\psfig{file=hei200c1.5a0.1.ps,angle=-90,width=4cm}
&
\psfig{file=hei200c1.5a1.0.ps,angle=-90,width=4cm}
\\
\heia\ $A=0$ $\chi^2/N=2$ 
& $A=0.1$ $\chi^2/N=2$ 
& $A=1$ $\chi^2/N=2$ \\
\psfig{file=hei200c2.0a0.0.ps,angle=-90,width=4cm}
&
\psfig{file=hei200c2.0a0.1.ps,angle=-90,width=4cm}
&
\psfig{file=hei200c2.0a1.0.ps,angle=-90,width=4cm}
\\
\end{tabular}
\caption[] {\small
\heia\ velocity-Delay maps $\Psi(V,\tau)$
with $\Delta v=200$~km~s$^{-1}$ $\Delta \tau=1$~d.
Columns vary $\chi^2/N=1,1.5,2$ and rows vary $A=0,0.1,1$.
}
\label{fig:6}
\end{figure*}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure*}
\begin{tabular}{ccc}
\heiia\ $A=0$ $\chi^2/N=1$ 
& $A=0.1$ $\chi^2/N=1$ 
& $A=1$ $\chi^2/N=1$ \\
\psfig{file=heii200c1.0a0.0.ps,angle=-90,width=4cm}
&
\psfig{file=heii200c1.0a0.1.ps,angle=-90,width=4cm}
&
\psfig{file=heii200c1.0a1.0.ps,angle=-90,width=4cm}
\\
\heiia\ $A=0$ $\chi^2/N=1.5$ 
& $A=0.1$ $\chi^2/N=1.5$ 
& $A=1$ $\chi^2/N=1.5$ \\
\psfig{file=heii200c1.5a0.0.ps,angle=-90,width=4cm}
&
\psfig{file=heii200c1.5a0.1.ps,angle=-90,width=4cm}
&
\psfig{file=heii200c1.5a1.0.ps,angle=-90,width=4cm}
\\
\heiia\ $A=0$ $\chi^2/N=2$ 
& $A=0.1$ $\chi^2/N=2$ 
& $A=1$ $\chi^2/N=2$ \\
\psfig{file=heii200c2.0a0.0.ps,angle=-90,width=4cm}
&
\psfig{file=heii200c2.0a0.1.ps,angle=-90,width=4cm}
&
\psfig{file=heii200c2.0a1.0.ps,angle=-90,width=4cm}
\\
\end{tabular}
\caption[] {\small
\heiia\ velocity-Delay maps $\Psi(V,\tau)$
with $\Delta v=200$~km~s$^{-1}$ $\Delta \tau=1$~d.
Columns vary $\chi^2/N=1,1.5,2$ and rows vary $A=0,0.1,1$.
}
\label{fig:7}
\end{figure*}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\section{Discussion}
\typeout{Discussion}
\typeout{Conclusion}
\section{Conclusion}
 
\begin{thebibliography}{}


\bibitem[\protect\citename{Blandford \& Payne} 2003]{bp82}
	Blandford, R.D., Payne, D.G.
	1982, MNRAS, 199, 883.
\bibitem[\protect\citename{Bottorof, et~al.} 1997]{b+97}
	Bottorof, M., Korista, K.T., Shlosman, I., Blandford, R.D.
	1997, ApJ, 479, 200.
\bibitem[\protect\citename{Chiang \& Murray} 1996]{cm96}
	Chiang, J., Murray, N.
	1996, ApJ, 466, 704.
\bibitem[\protect\citename{Done \& Krolik} 1996]{dk96}
	Done, C., Krolik, J.H.
	1996, ApJ, 463, 144.
\bibitem[\protect\citename{Horne, Welsh, Peterson} 2003]{hwp91}
	Horne, K., Welsh, W.F, Peterson, B.M.
	1991, ApJ 367, L5.
\bibitem[\protect\citename{Horne} 2003]{h94}
	Horne, K.,
	1994, ASP Conf. Ser. 69, 23.
\bibitem[\protect\citename{Horne, Korista, Goad} 2003]{hkg03}
	Horne, K., Korista, K.T., Goad, M.R.
	2003, MNRAS, 339, 367.
\bibitem[\protect\citename{Kollatschny} 2003]{k+01}
	Kollatschny, W., Bischoff, K., Robinson, E.L,
	Welsh, W.F. Hill, G.J.
	2001, A\&A, 379, 125.
\bibitem[\protect\citename{Kollatschny} 2003]{k03}
	Kollatschny, W.,
	2003, A\&A, 407, 461.
%(astro-ph/0306389).
\bibitem[\protect\citename{Perez, Robinson, de la Fuente} 1992]{prf92}
	Perez, E., Robinson, A., de la Fuente, L.
	1992, MNRAS, 256, 103.
\bibitem[\protect\citename{Proga, Stone, Kallman} 2000]{psk00}
	Proga, D., Stone, J.M., Kallman, T.R.
	2000, ApJ, 543, 686.
\bibitem[\protect\citename{Ulrich \& Horne} 1996]{uh96}
	Ulrich, M.-H., Horne, K.,
	1996, MNRAS, 283, 748.
\bibitem[\protect\citename{Welsh \& Horne} 1991]{wh91}
	Welsh, W.F., Horne, K.,
	1991, ApJ, 379, 586.

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