\documentclass[12pt,preprint]{aastex}
\shorttitle{The rotating accretion disk surrounding NGC\,7538\,S}
\shortauthors{Sandell et al.}
\slugcomment{Edited April 17, 2008}

\begin{document}

\def\arcmin{{$^{\prime}$}}
\def\arcsec{{$^{\prime\prime}$}}
\def\ptsec{$''\mskip-7.6mu.\,$}
\def\psec{$^s\mskip-7.6mu.\,$}
\def\Msun{\,{\rm M$_{\odot}$}}
\def\Lsun{\,{\rm L$_{\odot}$}}
\def\ltsim{$\stackrel{<}{\sim}$}
\def\gtsim{$\stackrel{>}{\sim}$}
\def\jtra#1#2{${\rm J}\!\!=\!\!{#1}\!\!\to\!\!{#2}$}

%** added
\def\degr{$^{\circ}$}
%\def\arcmin{''}

\title{A detailed study of the rotating accretion disk surrounding the high-mass protostar NGC\,7538\,S (Paper I)}


\author{G\"oran Sandell\altaffilmark{1}, Melvyn Wright\altaffilmark{2}, W. M. Goss\altaffilmark{3}}

\altaffiltext{1}{SOFIA-USRA, NASA Ames Research Center, MS N211-3,
Moffett Field, CA 94035, U.S.A.}
\email{Goran.H.Sandell@nasa.gov}
\altaffiltext{2}{Radio Astronomy Laboratory, University of California, Berkeley
601 Campbell Hall, Berkeley, CA 94720, U.S.A}
\altaffiltext{3}{National Radio Astronomy Observatory, P.O. Box O, Socorro, NM 87801, U.S.A.}

\begin{abstract}

We present deep high angular resolution observations  of the high-mass
protostar NGC\,7538\,S.  These observations confirm that NGC\,7538\,S is
surrounded by a rotating accretion disk, which drives a collimated
free-free jet and a very young, hot molecular outflow approximately
perpendicular to the rotating accretion disk.  Evidence for rotation is
seen in all optically thin molecular tracers, H$^{13}$CN J = $1 \to 0$,
HN$^{13}$C J = $1 \to 0$, H$^{13}$CO$^+$ J = $1 \to 0$, and DCN J = $3
\to 2$, although several molecules, particularly DCN and  H$^{13}$CO$^+$
appear to be affected by the hot molecular outflow.  CH$_3$CN J = 11
$\to$ 10 shows the disk very clearly, but is severely affected by the
outflow, especially at higher K-levels. Our new high-angular resolution
observations show that the rotationally supported part of the disk is
smaller than we previously estimated. The enclosed mass of the inner,
rotationally supported part of the disk (D = 5.5\arcsec{}, i.e 15,000
au) is $\sim$ 20 M$_{\odot}$.


\end{abstract}

\keywords{ISM: clouds -- (stars:) circumstellar matter -- stars:
formation -- stars: pre-main sequence -- submillimeter}

\section{Introduction}
\label{Intro}

How high-mass stars are formed is still under debate. High-mass stars
are believed to form the same way as low mass stars, i.e. with a
rotating accretion disk and driving an outflow, but in denser
environments and with much higher accretion rates \citep{Wolfire87,
Stahler00,Norberg00,McKee02}. However, others still argue that high-mass
stars are most likely formed by coalescence and mergers of
intermediate-mass protostars, see e.g. \citet{Bonnell98}.

Accretion disks are ubiquitous in young low- and intermediate-mass
stars, i.e. T Tauri and Herbig Ae stars
\citep{Simon01,Mannings97,Najita03}, which have sizes of one to a few
hundred AU and appear to be in Keplerian rotation. Disks are also common
in Class I objects, i.e. younger, more heavily embedded low- and
intermediate mass pre-main-sequence stars \citep{Brown99}, but there are
very few examples of confirmed disks for the very earliest stages of  a
low-mass protostar, the Class 0 phase \citep{Jorgensen04,Chandler05}. At
the Class 0 phase the temperature of the protostellar disk is of the
same order of that of the collapsing cloud core, and it is therefore an
observational challenge  to get enough contrast between the disk and the
cloud core.

The situation is even worse for high-mass stars, because they form in
much denser environments and always in clusters or small groups. The
survival time of disks in high-mass stars is furthermore expected to be
much shorter, because once the star is formed it will quickly photo
evaporate the disk as soon as the accretion from the surrounding cloud
starts to diminish, therefore allowing the uv-photons to reach the disk
surface. Yet there are several detections of disks around early B-stars;
Lkh$\alpha$\,101 (Sp. cl. B0) \citep{Tuthill02}. R Mon (Sp. cl. B0)
\citep{Fuente06}, MWC297 (Sp. cl. B1.5) \citep{Manoj07}, MWC\,349\,A
(Sp. cl. B  [e]) \citep{Weintroub08}, clearly confirming that disks do
exist around relatively massive stars.

Most young high-mass stars appear to drive outflows
\citep{Shepherd96,Zhang01,Zhang05,Beuther02b}, but whether they also
have accretion disks is less clear.  There have been many reports of
disks around high-mass stars, but only a few which appear well
supported. Two of the most clearcut cases are IRAS
$20126+4104$\citep{Cesaroni97,Cesaroni99, Cesaroni05,Zhang98}, and
AFGL\,490 \citep{Schreyer02,Shreyer06}. IRAS $20126+4104$ has a
luminosity of $\sim$ 1.3 10$^4$ \Lsun\ suggesting an early B star. The
star drives a parsec scale CO  outflow \citep{Wilking90,Shepherd00}, and
is surrounded by a rotating accretion disk with a diameter of $\sim$
15,000 A.U. \citep{Cesaroni05}. The observed rotation curve for an
edge-on Keplerian disk corresponds to $\sim$ 7 \Msun. The luminosity of
AFGL\,490, L $\sim$  2 10$^3$ \Lsun\ also suggests an early B-star. It
drives a  more compact outflow, 0.3~pc (corrected for inclination)
\citep{Lada81,Snell84} and is surrounded by a nearly face-on disk with a
radius  $\sim$ 1600 AU, which has  a disk mass of 1 \Msun\  and appears
to be in Keplerian rotation \citep{Schreyer06}. Another, even younger
high-mass protostar, NGC\,7538\,S, with a luminosity of $\sim$ 10$^4$
\Lsun,  which  is surrounded by a large, nearly edge-on disk with a
radius of 15,000 AU and a disk mass of $\sim$ 100 \Msun\ was reported by
\citet{Sandell03}. The disk drives a compact molecular outflow with a
size of 0.1 - 0.4 pc and shows a Keplerian-like rotation.

This disk is the target for our studies. In this paper (Paper I) we
present follow-up BIMA spectral line observations of several molecules
in the 3 and 1 mm bands, which were chosen to measure the rotation of
the disk surrounding NGC\,7538\,S. In a  companion paper
\citep[hereafter Paper II]{Wright08} we discuss high-angular resolution
continuum observations of NGC\,7538\,S and the Ultra-Compact \ion{H}{2}
regions NGC\,7538 IRS\,1 - 3 with BIMA, CARMA, and the VLA, which
provide us with a better mass estimate of the disk/envelope surrounding
the star.
% A third paper (Corder et al. 2008, in preparation), which also includes data from JCMT and Quabbin, looks at the large scale structure and outflow and accretion activity in the two star -forming cores NGC\,7538\,S, and NGC\,7538\,IRS\,1 - 3 with high-angular resolution.

%Paper I and II confirm that NGC\,7538\,S is surrounded
%by a massive, rotating  accretion disk. The higher angular resolution
%($\sim$ 3\arcsec{}) of these new observations compared to the data 
%presented in \citet{Sandell03} allow us to better characterize the disk and determine its physical properties,


\section{Observations and Data Reduction}

\subsection{BIMA array observations}
\label{BIMA}

Between 2002 and 2004 we obtained more observations on NGC\,7538\,S
with the BIMA array at  86 and 89 GHz. These observations are summarized
in Table \ref{tbl-1}. At 3.4~mm (87~GHz) we combined additional
data obtained in the B, C and D array configurations with the data
reported by \citep{Sandell03} to produce deep high fidelity maps in
H$^{13}$CN \jtra10, HCO$^+$ \jtra10, SO $2_2 \to 1_1$ and NH$_2$D
1$_{11}  \to  1_{01}$. We also improved the H$^{13}$CO$^+$ \jtra10,
HN$^{13}$C \jtra10, and SiO \jtra21, by adding a B-array track to the
existing C-array data. All these observations use the same correlator
setup and were reduced as described in  \citet{Sandell03}.

Table \ref{tbl-2} summarizes the spectral line observations at 1.4~mm
(220 GHz), which we have obtained with BIMA during the same time frame
as the 3.4~mm observations. These 1.4~mm observations were obtained in the B
and C configurations, and provide similar angular resolution as the 87
GHz data sets.  In this paper we discuss the results from the optically
thin DCN J = $3 \to 2$ and CH$_3$CN J = $12 \to 11$ (K = 0 to 5), which
were expected to be good tracers of the accretion disk. Our observations
also included SO  \jtra{5,5}{4,4}, H$_2$CO   3$_{03}  \to 2_{02}$ and 
3$_{22}  \to 2_{21}$, and  $^{13}$CO J = $2 \to 1$ (Table \ref{tbl-2}),
but the lines are optically thick and self-absorbed and do not provide
us any information on the deeply embedded accretion disk. We therefore
leave the discussion of these lines to a later paper. 

The 1~mm data were reduced and imaged in a standard way using MIRIAD
software \citep{Sault95}. The quasar 0102$+$584 was used as phase
calibrator and Mars and/or 3C84 for passband and flux calibration.  The
uncertainty in the absolute amplitude scale is $\sim$ 20\% at 1.4~mm,
but the relative amplitude of the spectral lines observed simultaneously
is $\sim$5 \%.

The BIMA array, like every interferometer, will filter out extended,
relatively uniform emission, resulting in an underestimate the
total emission (missing flux). Furthermore, extended emission will
cause negative features in the the spectra, which may look like
self-absorption. Since we expect to see self-absorption if the
protostellar disk is warmer than the surrounding cloud, it becomes
difficult, if not impossible, to judge what features are real, and what
are artifacts, unless we fill in missing short uv-spacings. We
therefore carried out observations with FCRAO at 3.4~mm band and with
JCMT at 1.4 mm to provide missing zero spacings for several key molecules.

\subsection{FCRAO observations}

The observations were carried out on November 9, 2004 by Dr. Mark
Heyer with the 14-m Five College Radio Astronomy Observatory (FCRAO)
telescope using the SEQUOIA 16 beam array receiver. The weather
conditions were excellent, resulting in a system temperature,
T$_{sys}$ $\sim$ 120~K. We used the dual channel correlator (DCC)
with a 50 MHz bandwidth and a spectral resolution of 48.8  kHz ( 0.16
km~s$^{-1}$). The DCC was configured to simultaneously cover  H$^{13}$CN
\jtra10 and HCO$^+$ \jtra10.  At 86 and 89 GHz the half-power beam width
(HPBW) is 58\arcsec\ and 57\arcsec, respectively, while the main-beam
efficiency, $\eta_{\rm mb} \sim$ 0.50. The observations were performed
using on-the-fly (OTF) mapping, covering a 9\arcmin\ $\times$ 9\arcmin\
area centered at \mbox{$\alpha_{2000.0}$ = 23$^h$ 13$^m$ 45\psec4},
\mbox{$\delta_{2000.0}$ = $+$61\degr{} 28\arcmin{} 10\ptsec5}, and
covering the whole molecular cloud associated with NGC\,7538. The OTF
maps were re-gridded to a cell size of 20\arcsec.

\subsection{JCMT observations}

Complementary single dish observations  (projects m04ai09 and m05ai07)
were carried out in service mode on the James Clerk Maxwell Telescope
(JCMT)\footnote{The JCMT is operated by the Joint Astronomy Centre,
on behalf of the UK Particle Physics and Astronomy Research Council,
the Netherlands Organization for Scientific Research, and the Canadian
National Research Council.} on Mauna Kea, Hawaii, between April 2004
and May 2005. With JCMT we obtained fully sampled maps of DCN \jtra32,
H$_2$CO   3$_{03}  \to 2_{02}$ and 3$_{22}  \to 2_{21}$, $^{13}$CO
\jtra21, and C$^{18}$O \jtra21, as well as long integration (10 - 30 min)
single spectra at the center position (NGC\,7538\,S. We also took deep
(long integration) spectra of $^{12}$CO and  C$^{17}$O \jtra21. All these
observations used receiver RxA3, a single beam SiS mixer covering the
1.3~mm spectral window. At 217 GHz the measured HPBW is 22\ptsec3 and
the main beam efficiency, $\eta_{\rm mb}$ = 0.60. All maps were done
in OTF-mode with heavy oversampling: 5\arcsec\ sampling interval  with
an integration time of 5 second per resolution element. The maps have a
size of 55\arcsec\ $\times$ 45\arcsec. We used the Digital Autocorrelator
Spectrometer (DAS) with 125 MHz bandwidth ($^{13}$CO and C$^{18}$O) or
250 MHz bandwidth (DCN, H$_2$CO) providing us with spectral resolutions
of 78.1 kHz and 156.2 kHz, respectively. Most of the observing was done in
wet weather conditions, resulting in system temperatures, T$_{sys}$ of 400
- 450~K. The receiver calibration was regularly checked on planets (Uranus
or Mars) and we always took reference spectra on NGC\,7538\,IRS\,1.

Our DCN setup also included the SiO \jtra43 transition at 217.10494
GHz. In total we acquired 10 maps, because the line is rather faint. Some
scans had poor baseline stability and had to be thrown out, and even
for most of the observations we had to use high order polynomials
for baseline subtraction. During the data reduction we discovered an
additional line in our spectra, which we identified as the SO$_2$
13$_{2,12} \to 13_{1,13}$ at 225.153689 GHz, i.e. in the upper
sideband. SiO and SO$_2$ show broad line wings, indicating that the
emission is strongly affected by the outflow. The DCN-map shows that
the emission is rather compact  with a size of $\sim$ 30\arcsec. When we
added it to the BIMA data, one cannot see any changes in the morphology
of the DCN emission. However, since the combined map had poorer signal
to noise due to insufficient integration time, we only make use of the
high-angular resolution BIMA map in this paper.

Both H$_2$CO transitions were observed simultaneously. We obtained
three maps with good quality. The coadded map matched well the noise
level we had in our BIMA data. At $^{13}$CO \jtra21 we obtained a
total of 7 maps, largely because we needed good SNR on the faint wings
from the outflow. The coadded map was of very good quality and was
successfully added to our BIMA data set on  $^{13}$CO. For C$^{18}$O
\jtra21 we obtained  4 maps, also of good quality, Since we never mapped
NGC\,7538\,S  with BIMA in C$^{18}$O, we have used this map stand-alone
to look at the large scale morphology of the cloud core.  

%SO2  13(2,12) - 13(1,13) at 225.153689 
% N       Amp.        Width (km/s  )    Pos'n (km/s  ) 
%                  1      0.190           6.79           -56.06

\section{Results and Analysis}

%All spectral line and continuum images, except NH$_2$D, peak
%approximately at the position of NGC\,7538\,S, where they  show a
%resolved, $\sim$ 10\arcsec\ elliptical source, which surrounded by
%fainter extended emission from the dense cloud core in which
%NGC\,7538\,S is embedded. NH$_2$D 1$_{11}  \to  1_{01}$, SO $2_2 \to
%1_1$, HCO$^+$ \jtra10, and H$^{13}$CN \jtra10 also trace  the narrow
%dust filaments \citep{Sandell04}, which runs through NGC\,7538\,S from
%southwest to northeast. Some molecules, in particular HCO$^+$, SiO, SO, $^{13}$CO and even H$_2$CO also trace high velocity outflows. Each molecule, however, appear to show
%morphological differences (Paper III). At high angular resolution one
%starts to see additional sub-structure (clumps), which may already have
%formed stars in their interior , or which may be in the process of
%forming stars. Deep VLA continuum observations from 6 cm to 1.3 cm only
%show a single double peaked source in the NGC\,7538\,S cloud core (Fig.
%\ref{fig-vla}), even though H$_2$O and CH$_3$CH maser observations and
%HCO$^+$ \jtra10 and CO \jtra32 maps show that there are other young
%stars in the vicinity, which drive outflows and excite maser emission.
%These observations will be discussed in detail in Paper II.

%

%\subsection{Line emission}

In Fig. \ref{fig-spectra}{} we show spectra towards NGC\,7538\,S of all
the molecular transitions, which have been observed with BIMA in the
3~mm and 1~mm band, except  the CH$_3$CN J = 11 $\to$ 10 lines, which we
will cover in Section \ref{mcn}. Although some of the changes in the
line profiles are due to  different  spatial resolution, this effect is
rather minor, especially since most of the spectral lines have been
observed with roughly the same angular resolution (Table \ref{tbl-1} \&
\ref{tbl-2}). Most of the differences in line shape results from whether
the lines are optically thick or thin, and whether they originate from
the disk, the outflow, or the cloud envelope. Almost all the the lines
observed in the 1~mm band are optically thick, have strong line wings,
and show deep self-absorption from the surrounding cloud envelope. The
same is also true for HCO$^+$ \jtra{10}, SiO \jtra{2}{1}, and SO 
\jtra{2,2}{1,1} in the 3~mm band. In this paper we are focusing on the
accretion disk, and we therefore limit our analysis to optically thin
high density tracers, which have dipole moments of 3 Debye or larger,
i.e.  H$^{13}$CN, HN$^{13}$C, DCN, H$^{13}$CO$^+$, CH$_3$$^{13}$CN, and
CH$_3$CN.  These molecules are expected to be good tracers of the gas in
the dense disk surrounding NGC\,7538\,S. Most of them are isotopomers,
which have molecular abundance ratios of $\lesssim$ 10$^{-10}$ compared to
H$_2$. One would therefore expect them to be optically thin, but as we
will see later, this is not the case for all of the lines. Several of
them are also affected by emission from the molecular outflow. we have 
therefore carefully inspected each image cube  to see whether the
line emission originates from the disk, the outflow,  or whether both
the disk and the outflow contribute to the emission. The gas in the
surrounding cloud core is also very dense and
colder than the gas in the disk. It can therefore absorb some of the
emission from the disk. However, since the surrounding envelope is much
more extended than the disk and relatively uniform, it is largely
filtered out in these interferometer observations, but may nevertheless
add some contribution to the line profiles observed towards the
accretion disk.


%In Fig.~\ref{fig-3mmspec} we show spectra of all molecular transitions observed
%in the 3~mm band observed with BIMA.  We did not detect DCO$^+$ \jtra10. The DCN
%\jtra10 is much weaker than the J = $3 \to 2$ transition and have different
%spectral line profile. We did not even detect the line in the B-array data,
%suggesting that DCN \jtra10 is more extended and completely dominated by
%emission form the dense cloud core surrounding the protostar. DCN \jtra32 and
%CH$_3$CN \jtra{12}{11} emission is only seen towards the protostellar core.


In order to determine the systemic velocity of the disk, we imported
spectra from BIMA images into the IRAM single dish spectral line reduction
package CLASS. CLASS has a really good Gaussian fitting routine, which allows
fitting for optical depth of lines with hyperfine structure (method hfs) or to
derive more accurate radial velocities by locking the velocity separation for
satellite lines to the main emission component as long as all the spectral
transitions are observed within a single band. For this analysis we also
included deep, single dish JCMT spectra of the CO isotopomers C$^{18}$O, and
C$^{17}$O J = $2 \to 1$ to
determine the systemic velocity of the cloud.The results of these Gaussian fits
are given in Table \ref{tbl-3}.  C$^{18}$O \jtra21 and DCN \jtra32 show a narrow
self-absorption feature at the cloud velocity or at slightly red-shifted
velocities, suggesting that both have an optical depth of at least one in the
surrounding cloud core. H$^{13}$CN \jtra10 shows evidence for
self-absorption in the main hyperfine component at high angular resolutions, see
Section \ref{h13cn}. Even C$^{17}$O J = $2 \to 1$ shows a weak hint of self-absorption
and a fit to the hyperfine splitting of the molecule (method hfs) gives an
optical depth $\tau \sim$ 0.25. The results from Table  \ref{tbl-3} suggest a
systemic velocity of $-$56.0 $\pm$ 0.2 km~s$^{-1}$ . This agrees very well with
what we derive from the rotation curve of  H$^{13}$CN \jtra10, while the DCN rotation curve would suggest a slightly more red-shifted systemic velocity,  $-$55.7~km~s$^{-1}$.

\subsection{The NGC\,7538\,S star forming core}
\label{core}

The NGC\,7538\,S star forming core is a cold, dense cloud core $\sim$
80\arcsec\ south of NGC\,7538 IRS\,1 \citep{Werner79,Zhang98,Sandell04}.
It has a luminosity of $\sim$ 10$^4$ \Lsun\ and harbors at least one
massive protostar, NGC\,7538\,S \citep{Sandell03}.  \citet{Zhang98}, who
mapped the NGC\,7538 molecular cloud in NH$_3$ with the VLA at high
angular resolution, found the  strongest ammonia emission towards
NGC\,7538\S, in good agreement with the sub-mm continuum imaging by
\citet{Sandell04}.  In the vicinity of NGC\,7538\,S \citeauthor{Zhang98}
found the NH$_3$ emission to be optically thick with a temperature of
$\sim$ 25 K.

Our H$^{13}$CN \jtra10 map  with FCRAO and BIMA is in good agreement
with the dust continuum and the NH$_3$ results. Overall we find
H$^{13}$CN to show the same cloud morphology as the dust continuum. This
is shown in Figure \ref{fig-h13cn_nh2d_450}, where we overlaid the integrated H$^{13}$CN
emission from our combined FCRAO and BIMA map on the 450 $\mu$m SCUBA
continuum  map  from \citet{Sandell04} for the region around
NGC\,7538\,S. The dust continuum and the H$^{13}$CN emission both peak
on NGC\,7538\,S and the narrow south-western filament shows up clearly in
both images. The dust emission appears somewhat more extended than 
H$^{13}$CN to the east of NGC\,7538\,S, and there are also some
differences to the north, i.e. the southernmost part of the NGC\,7538
IRS\,1 cloud core. Most of these differences are most likely due to
difference in temperature of the emitting gas and dust. Since
\citet{Zhang98} found very strong, cold NH$_3$ emission towards
NGC\,7538\,S, we decided to look for NH$_2$D emission as well, which we
could observe with the same frequency setup as H$^{13}$CN and HCO$^+$
(Section \ref{BIMA}, Table \ref{tbl-1}).  The NH$_2$D emission is quite
faint, especially towards NGC\,7538\,S, but  the narrow, lumpy,
southwestern filament shows up very well in the integrated NH$_2$D
emission (Figure  \ref{fig-h13cn_nh2d_450}b). However, the  NH$_2$D emission is even stronger
to the east of NGC\,7538\,S, where it shows a ``continuation'' of the
southwestern filament, which is not evident in dust continuum, nor is it
seen in H$^{13}$CN or any other of the molecules that we have imaged
towards NGC\,7538\,S. Examination of NH$_2$D spectra along the filaments
show broadened lines at the positions of the knots in the filaments and
sudden, small velocity shifts between the knots, suggesting that these
``clumps'' maybe gravitationally unstable and that they may already have
formed stars. The only exception is the  NH$_2$D clump at the tip of the
eastern filament. This is where we find the  strongest  NH$_2$D
emission, but the lines are very narrow ($\Delta$v = 0.9 km~s$^{-1}$),
suggesting that this condensation is a very cold, prestellar core.



We can use our high-quality spectral line and continuum data to
estimate the size and total mass of the NGC\,7538\,S star forming
core. \citep{Sandell04} quoted a radius  of 0.4 pc (30\arcsec{}) and
a total mass of  750 \Msun, assuming an average dust temperature of
30~K. Using our combined FCRAO and BIMA map and radially averaging the
data, we find that the emission has a steeper fall-off  to a radius about
20\arcsec\ and and then flattens to an r$^{-1}$ power law extending to
$\sim$ 38 - 40\arcsec\ from the cloud center and about constant at larger
radii, suggesting that the core  size is $\sim$ one pc (38\arcsec{}). If
we assume an average gas temperature of 25~K, consistent with the
temperature derived from NH$_3$, and an [H$^{13}$CN/H$_2$] abundance of
5 $\times$ 10$^{-11}$ \citep[see e.g.]{Sandell05} we find a core mass
of $\sim$ 4,000 \Msun. Since this is several  times higher than the mass
derived by \citeauthor{Sandell04}, we have therefore  re-analyzed their
850 and 450 $\mu$m SCUBA data. If we radially average the 450 $\mu$m
map shown in Figure xx, we get a core size of 34\arcsec, while the 850
$\mu$m emission suggests $\sim$ 40\arcsec.  We can therefore take the same
core size for the sub-mm emission, i.e. 1 pc. If we now assume that the
gas and dust is thermalized at 25~K , and take a $\beta$-index of 1.5,
the SCUBA maps give a total mass of $\sim$ 2,000\Msun, which is within a
factor of two of what we obtained from H$^{13}$CN. Within uncertainties
both mass estimates are in good agreement. The JCMT C$^{18}$O \jtra21
map, however, gives a mass of only $\sim$ 1,000 \Msun, if we assume
that  C$^{18}$O is optically thin. However, we know that this is not true
near the core center, and the assumption of optically thin emission will
therefore underestimate the total mass. Furthermore, a large fraction of
the CO is likely to be frozen onto dust grains, resulting in a depletion
of the CO gas phase abundance. \citet{Mitchell90} found $\sim$ 10\%
of the CO to be tied up into ice in the NGC\,7538 IRS\,9  cloud core,
and since the NGC\,7538\,S cloud core is even colder, the fraction
of solid to gas phase CO is likely to be  higher. The low core mass
deduced from C$^{18}$O is therefore a result of CO depletion and optical
depth. The  total mass of the the NGC\,7538\,S cloud core is therefore
$\sim$ 3,000 \Msun, corresponding to an average gas density of $\sim$
10$^5$ cm$^{-3}$. Since the gas density falls of as r$^{-1}$  and the
radial fall-off is even steeper  at shorter radii, the gas densities
exceed 10$^7$ cm$^{-3}$ near the center of the core. It is therefore
not surprising that high-mass stars are forming in the NGC\,7538\,S
cloud core.










%\section{Discussion}

%{\it I have not yet really sub-divided this section, nor have I figured out in
%which or
%determine the temperature of the disk. We have tried DCN \jtra10 and \jtra32, id
%did not work, because \jtra10 is dominated by the cloud core and we do not even
%see the disk. We tried CH$_3$CN, but here the emission is dominated by the hot
%high-velocity gas masking the emission from the underlying, much colder gas
%residing in the disk. Furthermore CH$_3$CN is severly optically thick at low
%K-levels. We also tried the 1~mm transitions of H$_2$CO, but the lines are
%heavily self-absorbed and contaminated by the hot outflow}



\subsection{The position of the central protostar, NGC\,7538\,S}

NGC\,7538\,S was detected in deep IRAC images with the Spitzer Space
Observatory at 4.5, 5.8, and 8 $\mu$m (Paper II). The position of the
mid-IR emission coincides within errors with the strongest OH maser
spots \citep{Argon00}, as well as with the dominant cluster of H$_2$O
masers \citep{Kameya90}. In paper II we also present VLA observations,
which show that the star drives a highly collimated free-free jet, with
the strongest emission knot coinciding with the IRAC position. In this
paper we have therefore adopted the position of NGC\,7538\,S as:
\mbox{$\alpha_{2000.0}$ = 23$^h$ 13$^m$ 44\psec98},
\mbox{$\delta_{2000.0}$ = $+$61\degr{} 26\arcmin{} 49\ptsec5}, which has
an uncertainty of $\pm$ 0\ptsec2.  This position lies on the symmetry
axis of the compact bipolar outflow imaged in HCO$^+$ \jtra{1}{0} and
coincides within errors with the dynamical center of the rotating disk
(Section ~\ref{h13cn}).

%and the peak of the CH$_3$CN \jtra{12}{11} emission, which is found to
%be dominated by emission from hot gas at the base of the outflow (Section
%\ref{mcn}).

\subsection{The cloud core and the accretion disk}

Both DCN \jtra32 and H$^{13}$CN \jtra10 show an elliptical source
approximately centered on NGC\,7538\,S superposed on more extended fainter
emission. In  Figure \ref{fig-1mm-dcn}a  we show the integrated DCN
emission, overlaid with the 3.6~cm continuum emission from  Paper II, and
the blue-shifted HCO$^+$ emission, which show how the jet and the outflow
relate to the disk-like structure seen in the integrated DCN image. In
Figure  \ref{fig-1mm-dcn}b we show the 1.4~mm continuum emission (Paper
II) with the same overlays as in Figure \ref{fig-1mm-dcn}a. The dust
continuum and the DCN emission look very similar, although there appears
to be more structure in the DCN emission than in the dust continuum
emission, even though both have been imaged with very similar spatial
resolution. The integrated DCN emission shows a ridge-like structure
extending to the northwest $\sim$ 4\ptsec5  west of NGC\,7538\,S.
This ridge or DCN ``clump'' is not seen in the dust continuum, but
it does show up in H$^{13}$CN, but only at high spatial resolution
(Figure  \ref{fig-h13cndisk}, right panel). As we can see from Figure
\ref{fig-1mm-dcn} this DCN condensation borders the western side of the
blue outflow, and could therefore be a dense gas clump compressed by  the
outflow (Section ~\ref{dcn}). A few arcseconds west of the DCN clump is
another IRAC (mid-Infrared) source, but the DCN clump is rather compact
($\sim$ 3\arcsec{}) and the positional offset is too large to suggest
an association with this source. The IRAC source is is clearly another
young star, because it excites an H$_2$O maser, powers a
small outflow and coincides with a faint dust continuum source (Paper II).
is therefore possible that some of the DCN emission in the ridge could
come from this source.

Gaussian fits to the dust continuum and to the integrated H$^{13}$CN
emission give a disk-size of $\sim$ 10\arcsec\ $\times$ 4\arcsec\ at a
p.a. of 58\degr\ $\pm$ 3\degr, centered 1\arcsec\ - 2\arcsec\ southwest
of the center of the accretion disk, i.e. the disk appears to be
somewhat asymmetric and more extended to the SW than it is to the NE.

Of all the molecules that we have observed in the 3~mm band, it appears
that the best molecular tracer of the disk is H$^{13}$CN \jtra10. As far
as we can tell, the H$^{13}$CN emission is only weakly contaminated by 
the high-velocity outflow, and we have sensitive maps obtained with
relatively high spatial spatial resolution ($\sim$ 3\ptsec9).  We also
observe a clear velocity gradient along the major axis of the disk in
HN$^{13}$C \jtra10 and H$^{13}$CO$^+$ \jtra10 in the same direction as in 
H$^{13}$CN, i.e. blue-shifted emission to the northeast and red-shifted
emission to the southwest. For these lines only have one B- and one
C-array track giving us an angular  resolution of $\sim$ 7\ptsec8 (Table
\ref{tbl-1}), and the data are rather noisy compared to H$^{13}$CN. A
position-velocity cut of H$^{13}$CO$^+$ along the outflow direction shows
blue-shifted emission to the northwest and red-shifted emission to the
southeast, i.e.  H$^{13}$CO$^+$ is clearly affected by the outflow, which
makes it very difficult with this angular resolution to dis-entangle how
much of the observed velocity gradient comes from the disk and how much
of it is due to the outflow.

At 1.4~mm we have high signal-to-noise maps in DCN \jtra32 and CH$_3$CN
\jtra{13}{12}, with even higher spatial resolution ($\sim$ 2\ptsec6)
than H$^{13}$CN \jtra10. However, although DCN \jtra32 appears to trace
the accretion disk, the emission is rather strongly affected by emission
from the outflow, making it difficult to accurately determine the
rotation curve for the disk, although the values we derive agree well
with  what we find from H$^{13}$CN (Section \ref{h13cn}). Although
\citet{Cesaroni05} were able to derive a rotation curve from CH$_3$CN
for the young high-mass star IRAS $20126+4104$, we find that CH$_3$CN is
completely dominated by emission from the outflow, which effectively
masks any emission from the underlying accretion disk (Section
\ref{mcn})


Below we discuss in detail the findings for these three molecules.


\subsubsection{H$^{13}$CN \jtra10}
\label{h13cn}

Emission from H$^{13}$CN \jtra10 is widespread over the whole NGC\,7538
molecular cloud, with the strongest emission in the whole cloud being centered
on NGC\,7538\,S. Here we are only interested in emission from the
disk, and we would prefer to completely filter out all the extended
emission surrounding the accretion disk. We have therefore created several map
versions, where we have excluded all short spacings, and we have also
experimented with weighting the uv-data in different ways.  However, since most
of our data come from relatively short spacings, this has a severe penalty in
signal-to noise. Figure \ref{fig-h13cndisk} shows the integrated H$^{13}$CN
emission with three different angular resolutions. We will base most of our
analysis on the central image, which was created by excluding all uv-spacings
shorter than 5 k$\lambda$ and using a robust weighting scheme, giving an angular
resolution of  4\ptsec0 $\times$ 3\ptsec7,  p.a. = 0.2\degr, and still resulting
in a rather good signal-to-noise ratio.  Figure \ref{fig-h13cncuts} shows position
velocity plots along the disk-plane (p.a. = 58\degr{}) and in the outflow
direction (p.a. = 145\degr{}). The H$^{13}$CN emission shows a very distinct
velocity gradient over the disk, with blue-shifted emission to the northeast and
red-shifted emission to the southwest. At the center of the accretion disk the
main hyperfine component (F = $2 \to 1$) appears to be self-absorbed, probably
because of hot gas at the center of the disk. The self-absorption is hardly
visible at lower angular resolution, i.e our naturally weighted map (Fig.
\ref{fig-spectra}), while the line is almost completely absent at our highest
angular resolution. The highest blue- and red-shifted emission peaks $\sim$ 
$\pm$ 2\ptsec5 from the center of the disk, suggesting a diameter of $\sim$
5\arcsec\  or $\sim$ 15,000 A.U. for the rotating disk. DCN \jtra32 gives very
similar results (Section ~\ref{dcn}).


We made Gaussian fits of spectra extracted from all three images in 
order to more precisely quantify the velocity gradient. These Gaussian fits were
made using method hfs in CLASS, which results in very reliable velocity
information, since it uses the information from all three hyperfine lines. We
also made Gaussian fitting by locking the hyperfine lines to the main line,
but since the lines are blended this require us to keep the line width constant
in order to get reliable fits. The two methods give similar results to within
$\pm$ 0.1 km~s$^{-1}$. In Table  ~\ref{tbl-2} we give the results obtained with
method hfs. We can see from this table that higher spatial resolution results in
larger velocity shifts at the edge of the disk and narrower line widths, as one
would expect, because we get less velocity smearing within the beam. At the
western side of the disk the emission from the surrounding cloud core is blended 
with the emission from the disk. This is seen better in DCN \jtra32, which
has negligible hyperfine splitting, see Fig. \ref{fig-disk-spectra}.

As we can see from the position velocity plot along the outflow, even H$^{13}$CN
shows some emission from the outflow, because the emission immediately north of
the disk is blue-shifted, while it is red-shifted to the south.


\subsubsection{DCN \jtra32}
\label{dcn}

The emission from DCN \jtra32 is more compact than H$^{13}$CN \jtra10
and also appears more lumpy than the H$^{13}$CN emission, c.f. Figures
\ref{fig-1mm-dcn} \& \ref{fig-h13cndisk}. To some extent this is to
be expected, since the spatial resolution is much higher in DCN than
in H$^{13}$CN (Tables \ref{tbl-1} \& \ref{tbl-2}). At the highest
angular resolution,  $\sim$ 3\ptsec5. that we could achieve from our
H$^{13}$CN observations  (Figure \ref{fig-h13cndisk}, right panel),
the H$^{13}$CN  do appear to show a second condensation $\sim$ 4\ptsec5
west of NGC\,7538\,S, which is also seen in DCN. However, the difference
in  morphology between the DCN emission and H$^{13}$CN emission is too
large to be a result from angular resolution alone.  To get a better
idea where the DCN emission comes from, we  created a set of images
with 1 km~s$^{-1}$ spacing over the whole velocity range where we see DCN
emission. These channel maps are shown in Figure \ref{fig-dcn-chann}.
At the highest red- and blue-shifted velocities, the emission peaks on
or near the center of NGC\,7538\,S, while at near cloud velocities the
emission is stronger to the NE or the SW of the protostar, depending on
whether we look at blue-shifted or red-shifted emission. At slightly
blue-shifted velocities ($\sim$ $- $58~km~s$^{-1}$ DCN shows an E-W
ridge with three dominant peaks. The strongest one is slightly  north
northwest, $\sim$ 1 - 2\arcsec,  of  NGC\,7538\,S, with another fainter
core at +9\arcsec,+2\arcsec\ relative to NGC\,7538\,S. To the west there
is another peak at $-$5\arcsec,+1\arcsec\ and an even fainter one at
$-$10\arcsec,+1\arcsec. None of the DCN peaks, except the central one,
coincide with any known object in the NGC\,7538\,S cloud core. The H$_2$O
maser and IRAC source, IRS\,11\,S, the other known young active object
in the vicinity of NGC\,7538\,S, is roughly halfway between the two
western cores. At the cloud velocity the strongest emission is $\sim$
$-$2\arcsec\ west of S, but here we see another very strong peak at
$-$3\arcsec,+4\arcsec. The line at this position is centered at  the cloud
velocity  ($-$56 km~s$^{-1}$), and has a  very narrow line width, $\sim$ 1
km~s$^{-1}$, with a faint blue-shifted shoulder. At red-shifted velocities
most of the DCN emission comes from an extended  ($\sim$ 10\arcsec{})
region southwest of NGC\,7538\,S.  Although each velocity interval shows
several red-shifted DCN clumps, the position of these clumps move when
going from one velocity to the next, suggesting velocity gradients or
turbulent gas. This is also seen in spectra from the southwestern part of
the core, which are much broader with  line widths of 4 - 5 km~s$^{-1}$.

If we integrate over 5.5  km~s$^{-1}$ centered on V$_{lsr}$ =
$-$56  km~s$^{-1}$, i.e. roughly the velocity spread that we see in
H$^{13}$CN, we  see a central  ``disk-like''  feature, similar to what
we see in H$^{13}$CN, but with a northwestern ridge curving up from the
southwestern edge of the ``disk'' , i.e. very similar to the integrated
DCN emission shown in Figure \ref{fig-1mm-dcn}. However, the channel
maps show that this is not really  a ridge, but a blending of the  DCN
clump at $-$5\arcsec,+1\arcsec.  The double-peaked ``disk'', however, is
centered about somewhat west ($\sim$ 1\arcsec{}) of the protostar. Even
though this ``disk'' has roughly the same position angle as the continuum
and H$^{13}$CN disk, it is also shifted about one arcsecond to the north,
making it questionable whether it is really a disk.

We have therefore made position velocity plots centered on the protostar
along the disk plane and in the outflow direction (Fig
\ref{fig-dcn-cuts}), i.e. the same cuts as we did for H$^{13}$CN. These
position velocity plots clearly demonstrate that DCN is strongly
affected by the outflow. The total velocity extent of the DCN emission
is $\sim$ 11 km~s$^{-1}$, which is far more than we would expect to see
from a rotating accretion disk. Furthermore, the cut along the  outflow
shows that  the blue-shifted emission is the northwest and red-shifted
emission to the south-east of the NGC\,7538\,S.  The ``high-velocity''
DCN outflow is much more compact, only a few arcseconds , than the
outflow we see in HCO$^+$,  which extends $\sim$ 8\arcsec\ to the
northwest and even further in the red-shifted outflow lobe. However, at
low blue-shifted velocities, DCN has a similar extent as HCO$^+$. In the
cut along the outflow, there is a clear blue-shifted velocity gradient
to the northeast, and red-shifted to the southwest. The red-shifted
emission to the southwest of the disk center is partly suppressed by 
red-shifted self-absorption , see Figure \ref{fig-3mm-spectra} and Table
\ref{tbl-3}, which quenches the emission on the red-side. There is
apparently a velocity component at $\sim$ $-$55 km~s$^{-1}$ extending
$\sim$10\arcsec\ to the southwest, which gives the appearance of a
velocity gradient across the disk. However, the velocity feature we
would associate with the disk, is the strongest red-shifted peak $\sim$
2\ptsec6 to the southwest at a velocity of  $-$53.5 km~s$^{-1}$.  The
corresponding blue-shifted peak is at 2\ptsec5 to the northeast  at a
velocity of $-$58.0 km~s$^{-1}$. There is, however another fainter even
more red-shifted (V$_{lsr}$ $\sim$ $-$51.5 km~s$^{-1}$) $\sim$ 2\arcsec\
to the southwest, which is probably from the outflow.

To get a better idea of where the blue- and red-shifted emission comes
from, we overlaid the blue- and red-shifted DCN emission in two
different velocity intervals on the integrated DCN emission of the cloud
core (Figure \ref{fig-dcn-outflow}).  At a velocity offset of $\pm$3
km~s$^{-1}$  most of the blue-shifted emission is to the north
northwest, i.e. what one would expect if the meission comes from the
disk surface and/or the shearing layer between the outflow and the
surrounding cloud. There is also a clear north-east southwest
gradient, although with a somewhat different position angle, p.a. $\sim$
40\degr, than what we deduced from H$^{13}$CN.  At higher velocities,
$\pm$4.5 km~s$^{-1}$ the blue- and red-shifted DCN emission moves
more in the outflow direction, suggesting that most of the emission
originates from the outflow. In both velocity intervals, however, we see
very little red-shifted emission to the east. This could suggest that
some of the red-shifted emission is neither associated with the disk nor
the outflow from NGC\,7538\,S, but instead comes from more red-shifted
gas clumps in the cloud core.  

Since DCN \jtra32 is strongly affected by the outflow, it is not a good
disk tracer. If the dominant velocity peaks seen in the position
velocity plot along the disk plane at $\sim$ $\pm$2\ptsec5 originate
from a rotating disk, the DCN emission would suggest a systemic velocity
of $-$55.8 km~s$^{-1}$, a velocity gradient of 4.5 km~s$^{-1}$ for a
disk size of  5\ptsec1, i.e. very similar to what we get from
H$^{13}$CN. We can also see this in Figure \ref{fig-disk-spectra}, where
we show spectra of both H$^{13}$CN and DCN in three positions of what we
interpret as the rotating accretion disk surrounding NGC\,7538\,S. Both
molecules are blue-shifted to the northeast, both show some evidence for
slightly red-shifted narrow self-absorption towards the center of the
disk and red-shifted emission to the southwest,. Here we have ignored
the strong, relatively narrow emission at $-$56 km~s$^{-1}$, which is
seen in DCN, but which is far less evident in H$^{13}$CN. The velocity
gradient is larger in DCN than in H$^{13}$CN, which is to be expected,
since the angular resolution is higher in DCN than in  H$^{13}$CN.


\subsubsection{ CH$_3$CN J = 12 $\to$ 11}
\label{mcn}

The emission from CH$_3$CN J = 12 $\to$ 11 is confined to the immediate
vicinity of NGC\,7538\,S (Fig. \ref{fig-mcn-disk}). The emission is well
resolved and shows an elliptical source centered at 0\psec2 $\pm$
0\psec4, $-$0\ptsec4 $\pm$ 0\ptsec1, relative to our nominal position
for NGC\,7538\,S, i.e. somewhat south of the stellar position. At  K =
0, which has an excitation energy of  68.9 K above ground,  the size of
the CH$_3$CN emission is $\sim$ 4\ptsec9 $\times$ 1\ptsec5 with a p.a.
of 70\degr. The emitting region gets progressively smaller for higher K
levels, suggesting that the gas is hotter closer to the star. At K = 3,
which has an excitation energy of 132.9 K, the size of the emitting
region 4\ptsec0 $\times$ 1\ptsec5 with a p.a. of 84\degr. At higher
K-levels the emission is faint and the source size more uncertain, but
appears to follow the same trend seen for lower K-levels, i.e. the
emission becomes more compact and we see a gradual increase in the
position angle. It would therefore appear that  CH$_3$CN traces the
accretion disk, although at low K-levels the position angle of the
emission differs from what what we observe in dust continuum and
H$^{13}$CN. At higher K-levels the CH$_3$CN emission becomes even more
misaligned, which we would not expect to observe if the emission
originates in the accretion disk, unless the inner disk is warped
relative to the colder, more extended disk.

CH$_3$CN  spectra towards the center of NGC\,7538\,S are shown in Fig.
\ref{fig-mcnspec}.  We detected all the K transitions, K = 0 to 6, and
the K = 2 and 3 transitions of  CH$_3$$^{13}$CN, which were included in
our frequency setting (Table \ref{tbl-2}).  In Table \ref{tbl-5} we give
results from Gaussian fits to the spectra presented in Fig.
\ref{fig-mcnspec}. We fitted the K = 0 to 3 levels simultaneously by
keeping the separation between the K components to their theoretical
value, but allowed the FWHM to be a free parameter and constrained to be
the same for all these K values.  The K-levels 4 to 6 were fitted
individually. It is clear from these fits that the line widths gets
broader for increasing K-value, which is what one would expect, if these
lines probe the innermost part of the accretion disk. However, the line
profiles are not well fitted with a single Gaussian, because they have a
broader underlying pedestal. There is also a hint of a narrow
self-absorption feature in the K = 0 to K = 3 transitions (Fig.
\ref{fig-mcnspec}), suggesting that there is cold, somewhat optically
thick CH$_3$CN gas in the surrounding cloud core.

This is better seen in position velocity plots. In Figure
\ref{fig-k01-cuts} we show position velocity plots along the disk and
outflow direction for the partially blended K = 0 and K = 1 transitions.
The narrow self-absorption is clearly seen in both transitions. Similar
self-absorption is even seen in the K = 3 transition, but slightly more
red-shifted. The position velocity plot in the outflow direction shows 
the blue-shifted wing of the K = 0 transition to the northwest and the
red-shifted wing extending to the southeast, as we would expect if the
wing emission originates in the outflow. That this is really the case is
shown in Fig. \ref{fig-k012do}, where we plot the integrated red- and
blue-shifted emission of the K = 1 and 3 transitions and overlay them on
the integrated emission from the line core of these lines. For K = 3 the
blue- and red-shifted line emission is well separated and aligned with
the outflow. The cut along the disk-plane, however, shows only a
marginal velocity gradient over the disk, yet, as we already seen, both
H$^{13}$CN \jtra{1}{0} and DCN \jtra{3}{2} show a strong velocity
gradient over the disk. Although this is somewhat surprising, it does
not contradict our earlier results. First of all, as we already seen,
CH$_3$CN  is strongly dominated by the outflow, which may mask the
emission from the accretion disk. It is also possible that the CH$_3$CN
emission is optically thick, which will make it difficult to see
rotation of the disk.  Since we detected emission from the K = 2 and 3
transitions of CH$_3$$^{13}$CN, we can use the line ratios to check
whether  CH$_3$CN is optically thin or thick.   The ratios of the
integrated CH$_3$CN/CH$_3$$^{13}$CN line intensities are about 3 - 10,
which strongly suggests that the CH$_3$CN lines are optically thick. 
Although CH$_3$CN is often optically thin, see e.g. \citet{Araya05}, it
is not completely uncommon to find optically thick  CH$_3$CN, especially
in high-mass star forming regions \citep{Pankonin01,Watson02,Remijan04},
 when thy are observed with high spatial resolution, like what we have
here.

CH$_3$CN is traditionally analyzed using a rotational temperature
equilibrium (RTE) analysis \citep[and references
therein]{Loren84,Araya05}. However, we know that some of the 
K-transitions are optically thick and that the source size changes as a
function of K-level. Furthermore, we also know that we have some
contribution from both the disk and the outflow, especially at low
K-levels. An RTE or  population-diagram analysis assumes that the gas is
optically thin and  in LTE at a single temperature, none of which is
strictly true in this case. Nevertheless, it is rather instructive to
look at the results of such an analysis. Since \citet{Araya05} have done
a recent in  depth discussion of population-diagram analysis for
CH$_3$CN, there is no reason for us to repeat any of the discussion
here. Following \citet{Araya05} we do a least squares fit linear fit of
the equation


\begin{displaymath}
ln (Z) = ln \biggr(\frac{N_{CH_3CN}}{Q(T_{rot})}\biggl)  -  \frac{E_{JK}}{kT_{rot}}
\end{displaymath}

\noindent where  Z = $\frac{N_{JK}}{g_{JK}}$. To minimize the effect
from the change in source size, we use the measured antenna temperatures
for the peak position of  CH$_3$CN ignoring any difference due to
coupling of the source, except for a small correction for the K = 4 and
K = 5 levels , which where imaged with a slightly different beam size
(Table \ref{tbl-5}). The results of this analysis is show in Figure
\ref{fig-mcn_rot}. The population-diagram indicates that the CH$_3$CN
emission cannot be characterized with a single rotational temperature.
We have therefore separately done a least squares fit to the three
lowest K-transitions, K = 0 to 2, for which the emission is likely to be
dominated the disk, and for K = 2 to 5, for which the outflow is
starting to dominate. The fit to the low K-transition give T$_{rot}$ =
52 $\pm$ 10 K, while the high K-transitionds give T$_{rot}$ = 147 $\pm$
40 K. Neither of these temperatures are very accurate. The low
K-transitions are definitely optically thick, which will lead to an
overestimate of the rotational temperature. Contribution from the
outflow will also raise the temperature. The temperature of the disk is
certainly less than 50 K and higher than 25 K, the temperature of the
surrounding cloud core, since we see some self-absorption from virtually
every molecule tracing the disk. The temperature of the outflow is not
well constrained from our observations, because we have poor
signal-to-noise at high K-levels, which could more accurately constrain
the temperature of the outflow. However, analysis of the two H$_2$CO
transitions 3$_{03}  \to 2_{02}$ and 3$_{22}  \to 2_{21}$, which are
dominated by the outflow, also indicate a temperature of $\geq$ 100 K,
in good agreement with what we derive from CH$_3$CN.
\citet{Kalenskii00}, who did single dish observations of  NGC\,7538\,S
in the \jtra65 and \jtra54 transitions of CH$_3$CN with a beam size of 
$\sim$40\arcsec,  derived a rotation temperature of $\sim$ 40 K, much
lower than what we observe. They also measure a different radial velocity
than we find. Since their beam covers most of the cold cloud core
surrounding NGC\,7538\,S, it appears that the CH$_3$CN
emission is dominated by the cloud core, which we filter out  in our BIMA observations,




%We also detected faint emission from  CH$_3$CH$_2$CN J =
%25$_{2,24} \to 24_{2,23}$ (V$_{lsr}$ = -56.3 $\pm$ 0.4 km$^{-1}$,  $\Delta$V =
%3.8 $\pm$ 0.6 km$^{-1}$) and integrated intensity of  2.0 $\pm$ 0.4
%K~km$^{-1}$). 

\section{Discussion}

\subsection{Is NGC\,7538\,S a high-mass star?}

Our observations confirm that NGC\,7538\,S lies in the center of a cold,
massive cloud core with a diameter of $\sim$ 1 pc, and a mass of 2,000 -
4,000 \Msun (Section \ref{core}), which therefore provides the necessary
conditions for the formation of high-mass stars, i.e. essentially the
whole core has a surface density, $\Sigma$ $\gtrsim$  1 g~cm$^{-2}$
\citep{McKee02,Krumholz08}.  The source coincides within errors with a
cold far-infrared source with a luminosity of $\sim$ 1.5 10$^4$ \Lsun\
\citep{Werner79,Thronson79}, suggesting an early B-star. IRS\,11, the
only near-IR source in the vicinity of NGC\,7538\,S, can only account
for about a tenth of this luminosity, and the same is true for the small
cluster of Spitzer 8 $\mu$ sources surrounding IRS\,11 (Paper II).
Therefore the bulk of the luminosity appears to be generated by
NGC\,7538\.S. This sources drives a highly collimated free-free jet
(Paper II), powers a massive, very young bipolar outflow
\citep{Sandell03}, and excites OH, CH$_3$OH, and H$_2$O masers
\citep{Argon00,Pestalozzi06,Kameya90}. OH 1665-MHz masers are only found
in young massive star forming regions \citep{Caswell98,Argon00}, mostly
associated with Ultra Compact \ion{H}{2} regions.  The same is true for 
Class II CH$_3$OH masers \citep{Minier03}, i.e. no CH$_3$OH maser have
yet been found toward a low or intermediate mass star. Although 
CH$_3$OH masers sometimes are associated with OH masers, the majority
are found in weak or radio quiet regions, and are therefore believed to
trace a younger, perhaps protostellar phase, in the evolution of
high-mass stars \citep{Caswell98,Ellingsen06}. The observed accretion
rate toward NGC\,7538\,S is $\textgreater$ 20$^{-4}$ \Lsun, perhaps even as high
as 10$^{-3}$ \Lsun\ (Sandell et al, in prep), which is far higher than what
have been found for low or intermediate mass protostars, providing
additional support for the high-mass nature of NGC\,7538\,S.




\subsection{Is NGC\,7538\,S surrounded by a rotating accretion disk?}

%\subsection{Disk mass}
%
% The disk is most clearly seen at 220 GHz, where it appears as an elliptical
% source surrounded by fainter extended emission.  A two component Gaussian fit
% gives a size of 7.6$^{\prime\prime}$ $\times$ 2.8$^{\prime\prime}$ at a
% position angle (p.a.) of 57$^\circ$ and a total flux density of 0.8 Jy.

% Assuming  \citet{Hildebrand83} dust opacity, a dust emissivity of 1.5, a
% gas--to--dust ratio of 100 and a dust temperature of 35 K gives a total disk
% mass of $\sim$ 85 M$_{\odot}$, in good agreement with the mass derived from
% molecular lines and with the dynamical mass.



\acknowledgements The
BIMA array is operated by the Universities of California (Berkeley),
Illinois, and Maryland with support from the National Science
Foundation

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\clearpage
% here starts Table 1

\begin{deluxetable}{lll}
%\tabletypesize{\scriptsize}
\tablecolumns{3}
\tablenum{1}
%\footnotesize  
\tablewidth{0pt} 
\tablecaption{BIMA 3 mm observing log.} 
\label{tbl-1}
\tablehead{
\colhead{Molecule} & \colhead{transition} & \colhead{rest frequency} \\ 
\colhead{}  &\colhead{}  & \colhead{[GHz]}  \\
\cline{1-3} 
}
\startdata
\cline{1-3}
\sidehead{Frequency setting: H$^{13}$CN \jtra10; Array configurations BCD, } 
\sidehead{\phantom{Frequency setting}HPBW = 6\ptsec0 $\times$ 5\ptsec7 pa = -25.8\degr{}}
\sidehead{Observing dates:  01/27/02, 01/31/02, 05/03/02, 08/09/03,}
\sidehead{\phantom{Observing dates: }11/04/03, 12/11/0312/12/03, 12/31/03} 
% best H13CN data set in t860/maps.087.20jul05
\cline{1-3}
NH$_2$D\phantom{XXXX} & 1$_{11}  \to  1_{01}$  F$^{\prime}$ - F$^{\prime\prime}$ = 0 - 1& 85.924747  \\
NH$_2$D & 1$_{11}  \to  1_{01}$  F$^{\prime}$ - F$^{\prime\prime}$  = 2 - 1 & 85.925684 \\
NH$_2$D &  1$_{11}  \to  1_{01}$  F$^{\prime}$ - F$^{\prime\prime}$ = 2 - 2/1 - 1 & 85.926263\\
NH$_2$D  &  1$_{11}  \to  1_{01}$  F$^{\prime}$ - F$^{\prime\prime}$ = 1 - 2 & 85.926858 \\
NH$_2$D &  1$_{11}  \to  1_{01}$  F$^{\prime}$ - F$^{\prime\prime}$ = 1 - 0 & 85.927721  \\

SO  & \jtra{2,2}{1,1} & 86.09355 \\
H$^{13}$CN & \jtra10 F = 1 - 1 & 86.338767 \\
H$^{13}$CN & \jtra10 F = 2 - 1 & 86.340184 \\
H$^{13}$CN  &\jtra10 F = 0 - 1 & 86.342274 \\
HCO$^+$  &\jtra10 & 89.188518 \\
\cline{1-3}
\sidehead{Frequency setting: H$^{13}$CO$^+$ \jtra 10; Array configurations BC, }
\sidehead{\phantom{Frequency setting}HPBW = 7\ptsec9 $\times$ 6\ptsec9 pa = -23.8\degr{}}
\sidehead{Observing dates: 12/03/01, 01/10/04 } 
\cline{1-3} 
H$^{13}$CO$^+$& \jtra10 & 86.754294 \\
SiO  & \jtra21 v=0  &  86.846998  \\
HN$^{13}$C  & \jtra10 F = 0-1 & 87.090735 \\
HN$^{13}$C  & \jtra10 F = 2-1 & 87.090859 \\
HN$^{13}$C  &  \jtra10 F = 1-1 & 87.090942 \\
%\cline{1-3}
%\sidehead{Frequency setting: C$^{18}$O  \jtra10; Array configurations: D}
%\sidehead{\phantom{Frequency setting}HPBW =  14\ptsec4 $\times$ 12\ptsec6 pa = 86.0\degr{}}
%\sidehead{Observing dates: 07/19/03}
%\cline{1-3}
%$^{13}$CO & \jtra 10 & 110.20135 \\
%C$^{18}$O & \jtra 10 & 109.78216 \\
\enddata
\end{deluxetable}

\begin{deluxetable}{llll}
%\tabletypesize{\scriptsize}
\tablecolumns{3}
\tablenum{2}
%\footnotesize  
\tablewidth{0pt} 
\tablecaption{BIMA 1 mm observing log.} 
\label{tbl-2}
\tablehead{
\colhead{Molecule} & \colhead{transition} & \colhead{rest frequency} \\ 
\colhead{}  &\colhead{}  & \colhead{[GHz]}  \\
%\cline{1-3} 
}
\startdata
\sidehead{Frequency setting: H$_2$CO 3$_{03}  \to 2_{02}$; array configurations: BC}
\sidehead{\phantom{Frequency setting:  }HPBW = 6\ptsec6 $\times$ 5\ptsec7 pa = 78.4\degr{}}
\sidehead{Observing dates:  10/9/02, 10/16/02} 
\cline{1-3}
SO  & \jtra{5,5}{4,4} &\phantom{1111111111} 215.22065 \\
H$_2$CO & 3$_{03}  \to 2_{02}$  &\phantom{1111111111}  218.22219 \\
H$_2$CO & 3$_{22}  \to 2_{21}$  &\phantom{1111111111}  218.47564  \\
\cline{1-3}
\sidehead{Frequency setting: DCN \jtra32;  array configurations: BC}
\sidehead{\phantom{Frequency setting:  }HPBW = 2\ptsec9 $\times$ 2\ptsec4 pa = 22.2\degr{}}
\sidehead{Observing dates: 10/13/02, 04/19/03, 05/01/03, 10/10/03,}
\sidehead{\phantom{Observing dates: }10/25/03, 01/03/04, 01/05/04}
\cline{1-3}
DCN    &   \jtra32 &\phantom{1111111111}   217.23853   \\
$^{13}$CO    &   \jtra 21 &\phantom{1111111111}   220.39869  \\
CH$_3$CN & 12$_0 \to 11_0$ &\phantom{1111111111}  220.74727  \\
CH$_3$CN & 12$_1 \to 11_1$ &\phantom{1111111111}  220.74302  \\
CH$_3$CN & 12$_2 \to 11_2$ &\phantom{1111111111}  220.73027  \\
CH$_3$CN & 12$_3 \to 11_3$ &\phantom{1111111111}  220.70903  \\
CH$_3$CN & 12$_4 \to 11_4$ &\phantom{1111111111}  220.6793  \\
CH$_3$CN & 12$_5 \to 11_5$ &\phantom{1111111111}  220.64109 \\
CH$_3$CN & 12$_6 \to 11_6$ &\phantom{1111111111}  220.59443  \\
CH$_3$$^ {13}$CN  & 12$_1 \to 11_1$ &\phantom{1111111111}  220.63377   \\
CH$_3$$^ {13}$CN  & 12$_2 \to 11_2$ &\phantom{1111111111}  220.62108  \\
CH$_3$$^ {13}$CN  & 12$_3 \to 11_3$ &\phantom{1111111111}  220.59994 \\
\enddata
\end{deluxetable}

\begin{deluxetable}{lccccc}
\tablecolumns{6}
\tablenum{3}
\tablewidth{0pt} 
\tablecaption{Gaussian fits of optically thin or moderately optically thin lines towards the center of the accretion disk.}

\label{tbl-3}
\tablehead{
\colhead{Molecule} & \colhead{Transition}& \colhead{HPBW} &\colhead{$\int T_{\rm MB} dV$} & \colhead{$\Delta V$} & \colhead{$V_{\rm LSR}$} \\
\colhead{ }         &\colhead{ }        &\colhead{[ \arcsec{} $\times$ \arcsec{}] }   & \colhead{[K km s$^{-1}$]}& \colhead{[km s$^{-1}$]}& \colhead{[km s$^{-1}$]} \\
}
\startdata
% C$^{18}$O&$1 \to 0$ & 14.4 $\times$ 12.6 &      2.25 $\pm$ 0.16 & 3.77 $\pm$ 0.28       &  $-$55.94 $\pm$ 0.14      \\
 % C=0.561  Area = 4.01 +/- 0.28
 C$^{18}$O &$2 \to 1$&  21.6 $\times$ 21.6   &  33.44 $\pm$ 0.21  &  4.68 $\pm$ 0.03  &  $-$56.42 $\pm$ 0.01  \\
 % class fit  23.409 +/- 0.152  -56.42 +/- 0.01 4.675 +/-  0.032
                & $\phantom{2 -- 1}$\tablenotemark{a}&  &  $-$1.22 $\pm$ 0.11 & 2.10 $\pm$ 0.20 &  $-$55.73 $\pm$ 0.11 \\         
 C$^{17}$O & $2 \to 1$ \tablenotemark{a}&    21.2 $\times$ 21.2 &       9.53  $\pm$ 0.03& 5.04 $\pm$  0.18 & $-$56.42 $\pm$ 0.02  \\
 % int (-61 to -51.3 6.53 K km/s  ; int(-51,-48) =0.16; rms noise = 0.053, 0.015 when binned to
 % 3.98 MHz; scale by 1/0.7 to get T_mb; from class 1.065x1.405x5.038 = 7.538/1.13 (opt depth %correction == 6.67 .. 9.53 K km/s
  H$^{13}$CO$^+$  & $1 \to 0$&  7.9 $\times$ 6.9 &       14.73  $\pm$ 1.00 &   4.20 $\pm$ 0.36   &   $-$55.96 $\pm$ 0.14    \\
  % C= 3.004 , Area 4.905 +/- 0.33 
 HN$^{13}$C  & $1 \to 0$\tablenotemark{b}& 7.8 $\times$ 7.1 & 5.40  $\pm$ 0.17 &  3.60  $\pm$ 0.10 &  $-$55.91 $\pm$ 0.36  \\
% C=2.923 Area 1.825  +/-  0.90 ; take area and error from single fit  1.849 +/- 0.058
SiO                   & $2 \to 1$\tablenotemark{c} &   8.2 $\times$ 7.1  &  7.85  $\pm$ 0.90 & 3.73 $\pm$ 0.33 & $-$56.23 $\pm$ 0.13\\
%C=2.8252 two component fit ; spike 2.778 +/-  0.32  -56.23 +/- 0.13  3.73 +/- 0.33
% pedestal  5.807 +/- 0.57   -56.34 +/- 0.51  13.6 +/- 0.36
H$^{13}$CN  & $1 \to 0$\tablenotemark{d}& 6.0 $\times$ 5.7 & 24.08  $\pm$ 0.10  &  4.95  $\pm$ 0.10&  $-$55.98 $\pm$ 0.10  \\
% C=4.7961 ; area 5.20 +/- 0.02  (5.22 from free fit); 5.02 +/- 0.02 FROM CONSTR. FIT  
% line width from locked fit 4.95; hfs  4.68  $\pm$ 0.23 
H$^{13}$CN  & $1 \to 0$\tablenotemark{d}& 4.0 $\times$ 3.7 & 24.86  $\pm$ 0.22 &  5.85  $\pm$ 0.05 &  $-$56.11 $\pm$ 0.17 \\
% C=11.149 ; data in 12jul  ; linewidth from locked fit  5.85;hfs  5.48  $\pm$ 0.03
NH$_2$D  & 1$_{11} \to 1_{01}$\tablenotemark{e}& 12.1 $\times$ 11.9 & 5.30  $\pm$ 0.06 &  1.35  $\pm$ 0.10 &  $-$56.28 $\pm$ 0.06  \\ 
% NH2D.cm in mosaic beam 10.14"x 9.84" C=1.6622, smoothed to 10.1x9.8  C=1.152
% area of inner 4 ; 4.60 +/- 0.05 >> 5.30 +/- 0.06
% new data  C=5.0687, beam=5.90 x 5.54 at -18.1, but has dv=2 km/s
DCN & $3 \to 2$ &  2.9 $\times$ 2.4 & 21.69 $\pm$ 0.84 &  6.89 $\pm$ 0.18 & $-$55.56 $\pm$ 0.18 \\
                             & $\phantom{3 -- 2}$\tablenotemark{a} &   & $-$2.88 $\pm$ 0.70 &  2.65 $\pm$ 0.01 & $-$54.85 $\pm$ 0.21 \\
% in t608 ; C = 3.7952 ; beam 2.87 x 2.38 , dv =1.5 km/s
\enddata
%Note - For those spectra where we only list the integrated intensity,

%$^a$ high velocity wings subtracted\\
%$^b$ no correction for hyperfine broadening\\
\tablenotetext{a}{Fit to self-absorption component }
\tablenotetext{b}{$\Delta V$ and $V_{\rm LSR}$ from method hfs}
            %This is $T_{\rm MB}$ $\times$ $\tau$ rather than line integral
\tablenotetext{c}{This is  the cloud component only. SiO is dominated by high velocity emission, which has a  line integral of  16.6  K km s$^{-1}$ and a line width of 13.6 km s$^{-1}$}
\tablenotetext{d}{$V_{\rm LSR}$ from method hfs}
\tablenotetext{e}{Fit with the inner four hyperfine components locked in velocity separation to the main hyperfine component. }
\end{deluxetable}


% here starts Table 4
\begin{deluxetable}{lcc}
%\tabletypesize{\normal}
\tablecolumns{3}
\tablenum{4}
\tablewidth{0pt} 
\tablecaption{Radial velocities and line-widths of H$^{13}$CN \jtra10  in the accretion disk}
\label{tbl-4}
\tablehead{
\colhead{Position\tablenotemark{a}} & \colhead{$V_{\rm LSR}$}&  \colhead{$\Delta V$}\\
\colhead{  }  &\colhead{ [km s$^{-1}$] }&\colhead{ [km s$^{-1}$] }\\
}

\startdata
\sidehead{HPBW = 6.0 $\times$ 5.7}
\cline{1-3}
northeast &   $-$56.59 $\pm$ 0.06  &  3.9   $\pm$ 0.1 \\
center      &   $-$55.98 $\pm$ 0.07  &  4.7  $\pm$ 0.1\\ 
southwest &  $-$55.19 $\pm$ 0.16  &  4.6   $\pm$ 0.4\tablenotemark{b}\\ 
\sidehead{HPBW = 4.0 $\times$ 3.7}
\cline{1-3}
northeast  &  $-$57.34 $\pm$ 0.11  &  3.1   $\pm$ 0.3 \\
center       & $-$56.00 $\pm$ 0.02  &  5.6  $\pm$ 0.1  \\
southwest &  $-$54.17  $\pm$ 0.59  &  4.4   $\pm$ 0.6\tablenotemark{b} \\
\sidehead{HPBW = 3.5 $\times$ 3.3}
\cline{1-3}
northeast  &  $-$57.76 $\pm$ 0.21  &  2.3   $\pm$ 1.0 \\
center\tablenotemark{c}        &  \nodata  &  \nodata \\
southwest & $-$54.33  $\pm$ 0.89  &  5.5   $\pm$ 0.8\tablenotemark{b} \\
\cline{1-3}
\enddata

\tablenotetext{a}{Positions southwest and northeast are at $\pm$2\ptsec5 from the center at a p.a. of 58\degr{}.}
\tablenotetext{a}{At the southwest position the red-shifted emission
from the disk is blended by emission from the surrounding cloud
core,  resulting in uncertain velocities  and broadened line widths.}
\tablenotetext{c}{The line is too deeply self-absorbed to result in a
successful fit.} 
\end{deluxetable}


% here starts Table 5
\begin{deluxetable}{lccr}
%\tabletypesize{\normal}
\tablecolumns{4}
\tablenum{5}
\tablewidth{0pt} 
\tablecaption{Line parameters for CH$_3$CN  \jtra{12}{11}  in the accretion disk}
\label{tbl-5}
\tablehead{
\colhead{K level} & \colhead{$V_{\rm LSR}$} &  \colhead{$\Delta V$} & \colhead{$\int T_{\rm MB} dV$}\\
\colhead{  }  &\colhead{ [km s$^{-1}$] }&\colhead{ [km s$^{-1}$] } &\colhead{ [K~km s$^{-1}$] }\\
}

\startdata
\sidehead{HPBW = 2.76 $\times$ 2.36\tablenotemark{a}}
\cline{1-4}
0        &   $-$56.4 $\pm$ 0.1 \tablenotemark{b} &  5.35  $\pm$ 0.17 &  16.6  $\pm$ 0.9\\
1        &   \nodata &  \nodata & 11.6 $\pm$  0.8\\ 
2        &  \nodata &  \nodata  & 9.4 $\pm$ 0.8 \\ 
3        & \nodata & \nodata & 12.0 $\pm$ 0.9\\
\sidehead{HPBW = 3.16  $\times$ 2.42\tablenotemark{a}}
\cline{1-4}
4     &  $-$56.9  $\pm$ 0.5  &  6.2   $\pm$ 1.3   & 5.4 $\pm$ 0.9\\
5     &  $-$55.3 $\pm$  1.3  &  7.3  $\pm$ 4.1    & 4.3 $\pm$ 1.6 \\
6     &  $-$56.6 $\pm$  0.4  &  1.8  $\pm$ 1.2    & 1.1 $\pm$ 0.4 \\
\sidehead{CH$^{13}$CN}
\cline{1-4}
2 &  $-$56.3  $\pm$ 1.6  &  7.5  $\pm$ 3.5  & 2.7 $\pm$ 1.1\\
3 &  $-$55.8  $\pm$ 0.6  &   2.8  $\pm$ 1.2  & 1.2 $\pm$ 0.5\\
\cline{1-4}
\enddata

\tablenotetext{a}{Image containing K-levels 0 to 3 have better uv-coverage
than images containing K levels 4, 5, and  6, and the K = 2 and 3
transitions of CH$^{13}$CN. The latter data set has instrumental problems
causing the data to be excessively noisy.} \tablenotetext{b}{CLASS fit
by keeping velocity separations between K-levels to their theoretical
values and forcing the line width to be the same for all transitions.}
\end{deluxetable}

\clearpage



\includegraphics[ scale=0.9,angle=-90]{spectra.ps}

\figcaption[]{
\label{fig-spectra}
Spectra  toward NGC\,7538\,S  at 3~mm (left panel) and 1~mm (right panel). The
grey vertical line marks the systemic velocity. In the 3~mm window HCO$^+$,
SiO and SO show strong line wings; both SO and HCO$^+$ are self-absorbed
at red-shifted velocities. At 1~mm all the spectra shown here exhibit line wings. $^{13}$CO \jtra21 
and H$_2$CO   3$_{03}  \to 2_{02}$ show deep self-absorption at red-shifted velocities. Even DCN \jtra32 is affected by some red-shifted self-absorption. }


\includegraphics[ scale=0.67,angle=-90]{h13cn_nh2d_450.ps}

\figcaption[]{
\label{fig-h13cn_nh2d_450}
Contour plots of total integrated H$^{13}$CN \jtra10 emission (left
panel) and of the NH$_2$D 1$_{11}  \to  1_{01}$ emission (right panel)
overlaid on a color image of  the 450 $\mu$m continuum emission. The
450 $\mu$m map is taken from \citet{Sandell04}. It has been cleaned and
restored with a 10\arcsec\ circular beam to better bring out the faint
low level dust emission. The peak flux of the 450 $\mu$m emission is
77.3 Jy~beam$^{-1}$. In order to better see the low level emission we
have enhanced the color image with four thick white contours plotted
logarithmically from 4 Jy~beam$^{-1}$ to half intensity. The H$^{13}$CN
emission is plotted with six logarithmic black contours, starting at 28
mJy~beam$^{-1}$  (3-$\sigma$) to peak intensity, 590 mJy~beam$^{-1}$. For
NH$_2$D we use an image with 12\arcsec\  resolution. The contours for
this image are plotted with  six black logarithmic contours going from  9
mJy~beam$^{-1}$ (3-$\sigma$) to peak intensity,  120 mJy~beam$^{-1}$. We
have overlaid the images with H$_2$masers (black triangles) and IRAC
8 $\mu$m sources (black star symbols) (Paper II), which pinpoint the
location of young stars in this region. we have also labeled the position
of NGC\,7538\,S.}


\includegraphics[ scale=0.7,angle=-90]{1mm-dcn.ps}
\figcaption[]{
\label{fig-1mm-dcn}
Gray scale images of  total integrated DCN \jtra32 emission (left panel)
and 1.4~mm continuum emission(right panel)  overlaid with black contours.}



\includegraphics[ scale=0.63,angle=-90]{h13cn-disks.ps}

\figcaption[]{
\label{fig-h13cndisk}
Grayscale images of Integrated H$^{13}$CN \jtra10 emission overlaid with
contours for three different angular resolutions. The image to the left
is created from all data sets using natural weighting, while the one in
the has been made with robust weighting and excluding all uv-spacings
shorter than 5 k$\lambda$. The image to the right, which has the highest
angular resolution, was done with natural weighting and excluding all
uv-spacings shorter than 10 k$\lambda$, shows the disk most clearly,
but has rather poor signal-to-noise. }

\includegraphics[ scale=0.6,angle=-90]{5r-cuts.ps}

\figcaption[]{
\label{fig-h13cncuts}
Position velocity cuts of H$^{13}$CN \jtra10 emission along the disk plane
(left panel) and along the outflow (right panel). }


\includegraphics[ scale=1.1,angle=-90]{dcn-channels.ps}

\figcaption[]{
\label{fig-dcn-chann}
DCN \jtra32 channel maps in grayscale overlaid with contours. Each panel
shows the DCN emission integrated over  a 1 km~s$^{-1}$ wide velocity
interval. The center velocity of each map is indicated at the top left
of each panel. The two star symbols mark the position of NGC\,7538\,S
(at 0\arcsec,0\arcsec{}) and IRS\,11\,S. The contours are linear
starting at 0.12 Jy~beam$^{-1}$ with a step size of 0.12 Jy~beam$^{-1}$.
}


\includegraphics[ scale=0.68,angle=-90]{dcn-cuts.ps}

\figcaption[]{
\label{fig-dcn-cuts}
Position velocity plots of DCN \jtra32 emission in grayscale overlaid
with contours. The contours are linear starting at  0.15 Jy beam$^{-1}$
and a step size of 0.10 Jy beam$^{-1}$. The left panel shows a cut along
the disk plane (p.a. = 58\degr{}), while the right panel shows a cut
along the outflow (p.a. = 145\degr{}). The systemic velocity is
indicated with a vertical line. The direction of the cuts is indicated
at top and bottom left of each figure. NGC\,7538\,S is at offset 0.}


\includegraphics[ scale=0.7,angle=-90]{dcn-outflow.ps}

\figcaption[]{
\label{fig-dcn-outflow}
Grayscale image of DCN \jtra32 emission overlaid with white contours
and integrated over 1.5 km~s$^{-1}$ (3 channels) centered on the cloud
velocity, $-$56~km~s$^{-1}$.  The greyscale image is overlaid with blue-
and red-shifted emission plotted with thick blue and red contours. In the
right panel we show emission integrated over 1.5  km~s$^{-1}$ and shifted
by 3 km~s$^{-1}$ relative to the cloud velocity, while the emission in
the right panel is shifted by 4.5 km~s$^{-1}$. The plane of the disk
is indicated by a line going through the center at a p.a. of 58\degr{}
and colored blue and red on the blue- and red-shifted side of the disk,
respectively. The position, extent, and direction  of the outflow is
indicated with arrows, blue to the northwest and red to the southeast.}


\includegraphics[ scale=1.0,angle=-90]{disk-spectra.ps}

\figcaption[]{
\label{fig-disk-spectra}
Spectra from the blue-shifted edge (NE), center, and red-shifted edge (SW)
of the disk for  the high angular resolution, robust weighted H$^{13}$CN
\jtra21  image (left panel) and for DCN \jtra32 (right panel).  For both
molecules we have indicated the systemic velocity and for H$^{13}$CN
additionally the velocities of the two hyperfine lines relative to the
main line, F = $2 \to 1$.}





\includegraphics[ scale=1.05]{mcn-disk.ps}

\figcaption[]{
\label{fig-mcn-disk}
BIMA contour images of integrated CH$_3$CN J = $12 \to 11$ for K-levels
0 to 5. For each K-level we have integrated the line emission over a
4.2  km~s$^{-1}$ wide velocity interval, except for K=4 and 5, where we
have used a wider velocity interval, 5.3  km~s$^{-1}$. The offsets are
relative to the center of the disk, \mbox{$\alpha_{2000.0}$ = 23$^h$
13$^m$ 44\psec98}, \mbox{$\delta_{2000.0}$ = $+$61\degr{} 26\arcmin{}
49\ptsec2}. The beam FWHM is 2\ptsec76 $\times$ 2\ptsec36  PA 22.9 \degr.}


\includegraphics[ scale=1,angle=-90]{mcn-spectra.ps}

\figcaption[]{
\label{fig-mcnspec}
Observed CH$_3$CN J = $12 \to 11$ spectra towards the center of
NGC\,7538\,S for K = 0 to 6. The grey vertical line indicates the
systemic velocity of the protostellar disk. The K = 0 and K = 1 spectra
are blended, which is seen in the bottom spectra. The velocity corresponds
to the K = 1 level, but we have also indicated with a grey line where the
systemic velocity fall for the K = 0 line.  The top spectrum includes
the CH$_3$$^{13}$CN K = 3 line, which  is separately labeled in the
panel. The peak ratio of CH$_3$CN to  CH$_3$$^{13}$CN for K = 3 is $\sim$
xx, indicating that the line is optically thick. Self absorption at the
systemic velocity of the cloud or at slightly red-shifted velocities is
seen in K-levels 0 to 3.}



\includegraphics[ scale=0.6,angle=-90]{k01-cuts.ps}

\figcaption[]{
\label{fig-k01-cuts}
Position velocity cuts of  CH$_3$CN J = $12 \to 11$ K = 0 and K=1 emission
along the disk plane (left panel) and along the outflow (right panel).}

\includegraphics[ scale=0.68,angle=-90]{k013disk-outflow.ps}

\figcaption[]{
\label{fig-k012do}
Greyscale plots enhanced with  contours of integrated  CH$_3$CN J
= $12 \to 11$ K = 1  emission (right panel) and K=3 emission (left
panel). Both K=1 and K=3 are integrated over 4.2 m~s$^{-1}$ as in Fig
~\ref{fig-mcn-disk}. These contour plots are overlaid with contours
of integrated high velocity emission, plotted in blue and red for the
blue-shifted and red-shifted wings of the emission. The integrated
blue- and red-shifted emission is aligned along the outflow direction
(p.a. $\sim$ 145\degr, demonstrating that CH$_3$CN is tracing the outflow,
not the disk. }

\includegraphics[ scale=0.8,angle=-90]{mcn_rot.ps}

\figcaption[]{
\label{fig-mcn_rot}
Population-diagram of  CH$_3$CN \jtra{12}{11} towards NGC\,7538\,S, see
discussion in Section \ref{mcn}. The solid curve shows a least squares
fit to the three lowest K-transition, K = 0 to K = 2, while the dashed
line is a fit for K = 2 to 5. The low K-transitions, which are likely to
be dominated by emission from the accretion disk, correspond to a
temperature of $\sim$ 50 K, while the high K-transitions, which are
dominated by the outflow, correspond to a temperature of 150 K. }

\end{document}

