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\begin{document}
\title{Photon Dominated Regions in NGC3603}
\subtitle{[CI] and mid-J CO line emission}
\author{
M. R\"ollig\inst{1},
C. Kramer\inst{2},
T. Minamidani\inst{4},
K. Sun\inst{2},
R. Simon\inst{2},
M. Cubick\inst{2},
M. Hitschfeld\inst{2},
%
     M.\,Aravena\inst{1} \and
     F.\,Bensch\inst{1} \and
%     A.\,Benz\inst{} \and
     F.\,Bertoldi\inst{1} \and
     L.\,Bronfman\inst{6} \and
%     M.\,Burton\inst{} \and
     M.\,Fujishita\inst{5} \and
     Y.\,Fukui\inst{3} \and
     U.U.\,Graf\inst{2} \and
     N.\,Honingh\inst{2} \and
     S.\,Ito\inst{3} \and
     H.\,Jakob\inst{2} \and
     K.\,Jacobs\inst{2} \and
     U.\,Klein\inst{1} \and
     B.-C.\,Koo\inst{6} \and
     J.\,May\inst{4} \and
     M.\,Miller\inst{2} \and
     Y.\,Miyamoto\inst{3} \and 
     N.\,Mizuno\inst{3} \and
     T.\,Onishi\inst{3} \and
     Y.-S.\,Park\inst{7} \and
     J.\,Pineda\inst{1} \and
     D.\,Rabanus\inst{2} \and
     H.\,Sasago\inst{3} \and
     R.\,Schieder\inst{2} \and
     J.\,Stutzki\inst{1} \and
     H.\,Yamamoto\inst{3} \and
     Y.\,Yonekura\inst{5}
}
\institute{ Argelander-Institut f\"ur Astronomie \thanks{Founded by merging of the
Sternwarte, Radiastronomisches Institut and Institut f\"ur Astrophysik und 
Extraterestrische Forschung}, Universit\"at Bonn, Auf dem H\"ugel 71, D-53121 Bonn, Germany
\and I. Physikalisches Institut, Universit\"at zu K\"oln, Z\"ulpicher Str. 77, D-50937 K\"oln,
Germany
\and
     Department of Astrophysics, Nagoya University, Chikusa-ku, Nagoya 464-8602, Japan
\and Department of Physics, Hokkaido University, Kita-ku, Sapporo 060-0810, Japan
     \and
     Department of Physical Science, Osaka Prefecture University,
     Osaka 599-8531, Japan
    \and
     Departamento de Astronom\'{i}a, Universidad de Chile, Casilla 36-D, Santiago, Chile
     \and
     Seoul National University, Seoul 151-742, Korea
}
\authorrunning{R\"ollig et al.}

\offprints{M. R\"ollig,\\ \email{roellig@astro.uni-bonn.de}}

\abstract{}
{
 We aim at deriving the excitation conditions of the
     gas as well as the local FUV intensities to get a coherent
picture of how the gas in NGC~3603 is energized by the central stars. }
{The NANTEN2-4m submillimeter telescope is used to map [Ci] 1.0, 2.1 and CO 4.3 and 7.6 lines in a $2'\times2'$ region around the central OB cluster HD~97950 in NGC 3603. These data are combined with C$^{18}$O 2--1 data,
HIRES/-processed IRAS 60 $\mu$m and 100 $\mu$m maps of the FIR continuum, and maps of IRAC on Spitzer.}
{
We used the HIRES far-infrared dust data to create a map of the FUV field heating the local dust. We can constrain the FUV field to values of $\chi=5-20\times10^3$ in units of the Draine field. Despite the large number of very massive O and WNL stars, the FUV field illuminating the PDR  is less intense than in the Orion Nebula because the interface is further away from the illuminating stars. Applying LTE and escape probability approximations, we can derive temperatures ($T_\mathrm{MM1}=26$~K, $T_\mathrm{MM2}=47$~K), column densities ($N_\mathrm{MM1}=1.6\times10^{22}$~cm$^{-2}$,$N_\mathrm{MM1}=2-5\times10^{22}$~cm$^{-2}$) and densities ($n_\mathrm{MM1}\ge10^{5.5}$, $n_\mathrm{MM2}\ge10^5$) for the two observed molecular clumps MM1 and MM2.
}
{...?}

\keywords{ISM: clouds} 

\maketitle

\section{Introduction}
Understanding the feedback between star formation and the interstellar medium (ISM) is important in order to understand the process of star formation. The physical and chemical properties of stars are the heritage of their parental clouds. Stars are born from interstellar gas and release metal-enriched material to the ISM when they die. Radiation from the stars is the prime heating source for gas and dust in  nearby molecular clouds and may additionally trigger velocity and density fluctuations, that stimulate further star formation. To understand the formation of these next generation stars, it is important to understand how the previous generation interacts with its parental clouds. The energy incident on  the clouds in the form of stellar far ultraviolet (FUV: 6~eV$ \le h\nu \le$ 13.6~eV) radiation  is countered by cooling emission of atomic fine-structure lines ([CI]370~$\mu$m, 610~$\mu$m, and [OI]63~$\mu$m, 145~$\mu$m) and by molecular rotational lines (CO, H$_2$O, OH, etc.). The cooling emission carries the imprint of the local physcial and chemical conditions and can be used to infer the type of environment conducive to maintaining star formation. 
 \begin{figure}
 \centering
 \includegraphics[width=7.5 cm,angle=-90]{ngc3603_co43_on_spitzer8mu_short_big.eps}
\caption{ 8~$\mu$m Spitzer/IRAC band (in MJy/sr) overlayed with CO 4--3 NANTEN2 observations presented in this paper. The position of the cluster is marked by the star. The boxes mark the position of the pillar heads. The crosses mark the positions along the cuts into MM1 and MM2.  Irac pixel size is 1.2".}\label{spitzer}
\end{figure}
%  \begin{figure*}
%  \begin{minipage}[hbt]{8.5cm}
%  \centering
%  \includegraphics[width=13 cm,angle=-90]{ngc3603_co43_on_spitzer8mu_short.eps}
%  \end{minipage}
%  \hfill
%  \begin{minipage}[hbt]{8.5cm}
%  \centering
%  \includegraphics[width=13 cm,angle=-90]{ngc3603_co43_on_spitzer5.8mu_short.eps}
%  \end{minipage}
% \caption{Spitzer/IRAC and NANTEN2 view of the central parts of NGC3603. Irac pixel size is 1.2". {\bf Left:} 8~$\mu$m IRAC band (in MJy/sr) overlayed with CO 4--3 NANTEN2 observations presented in this paper. {\bf Right:} 5.8~$\mu$m IRAC observation  (in MJy/sr) overlayed with NANTEN2 CO 4--3 data. The boxes mark the position of the pillar heads. The crosses mark the positions along the cuts into MM1 and MM2. }\label{spitzer}
% \end{figure*}
On their way into a molecular cloud, FUV photons are absorbed, and a depth-dependant chemical balance is established. Models of these so-called photon dominated regions (PDRs) typically predict a stratification of species like H/H$_2$, C$^+$/C/CO, and others. This stratification is found to be independent of the shape of the PDR \citep[e.g][]{gorti02}. However, observations often reveal [CI] emission coincident with that of CO \citep[e.g.][]{tatematsu99, ikeda02, sakai06}. Plane-parallel models cannot explain this behavior unless full face-on orientation is assumed. Spherical models under isotropic illumination show well-corellated [CI] and CO emission for low density clouds ($n\lesssim10^4$cm~$^{-3}$) but predict a limb brightening of the [CI] emission.
In this work we analyze the distribution of atomic carbon and warm CO in the NGC3603 star forming region and use PDR models to derive the excitation conditions of the gas.

\section{The NGC 3603 star forming region}
NGC 3603 is located in the Carina spiral arm ($l\approx 291.6^\circ, b\approx -0.5^\circ$) at a distance of about 6 kpc \citep{stolte06}. It is one of the most luminous (L$_\mathrm{bol}>10^7$ \lsun), optically visible HII regions in the Galaxy, with the massive OB cluster NGC~3603~YC (Young Cluster) as a power source \citep{goss69}. The compact core of the cluster was designated  HD~97950 due to its star-like appearance. As a comparison, NGC~3603 is 100 times more luminous than the Orion Nebula.  This young cluster 
can be considered a one of the few Galactic starburst clusters, which are essential for the understanding of extragalactic star formation. With a stellar
cluster mass of $\approx 10^4$ M$_\odot$ residing in a cloud of total gas mass
of $4\times 10^5$ M$_\odot$ \citep{grabelsky88}, it is the most compact 
Galactic star-forming regions outisde the Galactic center region \citep{stolte04}. To the 
south of the cluster is a giant molecular cloud (see Figure~\ref{spitzer}). The 
intensive radiation and fast stellar winds from the cluster are excavating large gaseous 
pillars\citep{brandner00}. Furthermore, CS observations by \citet{nuernberger02} show that the 
molecular environment also extends much further to the north ($>10$\arcmin), hosting numerous massive 
molecular clumps.  
\section{Observations}
We used the NANTEN2-4m telescope at 4865m altidute at Pampa la Bola in northern Chile 
to map the central  2\arcmin $\times$ 2\arcmin region of NGC3603. We observed the rotational transitions 
of $^{12}$CO  J=4$\to$3 (461.0408~GHz)  and J=7$\to$6 (806.6517~GHz) and the two fine-structure transitions of atomic carbon \CI, $^3$P$_1$-$^3$P$_0$ (492.1607~GHz) and $^3$P$_2$-$^3$P$_1$ (809.3446~GHz) (henceforth 1-0 and 2-1), between September and November 2006 with a 
dual-channel 460/810~GHz receiver. The exact line frequencies were taken from the {\it Cologne Database for Molecular Spectroscopy} CDMS \citep{mueller05,mueller01}. Double sideband (DSB) receiver temperatures
were $\approx$ 250~K in the lower frequency channel and $\approx$ 750~K in
the upper channel. The intermediate frequencies (IF) are
4~GHz and 1.5~GHz, respectively. The latter IF allows simultaneous
observations of the CO 7--6 line in the lower
sideband and the \CI  2--1 line in the upper sideband. These two lines were 
observed with one of
the two lower lines in the 460~GHz channel. As backends, we used two
acousto optical spectrometers (AOS) with bandwidths of
1GHz. The channel resolution was 0.37 km~s$^{-1}$ at 460~GHz
and 0.21 km~s$^{-1}$ at 806~GHz.
The pointing accuracy was checked regularly on Jupiter,
IRC+10216, and IRc2 in OrionA. The applied corrections
were always $<$20\arcsec and usually $<$
10\arcsec. To determine the atmospheric transmission, we measured 
the atmospheric emission 
at the reference position (RA$_\mathrm{J2000.0}=$11:15:08.85, Dec$_\mathrm{J2000.0}=$-61:16:50). Spectra 
of the two frequency 
bands were calibrated seperately,
and sideband imbalances were corrected using the
atmospheric model {\em atm} \citep[Atmospheric Transmission at Microwaves, cf.][]{pardo01}.
Observations
were taken on-the-fly (OTF), scanning in right
ascension at a speed of 2.5\arcsec/sec and sampling every 10\arcsec. The reference position was observed at the
beginning of each OTF scanning line.

Our reference position is RA$_\mathrm{J2000.0}$=11:15:08.85, Dec$_\mathrm{J2000.0}$=-61:16:50,
 73\arcsec south-east of the
central OB cluster (HD97950) at RA$_\mathrm{J2000.0}$=11:15:07.26, Dec$_\mathrm{J2000.0}$=-61:15:37.48.  
The half power beam widths (HPBW) deconvolved
from the observed full widths at half maxima
(FWHM) are 38.0\arcsec and 26.5\arcsec, in the lower
and upper receiver bands respectively. Beam efficiencies $B_{eff}$ are  50\% and 45\%, respectively \citep{simon07}. The forward efficiency, $F_{eff}=86$\% in both bands, was determinded from skydips. The raw data were calibrated to antenna temperatures $T_A^*$ and scaled to main beam temperatures T$_{mb}$ with tha factor $F_{eff}/B_{eff}$. We present all data in units of T$_{mb}$. Second order polynomial baselines were subtracted from all spectra. A few positions required higher order (up to 5th order) baselines to be subtracted. {\bf MOVE Along the two cuts all \CI(2--1) and few (1--0) spectra showed strong standing wave patterns. We corrected for standing waves by subtracting sinusoidal baselines.}
About 36\% of the total power is detected in at least two error beams \citep[for details see ][]{simon07,kramer07}
\section{Data}
\subsection{Dust and PAHs}

In Fig.\ref{spitzer} we show a map of integrated CO
4--3 intensities from NANTEN2 overlayed on an 8~$\mu$m image 
 taken with the Infrared Array
Camera (IRAC) on board the Spitzer space telescope\footnote{These
  post-BCD data were retrieved from the Spitzer archive (URL http://archive.spitzer.caltech.edu/). Because of
strong saturation effects, we chose the short exposure data.}. The position of the OB cluster is marked by
a star. The image shows prominent molecular clouds southwest and southeast
of the cluster position. Following \cite{nuernberger02}, we refer to
 them as MM1 and MM2, respectively.
The IRAC images show the sharp PDR interfaces between the HII region and
the molecular cloud. The positions of these intefaces match the 
pillar-like structures
observed in HST and VLT images \citep{brandner00}(ADD MORE). We 
also note a dusty filament, which 
connects MM1 and MM2 in a large arc 1.5' to 2' south of the western 
pillar head. This
filament is also visible as a slight enhancement ($\approx 80$~K$\cdot$km/s) in 
the CO 4--3 emission to the southwest. The strong 
 8~$\mu$m emission ($>$ 10$^4$ MJy/sr) is due to the 
 FUV flux produced by the OB cluster 
heating the gas and dust in the molecular clouds. The 8\,$\mu$m band, 
which includes strong PAH emission (7.6,7.8, and 8.6~$\mu$m), traces 
the PDR interface especially well.
  
\subsection{NANTEN2 observations}
\subsubsection{Maps of integrated intensity}
\begin{figure}[h]   
  \centering
  \includegraphics[angle=-90,width=8.5cm]{ngc3603_co43_76_ci10_21.eps}
% Peak integrated intensities:  
% CO 4-3: 284.72735595703 
% CO 7-6: 129.87705993652 
% CI 1-0: 29.338357925415 
% CI 2-1: 24.477132797241 

\caption{Velocity integrated maps ($200\arcsec\times200\arcsec$) of CO
4--3, 7--6, \CI\ 1--0, and 2--1 smoothed to a common angular resolution of
$38\arcsec$ (1.1~pc at 6~kpc), and integrated over a velocity
range from $6$ to $26$~km~s$^{-1}$. Colorscale and contours show the 
same data. Contours range
between 10 and 90\% of the peak intensities which are 285~K$\cdot$km~s$^{-1}$
for CO 4--3, 129~K$\cdot$km~s$^{-1}$ for CO 7--6, 29~K$\cdot$km~s$^{-1}$ for \CI\
1--0, and 24~K$\cdot$km~s$^{-1}$ for \CI\ 2--1.
%  
The position of the compact OB cluster is marked by a
white star. The position of the the pillars, as seen in the HST images,
are marked by white squares.
% 
Dashed lines and small crosses spaced by $22\arcsec$ mark two cut 
from the OB cluster
to the peak positions of the two clumps MM1 (short cut) and MM2 (long cut).
 The circle marks the resolution and the two white crosses mark 
the position of the 
CS(2-1) peaks \citep{nuernberger02} in MM1 and MM2.}
\label{fig-ngc3603-4-plots}   
\end{figure}
Fig. \ref{fig-ngc3603-4-plots} shows maps of integrated 
CO 4--3, 7--6, \CI\ 1--0, and 2--1 emission. The OB cluster position is marked
by a star. The two molecular clumps MM1 and MM2 are visible: MM1 to 
the southwest of the OB 
cluster and MM2 to the southeast. The peak intensities are 285~K$\cdot$km~s$^{-1}$
for CO 4--3, 129~K$\cdot$km~s$^{-1}$ for CO 7--6, 29~K$\cdot$km~s$^{-1}$ for \CI\
1--0, and 24~K$\cdot$km~s$^{-1}$ for \CI\ 2--1. MM2 is very prominent in all 
4 observed transitions
while MM1 is weaker in \CI\ 1--0, and clearly visible in the other three 
transitions. 
  
\begin{table*}[htb]
\caption{Observed integrated intensities $I=\int T_\mathrm{mb}\,d\mathrm{v}$ in units of K$\cdot$km~s$^{-1}$ , v$_\mathrm{LSR}$ in units of km~s$^{-1}$, and the line widths FWHM in units of km~s$^{-1}$ computed as 0$^\mathrm{th}$, 1$^\mathrm{st}$, and 2$^\mathrm{nd}$  moment of the spectra between v$=8...22$~km~s$^{-1}$. The positions lie along a line starting from the OB cluster. The cluster position has been omitted. Rotational transitions of CO are denoted 43 ($^{12}$CO 4-3) and 76 ($^{12}$CO 7-6). The atomic carbon fine-structure transitions are denoted 10 ($^3P_1-^3P_0$) and 21 ($^3P_2-^3P_1$). 
%The position 20\arcsec/-20\arcsec corresponds to the position of MM2, derived from 
%CS (2--1)\citep{nuernberger02}. 
}\label{tabobs} 
\centering  
\begin{tabular}{c|c|c|c|c|c|c|c|c|c|c|c|c}
\hline \hline
 $\Delta\alpha/\Delta\delta$ & $I_{43}$ & $\Delta$v$_{43}$ & v$_\mathrm{LSR}$& $I_{76}$ & $\Delta $v$_{76}$ & v$_\mathrm{LSR}$& $I_{10}$ & $\Delta$v$_{10}$& v$_\mathrm{LSR}$&$I_{21}$&$\Delta$v$_{21}$& v$_\mathrm{LSR}$ \\

 [ \arcsec /\arcsec ]&  [K$\cdot$km/s] & [km/s]& [km/s]& [K$\cdot$km/s] &  [km/s]&  [km/s]& [K$\cdot$km/s] & [km/s]& [km/s]& [K$\cdot$km/s] & [km/s]& [km/s]\\  \hline
%-10/70 & 7 & 0.0 & 12.6 & 8 & 9.6 & 14.9 & -3 & 15.6 & 14.2 & 2 & 0.0 & 18.7 \\
%0/50 & 25 & 0.0 & 16.3 & 12 & 8.7 & 14.0 & 7 & 10.4 & 14.0 & 0 & 0.0 & -3.6 \\
10/30 & 55 & 6.2 & 13.6 & 31 & 7.5 & 13.7 & 8 & 8.4 & 14.7 & 0 & 0.0 & 1.8 \\
20/10 & 154 & 6.9 & 13.9 & 76 & 7.0 & 13.4 & 14 & 9.0 & 14.3 & 8 & 3.7 & 14.5 \\
30/-10 & 273 & 7.7 & 14.4 & 128 & 7.3 & 13.7 & 24 & 6.0 & 14.9 & 22 & 4.7 & 14.8 \\
40/-30 & 303 & 8.3 & 14.3 & 132 & 7.8 & 13.8 & 29 & 6.3 & 14.3 & 24 & 5.9 & 14.0 \\
50/-50 & 232 & 7.5 & 13.8 & 93 & 7.7 & 13.9 & 24 & 7.0 & 14.1 & 14 & 4.2 & 13.6 \\
%20/-20 & 259 & 7.2 & 14.1 & 119 & 7.3 & 13.4 & 12 & 2.5 & 14.3 & 19 & 5.0 & 14.4 \\ \hline
%-10/70 & 7 & 0.0 & 12.6 & 8 & 9.6 & 14.9 & -3 & 15.6 & 14.2 & 2 & 0.0 & 18.7 \\
-30/60 & 49 & 7.1 & 13.6 & 25 & 7.6 & 13.5 & 2 & 0.0 & 25.8 & 5 & 5.8 & 14.6 \\
-50/50 & 93 & 5.8 & 13.3 & 41 & 7.0 & 13.4 & 10 & 8.3 & 12.9 & 7 & 4.6 & 13.1\\
 \hline \hline
\end{tabular}
\end{table*}

{\bf Both CO maps show the transition from the HII region to the molecular 
cloud, especially for MM2. MM1 presumably is smaller than our beam size 
\citep{nuernberger02}, hence it is not possible to infer detailed structure 
information from the maps.}
 The peak positions of CO 4--3, 7--6, and \CI\ 2--1 
match very 
well, while the
peak of the \CI\ 1--0 emission is shifted (~15\arcsec) to the south-east.  However
we note a very good spatial correlation between the CO and
 \CI\ emission. All peaks coincide within a beam radius. We cannot 
confirm the existance
of a standard C-CO layering as expected from simple 
edge-on plane-parallel PDR scenarios. 
It is possible to explain coincident \CI\ and CO emisison
 with a face-on configuration,
but the plainly visible pillar structures in the HST observations 
and the very sharp interface
visible in the IRAC image in Fig.\ref{spitzer} clearly 
show a prominent, edge-on 
 PDR interface. 
The velocity structure of the observed field is shown in the CO 4--3 velocity
channel maps (Fig.\,\ref{fig-ngc3603-co43-channels}). From the channel
 maps, it is obvious
that the emission in MM1 shows a smaller kinematic range than MM2. 
MM1 is not 
observable at velocities redder than 16~km~s$^{-1}$, while 
the emission in MM2 extends up
to 21~km~s$^{-1}$. At larger velocities, the emission gradually shifts to the
southwest.    
\begin{figure}[h]   
  \centering
  \includegraphics[angle=-90,width=8.5cm]{ngc3603-co43-channels.eps}
\caption{Velocity structure of the observed field: CO 4--3 velocity
channels of 1~km~s$^{-1}$ width.  Contours range between 5 and
45~K$\cdot$km~s$^{-1}$ in steps of 5~K$\cdot$km~s$^{-1}$. }
\label{fig-ngc3603-co43-channels}   
\end{figure}   
\subsubsection{Spectra along a cut through the region}
\begin{figure}[h]   
  \centering   
  \includegraphics[angle=-90,width=8.5cm]{ngc3603-cut_spectra.eps}
  \caption{Spectra along two cut connecting
    the OB cluster and the centre of MM1 (bottom) and MM2 (top). 
    All data are at a
    common resolution of $38\arcsec$ and on the main beam scale.} 
\label{fig-ngc3603-cut-spectra}   
\end{figure} 
The spectra along the two cuts to the peak positions in MM1 and MM2, 
shown in Fig.\ref{fig-ngc3603-cut-spectra},
 show the kinematic
structure of the interface regions and the molecular clumps. 
The spectra at the positions 30\arcsec/-10\arcsec, 40\arcsec/-30\arcsec, and 50\arcsec/-50\arcsec 
do not show simple Gaussian 
line profiles. \cite{nuernberger02} observed similar line profiles in their
CS 3--2 and 2--1 observations of MM2. They used two Gaussian components
seperated by 3~km~s$^{-1}$ to fit the emission profiles. Our analysis
showed that it is not possible to use a similar two component 
Gaussian fit to reproduce our observations at all positions. 
We derived the first three moments of the spectral line, i.e. 
integrated intensity, mean velocity, and FWHM, over the channels in the range 
$v=6-22$~km~s$^{-1}$.
 At the offsets -10\arcsec/70\arcsec and 0\arcsec/50\arcsec we don't find
sufficient emission to apply any reasonable analysis, and we
 omit these two positions
in the following. The derived moments are
given in  Table \ref{tabobs}.


\begin{table*}[htb]
\caption{Line ratios R$_{74}$ ($I_{76}/I_{43}$), R$_{21}$ ($I_{21}/I_{10}$) and R$_{14}$ ($I_{10}/I_{43}$) for all positions along the two cuts. The LTE excitation temperature is derived from the optically thick $I_{43}$ emission.  The C column densities are derived under the assumption of LTE and optically thin \CI emission. REPHRASE CAPTION!!!! Values of the integrated intensities of C$^{18}$O 2--1 as presented in \cite{nuernberger02} along the two cuts, the LTE excitation temperature as derived from $I_{43}$, the LTE column densities of C$^{18}$O, and the total gas column density, asuming an isotope ratio of 500 and CO:H$_2$=8$\times10^{-5}$ \citep{frerking82}, i.e. an assumed ratio of C$^{18}$O/H$_2$=2$\times10^{-7}$.}\label{tablte}
\centering
\begin{tabular}{c|c|c|c|c|c|c|c|c|c}
 \hline \hline
 $\Delta\alpha/\Delta\delta$ &  R$_{74}$ &R$_{21}$ & R$_{14}$&T$_\mathrm{ex}$& N(C)&$\int\,T_\mathrm{mb}(\mathrm{C}^{18}\mathrm{O})dv$ & N$_\mathrm{C18O}$&N$_\mathrm{tot}$&N(C)/N$_\mathrm{tot}$ \\

 [\arcsec / \arcsec ]  & & & &[K]&cm$^{-2}$ & [K km s$^{-1}]$ &[10$^{15}$cm$^{-2}]$&[10$^{21}$cm$^{-2}]$& \\ \hline
%-10/70 & 1.10 & -- & -- & -- & -- & 0.7 &  -- & --& -- \\ 
%0/50 & 0.47 & -- & -- & 10 & -- & 1.5 &  1.31 & 6.55& -- \\
10/30 & 0.56 & 0.04 & 0.15 & 18 & 1.28$\times 10^{17}$ & 1.6 &  1.89 & 9.47& 1.4$\times 10^{-5}$  \\
20/10 & 0.50 & 0.63 & 0.09 & 32 & 1.91$\times 10^{17}$ & 1.9 & 3.5 & 17.5&1.1$\times 10^{-5}$  \\
30/-10 & 0.47 & 0.90 & 0.09 & 46 & 3.59$\times 10^{17}$ & 4.2 &  10.4 & 51.8&6.9$\times 10^{-6}$  \\
40/-30 & 0.44 & 0.85 & 0.10 & 47 & 4.21$\times 10^{17}$ & 4.3 &  10.8 & 54.1&7.8$\times 10^{-6}$  \\
50/-50 & 0.40 & 0.59 & 0.11 & 41 & 3.48$\times 10^{17}$ & 2.1 &  4.75 & 23.7&1.5$\times 10^{-5}$  \\
%20/-20 & 0.46 & 1.54 & 0.05 & 46 & 1.88$\times 10^{17}$& 4.7 & 11.7 & 58.6&3.2$\times 10^{-6}$  \\
%-10/70 & 1.10 & -- & -- & -- & --& 0.7 & --&--&\\
-30/60 & 0.52 & 2.72 & 0.04 & 15 & 1.$\times 10^{17} $& 1.3 &  1.41 & 7.05&1.4$\times 10^{-5}$  \\
-50/50 & 0.45 & 0.68 & 0.12 & 26 & 1.51$\times 10^{17}$& 2.1 &  3.23 & 16.2&9.3$\times 10^{-6}$  \\
\hline \hline
\end{tabular}
\end{table*}
% \begin{table}[htb]
% \caption{Values of the integrated intensities of C$^{18}$O 2--1 as presented in \cite{nuernberger02} along the two cuts, the LTE excitation temperature as derived from $I_{43}$, the LTE column densities of C$^{18}$O, and the total gas column density, asuming an isotope ratio of 500 and CO:H$_2$=8$\times10^{-5}$ \citep{frerking82}, i.e. an assumed ratio of C$^{18}$O/H$_2$=2$\times10^{-7}$.
% }\label{columnlte}
% \centering
% \begin{tabular}{c|c|c|c|c|c}
%  \hline \hline
% $\Delta \alpha $/$\Delta \delta $&$\int\,T_\mathrm{mb}dv$ & T$_\mathrm{ex}$& N$_\mathrm{C18O}$&N$_\mathrm{tot}$&N(C)/N$_\mathrm{tot}$ \\

%  [ \arcsec /\arcsec ] & [K km s$^{-1}]$ &[K]&[10$^{15}$cm$^{-2}]$&[10$^{21}$cm$^{-2}]$&\\\hline
% %-10/70 & 0.7 & -- &  -- & --& -- \\ 
% %0/50 & 1.5 & 10 & 1.31 & 6.55& -- \\
% 10/30 & 1.6 & 18 & 1.89 & 9.47& 1.4$\times 10^{-5}$  \\
% 20/10 & 1.9 & 32 & 3.5 & 17.5&1.1$\times 10^{-5}$  \\
% 30/-10 & 4.2 & 46 & 10.4 & 51.8&6.9$\times 10^{-6}$  \\
% 40/-30 & 4.3 & 47 & 10.8 & 54.1&7.8$\times 10^{-6}$  \\
% 50/-50 & 2.1 & 41 & 4.75 & 23.7&1.5$\times 10^{-5}$  \\
% 20/-20 & 4.7 & 46 & 11.7 & 58.6&3.2$\times 10^{-6}$  \\
% %-10/70 & 0.7 & --&--&--&\\
% -30/60 & 1.3 & 15 & 1.41 & 7.05&1.4$\times 10^{-5}$  \\
% -50/50 & 2.1 & 26 & 3.23 & 16.2&9.3$\times 10^{-6}$  \\
% \hline \hline
% \end{tabular}
% \end{table}
\subsection{Analysis}
\subsubsection{LTE -- Column densities and temperatures}
In Table \ref{tablte} we give the line ratios R$_{74}$ ($I_{76}/I_{43}$),
 R$_{21}$ ($I_{21}/I_{10}$) and R$_{14}$ ($I_{10}/I_{43}$) for all 
positions along the 
two cuts. We computed the LTE temperatures using the optically thick
CO 4--3 emission. We derive temperatures of $\approx$45~K for the 
peak position in
MM2 and $\approx$25~K for MM1. This is consistent with estimates 
from the \CI line ratio.  R$_{21}$ is a 
sensitive function of the \CI\
excitation temperature.  In the optically thin limit and assuming LTE,
$T_{\rm ex}=38.3\,{\rm K}/\ln[2.11/R_{21}]$. In MM2 we 
find ratios between 
0.6 and 0.9
which correspond to temperatures between 30 and 45~K.
NOT VALID FOR ALL POINTS. MAYBE REMOVE CS POSITION AT ALL.
 For MM1 the \CI line ratio 
gives a temperature estimate of $\approx$\, 33~K. We then used the 
excitation temperature to compute the column density of atomic carbon 
under the assumption of LTE and optically thin emission. The results 
are also given in Table \ref{tablte}. 
% \begin{figure}[h]   
%   \centering   
%   \includegraphics[angle=-90,width=8cm]{ngc3603-overlay-tdust-co43.eps}
%   \caption{Values of the dust temperature derived from the HIRES 60, and 
% 100~$\mu$m
% fluxes as color map. Overlayed in thin contours 
% is the NANTEN2 CO 4--3 map. The central OB cluster is marked by a filled 
% triangle. 
% The positions of prominent IR sources as given by \cite{frogel77} are marked by
% stars. The two pillar heads are denoted by the squares.}  
% \label{fig-ngc3603-tdust}
% \end{figure}
% CHECK TDUST AGAIN AND GIVE NUMBERS AT CUTPOSITIONS
% These gas temperatures compare well with the dust temperatures as 
% derived from the IRAS 60~$\mu$m and 100~$\mu$m ratios, 
% using $T_\mathrm{d}=95.94/(ln\left[(1.67)^{4.5}f_\nu(100)/f_\nu(60)\right])$
%  \citep{schwering88,hildenbrand83}. Fig.~\ref{fig-ngc3603-tdust}
% shows the resulting dust temperature map. Due to the higher cooling 
% efficiency of dust particles compared to the gas, we expect
%  $T_\mathrm{d}\le T_\mathrm{gas}$.

We estimate dust temperatures from the ratio of HIRES
60~$\mu$m and 100~$\mu$m data, assuming blackbody emission with a
spectral index of 1.5 for the dust. For temperatures below 100~K
the dust temperature can be approximated according to
$T_D=-87.4/\ln(2.149^{-4}R_{60/100})$.  Along the two cuts we find almost 
constant dust temperatures of 25~K and 27~K for MM1 and MM2, respectively.
These temperatures are only rough estimates, of the cool dust 
 because of large beam filling effects. 
   
%  Across MM1 and
%  MM2 we find dust temperatures between 35 and 40~K. Towards the
%  eastern interface of MM2 the dust temperature increases up to
%  almost 60~K.      
 To derive the total column densities we use the integrated
 intensity of C$^{18}$O 2--1 as presented in \cite{nuernberger02}.
 Assuming an isotope ratio of 500 and CO:H$_2$=8$\times10^{-5}$ 
\citep{frerking82}, i.e. an assumed ratio of
 C$^{18}$O/H$_2$=2$\times10^{-7}$, we compute the column densities
 along the two cuts.
For MM1, we find a total column density of 1.6$\times10^{22}$~cm$^{-2}$;
 for MM2, $N=2...5\times10^{22}$~cm$^{-2}$. 
 Table \ref{tablte} summarizes the results and also gives the ratio
 N(C)/N$_\mathrm{tot}$. We find that the 
relative abundance of atomic carbon drops towards the peak positions
with values of  $9.3\times10^{-6}$ (MM1)and $6.9-7.8\times10^{-6}$ (MM2) and 
increases at positions towards as well as away from the OB cluster.
{\bf Even though the spatial resolution of our maps is rather coarse,
this could be an indication for a C/CO stratification, because in this case
we would expect limb brightened [CI] emission.}
% \begin{figure}[h]   
%   \centering   
%   \includegraphics[angle=-90,width=8cm]{ngc3603-overlay-fuv-co43.eps}
%   \caption{Values of the FUV field derived from the HIRES 60, and 100~$\mu$m
% fluxes as color map. The strong, dashed contours correspond to values of $\chi$\,=\,
% 1000,\,2000, and 5000 in units of the Draine field. Overlayed in thin contours 
% is the NANTEN2 CO 4--3 map. The central OB cluster is marked by a filled triangle. 
% The positions of prominent IR sources as given by \cite{frogel77} are marked by
% stars. The two pillar heads are denoted by the squares.}  
% \label{fig-ngc3603-fuv}   
% \end{figure}   

 \begin{figure*}
 \begin{minipage}[hbt]{8.5cm}
 \centering
  \includegraphics[angle=-90,width=8cm]{ngc3603-overlay-fuv-co43.eps}

% \includegraphics[width=13 cm,angle=-90]{ngc3603_co43_on_spitzer8mu_short.eps}
 \end{minipage}
 \hfill
 \begin{minipage}[hbt]{8.5cm}
 \centering
 \includegraphics[width=7 cm,angle=-90]{ngc3603_fuv_on_spitzer5.8mu_short_big.eps}
 \end{minipage}
\caption{{\bf Left:}Values of the FUV field derived from the HIRES 60, and 100~$\mu$m
 fluxes as color map. The strong, dashed contours correspond to values of $\chi$\,=\,
 1000,\,2000, and 5000 in units of the Draine field. Overlayed in thin contours 
 is the NANTEN2 CO 4--3 map. The central OB cluster is marked by a star.  The two pillar heads 
are denoted by the squares.
{\bf Right:}Spitzer/IRAC 5.8~$\mu$m observation  (in MJy/sr) overlayed with FUV fluxes as derived from IRAS/HIRES flux ratios. The contours correspond to values of $\chi$\,=\,2000, 3000, 4000, and 5000. IRAC pixel size is 1.2". The boxes mark the position of the pillar heads. The crosses mark the positions along the cuts into MM1 and MM2. }\label{fig-ngc3603-fuv}
\end{figure*}


\subsubsection{FUV intensities}
\begin{figure*}[hbt]   
  \centering   
  \includegraphics[angle=0,width=15cm]{ngc3603_escprob_paper.eps}
  \caption{Comparison of the observed line ratios $^{12}$CO7--6/$^{12}$CO4--3, \CI 1--0 /$^{12}$CO4--3, and \CI 2--1/ \CI 1--0 with results from an escape probability model at the peak positions of MM1 and MM2. The middle, solid contours represent the observed ratios, the outer dash-dotted contours represent the 20\% uncertainties. The grey-scale image shows the reduced $\chi^2$ of the fit. The white, dotted contours correspond to $\chi^2$ values of 1, 2, and 5.}  
\label{fig-ngc3603-escprob}   
\end{figure*}   
We use IRAS data to derive the FUV continuum in the observed region.
To this end  we obtained 
 high resolution (HIRES) 60
  and 100~$\mu$m images (2\degree$\times$2\degree) from the IPAC data center\footnote{http://www.ipac.caltech.edu/}. Enhanced
  resolution images of $\sim1'$ resolution were created using the
  maximum correlation method \citep{aumann90}. Following \cite{nakagawa98},
  we combined these two data sets to create a map of
  far-infrared intensities between 42.5~$\mu$m
  and 122.5~$\mu$m \citep{helou88}. Under the assumption that the
  FUV energy absorbed by the grains is reradiated in the far-infrared (FIR),
  we then computed the FUV fluxes
  ($\chi$) from the emergent FIR
  intensities \citep[cf.][]{kramer05} $I_{\rm FIR}$, using $\chi/\chi_0=4\pi~I_{\rm FIR}$, with $\chi_0=2.7\times 10^{-3}$~erg~s$^{-1}$~cm$^{-2}$ 
\citep{draine78}.  The resulting map of the FUV continuum is shown in the left panel in
Fig. \ref{fig-ngc3603-fuv}.  The dashed contours correspond 
to values of $\chi$\,=\,
1000,\,2000, and 5000. Overlayed in thin contours 
is the NANTEN2 CO 4--3 map. The central OB cluster is marked by a
 star.  The two pillar heads are denoted by the squares. At 
the peak position of
MM1, we find FUV fields of $\chi=3460$. Along the cut in MM2, we 
find that $\chi$ gradually increases from 3350 at the position of 
the OB cluster 
to 5230 at the peak position. Due to the low spatial resolution
of the HIRES data, these values are lower limits since beam dilution effects
are not negligible. 
   
To estimate upper limits for the total FUV flux, we consider the 
total luminosities of the
most massive O stars in the central OB cluster. The most
massive members of the OB cluster are 3 WNL stars, 
6 O3 stars (III+V) and a dozen more O stars 
\citep{drissen95}. They produce 
the FUV flux that dominates the heating of the PDRs and the 
molecular clouds.  At an 
effective temperature of 24000~K the ratio of the
 FUV energy density to the total energy density emitted by the star
 $\Phi_\mathrm{FUV}/\Phi_\mathrm{tot}\approx0.7$ is maximal 
if we assume pure black body emission. At higher temperature 
relatively more energy is emitted in the EUV range
 ($13.6\,\mathrm{eV}< h\nu < 130\,\mathrm{eV}$). {\bf Please note, that
\citet{pauldrach98} showed in model calculations that for 
effective temperatures below 45000~K, the ratio of FUV to EUV 
photon rates is considerably higher than the ratio derived for 
pure blackbody spectra \citep[see also][]{brandner00}. This
is because EUV photons are absorbed in the ionization front.
In the following we neglect this effect and assume pure blackbody
characteristics.}

{\bf Applying effective temperatures and luminosities as given by
 \citet{panagia73} we calculated a total FUV luminosity of
 $2.4\times10^{40}$~erg~s$^{-1}$ from the contribution of each cluster
 member. Depending on the distance �from the cluster $d$, in units of
 pc, the FUV flux is $\chi=7.2\times10^4 d^{-2}$. At a distance of 6~kpc,
 one parsec equals an angular distance of 34\arcsec, i.e.somewhat smaller
 than the projected distance between the cluster and edge of MM2 as seen
 for example in Fig.~\ref{spitzer} ($\approx 46$\arcsec). If we assume
 that the cluster and the molecular clouds are situated in the same
 plane the FUV field at the peak position in MM2 drops to $\chi\approx7000$.
 This is of the same order as the flux at the MM2-peak derived from the 
IRAS data. However, an increasing FUV field towards the cluster cannot
 be seen in Fig.~\ref{fig-ngc3603-fuv}. Obviously, we expect the peak
 of molecular emission to be further away from the cluster than the
 interface region. Consequently, the FUV field should drop along the
 cut into MM2.  Fig.~\ref{fig-ngc3603-fuv} shows the opposite. One
 reason is the low resolution of the HIRES maps. Beam sizes vary from
 $\sim$33\arcsec to over 120\arcsec across the maps, hence the FUV
 values in Fig.~\ref{fig-ngc3603-fuv} might be considerably beam
 dilluted. In the right panel in Fig.~\ref{fig-ngc3603-fuv} we overlayed
 the FUV fields derived from the HIRES data on 5.8$\mu m$ Spitzer/IRAC observations
of NGC~3603 to illustrate the beam filling effect:
% The FUV map was derived from HIRES data measured at 
60 and 100$\mu$m emission can only be measured if dust is present at all.
 The Spitzer map shows no dust emisssion between the interface and the
 cluster. The HIRES beam size at the cluster position is almost circular
 with a 
FWHM of $\sim 35$\arcsec.  Hence the only contribution to the IRAS/HIRES
 fluxes at the cluster position can come from the interface regions of MM1
 and MM2. Even so, the beam dillution is significant and the derived FUV
 fluxes at the cluster position are a factor 20 smaller than the estimates
 from the speactral types. At the MM2-peak the beam is almost fully filled
 and the FUV fluxes are consistent with the assumption that the molecular
 cloud and the cluster lie in almost the same plane. This also supports the 
assumption that the FUV irradiation of the OB cluster created the pillars seen in the HST/VLT images. 

%The above analysis is also consistent with the FUV field determined from 
%[CII] fluxes measured by ISO satellite.
The derived FUV fluxed can be used to estimate the ratio $I_\mathrm{CII}/I_\mathrm{FUV}$,
i.e. the fraction of FUV energy that is reemitted in the the [CII] 158$\mu$m 
cooling line. 
 We retrieved the [CII] spectrum 
from the ISO data archive\footnote{http://isowww.estec.esa.nl/ida/}
 and compute an integrated intensity of 
$2\times10^{-3}$erg~s$^{-1}$~cm$^{-2}$~sr$^{-1}$.
Most of the FUV energy that irradiates the cloud is reradiated in the 
continuum, but a small fraction
is reemitted in cooling lines, as the [CII] 158$\mu$m line. 
Applying the FUV flux derived from the HIRES data, we estimate 
$I_\mathrm{CII}/I_\mathrm{FUV}\approx 0.2..0.3\%$. This is consistent with
similar results from regions of active star formation, e.g. nuclear regions of galaxies, 
where approximately 0.1 to 1 \% of the total 
FUV input is reradiated in the [CII] line \citep{stacey91}. However this remains a rough 
estimate because of the large beam sizes.
% and the unknown contribution of the 
%HII region to the measured CII flux. 

We conclude that that the FUV flux, efficiently illuminating the molecular 
clumps MM1 and MM2 
 ranges between $2\times10^{4}$ (from the FUV radiation of the cluster members) and $5\times10^{3}$ (from the FIR data) in units of the Draine field. Approximately 0.2 to 0.3\% of the total FUV energy 
is reemitted in the [CII] 158$\mu$m cooling line. }  


\subsubsection{Escape Probability -- density and temperatures}

In Figure \ref{fig-ngc3603-escprob} we show a comparison of the observed line ratios $R_{74}$, $R_{14}$, and $R_{21}$ with results from an escape probability (EP) model at the peak positions of MM1 and MM2.(REF EP STUTZKI et al. ?????)(ONE SENTENCE ON EP MODEL){\bf We assumed a CO:C abundance ratio of 10:1, consistent with the values from Table~\ref{tablte}.} The solid contours represent the observed ratios, the dash-dotted contours flanking the solid contours represent 20\% uncertainties. The grey-scale image shows the $\chi^2$ of the fit:
\begin{equation}
\chi^2=\sum_{i=1}^3\left(\frac{R_i^{obs}-R_i^{mod}}{\sigma_i}\right)^2
\end{equation}
with the observed and modelled line ratios $R_i^{obs}$, and $R_i^{mod}$ and the error $\sigma_i$ which we assumed to be 20\% for all ratios. The white, dotted contours correspond to $\chi^2$ values of 5. At both positions the escape probability model gives a good constraint on the kinetic temperatures which are 35, and 40~K for MM1 and MM2, respectively. These temperatures are in good accord with the temperatures calculated under the assumption of LTE. It is not possible to reasonably constrain the gas density from EP analysis. The region of minimum $\chi^2$ is very shallow and the numerical values of the particular absolute minima are not very significant given the overall uncertainties. Even so, it is possible to estimate lower limits for the gas densities. Figure \ref{fig-ngc3603-escprob} shows that we expect densities of $n\ge10^{5.5}$~cm$^{-3}$ and $n\ge10^{5}$~cm$^{-3}$ for the peak positions of MM1 and MM2 respectively.
{\bf The high density for MM1 is consistent with the analysis of \cite{nuernberger02} who derrived a larger total column density than that of MM2 ($1\times10^{23}$ vs. $0.8\times10^{23}$~cm$^{-2}$) but much smaller spatial sizes ($R_\mathrm{MM1}=0.4$~pc, $R_\mathrm{MM2}=1$~pc). Using the LTE column densities from Table~\ref{tablte}, a density of $10^5$~cm$^{-3}$ translates into spatial sizes of 0.2 pc, or 6\arcsec in the distance of NGC~3603. However, the IRAC maps show much larger spatial sizes of approximately 100\arcsec for MM2. Assuming a homogenous density of $10^5$~cm$^{-3}$ would imply a much too large total column density of $\approx10^{24}$~cm$^{-2}$. This is a strong indication for a very clumpy density structure along the line of sight. The application of clumpy PDR models to the observations will 
be presented in another paper.      
}

\section{Summary}
We used the NANTEN2-4m telecope to, map the emission of atomic carbon and CO in the vicinity of the central OB cluster in the Galactic star forming region NGC~3603. These data are the first observations of CO 4--3, CO 7--6, CI 1--0, and CI 1--0 in NGC~3603, with simultaneously observed CO 7--6 and CI 2--1 lines.  We presented the fully sampled 200\arcsec$\times$200\arcsec maps integrated over the full velocity range as well as channel maps of the CO 4--3 transition. The observed field includes the central OB cluster position as well as the two adjacent molecular clouds MM1 and MM2 hosting two pillar-like formations observed by the HST and similar in appearance to the famous pillar structures in the M16. 
We selected two cuts from the OB cluster position to the peak emission in MM1 and MM2. The spectra along the two cuts show a rich kinematic structure, especially in MM2. The observed maps show the very strong correlation between the spatial distribution of C and CO. This implies either a face-on configuration of the clouds, i.e. both clouds beeing not in the same plane as the OB cluster and thus beeing illuminated face-on, or a more complex configuration, for instance a clumpy composition of many small clumps.  

Assuming LTE we derived excitation temperatures for both clouds from the observed line ratios. The temperature derived from LTE are 26~K and 47~K for the peak positions of MM1 and MM2 respectively. Assuming optically thin emission we find column densities of atomic carbon of 1.5 and 4.2$\times10^{17}$~cm$^{-2}$ in MM1 and MM2. Taking into account the C$^{18}$O 2--1 observation presented by \cite{nuernberger02} we can derive total column densities of $1.6\times10^{22}$~cm$^{-2}$ and $2-5\times10^{22}$~cm$^{-2}$ for MM1 and MM2, i.e. an observed ratio of N(C)/N of 8-9$\times10^{-6}$.
Using an escape probability model we derive lower limits for the local gas densities of $n\ge10^{5.5}$~cm$^{-3}$ and $10^{5}$~cm$^{-3}$ in MM1 and MM2.

We used HIRES/IRAS far-infrared data to narrow down the value of the FUV field at the positions of the two molecular clouds. Consisten with estimates from spectral type approximations and with [CII] observations by ISO we find $\chi\approx5-20\times1034$ in units of the Draine field.

Further observations with APEX and Herschel will provide the data to further study the physical and chemical conditions in NGC3603. 




\begin{acknowledgements} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  
  
  We made use of the
  NASA/IPAC/IRAS/HiRES data reduction facilities.  Data reduction of
  the spectral line data was done with the {\tt gildas} software
  package supported at IRAM (see {\tt
    http://www.iram.fr/IRAMFR/GILDAS}).

This work is financially supported in part by a Grant-in-
Aid for Scientific Research from the Ministry of Education,
Culture, Sports, Science and Technology of Japan (No.
15071203) and from JSPS (No. 14102003 and No. 18684003),
and by the JSPS core-to-core program (No. 17004). This work
is also financially supported in part by the grant SFB494
of the Deutsche Forschungsgemeinschaft, the Ministerium
f\"ur Innovation, Wissenschaft, Forschung und Technologie des
Landes Nordrhein-Westfalen and through special grants of the
Universit\"at Bonn and 
Universit\"at zu K\"oln.

\end{acknowledgements}   
   
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\end{document}
