%From: guillem@astrosmo.unam.mx (Guillem Anglada)
%Date: Sun, 23 Feb 1997 13:34:48 -0600
%Apparently-To: heinz@cuevano.ugto.mx
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%%Local%definitions%%%%%%%%%%%%
\newcommand{\kms}   {km~s$^{-1}$}
\newcommand{\cmt}   {cm$^{-3}$}
\newcommand{\lo}    {$L_{\sun}$}
\newcommand{\mo}    {$M_{\sun}$}
\newcommand{\nh}    {NH$_3$}
\newcommand{\hho}   {H$_2$O}
\newcommand{\juc}   {\mbox{$J$=1$\rightarrow$0}}
\newcommand{\et}    {et al.}
\newcommand{\eg}    {e.\,g.,}
\newcommand{\rmaa}  {RevMexAA}
\newcommand{\aujp}  {Aust.\ J.\ Phys.}


\begin{document}

\doublespace

%Title%page%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\received{August 7, 1995}
\accepted{December 6, 1995}

\lefthead{Anglada, Estalella, Pastor, Rodr\'{\i}guez, and Haschick}
\righthead{A CS and NH$_3$ Survey of H$_{\bf2}$O Masers}

\slugcomment{
To appear in {\em The Astrophysical Journal}, May 20, 1996 issue.
%Printed \today
}

\title{A CS and NH$_{3}$ Survey of Regions \\
with H$_{\bf2}$O Maser Emission}

\author{Guillem Anglada, Robert Estalella, and Josefa Pastor,}
\affil{Departament d'Astronomia i Meteorologia, Universitat de Barcelona, \\
Av.\ Diagonal 647, E-08028 Barcelona, Spain}

\author{Luis F. Rodr\'{\i}guez,}
\affil{Instituto de Astronom\'{\i}a, UNAM, Apdo.\ Postal 70-264, 04510
M\'exico, D.F., Mexico}

\and

\author{Aubrey D. Haschick}
\affil{Haystack Observatory, Off Route 40, Westford, MA 01886}

%End%of%title%page%%%%%%%%%%%%%%%%%%%%%%%%%

%\clearpage
\singlespace

\begin{abstract}

We present CS(\juc) and \nh(1,1) observations towards 172 different star
forming regions (99 observed in both molecules) associated with \hho\
maser emission. We make a comparative study between the physical
parameters obtained from the CS and \nh\ spectra, and their relationship
with the \hho\ maser emission. We compare the detection rates, line
intensities, line widths and central velocities of the CS and \nh\
emissions. We find a relationship between the velocity range of the \hho\
maser emission and its luminosity, being the masers with high velocity
components more luminous than masers without high velocity components,
suggesting that the maser pumping mechanism is related to kinetic energy
dissipated when small maser condensations move through the molecular
cloud.  We find that both the CS and the \nh\ lines are significantly
wider in regions with \hho\ masers than in other regions. Furthermore, for
the first time, we find evidence that these line widths increase with the
\hho\ maser luminosity. These results suggest that the presence of \hho\
maser emission is intrinsically associated with an increase of the thermal
and turbulent energy of the ambient cloud, in agreement with the current
models which propose that the \hho\ maser emission originates in shocked
regions, such as those associated with the outflows from young stellar
objects. 
    

\end{abstract}

\keywords{
ISM: clouds ---
ISM: molecules ---
masers ---
radio lines: molecular: interstellar ---
stars: formation of
}

\clearpage
%\twocolumn

\section{Introduction}

Since its discovery (Cheung \et\ 1969), \hho\ maser emission at
22.235080~GHz ($6_{16}$$\rightarrow$$5_{23}$ transition) from more than
500 non-stellar sources near \ion{H}{2} regions or infrared sources
associated with molecular clouds have been detected.  Genzel \& Downes
(1977, 1979) showed the close relationship between \hho\ maser emission
and recent star formation.  Dinger \& Dickinson (1980) made a catalogue
containing the interstellar \hho\ masers that had been detected by that
time (195 sources).  By 1983 the total number of detected \hho\ masers had
increased by $\sim50$\%, and Braz \& Epchtein (1983) compiled a new
catalogue with 288 interstellar \hho\ masers located in the galactic
plane. Afterwards, Cesaroni \et\ (1988) published a new catalogue, which
included both stellar and interstellar \hho\ masers (a total of 526
sources), with declination higher than $-30^\circ$.  The sources of this
catalogue were reobserved with the Medicina 32 m telescope (Comoretto \et\
1990), providing a large sample of \hho\ maser spectra taken with the same
instrument and in the same epoch. Palagi \et\ (1993) associated 262 of
these sources with star forming regions. Brandt \et\ (1994) presented an
update of the Comoretto \et\ (1990) catalogue, with 214 new sources (152
of them potentially associated with star forming regions). Codella \et\
(1994, 1995) reported 35 newly detected maser sources north of declination
$-30^\circ$ associated with star forming regions. For declinations below
$-30^\circ$ no such a complete study has been performed (lists of southern
hemisphere \hho\ masers can be found in \eg\ Braz \& Epchtein 1983; Braz
\et\ 1989; Scalise \et\ 1989). 

In addition to the compilation of increasingly more extensive catalogues,
an important effort has been made, especially in the last few years, in
order to study the excitation mechanism of maser emission and the
relationship between \hho\ maser emission and other signposts of star
formation.  In particular, these issues include the stage of the early
stellar evolution in which the \hho\ maser emission starts, the duration
of the maser activity, its relationship with the outflow phenomenon and
the role of shocks in the maser excitation (\eg\ Henning \et\ 1992; Felli,
Palagi, \& Tofani 1992; Xiang \& Turner 1995; Tofani \et\ 1995), as well
as the relationship with FIR emission, ultracompact \ion{H}{2} regions and
high density gas (\eg\ Scalise \et\ 1989; Wood \& Churchwell 1989;
Churchwell \et\ 1990; Palla \et\ 1991, 1993; Plume \et\ 1992; Palagi \et\
1993; Wilking \et\ 1994; Persi, Palagi, \& Felli 1994; Codella \et\ 1994,
1995; Codella \& Felli 1995; Zinchenko \et\ 1995). 

In this paper we report CS (\juc) and \nh\ ($J,K$)=(1,1) observations
toward a large sample of \hho\ maser regions. We observed a total of 172
sources, 107 of which were observed in CS and 164 in \nh. The main purpose
of this work was to study the relationship between the parameters that
characterize the high velocity \hho\ maser emission, which originates in
very small ($\sim10$~AU) and very dense ($10^7$--$10^9$~\cmt) regions, and
those that characterize the molecular emission coming from quiescent, more
extended (0.1--1.0~pc) high density ($10^4$--$10^5$~\cmt) regions, traced
by the CS and \nh\ emissions.  These relationships may provide significant
information about the physics of these regions and the interaction of
maser condensations with the surrounding molecular medium. In \S 2 we
describe our \nh\ and CS observations, in \S 3 we present the results
obtained in these observations, and in \S 4 we analyze and discuss these
results: we compare the CS and \nh\ line parameters ($\S 4.1$), we analyze
the statistical properties of our \hho\ masers sample ($\S 4.2$), and we
study the relationship between the \hho\ maser emission and the ambient
dense molecular gas traced by the CS and \nh\ emissions ($\S 4.3$). In $\S
5$ we give the conclusions of our analysis. 


\section{Observations}

The observations were carried out between 1986 and 1990 with the 37~m
radio telescope at Haystack Observatory\footnote{Radio astronomy at
Haystack Observatory of the Northeast Radio Observatory Corporation is
supported by the National Science Foundation.} (Westford, Massachusetts). 
We observed the emission of the ($J,K$)=(1,1) inversion transition of the
\nh\ molecule at 23.694496 GHz, and the emission of the \juc\ rotational
transition of the CS molecule at 48.990968 GHz. 

Most \nh\ observations were made in 1986 August and September.  At the
frequency of the observed \nh\ transition the half-power beamwidth of the
radio telescope was 1$\farcm$4 and the beam efficiency at an elevation of
45$^\circ$ was $\sim32$\%.  The observations were made using the total
power, position-switching mode.  We used a cooled K band maser receiver
and a 512 channel digital autocorrelation spectrometer with an effective
bandwidth of 13.3 MHz, which gives a velocity coverage of $\sim168$~\kms\
at the frequency of 23.7~GHz.  The spectra were taken using unity
weighting.  The calibration was carried out with a noise tube.  The system
temperature obtained ranged from 100 to 290 K, depending on source
elevation and atmospheric conditions. Pointing was checked to be better
than $\sim15^{\prime\prime}$ by observing continuum unresolved sources. 
All the spectra were corrected for elevation-dependent gain variations and
for atmospheric attenuation.  After Hanning weighting, the spectral
resolution was $\delta V \simeq 0.8$~\kms. Two additional sources were
observed in 1988 February and May (AFGL~5142 and AFGL~5157,
Verdes-Montenegro et al.\ 1989) and another in 1990 February (L1448~N),
using 1024 channels with an effective bandwidth of 6.67~MHz, giving a
velocity coverage of $\sim84$~\kms\ and providing a spectral resolution of
$\delta V \simeq 0.2$~\kms. 

The CS observations were made in 1987 August and 1988 August.  At the
frequency of the observed CS transition the half-power beamwidth of the
radio telescope was 41$^{\prime\prime}$ and the beam efficiency at an
elevation of 45$^\circ$ was $\sim9$\%.  The observations were made using
the total power, position-switching mode.  We used a cooled K band maser
receiver and a 512 channel digital autocorrelation spectrometer with an
effective bandwidth of 13.3 MHz, which gives a velocity coverage of
$\sim82$~\kms\ at the frequency of 49.0~GHz.  The system temperature
obtained ranged from 160 to 280 K, depending on source elevation and
atmospheric conditions.  Calibration of the CS observations was made in a
similar way as the \nh\ observations.  After Hanning weighting, the
spectral resolution was $\delta V \simeq 0.4$~\kms. For the sources
Orion~KL-A, NGC~2024, NGC~2071, and NGC~7538~S we used 1024 channels, with
an effective bandwidth of 6.67~MHz, giving a velocity coverage of
$\sim41$~\kms\ and providing a spectral resolution of $\delta V
\sim0.1$~\kms. 

We compiled an initial catalogue which contained the positions of the
interstellar \hho\ masers known at the starting epoch of the observations
(1986 August).  Sources that were not observable from Haystack
Observatory, with declination below $-38^\circ$, were not included.  In
the catalogue, we considered as a single source the masers whose positions
were separated by less than $20''$, an angular distance significantly
smaller than the resolution of our telescope.  Masers whose angular
separation was greater than $20''$ were considered as different sources.
The projected physical separation in all these cases was larger than 1~pc,
except for Mon~R2(1) and Mon~R2(2). Even for the case of these two masers,
which are separated $1\farcm2$, (corresponding to only 0.27~pc), it seems
adequate to consider them as two different sources since they are probably
associated with different excitation sources (Torrelles \et\ 1990).  The
resulting initial catalogue of \hho\ maser sources contained 204 positions
and is given in Table~1.  After a total observing time of about 500~h
devoted to this program, we completed observations of 107 sources in CS
and 164 in \nh.  We observed, at least in one of these two molecules, a
total of 172 sources (80\% of the initial catalogue), 99 out of them being
observed in both molecules.  In some of the sources observed in \nh, four
additional positions $1\farcm2$ apart from the nominal position given in
Table~1 were also observed. 

In Table~1 we also give, for the observed sources, the central velocity of
the observed bandwidth, $V$, the 1-$\sigma$ sensitivity per spectral
channel, and whether the emission was detected or not.  The detection
criterion takes into account the spectral line width as compared with the
spectral resolution.  Therefore, we defined the signal-to-noise ratio of a
spectrum as
$\mbox{\em SNR}=(T_{\rm A}^\ast/\sigma) (\Delta V/\delta V)^{1/2}$, where
$T_{\rm A}^\ast$ is the line intensity, 
$\sigma$ is the sensitivity, $\Delta V$ is the line width and
$\delta V$ is the spectral resolution.  We considered as detections the
spectra with $\mbox{\em SNR}>3$, though detections with $\mbox{\em SNR}<5$
were considered as questionable (indicated with a question mark in Table~1).


\section{Observational Results}

In Table~2 we present the line parameters obtained from Gaussian fits to
the spectra, after having subtracted a polynomical baseline.  For the \nh\
lines the parameters in Table~2 correspond to the main line.  We give, for
each region, the antenna temperature corrected for elevation-dependent gain
variations and for atmospheric attenuation, $T^\ast_{\rm A}$, the central
velocity of the line, $V$, and the line width (full width at half maximum
intensity), $\Delta V$, with their respective formal errors. The
velocities in the spectra have been corrected for the errors introduced by
the Haystack Observatory autocorrelator ($\lesssim 0.2$~\kms), according
to the specifications given by Ball \& Haschick (1988), and Ball (1989). 

Out of the 172 sources observed in at least one of the two molecules, 95\%
were observed in \nh\ while 62\% were observed in CS (Table~3).  We
detected \nh\ in 58\% of the \hho\ masers observed.  Apparently the CS
detection rate was higher, 72\%, but it must be noted that we
preferentially observed in CS those sources that had already been detected
in \nh.  On the other hand, a direct comparison is difficult due to the
different sensitivities in the observations.  In summary, 106 sources out
of 172 (62\%) were detected in at least one of the two molecules, which
indicates a remarkable degree of association with the \hho\ maser
emission.  Plume \et\ (1992), from a survey of CS ($J$=7$\rightarrow$6) in
regions of star formation traced by the presence of \hho\ masers, found a
very similar detection rate (58\%; 104 out of 179 \hho\ maser sources). In
a much smaller sample, Zinchenko et al.\ (1995) detected CS
($J$=2$\rightarrow$1) in 27 out of 29 \hho\ masers. 

In our survey, the detection rates of the two molecules for the regions
observed both in CS and in \nh\ were very similar (Table~4).  Out of the
99 regions observed in CS and \nh, 75 were detected in CS while 77 were
detected in \nh, 66 being detected in both molecular transitions.  These
results seem to indicate that the CS and \nh\ molecules are excited under
similar physical conditions. 


\section{Discussion}

\subsection{Comparison of the CS and \nh\ emissions}

In a previous work, Pastor \et\ (1991) compared in detail maps of the CS
(\juc) and \nh\ ($J,K$)=(1,1) emissions in several star forming regions. 
In the present work we observed CS and \nh\ spectra toward a large number
of \hho\ maser positions.  This allowed us to make a statistically more
significant comparison between the CS and \nh\ emissions, but restricted
to the spectral parameters and to a single position per source, thus
lacking the information about the extension of the emission. 


\subsubsection{Line intensities}

In Figure 1 we show the plot of the CS line intensities (as measured by
the corrected antenna temperature) vs.\ \nh\ line intensities for the
sources that were detected in both molecules. The CS line intensities are,
in general, greater than that of \nh. The distribution of the ratio
$T_{\rm A}^{\ast}({\rm CS})/T_{\rm A}^{\ast}({\rm NH_3})$ has an average
of 2.3, with a lower limit of 0.7 and an upper limit of 5.7. 

The difference in line intensity between the two molecules could be 
attributed to differences in the excitation temperature or optical depth 
of the two transitions. However, the different coupling factor of the 
sources with the antenna beam at the two frequencies can also explain the 
difference observed in the line intensities. 

As it is shown in Appendix A, for the Haystack antenna and a uniform
circular source of the same size at the two frequencies, the value of the
ratio $T_{\rm A}^{\ast}({\rm CS})/T_{\rm A}^{\ast}({\rm NH_3})$ ranges
from 0.28 for extended sources (due to the difference in beam efficiency
at the two frequencies) to 1.2 for unresolved sources (due to the
difference in beam size and aperture efficiency).  Since the size of the
sources in CS is in general larger than in \nh, this ratio can be higher.
For instance, Pastor et al.\ (1991) found that the median ratio of sizes
of sources in CS (\juc) and \nh\ ($J$,$K$)=(1,1) is 2.3. For this value of
the source size ratio, the ratio $T_{\rm A}^{\ast}({\rm CS})/T_{\rm
A}^{\ast}({\rm NH_3})$ can be as high as 6.4 for unresolved sources (see
Fig.~16 in Appendix A). 

Thus, the differences in the coupling factors of the sources with the
antenna beam can easily account for the observed range of the ratio of the
line intensities. 


\subsubsection{Line widths}

In our sample, the observed line widths typically lie between 2 and
5~\kms\ for CS ($\sim72$\% of the sources) and between 1 and 4~\kms\ for
\nh\ ($\sim75$\% of the sources) (Table~2).  Churchwell et al.\ (1990),
from a study of the \nh\ and \hho\ emissions in a sample of ultracompact
\ion{H}{2} regions, obtain a similar result (71\% of the sources with \nh\
line widths between 1.5 and 4~\kms). 

In Figures 2 and 3 we show the distribution of the CS and \nh\ line
widths, corrected for the spectral channel width.  The average of $\Delta
V({\rm CS})$ is 3.7~\kms\ while the average of $\Delta V(\mbox{\nh})$ is
3.0~\kms. Churchwell et al.\ (1990) find a similar average, $\Delta
V(\mbox{\nh}) = 3.1$~\kms, for a sample in which most sources are
associated with \hho\ masers.  These \nh\ line widths are significantly
larger than those found in other regions not associated with \hho\ maser
emission.  For instance, Benson \& Myers (1989), in a study on dense
condensations in dark clouds, find $\Delta V(\mbox{\nh}) = 0.45$~\kms\ for
condensations associated with a star, and $\Delta V(\mbox{\nh}) =
0.27$~\kms\ for condensations without a star. These figures correspond to
the intrinsic widths of the hyperfine components, and hence they cannot be
directly compared with ours.  However, taking into account the hyperfine
broadening as a function of opacity (Ho 1977), these intrinsic line widths
would correspond, even for high opacities, to observed line widths less
than 1.5~\kms, which is significantly smaller than the line widths
obtained by us and by Churchwell et al.\ (1990).  Zinchenko et al.\ (1995)
also obtained large CS ($J$=2$\rightarrow$1) line widths in a sample of
\hho\ masers. These results, therefore, seem to indicate that the \hho\
maser emission is associated with a notable perturbation of the dense
molecular gas, which is reflected in a significant broadening of the
lines. 

The distribution of the CS line widths is shifted toward larger line
widths than that of \nh\ (see Figs.\ 2 and 3).  These significant
differences between the widths of the two lines, the CS lines being
generally broader than the \nh\ ones, have been previously found in other
regions (\eg\ Pastor \et\ 1991 and references therein).  Both
distributions have very similar standard deviations ($\sim1.6$~\kms),
though they differ in shape.  For the case of \nh, there is a large
difference in the number of sources between the first and the second bins
(corresponding to line widths less and greater than 0.75~\kms).  This is
probably a consequence of not having corrected the \nh\ line widths for
the effects of opacity and overlapping of hyperfine components. 

In Figure 4 we compare the CS and the \nh\ line widths, corrected for the
spectral channel width, for sources clearly detected ($\mbox{\em SNR}>5$)
in both molecules (a total of 61 sources). As the errors in the CS and 
the \nh\ line widths are similar (see Table~2), we performed a linear fit 
to the data considering the same error in both axes. The fit gives
\begin{equation} 
\Delta V({\rm CS}) = 1.1~\Delta V(\mbox{\nh}) + 0.3~{\rm km~s}^{-1}, 
\end{equation} 
with a correlation coefficient $r=0.8$.  This result suggests that the 
difference between the CS and \nh\ line widths is better described as an 
additive term than as a multiplicative factor.  The fit obtained from our 
sample is very similar to that obtained by Pastor \et\ (1991) from a 
detailed study of 6 star forming regions.  Thus, we confirm with a large 
sample of sources the relationship obtained by Pastor \et\ (1991) and we 
extend its validity up to larger line widths ($\sim10$~\kms\ vs.\ 
$\sim2$~\kms). 

The fact that the CS lines are wider than those of the \nh\ may indicate
that CS traces regions dynamically more active. This could happen, for
instance, if the dynamics of the cloud affects the chemistry of these
molecules. Alternatively, the difference in line widths could be
attributed to differences in the size in the region traced by each
molecule.  It is well known (\eg\ Larson 1981) that the line width
correlate with the size of the cloud, although the physical basis of this
correlation, which is related with the role of the internal motions in the
cloud support, is still not well established. For the non-thermal
component of the line width, the line width-size relation goes as $\Delta
V_{\rm NT}\propto R^{\,q}$, with the index $q\simeq0.5$ for low-mass cores,
and $q\simeq0.2$ for high-mass cores (\eg\ Caselli \& Myers 1995). If the
fact that CS lines are found to be broader than those of \nh\ is
interpreted in terms of this relationship, this would imply that regions
traced by CS should be larger than those traced by \nh. Although from our
data we do not obtain direct information about the cloud size, it is a
general result that, for regions mapped in both molecules, the CS emission
is found to be more extended than that of the \nh\ (\eg\ Zhou \et\ 1989;
Pastor \et\ 1991), in agreement with this interpretation. If the
difference between CS and \nh\ line widths is an additive term as our
results suggest, this would imply that the ratio between CS and \nh\
sizes, $R({\rm CS})/R({\rm NH_3})$, should be higher for smaller sources.
A difference in line width of 0.3~\kms\ represents, for the line
width-size relation given by Caselli \& Myers (1995) for high-mass cores
(which seems more adequate for our sources), that the ratio 
$R({\rm CS})/R({\rm NH_3})\simeq3$ for sources of the order of 0.1~pc and 
$R({\rm CS})/R({\rm NH_3})\simeq2$ for sources of the order of 1~pc. 
These values for the size ratio are consistent with the (limited) 
currently available comparative studies (\eg\ Pastor \et\ 1991; Morata 
\et\ 1995) of regions mapped in CS and \nh. 


\subsubsection{Velocities}

In Figure 5, the central velocities of the CS spectra have been plotted
vs.\ those of the \nh\ spectra.  The result of the best linear fit to the
data (considering the same error in both axes) is
\begin{equation}
V({\rm CS}) = 1.00~V(\mbox{\nh}) + 0.12~{\rm km~s}^{-1},
\end{equation}
with a correlation coefficient $r=1.0$.  This relation indicates that
both molecules are roughly tracing the same region.  Given the large
number of sources observed, we are able to measure small discrepancies.
Particularly, it can be noted that this straight line with unity slope
does not pass through the origin. Figure 6 shows that the distribution 
of the difference $V({\rm CS})-V(\mbox{\nh})$ is not centered on zero 
(mean $=0.15\pm0.07$~\kms). Although this is only a 2-$\sigma$ result, it 
is rather significant since the probability of obtaining a value outside 
the 2-$\sigma$ interval is only 5\%. This result and the symmetry of the 
distribution about its mean value suggest that there is a real 
systematic shift of the CS line velocities relative to the \nh\ ones. 

The CS observations were made using a nominal value for the frequency of
the \juc\ transition of 48.990968~GHz, while 48.990964~GHz is the value
recommended at present (Lovas 1986).  Due to this small difference, the
measured velocities of the CS lines must be corrected by $-0.024$~\kms.
After this correction, the mean value of the difference in velocity is
$V({\rm CS}) - V(\mbox{\nh}) = 0.12 \pm 0.07$~\kms.  The estimated
uncertainty of the theoretically predicted frequencies of the two
transitions is 4.5~kHz for the CS and 0.05~kHz for the \nh\ (1-$\sigma$;
Lovas 1986), which corresponds to an uncertainty in the difference in
velocity of 0.03~\kms. Therefore, it is plausible that at least part of
the observed difference in the CS and \nh\ velocities is real and not a
consequence of the poor knowledge of the frequencies. This difference
could have an instrumental origin. As it was said in \S~3, a correction of
$\sim0.2$~\kms\ was applied to the line velocities in order to correct for
the errors introduced by the Haystack Observatory autocorrelator (Ball \&
Haschick 1988; Ball 1989).  Since before applying these corrections the
difference in velocity was of the same order but opposite sign, this could
indicate that the correction has been overestimated.  Benson \& Myers
(1989) found a difference of 0.07~\kms\ between the velocities of
C$^{18}$O and those of \nh, for a sample of 18 sources. Alternatively, the
observed velocity shift between CS and \nh\ lines might have a physical
origin as a consequence of opacity effects in clouds dominated by
systematic (expanding/contracting) motions.  As CS tends to trace larger
regions than \nh\ (Pastor \et\ 1991; see also \S~4.1.1 and 4.1.2), and
because of opacity effects, the CS emission will tend to present a larger
contribution from the outer part of the cloud nearest to the observer,
while the \nh\ traces preferentially the core of the cloud. As we find
that CS is slightly red shifted with respect to \nh, this could indicate a
trend to the presence of infall motions in the outer parts of the cloud.
However, we note that this is only a minor effect in our data, from which
no strong physical constraints can be derived. 

The distribution of the difference in velocity between CS and \nh\ (Fig.\
6) has a standard deviation of 0.6~\kms.  This is a relatively high value
when compared with the results obtained in other studies, such as Pastor
\et\ (1991), where they find that these two velocities agree within
$\sim0.1$~\kms.  This fact further suggests that the CS and \nh\
emissions, although roughly originating in the same region, are not
tracing exactly the same beam averaged column density of gas. This can be
due to differences in the size of the emitting region or to differences in
the opacity and excitation between these two molecules.  Given the large
number of sources in our sample, one expects to find some regions with
large velocity inhomogeneities, i.e.\ large velocity gradients or
turbulence, and thus, larger differences between the CS and the \nh\
velocities.  The existence of large velocity inhomogeneities is also
supported by the large line widths (up to 10~\kms) found in some regions
of our sample, whereas Pastor \et\ (1991) found maximum line widths of
$\sim 3$~\kms. 


\subsection{The \hho\ masers sample}

In this section we study the parameters of the \hho\ maser emission in
order to analyze how it is related to the CS and \nh\ emissions. 
Hereafter, unless indicated otherwise, we will only consider the \hho\
masers toward whose positions CS or \nh\ emission has been detected.  In
Table~5 we give the parameters that characterize these \hho\ masers.  The
characterization of the \hho\ maser emission is difficult due to its high
temporal variability.  Since we compiled this table in 1991, only
references prior to this date were used. In making Table~5, in general, we
took into account different observations for each source, although the
list of references used for each source (given in the table) was not
intended to be exhaustive.  We estimated from the published plots of the
spectra those parameters whose values were not explicitly given in the
references. 

In Table~5 we give the minimum and maximum of the velocity range over
which the \hho\ maser emission extends, $V_{\rm min}$ and $V_{\rm max}$. 
These are the minimum and maximum velocities at which some emission
component appears in any of the spectra used for each source. 

For each \hho\ maser spectrum we determined the velocity of the maximum of
the emission, the mean velocity of the detected components, and the
intensity-weighted mean velocity.  In Table~5 we give, for each source,
the velocity of the absolute maximum of all the spectra, 
$V_{\rm m}({\rm H_2O})$; the average, for all the spectra, of the mean 
velocities, 
$V_{\rm a}({\rm H_2O})$; and the average, for all the spectra, of the 
weighted mean velocities, i.e.\ the velocity centroid, 
$V_{\rm c}({\rm H_2O})$.  It must be noted that this determination of the 
velocity centroid of the maser emission, $V_{\rm c}({\rm H_2O})$, is 
independent of the calibration of the different telescopes used in taking 
the spectra.  In addition, for a more direct comparison, we also give in 
Table~5 the velocity of the high density gas, $V_0$, derived from our CS 
and \nh\ observations. 

An estimate of the distance to each source is also given in Table~5.  For
sources with unknown distance or with an available kinematic distance
determined from the \hho\ maser velocity, we obtained the kinematic
distances from the velocity $V_0$ of the high density gas, using the
galactic rotation curve of Fich, Blitz \& Stark (1989).  We give this
distance in the cases where there is no twofold distance ambiguity, or
where the ambiguity has been resolved.  No distance estimate could be
obtained for 9 of our sources. 

Finally, we also give in Table~5 the isotropic luminosity of the maser 
emission, $L$(\hho). For each spectrum the luminosity can be obtained from
\begin{equation}
\left[{L({\rm H_2O}) \over {L_{\sun}}}\right] = 2.30\times10^{-8}
\left[{\int S_V dV \over {\rm Jy~km~s}^{-1}}\right]
\left[{D \over {\rm kpc}} \right]^2,
\end{equation}
where $D$ is the distance to the source, and the integral of the observed
flux density extends over all the components of the spectrum.  For those
cases where this integral was not given in the literature, we
estimated it from the published spectra.  The luminosities given in the
table, for 96 of the 106 sources in which we detected CS or \nh,
correspond to the maximum luminosity reported.

The sources of our sample cover a wide range of distances, as can be seen
both in the plot of their positions projected onto the galactic plane
(Fig.\ 7) and in a histogram of the distances (Fig.\ 8).  In Figure~7 it
can be seen as well that our sample is distributed over a significant
portion of the galactic plane that is visible from the northern
hemisphere.  Thus, our sample appears to be representative of the masers
of the Galaxy. 

Figure~9a shows the distribution of the luminosity of 96 \hho\ masers of
our sample (Table~5).  This histogram shows a symmetrical distribution
centered on $L(\mbox{\hho})=2\times10^{-5}$~\lo, and with luminosities
that range from $\sim10^{-8}$~\lo\ up to $\sim10^{-2}$~\lo.  From this
distribution one could conclude that the typical luminosity of galactic
\hho\ masers is $\gtrsim10^{-5}$~\lo.  Nevertheless, the plot of the maser
luminosity vs.\ the distance to the source (Figure~10), suggests that the
selection effects may lead to erroneous conclusions.  As can be seen in
this figure, the number of low luminosity masers lowers as the distance
increases, which indicates that our sample is limited by instrumental
sensitivity.  In Figure~9b we plotted the distribution of the nearby
masers, with distances smaller than 2~kpc. This distribution appears to be
complete down to $L(\mbox{\hho})\simeq10^{-7}$~\lo\ and is centered on
$L(\mbox{\hho})=2\times10^{-6}$~\lo.  The comparison of Figure~9a with
Figure~9b makes clear the lack of low luminosity masers in the former, so
that it seems that high luminosity masers are overabundant in our sample
(Table~5) due to selection effects.  Consequently, a less biased estimate
of the typical luminosity of galactic \hho\ masers seems to be
$\sim10^{-6}$~\lo. 

In Figure~11 we show a histogram of the velocity range over which the
\hho\ maser emission extends, i.e.\ 
$V_{\rm max}(\mbox{\hho})-V_{\rm min}(\mbox{\hho})$.  As can be seen in 
this figure, our sample contains a great variety of \hho\ maser spectra, 
from simple up to very complex ones (\eg\ W51~Main/S, whose components 
extend over $\sim200$~\kms).  However, most of the masers, 85\% of the 
sample, do not have very high velocity components and their velocity 
ranges are $\lesssim 40$~\kms. 

In Figure~12 we plotted the maser velocity range vs.\ the maser
luminosity. From this figure it is clear that the only masers which
exhibit a very extended velocity range are the highly luminous ones,
whereas the low luminosity masers do not exhibit high velocity components.
Reid \& Moran (1988) note that since \hho\ maser emission appears to
originate in outflowing condensations, the most likely source for pumping
the masers is the kinetic energy dissipated by the small maser
condensations as they plow through the ambient molecular cloud. After
modeling this interaction, these authors find that the isotropic maser
luminosity is expected to be proportional to the cube of the velocity of
the maser condensations, $L({\rm H_2O})\propto v^3$. This result is in
rough agreement with the trend found in our data, in the sense that only
the most luminous masers present a wide range of velocities.  Nonetheless,
a detailed comparison is not possible from our results since this
relationship may be masked by some unavoidable effects.  Firstly,
selection effects can be important.  The intensity of the high velocity
components is usually $\lesssim 10$\% of the intensity at the maximum. 
Consequently, the detection of these components strongly depends on the
distance to the source and the sensitivity of the observations.  So, for a
distant low intensity \hho\ maser emission source, its high velocity
components would as a result be undetectable, leading to the wrong
conclusion that this source does not have any high velocity component. 
Secondly, the observed radial velocity ranges are only lower limits to the
real velocities. Thereby, both the selection effects and the projection
effects will always tend to decrease the apparent velocity range of the
maser emission on the spectrum.  Despite these limitations, we can draw
the conclusion that masers with high velocity components are more luminous
than masers without high velocity components. 

Figure~13 shows this result more clearly.  In Figure~13b we present the
luminosity distribution of the masers with velocity range $<2$~\kms, and
in Figure~13c the same for the masers with velocity range $>40$~\kms. The
first ones are, on average, $\sim100$ times less luminous than the second
ones, the luminosity average of each subgroup being
$\sim2\times10^{-6}$~\lo\ and $\sim2\times10^{-4}$~\lo, respectively. 
Genzel \& Downes (1977) obtained similar conclusions from a study with 69
\hho\ maser sources:  ``single'' \hho\ masers were $\sim100$ times less
intense than ``complex'' masers, the median of their luminosities being
$\sim8\times10^{-6}$~\lo\ and $\sim8\times10^{-4}$~\lo, respectively.  It
must be noted here that, although both studies have 44 sources in common,
our sample is larger (92 sources) and, in addition, later observations of
these sources have been taken into account. 

A recent study of the statistical properties and distribution of 88 \hho\
masers associated with star forming regions can be found in Palagi et al.\
(1993). 

\subsection{Comparison of the \hho\ maser emission with the CS and \nh\
emissions}

In this section we will compare the characteristics of the very small and
very dense spots, where the \hho\ maser emission originates, with those of
the more extended high density molecular gas, traced by the CS and \nh\
emissions. 

Firstly, we will discuss the kinematics of the studied regions and compare
the velocity of the \hho\ masers with the velocity of the high density gas
traced by the CS or \nh\ emissions.  In Figure~14 we show the histograms
of the difference in velocity between the \hho\ maser and the high density
gas (see Table~5), taking for the maser the velocity at maximum, $V_{\rm
m}$(\hho) (Fig.~14a), the average velocity, $V_{\rm a}$(\hho) (Fig.~14b),
and the velocity centroid, $V_{\rm c}$(\hho) (Fig.~14c).  These three
distributions do not differ significantly, as can be inferred from their
statistical parameters:  the average is $\sim-1$~\kms, the median is
$\sim0$~\kms, and the standard deviation $\sim11$~\kms.  We obtained a
distribution of $V_{\rm m}({\rm H_2O})- V_{0}$ very similar to that
obtained by Churchwell \et\ (1990), although our sample is much larger
than the sample they used.  For the three distributions the average of
$V(\mbox{\hho})-V_0$ is negative because of the presence of a few sources
with $V(\mbox{\hho}) \ll V_0$.  This asymmetry in the velocity difference
distribution is also noted by Zinchenko et al.\ (1995) in a sample of 27
\hho\ masers detected in CS, who suggest that this asymmetry could mean
that the maser emission is beamed preferably in the direction of its
movement relative to its parent cloud. 

In fact, in our sample there are six sources (G13.19+0.04, W43~Main~(2),
G31.25$-$0.11, S76~W, G12.21$-$0.10, and GGD~29) with 
$|V({\rm H_2O})-V_0| > 30$~\kms, the maser velocity being in general the 
smaller one.  On the other hand, in 92\% of the sources (98 out of 106) 
the velocity of the cloud either falls inside (70\%; 74 out of 106) or at 
less than 10~\kms\ from the velocity range of the maser emission.  
However, in the regions G13.19+0.04, W43~Main~(2), G31.25$-$0.11 and 
S76~W the velocity of the cloud is more than 20~\kms\ outside the maser 
velocity range, which is $>10$~\kms\ in all of them.  For these 
particular sources, 4\% of our sample, it seems that the molecular and 
the maser emissions are physically separated, although they appear very 
close in projection on the sky.  This rate agrees with the serendipitous 
detection rate found by Churchwell et al.\ (1990), $\sim5$\%, who used 
criteria similar to ours in order to sort
out these sources.  The other two sources with a difference in velocity
between the \hho\ maser and the molecular cloud $>30$~\kms\ are
G12.21$-$0.10 and GGD~29.  G12.21$-$0.10 is a maser with a very complex
spectrum and a large velocity range.  The velocity of the cloud falls
inside the maser velocity range, although the velocity difference between
the \hho\ maser (strongest component) and the molecular cloud is
$\sim33$~\kms.  The case of GGD~29 is similar, but its spectrum is not as
complex as for G12.21$-$0.10.  Rodr\'{\i}guez \et\ (1980) pointed out that
high-velocity \hho\ maser emission is often found in the vicinity of the
GGD objects and this causes a shift of the centroid of emission with
respect to the velocity of the related dark cloud. 

Therefore, despite the wide velocity range over which the \hho\ maser
emission extends, on average, the characteristic velocity of the maser
emission and the velocity of the ambient molecular cloud are very
similar.  This good agreement suggests a dynamical relationship between
the molecular material and the \hho\ masers, as has also been suggested
by other studies (\eg\ Churchwell \et\ 1990; Torrelles \et\ 1992).

In Figure~15 we show the maser luminosity vs.\ the CS and \nh\ line widths 
(Table~2), corrected for the spectral channel width, for sources 
detected with a $\mbox{\em SNR}>5$. For both the CS lines (Fig.~15a) and the 
\nh\ lines (Fig.~15b), in general, the widest lines are associated with the 
most luminous \hho\ masers. We performed a linear fit to the logarithm of 
the data. As  the uncertainty in the maser luminosity (mainly due to the 
variability of the maser emission and errors in the distance) is much higher 
than the error in the CS and \nh\ line widths, we considered the line 
widths as the independent variable in the fit and we only  considered 
errors in the vertical axis. The fit gives 
\begin{equation}
\left[\frac{L(\mbox{\hho})}{\mbox{\lo}}\right] = 10^{-6.7\pm0.3} 
\left[\frac{\Delta V{\rm (CS)}}{\mbox{\kms}}\right]^{3.7\pm0.6}, 
\end{equation}
\begin{equation}
\left[\frac{L(\mbox{\hho})}{\mbox{\lo}}\right] = 10^{-5.9\pm0.2} 
\left[\frac{\Delta V{\rm (NH_3)}}{\mbox{\kms}}\right]^{3.1\pm0.5}, 
\end{equation}
with a correlation coefficient $r=0.6$, in both cases.

Therefore, the most luminous masers appear to be associated with a larger
perturbation of the molecular gas, as traced by the CS and \nh\ line
widths.  This result is in agreement with that found in \S~4.1.2; that is,
regions with \hho\ masers present significantly broader CS and \nh\ lines
than other regions, indicating that maser emission is associated with a
perturbation of the ambient gas. 

Furthermore, in the formulation of Reid \& Moran (1988), the maser
luminosity is a consequence of the dissipation in the ambient cloud of the
kinetic energy of maser condensations associated with outflow motions from
a young star, resulting in $L({\rm H_2O})\propto v^3$ (\S~4.2).  If the
velocity of the maser condensations contribute significantly to the
velocity dispersion in the ambient cloud, as measured by the observed line
widths, one would expect a similar dependence, $L({\rm H_2O})\propto
(\Delta V)^3$, which is consistent with the results of Eqs.~4 and 5. The
relationship between luminosity and line width found here is also in
agreement with the trend found in \S~4.2 between the luminosity and the 
velocity range of the maser emission. 

On the other hand, theoretical models generally require the presence of
shocks in order to produce density and temperature suitable for the
excitation of \hho\ maser emission (\eg\ Kylafis \& Norman 1986;
Hollenbach \& McKee 1989; Elitzur, Hollenbach, \& McKee 1989).  For
example, Hollenbach \& McKee (1989) performed detailed numerical
calculations of the structure of a shock wave as it propagates in a
relatively high density medium, and of the excitation of the \hho\
molecule under these conditions.  These authors concluded that the
resulting physical conditions in the postshock gas (such as those produced
by high-velocity outflows from young stellar objects) provide an ideal
site for \hho\ maser emission.  All these results suggest that \hho\ maser
emission is intrinsically associated with a significant perturbation of
the ambient molecular gas, which leads to an increase of the thermal and
turbulent energy and results in a broadening of the CS and \nh\ lines. 

Churchwell et al.\ (1990), in a sample of sources associated with \hho\
masers, found a weak correlation between the \nh\ line widths and the
far-infrared luminosity $L_{\rm FIR}$ (with line width increasing with
luminosity). These authors proposed two possible interpretations for this
result:  first, increasing $L_{\rm FIR}$ is accompanied by increasing
mechanical energy input to the ambient molecular cloud via stellar winds;
second, more massive (hence, more luminous) stars are formed out of more
massive molecular clumps and hence out of regions with larger line widths
(from the line width-clump mass relationship). 

On the other hand, Wouterloot \& Walmsley (1986), Palla \et\ (1991, 1993),
Henning \et\ (1992), Palagi \et\ (1993), Codella \et\ (1994), and Wilking
\et\ (1994) found that the \hho\ maser luminosity increases with the
far-infrared luminosity of the associated IRAS sources. Whether or not
this correlation represents a real physical relationship is a matter of
discussion at the moment. 

Therefore, correlations between the maser luminosity, $L$(\hho), and the
luminosity of the associated IRAS source, $L_{\rm FIR}$, (Wouterloot \&
Walmsley 1986; Palla \et\ 1991, 1993; Henning \et\ 1991; Palagi \et\ 1993;
Codella \et\ 1994; Wilking \et\ 1994), between $L_{\rm FIR}$ and the \nh\
line widths, $\Delta V(\mbox{\nh})$, (Churchwell \et\ 1990), and between
$L$(\hho) and the line widths, $\Delta V({\rm CS})$ and $\Delta
V(\mbox{\nh})$, (this work), have been found recently. Then, our results
provide additional physical meaning to the previous two correlations and
confirm them independently.  These three correlations could naturally be
gathered in the following scenario:  1) the infrared source (tracing a
young stellar object) is responsible for the excitation, possibly through
the energy associated with strong stellar winds, of the maser emission in
the small, very high density nearby condensations; 2) these maser
condensations are accelerated by the stellar outflow and are seen as high
velocity components in the spectra of some masers; 3) the stellar winds,
and also the high velocity maser condensations, inject mechanical energy
and momentum into the surrounding molecular gas, increasing the turbulence
and the kinetic temperature, which is observed as an increase in the
molecular line widths. 

\section{CONCLUSIONS}

We observed the emissions of the \juc\ rotational transition of the
CS molecule and the $(J,K)=(1,1)$ inversion transition of the \nh\
molecule toward 172 star forming regions associated with \hho\ maser
emission.  We observed 164 sources in \nh\ and 107 in CS.  Out of these
sources, 99 were observed in both molecules.  We obtained from the
literature the parameters that characterize the \hho\ maser emission in
those sources that were detected in CS or \nh.  Our main results can be
summarized as follows:

\begin{enumerate}

\item  In the regions that were observed both in CS and in \nh\ the
detection rate was very similar, which suggests that the CS and the \nh\
molecules are excited under similar physical conditions. We detected
106 sources out of the 172 that were observed in CS or in \nh.
This high detection rate ($\sim60\%$) indicates a remarkable degree of
association of the CS and \nh\ emissions with the \hho\ maser emission.

\item In general, the observed line widths are larger for the CS than
for the \nh.  The CS line widths typically lie between 2 and 5~\kms\
($\sim72\%$ of the sources), with an average of 3.7~\kms, while the \nh\
line widths typically lie between 1 and 4~\kms\ ($\sim75$\% of the
sources), with an average of 3.0~\kms.

\item We found a linear relationship between the CS and \nh\ line widths,
$\Delta V(\mbox{CS}) = 1.1~\Delta V(\mbox{\nh}) + 0.3~\mbox{\kms}$.  Since
the slope is approximately unity, the relationship between the line widths
appears to be well described as an additive term confirming previous 
results (Pastor \et\ 1991).

\item The central velocities of the CS and \nh\ lines are very similar,
indicating that both molecules are roughly tracing the same region.
Nevertheless, our observations reveal a systematic shift of 0.12~\kms\
between the velocities of the CS and \nh\ lines.  This shift may have an
instrumental origin.  The distribution of the difference in velocity between
CS and \nh\ has a standard deviation of $\sim0.6$~\kms, which is quite large
as compared with other studies, suggesting that the regions associated with
\hho\ maser emission present larger velocity inhomogeneities.

\item The luminosity of the studied \hho\ masers ranges from
$\sim10^{-8}$~\lo\ to $\sim10^{-2}$~\lo, with an average of
$L(\mbox{\hho})=2\times10^{-5}$~\lo.  However, for the masers located at
distances smaller than 2~kpc, where the selection effects due to the
instrumental sensitivity are less important, the mean value of $L$(\hho) is
2$\times10^{-6}$~\lo.

\item We found a relationship between the velocity range over which
the \hho\ maser emission extends and the luminosity of this emission.
Only the masers which exhibit a very extended velocity range are highly
luminous, while the low-luminosity masers do not exhibit high-velocity
components.  The average luminosity is $\sim2\times10^{-4}$~\lo\ for the
masers with a velocity range $>40$~\kms, and $\sim2\times10^{-6}$~\lo\ for
the masers with a velocity range $<2$~\kms.  This result suggests that
the energy source for pumping the masers may be related to the kinetic
energy dissipated by the small maser condensations as they move through
the ambient molecular cloud.

\item Despite the wide maser velocity range, we found that the
characteristic velocity of the maser emission and the velocity of the
ambient molecular cloud (traced by the CS and \nh\ emissions) are very
similar.  The good agreement between these velocities suggests a
dynamical relationship between the molecular material and the \hho\
masers, as has also been suggested by other studies (Churchwell \et\
1990; Torrelles \et\ 1992).

\item We found that the CS and \nh\ lines are significantly wider in
regions with an associated \hho\ maser than in other regions. 
Furthermore, we found a correlation between the observed line widths of
both the CS and the \nh\ lines and the maser luminosity, with the maser
luminosity increasing with the line width. This correlation is consistent
with a relation $L({\rm H_2O})\propto(\Delta V)^3$, in agreement with what
is expected if the maser luminosity is a consequence of the dissipation in
the ambient cloud of the kinetic energy of outflowing maser condensations. 
These results suggest that the \hho\ maser emission is intrinsically
associated with an increase in the thermal and turbulent energy of the
ambient cloud; this perturbation of the ambient high density gas results
in a broadening of the observed CS and \nh\ lines.  This scenario
coincides with that obtained in theoretical models in which the \hho\
maser emission originates in a natural way in shocked regions, as those
associated with outflows in young stellar objects. 

\end{enumerate}

\acknowledgments
We thank G. Comoretto for providing us with a computer-readable version of the
Arcetri atlas of \hho\ masers.
We thank G. Gonz\'alez-Casado for his help in data analysis at the early
stages of this work. 
We thank an anonymous referee for useful comments.
G. A. acknowledges financial support from CIRIT de Catalunya (Spain).
G. A. and R. E. are partially supported by DGICYT grant PB92-0900 (Spain).
L. F. R. thanks CONACyT and DGAPA-UNAM for financial support.


\appendix

\section{On the antenna temperature ratio}

Let us suppose a lossless antenna working at frequency $\nu$ (or 
wavelength $\lambda$), with a gaussian main beam of FWHM $\theta_{\rm 
A}$. The main beam solid angle, $\Omega_{\rm M}$, is given by
\begin{equation}
\Omega_{\rm M} = \frac{\pi}{4\ln{2}}\, \theta_{\rm A}^2.
\end{equation}
The beam efficiency, $\eta_{\rm M}$, and the aperture efficiency, 
$\eta_{\rm A}$, of the antenna are defined as $\eta_{\rm M} = \Omega_{\rm 
M}/\Omega_{\rm A}$ and $\eta_{\rm A} = A_{\rm e}/(\pi D^2/4)$, where 
$\Omega_{\rm A}$ is the antenna solid angle (the integral over $4\pi$ 
stereoradians of the antenna power pattern), $A_{\rm e}$ is the effective 
aperture of the antenna, $A_{\rm e}=\lambda^2/\Omega_{\rm A}$, and $D$ the 
antenna diameter. The ratio between the two efficiencies is given by
\begin{equation}
\frac{\eta_{\rm M}}{\eta_{\rm A}}=\frac{\pi^2}{16\ln{2}}
\left(\frac{D\theta_{\rm A}}{\lambda}\right)^2.
\end{equation}
If the antenna is diffraction limited, this ratio is essentially 
independent of the operating wavelength. 

Let us consider a small circular radio source, with diameter 
$\theta_{\rm S}$ or solid angle $\Omega_{\rm S} = \pi\theta_{\rm S}^2/4$, 
and with uniform brightness temperature $T_{\rm B}$.
The antenna temperature obtained when the antenna points to the 
center of the source can be easily shown to be
\begin{equation}
T_{\rm A}^\ast = \eta_{\rm M}\,T_{\rm B}
\left[1-\exp\left(-\Omega_{\rm S}/\Omega_{\rm M}\right)\right] =
\eta_{\rm M}\,T_{\rm B}
\left[1-\exp\left(-\ln{2}\,\theta_{\rm S}^2/\theta_{\rm A}^2\right)\right].
\end{equation}

Now, let us consider two different frequencies, $\nu_1$ and $\nu_2$. The 
size of the source can depend on the frequency, and let $f$ be the ratio of 
source sizes, $f= {\theta_{\rm S}}_2/{\theta_{\rm S}}_1$. The 
ratio of the antenna temperatures observed is given by 
\begin{equation}
\frac{{T_{\rm A}^\ast}_2}{{T_{\rm A}^\ast}_1} =
\frac{{\eta_{\rm M}}_2}{{\eta_{\rm M}}_1}\,
\frac{1-\exp\left(-\ln{2}\,{\theta_{\rm S}}_2^2/{\theta_{\rm A}}_2^2\right)}
{1-\exp\left(-\ln{2}\,{\theta_{\rm S}}_1^2/{\theta_{\rm A}}_1^2\right)}. 
\end{equation}
The limit of this ratio for sources unresolved at both frequencies is
\begin{equation}
\lim_{{\theta_{\rm S}}_1 \rightarrow 0} 
\frac{{T_{\rm A}^\ast}_2}{{T_{\rm A}^\ast}_1} =
f^2\, \left(\frac{{\Omega_{\rm A}}_2}{{\Omega_{\rm A}}_1}\right)^{-1} \simeq
f^2\, \left(\frac{\nu_2}{\nu_1}\right)^2\, 
\frac{{\eta_{\rm M}}_2}{{\eta_{\rm M}}_1}, 
\end{equation}
while the limit for extended sources is
\begin{equation}
\lim_{{\theta_{\rm S}}_1 \rightarrow \infty} 
\frac{{T_{\rm A}^\ast}_2}{{T_{\rm A}^\ast}_1} = 
\frac{{\eta_{\rm M}}_2}{{\eta_{\rm M}}_1}. 
\end{equation}

The ratio given by Eq.\ A4 is shown in Figure 16 as a function of source 
size. The values used for the figure are those of the Haystack antenna 
for the \nh\ ($J$,$K$)=(1,1) and the CS (\juc) transitions. That is,
$\nu_1=23.69$~GHz, ${\eta_{\rm M}}_1=0.32$, and
$\nu_2=48.99$~GHz, ${\eta_{\rm M}}_2=0.09$.
For sources of equal size at the two frequencies ($f=1$), the ratio 
ranges from 0.28 (source resolved) to 1.2 (source unresolved). If we 
consider the dependence of source size on frequency, the limit for 
unresolved sources varies. For $f=2.3$, i.e.\ sources 2.3 times larger in CS 
than in \nh\ (see Pastor et al.\ 1991), the ratio for unresolved sources is 6.4.

\clearpage
%Table%3%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{deluxetable}{lrr}
\tablewidth{8.8cm} 
\tablecaption{Summary of the sources observed in CS or NH$_3$}
\tablehead{& \colhead{CS} & \colhead{NH$_3$}}
\startdata
Observed sources                     & 107 & 164 \nl
Detected sources ({\em SNR}$>$5)     & 75  & 82  \nl
Detected sources (3$<${\em SNR}$<$5) & 2   & 13  \nl
Non-detected sources ({\em SNR}$<$3) & 30  & 69
\enddata
\end{deluxetable}

%\clearpage
%Table%4%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{deluxetable}{lrrr}
\tablewidth{0pt}
\tablecaption{Summary of the sources observed both in CS and NH$_3$}
\tablehead{
&\colhead{Detected}        &\colhead{Detected}            &\colhead{Non-detected} \nl
&\colhead{in CS}           &\colhead{in CS}               &\colhead{in CS}        \nl
&\colhead{({\em SNR}$>$5)} &\colhead{(3$<${\em SNR}$<$5)} &\colhead{({\em SNR}$<$3)} 
} 
\startdata
Detected in NH$_3$\ ({\em SNR}$>$5)     &~~~~~~61~~~~~~ &     1~~~~~~ &      9~~~~~~ \nl
Detected in NH$_3$\ (3$<${\em SNR}$<$5) &       4~~~~~~ &~~~~~0~~~~~~ &      2~~~~~~ \nl
Non-detected in NH$_3$\ ({\em SNR}$<$3) &       8~~~~~~ &     1~~~~~~ &~~~~~13~~~~~~ \enddata
\end{deluxetable}


\end{document}
