# Poincaré inequality for one forms on four manifolds with bounded Ricci
curvature

Shouhei Honda and Andrea Mondino Graduate School of Mathematical Sciences, The
University of Tokyo<EMAIL_ADDRESS>Mathematical Institute,
University of Oxford<EMAIL_ADDRESS>
###### Abstract

In this short note, we provide a quantitative global Poincaré inequality for
one forms on a closed Riemannian four manifold, in terms of an upper bound on
the diameter, a positive lower bound on the volume, and a two-sided bound on
Ricci curvature. This seems to be the first non-trivial result giving such an
inequality without any higher curvature assumptions. The proof is based on a
Hodge theoretic result on orbifolds, a comparison for fundamental groups, and
a spectral convergence with respect to Gromov-Hausdorff convergence, via a
degeneration result to orbifolds by Anderson.

##  1 Introduction

Let $M$ be a closed Riemannian $n$-manifold, let $\Delta^{H,k}$ be the Hodge
Laplacian acting on $k$-forms on $M$ and denote by

$0\leq\lambda^{H,k}_{0}\leq\lambda^{H,k}_{1}\leq\lambda^{H,k}_{2}\leq\cdots\to\infty$

the $i$-th eigenvalues $\lambda^{H,k}_{i}=\lambda_{i}^{H,k}(M)$ of
$\Delta^{H,k}$ counted with their multiplicities. Let $\nu^{H,k}$ be the first
positive eigenvalue, namely

$\nu^{H,k}=\min\\{\lambda^{H,k}_{i}|\lambda^{H,k}_{i}>0\\}.$

It is natural to ask whether there exists a quantitative positive lower bound
on $\nu^{H,k}$ in terms of a certain restriction on curvature and sizes of
$M$, for example its diameter $\mathrm{diam}=\mathrm{diam}(M)$ and its volume
$\mathrm{vol}=\mathrm{vol}(M)$.

In the case when $k=0$, namely, considering the (minus) Laplacian
$-\Delta=-\mathrm{tr}(\mathrm{Hess})$ acting on functions, it is well-known
that

$\nu^{H,0}=\lambda_{1}^{H,0}\geq C(n,D,K)>0$ (1)

where $D$ is an upper bound on $\mathrm{diam}(M)$ and $K$ is a lower bound on
Ricci curvature $\mathrm{Ric}$.

In the case when $k\geq 1$, Gallot-Meyer [GM73] proved a similar estimate
under the assumption of a positive lower bound of the curvature operator.

Next let us focus on the case $k=1$. Recalling the Bochner formula for one
forms:

$\frac{1}{2}\Delta|\omega|^{2}=|\nabla\omega|^{2}-\langle\Delta^{H,1}\omega,\omega\rangle+\langle\mathrm{Ric},\omega\otimes\omega\rangle,$
(2)

it is natural to restrict Ricci curvature in order to get a quantitative lower
estimate on $\nu^{H,1}$. However, in authors’ knowledge, there is no such a
result, except for a trivial case, $\mathrm{Ric}\geq K>0$, which yields
$\nu^{H,1}\geq K$ just by integrating (2) over $M$ for an eigen-one-form
$\omega$.

The main purpose of this note is to provide a positive result along this
direction in dimension $4$, more precisely, we will show that

$\nu^{H,1}\geq C(D,v)>0$

under the assumptions: $n=4$, $\mathrm{diam}\leq D<\infty$, $\mathrm{vol}\geq
v>0$ and $|\mathrm{Ric}|\leq 1$. See Theorem 2.

In the next section, we will explain how to prove the claim above. Let us
emphasize that our techniques are completely different from previous ones,
based on calculus starting from a Bochner-Weitzenböck formula.

##  2 Main Result and Proof

Let us start by recalling the definition and some basic properties of
orbifolds, we refer the reader to [S56, KL14, C21] for a more comprehensive
introduction.

A _local model_ is a pair $(\hat{U},G)$, where $\hat{U}\subset\mathbb{R}^{n}$
is a connected open subset and $G$ is a finite group acting smoothly and
effectively on $U$, on the right (_effectiveness_ means that the homomorphism
$G\to{\rm Diff}(\hat{U}_{\alpha})$ is injective).

A _smooth map_ between local models $(\hat{U}_{1},G_{1})$ and
$(\hat{U}_{2},G_{2})$ is the datum of a smooth map
$\hat{f}:\hat{U}_{1}\to\hat{U}_{2}$ and a homomorphism $\phi:G_{1}\to G_{2}$
such that $\hat{f}$ is $\phi$-equivariant, i.e.
$\hat{f}(xg_{1})=\hat{f}(x)\phi(g_{1})$. Let us explicitly point out that
$\phi$ is not assumed injective or surjective. An _embedding_ is a smooth map
between local models so that $\hat{f}$ is an embedding; in this case, the
effectiveness implies that $\phi$ is injective.

######  Definition 1 (Orbifold).

An _atlas_ for an $n$-dimensional orbifold $\mathcal{O}$ is the datum of:

  * •

A Hausdorff paracompact space $|\mathcal{O}|$;

  * •

An open covering $\\{U_{\alpha}\\}$ for $|\mathcal{O}|$;

  * •

For each $U_{\alpha}$ there exists a local model
$(\hat{U}_{\alpha},G_{\alpha})$ and a homeomorphism
$\varphi_{\alpha}:U_{\alpha}\to\hat{U}_{\alpha}/G_{\alpha}$ with the following
property: if $x\in U_{1}\cap U_{2}$, then there is a local model
$(\hat{U}_{3},G_{3})$ with $x\in U_{3}$, together with local embeddings
$(\hat{U}_{3},G_{3})\to(\hat{U}_{1},G_{1})$ and
$(\hat{U}_{3},G_{3})\to(\hat{U}_{2},G_{2})$.

Two atlases are equivalent if they are both included in a third atlas.

An _orbifold_ $\mathcal{O}$ is an equivalence class of atlases.

An orbifold $\mathcal{O}$ (with a given atlas) is _oriented_ if each
$\hat{U}_{\alpha}$ is oriented, moreover the action of $G_{\alpha}$ as well as
the embeddings $\hat{U}_{3}\to\hat{U}_{1}$ and $\hat{U}_{3}\to\hat{U}_{2}$
preserve the orientation. The orbifold $\mathcal{O}$ is compact (resp.
connected) if $|\mathcal{O}|$ is so.

For a given point $x\in|\mathcal{O}|$ and local model $(\hat{U},G)$ around
$x$, consider $\hat{x}\in\hat{U}$ which projects to $x$. The _local group_
$G_{x}$ is the stabilizer group $\\{g\in G\colon\hat{x}g=\hat{x}\\}$. It is
always possible to find a local model so that $G=G_{x}$.

The regular part $|\mathcal{O}|_{reg}\subset|\mathcal{O}|$ is the subset of
points $x\in|\mathcal{O}|$ such that $G_{x}=\\{1_{G}\\}$.
$|\mathcal{O}|_{reg}$ is a smooth manifold, moreover it is open and dense in
$|\mathcal{O}|$.

A _smooth map_ (resp. $C^{k,\alpha}$-map)
$f:\mathcal{O}_{1}\to\mathcal{O}_{2}$ between orbifolds is given by a
continuous map $|f|:|\mathcal{O}_{1}|\to|\mathcal{O}_{2}|$ such that for each
$x\in\mathcal{O}_{1}$ there are local models $(\hat{U}_{1},G_{1})$ and
$(\hat{U}_{2},G_{2})$ around $x$ and $f(x)$, and a smooth (resp.
$C^{k,\alpha}$-map) $\hat{f}$ between the local models so that the diagram
with the projections onto $U_{1}$ and $U_{2}$ commutes.

######  Remark 1.

One can define the _tangent bundle_ $T\mathcal{O}$ as a suitable orbifold,
which coincides with the usual tangent bundle when restricted to the regular
part (we refer to [KL14] for the precise definitions). Similarly for the
cotangent bundle $T^{*}\mathcal{O}$, and their tensor products. A section for
such bundles is said to be _smooth_ (resp. of class $C^{k,\alpha}$) if it is
so as a map between orbifolds. In particular, we will use such a terminology
in the proof of the main theorem, when saying that a Riemannian metric $g$ on
$\mathcal{O}$ is of class $C^{1,\alpha}$.

On an orbifold $\mathcal{O}$, one can define differential forms and study de
Rham cohomology [S56] (see also [C21] for an introduction). We denote by
$H^{k}_{dR}(\mathcal{O})$ the $k^{th}$-de Rham cohomology group of
$\mathcal{O}$.

The following lemma is well-known to experts, we include it with a proof for
the reader’s convenience.

######  Lemma 1.

Let $\mathcal{O}$ be an $n$-dimensional orientable orbifold. Then the first
Betti number $b_{1}(|\mathcal{O}|)$, defined as the rank over $\mathbb{Z}$ of
the fundamental group $\pi_{1}(|\mathcal{O}|)$, coincides with the rank over
$\mathbb{R}$ of the first de Rham cohomology group $H^{1}_{dR}(\mathcal{O})$.

###### Proof.

By Poincaré duality for the de Rham cohomology of orbifolds [S56, Theorem 3],
it holds that $H^{1}_{dR}(\mathcal{O})=H^{n-1}_{dR}(\mathcal{O})$.

The de Rham Theorem for orbifolds [S56, Theorem 1], gives that
$H^{n-1}_{dR}(\mathcal{O})=H^{n-1}(|\mathcal{O}|,\mathbb{R})$, where the
latter is the $(n-1)$-th real singular cohomology group.

By Poicaré duality with coefficients in $\mathbb{R}$ [S56], it holds that the
$(n-1)$-th real singular cohomology group and the $1^{st}$ real singular
homology group coincide:
$H^{n-1}(|\mathcal{O}|,\mathbb{R})=H_{1}(|\mathcal{O}|,\mathbb{R})$.

Finally, It is a general fact that ${\rm
Rk}_{\mathbb{R}}(H_{1}(X,\mathbb{R}))={\rm Rk}_{\mathbb{Z}}(\pi_{1}(X))$ for
any topological space $X$, where the latter is the rank over $\mathbb{Z}$ of
the (classical) fundamental group.

∎

We are now in a position to prove the main result of the note.

######  Theorem 2.

Let $M$ be a closed Riemannian manifold of dimension at most $4$. If
$|\mathrm{Ric}|\leq 1$, $\mathrm{diam}\leq D<\infty$ and $\mathrm{vol}\geq
v>0$, then

$\nu^{H,1}\geq C(D,v)>0.$

Thus, in other words, the global Poincaré inequality:

$\inf_{\eta}\int_{M}|\omega-\eta|^{2}\mathop{}\\!\mathrm{d}\mathrm{vol}\leq
C(D,v)^{-1}\int_{M}\left(|\delta\omega|^{2}+|d\omega|^{2}\right)\mathop{}\\!\mathrm{d}\mathrm{vol}$
(3)

holds for any smooth $1$-form $\omega$ on $M$, where the infimum in the left-
hand-side of (3) runs over all harmonic one forms $\eta$ on $M$.

###### Proof.

Note that it is enough to consider the case when the dimension is $4$ because
other cases can be reduced to the 4D case after taking the product of a lower
dimensional flat torus.

Firstly let us discuss the case when $M$ is orientable. We will argue by
contradiction. If it is not the case, then there exist a sequence of closed
oriented Riemannian $4$-manifolds $M_{i}$ with $|\mathrm{Ric}|\leq 1$,
$\mathrm{diam}\leq D<\infty$ and $\mathrm{vol}\geq v>0$ such that

$\nu^{H,1}(M_{i})\to 0.$ (4)

It follows from [A89, A90, CC97] with [CN15] that after passing to a
subsequence, there exists a compact Riemannian $4$-orbifold $\mathcal{O}$
endowed with a Riemannian metric $g\in W^{2,p}$ for any $p<\infty$ (thus, in
particular, $g\in C^{1,\alpha}$ for any $\alpha<1$), such that $M_{i}$
measured Gromov-Hausdorff (mGH) converge to $\mathcal{O}$ and the limit
measure is the Hausdorff measure of dimension $4$. Note that $\mathcal{O}$ is
orientable by [H17b]. From [H17a], the spectral convergence for the Hodge
Laplacian acting on $1$-forms holds for the convergence $M_{i}\to\mathcal{O}$,
namely $\lambda^{H,1}_{j}(M_{i})\to\lambda^{H,1}_{j}(\mathcal{O})$ for any
$j$. In particular

$\limsup_{i\to\infty}b_{1}(M_{i})\leq b_{1}^{H}(\mathcal{O}),$

where $b^{H}_{1}(\mathcal{O})$ denote the dimension of the space of harmonic
one forms on $X$. Moreover the inequality must be strict:

$\limsup_{i\to\infty}b_{1}(M_{i})<b_{1}^{H}(\mathcal{O}).$

because of (4).

On the other hand, applying [SW01, Theorem 1.1] for any sufficiently large
$i$, there exists a surjective homomorphism from $\pi_{1}(M_{i})$ to
$\pi_{1}(|\mathcal{O}|)$; here we used that the revised fundamental group
(used in [SW01]) of an orbifold coincides with the classical fundamental
group, since every orbifold is semi-locally simply connected (as each point
admits a contractible neighbourhood). In particular, considering their ranks,
we have

$\liminf_{i\to\infty}b_{1}(M_{i})\geq b_{1}(|\mathcal{O}|).$

Since, by Hodge theory, linearly independent harmonic 1-forms on $\mathcal{O}$
generate different classes in $H^{1}_{dR}(\mathcal{O})$, Lemma 1 yields

$b_{1}^{H}(\mathcal{O})\leq b_{1}(|\mathcal{O}|).$ (5)

As a summary

$\limsup_{i\to\infty}b_{1}(M_{i})<b_{1}^{H}(\mathcal{O})\leq
b_{1}(|\mathcal{O}|)\leq\liminf_{i\to\infty}b_{1}(M_{i}),$

which is a contradiction.

Finally, let us discuss the case when $M$ is non-orientable. Take the two-
sheeted orientable Riemannian covering $\pi:\tilde{M}\to M$. Note that any
harmonic one form on $\tilde{M}$ comes from the pull-back of a harmonic one
form on $M$ because of $b_{1}(\tilde{M})=b_{1}(M)$. Thus applying (3) to
$\tilde{M}$ completes the proof. ∎

As an immediate consequence of the proof above we obtain the following.

######  Corollary 3.

Let $M_{i}$ be a sequence of Riemannian $4$-manifolds with $|\mathrm{Ric}|\leq
1$, Gromov-Hausdorff converging to a $4$-dimensional $C^{1,\alpha}$-Riemannian
orbifold $\mathcal{O}$. Then for any sufficiently large $i$:

$b_{1}(M_{i})=b_{1}^{H}(\mathcal{O})=b_{1}(|\mathcal{O}|)=b_{1}(|\mathcal{O}|_{reg}).$

Let us make some small observation on other related spectral gap results. Let
$\mathbb{R}^{n}/\mathbb{Z}^{n}$ be the $n$-torus with the canonical flat
Riemannian metric $g$. Then one can easily find a smooth family of Riemannian
metrics $g_{\epsilon}$ on $\mathbb{R}^{n}/\mathbb{Z}^{n}$ satisfying that
$g_{\epsilon}$ has no parallel vector fields and that $g_{\epsilon}$ converge
smoothly to $g$ as $\epsilon\to 0$. This observation tells that in general,
for any dimension, under any negative lower bound and any positive upper bound
on any curvature, there is no quantitative spectral gap for the connection
Laplacian $\nabla^{*}\nabla$ acting on one forms.

On the other hand, in the case when the Ricci curvature is non-negative, any
harmonic one form must be parallel because of (2). Combining this observation
with the trivial point-wise inequality:

$|d\omega|+|\delta\omega|\leq C|\nabla\omega|$

for any smooth one form $\omega$, we obtain the following.

######  Corollary 4.

Let $M$ be a closed Riemannian manifold of dimension at most $4$ with
$0\leq\mathrm{Ric}\leq 1$, $\mathrm{diam}\leq D<\infty$ and $\mathrm{vol}\geq
v>0$. Then the first positive eigenvalue, denoted by $\nu^{C,1}$, of
$\nabla^{*}\nabla$ acting on one forms satisfies

$\nu^{C,1}\geq C(D,v)>0.$

Note that thanks to the spectral convergence results established in [H17a], we
can also give the corresponding results for limit spaces.

Finally let us conclude the note by proposing a (maybe well-known for experts)
conjecture. Notice that, in sharp contrast with the case of functions (1), see
[CC90], it is not possible to remove the lower bound on the volume.

######  Conjecture 5.

Let $M$ be a closed Riemannian $n$-manifold with $\mathrm{Ric}\geq-1$,
$\mathrm{diam}\leq D<\infty$ and $\mathrm{vol}\geq v>0$. Then

$\nu^{H,1}\geq C(n,D,v)>0.$

It is also natural to ask the same question for non-collapsed
$\operatorname{RCD}(K,N)$ spaces.

Acknowledgement. This work was conducted at the The Erwin Schrödinger
International Institute for Mathematics and Physics (ESI), where both the
authors were partially supported to participate in the workshop, Synthetic
Curvature Bounds for Non-Smooth Spaces: Beyond Finite Dimension. We would like
to express our gratitude to the organizers of the workshop and to the ESI for
providing an excellent working environment.

The first named author acknowledges support of the Grant-in-Aid for Scientific
Research (B) of 20H01799, the Grant-in-Aid for Scientific Research (B) of
21H00977 and Grant-in-Aid for Transformative Research Areas (A) of 22H05105.

The second named author acknowledges support by the European Research Council
(ERC), under the European Union Horizon 2020 research and innovation
programme, via the ERC Starting Grant “CURVATURE”, grant agreement No. 802689.

## References

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# Infall and outflow motions in the high-mass star forming complex G9.62+0.19

Tie Liu11affiliation: Department of Astronomy, Peking University, 100871,
Beijing China<EMAIL_ADDRESS><EMAIL_ADDRESS>, Yuefang Wu11affiliation:
Department of Astronomy, Peking University, 100871, Beijing China;
<EMAIL_ADDRESS><EMAIL_ADDRESS>, Sheng-Yuan Liu22affiliation: Institute
of Astronomy and Astrophysics, Academia Sinica, Taipei, Taiwan , Sheng-Li
Qin33affiliation: I. Physikalisches Institut, Universität zu Köln, Zülpicher
Str. 77, 50937 Köln, Germany 44affiliation: National Astronomical
Observatories, Chinese Academy of Sciences, Beijing, 100012 , Yu-Nung
Su22affiliation: Institute of Astronomy and Astrophysics, Academia Sinica,
Taipei, Taiwan , Huei-Ru Chen55affiliation: Institute of Astronomy and
Department of Physics, National Tsing Hua University, Hsinchu, Taiwan
22affiliation: Institute of Astronomy and Astrophysics, Academia Sinica,
Taipei, Taiwan and Zhiyuan Ren11affiliation: Department of Astronomy, Peking
University, 100871, Beijing China<EMAIL_ADDRESS><EMAIL_ADDRESS>
###### Abstract

We present the results of a high resolution study with the Submillimeter Array
towards the massive star forming complex G9.62+0.19. Three sub-mm cores are
detected in this region. The masses are 13, 30 and 165 M☉ for the northern,
middle and southern dust cores, respectively. Infall motions are found with
HCN (4-3) and CS (7-6) lines at the middle core (G9.62+0.19 E). The infall
rate is $4.3\times 10^{-3}~{}M_{\odot}\cdot$yr-1. In the southern core, a
bipolar-outflow with a total mass about 26 M☉ and a mass-loss rate of
$3.6\times 10^{-5}~{}M_{\odot}\cdot$yr-1 is revealed in SO ($8_{7}-7_{7}$)
line wing emission. CS (7-6) and HCN (4-3) lines trace higher velocity gas
than SO ($8_{7}-7_{7}$). G9.62+0.19 F is confirmed to be the driving source of
the outflow. We also analyze the abundances of CS, SO and HCN along the
redshifted outflow lobes. The mass-velocity diagrams of the outflow lobes can
be well fitted by a single power law. The evolutionary sequence of the cm/mm
cores in this region are also analyzed. The results support that UC Hii
regions have a higher blue excess than their precursors.

Massive core:pre-main sequence-ISM: molecular-ISM: kinematics and dynamics-
ISM: jets and outflows-stars: formation

††slugcomment: Accepted to ApJ

##  1 Introduction

High-mass stars play a major role in the evolution of the Galaxy. They are the
principal sources of heavy elements and UV radiation (Zinnecker & Yorke,
2007). However, the formation and evolution of high-mass stars are still
unclear. A possible evolution sequence of high-mass stars from infrared dark
clouds to classic Hii regions has been suggested (Van der Tak & Menten, 2005).
But one of the major topics whether high-mass stars form through accretion-
disk-outflow, like low-mass ones (Shu, Adams & Lizano, 1987), or form via
collision-coalescence (Wolfire, & Cassinelli, 1987; Bonnell et al., 1998) is
still far from solved.

Yet more and more observations at various resolutions seem to support the
accretion-disk-outflow models rather than collision-coalescence models. Disks
are detected in several high-mass star forming regions (Patel et al., 2005;
Jiang et al., 2005; Sridharan, Williams, & Fuller, 2005). Outflows are found
with a high detection rate as in low-mass cores in single-dish surveys (Wu et
al., 2004; Zhang et al., 2005; Qin et al., 2008a). High resolution studies
have also confirmed that molecular outflows are common in high-mass star
forming regions (Su, Zhang, & Lim, 2004; Qiu et al., 2007; Qin et al., 2008b,
c; Qiu et al., 2009). Searching for inflow motions also has made large
progress in recent years (Wu & Evans, 2003; Fuller, Williams, & Sridharan,
2005; Wyrowski et al., 2006; Klaassen, & Wilson, 2007; Wu et al., 2007, 2009;
Furuya, Cesaroni, & Shinnaga, 2011). Both infall and outflow motions in the
massive core JCMT 18354-0649S are detected (Wu et al., 2005), and further
confirmed by higher resolution observations (Liu et al., 2011). Although
accretion-disk-outflow systems are found in high-mass star forming regions,
there may be differences between low- and high-mass formation.

The infall motion can be detected via ”blue profile”, a double-peaked profile
with the blueshifted peak being stronger for optically thick lines and a
single peak at the absorption part of optically thick lines for optically thin
lines, which is caused by self absorption of the cooler outer infalling gas
towards the warmer central region (Zhou et al., 1993). In contrast, the ”red
profile” where the redshifted peak of a double-peaked profile being stronger
for optically thick lines is suggested as indicators for outflow motions.
Mardones et al. (1997) defined the ”blue excess” in a survey, E, as E = (NB-
NR)/NT (Mardones et al. 1997), where NT is number of sources, NB and NR mark
the number of sources with blue and red profiles, respectively. The blue
excess seems to be no significant differences among the low-mass cores in
different evolutionary phases. However, using the IRAM 30 m telescope, Wu et
al. (2007) found that UC Hii regions show a higher blue excess than their
precursors, indicating fundamental differences between low- and high-mass-star
forming conditions. The searches need to be expanded.

Located at a distance of 5.7 kpc (Hofner et al., 1994), G9.62+0.19 is a well
studied high-mass star forming region containing a cluster of Hii regions,
which are probably at different evolutionary stages. Multiwavelength VLA
observations have identified nine radio continuum sources (denoted from A-I)
(Garay et al., 1993; Testi et al., 2000), and components C-I are very compact
($<5\arcsec$ in diameter) (Garay et al., 1993; Testi et al., 2000). As
revealed in NH3 (4,4), (5,5) and CH3CN (J=6-5), component F is a hot molecular
core (HMC) and hence likely the youngest source in the region (Cesaroni et
al., 1994; Hofner et al., 1994, 1996b). G9.62+0.19 E is a young massive star
surrounded by a very small UC Hii region and a dusty envelope (Hofner et al.,
1996b), while G9.62+0.19 D a small cometary UC Hii region excited by a B0.5
ZAMS star (Hofner et al., 1996b; Testi et al., 2000). Both G9.62+0.19 E and
G9.62+0.19 D seem to be at a more evolved stage than G9.62+0.19 F. Thus G9.62
complex is an ideal sample to examine massive star forming activities
including outflow and infall motions.

Maser emissions of NH3, H2O, OH, and CH3OH, as well as the strong thermal NH3
emissions were detected along a narrow region with projected length
$20\arcsec$ and width$\leq 2\arcsec$ (Hofner et al., 1994). A possible
explanation for this alignment is compression of the molecular gas by shock
front originating from an even more evolved Hii region to the west of the
star-forming front (Hofner et al., 1994). High-velocity molecular outflows
also have been detected in this region, and G9.62+0.19 F is believed to be the
driving source (Gibb, Wyrowski, & Mundy , 2004; Hofner, Wiesemeyer, & Henning
, 2001; Su et al., 2005). However, most of previous work was carried out at
low frequencies, probing low excitation conditions. To exam the hot dust/gas
environment and dynamical processes in this region, higher resolution studies
at high frequencies are needed. In this paper we report the results of the
Submillimeter Array (SMA111Submillimeter Array is a joint project between the
Smithsonian Astrophysical Observatory and the Academia Sinica Institute of
Astronomy and Astrophysics and is funded by the Smithsonian Institution and
the Academia Sinica.) observations toward G9.62+0.19 region at 860 $\micron$.

##  2 Observations

The observations of G9.62+0.19 with the SMA were carried out on July 9th, 2005
with seven antennas in its compact configuration at 343 GHz for the lower
sideband (LSB) and 353 GHz for the upper sideband (USB). The Tsys ranges from
210 to 990 K with a typical value of 380 K at both sidebands during the
observations. The observations had two fields for the G9.62+0.19 complex to
cover the entire region with emissions. One phase reference center was
RA(J2000) = 18h06m14.21s and DEC(J2000) = -$20\arcdeg 31\arcmin 46.2\arcsec$,
and the other was RA(J2000) = 18h06m15.00s and DEC(J2000) = -$20\arcdeg
31\arcmin 34.20\arcsec$. Uranus and Neptune were observed for antenna-based
bandpass calibration. QSOs 1743-038 and 1911-201 were employed for antenna-
based gain correction. Neptune was used for flux-density calibration. The
frequency spacing across the spectra band was 0.8125 MHz, corresponding to a
velocity resolution of $\sim$0.7 km s-1.

MIRIAD was employed for calibration and imaging (Sault et al., 1995). The
imaging was done to each field separately and the mosaic continuum map was
made using a linear mosaicing algorithm (task ”linmos” in MIRIAD). The 860
$\micron$ continuum data was acquired by averaging over all the line-free
channels in both sidebands. The spectral cubes were constructed using the
continuum-subtracted spectral channels smoothed into a velocity resolution of
1 km s-1. Additional self-calibration with models of the clean components from
previous imaging process was performed on the continuum data in order to
remove residual errors due to phase and amplitude problems, and the gain
solutions obtained from the continuum data were applied to the line data. The
synthesized beam size of the continuum emission with robust weighting of 0.5
is $2.76\arcsec\times 1.88\arcsec$ (P.A.=$21.4\arcdeg$).

##  3 Results

###  3.1 Continuum emission

The 860 $\micron$ continuum image combining the visibility data from both
sidebands is shown in Figure 1 . Three sub-mm cores are detected. The known cm
and mm continuum components (Testi et al., 2000) of B, C, D, E, F, G, H, and I
are marked by plus signs. Water masers (Hofner, & Churchwell, 1996a) are
marked by open squares and methanol masers (Norris et al., 1993) by triangles.
The near-IR sources (Persi et al., 2003; Testi et al., 1998; Linz et al.,
2005) are marked by filled circles. IRAC sources are taken from the database
of Galactic Legacy Infrared Mid-Plane Survey Extraordinaire (GLIMPSE)
222http://irsa.ipac.caltech.edu/data/SPITZER/GLIMPSE/ and labeled with
asterisks. The northern core is located at south-east of G9.62+0.19 C, and the
middle core is associated with G9.62+0.19 E. The 860 $\micron$ continuum
emission at the southern core is concentrated on the hot molecular core
G9.62+0.19 F and extends to G9.62+0.19 D in the south and to G9.62+0.19 G in
the north.

Gaussian fits were made to the continuum. The northern core seems to be a
point-like source. The middle core is very compact with a deconvolved size of
$\sim 1.4\arcsec$. The southern core is found to be elongated from north to
south with an average size of $2.4\arcsec$, containing at least three sources,
D, F, and G. F is at its peak position. The peak positions, sizes, peak
intensities and total fluxes of these three sub-mm cores are listed in Column
2-5 in Table 1. The physical properties of these cores will be further
discussed in section 4.2.

###  3.2 Line emission

Tens of molecular transitions including hot molecular lines CH3OH, HCOOCH3,
and CH3OCH3 are detected toward both the middle and southern sub-mm cores,
indicating these two cores are hot and dense (Qin et al., 2010). Figure 2
presents the full LSB and USB spectra in the UV domain over the shortest
baseline. The strongest lines are identified and labeled on the plots. Only
HCN (4-3) and CS (7-6) line emissions are detected towards the northern core
with our sensitivity. Thus we mainly focus on the middle and southern cores in
this paper. The systemic velocities of 2.1 km s-1 for the middle core and 5.2
km s-1 for the southern core are obtained by averaging the Vlsr of multiple
singly peaked lines. Six transitions of the thioformaldehyde (H2CS) and
molecular transitions SO ($8_{7}$-77), CS (7-6), HC15N (4-3) and HCN (4-3) are
analyzed here, while the others will be discussed in another paper. We have
made gaussian fits to the beam-averaged spectra, and present the observed
parameters of these lines in Table 2.

####  3.2.1 Line emission at the middle sub-mm core

The integrated intensity maps of four transitions of H2CS towards the middle
core are shown in the upper panels of Figure 3. From (a) to (d), the upper
level energy of H2CS transitions varies from $\sim 90$ K to $\sim 400$ K. The
H2CS emission is spatially coincident with continuum emission of the middle
core very well. The Position-Velocity (P-V) diagram and first moment map of
H2CS (102,8-92,7) emission are presented in Figure 4. The P-V diagram is
constructed across the peak of the continuum along the N-S direction. From P-V
diagram two emission peaks are clearly revealed. The velocities of the two
emission peaks are at 1 and 3 km s-1 with $1.5\arcsec$ spatial separation,
indicating a velocity gradient in N-S direction. The first moment map also
shows velocity changes in N-S direction. The small velocity gradient detected
in H2CS (102,8-92,7) emission may indicate a disk with a low inclination along
the line of sight, which requires further confirmation with higher angular
resolution observations and other molecular line tracers.

The spectra and integrated intensity maps of HC15N (4-3) and SO ($8_{7}$-77)
are presented in Figure 5. The two spectra seem to be symmetric, and their
cores are associated with that of the continuum emission very well.

Figure 6 presents the spectra and P-V diagrams of HCN (4-3) and CS (7-6)
emissions of the middle core. HCN (4-3) and CS (7-6) show asymmetric profile.
The blue and red emission peaks of HCN (4-3) are around 0 km s-1 and 6 km s-1,
respectively. The blueshifted emission of CS (7-6) peaks around 1 km s-1,
while the redshifted around 4 km s-1. We can see the blueshifted emission of
both HCN (4-3) and CS (3-2) is always stronger than the redshifted emission
and the absorption is also redshifted, which are blue profiles (see Sect. 1).
Besides the ”blue profile”, some weak absorption dips are found around 10 km
s-1 in both the spectra and P-V diagrams of HCN (4-3) and CS (7-6), and
further observations are needed to determine the properties of these
absorption dips. In this paper we only pay attention to the ”blue-profile”
found in CS (7-6) and HCN (4-3) emission.

The integrated intensity maps of HCN (4-3) and CS (7-6) towards the middle
core are presented in Figure 7. The HCN (4-3) and CS (7-6) are associated with
the dust emission.

####  3.2.2 Line emission at the southern core

The integrated intensity maps of four transitions of H2CS at the southern core
are shown in the lower panels of Figure 3. The upper level energy of H2CS
transitions varies from $\sim 90$ K to $\sim 400$ K from panel (e) to panel
(h). As the upper level energy increases, the emission peak of the different
transitions of H2CS moves from S-E to N-W, indicating a temperature gradient
in the southern core.

Averaged spectra of SO ($8_{7}$-77), HC15N (4-3), HCN (4-3) and CS (7-6) at
the southern core are presented in Figure 8. The spectra of SO ($8_{7}$-77)
and HC15N are averaged over a region of 4$\arcsec$, while HCN (4-3) and CS
(7-6) are averaged over a region of 6$\arcsec$. SO ($8_{7}$-77) emission has a
total velocity extent of larger than 20 km s-1. From gaussian fit to the
spectrum, the peak velocity of SO emission is $5.1\pm 0.1$ km s-1, coincident
very well with the systemic velocity 5.2 km s-1. HC15N (4-3) has a velocity
extent of about 15 km s-1. The velocity extents of CS (7-6) and HCN (4-3) are
as high as 40 km s-1 and 60 km s-1, respectively. Emission wings are clearly
detected from the spectra of the four lines. A ”red-profile” is significantly
exhibited in the spectra of CS (7-6) and HCN (4-3), of which the redshifted
emission is always stronger than the blueshifted emission with an absorption
dip at the blueshifted side of the systemic velocity (5.2 km s-1). This
profile is caused by absorption of the colder blueshifted gas in front of the
hot core, indicating outflow motions. The ”red-profile” is consistent with
that detected using single dish observations (see Figure 6 of Hofner,
Wiesemeyer, & Henning  (2001)).

The integrated intensity maps of HC15N (4-3) and SO ($8_{7}$-77) at the
southern core are presented in Figure 9. To avoid the influence of outflow
motions, both the maps are integrated from 2 km s-1 to 8 km s-1. Both the
emission of HC15N (4-3) and SO ($8_{7}$-77) coincides with the cm/mm component
F, and extends from D to G.

As shown in the left panels of Figure 10, the high velocity gas of HC15N (4-3)
and SO ($8_{7}$-77) can be identified by the vertically dashed lines in the
P-V diagrams. For SO ($8_{7}$-77), we integrate from -4 km s-1 $\leq$ V $\leq$
0 km s-1 for the blue wing and 10 km s-1 $\leq$ V $\leq$ 14 km s-1 for the red
wing, and present the contour map in (c) of Figure 10. For HC15N (4-3), only
the red wing emission is presented in (d) of Figure 10. The high velocity
emission of both HC15N (4-3) and SO ($8_{7}$-77) is associated with core F,
indicating that core F is the driven source of the outflow. The blue and red
wings of SO ($8_{7}$-77) overlap to a large extent in the contour maps, and
hence the molecular outflow revealed by SO ($8_{7}$-77) is observed close to
its flow axis.

Figure 11 presents the channel maps of CS (7-6) emission. The redshifted high-
velocity gas seems to be elongated from north-east to south-west, while the
blueshifted high-velocity gas from north to south. The high velocity gas
revealed by CS (7-6) is also very obvious in the P-V diagram in Figure 13(d).
As shown in the P-V diagram, the blueshifted high-velocity gas extends about
8$\arcsec$ from north to south. The high-velocity emission integrated over the
wings (-12 km s-1 $\leq$ V $\leq$ -5 km s-1 for the blue wing and 15 km s-1
$\leq$ V $\leq$ 22 km s-1 for the red wing) is presented in Figure 13(e).

Figure 12 is the channel maps of HCN (4-3) emission. The maximum of
absorptions appears at around 0 km s-1. The redshifted high-velocity gas seems
to be elongated from west to east, while the blueshifted high-velocity gas
from north to south. At very high velocity channels (V$\leq$ -16 km s-1), the
blueshifted emission is totally located at south-east. By comparing the
channel maps and P-V diagrams (see Figure 13) of HCN (4-3) and CS (7-6) at
velocity intervals -12 km s-1 $\leq$ V $\leq$ -5 km s-1 and 15 km s-1 $\leq$ V
$\leq$ 22 km s-1, we find similar structures in CS (7-6) and HCN (4-3)
emissions. The high-velocity emission of HCN (4-3) integrated from -12 km s-1
to -5 km s-1 for the blue wing and from 15 km s-1 to 22 km s-1 for the red
wing is presented in the panel (b) of Figure 13\. As of CS (7-6), the
blueshifted gas revealed by HCN (4-3) is elongated from north to south with
the emission center located between G9.62+0.19 F and G9.62+0.19 D, while the
redshifted gas from north-east to south-west. Two clumps are found in the
blueshifted high-velocity emission of HCN (4-3), which locate at north-west
and south-east of F, respectively.

In order to reveal the very high velocity emission traced by HCN (4-3) but not
CS (7-6), we integrate over the wings at much higher velocities (-20 km s-1
$\leq$ V $\leq$ -13 km s-1 for the blue wing and 23 km s-1 $\leq$ V $\leq$ 39
km s-1 for the red wing), and present the integrated emission map in Figure
13(c). The redshifted emission is elongated from north-east to south-west with
the emission center located between G9.62+0.19 F and G9.62+0.19 G, while the
blueshifted emission center located between G9.62+0.19 F and G9.62+0.19 D. It
is clearly seen that the high velocity gas traced by SO ($8_{7}$-77), CS (7-6)
and HCN (4-3) have different spatial distributions, which should be caused by
the complicated interactions between the outflow and the ambient gas. It may
also indicate a change of the outflow axis. The change of outflow axis is also
found in IRAS 20126+4104 (Su et al., 2007) and JCMT 18354-0649S (Liu et al.,
2011).

From the integrated emission maps of SO ($8_{7}$-77), HCN (4-3) and CS (7-6)
high velocity gas, it is clearly seen that G9.62+0.19 F is located at the
middle of the redshifted and blueshifted lobes, suggesting G9.62+0.19 F is the
outflow driving source.

##  4 Discussion

###  4.1 Rotational temperature of H2CS transitions

Six transitions of H2CS have been detected in the middle and southern cores,
enabling us to estimate the rotational temperature. Under the assumptions that
the gas is optically thin under local thermodynamic equilibrium and the gas
emission fills the beam, the rotation temperature and beam-averaged column
density can be estimated using the Rotational Temperature Diagram (RTD) by
(Cummins, Linke, &Thaddeus, 1986; Turner et al., 1991; Liu, et al., 2002)

$\textrm{ln}(\frac{N_{u}}{g_{u}})=\textrm{ln}(\frac{N_{T}}{Q_{rot}})-\frac{E_{u}}{T_{rot}}=\textrm{ln}[2.04\times
10^{20}\frac{\int~{}I(Jy~{}beam^{-1})dv(km~{}s^{-1})}{\theta_{a}\theta_{b}(arcsec^{2})g_{I}g_{K}\nu^{3}(GHz^{3})S\mu^{2}(debye^{2})}]$
(1)

where Nu is the observed column density of the upper energy level, gu is the
degeneracy factor in the upper energy level, NT is the total beam-averaged
column density, Qrot is the rotational partition function, Eu is the upper
level energy in K, Trot is the rotation temperature, $\int$ I dv is the
integrated intensity of the specific transition, $\theta_{a}$ and $\theta_{b}$
are the FWHM beam size, gK is the K-ladder degeneracy, gI is the degeneracy
due to nuclear spin, $\nu$ is the rest frequency, and S is line strength and
$\mu$ the permanent dipole moment. For H2CS, the interchangeable nuclei are
spin $\frac{1}{2}$, leading to ortho- and para-forms with gI equaling
$\frac{3}{4}$ and $\frac{1}{4}$, respectively (Blake et al., 1987; Turner et
al., 1991). The partition function Qrot of H2CS is (Blake et al., 1987)

$Q_{rot}=2[\frac{\pi(kT_{rot})^{3}}{h^{3}ABC}]^{\frac{1}{2}}$ (2)

where k and h are the Boltzmann and Planck constants, respectively, and A, B,
and C are the rotation constants. Thus the rotation temperature Trot and total
column density NT can be estimated by least-squares fitting to the multiple
transitions. We applied the RTD method towards D, E, F, G (see Figure 14), and
the fitting results are listed in the second and third columns of Table 3\.
The rotational temperature of the middle core (E) is 83$\pm$21 K. In the
southern core, the rotational temperature estimated decreases from G (91 K) to
F (83 K) and D (43 K), suggesting the temperature gradient in the southern
core. The total column density of H2CS ranges from 1.3$\times$1015 (G) to
3.8$\times$1015 cm-2 (D).

However, the filling factor and the optical depth correction were not taken
account of in the RTD method. To investigate their effect we applied the
Population Diagram (PD) analysis (Goldsmith, & Langer, 1999; Wang et al.,
2010). In the PD analysis, we have

$\textrm{ln}(\frac{\hat{N_{u}}}{g_{u}})=\textrm{ln}(\frac{N_{T}}{Q_{rot}})-\frac{E_{u}}{T_{rot}}+\textrm{ln}(f)-\textrm{ln}(\frac{\tau}{1-e^{-\tau}})$
(3)

where $\hat{N_{u}}$ is the inferred column density of the upper energy level
from the PD analysis, f is the source filling factor and $\tau$ is the optical
depth. The optical depth $\tau$ can be expressed by (Remijan et al., 2004)

$\tau=\frac{8\pi^{3}S\mu^{2}\nu}{3k\Delta\textrm{v}T_{rot}}\frac{N_{T}}{Q_{rot}}e^{-\frac{E_{u}}{T_{rot}}}$
(4)

where $\Delta$v is the FWHM line width. Under LTE, the upper-level
populations, $\hat{N_{u}}$, can be predicted according to the right-hand side
of Equation (3) for a given set of total column density, NT, rotational
temperature, Trot, and source filling factor, f. The expected $\hat{N_{u}}$
were evaluated for the parameter space of Trot = 10-500 K, NT = 1014-1017
cm-2, and f between 0.01 and 1.0. To compare the observed $N_{u}$ and the
inferred $\hat{N_{u}}$, we calculate the $\chi^{2}$ as:

$\chi^{2}=\sum(\frac{N_{u}-\hat{N_{u}}}{\delta~{}N_{u}})^{2}$ (5)

where $\delta~{}N_{u}$ is the 1 $\sigma$ error of observed upper-state column
density. Although the $\chi^{2}$ is a good representation of the goodness of
fit, the parameter set with the lowest $\chi^{2}$ may not actually represent
physical parameters very well due to the uncertainties of the observed data.
In order to find a representative parameter set, we compute a weighted mean
and standard deviation for all the parameters, with the weights being the
inverse of the $\chi^{2}$. All the parameter sets where the inferred upper-
level population $\hat{N_{u}}$ corresponds with the observed upper-level
population $N_{u}$ within 3 $\sigma$ are used to compute the weighted means
and standard deviations. The derived rotational temperature, total column
density and filling factor of each component are list in the [3-5] columns of
Table 3. The inferred optical depths of each line transition are listed in the
last six columns of Table 3. The rotational temperatures of D, E, F, G are
estimated to be 42$\pm$34, 92$\pm$74, 51$\pm$23 and 105$\pm$37 K,
respectively. A temperature gradient in the southern core is also revealed as
in the RTD method. The four components D, E, F, G has similar total column
densities as high as 4$\times 10^{16}$ cm-2, about an order of magnitude
higher than those obtained from RTD method, which are mainly due to the small
source filling factor ($<$0.5). The optical depths of H2CS (100,10-90,9) at
the four components are all much larger than one, while the other transitions
are always optically thin except H2CS (102,9-92,8) line at G.

###  4.2 Core properties

In the optically thin case, the total dust and gas masses of the three sub-mm
cores can be obtained with the formula
$M=S_{\nu}D^{2}/\kappa_{\nu}RB_{\nu}(T_{d})$ (Hildebrand , 1983), where
$S_{\nu}$ is the flux at 860 $\micron$, D is the distance, R=0.01 is the mass
ratio of dust to gas, and $\kappa_{\nu}$ is dust opacity per unit dust mass.
$B_{\nu}(T_{d})$ is the Planck function at a dust temperature of Td. We assume
that Td equals the rotational temperature of H2CS. For the northern core,
since only CS (7-6) (upper energy Eu = 65.8 K) and HCN (4-3) (Eu = 42.5 K)
exhibit strong emission lines, we assume Td to be 50 K. Together with the
measurements at centimeter and millimeter wavelengths, Su et al. (2005)
extrapolated the ionized gas emission at mm/submm wavelengths, and found that
the 0.85 mm continuum associated with components D, E, and F are dominated by
thermal dust emission. They have derived opacity index $\beta$ of components E
and F to be 1.2, and 0.8, respectively. For the northern sub-mm core,
${\beta}=1.5$ is assumed. Using the above dust opacity indexes, we adopt
$\kappa_{\nu}$=2.0, 1.8, and 1.5 cm2g-1 for the northern, middle and southern
cores, respectively (Ossenkopf & Henning, 1994). At the distance of 5.7 kpc ,
we get the total dust and gas masses for these three cores, and list all the
parameters in Table 1. The deduced masses for the northern, middle and
southern cores are 13, 30, 165 M☉, respectively. The column density of H2 are
1.2$\times 10^{24}$ and 2.1$\times 10^{24}$ cm-2 for the middle and southern
sub-mm cores, respectively.

###  4.3 Infall properties in the middle core

In the middle core, both CS(7-6) and HCN(4-3) emission exhibits ”blue profile”
feature, indicating infall motions of the gas envelope toward the central star
(Keto, Ho,& Haschick, 1988; Zhou et al., 1993; Zhang, Ho, & Ohashi, 1998; Wu &
Evans, 2003; Wu et al., 2005, 2007; Fuller, Williams, & Sridharan, 2005;
Wyrowski, 2007; Sun, & Gao, 2008). The velocity difference (0.9 km s-1)
between the absorption dip in CS (7-6) spectrum (3 km s-1) and the systemic
velocity (2.1 km s-1) is taken as the infall velocity $V_{in}$. Since both HCN
(4-3) and CS (7-6) emissions are not resolved towards the middle core, we
simply take the dust core size as the radius of the infall region, which may
underestimate the infall rate derived below. The kinematic mass infall rate
can be calculated using dM/dt=$4{\pi}R_{in}^{2}nmV_{in}$. n=1.5$\times
10^{7}$cm-3 is the number density of this dust core. Taking Helium into
account, the mean molecular mass m is 1.36 times of H2 molecule mass. The
infall rate calculated is $4.3\times 10^{-3}~{}M_{\odot}\cdot$yr-1. For
comparison, the $V_{in}$ from pure free-infall assumption is also derived with
the formula $V_{in}^{2}=2GM/R_{in}$. The pure free-infall velocity is
$V_{in}=3.6~{}$km s-1 and thus the ”gravitational” mass infall rate is
$1.7\times 10^{-2}~{}M_{\sun}\cdot$yr-1, which is larger than the kinematic
infall rate.

###  4.4 Outflow properties in the southern core

####  4.4.1 Shock chemistry in the outflow region of the southern core

Observations have suggested that there are important differences in molecular
abundances in different outflow regions (Bachiller et al., 1997; Choi et al.,
2004; Jörgensen, Schöier, & van Dishoeck, 2004; Codella et al., 2005).
Significant abundance enhancements are found in the shocked region for sulfur-
bearing molecules (Bachiller et al., 1997; Jörgensen, Schöier, & van Dishoeck,
2004), and the abundance of HCN in outflow regions is related to atomic carbon
abundance (Choi, 2002). However, previous studies of the chemical impact of
outflows are confined to the well collimated outflows around Class 0 sources,
while such studies especially high resolution studies on massive outflows are
rare (Bachiller et al., 1997; Jörgensen, Schöier, & van Dishoeck, 2004; Arce
et al., 2007).

A red and bright IRAC source is found to be associated with the southern core.
The magnitudes of the IRAC source at 3.6 $\micron$, 4.5 $\micron$ and 5.8
$\micron$ are $10.102\pm 0.093$, $8.361\pm 0.108$ and $7.778\pm 0.302$ mag,
respectively. The [3.6-4.5] color is as large as 1.74, indicating shocked
emission in the southern core (Takami et al., 2010). Maser emissions of NH3,
H2O, OH, and CH3OH, as well as the strong thermal NH3 emissions also uncover
the existence of the shocked gas (Hofner et al., 1994). Outflows can be
revealed from shocked H2 emission probed by the strong and extended emission
at the 4.5 $\micron$ band (Qiu et al., 2008; Takami et al., 2010). Thus the
massive outflow in the southern core of G9.62 complex provides an ideal sample
to study shock chemistry.

The fractional abundance of a certain molecule is defined as
$\chi=N_{T}/N_{H_{2}}$, where $N_{T}$ is the total column density of a
specific molecule and $N_{H_{2}}$ is the H2 column density. Assuming that the
gas is optically thin and the emission fills the beam, the beam-averaged total
column density of a specific molecule can be obtained from:

$N_{T}=2.04\times
10^{20}\frac{\int~{}I(Jy~{}beam^{-1})dv(km~{}s^{-1})Q_{rot}e^{E_{u}/T_{rot}}}{\theta_{a}\theta_{b}(arcsec^{2})g_{I}g_{K}\nu^{3}(GHz^{3})S\mu^{2}(debye^{2})}$
(6)

Assuming that Trot of HC15N equals to that of H2CS and the gas is optically
thin, $N_{T}$ of HC15N is calculated to be $3.0\times 10^{13}$ cm-2 at the
core region. At the galactocentric distance of 3 kpc for G9.62+0.19 (Scoville
et al.1987,Hofner et al.1994), the abundance ratio
[14N]/[15N]$~{}\approx~{}350$ (Wilson and Rood. 1994). Thus the total column
density of HCN at the core region should be $1.1\times 10^{16}$ cm-2.
Therefore, the fractional abundance of HCN relative to H2 at the core region
is $5.2\times 10^{-9}$. HCN appears to be greatly enhanced in the outflow
regions of the L1157 (Bachiller et al., 1997), while has similar abundances in
the outflow region and the ambient cloud of NGC 1333 CIRAS 2A (Jörgensen,
Schöier, & van Dishoeck, 2004). Owing to the lack of a direct estimation of
the H2 column density towards the outflow region, the fractional abundance of
HCN in the outflow region is also assigned to $5.2\times 10^{-9}$ in
calculating the outflow parameters. Since the HC15N emission traces outflowing
gas at much lower velocity than HCN, perhaps HCN could be more enhanced in the
high velocity component. With the possibility of higher opacity and the lack
of direct H2 column density measurement, the derived fractional abundance
perhaps is a lower limit anyway. Su et al. (2007) estimate an HCN abundance of
$\sim 1-2\times 10^{-8}$ in the massive outflow lobes of IRAS 20126+4104,
which is comparable to our estimation here.

Since the blueshifted outflow gas traced by CS (7-6) and HCN (4-3) suffers
self-absorption, the abundance ratios among SO ($8_{7}-7_{7}$), CS (7-6), and
HCN (4-3) were inferred from the beam-averaged spectra taken from the
redshifted outflow lobe. The abundance ratio as a function of flow velocity
(the outflow velocity relative to the systemic velocity) of [CS/SO] is
obtained assuming five different excitation temperatures in the left panel of
Figure 15\. It can be seen that the abundance ratio of [CS/SO] increases with
the excited temperature. At each excitation temperature, the abundance ratio
of [CS/SO] has lower values at flow velocities less than 6 km s-1, and higher
values when Vflow larger than 8 km s-1, whereas the abundance ratio seems to
be constant at flow velocities between 6 km s-1 and 8 km s-1. There are two
reasons for the lower abundance ratio when V${}_{flow}~{}<$ 6 km s-1: first,
the flux missing of CS (7-6) due to the interferometer is more serious than SO
($8_{7}-7_{7}$); second, CS (7-6) may be more optically thick at lower flow
velocities than SO ($8_{7}-7_{7}$). As shown in the P-V diagrams, the emission
region of CS (7-6) is much larger than SO ($8_{7}-7_{7}$) at high velocities.
The higher abundance ratio when V${}_{flow}~{}>$ 8 km s-1 is due to the
smaller filling factor of SO ($8_{7}-7_{7}$) emission. We propose the mean
observed value between 6 km s-1 and 8 km s-1 can represent the actual
abundance ratio of [CS/SO]. Assuming a typical excitation temperature of
Tex=30 K (Wu et al., 2004), the abundance ratio of [CS/SO] at the redshifted
lobe is inferred as 0.7. Nilsson et al. (2000) find that the [SO/CS] abundance
ratios are strongly enhanced in the Orion A and NGC 2071 outflows where the
[SO/CS] ratios are estimated to be about 24 and 2.2, respectively. However,
the [SO/CS] abundance ratio in the outflow of G9.62+0.19 is found to be 1.4,
much lower than that found in Orion A outflow.

As shown in the right panel of Figure 15, the abundance ratio of [CS/HCN]
decreases linearly with the flow velocity. To avoid the missing flux
difficulty, the abundance ratio is calculated at high flow velocities larger
than 7 km s-1. The decreasing of the abundance ratio with velocity is because
that the emission region traced by CS (7-6) is always smaller than HCN (4-3),
leading to smaller filling factor for CS (7-6), which can be verified easily
by comparing the channel maps between CS (7-6) in Figure 11 and HCN (4-3) in
Figure 12 at high velocities. We fitted the observed data with a linear
function, and adopted the value at flow velocity of 10 km s-1 as the actual
abundance ratio of [CS/HCN] in the outflow region, which is [CS/HCN]=1.2.
Since HCN fractional abundance is $5.2\times 10^{-9}$, the fractional
abundances of CS and SO are deduced to be $6.2\times 10^{-9}$ and $8.9\times
10^{-9}$, respectively.

####  4.4.2 Properties of the bipolar-outflow traced by SO ($8_{7}-7_{7}$)
emission

The SO ($8_{7}-7_{7}$) emission in the southern core shows line wings,
suggesting outflow motions. From the integrated intensity map in Figure 10(c),
we find the outflow lobes revealed by SO ($8_{7}-7_{7}$) emission peak at
different position with different position angle compared with previously
reported H2S ($2_{2,0}-2_{1,1}$) (Gibb, Wyrowski, & Mundy , 2004) and HCO+
(1-0) data (Hofner, Wiesemeyer, & Henning , 2001). But in the same sense, the
blue- and red-lobes revealed by SO overlap to a large extent as well as HCO+
(1-0) and H2S ($2_{2,0}-2_{1,1}$) data, consistent with the argument of the
outflow being viewed pole-on (Hofner, Wiesemeyer, & Henning , 2001).

The total mass of each outflow lobe is given by:

$M_{flow}=1.04~{}\times~{}10^{-4}D^{2}\frac{Q_{rot}e^{E_{u}/T_{rot}}}{\chi\nu^{3}S\mu^{2}}\int\frac{\tau}{1-e^{-\tau}}S_{\nu}dv$
(7)

where Mflow, D, Sν, $\chi$, and $\tau$ are the outflow gas mass in M☉, source
distance in kpc, line flux density in Jy, relative abundance to H2, and
optical depth. The other parameters have the same units as in equation (1).
The fractional abundance of SO is taken as $8.9\times 10^{-9}$ (see
Sec.4.4.1). Assuming an excitation temperature of 30 K and the outflowing gas
is optically thin, the inferred outflow masses are 13 M☉ for each of red and
blueshifted lobes. Thus, the momentum can be calculated by $P=\sum$M(v)dv, and
the energy by $E=\sum{\frac{1}{2}}$M(v)v2dv, where $v$ is the flow velocity.
The derived parameters are listed in Table 4. The momentum and energy of the
red lobe are 82 M${}_{\sun}\cdot$km s-1 and $5.4\times 10^{45}$ erg. For the
blue lobe, the momentum and energy are calculated to be 86 M${}_{\sun}\cdot$km
s-1 and $5.8\times 10^{45}$ erg. The dynamical timescale tdyn is estimated as
R/Vchar, where R ($\sim$ 0.06 pc) is adopted as the mean size of the outflow
lobes assuming a collimation factor of unity, and Vchar ($\sim$ 5.5 km s-1) is
assumed as the mass weighted mean velocity. Thus, the dynamic timescale is
estimated to be $1\times 10^{4}$ year, which may be underestimated due to the
uncertainty of the outflow scale. The mechanical luminosity L, and the mass-
loss rate $\dot{M}$ are calculated as L=E/t, $\dot{M}=P/(tV_{w})$, where the
wind velocity Vw is assumed to be 500 km s-1 (Lamers et al., 1995). The
mechanical luminosity L and the total mass-loss rate are estimated to be 9.3
L☉ and $3.6\times 10^{-5}$ M☉$\cdot$yr-1, respectively.

####  4.4.3 Very high-velocity gas detected in CS (7-6) emission

The CS (7-6) emission at the southern core shows ”red-profile” with wide
wings. We take $6.2\times 10^{-9}$ as the fractional abundance of CS relative
to H2 along the outflow lobes. Assuming Tex = 30 K, we derive the parameters
for the CS outflow (Table 4) with the same method used for SO ($8_{7}-7_{7}$).
The outflow masses at very high velocities (v${}_{flow}~{}>~{}$10 km s-1) are
3.7 M☉ and 5.5 M☉ for the blueshifted and redshifted lobes, respectively. The
momentum and energy of the blueshifted lobe at very high velocities are
calculated to be 47 M${}_{\sun}\cdot$km s-1 and $6.0\times 10^{45}$ erg. For
the redshifted lobe, the momentum and energy at extremely high velocities are
calculated to be 68 M${}_{\sun}\cdot$km s-1 and $8.7\times 10^{45}$ erg, which
are similar to the blueshifted lobe.

####  4.4.4 Very high-velocity gas detected in HCN (4-3) emission

As discussed before, HCN (4-3) has a velocity extent of at least 60 km s-1,
which traces extremely high-velocity (EHV) gas. Adopting an excited
temperature of 30 K, and an HCN-to-H2 abundance ratio of $5.2\times 10^{-9}$,
the parameters of the outflow are calculated and listed in Table 4. The
outflow mass at very high velocities (v${}_{flow}~{}>~{}$10 km s-1) are 5.2 M☉
and 17.6 M☉ for the blueshifted and redshifted lobes, respectively. The
momentum and energy of the blueshifted lobe at very high velocities are 85
M${}_{\sun}\cdot$km s-1 and $1.4\times 10^{46}$ erg. For the redshifted lobe,
the momentum and energy at very high velocities are 294 M${}_{\sun}\cdot$km
s-1 and $5.5\times 10^{46}$ erg, which are larger than the blueshifted lobe.

####  4.4.5 Mass-Velocity diagrams

A broken power law, $dM(v)/dv\propto v^{-\gamma}$ usually exhibits in
molecular outflows near young stellar objects (Chandler et al., 1996; Lada, &
Fich, 1996; Ridge, & Moore, 2001; Su, Zhang, & Lim, 2004; Qiu et al., 2007,
2009). The slope, $\gamma$, typically ranging from 1 to 3 at low outflow
velocities, and often steepens at velocities larger than 10 km s-1 — with
$\gamma$ as large as 10 in some cases (Arce et al., 2007). Assuming optically
thin, the mass-velocity diagrams of the outflow at the southern core of
G9.62+0.19 complex are shown in Figure 16. SO ($8_{7}-7_{7}$), CS (7-6), HCN
(4-3) results were all used in the mass spectra. We calculate the outflow mass
traced by CS (7-6) and HCN (4-3) from Vflow of 10 km s-1 to avoid the
absorption of the spectra. Instead of broken power law appearance, the mass-
velocity diagram of blueshifted lobe can be well fitted by a single power law
with a power indexes of $2.28\pm 0.23$. The mass-velocity diagram of
redshifted lobe can be well fitted by a single power law with a power indexes
of $1.70\pm 0.17$ even though the mass drops more rapidly after 25 km s-1. As
marked by the dashed ellipse in the right panel, the outflow mass revealed by
CS (7-6) is much lower than that revealed by HCN (4-3) at very high
velocities. Despite the CS data, the mass-velocity diagram of redshifted lobe
at velocities smaller than 25 km s-1 can be fitted by a single power law with
a much smaller power indexes of $1.08\pm 0.09$. However, no significant slope
changes are found in both the red- and blue-shifted lobes of the outflow at
the southern core, which are very different from those previous works.

###  4.5 Different evolutionary stages of the three dust cores

The northern core has the smallest diameter and mass among the three cores. It
seems likely to be a point source after deconvolution. It is located south of
the nominal radio UC Hii region G9.62+0.19 C. In this region, eight near-IR
sources are detected in a diffuse near-IR nebulosity at the west of the radio
emission peak (Persi et al., 2003). The reddest one c7
(18h06m14.34s,-20$\arcdeg$31$\arcmin$25.0$\arcsec$) is located within
$1\arcsec$ of the radio peak, while the faintest one c8
(18h06m14.42s,-20$\arcdeg$31$\arcmin$27.4$\arcsec$) seems to be associated
with the sub-mm core detected in SMA observation. Source c8 is too faint to be
detected even at H band and also shows no emission at 12.5 $\micron$. In
contrast to the bright, rich molecular spectrum forest in the middle and
southern sub-mm cores, the northern sub-mm core lacks strong molecular
emissions. There is also no other early star forming signature such as masers
associated with it. Since it is with near-IR emission and at the edge of the
UC Hii region G9.62+0.19 C, the northern core may be just a remnant core in
the envelope of UC Hii region G9.62+0.19 C, which needs further observations.

The middle core is associated with the hyper-compact Hii region G9.62+0.19 E
(Garay et al., 1993; Kurtz, & Franco, 2002). OH, H2O, and NH3 (5,5) masers
have been detected near the radio emission peak (Forster & Caswell, 1989;
Hofner et al., 1994; Hofner, & Churchwell, 1996a). Periodic class II methanol
masers are also found in G9.62+0.19 E (van der Walt, Goedhart, & Gaylard,
2009; Goedhart, Gaylard, & van der Walt, 2005; Norris et al., 1993). Methanol
masers are believed to be a good tracer of young massive star forming regions
at stages earlier than relatively evolved UC Hii regions (Longmore et al.,
2007). No infrared source coincides with G9.62+0.19 E (Persi et al., 2003).
Hot molecular CH3CN lines are detected in this region, and a kinematic
temperature of Tk = 108 K was obtained from CH3CN emission with LVG model
(Hofner et al., 1996b), which is coincident with the rotational temperature
(Trot = 92 K) obtained from H2CS emission. A spectra forest including hot
molecular lines, such as CH3OH, is detected towards G9.62+0.20 E, suggesting
this core is in a hot phase. Infall motions are traced by CS (7-6) and HCN
(4-3) lines, indicating active star forming in this region. All above suggest
that G9.62+0.20 E is forming a massive young star.

The 860 $\micron$ dust emission of the southern core peaks at G9.62+0.19 F,
and extends from north to south. A hump structure is found to the southeast of
the emission peak, indicating another possible sub-mm core. The previously
recognized mm/cm cores (G9.62+0.19 D, G) are at the edges of the southern
core. G9.62+0.19 G is a weak radio source (Testi et al., 2000), while
G9.62+0.19 D is consistent with an isothermal UC Hii region excited by a B0.5
star (Hofner et al., 1996b). Weaker radio emission was found at core F. H2O
and OH masers are found across the whole sub-mm core from north to south
(Forster & Caswell, 1989; Hofner, & Churchwell, 1996a). A near-IR source with
large NIR excess is found to be associated with G9.62+0.19 F (Testi et al.,
1998; Persi et al., 2003). With higher resolution observations Linz et al.
(2005) found four near-IR objects (F1-F4) in this core. F4 is with little
emission at K band but becomes redder at longer wavelengths, which seems to
correspond to the bright IRAC source with large excess at 4.5 $\micron$. This
object is the dominating and closest associated source of core F. Core F is
also confirmed to be the driving source of an active outflow. All of above
imply that G9.62+0.19 F is a very young massive star forming region.

###  4.6 Blue excess in high-mass star forming regions

Wu et al. (2007) found that UC Hii regions show a higher blue excess than UC
Hii precursors with the IRAM 30 m telescope. Wyrowski et al. (2006) also
detected large blue excess in UC Hii regions. ”Blue profile” was detected with
CS (7-6) and HCN (4-3) lines in UC Hii region G9.62+0.19 E, while ”red
profile” in hot molecular core G9.62+0.19 F, which coincides with their
argument. The detection of infall signature in G9.62+0.19 E also coincides the
interpretation that material is still accreted during the UC Hii phase (Wu et
al., 2007; Keto, 2002). Around younger cores, the outflow is more active and
cold than UC Hii regions, which leads to more ”red profile”. While in UC Hii
regions, the outflows become weak. The surrounding gas of UC Hii regions is
thermalized and the temperature gradient towards the central star is more
likely to cause ”blue profile”, which results in the higher blue excess than
UC Hii precursors.

##  5 Summary

We have observed the G9.62+0.19 complex with the Submillimeter Array (SMA)
both in the 860 $\micron$ continuum and molecular lines emission. The main
results of this study are as follows:

1\. Dust continuum at 860 $\micron$ reveals three sub-mm cores in G9.62+0.19
star forming complex. With H2CS as the rotational temperature prober, the
temperatures of E and F are estimated to be 92$\pm$74 and 51$\pm$23 K,
respectively. The mass calculated are 13, 30, and 165 M☉ for the northern,
middle and southern core.

2\. In the middle core, HCN (4-3) and CS (7-6) spectra exhibit infall
signature. The infall rate calculated is $4.3\times 10^{-3}$
M${}_{\sun}\cdot$yr-1. The detection of infall signature in G9.62+0.19 E
coincides the interpretation that material is still accreted after the onset
of the UC Hii phase (Wu et al., 2007).

3\. In the southern core, high-velocity gas is detected in SO ($8_{8}-7_{7}$),
CS (7-6) and HCN (4-3) lines. A bipolar-outflow with a total mass about 26 M☉
and a mass-loss rate of $3.6\times 10^{-5}$ M${}_{\sun}\cdot$yr-1 is revealed
in SO ($8_{8}-7_{7}$) line wing emission. G9.62+0.19 F is confirmed to be the
driving source of the outflows in the southern sub-mm core. The abundance
ratios of [CS/SO] and [CS/HCN] in the outflow region are found to be 0.7 and
1.2, respectively. The abundance ratio [CS/HCN] decreases with the flow
velocity, indicating smaller outflow regions revealed by CS (7-6) than that
revealed by HCN (4-3). The mass-velocity diagrams of the blueshifted and
redshifted outflow lobes can be well fitted by a single power law. The power
indexes for the blueshifted and redshifted lobes are $2.28\pm 0.23$ and
$1.70\pm 0.17$. No significant slope changes are found in the mass-velocity
diagrams.

4\. The evolutionary sequence of the cm/mm cores in this region are also
analyzed. The northern core may be just a remnant core in the envelope of UC
Hii region G9.62+0.19 C, which needs further observations. The middle core
(G9.62+0.19 E) is in a hyper-compact Hii region. Core G9.62+0.19 F is
confirmed to be a hot molecular core.

5\. The detection of blue profiles at the hyper-compact Hii region E and the
red profiles at the hot molecular core F supports the results of single-dish
observations that UC Hii regions have a higher blue excess than their
precursors.

## Acknowledgment

We are grateful to the SMA staff making the observations. This work is funded
by Grants of NSFC No 10733030 and 10873019.

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Figure 1: The 860 $\micron$ continuum emission image. The contour levels are
from 0.03 Jy beam-1 (3$\sigma$) in steps of 0.06 Jy beam-1 (6$\sigma$). The
known cm and mm continuum components (Testi et al., 2000) of B, C, D, E, F, G,
H, and I are marked by plus signs. Water masers (Hofner, & Churchwell, 1996a)
are marked by open squares and methanol masers (Norris et al., 1993) by
triangles. The near-IR sources (Persi et al., 2003; Testi et al., 1998; Linz
et al., 2005) are marked by filled circles. IRAC sources are marked with
asterisks. Figure 2: The full LSB and USB spectra in the UV domain over the
shortest baseline. The strongest lines are identified and labeled on the
plots. Figure 3: Integrated intensity maps of four transitions of H2CS at the
middle (upper panels) and southern cores (lower panels). The known cm and mm
continuum components are marked by plus signs as in the continuum map. The
contour levels in all the panels are from 3$\sigma$ in steps of 3$\sigma$. The
rms levels are 0.3, 0.3, 0.3 and 0.2 Jy beam${}^{-1}\cdot$km s-1 for H2CS
(100,10-90,9) in panels (a) and (e), H2CS (102,8-92,7) in panels (b) and (f),
H2CS (103,7-93,6) in panels (c) and (g), and H2CS (105-95) in panels (d) and
(h), respectively. Figure 4: The P-V diagram (left) and First moment map
(right) of H2CS (102,8-92,7) emission at the middle core. (a) The contours of
the P-V diagram are from 0.6 to 1.4 in steps of 0.2 Jy beam-1 (1$\sigma$). (b)
contour plot of H2CS (102,8-92,7) integrated intensity image overlayed on the
first moment map. The contours are from 0.9 (3$\sigma$) in steps of 0.9 Jy
beam${}^{-1}\cdot$km s-1. The First moment map is constructed from the data
after imposing a cutoff of 3$\sigma$. Figure 5: Spectra and integrated
intensity maps of HC15N (4-3) (upper panels) and SO ($8_{7}-7_{7}$) (lower
panels) at the middle core. The systemic velocity is marked with the thick
vertical dashed lines at the spectra panels. The known cm and mm continuum
components of C, and E are marked by plus signs at the integrated maps as the
continuum map. (a) the beam-averaged spectrum of HC15N (4-3) at E, (b) the
integrated intensity map of HC15N (4-3). The contour levels are -1.2
(6$\sigma$), 1.2, 2.4, 4.2, 6.6, 9.6 Jy beam${}^{-1}\cdot$km s-1, (c) the
beam-averaged spectrum of SO ($8_{7}-7_{7}$) at E. (d) the integrated
intensity map of SO ($8_{7}-7_{7}$). The contour levels are -1.2 (6$\sigma$),
1.2, 2.4, 4.2, 6.6, 9.6, 13.2, 17.4, 22.2 Jy beam${}^{-1}\cdot$km s-1. Figure
6: Beam-averaged spectra and Position-Velocity (P-V) diagrams of HCN (4-3)
(upper panels) and CS (7-6) (lower panels) at the middle core. The P-V
diagrams are cut along a position angle of 0$\arcdeg$. (a) the beam-averaged
spectrum of HCN (4-3) at E, (b) the P-V diagram of HCN (4-3). The contour
levels are -1.5 (5$\sigma$), -0.9, 0.9, 1.5, 2.1, 2.7, 3,3, 3.9, 4.5 Jy
beam-1, (c) the beam-averaged spectrum of CS (7-6) at E. (d) the P-V diagram
of CS (7-6). The contour levels are -1.5 (5$\sigma$), -0.9, 0.9, 1.5, 2.1,
2.7, 3,3, 3.9, 4.5 Jy beam-1. Figure 7: Integrated intensity maps of HCN (4-3)
(left) and CS (7-6) (right) at the middle core. The contour levels in both
maps are from 1.5 (5$\sigma$) in steps of 3 Jy beam${}^{-1}\cdot$km s-1. HCN
(4-3) is integrated from -3 to 7 km s-1, while CS (7-6) from -1 to 6 km s-1
Figure 8: Averaged spectra of SO ($8_{7}-7_{7}$) (upper-left), HC15N (4-3)
(lower-left), HCN (4-3) (upper-right) and CS (7-6) (lower-right) at the
southern core. The spectra of SO ($8_{7}-7_{7}$) and HC15N (4-3) are averaged
over a region of 4$\arcsec$, while HCN (4-3) and CS (7-6) are averaged over a
region of 6$\arcsec$. HCN $\nu 2=1$ (4-3) emission is marked by the arrow in
the upper-right panel, which can be clearly distinguished from the red wing of
HCN (4-3). Figure 9: The integrated intensity maps of HC15N (4-3) (left panel)
and SO ($8_{7}-7_{7}$) (right panel) at the southern core. To avoid the
influence of outflow motions, both the maps are integrated from 2 km s-1 to 8
km s-1. The contour levels are (a) -1.2 (6$\sigma$), 1.2, 2.4, 4.2, 6.6, 9.6,
13.2, 17.4 Jy beam${}^{-1}\cdot$km s-1 for HC15N (4-3), (b) -1.2 (6$\sigma$),
1.2, 2.4, 4.2, 6.6, 9.6, 13.2, 17.4, 22.2, 27.6, 33.6 Jy beam${}^{-1}\cdot$km
s-1 for SO ($8_{7}-7_{7}$) Figure 10: P-V diagrams and integrated intensity
maps of SO ($8_{7}-7_{7}$) (upper panels), and HC15N (4-3) (lower panels) at
the southern core. The P-V diagrams are cut along N-S direction. The vertical
solid line in P-V diagrams labels the systemic velocity. The dashed and solid
contours in the right panels show the red- and blue-shifted emission,
respectively. The integral velocity intervals are marked by thick dashed lines
in the P-V diagrams. For both SO ($8_{7}-7_{7}$) and HC15N (4-3), the blue-
shifted emission is integrated from -4 km s-1 to 0 km s-1, while the red-
shifted emission from 10 km s-1 to 14 km s-1 in the integrated intensity maps.
(a) P-V diagram of SO ($8_{7}-7_{7}$). The contours are from 0.6 (3$\sigma$)
in steps of 0.6 Jy beam-1. (b) P-V diagram of HC15N (4-3). The contours are
from 0.6 (3$\sigma$) in steps of 0.4 Jy beam-1. (c) Integrated intensity maps
of SO ($8_{7}-7_{7}$) at line wings. The contours are from 1 (5$\sigma$) in
steps of 1 Jy beam${}^{-1}\cdot$km s-1 for both red- and blue-shifted
emission. (d) Integrated intensity maps of HC15N (4-3) at red wing. The
contours are 0.6 (3$\sigma$), 1.2, 2, 3 Jy beam${}^{-1}\cdot$km s-1. Figure
11: CS (7-6) channel maps at the southern core, which is smoothed to a
velocity resolution of 3 km s-1. The contours are -0.6 (3$\sigma$), 0.6, 1.2,
2.4, 4.8, 7.2, 9.6 Jy beam-1. Figure 12: HCN (4-3) channel maps at the
southern core, which is smoothed to a velocity resolution of 4 km s-1. The
contours are -0.6 (3$\sigma$), 0.6, 1.2, 2.4, 3.6, 4.8, 7.2 Jy beam-1. Figure
13: P-V diagrams and integrated intensity maps of HCN (4-3) (upper panels),
and CS (7-6) (lower panels) at the southern core. The P-V diagrams are cut
along N-S direction. The vertical solid line in P-V diagrams labels the
systemic velocity. The dashed and solid contours in the right panels show the
red- and blue-shifted emission, respectively. The blue- and red-shifted
emission in the integrated maps are integrated from -12 km s-1 to -5 km s-1
and 15 km s-1 to 22 km s-1, respectively in (b) and (e) panels. (a) P-V
diagram of HCN (4-3). The contours are from 0.9 (3$\sigma$) in steps of 1.2 Jy
beam-1. (b) Integrated intensity maps of HCN (4-3) at line wings. The contours
are 1.5 (5$\sigma$), 4.5, 7.5, 10.5 Jy beam${}^{-1}\cdot$km s-1. (c) The
integrated intensity maps of HCN (4-3) at extremely high velocities. The blue-
and red-shifted emission in the integrated maps are integrated from -20 km s-1
to -13 km s-1 and 23 km s-1 to 39 km s-1, respectively. The contours are from
1.5 (5$\sigma$) in steps of 3 Jy beam${}^{-1}\cdot$km s-1 for both blue- and
red-shifted emission. (d) P-V diagram of CS (7-6). The contours are from 0.9
(3$\sigma$) in steps of 1.2 Jy beam-1. (e) Integrated intensity maps of CS
(7-6) at line wings. The contours are 1.5 (5$\sigma$), 4.5, 7.5, 10.5 Jy
beam${}^{-1}\cdot$km s-1

Figure 14: Population diagrams of H2CS towards four cm/mm cores. The names of
the cores are labeled on the upper-right corner of each panel. Open circles in
blue represent the observed data. The vertical bars present 3$\sigma$ errors
of ln(Nu/gu) due to the uncertainties of integrated intensities. The solid
line shows the linear least-squares fitting using the Rotational Temperature
Diagram method. Crosses in red mark the weighted mean results from Population
Diagram analysis. The inferred parameters from the Population Diagram analysis
are presented on the upper-right corners of each panel.

Figure 15: Abundance ratios of [CS/SO] (left) and [CS/HCN] (right) versus flow
velocity along the redshifted lobe. We range the excitation temperature from
10 K to 50 K to derive the abundance ratios of [CS/SO]. The excitation
temperature in calculation of abundance ratios of [CS/HCN] is assumed to be 30
K. The solid line in the right panel is the linear least-squares fitting, and
the fitting results are presented in the upper-right corner.

Figure 16: Mass-Velocity relationships for the outflow lobes. Left :
blueshifted lobe; right: redshifted lobe. The solid lines in both panels show
the power law fit towards all the data. The dashed line in the right panel
shows the power law fit towards the HCN and SO data up to Vflow = 25 km s-1.
The fitting results are presented in the lower-left corners.

Table 1: Parameters of 860 $\micron$ continuum emission | R.A. | Decl. | Deconvolution sizes | Ipeak | Sν | TdaaThe dust temperature is assumed to be the same as the rotational temperature of H2CS transitions |  $\beta$aaThe dust temperature is assumed to be the same as the rotational temperature of H2CS transitions | Mass | N${}_{H_{2}}$
---|---|---|---|---|---|---|---|---|---
Name | (J2000) | (J2000) | ($\arcsec~{}\times~{}\arcsec$) | (Jy beam-1) | (Jy) | (K) |  | (M☉) | ($10^{24}$ cm-2)
Northern core | 18:06:14.447 | -20:31:28.253 | Point source | 0.20$\pm$0.02 | 0.26 | 50 | 1.5 | 13 |
Middle core | 18:06:14.668 | -20:31:31.830 |  $1.48\arcsec\times 1.29\arcsec$ (P.A.=$-37.8\arcdeg$) | 0.76$\pm$0.04 | 1.07 | 92 | 1.2 | 30 | 1.2
Southern core | 18:06:14.889 | -20:31:40.149 |  $4.71\arcsec\times 1.26\arcsec$ (P.A.=$-20.2\arcdeg$) | 0.95$\pm$0.12 | 2.52 | 51 | 0.8 | 165 | 2.1

Table 2: Observed parameters of the lines

Molecule | Transition | Frequency | Eu | rms | VlsrbbThe opacity index $\beta$ is obtained from Su et al. (2005) | IntensitybbThe Vlsr, Intensity and FWHM of each transition are derived from single gaussian fit towards the beam-averaged spectra. | FWHMbbThe Vlsr, Intensity and FWHM of each transition are derived from single gaussian fit towards the beam-averaged spectra.
---|---|---|---|---|---|---|---
|  | (GHz) | (K) | (Jy beam-1) | (km s-1) | (Jy beam-1) | (km s-1)
|  |  |  |  | D | E | F | G | D | E | F | G | D | E | F | G
H2CS | 100,10-90,9 | 342.946 | 90.6 | 0.3 | 5.5$\pm$0.2 | 2.7$\pm$0.2 | 5.9$\pm$0.2 | 6.0$\pm$0.5 | 1.9$\pm$0.3 | 1.4$\pm$0.2 | 1.7$\pm$0.1 | 0.9$\pm$0.2 | 2.7$\pm$0.4 | 3.1$\pm$0.5 | 4.3$\pm$0.6 | 3.8$\pm$1.1
| 102,9-92,8ccfootnotemark:  | 343.322 | 143.3 | 0.3 | 4.0$\pm$0.5 | 2.2$\pm$1.1 |  | 4.9$\pm$0.3 | 0.9$\pm$0.2 | 1.4$\pm$0.3 |  | 1.1$\pm$0.3 | 4.0$\pm$0.6 | 4.4$\pm$1.6 |  | 1.9$\pm$0.6
| 102,8-92,7 | 343.813 | 143.3 | 0.3 | 6.0$\pm$0.3 | 2.5$\pm$0.4 | 4.9$\pm$0.5 |  | 1.3$\pm$0.2 | 0.9$\pm$0.1 | 0.8$\pm$0.2 |  | 3.0$\pm$0.7 | 5.5$\pm$0.9 | 3.9$\pm$1.3 |
| 103,8-93,7ddBlended with H2CS (103,7-93,6) | 343.410 | 209.1 | 0.3 | 6.2$\pm$0.8 | 2.4$\pm$0.7 | 5.0$\pm$0.3 |  | 1.1$\pm$0.7 | 1.1$\pm$0.1 | 2.1$\pm$0.3 |  | 3.3$\pm$0.7 | 4.1$\pm$0.5 | 2.7$\pm$0.6 |
| 103,7-93,6eeBlended with H2CS (103,8-93,7) | 343.414 | 209.1 | 0.3 | 5.8$\pm$2.8 | 2.6$\pm$0.2 | 5.5$\pm$0.3 | 5.8$\pm$0.2 | 0.7$\pm$0.2 | 2.0$\pm$0.2 | 2.4$\pm$0.3 | 1.5$\pm$0.3 | 5.9$\pm$0.8 | 4.0$\pm$0.5 | 2.9$\pm$0.6 | 2.3$\pm$0.5
| 105,6/5-95,5/4ffThe two transitions of H2CS (105,6-95,6) and (105,6-95,6) have the same frequency, line strength and permanent dipole moment. Therefore they has same contributions to the observed line profile. | 343.203 | 419.2 | 0.2 |  | 1.8$\pm$0.4 | 5.9$\pm$0.3 | 5.9$\pm$0.2 |  | 0.6$\pm$0.2 | 0.7$\pm$0.2 | 0.9$\pm$0.2 |  | 3.2$\pm$1.0 | 2.4$\pm$0.8 | 1.5$\pm$0.4
SO | 88-77 | 344.311 | 87.5 | 0.2 | 4.9$\pm$0.1 | 2.2$\pm$0.1 | 5.0$\pm$0.1 | 4.4$\pm$0.1 | 2.9$\pm$0.1 | 4.0$\pm$0.1 | 5.5$\pm$0.1 | 3.5$\pm$0.1 | 3.9$\pm$0.2 | 5.3$\pm$0.2 | 9.0$\pm$0.2 | 8.2$\pm$0.3
HC15N $\nu$=0 | 4-3 | 344.200 | 41.3 | 0.2 | 6.1$\pm$0.4 | 2.6$\pm$0.1 | 5.2$\pm$0.1 | 4.8$\pm$0.3 | 0.6$\pm$0.1 | 2.1$\pm$0.1 | 2.8$\pm$0.1 | 1.1$\pm$0.1 | 3.6$\pm$1.0 | 4.8$\pm$0.3 | 8.0$\pm$0.3 | 7.5$\pm$0.8
CS | 7-6 | 342.883 | 65.8 | 0.3 |  |  |  |  |  |  |  |  |  |  |  |
HCN $\nu$=0 | 4-3 | 354.505 | 42.5 | 0.3 |  |  |  |  |  |  |  |  |  |  |  |

aafootnotetext: Not all the detected lines are listed in this table. The
others will be presented in another paper.

bbfootnotetext: Blended with H${}_{2}^{13}$CO (51,4-41,4) at 343.325713 GHz.

Table 3: The physical parameters of H2CS transitions obtained with Rotational
Temperature Diagram (RTD) method and Population Diagram (PD) analysis

Core | RTD |  | PD
---|---|---|---
| Trot (K) | Ntot (1015 cm-2) |  | Trot (K) | Ntot (1016 cm-2) | f | $\tau$
|  |  |  |  |  |  | (100,10-90,9) | (102,9-92,8) | (102,8-92,7) | (103,8-93,7) | (103,7-93,6) | (105,6/5-95,6/4)
D | 43$\pm$9 | 3.8$\pm$2.9 |  | 42$\pm$34 | 4.2$\pm$2.9 | 0.46$\pm$0.24 | 6.4$\pm$4.4 | 0.7$\pm$0.5 | 0.9$\pm$0.6 | 0.4$\pm$0.5 | 0.2$\pm$0.3 |
E | 83$\pm$21 | 2.5$\pm$1.6 |  | 92$\pm$74 | 3.6$\pm$3.0 | 0.26$\pm$0.23 | 4.1$\pm$4.3 | 0.7$\pm$0.7 | 0.6$\pm$0.6 | 0.7$\pm$0.8 | 0.7$\pm$0.8 | 0.1$\pm$0.1
F | 83$\pm$7 | 2.6$\pm$0.6 |  | 51$\pm$23 | 4.0$\pm$2.9 | 0.34$\pm$0.23 | 3.9$\pm$3.1 |  | 1.1$\pm$0.9 | 1.1$\pm$1.2 | 1.1$\pm$1.2 | 0.0$\pm$0.1
G | 91$\pm$17 | 1.3$\pm$0.7 |  | 105$\pm$37 | 3.7$\pm$3.1 | 0.12$\pm$0.18 | 2.5$\pm$2.7 | 2.4$\pm$2.3 |  |  | 2.4$\pm$2.1 | 0.3$\pm$0.3

aafootnotetext: The rotational temperature and total column density of H2CS
transitions derived from RTD analysis are presented in the second and third
columns, while those derived from PD analysis are shown in the forth and fifth
columns. The sixth column gives the filling factor of each source inferred
from PD analysis. The last six columns exhibit the optical depth of each
transition using PD analysis.

Table 4: Outflow parameters of the southern core Molecule | Velocity interval | M | P | E
---|---|---|---|---
| (km s-1) | (M☉) | (M${}_{\sun}~{}\cdot~{}km~{}s^{-1}$) | ($10^{45}$erg)
Component | Blue | Red | Blue | Red | Blue | red | Blue | Red
SO | [-4,0] | [10,14] | 13 | 13 | 86 | 82 | 5.8 | 5.4
CS | [-12,-5] | [15,22] | 3.7 | 5.5 | 47 | 68 | 6.0 | 8.7
HCN | [-20,-5] | [15,39] | 5.4 | 17.6 | 85 | 294 | 14.1 | 54.6