# The internal proper motion kinematics of NGC 346: past formation and future
evolution

E. Sabbi Space Telescope Science Institute, 3700 San Martin Dr, Baltimore, MD
21218, USA  P. Zeidler AURA for the European Space Agency (ESA), ESA Office,
Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218,
USA  R.P. van der Marel Space Telescope Science Institute, 3700 San Martin Dr,
Baltimore, MD 21218, USA  A. Nota  European Space Agency (ESA), ESA Office,
Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218,
USA  J. Anderson Space Telescope Science Institute, 3700 San Martin Dr,
Baltimore, MD 21218, USA  J.S. Gallagher Department of Astronomy, University
of Wisconsin–Madison, 5534 Sterling, 475 North Charter Street, Madison, WI
53706, USA  D.J. Lennon  Instituto de Astrofísica de Canarias,E-38 200 La
Laguna, Tenerife, Spain  Dpto. Astrofísica, Universidad de La Laguna, E-38 205
La Laguna, Tenerife, Spain  L.J. Smith Space Telescope Science Institute, 3700
San Martin Dr, Baltimore, MD 21218, USA  M. Gennaro Space Telescope Science
Institute, 3700 San Martin Dr, Baltimore, MD 21218, USA

###### Abstract

We investigate the internal kinematics of the young star-forming region NGC
346 in the Small Magellanic Cloud. We used two epochs of deep F555W and F814W
Hubble Space Telescope ACS observations with an 11-year baseline to determine
proper motions, and study the kinematics of different populations, as
identified by their color-magnitude diagram and spatial distribution
characteristics. The proper motion field of the young stars shows a complex
structure with spatially coherent patterns. NGC 346 upper-main sequence and
pre-main sequence stars follow very similar motion patterns, with the outer
parts of the cluster being characterized both by outflows and inflows. The
proper motion field in the inner $\sim 10$ pc shows a combination of rotation
and inflow, indicative of inspiraling motion. The rotation velocity in this
regions peaks at $\sim 3$ km/s, whereas the inflow velocity peaks at $\sim 1$
km/s. Sub-clusters and massive young stellar objects in NGC 346 are found at
the interface of significant changes in the coherence of the proper motion
field. This suggests that turbulence is the main star formation driver in this
region. The similar kinematics observed in the metal-poor NGC 346 and the
Milky Way star-forming regions suggest that the differences in the cooling
conditions due to the different amounts of metallicity and dust density
between the SMC and our Galaxy are too small to alter significantly the
process of star clusters assembly and growth. The main characteristics of our
findings are consistent with various proposed star cluster formation models.

††facilities: HST(ACS)††software: astropy (Astropy Collaboration et al., 2013,
2018)

##  1 Introduction

Regions of massive star formation (SF) are important to study for the insight
they provide into the origin of the stellar mass distribution, the formation
of massive stars ($M>8\,M_{\odot}$), and the formation and evolution of
associations and star clusters. Nevertheless, the process whereby stars form
in giant molecular clouds is still a poorly constrained problem.

The first few million years, during which stars are still forming and the
region still contains a significant amount of gas, set the conditions for the
subsequent evolution of the stellar system. This initial stage is regulated by
gas and stellar dynamics, stellar evolution, and radiative transfer. However,
the complex interplay between these quantities is poorly understood by theory
and lacks sufficient observational constraints (i.e. Elmegreen, 2007; Price &
Bate, 2009; Portegies Zwart et al., 2010; Krumholz, 2014; Kruijssen et al.,
2019).

Figure 1: Left Panel: Mosaic footprint of the area mapped by the programs
GO-10248 and GO-13680 superimposed on the DSS image. Right Panel: HST color-
composite image obtained combining the exposures taken by the program
GO-10248. F555W is in blue and F814W in red. The positions of NGC 346 and BS90
are highlighted for convenience. North is left, East is down.

This shortfall of information leaves many essential and critical properties
uncertain, such as the duration and the efficiency of the SF process, and
hence the probability that a cluster will survive the rapid ejection of gas
caused by its first supernova explosions (Carpenter et al., 2000; Lada & Lada,
2003; Chevance et al., 2020). The internal kinematics of young star clusters
and associations carries the signature of the process that led to the systems’
formation. Radial velocity and proper motion (PM) studies can gather
information on the dynamical state of gas and stars, and test different models
of SF (Elmegreen, 2002; Parker et al., 2014). Currently, theories describing
the onset and development of SF can be divided into two competing scenarios: a
rapid process, which proceeds on a dynamical timescale, comparable to the
freefall collapse of the molecular cloud (e.g., Elmegreen, 2000; Dobbs et al.,
2011; Hartmann et al., 2012; Grudić et al., 2018; Jeffreson & Kruijssen,
2018); and a slow one that persists for multiple freefall timescales (e.g.
McKee, 1989; Tan et al., 2006; Krumholz & McKee, 2020)

Astrometric measurements by ESA’s Gaia spacecraft (Gaia Collaboration et al.,
2016) have already provided spatial and kinematic clustering properties for
several star-forming regions in the Milky Way, including Orion (Großschedl et
al., 2018; Kounkel et al., 2018; Getman et al., 2019; Kuhn et al., 2019),
Taurus (Luhman, 2018; Galli et al., 2019), $\rho$ Oph (Cánovas et al., 2019),
Serpens (Herczeg et al., 2019), NGC 6530 (Kuhn et al., 2019), and IC 5070
(Kuhn et al., 2020).

In this work we extend this type of investigation for the first time to a low
metallicity environment ($Z=0.2Z_{\odot}$, Russell & Dopita, 1992; Rolleston
et al., 2003; Hunter et al., 2007), such as the Small Magellanic Cloud (SMC),
to explore whether different global conditions (e.g., as large-scale dynamics
and metallicity) can affect the duration of SF.

As the brightest and largest SMC star-forming region, NGC 346, located in the
northern part of the galaxy bar, is one of the best-studied extra-galactic
young clusters. In an attempt to better understand the formation mechanism and
early evolution of NGC 346, here we take advantage of the Hubble Space
Telescope’s (HST) exquisite astrometric capabilities and longevity to measure
the PM displacements of high, intermediate, and low-mass ($\sim 8$ to $\sim
1\,{\rm M_{\odot}}$) stars and infer the system’s internal kinematics.

GO | Date | Filter | Pointing | N $\times$ Exp. time (s) | GO | Date | Filter | Pointing | N $\times$ Exp. time (s)
---|---|---|---|---|---|---|---|---|---
10248 | July 2004 | F555W | Center | 1 $\times$ 380 | 13680 | July 2015 | F555W | Center | 3 $\times$ 450
|  |  | North | 4 $\times$ 456 |  |  |  | North | 4 $\times$ 450
|  |  | South | 4 $\times$ 483 |  |  |  | South | 4 $\times$ 450
|  | F814W | Center | 1 $\times$ 380 |  |  | F814W | Center | 2 $\times$ 450
|  |  | North | 4 $\times$ 484 |  |  |  | North | 4 $\times$ 450
|  |  | South | 4 $\times$ 450 |  |  |  | South | 4 $\times$ 450
Table 1: List of the observations analyzed in this paper. The first and sixth
columns report the proposal IDs, the observing dates are listed in columns two
and seven, the used filters are in columns three and eight, the covered
regions in columns four and nine. Exposure times are in columns five and ten.

The left panel of Fig. 1 shows the footprint of the HST mosaic superimposed on
the Digitized Sky Survey (DSS) image, while the right panel shows the HST
color-composite image. Here NGC 346 appears as a vast agglomeration of bright
white stars, still embedded in diffuse ionized gas (H$\alpha$ and Nii, shown
in blue), extending over $\sim 50$ pc from the northwest to the southeast. The
star-forming region contains a “plethora” of massive stars (Niemela et al.,
1986; Massey et al., 1989; Evans et al., 2006; Dufton et al., 2019) that are
ionizing the relatively isolated, large Hii region N66. O and B stars are
embedded in an extended halo of pre-main sequence (PMS) stars (Nota et al.,
2006), organized in several sub-clusters, clumps, and asterisms (Sabbi et al.,
2007; Gouliermis et al., 2014).

In Cignoni et al. (2011) we studied the SF history of the region and found
that SF started, with remarkable synchronization, about $\sim 6$ Myr ago.
Then, progressing inward, it peaked $\sim 3$ Myr ago, and is now continuing at
a lower rate. Similar conclusions were recently reached by Dufton et al.
(2019).

Extended CO clouds are still associated with NGC 346 (Rubio et al., 2000;
Müller et al., 2015; Neelamkodan et al., 2021), and Spitzer observations
revealed a multitude of young stellar objects (YSOs, Simon et al., 2007;
Sewiło et al., 2013) associated with the sub-clusters and asterisms identified
by Sabbi et al. (2007). Rubio et al. (2018) analyzed $HK$ spectra of three
YSOs and concluded that these are likely $\sim 25-26\,M_{\odot}$ Class I type,
suggesting that, at least in the central cluster, star formation is still
ongoing.

The bright clump of red stars to the north of NGC 346 is the core of the star
cluster BS90. NGC 346 and BS90 are considered non-interacting, and their
proximity is likely a simple visual alignment (Bica & Schmitt, 1995). Using
the synthetic color-magnitude diagram (CMD) method initially introduced by
Tosi et al. (1991), Sabbi et al. (2007) concluded that the cluster is $4.5\pm
0.1\,{\rm Gyr}$ old, with metallicity $Z=0.02$, $E(B-V)=0.08$, distance
modulus $(m-M)_{0}=18.9$, and a total mass $\sim 8\times 10^{4}\,{\rm
M_{\odot}}$. The halo of BS90 partially overlaps in projection with NGC346,
and the two clusters are embedded in the SMC field, making it impossible to
separate the different stellar populations using only their coordinates, or
the characteristics of their CMDs.

Figure 2: 1-D position rms in mas as a function of magnitude. The two upper
panels show the results for the $1^{st}$ epoch, while the two lower panels
show the results for the second epoch. The F555W filter is to the left and
F814W to the right. In both filters and epochs, we marked all the sources with
positional errors $<1$ mas and photometric errors $<0.1$ in orange. Sources
with photometric rms $<0.2$ in both filters and with positional rms in F814W
$<3$ mas in both epochs are in blue. Figure 3: The
$m_{F555W}-m_{F814W},m_{F814W}$ CMD of the stars detected in the NGC 346
region, with photometric rms $<0.1$ in both F814W and F555W filters. Sources
with positional rms $<0.1$ mas/yr in both X and Y directions and in both
epochs have been highlighted as follow: RGB stars in the magnitude range
$17.9<m_{F814W}<20.4$ and color $m_{F555W}-m_{F814W}>0.5$ are shown in red,
and UMS stars in the magnitude ranges $17.9<m_{F814W}<20.9$ and color
$m_{F555W}-m_{F814W}<0.1$ are shown in blue. LMS stars fainter than
$m_{F814W}<21.9$ and to the left of the line connecting
$m_{F555W}-m_{F814W}=0.7$, $m_{F814W}<21.9$ to $m_{F555W}-m_{F814W}=1.3$,
$m_{F814W}<24.0$ are marked in green. PMS stars fainter than $m_{F814W}>21.2$,
to the right of the line connecting $m_{F555W}-m_{F814W}=0.75$,
$m_{F814W}<21.2$ to $m_{F555W}-m_{F814W}=1.5$, $m_{F814W}<24.0$, with
photometric rms $<0.2$ in both F814W and F555W, and positional rms $<0.3$
mas/yr in both X and Y are shown in purple.

The paper is organized as follows: section 2 contains a description of the
observations and the photometric analysis. We discuss the characteristics of
the stellar populations found in the region in Section 3. We present PM
measurements in Section 4, and in Section 5 we analyze the kinematics of the
various populations. In Section 6 we focus our attention on NGC 346 internal
kinematics, and We present our conclusions in Section 7.

##  2 Observations and Data Reduction

Figure 4: 1-D PM rms in mas/yr as a function of magnitude. The F555W filter is
to the left and F814W to the right. The sources with positional errors $<1$
mas and photometric errors $<0.1$ are marked in orange. Sources with
photometric rms $<0.2$ in both filters and and with positional rms in F814W
$<3$ mas in both epochs are in blue. Figure 5: The VPDs of the PMs measured in
the NGC 346–N66 region. Each point corresponds to the proper motion of one
star. Only stars that meet the astrometry and photometry selection criteria
are considered. Measurement using the F555W filter are shown in the left
panel. The corresponding results for the F814W filter are shown in the right
panel. Median errors along the X and Y directions are shown in the upper right
corner.

(HST)’s Wide-Field Channel (WFC) of the Advanced Camera for Surveys (ACS;
pixel scale $\sim 50$ mas pixel-1) initially observed NGC 346 through the
filters F555W and F814W in July 2004 (GO-10248, PI A. Nota). To measure the
star-forming region’s internal kinematics, we repeated these observations in
July 2015, using the same orientation and filter set (GO-13680, PI. E. Sabbi).
In both epochs, images were taken at three different pointing positions, each
covering an area of $200\arcsec\times 200\arcsec$. In the first epoch, for
each filter, a single long exposure was taken at the nominal center of the
cluster. The other two pointings were spaced by $\sim 1\arcmin$ off the
cluster’s center towards the northeast and the southwest, respectively. A
four-step dither pattern was applied in each filter for both the northern and
the southern pointings to remove hot pixels, better sample the point spread
function (PSF), and fill in the detector gap. In the second epoch, the central
pointing consisted of three-dithered exposures in F555W and two-dithered
exposures in F814W. As in the first epoch, we acquired four exposures per
filter for both the northern and southern pointing. However, no dither
stepping was applied to F555W filter observations covering the southern
portion of the mosaic. Table 1 summarizes the list of the observations. The
observations analyzed in this paper can be downloaded from the Mikulski
Archive for Space Telescopes (MAST) via https://doi.org/10.17909/y1cf-m826.
(catalog 10.17909/y1cf-m826)

We carried out the analysis of the data directly on the bias-subtracted, flat-
field and charge-transfer-efficiency (CTE) corrected _flc exposures produced
by the standard calibration pipeline CALACS v10.2.4. Compared to drizzled
(_drc) images, _flc data have the advantage of not being re-sampled, thus
providing a more direct representation of the astronomical scene. However,
_flc exposures are still affected by geometric distortion. To take into
account this effect, we created a distortion-free reference frame using the
geometric distortion correction for the ACS/WFC detectors described in
Anderson & King (2006)111The geometric distortion correction used in this
paper is available for download at https://www.stsci.edu/ jayander/STDGDCs/,
and we related the photometry and astrometry of each exposure to that frame.

We analyzed all images using the Fortran routine
hst1pass222https://www.stsci.edu/ jayander/HST1PASS/ (Anderson et al. 2022, in
prep.). The program performs a single pass of finding and measures each star
in each exposure by fitting a library of spatially variable empirical
PSFs333https://www.stsci.edu/ jayander/STDPSFs/, ignoring any contribution
from neighbors.

Seasonal and orbital thermal changes can cause variations in the optical path
length of HST up to a few microns within the timescale of an orbit (Bély et
al., 1993; Lallo et al., 2006). These changes affect the telescope’s focus and
translate to small but measurable differences in the PSF from one exposure to
another, possibly affecting the precision with which source positions are
determined. To take into account these effects, in each image, we measured the
average residuals after the subtraction of the empirical PSF-library from the
bright (S/N $>$ 150), isolated (out to a 10-pixel radius), and non-saturated
stars. We then applied, for each image, the correction to the PSF that
minimizes its residuals and ran the photometry on all the sources with S/N $>$
3 and without companions within 3 pixels. This approach allowed us to create
for each exposure a catalog of X and Y coordinates in pixels, magnitudes,
quality of the fit (qfit, as defined in Anderson et al., 2008) and $\chi^{2}$
of the fit.

The three pointing positions allowed us to observe the same stars both close
and far from the readout amplifiers, thus verifying that in both epochs the
CTE residuals were negligible both in stellar magnitudes and positions. We
derived the photometric zero points by matching our observations to the NGC
346 photometric catalog published by Sabbi et al. (2007), and available for
download from VizieR444https://vizier.u-strasbg.fr/viz-bin/VizieR

We used a six-parameter linear transformation based on the cross-identified,
well-measured, and non-saturated stars to match all the exposures in a common
photometric and astrometric reference frame for each epoch$+$filter
combination. We obtained the initial reference frame positions by averaging
the single-image positions. For both filters, the median 1-D rms in the
position of the bright stars ($18<m<21$) is less than 0.5 mas (=0.01 pxl) in
the first epoch and 0.7 mas (0.015 pxl) in the second epoch. Fig. 2 shows the
position rms as a function of magnitude.

##  3 Stellar Content

Figure 6: PM VPDs measured in the F814W filter for three evolutionary phases,
selected using the CMD shown in Fig. 3. RGB stars are shown in the left pabel.
LMS stars are in the central panel and UMS stars are in the right panel. For
each population, the median error in the $\mu_{x}$ and $\mu_{y}$ directions is
shown in the upper right corner.

The inspection of the CMD in Fig. 3 reveals a complex history of SF,
characterized by episodes of different intensity. A detailed analysis of the
region SF history is presented in Cignoni et al. (2011). Here, we will briefly
discuss the properties of the CMD that will be useful for the subsequent
analysis.

Above $m_{F814W}\simeq 21$, the CMD shows two well-defined sequences: the blue
($-0.3\leq m_{F555W}-m_{F814W}\leq 0.4$) upper main sequence (UMS), and the
red giant branch (RGB), with ($m_{F555W}-m_{F814W}\geq 0.8$). The UMS includes
intermediate and high-mass stars ($M\gtrsim 3\,M_{\odot}$) that formed between
$\lesssim 2$ and $\sim 600$ Myr ago. The youngest component belongs to NGC
346, while the remaining stars are associated with the SMC field.

The RGB consists of evolved low-mass stars ($\lesssim 2\,M_{\odot}$)
characteristic of a stellar population older than $\sim 1$ Gyr. The compact
group of stars around $m_{F814W}\simeq 18.5$ and $m_{F555W}-m_{F814W}\simeq
1.0$ is the red clump (RC) and corresponds to the core Helium burning phase
for stars in the mass range between $\sim 1$ and $\sim 2.5\,M_{\odot}$, with a
main-sequence lifetimes ranging between $\sim 1$ and 10 Gyr. The older stellar
population includes both SMC and BS90 stars. A few bright ($m_{F814W}<18$)
evolved red super-giants connect the UMS to the top of the RC.

Figure 7: Distribution of low-mass stars, as selected from the RGB and LMS
VPDs. Upper-Left Panel : $m_{F555W}-m_{F814W},m_{F814W}$ CMD centered on the
RGB evolutionary phase. Stars that in the RGB VPD are within 0.03 mas/yr from
the over-density peak at $\mu_{x}=-0.04$ mas/yr and $\mu_{y}=-0.02$ mas/yr are
shown in purple, while stars more than 0.08 mas/yr away from the peak are in
pink. Upper-Middle Panel : Spatial distribution of the sources found within
0.03 mas/yr from the over-density peak in the RGB VPD superimposed on the
F555W HST image. Upper-Right Panel : Spatial distribution of the RGB stars
found more than 0.08 mas/yr away from the over-density peak in the RGB VPD.
Lower-Left Panel : Portion of the $m_{F555W}-m_{F814W},m_{F814W}$ CMD centered
on the LMS evolutionary phase. Stars that in the LMS VPD are within 0.03
mas/yr from $\mu_{x}=-0.04$ mas/yr and $\mu_{y}=-0.02$ mas/yr are shown in
dark green, while stars more than 0.08 mas/yr away are in light green. The
spatial distribution of the two groups of stars is shown in the Lower-Middle
Panel and Lower-Right Panel respectively.

The majority of the stars below $m_{F814W}\sim 22$ are low-mass main-sequence
(LMS) stars. This sequence includes stars that formed between a few tens of
Myr and several Gyr ago and belong either to the SMC field or BS90. NGC 346
stars below $\sim 3\,M_{\odot}$ are still in the pre-main sequence (PMS)
phase, and populate the faint ($m_{F814W}>20$) cloud of red
($m_{F555W}-m_{F814W}>1.0$) sources to the right of the LMS.

##  4 Proper Motions

The first step in measuring PM displacements is to define the reference
system. We considered basing the absolute astrometric reference frame on the
Gaia Early Data Release 3 (EDR3; Gaia Collaboration et al., 2021) catalog.
However, below $m_{\rm F814W}=18$ (which corresponds to our saturation
threshold), there are fewer than 600 stars in EDR3 with position errors
$<1\,{\rm mas}$ and PM errors $<1\,{\rm mas/yr}$ in common with our catalog.
Furthermore, this list includes both the young and old stellar populations,
that could have different relative motions. Thus, to create reliable
astrometric reference frames, we would have had to project the stars to the
positions they had in 2004. Given that the average PM uncertainty for these
stars is 0.9 mas/yr, the reference frame of the first epoch would not meet the
required astrometric accuracy. We, therefore, decided to follow the same
approach used by Bellini et al. (2014) and to create a network of reference
sources directly from our catalog. The PM displacement of each source is then
measured relative to this reference network.

We measured the PM of NGC 346 stars with respect to the RGB stellar population
since the latter can be easily identified in the CMD (Fig. 3) using color and
magnitude selections. We used the F814W exposures acquired in the first epoch
to determine the average position of the RGB stars and create the reference
network. In total, we identified more than 1400 RGB stars with photometric
error $<0.1$ magnitudes in both filters and epochs and with position errors
$<1.0\,{\rm mas}$ in both epochs. We then applied the six-parameter global
transformations needed to translate stellar positions in each exposure onto
the reference frame system. To limit the number of mismatches, we considered
only stars whose coordinates in the master-frame match to within 2.5 pixels
($0.125\arcsec$).

To mitigate the effect of small, uncorrected systematics in, e.g., the HST
geometric-distortion solutions and PSF models, we applied local corrections
derived from the average residuals between the transformed positions of the
closest N=30 RGB reference stars. The median distance of the furthest
reference star is 600 pixels ($\sim 30\arcsec$).

Figure 8: VPDs of the PMs for the UMS stars. The left panel shows the
$5.48\times 10^{-17}\,erg/cm^{2}/\mathrm{\AA}/s^{-1}$ isophotal contour level
superimposed on the F555W image. The contour has been used to separate the
sources likely associated with the NGC 346–N66 complex from the stars
belonging to the young SMC field. The central panel shows the PM VPD of the
young SMC field, and the right panel shows the VPD of the PMs for the NGC346
stars.

For each epoch, we computed the final position of each star as the sigma-
clipped mean of the transformed positions of all images in the F814W filter at
that epoch. We repeated the same analysis for the data taken in the F555W
filter. In each filter, we defined the PM of each star as the difference
between its position in the second and the first epoch, divided by the 11
years temporal baseline. We estimated the PM errors by adding the positional
errors in each epoch in quadrature and dividing by the temporal baseline.

For the analysis of the PMs, we considered only sources with photometric
errors $<0.1$ magnitude in both filters and epochs and with X and Y positional
errors $<1.0$ mas in both epochs. As shown in Fig. 2, only sources in the
magnitude range $18<m<23$ met both our astrometric and photometric
requirements.

Fig. 4 shows the PM 1-D rms of the PMs as a function of magnitude. PM
measurements in the F555W filter are affected by larger errors because of the
smaller number of dithers in the second epoch’s southern pointing, and the
higher background level, caused by the ionized gas. Therefore, we decided to
measure PMs primarily using the F814W filter, although we verified that the
F555W observations provide consistent results. After the selections in
photometry and position errors, the average PM rms in the F814W filter is
$0.06\pm 0.02$ mas/yr and $0.07\pm 0.02$ mas/yr in the F555W. For consistency
with previous studies of NGC 346 (e.g. Sabbi et al., 2008; Cignoni et al.,
2011; Gouliermis et al., 2014), in this work we adopted 60.4 kpc as the
nominal distance of the system. Thus, the average PM rms555Depending on the
method and studied region, the reported distance of the SMC in the literature
varies from less than 40 (Groenewegen, 2013) to almost 100 (Issa, 1989) kpc.
While it is beyond the scope of this paper to discuss the challenges and
merits of the various techniques, we noticed that the uncertainties on the
distance of NGC 346 considerably affect the magnitude and the dispersion of
all the velocity distributions studied here. in the F814W filter is $17.2\pm
5.7$ km/s and $20.1\pm 5.7$ km/s in the F555W filter. While the PM
uncertainties for most individual stars are too large to resolve their
internal motion within the cluster, the averaged PMs for a population of stars
or over a spatial subregion of the cluster are accurate enough to study the
internal cluster kinematics, since averaging decreases the uncertainties by
$N^{-1/2}$.

Figure 9: Central plot: VPD of the stars in NGC 346 expressed in km/s instead
of mas/yr. The error bars represent the typical standard deviations in a bin.
This information was used to determine the size of the binning step. Upper
histogram: Velocity distribution along the X direction. The systemic velocity
(marked by the dashed-dotted black line) is $v_{sys_{x}}=-8.44\pm 0.20$ km/s.
The distribution best fit (Orange continuous line) is achieved combining two
Gaussians. The center of the stronger component (blue dashed line) is at
$v_{x1}=-2.19\pm 0.13$ km/s from NGC 346 systemic velocity, with dispersion
$\sigma_{x1}=6.48\pm 0.20$ km/s and number of stars at the peak
$a_{x1}=160.14\pm 4.72$. The broader component (green dashed line) is at
$v_{x2}=7.80\pm 1.87$ km/s from the systemic velocity, with dispersion
$\sigma_{x2}=18.61\pm 2.71$ km/s and $a_{x2}=38.39\pm=4.88$ stars. Side
histogram: Velocity distribution along the Y direction. The systemic velocity
(marked by the dashed-dotted black line) is $v_{sys_{y}}=10.39\pm 0.33$ km/s.
The distribution best fit (Orange continuous line) results from the
combination of three Gaussian curves. The stronger component (blue dashed
curve) is redshifted from NGC 346 systemic velocity by $v_{y1}=10.16\pm 0.38$
km/s with dispersion $\sigma_{y1}=7.30\pm 0.33$ km/s and $a_{y1}=111.46\pm
5.24$ stars at the peak. The broader component (green dashed line) is at
$v_{y2}=-12.47\pm 2.16$ km/s from NGC 346 systemic velocity, with dispersion
$\sigma_{y2}=12.27\pm 2.29$ km/s and $a_{y2}=56.78\pm 2.05$ stars. The third
component (purple dashed line) is fitted with a Gaussian function with center
$v_{y3}=-1.37\pm 0.23$ km/s from NGC 346 systemic velocity,
$\sigma_{y3}=3.09\pm 0.30$ km/s, and $a_{y3}=58.90\pm 2.65$ stars.

The vector-point diagram (VDP, Fig. 5) of the PMs in the NGC 346 region shows
a complex structure with indications of multiple peaks in the higher density
part of the plots and an elongated structure toward the lower right corner. It
is clear from the inspection of Fig. 5, that this plot alone is not sufficient
to separate the different populations.

##  5 Kinematics of the Stellar Populations

The internal dynamics of the SMC is strongly affected by its recent history of
interaction with the Large Magellanic Cloud, with the SMC being in the process
of tidal disruption (Zivick et al., 2018). The numerous attempts to derive the
internal motions of the various SMC components using either line-of-sight
(Stanimirović et al., 2004; Harris & Zaritsky, 2006; Evans & Howarth, 2008;
Dobbie et al., 2014) or PM (Kallivayalil et al., 2006, 2013; van der Marel &
Sahlmann, 2016; Zivick et al., 2018) measurements have thus far provided
contradicting results, highlighting how, especially on small scales, younger
and older stars in the field of the SMC may have different kinematics.

To better understand the behavior of the various stellar populations in the
NGC 346 region, in the following analysis we will take advantage of the fact
that for each star we have three primary bits of information:

  * •

The position projected on the sky (Fig. 1);

  * •

The position in the CMD (Fig. 3);

  * •

The position in the VPD (Fig. 5).

As a starting point, we used the CMD to separate RGB, LMS, and UMS stars, and
then analyzed the motion of the three stellar components separately. The VPDs
for the three populations are shown in Fig. 6.

###  5.1 Low-Mass Stars in the SMC Field

In this section we will examine the motion of the stars with mass $M\lesssim
2\,M_{\odot}$ in the SMC field. As discussed in section 3, this group of stars
can be divided in RGB and LMS stars. The left panel of Fig. 6 shows the VDP of
the RGB stars. Since the reference frame and the transformations are based on
the RGB stars, the weighted average of this population in the VDP is by
construction centered on zero ($\mu_{x}=-0.0061\pm 0.0003\,{\rm mas/yr}$,
$\mu_{y}=-0.0028\pm 0.0002\,{\rm mas/yr}$).

The properties of the RGB stars selected using their positions in the VPD of
the PMs are shown in the three upper plots of Fig 7. In the CMD (upper-left
panel) sources within 0.03 mas/yr (corresponding to a velocity dispersion of
$\sim 8.5$ km/s) from the over-density peak found at at $\mu_{x}=-0.04\,{\rm
mas/yr}$ and $mu_{y}=-0.02\,{\rm mas/yr}$ are characterized by a small color
dispersion. The RC of this populations is compact and well defined, suggesting
that this group of stars has similar ages, chemical composition, distance, and
it is affected by comparable dust extinction. Spatially, these sources are all
concentrated around the nominal position of the 4.5 Gyr old BS90 cluster, as
shown by the density contours in the upper-middle panel.

In contrast the stars that are found more than 0.08 mas/yr away from the
density peak are likely part of the old field of the SMC. In this case the RC
shows a broader dispersion in magnitude, suggesting that the population could
be distributed along a broader line of site, and include stars that formed
over a larger period of time. This is further supported by the fact that the
brighter portion of the RC terminates in the V-like shape formed by the red
and blue edges of the helium-burning phase typically observed in the CMDs of
stellar populations younger than 1 Gyr, suggesting that this component formed
stars for several billion years. These sources cover the entire studied region
(as shown in the upper right panel). The impact of BS90 on the PM measurements
is negligible: in fact after removing the RGB stars found within $75\arcsec$
from the center of BS90, the weighted average of the RGB in the VPD remains
$\mu_{x}=0.0020\pm 0.0001\,{\rm mas/yr},\,\mu_{y}=0.0002\pm 0.0002\,{\rm
mas/yr}$.

Figure 10: Spatial distribution of the stars found within $0.5\,\sigma$ from
the three Gaussian peaks found in the side histogram of Fig. 9. The left panel
shows the distribution of the stars associated with the broader green
Gaussian, the central panel the distribution of the stars associated with the
narrow magenta Gaussian, and the right panel the distribution of the stars
found under the blue Gaussian. The arrows indicate the average motion of the
stars found in the higher density regions, after the mean motion of NGC 346
has been subtracted.

The middle panel of Fig. 6 shows the PM VPD of the LMS stars. In addition to
stars from the old field and BS90, this plot also includes the SMC’s younger
($\sim 50-100$ Myr to $\lesssim 1$ Gyr) component. The VPD is centered at
$\mu_{x},\mu_{y}=0,0$ mas/yr, but the presence of BS90 can still be recognized
in the second higher density contour. The properties of the LMS stars are
highlighted in the three lower panels of Fig 7. As for the RGB stars, the
sources found within 0.03 mas/yr from $\mu_{x}=-0.04$, $\mu_{y}=-0.02$ are
concentrated around the center of BS90 and in the CMD are distributed along a
tight and well-defined sequence, suggesting that they all belong to a coeval
stellar population, with negligible distance variation. On the contrary, the
remaining stars show a uniform spatial distribution and a much broader LMS, as
expected for field stars, affected by different reddening, distance, and
possibly metallicity. These results imply that BS90 has a velocity of
$v_{x}=-11.5\pm 0.5,\,v_{y}=-5.7\pm 0.7$ km/s (corresponding to
$v_{RA}=5.34\pm 0.70,\,v_{Dec}=11.67\pm 0.50$ km/s) relative to the more
broadly distributed field RGB population.

Figure 11: Motion of the stars within the isophotal contour shown in Fig 8.
The left panel shows the motion of the UMS stars, while the right panel is for
the PMS stars. Each arrow indicates the average direction of the stars found
within a $200\times 200$ pixel grid, after subtracting the total NGC 346
motion. The arrow length, increased 10,000 times, corresponds to the measured
displacement. In the left panel the contamination of the SMC young field was
statistically removed. Green, blue and magenta colors were used to highlight
different directions. Yellow star symbols mark the position of the YSOs
identified by Sewiło et al. (2013). The green + symbol highlights the position
of the photometric center, while the rotation center is marked with the red X.
The density contours highlight the spatial distribution of the PMS stars.

###  5.2 Intermediate and High-Mass Stars

The distribution of the UMS stars in the VPD (Fig. 6, right panel) is quite
different from those observed for the RGB and LMS stars. This is the only
diagram that shows an elongated structure in the upper left part
($\mu_{x}\simeq-0.025\,{\rm mas/yr}$, $\mu_{y}\simeq 0.03\,{\rm mas/yr}$),
associated with the NGC 346–N66 system.

To better separate NGC 346 stellar content from the young SMC field, we used
the isophotal contour level $5.48\times 10^{-17}\,erg/cm^{2}/\mathrm{\AA}/s$
(Fig. 8 \- left panel). The central panel shows the VPD of the stars outside
the isophotal level. The majority of these stars most likely belong to the SMC
field. The right panel shows the VPD of the stars inside the isophotal
contour. The plot here shows two separate peaks, embedded in an extended halo.
The majority of these sources likely belong to NGC 346.

The VPD of the SMC young field is clearly shifted to the right of NGC 346 and
peaks at $\mu_{x}=0.043\,{\rm mas/yr}$, $\mu_{y}=-0.040\,{\rm mas/yr}$, with
an extended and broad tail towards the lower-right part of the diagram.
Contrary to what is found by Zivick et al. (2018), both the Kolmogorov-Smirnov
test and the Cramér-von Mises criterion reject the hypothesis that young (UMS)
and old (RGB) field stars have similar kinematics. The discrepancy between
Zivic’s and our results is likely due to the recent star formation history of
the NGC 346 region. Cignoni et al. (2011) reported an elevated star formation
rate over the past 100 Myr compared to the rest of the SMC. We suggest that
the elevated and localized activity occurred in the past $\sim 100$ Myr likely
dominates the kinematics of the young field stars, and is the culprit for the
observed difference.

Figure 12: PM VPD of the PMS stars, measured in the F814W filter. The median
error in the $\mu_{x}$ and $\mu_{y}$ directions is shown in the upper right
corner

##  6 NGC 346

###  6.1 Upper Main Sequence Stars

Figure 13: Left panels: $v_{\theta}$ (upper panel) and $v_{\rho}$ (lower
panel) components of the velocity as a function of the distance from the
rotation center. Sources that lie within $2\,\sigma$ from
($v_{\theta},v_{\rho}=0,0$) are shown in blue, and the remaining sources are
in grey. The continuous yellow line marks the mean value of the distribution.
The dashed yellow lines mark the + and -1 standard deviation. Right Panels:
Zoom in of the $v_{\theta}$ and $v_{\rho}$ $1\sigma$ variation as a function
of the distance from the rotation center.

Fig. 9 shows the velocity distribution of the NGC 346 stars in km/s. The
systemic velocity of NGC 346 with respect of the RGB stars (defined as the
median of the velocities of all the sources within the isophotal contour shown
in the left panel of Fig. 8) is $v_{sys,x}=-8.44\pm 0.20\,{\rm km/s}$ and
$v_{sys,y}=10.39\pm 0.33\,{\rm km/s}$ (which correspond to
$v_{sys,RA}=-10.64\pm 0.33\,{\rm km/s}$ and $v_{sys,Dec}=8.12\pm 0.20\,{\rm
km/s}$).

The distribution of the PMs appears double-peaked and surrounded by an
extended halo. To confirm that the two peaks are not an artifact of a too
aggressive binning and take into proper account measurement errors, we ran an
extensive Markov chain Monte Carlo (MCMC) Bayesian inference comparing a
single Gaussian with the sum of two and three functions. Both the Akaike (AIC;
Akaike, 1974), and the Bayesian information criterion (BIC; Schwarz, 1978)
favor three Gaussians (two narrow peaks + a broader component) in the
Y-direction. In the X-direction, the two narrow peaks are almost aligned;
thus, we tested only the one and two peak hypotheses. The favored results are
shown in the two histograms in Fig. 9.

Although the test run above is not a formal fitting of the distribution of
motions, the parameters of that define the Gaussian functions favored by the
Bayesian inference can be used to select the stars that likely belong to the
different moving groups. In particular, Fig. 10 shows the spatial distribution
of the stars found within $0.5\,\sigma$ from the Fig. 9 Gaussian curve peaks.
The component characterized by the broader velocity dispersion
($\sigma_{x2}=18.61\pm 2.71,\,\sigma_{y2}=12.27\pm 2.29$ km/s) is also the
most extended and covers the entire NGC 346 complex (left panel). With the
respect to the NGC 346 systemic velocity, these stars are moving from
northwest to southeast with a mean velocity $v_{x2}=7.80\pm
1.87,\,v_{y2}=-12.47\pm 2.16$ km/s.

The stars associated with the magenta (central panel) and the blue (right
panel) Gaussian curves are clustered within the inner 8.8 pc from the
photometric center of NGC 346. With respect to the NGC 346 median motion, most
of the stars in the magenta component seem to move along an arch from South to
North. After the subtraction of the NGC 346 systemic velocity, the mean
velocity in the Y-direction is $v_{y3}=-1.37\pm 0.23$ km/s, and the velocity
dispersion $\sigma_{y3}=3.09\pm 0.30$ km/s. The blue component moves in the
opposite direction to the green one, from the center to the northwest. The
mean velocity in the Y-direction is redshifted compared to NGC 346 median
velocity by $v_{y1}=10.16\pm 0.38$ km/s, with velocity dispersion
$\sigma_{y1}=7.30\pm 0.33$ km/s. Combined, the two components along the
X-direction are on average blueshifted compared to NGC 346 systemic velocity
by $v_{x1}=-2.19\pm 0.13$ km/s and $\sigma_{x1}=6.48\pm 0.20$ km/s.

Fig. 10 reveals a complicated internal kinematics for NGC 346. The system
appears dynamically hot, with large velocity dispersion and sudden changes in
directions.

The comparison between the VPDs of the SMC young field and NGC 346 UMS stars
(Fig. 8) shows a certain level of overlap between the motions of the two
populations. To address the impact of field contamination, we measured the
stellar density of UMS stars between $17.9<m_{F814W}<20.4$, that meet our
photometry and astrometry requirements, at a distance greater than
$R>150\arcsec$ (corresponding to $R\simeq 44\,{\rm pc}$) from the center of
NGC 346. This yield a stellar density of $<0.01$ star per squared arcsecond.
We then divided the region inside the isophotal contour shown in Fig. 8 in a
$200\times 200$ pixel grid, and we measured the density of the UMS stars in
each cell. Assuming a uniform distribution and 100% completeness for the UMS
stars of the SMC young field, we estimate that the field contamination in the
various cells ranges from 5 to 30%, with an average value of 12%. We noticed
that this is likely an upper limit, since the NGC 346 region is likely more
incomplete, due to the higher crowding and background level, than the outer
parts of the image.

We statistically removed the contamination of the SMC young field from NGC 346
systemic velocity with the respect of the RGB, which became
$v_{sys,x}=-9.87\pm 0.23\,{\rm km/s}$ and $v_{sys,y}=11.82\pm 0.37\,{\rm
km/s}$, and in equatorial coordinates it corresponds to $v_{sys,RA}=-11.64\pm
0.37\,{\rm km/s}$ and $v_{sys,y}=10.07\pm 0.23\,{\rm km/s}$. As shown in Fig.
11 (left panel), after statistically removing the field contamination, the
center, and possibly the entire upper part, of the NGC 346 complex, seems to
rotate clockwise, once the systemic velocity of NGC 346 is subtracted. The
lower half of the system appears to move away from the complex as if NGC 346
is breaking into two parts.

###  6.2 Pre Main Sequence Stars

Because of NGC 346 young age, stars below $\sim 3\,M_{\odot}$ are still in the
PMS evolutionary phase. With the exception of a few small clumps, these stars
are mainly concentrated within the isophotal contour shown in Fig. 8.

Most of the PMS stars do not meet our PM selection criteria, likely because of
the elevated level of stellar crowding and high background. However, in Fig. 3
CMD, PMS stars fainter than $m_{F814W}>21.2$ represent the cleanest sample of
NGC 346 stars. We therefore decided to relax the selection criteria (blue
stars in Figs. 2 and 4) to perform a second, independent, analysis, although
affected by larger uncertainties, of NGC 346 internal kinematics.

Fig. 12 shows the VPD for the PMS stars with photometric rms $<0.2$ in both
the F555W and F814W filters, and with positional rms in F814W $<3$ mas in both
epochs (purple sources in the CMD shown in Fig. 3). As in the case of NGC 346
UMS stars, the plot shows two clear peaks, surrounded by an extended halo, in
the upper left part of the diagram. A third, weaker peak is visible towards
the lower right part of the plot.

As we did for NGC 346 UMS stars, we divided the PMS stars in a $200\times 200$
pixel grid and for each cell we measured the average motion of the PMS stars,
corrected for the cluster’s systemic velocity. Since this group of stars was
selected using the CMD, where the field contamination is negligible, no
further correction was needed. Although the plot appears noisier than in the
case of the UMS stars, the two distributions are qualitatively very similar.
Both diagrams suggest that the upper part of the NGC 346 is rotating. The
southern end of the system, on the other end, displays an entirely different
motion, resembling an outflow.

###  6.3 Velocity and Velocity Dispersion Profiles

We derived for each UMS star in NGC 346 the radial ($v_{\rho}$) and tangential
($v_{\theta}$) velocity components to study the profile of the cluster mean
velocity and velocity dispersion. To start, we consider as the rotation center
NGC 346’s photometric center ($X=3501.43,\,Y=3568.69$, corresponding to
$R.A.=14.7706984,\,Dec=-72.1775412,\,ICRS$), whose position in Fig. 11 is
marked by the green cross symbol.

We subtracted the system’s mean PM from each star, and then we derived the
$v_{\rho}$ and $v_{\theta}$ components for each source. In this reference
system, within the inner $R\sim 11-13$ pc, both $v_{\rho}$ and
$v_{\theta}\propto r$, with fitted slope $\sim 0.3$ and $\sim 0.2$ km/s/pc,
respectively, suggesting that the star-forming regions is rotating as a rigid
body, and expanding.

Given the evidence for rotation, we then proceeded to identify the center of
rotation, which need not coincide with the photometric center. We looped
through a $20\times 20$ pixel grid, and for each grid element, after having
subtracted the mean PM of the stars found within 10 pc, we derived the sigma-
clipped mean $\overline{v_{\theta}}$ value of the stars found within the same
radius. We considered as center of rotation the grid point that gave the
largest $|\overline{v_{\theta}}|$, found at
$RA=14.7575892,\,Dec=-72.1779791,\,ICRS$ ($X=3502.35,\,Y=3845.09$), $\sim 4.5$
pc west of the photometric center. In Fig. 11 the position of the rotation
center is marked with a red X symbol.

Fig. 13 shows $v_{\theta}$ and $v_{\rho}$ as a function of distance from NGC
346’s rotation center. Despite the large dispersion, $v_{\theta}$ (upper-right
panel) appears to increase between $\sim 0.5$ and 3.5 pc (where it reaches the
maximum value $v_{\theta_{max}}=-3.2\,{\rm km/s}$) at $0.2\,{\rm km/s/pc}$,
and then progressively decrease to almost zero at 10 pc
($v_{\theta_{10\,pc}}=-0.5\,{\rm km/s}$).

Within the inner 4 pc $v_{\rho}$ is negative and almost constant, indicative
of an inflow in the inner regions. Instead, between $\sim 3.7$ and $\sim 8$ pc
it increases with the distance with fitted slope $\sim 0.2$ km/s/pc,
indicative of expansion of the outer regions (Fig. 13, lower-right panel).
Similar expansions have been observed also in some young Milky Way star
clusters (Kuhn et al., 2019) and predicted by numerical simulations of the
stellar feedback impact on young star cluster evolution (Grudić et al., 2022).

The combination of rotation and inflow in the central regions is suggestive of
inspiraling motion. Fig. 14 shows the spatial distribution and direction of
motion of NGC 346’s individual UMS stars in the new reference system. In this
plot the majority of the stars above $Y=-500$ pixels is spiraling from the
north east towards the rotation center. A logarithmic spiral is overdrawn to
guide the eye. The distribution of YSOs and sub-clusters aligns well with this
motion.

We speculate that in proximity of the center, the stream of spiraling stars
bend behind NGC 346 and re-emerge below $Y=-500$ as one of the two tails of
stars that are moving toward the southeast, away from NGC 346. The dashed red
line in Fig. 14 suggests the possible path followed by these sources.

A narrow stream of stars (indicated by the dashed blue line) and YSOs seems to
connect the bright small cluster to the east of NGC 346 (Sc-13 in the
classification by Sabbi et al., 2007) to the outer tail. These streams,
inflows, and outflows of stars are reminiscent of the filament-like structures
that are feeding the growth of star-forming regions in the hierarchical
collapse models.

Hydrodynamic simulations of turbulent molecular clouds predict that rotation
is a common characteristic of embedded massive ($>1000\,M_{\odot}$, Lee &
Hennebelle, 2016; Mapelli, 2017; Ballone et al., 2020) star clusters, with the
rotation curves increasing from the center, peaking approximately at 1-2 half
mass radii, and then decreasing in the outer regions, where they can become
slightly retrograde (e.g. Tiongco et al., 2017). Over time, the rotation of
star cluster is expected to decrease because of stellar mass loss and two-body
relaxation (Einsel & Spurzem, 1999; Ernst et al., 2007; Kim et al., 2008;
Hurley & Shara, 2012; Tiongco et al., 2017).

Evidence for internal rotation in NGC 346 has been also found over the central
$\sim 1\,arcmin^{2}$ by Zeidler et al. (2022 - submitted) using line-of-sight
velocities obtained with the ESO Multi-Object Spectroscopic Explorer (MUSE,
Bacon et al., 2010). Similarly to what we observed in the PM distribution, the
MUSE dataset shows two statistically significant velocity groups, and a
possible third one. Like the magenta and blue groups shown in Fig. 10, one
velocity group is more centrally concentrated, while the other one appears
elongated along the northwest-southeast direction. As in the case of the PMs,
the more centrally concentrated group is rotating with an angular velocity of
$\Omega=-0.41\pm 0.07\,{\rm Myr}^{-1}$, which translates to $v_{\rm
rot,RV}^{5\,{\rm pc}}=-1.98\pm 0.34\,{\rm km}/{\rm s}$ and $v_{\rm
rot,RV}^{10\,{\rm pc}}=-3.95\pm 0.67\,{\rm km}/{\rm s}$, at a radial distance
from the center of 5 and 10 pc, respectively, comparable to the results of
this work. Unfortunately the MUSE field of view is too small to provide any
information about the motion of the NGC 346 outskirts.

##  7 Discussion & Conclusions

The star-forming complex NGC 346 presents several challenges to cluster
formation models. The sound crossing time is $t_{S}=50\,pc/c_{S}\sim 2\times
10^{8}$ Myr; thus, the two edges of the NGC 346 parental cloud were not in
thermal contact with each other on a freefall collapse timescale and should
therefore present considerable age differences. However, all NGC 346 stars
fall in the age range 2-6 Myr (Evans et al., 2006; Sabbi et al., 2007; Cignoni
et al., 2013; Dufton et al., 2019), raising the question of how star formation
developed in such a synchronized manner over such a wide scale. The Upper
Scorpius OB association (Preibisch & Zinnecker, 1999), the Serpens molecular
clouds (Herczeg et al., 2019), and the NGC 7000 and IC 5070 Nebulae (Kuhn et
al., 2020) pose similar challenges to all the models of cloud collapse that do
not include an accelerating star formation rate.

The spatial and kinematic clustering in young stellar systems can provide
valuable constraints on the conditions that led to the onset of star formation
(e.g., Elmegreen, 2002; Parker et al., 2014; Kuhn et al., 2019). Therefore, we
used two epochs of deep HST/ACS observations with a temporal baseline of 11
years (https://doi.org/10.17909/y1cf-m826 (catalog 10.17909/y1cf-m826)) to
measure the PM displacements of the stars in the star-forming region NGC 346,
and reconstruct the cluster kinematics.

  * •

Our analysis of NGC 346 stellar PMs reveals a complex pattern of inflows and
outflows. The star-forming region’s inner $\sim 10$ pc is rapidly rotating,
following a spiraling movement towards the center from the outer north-east
end. Increasing rotation with the distance from the center is commonly found
in the most up-to-date hydrodynamic simulations of turbulent molecular clouds
(Lee & Hennebelle, 2016; Mapelli, 2017; Ballone et al., 2020).

  * •

NGC 346 is characterized by a clumpy structure, with at least 15 different
sub-clusters and asterisms (Sabbi et al., 2007; Hennekemper et al., 2008),
that often host recently formed YSOs (Simon et al., 2007; Sewiło et al.,
2013). When we compared the position of sub-clusters and massive YSOs with NGC
346 motion patter, we found that over-densities tend to concentrate at the
interface of significant changes in the coherence of the motion field, where
we expect to see substantial gas friction and compression. This behaviour
appears to be in good agreement with the predictions of rapid star formation
in turbulent molecular cloud scenarios (e.g., Klessen et al., 2000; Bonnell &
Bate, 2002; Bonnell et al., 2003).

  * •

NGC 346 shows a large velocity dispersion, and it is increasingly expanding
with the distance from the center. Similar behavior is an expected outcome,
for example, of global hierarchical collapse models (Vázquez-Semadeni et al.,
2017, 2019), where the collapse of the parental cloud starts as small-scale
events within a larger structure and culminates after a few Myr as a series of
filamentary flows that accrete onto massive central clumps. These “river-like”
structures drive the system accretion motions “down the gravitational
potential” and are responsible for the late appearance of massive stars and
their segregation in the central clumps. In agreement with this picture, the
PMs studied in this paper revealed longitudinal inflows and outflows that
extend over tens of parsecs. These motions could be at the origin of NGC 346’s
elevated degree of mass segregation reported by Sabbi et al. (2008).

  * •

The inspection of the motion field of both UMS and PMS stars indicates that
the upper part of NGC 346 is rotating along a coherent spiral-like pattern
(Fig. 14). Both Cignoni et al. (2011) and Dufton et al. (2019) noted that the
massive stars in the center of the system likely formed a couple of million
years later than the outer part of the cluster. We speculate that the
spiraling motion has been feeding this more recent episode of SF.

  * •

On a broader scale, our PMs analysis also showed a difference in the relative
motions of young ($<600\,{\rm Myr}$) UMS and old ($>1\,{\rm Gyr}$) RGB field
stars. From the analysis of line-of-sight velocities of stars and gas
Stanimirović et al. (2004); Harris & Zaritsky (2006); Evans & Howarth (2008);
Dobbie et al. (2014) proposed for the SMC possible age-dependent internal
kinematics. On the other hand, Zivick et al. (2018) did not find significant
differences between the PMs of UMS and RGB stars in 30 HST fields. We believe
that the elevated SF rate in the NGC 346 region over the past $\sim 100\,{\rm
Myr}$ is the main reason behind the difference between our and Zivick’s
findings. In particular, our results show how on a small scale, the specific
recent SF history of a region likely dominates the local kinematics. This test
highlights the need for a uniform-coverage high-precision astrometric study of
the entire SMC to reconstruct the galaxy’s internal dynamic and evolution
through its history of interactions with the LMC and the MW.

Figure 14: Spatial distribution of NGC 346 UMS stars. The arrows indicates the
direction of the motion with the respect of the rotation center, while their
length is proportional to their velocity. As in Fig. 10 the yellow stars mark
the position of the massive YSOs. The red logarithmic spiral, described by the
equation $x=cos(\theta)e^{0.21\theta}$ $y=sin(\theta)exp^{0.21\theta}$, is not
a fit, and has been superimposed only to guide the eye. The dashed line
connect the stars in the center to the tail of stars that appear to escape NGC
346 from the south west. The dashed blue line highlight the stream of stars
that connect the small cluster to the west to the southern tail.

Our new measurements for the NGC 346 region represent the first attempt to
infer the conditions that induced star formation in a metal-poor giant
molecular cloud. We demonstrated that the velocity field of the star-forming
region is complex and well matches the conditions predicted by recent
hydrodynamic simulations and hierarchical collapse models. The similarities
between our results and those found for star-forming regions in the Milky Way
suggest that the differences in the cooling conditions due to the different
amounts of metallicity and dust density between the SMC and our Galaxy are too
small to alter significantly the process of star clusters assembly and growth.
By extending this type of study to a broader range of star formation rates and
stellar densities and by comparing the results to theoretical predictions, we
can gain new insights into star formation and open a new pathway toward
validating or repudiating specific models.

We thank an anonymous referee for carefully reading this manuscript and
helping us improve the quality of the paper. We are grateful to M. Gieles, L.
Strolger, and R. Klessen for the useful suggestions and discussions. The HST
observations used in this paper are associated with program Nos. 10248 and
13680. The specific observations analyzed in this paper can be accessed from
MAST at the Space Telescope Science Institute via
https://doi.org/10.17909/y1cf-m826 (catalog 10.17909/y1cf-m826). Support for
the program 13680 was provided through a grant from the Space Telescope
Science Institute. This work is based on observations obtained with the
NASA/ESA Hubble Space Telescope, at the Space Telescope Science Institute,
which is operated by the Association of Universities for Research in
Astronomy, Inc., under NASA contract NAS 5-26555. This work has made use of
data from the European Space Agency (ESA) mission Gaia
(https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and
Analysis Consortium (DPAC,
https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has
been provided by national institutions, in particular the institutions
participating in the Gaia Multilateral Agreement.

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