Sequential Star Formation in the filamentary structures of Planck
  Galactic cold clump G181.84+0.31
  We present a multi-wavelength study of the Planck cold clump G181.84+0.31,
which is located at the northern end of the extended filamentary structure
S242. We have extracted 9 compact dense cores from the SCUBA-2 850 um map, and
we have identified 18 young stellar objects (YSOs, 4 Class I and 14 Class II)
based on their Spitzer, Wide-field Infrared Survey Explorer (WISE) and
Two-Micron All-Sky Survey (2MASS) near- and mid-infrared colours. The dense
cores and YSOs are mainly distributed along the filamentary structures of
G181.84 and are well traced by HCO$^{+}$(1-0) and N$_{2}$H$^{+}$(1-0)
spectral-line emission. We find signatures of sequential star formation
activities in G181.84: dense cores and YSOs located in the northern and
southern sub-structures are younger than those in the central region. We also
detect global velocity gradients of about 0.8$\pm$0.05 km s$^{-1}$pc$^{-1}$ and
1.0$\pm$0.05 km s$^{-1}$pc$^{-1}$ along the northern and southern
sub-structures, respectively, and local velocity gradients of 1.2$\pm$0.1 km
s$^{-1}$pc$^{-1}$ in the central substructure. These results may be due to the
fact that the global collapse of the extended filamentary structure S242 is
driven by an edge effect, for which the filament edges collapse first and then
further trigger star formation activities inward. We identify three
substructures in G181.84 and estimate their critical masses per unit length,
which are $\sim$ 101$\pm$15 M$_{\odot}$ pc$^{-1}$, 56$\pm$8 M$_{\odot}$
pc$^{-1}$ and 28$\pm$4 M$_{\odot}$ pc$^{-1}$, respectively. These values are
all lower than the observed values ($\sim$ 200 M$_{\odot}$ pc$^{-1}$),
suggesting that these sub-structures are gravitationally unstable.
