Spatial Statistics in Star Forming Regions: Is Star Formation Driven By
  Column Density Alone?
  Star formation is known to occur more readily where more raw materials are
available. This is often expressed by a 'Kennicutt-Schmidt' relation where the
surface density of Young Stellar Objects (YSOs) is proportional to column
density to some power, $\mu$. The aim of this work was to determine if column
density alone is sufficient to explain the locations of Class 0/I YSOs within
Serpens South, Serpens Core, Ophiuchus, NGC1333 and IC348, or if there is
clumping or avoidance that would point to additional influences on the star
formation. Using the O-ring test as a summary statistic, 95 per cent confidence
envelopes were produced for different values of $\mu$ from probability models
made using the Herschel column density maps. The YSOs were tested against four
distribution models: the best-estimate of $\mu$ for the region, $\mu=0$ above a
minimum column density threshold and zero probability elsewhere, $\mu=1$, and
the power-law that best represents the five regions as a collective, $\mu=2.05
\pm 0.20$. Results showed that $\mu=2.05$ model was consistent with the
majority of regions and, for those regions, the spatial distribution of YSOs at
a given column density is consistent with being random. Serpens South and
NGC1333 rejected the $\mu = 2.05$ model on small scales of $\sim 0.15
\mathrm{pc}$ which implies that small-scale interactions may be necessary to
improve the model. On scales above 0.15 pc, the positions of YSOs in all five
regions can be well described using column density alone.
