Spatial statistics in star-forming regions

Abstract

Observational studies of star formation reveal spatial distributions of Young Stellar Objects (YSOs) that are `snapshots' of an ongoing star formation process. Using methods from spatial statistics it is possible to test the likelihood that a given distribution process could produce the observed patterns of YSOs. I determine the sensitivity of the spatial statistical tests Diggle's G function (G), the `free-space' function (F), Ripley's K and O-ring for application to astrophysical data. To do this I applied each test to simulated data containing 2D Gaussian clusters projected on a random distribution of background stars. By varying the number of stars within the Gaussian cluster and the number of background stars I determined the ability of the tests to reject complete spatial randomness (CSR) with changing signal-to-noise. Ripley's K and O-ring were shown to be much more sensitive to Gaussian clusters than G and F. I then apply the O-ring test 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. Star formation is known to occur more readily where more raw materials are available, a relationship that is often expressed in the form of a 'Kennicutt--Schmidt' relation where the surface density of Young Stellar Objects (YSOs) is proportional to column density to some power, μ. Using the O-ring test as a summary statistic, confidence envelopes were produced for different values of μ from probability models made using the Herschel column density maps. The YSOs were tested against four distribution models: the best-estimate of μ for the region, μ = 0 (i.e. random) above a column density threshold and zero probability elsewhere, μ = 1, and the power-law that best represents the five regions as a collective, μ = 2.05 ± 0.20. Serpens South and NGC1333 rejected the μ = 2.05 model on small scales of ~ 0.15 pc which implies that small-scale interactions may be influencing their distribution. On scales above 0.15 pc, the positions of YSOs in all five regions can be well described using column density alone.