Fitting density models to observational data - The local Schmidt law in molecular clouds

Abstract

We consider the general problem of fitting a parametric density model to discrete observations, taken to follow a non-homogeneous Poisson point process. This class of models is very common, and can be used to describe many astrophysical processes, including the distribution of protostars in molecular clouds. We give the expression for the likelihood of a given spatial density distribution of protostars and apply it to infer the most probable dependence of the protostellar surface density on the gas surface density. Finally, we apply this general technique to model the distribution of protostars in the Orion molecular cloud and robustly derive the local star formation scaling (Schmidt) law for a molecular cloud. We find that in this cloud the protostellar surface density, ${\Sigma }_{\mathrm{YSO}}$, is directly proportional to the square gas column density, here expressed as infrared extinction in the $K$-band, $A_K$: more precisely, ${\Sigma }_{\mathrm{YSO}}=(1.65\pm 0.19)A_K^{(2.03\pm 0.15)}$ stars pc${}^{-2}$.

6 pages, A&A in press. References fixed

References in corpus (4)

• The Spitzer Space Telescope Survey of the Orion A & B Molecular Clouds - Part I: A Census of Dusty Young Stellar Objects and a Study of their Mid-IR Variability
• NICEST, a near-infrared color excess method tailored for small-scale structures
• Orion Revisited - I. The massive cluster in front of the Orion Nebula Cluster
• A First Look at the Auriga-California Giant Molecular Cloud With Herschel and the CSO: Census of the Young Stellar Objects and the Dense Gas

Cited by in corpus (23)

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• The Spitzer Space Telescope Survey of the Orion A and B Molecular Clouds II: the Spatial Distribution and Demographics of Dusty Young Stellar Objects
• Molecular clouds have power-law probability distribution functions
• Fragmentation of massive dense cores down to ~1000 AU: Relation between fragmentation and density structure
• Herschel-Planck dust optical depth and column density maps - II. Perseus
• A catalogue of dense cores and young stellar objects in the Lupus complex based on Herschel Gould Belt Survey observations
• The Galactic Thick Disc density profile traced with RR Lyrae stars
• HP2 survey: III The California Molecular Cloud--A Sleeping Giant Revisited
• An HST Survey for 100-1000 AU Companions around Young Stellar Objects in the Orion Molecular Clouds: Evidence for Environmentally Dependent Multiplicity
• The role of spiral arms in Milky Way star formation
• Low Mass Stars as Tracers of Star and Cluster Formation
• Protostars at Low Extinction in Orion A
• The YSO Population in the Vela-D Molecular Cloud
• W51North: A protocluster emerging out of a thermally inhibited fragmenting cloud
• A new method for deriving the stellar birth function of resolved stellar populations
• The Photo-Astrometric Vertical Tracer Density of the Milky Way I: The Method
• Three-dimensional extinction mapping and selection effects
• Probing the Global Dust Properties and Cluster Formation Potential of the Giant Molecular Cloud G148.24+00.41
• The dense-gas mass versus star formation rate relation: a misleading linearity?
• Spatial Statistics in Star Forming Regions: Is Star Formation Driven By Column Density Alone?
• A cautionary note about composite Galactic star formation relations
• A new method to unveil embedded stellar clusters
• zoomies: A tool to infer stellar age from vertical action in Gaia data