Universal Scaling Relations in Scale-Free Structure Formation

David Guszejnov; Philip F. Hopkins; Michael Y. Grudić

doi:10.1093/mnras/sty920

paper

Universal Scaling Relations in Scale-Free Structure Formation

arXiv:1707.05799 · doi:10.1093/mnras/sty920

Abstract

A large number of astronomical phenomena exhibit remarkably similar scaling relations. The most well-known of these is the mass distribution $d N / d M \propto M^{- 2}$ which (to first order) describes stars, protostellar cores, clumps, giant molecular clouds, star clusters and even dark matter halos. In this paper we propose that this ubiquity is not a coincidence and that it is the generic result of scale-free structure formation where the different scales are uncorrelated. We show that all such systems produce a mass function proportional to $M^{- 2}$ and a column density distribution with a power law tail of $d A / d ln Σ \propto Σ^{- 1}$ . In the case where structure formation is controlled by gravity the two-point correlation becomes $ξ_{2 D} \propto R^{- 1}$ . Furthermore, structures formed by such processes (e.g. young star clusters, DM halos) tend to a $ρ \propto R^{- 3}$ density profile. We compare these predictions with observations, analytical fragmentation cascade models, semi-analytical models of gravito-turbulent fragmentation and detailed "full physics" hydrodynamical simulations. We find that these power-laws are good first order descriptions in all cases.

12 pages, 6 figures, 2 tables, submitted to MNRAS

Universal Scaling Relations in Scale-Free Structure Formation

Abstract

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