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The scaling relations and star formation laws of ministarburst complexes

The scaling relations and the star formation laws for molecular cloud complexes in the Milky Way is investigated. We compare their masses $M_{\rm gas}$, mass surface densities $Σ_{M_{\rm gas}}$, radii $R$, velocity dispersions $σ$, star formation rates $SFR$, and SFR densities $Σ_{\rm SFR}$ with those of structures ranging from cores, clumps, Giant Molecular Clouds (GMCs), to Molecular Cloud Complexes (MCCs), and to Galaxies, spanning 8 orders of magnitudes in size and 13 orders of magnitudes in mass. MCC are mostly large ($R>50$ pc), massive ($\sim 10^{6}$\,\msun) gravitationally unbound cloud structures. This results in the following universal relations: $σ\sim R^{0.5}$, $M_{\rm gas}\sim R^{2}$, $Σ_{\rm SFR}\sim Σ_{M_{\rm gas}}^{1.5}$, ${SFR}\sim {M_{\rm gas}}^{0.9}$, and ${SFR}\sim σ^{2.7}$. Variations in the slopes and the coefficients of these relations are found at individual scales signifying different physics acting at different scales. Additionally, there are breaks at the MCC scale in the $σ-R$ relation and between the starburst and the normal star-forming objects in the $SFR-M_{\rm gas}$ and $Σ_{\rm SFR}$-$Σ_{\rm M_{\rm gas}}$ relations. We propose to use the Schmidt-Kennicutt diagram to distinguish the starburst from the normal star-forming structures by applying a $Σ_{M_{\rm gas}}$ threshold of $\sim100$\,\msun pc$^{-2}$ and a $Σ_{\rm SFR}$ threshold of 1\,\msun yr$^{-1}$ kpc$^{-2}$. Mini-starburst complexes have enhanced $Σ_{\rm SFR}$ ($>$1\,\msun yr$^{-1}$ kpc$^{-2}$), probably caused by dynamic events such as radiation pressure, colliding flows, or spiral arm gravitational instability. Because of the dynamical evolution, gravitational boundedness does not play a significant role in characterizing the star formation activity of MCCs, especially the mini-starburst complexes.