Investigating the Young Stellar Populations and Hierarchies in Nearby Galaxies with the UVIT. III. Evidence for a Largest Scale of Correlated Stellar Structures and a Non-universal Fractal Dimension

Abstract: Scale-free turbulent motions, gravitational collapse and galactic dynamics govern galactic-scale, hierarchical organization of star formation (SF) within galaxies. Past studies suggest that properties of SF hierarchies depend upon host galaxy properties and interstellar medium (ISM) conditions. To characterize SF hierarchies, we performed two-point correlation function analysis on ~25000 UV-selected star-forming clumps (SFCs) identified in a morphologically diverse sample of 8 classic spirals, 6 flocculent spirals and 3 dwarf irregulars. We found that SF hierarchies in galaxies exhibit a maximum spatial scale -- the correlation length ($l_{\rm corr}$) -- largest scale up to which SF is spatially correlated, presumably owing to ISM turbulence. The $l_{\rm corr}$ values range from ~100 pc to 3.4 kpc and exhibit strong dependence on the galaxy's stellar mass, morphology and nature of spiral arms. This suggests that a galaxy's gravitational potential and spiral structure place an upper limit on the sizes of the largest, hierarchically structured SF complexes. Connecting $l_{\rm corr}$ with turbulence injection sources suggests that stellar feedback in dwarf irregulars, whereas disk instabilities and spiral structure in classic/flocculent spirals dominate towards sustaining their SF hierarchies up to the $l_{\rm corr}$ scale. These hierarchies disperse to near-random distributions on timescales ($T_{\rm dis}$) ranging from 20-160 Myr. The broad range of derived $l_{\rm corr}$, projected fractal dimension ($D_2$ $\in$ 0.71$-$1.73), and $T_{\rm dis}$ indicates a non-universal, galaxy-specific nature of SF hierarchies. In this work, full coverage of each galaxy's star-forming extent with the AstroSat-UltraViolet Imaging Telescope uniquely enabled us to connect global parameters of SF hierarchies with large-scale galaxy properties.