2018ApJ...869...11C

We investigate star-forming scaling relations using Bayesian inference on a comprehensive data sample of low- (z < 0.1) and high-redshift (1 < z < 5) star-forming regions. This full data set spans a wide range of host galaxy stellar mass (M_* ∼ 10⁶-10¹¹ M_☉) and clump star formation rates (SFR ∼ 10^–5 -10² M_☉ yr^–1). We fit the power-law relationship between the size (r_Hα) and luminosity (L_Hα) of the star-forming clumps using the Bayesian statistical modeling tool Stan, which makes use of Markov Chain Monte Carlo (MCMC) sampling techniques. Trends in the scaling relationship are explored for the full sample and subsets based on redshift and selection effects between samples. In our investigation, we find neither evidence of redshift evolution of the size-luminosity scaling relationship nor a difference in slope between lensed and unlensed data. There is evidence of a break in the scaling relationship between high and low SFR surface density (Σ_SFR) clumps. The size-luminosity power-law fit results are L_Hα ∼ r_Hα^2.8 and L_Hα ∼ r_Hα^1.7 for low and high Σ_SFR clumps, respectively. We present a model where star-forming clumps form at locations of gravitational instability and produce an ionized region represented by the Stromgren radius. A radius smaller than the scale height of the disk results in a scaling relationship of L ∝ r³ (high Σ_SFR clumps), and a scaling of L ∝ r² (low Σ_SFR clumps) if the radius is larger than the disk scale height.