tokens: luminosity of 3D H α clumps ranges from ∼10 per cent–95 per cent, while the contribution to H α luminosity from individual 3D clumps ranges from less than 1 per cent to ∼90 per cent. This large range results from the short time-scale of star formation traced by H α and thus the clumpiness of H α emission. Most individual 3D clumps contribute less than 10 per cent to total H α luminosity, while only one or two largest clumps contribute most of the H α flux. The gas in H α clumps is not bound, with virial parameters (equation 1 ) larger than 1 by orders of magnitude. 4.4 Origins of giant stellar clumps Gravitational instability can induce fragmentation of the galactic disc, thus leading to growth of clumps. Stability criterion to linear axisymmetric perturbations for gaseous discs can be described by the Toomre parameter (Safronov 1960 ; Toomre 1964 ): where κ is the epicycle frequency, σ is the velocity dispersion, and Σ is the mass surface density. A disc is unstable if Q ≲ 1. Observations (e.g. Puech 2010 ; Girard et al. 2018 ) found that clumpy galaxies are marginally stable, with Toomre Q ∼ 1. Most H α clumps in high-redshift galaxies are located in regions where Q is low (Genzel et al. 2011 ; Wisnioski et al. 2012 ; Mieda et al. 2016 ). In galaxy formation simulations (Inoue et al. 2016 ; Oklopčić et al. 2017 ) gas clumps also coincide with regions of Q 1, albeit with large scatter of Q value. Inoue et al. ( 2016 ) also found that stellar clumps coincide with regions of low stellar Q . In Meng et al. ( 2019 ) we studied the distribution of Q in our simulations, accounting for different phases of the gas and stars. Such multicomponent Q more accurately describes the linear stability criterion in realistic galaxies. We found that strong feedback from young stars disperses gas around them, leading to spatial anticorrelation of dense gas and stars up to 50 Myr old. Here we analogously find that locations of 2D UV clumps do not coincide with the regions of low Q . This is because low Q regions closely trace high gas density, while rest-frame UV clumps trace young stars. The average value of Q in 2D UV clump regions ranges from 2.1 to 3.6, which is larger than the median value of Q = 0.5–1.0 weighted by molecular gas mass in Meng et al. ( 2019 ). For H α clumps Q = 1.4–3.3 is closer to the gas values, as expected for very young stars. The discrepancy in location of gas and young stars is also seen in the simulations of Oklopčić et al. ( 2017 ), where they find that the gas clumps coincide with the location of instantaneous star formation, but not of the SFR averaged over more than 10 Myr. If clumps form out of instability of a self-gravitating disc, the wavelength of the fastest growing perturbation is The effective radius of a fully formed clump may not exactly correspond to this scale, but it can still be used as a rough guide. If we take λ T /2 for R clump , and approximate the disc rotation velocity profile as flat, then , and we obtain
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