Nearby dwarf galaxies exhibit tight correlations between their global stellar and dynamical properties, such as circular velocity, mass-to-light ratio, stellar mass, surface brightness, and metallicity. Such correlations have often been attributed to gas or metal-rich outflows driven by supernova energy feedback to the interstellar medium. We use high-resolution cosmological simulations of high-redshift galaxies with and without energy feedback, as well as analytic modeling, to investigate whether the observed correlations can arise without supernova-driven outflows. We find that the simulated dwarf galaxies exhibit correlations similar to those observed as early as z~10, regardless of whether supernova feedback is included. We also show that the correlations can be well reproduced by our analytic model that accounts for realistic gas inflow but assumes no outflows, and star formation rate obeying the Kennicutt-Schmidt law with a critical density threshold. We argue that correlations in simulated galaxies arise due to the increasingly inefficient conversion of gas into stars in low-mass dwarf galaxies rather than supernova-driven outflows. We also show that the decrease of the observed effective yield in low-mass objects, often used as an indicator of gas and metal outflows, can be reasonably reproduced in our simulations without outflows. We show that this trend can arise if a significant fraction of metals in small galaxies is spread to the outer regions of the halo outside the stellar extent via mixing. In this case the effective yield can be significantly underestimated if only metals within the stellar radius are taken into account. Measurements of gas metallicity in the outskirts of gaseous disks of dwarfs would thus provide a key test of such explanation.
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