Star-forming dwarf galaxies have properties similar to those expected in high-redshift galaxies. Hence, these local galaxies may provide insights into the evolution of the first galaxies, and the physical processes at work. We present a sample of eleven potential local analogs to high-$z$ (LAHz) galaxies. The sample consists of blue compact dwarf galaxies, selected to have spectral energy distributions that fit galaxies at $1.5<z<4$. We use SOFIA-HAWC+ observations combined with optical and near-infrared data to characterize the dust properties, star formation rate (SFR) and star formation histories (SFH) of the sample of LAHz. We employ Bayesian analysis to characterize the dust using two-component black-body models. Using the LIGHTNING package we fit the spectral energy distribution of the LAHz galaxies over the FUV-FIR wavelength range, and derive the SFH in five time-steps up to a look-back time of 13.3 Gyr. Of the eleven LAHz candidates, six galaxies have SFH consistent with no star formation activity at look-back times beyond 1 Gyr. The remaining galaxies show residual levels of star formation at ages $gtrsim$1,Gyr, making them less suitable as local analogs. The six young galaxies stand out in our sample by having the lowest gas-phase metallicities. They are characterized by warmer dust, having the highest specific SFR, and the highest gas mass fractions. The young age of these six galaxies suggests that merging is less important as a driver of the star formation activity. The six LAHz candidates are promising candidates for studies of the gas dynamics role in driving star formation.
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