We identify an abundant population of extreme emission line galaxies (EELGs) at redshift z~1.7 in the Cosmic Assembly Near-IR Deep Extragalactic Legacy Survey (CANDELS) imaging from Hubble Space Telescope/Wide Field Camera 3 (HST/WFC3). 69 EELG candidates are selected by the large contribution of exceptionally bright emission lines to their near-infrared broad-band magnitudes. Supported by spectroscopic confirmation of strong [OIII] emission lines -- with rest-frame equivalent widths ~1000AA -- in the four candidates that have HST/WFC3 grism observations, we conclude that these objects are galaxies with 10^8 Msol in stellar mass, undergoing an enormous starburst phase with M_*/(dM_*/dt) of only ~15 Myr. These bursts may cause outflows that are strong enough to produce cored dark matter profiles in low-mass galaxies. The individual star formation rates and the co-moving number density (3.7x10^-4 Mpc^-3) can produce in ~4 Gyr much of the stellar mass density that is presently contained in 10^8-10^9 Msol dwarf galaxies. Therefore, our observations provide a strong indication that many or even most of the stars in present-day dwarf galaxies formed in strong, short-lived bursts, mostly at z>1.
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