Probing the Star Formation Main Sequence down to $10^{8}$ M$_\odot$ at $1.0<z<3.0$

We investigate the star formation main sequence (MS) (SFR-M$_{\star}$) down to 10$^{8-9}\mathrm{M}_\odot$ using a sample of 34,061 newly-discovered ultra-faint ($27\lesssim i \lesssim 30$ mag) galaxies at $1<z<3$ detected in the GOODS-N field. Virtually these galaxies are not contained in previous public catalogs, effectively doubling the number of known sources in the field. The sample was constructed by stacking the optical broad-band observations taken by the HST/GOODS-CANDELS surveys as well as the 25 ultra-deep medium-band images gathered by the GTC/SHARDS project. Our sources are faint (average observed magnitudes $<i>\sim28.2$ mag, $<H>\sim27.9$ mag), blue (UV-slope $<\beta>\sim-1.9$), star-forming (rest-frame colors $<U-V>\sim0.10$ mag, $<V-J>\sim0.17$ mag) galaxies. These observational characteristics are identified with young (mass-weighted age $<\mathrm{t_{M-w}}>\sim0.014$ Gyr) stellar populations subject to low attenuations ($<\mathrm{A(V)}>\sim0.30$ mag). Our sample allows us to probe the MS down to $10^{8.0}\,\mathrm{M}_\odot$ at $z=1$ and $10^{8.5}\,\mathrm{M}_\odot$ at $z=3$, around 0.6 dex deeper than previous analysis. In the low-mass galaxy regime, we find an average value for the slope of 0.97 at $1<z<2$ and 1.12 at $2<z<3$. Nearly $\sim$60% of our sample presents stellar masses in the range $10^{6-8}$ M$_\odot$ between $1<z<3$. If the slope of the MS remained constant in this regime, the sources populating the low-mass tail of our sample would qualify as starburst galaxies.