EPOCHS I. The Discovery and Star Forming Properties of Galaxies in the Epoch of Reionization at $6.5 < z < 18$ with PEARLS and Public JWST data

We present in this paper the discovery, properties, and a catalog of 1165 high redshift $6.5 < z < 18$ galaxies found in deep JWST NIRCam imaging from the GTO PEARLS survey combined with data from JWST public fields. We describe our bespoke homogeneous reduction process and our analysis of these areas including the NEP, CEERS, GLASS, NGDEEP, JADES, and ERO SMACS-0723 fields with over 214 arcmin$^{2}$ imaged to depths of $\sim 30$ mag. We describe our rigorous methods for identifying these galaxies, involving the use of Lyman-break strength, detection significance criteria, visual inspection, and integrated photometric redshifts probability distributions predominately at high redshift. Our sample is a robust and highly pure collection of distant galaxies from which we also remove brown dwarf stars, and calculate completeness and contamination from simulations. We include a summary of the basic properties of these $z > 6.5$ galaxies, including their redshift distributions, UV absolute magnitudes, and star formation rates. Our study of these young galaxies reveals a wide range of stellar population properties as seen in their colors and SED fits which we compare to stellar population models, indicating a range of star formation histories, dust, AGN and/or nebular emission. We find a strong trend exists between stellar mass and $(U-V)$ color, as well as the existence of the `main-sequence' of star formation for galaxies as early as $z \sim 12$. This indicates that stellar mass, or an underlying variable correlating with stellar mass, is driving galaxy formation, in agreement with simulation predictions. We also discover ultra-high redshift candidates at $z > 12$ in our sample and describe their properties. Finally, we note a significant observed excess of galaxies compared to models at $z > 12$, revealing a tension between predictions and our observations.