Two Small Temperate Planets Transiting Nearby M Dwarfs in K2 Campaigns 0 and 1

The prime Kepler mission revealed that small planets (<4 {R}[SUB]\oplus [/SUB]) are common, especially around low-mass M dwarfs. K2, the repurposed Kepler mission, continues this exploration of small planets around small stars. Here we combine K2 photometry with spectroscopy, adaptive optics imaging, and archival survey images to analyze two small planets orbiting the nearby field-age M dwarfs, K2-26 (EPIC 202083828) and K2-9. K2-26 is an {{M}}1.0+/- 0.5 dwarf at 93 ± 7 pc from K2 Campaign 0. We validate its planet with a day period of 14.5665 and estimate a radius of {2.67}[SUB]-0.42[/SUB][SUP]+0.46[/SUP] {R}[SUB]\oplus [/SUB]. K2-9 is an {{M}}2.5+/- 0.5 dwarf at 110 ± 12 pc from K2 Campaign 1. K2-9b was first identified by Montet et al.; here we present spectra and adaptive optics imaging of the host star and independently validate and characterize the planet. Our analyses indicate K2-9b is a {2.25}[SUB]-0.96[/SUB][SUP]+0.53[/SUP] {R}[SUB]\oplus [/SUB] planet with a 18.4498 day period. K2-26b exhibits a transit duration that is too long to be consistent with a circular orbit given its measured stellar radius. Thus, the long transits are likely due to the photoeccentric effect and our transit fits hint at an eccentric orbit. Both planets receive low incident flux from their host stars and have estimated equilibrium temperatures