The first Hi-GAL observations of the outer Galaxy: a look to star formation in the third Galactic quadrant in the longitude range 216.5 < l < 225.5

We present the first Herschel PACS and SPIRE photometric observations in a portion of the outer Galaxy ($216.5^{\circ} \lesssim \ell \lesssim 225.5^{\circ}$ and $-2^{\circ} \lesssim b \lesssim 0^{\circ}$) as a part of the Hi-GAL survey. The maps between 70 and 500 $\mu$m, the derived column density and temperature maps, and the compact source catalog are presented. NANTEN CO(1-0) line observations are used to derive cloud kinematics and distances, so that we can estimate distance-dependent physical parameters of the compact sources (cores and clumps) having a reliable spectral energy distribution, that we separate in 255 proto-stellar and 688 starless. Both typologies are found in association with all the distance components observed in the field, up to $\sim 5.8$ kpc, testifying the presence of star formation beyond the Perseus arm at these longitudes. Selecting the starless gravitationally bound sources we identify 590 pre-stellar candidates. Several sources of both proto- and pre-stellar nature are found to exceed the minimum requirement for being compatible with massive star formation, based on the mass-radius relation. For the pre-stellar sources belonging to the Local arm ($d\lesssim1.5$ kpc) we study the mass function, whose high-mass end shows a power-law $N(\log M) \propto M^{-1.0 \pm 0.2}$. Finally, we use a luminosity vs mass diagram to infer the evolutionary status of the sources, finding that most of the proto-stellar are in the early accretion phase (with some cases compatible with a Class I stage), while for pre-stellar sources, in general, accretion has not started yet.