E-INSPIRE -- I. Bridging the gap with the local Universe: Stellar population of a statistical sample of ultra-compact massive galaxies at $z<0.3$

This paper presents the first effort to Extend the Investigation of Stellar Populations In RElics (E-INSPIRE). We present a catalogue of 430 spectroscopically-confirmed ultra-compact massive galaxies (UCMGs) from the Sloan Digital Sky Survey at redshifts $0.01<z<0.3$. This increases the original INSPIRE sample eightfold, bridging the gap with the local Universe. For each object, we compute integrated stellar velocity dispersion, age, metallicity, and [Mg/Fe] through spectroscopic stellar population analysis. We infer star formation histories (SFHs), metallicity evolution histories (MEHs) and compute the Degree of Relicness (DoR) of each object. The UCMGs, covering a wide range of DoR from 0.05 to 0.88, can be divided into three groups, according to how extreme their SFH was. The first group consists of 81 extreme relics ($\text{DoR}\gtrsim0.6$) that have formed the totality of their stellar mass by $z\sim2$ and have super-solar metallicities at all cosmic epochs. The second group ($0.3\lesssim\text{DoR}\lesssim0.6$) contains 293 objects also characterised by peaked SFHs but with a small percentage of later-formed stars and with a variety of MEHs. The third group ($\text{DoR}\lesssim0.3$), has 56 objects that cannot be considered relics since they have extended SFHs and formed a non-negligible fraction ($>25\%$) of their stellar mass at $z<2$. We confirm that an efficient method of finding relics is to select UCMGs with large velocity dispersion values but we believe that the most efficient way is to select high velocity dispersion objects that also have super-solar metallicities and high [Mg/Fe].