Aims. We aim at finding candidates of potential survivors of high-redshift compact galaxies in SDSS, as targets for more detailed follow-up observations. Methods. From the virial theorem it is expected that for a given mass, compact galaxies have stellar velocity dispersion higher than the mean due to their smaller sizes. Therefore velocity dispersion coupled with size (or mass) is an appropriate method to select relics, independent of the stellar population properties. Based on these consideration we design a set of criteria using distribution of early-type galaxies from SDSS on the log$_{10}$(R$_{0}$)-log$_{10}$($sigma_{0}$) plane to find the most extreme objects on it. Results. We find 76 galaxies at 0.05 < z < 0.2, which have properties similar to the typical quiescent galaxies at high redshift. We study how well these galaxies fit on well-known local universe relations of early-type galaxies such as the fundamental plane, the red sequence or mass-size relations. As expected from the selection criteria, the candidates are located in an extreme corner of mass-size plane. However, they do not extend as deeply into the so-called zone of exclusion as some of the high-redshift compact galaxies (red nuggets) found at high redshift, being a factor 2-3 less massive at a given intrinsic scale size. Our candidates are systematically offset from scaling relations of average early-type galaxies, while being in the mass-size range expected for passive evolution of the red nuggets from their high redshift to the present. Conclusions. The 76 selected candidates form a well suited set of objects for further follow-up observations. We argue that selecting a high velocity dispersion is the best way to find analogues of compact high redshift galaxies in the local universe.
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