Abstract We present here a new and homogeneous sample of 3340 galaxies selected from the Sloan Digital Sky Survey (SDSS) based solely on the observed strength of their $\mathrm{H}\delta$ hydrogen Balmer absorption line. The presence of a strong $\mathrm{H}\delta$ line within the spectrum of a galaxy indicates that the galaxy has undergone a significant change in its star-formation history within the last Gigayear. Therefore, such galaxies have received considerable attention in recent years, because they provide an opportunity to study galaxy evolution in action. These galaxies are commonly known as “post-starburst”, “E$+$A”, “k$+$a”, and $\mathrm{H}\delta$-strong galaxies. Their study has been severely hampered by the lack of a large, statistical sample of such galaxies. In this paper, we rectify this problem by selecting a sample of galaxies which possess an absorption $\mathrm{H}\delta$ equivalent width of $\mathrm{EW}(\mathrm{H}\delta_{\mathrm{max}})-\Delta \mathrm{EW}(\mathrm{H}\delta_{\mathrm{max}}) \gt 4 \,{Å}$$\mathrm{EW}(\mathrm{H}\delta_{\mathrm{max}})-\Delta \mathrm{EW}(\mathrm{H}\delta_{\mathrm{max}}) \gt 4 \,$Å from 106682 galaxies in the SDSS. The measured abundance of our $\mathrm{H}\delta$-strong (HDS) galaxies is $2.6 \pm 0.1 \%$ of all galaxies within a volume-limited sample of $0.05 < z < 0.1$ and $M_{r^{*}} <-20.5$, which is consistent with previous studies of such galaxies described in the literature. We find that only 25 of our HDS galaxies in this volume-limited sample ($3.5 \pm 0.7\%$) show no, or little, evidence for [O II] and $\mathrm{H}\alpha$ emission lines, thus indicating that true E$+$A galaxies (as originally defined by Dressler and Gunn) are extremely rare objects at low redshift, i.e., only $0.09 \pm 0.02\%$ of all galaxies in this volume-limited sample are true E$+$A galaxies. In contrast, $89 \pm 5\%$ of our HDS galaxies in the volume-limited sample have significant detections of the [O II] and $\mathrm{H}\alpha$ emission lines. Of these, only 131 galaxies are robustly classified as Active Galactic Nuclei (AGNs) and, therefore, a majority of these emission-line HDS galaxies are star-forming galaxies. We find that $52 \pm 12\%$ ($27/52$) of the galaxies in our volume-limited HDS sample that possess no detectable [O II] emission, do however possess detectable $\mathrm{H}\alpha$ emission lines. These may be dusty star-forming galaxies. We provide the community with this new catalog of $\mathrm{H}\delta$-strong galaxies to aid in our understanding of these galaxies, via detailed follow-up observations, as well as providing a low-redshift sample for comparison with higher redshift studies of HDS galaxies.
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