An Observed Evidence for the Primordial Origin of Galaxy Sizes

We present an observational evidence supporting the scenario that the protogalactic angular momenta play an important role in molding the optical sizes of present galaxies. Analyzing the NASA-Sloan Atlas catalog in the redshift range of $0.02\le z<0.09$, we observationally determine the probability density distributions, $p(r_{50})$ and $p(r_{90})$, where $r_{50}$ and $r_{90}$ denote the galaxy sizes enclosing $50\mathrm{\%}$ and $90\mathrm{\%}$ of their $r$-band luminosities, respectively. Both of the distributions are found to be well described by a bimodal Gamma mixture model, which is consistent with the recent numerical results. Classifying the local galaxies by their ratios, $r_{50}\mathrm{/}{r}_{90}$, we also show that for the case of late-type galaxies with $r_{50}\mathrm{/}{r}_{90}\ge 0.45$ both of $p(r_{50})$ and $p(r_{90})$ exhibit no bimodal feature, following a unimodal Gamma model. Assuming the existence of a linear causal correlation between $\{r_{50},r_{90}\}$ of the late-type galaxies and the primordial spin factor, $\tau$, defined as the degree of misalignments between the initial tidal and protogalaxy inertia tensors, we reconstruct the probability density distributions, $p(\tau )$, directly from the observationally determined $p(r_{50})$ and $p(r_{90})$ of the late-type galaxies. It is shown that the reconstructed $p(\tau )$ is in an excellent agreement with the real distribution of $\tau$ that was determined at the protogalactic stages by numerical experiments. A critical implication of our result on reconstructing the initial conditions from observable galaxy sizes is discussed.