An Observed Evidence for the Primordial Origin of Galaxy Sizes

TL;DR

The paper addresses whether present galaxy optical sizes $r_{50}$ and $r_{90}$ retain memory of primordial angular momentum encoded in the spin factor $\tau$. Using the NASA-Sloan Atlas for $0.02 \le z < 0.09$, it derives $p(r_{50})$ and $p(r_{90})$ across three stellar-mass bins, finding bimodal Gamma mixtures overall but unimodal Gamma behavior for late-type galaxies with $r_{50}/r_{90} \ge 0.45$. It then adopts a linear $r$–$\tau$ relation $\tau = \alpha (r - r_{min})$ with $\alpha$ Gaussian, reconstructing $p(\tau)$ via $p(\tau) = \int p(r, \alpha) \, d\alpha$, using Gamma fits to $p(r)$ and slopes from simulations. The reconstructed $p(\tau)$ matches the protogalactic distributions from prior work (ML24b) in both shape and scale dependence, providing observational evidence for a causal link between primordial angular momentum and present galaxy sizes and suggesting the feasibility of reconstructing initial tidal fields from size data. This motivates future efforts to recover $\tau$-fields on galactic scales.

Abstract

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 $50\%$ and $90\%$ 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, $r_{50}/r_{90}$, we also show that for the case of late-type galaxies with $r_{50}/r_{90}\ge 0.45$ 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, $τ$, defined as the degree of misalignments between the initial tidal and protogalaxy inertia tensors, we reconstruct the probability density distributions, $p(τ)$, directly from the observationally determined $p(r_{50})$ and $p(r_{90})$ of the late-type galaxies. It is shown that the reconstructed $p(τ)$ is in an excellent agreement with the real distribution of $τ$ 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.

Figures (4)

• Figure 1: Scatter plots of the redshifts and the half-light sizes of the NASA-Sloan-Atlas galaxies in three different stellar-mass ranges, with the locations of two redshift cutoffs, $z_{\rm min}$ and $z_{\rm max}$ (vertical red lines) applied to exclude those galaxies the angular sizes of which are smaller than the photometry seeing at $z_{\rm max}$ (horizontal red lines).
• Figure 2: Probability density distributions of the half-light sizes of the selected local galaxies (red filled circles with Poisson errors) from the NASA-Sloan-Atlas catalog along with the best-fit Gamma mixture model (black thick solid lines) composed of two distinct modes (black thin solid lines) in three different stellar-mass ranges for three different cases of galaxy light concentrations, $r_{50}/r_{90}$.
• Figure 3: Same as Fig. \ref{['fig:pro50']} but of the $90\%$-light sizes.
• Figure 4: Reconstructed probability density distributions of the primordial spin factor from those of the observed galaxy optical sizes via Eq. (\ref{['eqn:ptau_re']}) in three different $m_{\star}$ ranges. The reconstructed distributions match the real ones determined by numerical simulations directly from protogalactic inertia and initial tidal fields smoothed on three different scales.