Model-Independent Inference of Galaxy Star Formation Histories in the Local Volume

TL;DR

The paper addresses the limitation of fixed-parametric SFH templates by developing a model-independent framework to infer galaxy star formation histories in the Local Volume. It generates $10^4$ randomized SFHs per galaxy on a common $t$-grid and filters them to match observed present-day and time-averaged SFRs, yielding distributions for the SFH slope $\eta$ and the half-mass formation time $t_{50}$. The results show that most LV galaxies favor flat or rising SFHs (≈70% with $|\eta|\leq0.01$), with strong, monotonic correlations between $\eta$, $t_{50}$ and the SFR ratio $R = SFR_0/\langle SFR \rangle$; $t_{50}$ clusters near 7.72–7.86 Gyr, and there is only a weak dependence on stellar mass. This data-driven approach challenges traditional declining SFH templates and provides a scalable method to infer SFHs without assuming a functional form, with potential applications to higher-redshift samples and additional observational constraints.

Abstract

Understanding the diversity of star formation histories (SFHs) of galaxies is key to reconstructing their evolutionary paths. Traditional models often assume parametric forms such as delayed-tau or exponentially declining models, which may not reflect the actual variety of formation processes. We aim to assess what types of SFHs are consistent with the observed present-day star formation rates (${\text{SFR}}_0$) and time-averaged star formation rates ($\langle \text{SFR} \rangle$) of galaxies in the Local Volume, without assuming any fixed functional form. We construct a non-parametric framework by generating large ensembles of randomized SFHs for each galaxy in the sample. For each SFH, we compute its predicted stellar mass and present-day SFR and retain only those consistent with the observed values within a 20% tolerance. We then infer the statistical distribution of power-law slopes $η$ (fitted as ${\text{SFR}}(t) \propto (t-t_{\text{start}})^η$) and 50% stellar mass formation times $t_{50}$. Both $η$ and $t_{50}$ correlate strongly with the SFR ratio (Spearman $ρ> 0.75$, $p \ll 10^{-16}$), indicating that the shape and timing of star formation are primarily governed by this ratio. The $t_{50}$ distribution shows sharp spikes near 7.74 and 7.86 Gyr, which we attribute to grid discretization combined with filtering, rather than a physical bimodality. Our results confirm that strongly declining SFH templates are disfavored in the Local Volume: most systems are consistent with flat long-term SFHs, with only mild decline or occasional rising. Importantly, this is demonstrated through a fully model-independent, data-driven approach, with per-galaxy uncertainties quantified using the standard error of $η$ and $t_{50}$ from the ensemble of accepted SFHs.

Figures (11)

• Figure S1: Fraction of galaxies classified as flat, declining, or rising SFHs based on the median slope $\eta$. Flat is defined as $|\eta|\leq0.01$, declining as $\eta<-0.01$, and rising as $\eta>0.01$. These thresholds reflect a tolerance zone that prevents tiny fluctuations from being misclassified as trends. The left panel is for all galaxies while the right panel is for galaxies with $M_{*} < 3 \times 10^{9} M_{\odot}$
• Figure S2: Distribution of median SFH slope $\eta$ across the galaxy sample. The distribution peaks near $\eta = 0$, indicating that flat SFHs are statistically dominant. A small tail toward negative $\eta$ suggests that moderately declining SFHs are possible for some galaxies, but strongly declining or rising histories are rare. The histogram contains 555 galaxies (see Section \ref{['sec:3']})
• Figure S3: Distribution of $t_{50}$ values across the galaxy sample. The strong peaks near $t_{50}$$\approx$ 7.72 and 7.86 Gyr indicates that most galaxies formed half of their stellar mass relatively late in cosmic time. The~discrete structure arises from resolution limits in the time grid, but~the concentration toward recent formation is~robust. The histogram contains 555 galaxies (see Section \ref{['sec:3']}).
• Figure S4: Scatter plot of the 555 median SFH slope $\eta$ for each galaxy versus the observed SFR ratio $R = \mathrm{SFR}_0 / \langle\mathrm{SFR}\rangle$ (from 2020MNRAS.497...37K). Each point represents the median $\eta$ from the ensemble of accepted SFHs for that galaxy; medians are used because the underlying $\eta$ distributions are often skewed. Galaxies with higher $R$ tend to exhibit rising SFHs.
• Figure S5: Formation time $t_{50}$ versus $R = \mathrm{SFR}_0 / \langle\mathrm{SFR}\rangle$ (from 2020MNRAS.497...37K). Points show median $t_{50}$ values per galaxy with $\pm\sigma_{\mathrm{med}}$ (standard error of the median) as vertical error bars; higher-$R$ galaxies form their stellar mass later.