The link between star formation and gas in nearby galaxies

The study investigates how star formation in galaxies is linked to their interstellar medium, specifically neutral (HI) and molecular (H2) gas masses, and how observational biases affect inferred relations. Building on the known star-forming sequence (SFS), which correlates star formation rate (SFR) with stellar mass, and the empirical molecular Kennicutt–Schmidt relation linking SFR surface density to molecular gas, the paper addresses whether star formation in typical nearby galaxies is primarily regulated by the amount of gas available or by variations in the efficiency of converting molecular gas into stars. The purpose is to re-analyze representative nearby galaxy samples using a Bayesian approach that accounts for detection limits, missing data, and measurement uncertainties, thereby clarifying the intrinsic scaling relations and the role of gas accretion and outflows in regulating star formation.

Prior work established a relatively tight and redshift-dependent SFR–stellar mass relation (the SFS), suggesting common star formation behavior among star-forming galaxies and likely connections to gas accretion and halo growth. Observations on sub-kpc scales and globally have shown strong correlations between SFR and molecular gas (the Kennicutt–Schmidt relation), interpreted as both processes requiring cold, dense gas. Large surveys (xGASS, xCOLD GASS) enabled studies of neutral and molecular gas across representative nearby samples. Several analyses reported that molecular gas depletion time varies with offset from the SFS (with an approximate slope of −0.5), implying changing conversion efficiencies, potentially due to ISM processes such as turbulence. However, these interpretations are vulnerable to selection effects because many galaxies have gas or SFR measurements below detection thresholds. Bayesian and hierarchical methods have been advocated to mitigate biases from measurement error, censoring, and non-detections.

Data: The analysis combines two surveys of nearby (0.01 < z < 0.05) galaxies: xGASS (1179 galaxies with stellar masses ~10^9–10^11.5 M⊙, providing HI and SFRs) and xCOLD GASS (532 galaxies with similar redshift/mass distribution, providing CO-based H2). The catalogs are outer-joined via GASS IDs, yielding 1234 galaxies. Updated SDSS DR7 median stellar masses (with ~0.08–0.1 dex uncertainties for >80% of galaxies) replace original values. Two working subsamples are used: a representative xGASS/xCOLD GASS sample of 1012 galaxies (nominally spanning 9 ≤ log M⋆ ≤ 11) and an extended sample of 1066 galaxies including 54 additional sources with H2 information, many of which are starbursts. Handling uncertainties and censoring: About 30% of SFRs lack reported uncertainties; uncertainties are imputed via regression on SFR and M⋆. SFRs below their uncertainty are treated as censored. HI and H2 non-detections are assigned measurement errors based on catalog limits (HI: 1/5 of 5σ; H2: 1/3 of 3σ). Missing entries are assumed Missing At Random. Statistical model: At fixed stellar mass, the true joint distribution of SFR, M_HI, and M_H2 is modeled as a two-component mixture: (i) a discrete zero-component for galaxies with vanishing SFR and gas masses; (ii) a continuous component for all others. The continuous joint distribution is constructed with a Gaussian copula capturing correlations via a 3×3 correlation matrix and arbitrary one-dimensional marginals. Each marginal (SFR, HI, H2) is modeled as a mixture of two gamma distributions: a dominant component for typical star-forming galaxies (parameters α_SF, β_SF) and a sub-dominant high-SFR/gas outlier component (α_out, β_out) with fraction f_out. The peak (mode) of the main gamma component defines the SFS, NGS, and MGS at a given M⋆. Stellar-mass dependences of the primary gamma parameters are modeled as linear functions of log M⋆ (parameterized by slope angles and perpendicular distances), while α_out, β_out, and f_out are held independent of M⋆. The zero-component fraction π0 depends on M⋆ via a logistic function with linear logit. Inference: Likelihoods accounting for correlated errors, censoring, and missingness are computed with LEO-Py. Very weak, bounded uniform priors are adopted. Posterior sampling uses the affine-invariant MCMC ensemble sampler emcee with 1720 walkers for 15,000 steps (first 4000 as burn-in), run in parallel (MPI on 864 cores). For computational efficiency, stellar mass measurement uncertainties are ignored, shown to have negligible impact on results. Derived constructs: The study defines the star-forming plane (SFP) by measuring Δ log SFR, Δ log M_HI, Δ log M_H2 relative to the peaks of SFS/NGS/MGS and performing a principal component analysis within probability isosurfaces (10/50/90%) sampled from the model using marching cubes. Mock catalogs are generated by drawing M⋆ from the observed distribution, sampling the model’s joint distribution, adding observational errors from regressions, and applying survey detection limits to compare apparent (mock) to intrinsic (true) distributions. Analytic evolutionary modeling: A simplified model links SFR to total gas mass via SFR(t) = M_gas(t)/t_dep(M⋆, SFR, t), with t_dep = t_dep,H2/f_H2 estimated empirically from SFS/NGS/MGS and t_dep,H2 ∝ SFR^−0.24. Two scenarios are considered: (i) approximately constant M_gas (equilibrium); (ii) time-dependent M_gas with downsizing (earlier peaks and faster declines in more massive systems).

• Intrinsic scaling relations (representative sample):
  • Star-forming sequence (SFS) slope ≈ 0.54 with upward/downward scatter at M⋆ ~ 10^10 M⊙ of +0.38 dex / −0.53 dex.
  • Neutral gas sequence (NGS) slope ≈ 0.33 with similar scatter to SFS.
  • Molecular gas sequence (MGS) slope ≈ 0.69 with the lowest scatter (~0.31 dex). The steeper, tighter MGS suggests SFS may arise from correlations between M_H2–M⋆ and SFR–M_H2.
• Star-forming plane (SFP): When SFR, M_HI, and M_H2 are measured relative to their respective sequences, galaxies populate an approximately two-dimensional plane whose orientation is nearly independent of stellar mass. The SFR–M_H2 projection is close to an edge-on view of this plane and corresponds to a tight, intrinsic molecular Kennicutt–Schmidt relation.
• Importance of bias modeling: Apparent (mock) versus intrinsic (true) relations differ substantially due to censoring and errors; omission of non-detections steepens the observed SFR–M_H2 relation because low M_H2 galaxies are preferentially censored.
• Depletion times versus SFS offset (extended sample):
  • Observationally (detections and mocks), t_dep,H2 appears to scale roughly as ∝ SFR^−0.5, consistent with prior literature. However, the model-predicted intrinsic scaling for typical offsets (−0.5 to 0.5 dex) is significantly shallower: t_dep,H2 ∝ SFR^−0.24 and total-gas depletion time t_dep,tot ∝ SFR^−0.32.
  • For non-starbursting galaxies (Δ log SFR ≲ 0.6–0.7), the molecular depletion time varies weakly with SFR and M⋆; in starbursts (≥0.6–0.7 dex above SFS), the slope steepens (α2 ≈ −0.68 ± 0.11), indicating elevated efficiency.
  • Uncertainty quantification at M⋆ ≈ 10^10 M⊙ yields a median slope α1 ≈ −0.25 with 2σ range roughly −0.34 to −0.13.
• Empirical formulae for typical star-forming galaxies:
  • t_dep,H2(M⋆, SFR) = 0.87 Gyr (M⋆/10^10 M⊙)^0.15 (SFR_SFS/SFR)^0.28 ≈ 0.79 Gyr (M⋆/10^10 M⊙)^0.28 (SFR / Myr^−1)^−0.24.
  • M_H2(M⋆, SFR) = 7.9×10^8 M⊙ (M⋆/10^10 M⊙)^0.28 (SFR / Myr^−1)^0.76. These suggest no explicit redshift dependence of t_dep,H2 once M⋆ and SFR are given, consistent with observed trends when accounting for the redshift evolution of the SFS normalization.
• Gas content as primary driver: Variations in molecular and total gas masses track changes in SFR across the SFS; molecular-to-neutral ratios are roughly constant across the SFS at fixed M⋆ but increase with M⋆ (MGS slope > NGS slope). Starbursts’ elevated SFRs are linked to higher conversion efficiency rather than solely larger gas reservoirs.
• Evolutionary implications: A constant M_gas equilibrium model predicts linear SFS and disagrees with observed sub-linear slopes. A downsizing M_gas model reproduces sub-linear slopes of SFS/NGS/MGS, late-time quenching trends, and steeper high-z slopes, aligning qualitatively with observations.

The analysis shows that, for typical nearby star-forming galaxies, SFRs are tightly coupled to molecular and total gas masses, while the molecular gas depletion time varies only weakly with SFR and stellar mass. This addresses the central question by indicating that star formation activity is regulated primarily by processes that set the total gas content—such as cosmological inflows, cooling, fountains, and feedback-driven outflows—rather than large variations in the efficiency of converting molecular gas into stars. The approximately universal star-forming plane, largely independent of stellar mass, encapsulates these correlations and supports a picture where gas supply and removal govern galaxy-wide SFRs. Starbursts lie above the SFS with steeper depletion-time scalings, consistent with episodic boosts in conversion efficiency likely tied to ISM state changes from mergers or instabilities. The derived redshift-invariant forms for t_dep,H2 and M_H2 as functions of M⋆ and SFR suggest a unified framework wherein the observed redshift evolution of scaling relations arises predominantly from evolving SFS normalizations linked to halo accretion histories.

This work introduces a multi-dimensional Bayesian framework that corrects for detection limits, uncertainties, and missing data to infer intrinsic relationships among SFR, HI, and H2 in nearby galaxies. Key contributions include: (i) precise intrinsic slopes and scatters of the SFS, NGS, and MGS; (ii) identification of an approximately stellar-mass-independent star-forming plane; (iii) demonstration that molecular and total gas depletion times in normal star-forming galaxies depend only weakly on SFR and M⋆, with stronger efficiency variations confined to starbursts; and (iv) empirical formulae linking t_dep,H2 and M_H2 to M⋆ and SFR without explicit redshift dependence. These findings favor a gas-supply regulation of star formation in typical galaxies and provide constraints on galaxy gas accretion histories. Future work should extend this Bayesian, multi-dimensional approach to larger, representative high-redshift samples, integrate multi-observatory constraints (e.g., ALMA, radio continuum, future HI with SKA pathfinders), and refine systematics (conversion factors, aperture/beam corrections) to map the evolution of the SFP and depletion times across cosmic time.

Results may be affected by: (i) modeling choices for marginal distributions (gamma versus lognormal) which slightly shift inferred slopes (e.g., α1 from −0.25 to −0.22) and change SFS/NGS/MGS slopes by up to ~0.1; (ii) observational systematics including CO–H2 conversion factors, flux aperture corrections, beam-size matching, and SFR calibrations; (iii) use of catalog data as provided and assumptions about missingness (MAR); (iv) ignoring stellar mass uncertainties during MCMC for computational efficiency (shown to have minimal impact); and (v) applicability limited to nearby galaxies, with potential selection biases and censored data influencing naive (non-modeled) trends. While these do not qualitatively alter the conclusions, they introduce uncertainties in quantitative parameters.