Cloud-scale gas properties, depletion times, and star formation efficiency per free-fall time in PHANGS--ALMA

This study analyzes 67 galaxies in the PHANGS-ALMA survey to reveal how cloud-scale gas properties, particularly gas surface density and virial parameter, influence molecular gas depletion times and star formation efficiency, while highlighting the sensitivity of these results to CO-to-H2 conversion factors and their potential for comparison with numerical simulations.

The Gist

Imagine a galaxy as a giant, bustling city. In this city, the "buildings" are stars, and the "construction materials" are clouds of molecular gas. For decades, astronomers have known that where there is more gas, there are usually more stars being built. But a big mystery remained: How exactly does the nature of the gas cloud affect how fast and efficiently it turns into stars?

Is it like a pile of bricks that collapses instantly under its own weight? Or is it a pile of bricks held together by a chaotic wind, making it hard to build anything?

This paper, by Adam Leroy and a massive team of collaborators, uses a powerful new telescope (ALMA) to look at 67 nearby galaxies in extreme detail. They didn't just look at the whole galaxy; they zoomed in to look at individual "construction sites" (clouds) and asked: What makes some clouds build stars quickly, while others sit idle?

Here is the breakdown of their findings using simple analogies.

1. The Setup: Measuring the "Construction Sites"

The team divided these galaxies into thousands of small neighborhoods (about 1.5 kilometers across). In each neighborhood, they measured two main things:

• The Depletion Time ($\tau_{dep}$): How long it would take for the current supply of gas to run out if the stars kept being born at the current speed. (Think of this as the "fuel gauge" for the construction crew).
• The Efficiency ($\epsilon_{ff}$): How good the gas is at turning itself into stars compared to how fast it should collapse under gravity. (Think of this as the "skill level" of the construction crew).

They then compared these numbers to the physical properties of the gas clouds themselves:

• Density: How packed the gas is.
• Turbulence (Speed): How chaotic and fast-moving the gas is.
• Virial Parameter: A fancy way of asking, "Is this cloud held together by its own gravity, or is it flying apart?"

2. The Big Surprise: Gravity Isn't the Only Boss

The Theory: Astronomers used to think that if a gas cloud was very dense and tightly held together by its own gravity (low "Virial Parameter"), it would collapse and make stars very efficiently. If it was loose and chaotic, it would make few stars.

The Reality: The data showed the opposite in the centers of galaxies!

• The Finding: In the busy, crowded centers of galaxies, the gas clouds were actually less tightly bound by their own gravity (high Virial Parameter), yet they were forming stars super efficiently.
• The Analogy: Imagine a construction site in a city center. You might expect the building to be held together by its own bricks (self-gravity). But instead, the whole city is shaking and pushing the bricks together (the gravity of the surrounding city/stars). The gas isn't collapsing because it is heavy; it's collapsing because the entire galaxy is squeezing it.
• The Lesson: In the centers of galaxies, the "neighborhood pressure" (stellar gravity) is so strong that it forces the gas to make stars, even if the gas cloud itself looks like it's falling apart.

3. The "Speed Limit" of Star Formation

The team found a very clear rule: Denser gas makes stars faster.

• The Analogy: Think of gas density like the traffic on a highway. If the cars (gas molecules) are packed tightly together, they are more likely to bump into each other and form a pile-up (a star). If they are spread out, they rarely meet.
• The Result: The time it takes to use up the gas (depletion time) gets shorter as the gas gets denser. This makes sense, but the team found the relationship wasn't as simple as a straight line. It's a bit more complex, suggesting that while density is key, other factors (like the "starburst" effect in busy centers) speed things up even more.

4. The "Secret Ingredient": The Conversion Factor

One of the most important parts of this paper is a warning about how we measure gas.

• The Problem: We can't see the gas directly; we see a tracer (Carbon Monoxide, or CO) and have to guess how much actual Hydrogen gas is there. This guess is called the "conversion factor" ($\alpha_{CO}$).
• The Twist: In the busy centers of galaxies, the gas is so hot and bright that it glows more efficiently. If you use a "standard" conversion factor (like the one used for the quiet Milky Way), you will underestimate how much gas is there.
• The Impact: When the team corrected for this "glow" (using a new, smarter conversion factor), the results changed dramatically. The gas in the centers looked even denser, and the star formation looked even more efficient. Without this correction, the whole picture looks wrong.

5. The "Chaos" Factor (Velocity Dispersion)

The team also looked at how fast the gas is moving (turbulence).

• The Finding: They found a strong link between how fast the gas is moving and how fast stars are forming.
• The Analogy: Imagine a blender. If you turn it on high (high turbulence), the ingredients mix fast. In galaxies, the "blender" speed (gas velocity) is actually a good predictor of how fast stars are being made. Surprisingly, this relationship held up even better than the relationship with the "gravity" of the cloud. It suggests that the energy in the gas is a major driver of star formation.

6. The Takeaway: Why This Matters

This paper is a massive step forward because it uses the largest, most uniform dataset ever assembled for this kind of study.

• For Simulations: The authors say, "Hey, computer modelers! Here is a clean, simple set of rules and numbers. Try to build a simulation that matches this." They provided a "checklist" so other scientists can easily compare their computer models to real life.
• For Understanding: It tells us that star formation isn't just about a single cloud collapsing in isolation. It's about the whole galaxy environment. The pressure from the galaxy's center, the heat from nearby stars, and the chaotic motion of the gas all work together to decide when and where stars are born.

In a nutshell:
Stars form faster when the gas is dense and the galaxy is "squeezing" it. The old idea that "only self-gravity matters" is too simple. The environment of the galaxy is the real boss, and to understand it, we have to be very careful about how we measure the invisible gas.

Technical Summary

1. Problem Statement

The fundamental question driving this research is: How do the initial physical properties of parent molecular clouds affect the efficiency and rate of star formation?

While theory and simulations suggest that cloud properties (density, velocity dispersion, virial parameter) should dictate star formation rates, observational evidence across large galaxy samples has been mixed or weak. Previous studies often focused on single galaxies or specific prototypes, lacking the statistical power to distinguish between universal physical laws and environmental variations. Furthermore, there is a need to bridge the gap between "cloud-scale" physics (~100 pc) and "galaxy-scale" star formation rates (kpc scales) to test theoretical models of turbulence-regulated star formation.

2. Methodology

The authors utilize the PHANGS–ALMA survey, the largest homogeneous dataset of molecular gas in nearby galaxies, to perform a cross-scale analysis.

• Sample: 67 massive, star-forming disk galaxies (log$_{10} M_*$ > 9.75) within 20 Mpc.
• Spatial Resolution:
  • Cloud-scale: 150 pc (FWHM) resolution using CO (2-1) emission to trace molecular gas.
  • Regional Scale: The galaxies are divided into 1.5 kpc diameter hexagonal regions.
• Data Processing:
  • Mass-Weighted Averaging: Within each 1.5 kpc region, cloud-scale properties (surface density $\Sigma_{mol}$, velocity dispersion $\sigma_{mol}$, free-fall time $\tau_{ff}$, virial parameter $\alpha_{vir}$) are calculated for individual lines of sight where CO is detected. These are then averaged using a mass-weighting scheme (weighted by local gas surface density) to derive region-averaged cloud properties ($\langle X_{cloud} \rangle$).
  • Star Formation Rate (SFR): Calculated using a combination of H$\alpha$ (narrowband) and WISE 22$\mu$m (mid-IR) data to minimize dust extinction uncertainties.
  • CO-to-H$_2$ Conversion ($\alpha_{CO}$): A critical component of the methodology is the adoption of a variable $\alpha_{CO}$ prescription (Schinnerer & Leroy 2024) that accounts for metallicity, excitation, and emissivity variations (particularly in high surface density inner regions), rather than a fixed Galactic value.
• Key Metrics Calculated:
  • Molecular Gas Depletion Time: $\tau_{dep}^{mol} = \Sigma_{mol} / \Sigma_{SFR}$ (time to consume gas at current SFR).
  • Star Formation Efficiency per Free-Fall Time: $\epsilon_{ff}^{mol} = \tau_{ff} / \tau_{dep}^{mol}$ (efficiency relative to gravitational collapse).
• Selection Criteria: Regions are selected if the CO flux completeness ($f_{comp}$) > 50% and the mass-weighted mean cloud surface density $\langle \Sigma_{cloud}^{mol} \rangle > 20 M_\odot \text{pc}^{-2}$, ensuring robust cloud-scale measurements.

3. Key Contributions

• Systematic Cross-Scale Analysis: This is the first systematic attempt to correlate cloud-scale gas properties with star formation efficiency across a large, representative sample of 67 galaxies (841 regions).
• Methodological Standardization: The paper provides a reproducible "recipe" (Appendix A) for comparing observational data with numerical simulations, specifically addressing how to handle mass-weighted averages and resolution effects.
• Variable $\alpha_{CO}$ Impact: The study rigorously demonstrates how the choice of the CO-to-H$_2$ conversion factor fundamentally alters the observed correlations, highlighting the necessity of accounting for excitation and emissivity variations in inner galaxies.

4. Key Results

A. Depletion Time vs. Free-Fall Time

• Positive Correlation: There is a positive correlation between the molecular gas depletion time ($\tau_{dep}^{mol}$) and the gravitational free-fall time ($\langle \tau_{ff}^{cloud} \rangle$).
• Slope: The best-fit relation is $\tau_{dep}^{mol} \propto \langle \tau_{ff}^{cloud} \rangle^{0.5}$, which is shallower than the linear expectation ($\tau_{dep} \propto \tau_{ff}$) for a fixed efficiency.
• Efficiency: The median star formation efficiency per free-fall time is $\epsilon_{ff}^{mol} \approx 0.39\%$, with a scatter of $\sim 0.3$ dex (factor of 2).
• Galaxy-to-Galaxy Scatter: Normalizing by galaxy-average values sharpens the correlation, indicating that roughly half the scatter is due to global galaxy properties (e.g., mass, metallicity) and half is intrinsic to the regions.

B. Anti-Correlations with Density and Velocity Dispersion

• Surface Density: $\tau_{dep}^{mol}$ anti-correlates with cloud-scale surface density ($\langle \Sigma_{cloud}^{mol} \rangle$).
• Velocity Dispersion: $\tau_{dep}^{mol}$ anti-correlates with cloud-scale velocity dispersion ($\langle \sigma_{cloud}^{mol} \rangle$).
• Interpretation: These anti-correlations are consistent with the idea that higher density gas collapses faster. The $\tau_{dep}$ vs. $\langle \sigma_{cloud}^{mol} \rangle$ relation is highlighted as particularly robust because it is less sensitive to the $\alpha_{CO}$ conversion factor and resolution effects than surface density measurements.

C. The Virial Parameter Anomaly

• Contrary to Theory: Theoretical models predict that gas with a lower virial parameter ($\alpha_{vir}$, indicating stronger self-gravity) should form stars more efficiently (lower $\tau_{dep}$).
• Observation: The authors find a weak anti-correlation (or no significant correlation) between $\tau_{dep}^{mol}$ and $\langle \alpha_{vir}^{cloud} \rangle$. In fact, regions with higher $\alpha_{vir}$ (less self-bound) often show shorter depletion times (higher efficiency).
• Explanation: This is attributed to the dominance of stellar gravity in the inner regions of galaxies. In these high-density environments, the gas is bound by the galactic potential (stars) rather than its own self-gravity. Since $\alpha_{vir}$ is calculated using only gas self-gravity, it fails to capture the true dynamical state, leading to high $\alpha_{vir}$ values in regions that are actually efficiently forming stars due to external pressure and stellar potential.

D. The Critical Role of $\alpha_{CO}$

• Sensitivity: The results are highly sensitive to the CO-to-H$_2$ conversion factor.
• Fixed vs. Variable: If a fixed Galactic $\alpha_{CO}$ is used, the correlations between $\tau_{dep}$ and gas properties disappear or reverse (e.g., $\tau_{dep}$ appears longer in high-density regions).
• Conclusion: The inclusion of excitation and emissivity corrections (which lower $\alpha_{CO}$ in high surface density inner regions) is essential to recover the physically expected trends where dense gas forms stars faster.

5. Significance and Future Directions

• Benchmark for Simulations: The paper provides a clean, reproducible set of measurements (Table 2) that numerical simulations can directly compare against. The authors argue that simulations should be able to reproduce these specific scaling relations if they correctly model the interplay between gas physics, stellar feedback, and galactic potentials.
• Reconciling Theory and Observation: The results suggest that simple turbulence-regulated star formation models (which assume isolated clouds) are insufficient. The dynamical state of molecular gas in real galaxies is heavily influenced by the large-scale galactic potential (stellar gravity), which must be included in theoretical frameworks.
• Next Steps: The authors emphasize the need for:
  1. Direct comparisons with simulations using the provided methodology.
  2. Higher resolution observations ($\lesssim 10$ pc) to resolve individual cloud dynamics and reduce ambiguity in velocity dispersion measurements.
  3. Improved SFR tracers (e.g., IFU H$\alpha$) to reduce uncertainties in $\tau_{dep}$.
  4. Better constraints on $\alpha_{CO}$, which remains the largest systematic uncertainty in the field.

In summary, this paper establishes that while cloud-scale gas density is a primary driver of star formation rates, the efficiency of this process is modulated by the galactic environment, particularly stellar gravity, and is critically dependent on accurate molecular gas mass estimates via variable $\alpha_{CO}$.