PHIBSS: Unified Scaling Relations of Gas Depletion Time and Molecular Gas Fractions

Abstract: This paper provides an update of our previous scaling relations (Genzel et al.2015) between galaxy integrated molecular gas masses, stellar masses and star formation rates, in the framework of the star formation main-sequence (MS), with the main goal to test for possible systematic effects. For this purpose our new study combines three independent methods of determining molecular gas masses from CO line fluxes, far-infrared dust spectral energy distributions, and ~1mm dust photometry, in a large sample of 1444 star forming galaxies (SFGs) between z=0 and 4. The sample covers the stellar mass range log(M*/M_solar)=9.0-11.8, and star formation rates relative to that on the MS, delta_MS=SFR/SFR(MS), from 10^{-1.3} to 10^{2.2}. Our most important finding is that all data sets, despite the different techniques and analysis methods used, follow the same scaling trends, once method-to-method zero point offsets are minimized and uncertainties are properly taken into account. The molecular gas depletion time t_depl, defined as the ratio of molecular gas mass to star formation rate, scales as (1+z)^{-0.6}x(delta_MS)^{-0.44}, and is only weakly dependent on stellar mass. The ratio of molecular-to-stellar mass mu_gas depends on (1+z)^{2.5}x (delta_MS)^{0.52}x(M*)^{-0.36}, which tracks the evolution of the specific star formation rate. The redshift dependence of mu_gas requires a curvature term, as may the mass-dependences of t_depl and mu_gas. We find no or only weak correlations of t_depl and mu_gas with optical size R or surface density once one removes the above scalings, but we caution that optical sizes may not be appropriate for the high gas and dust columns at high-z.

• The paper presents a unified model by merging CO, dust SED, and 1mm photometry data to analyze gas depletion time and molecular gas fractions across redshifts 0–4.
• It utilizes power-law functions to characterize dependencies on redshift, stellar mass, and deviation from the star-formation main sequence.
• The findings suggest a stable star formation efficiency over cosmic time, enhancing predictions for molecular gas content in distant galaxies.

Overview of "PHIBSS: Unified Scaling Relations of Gas Depletion Time and Molecular Gas Fractions"

The paper "PHIBSS: Unified Scaling Relations of Gas Depletion Time and Molecular Gas Fractions" represents a significant synthesis of observational data related to the molecular gas content in star-forming galaxies (SFGs) across a large range of redshifts from 0 to 4. The authors update previous scaling relations, particularly expanding on the work of Genzel et al. (2015), and provide a comprehensive analysis involving a large dataset comprising 1,444 measurements of molecular mass in galaxies. This dataset integrates measurements derived from CO line fluxes, far-infrared dust spectral energy distribution (SED) fits, and single-band dust photometry at 1 mm.

Key Findings and Methodology

• Scaling Relations: The study performs a multi-dimensional analysis of the scaling relations for gas depletion time, $t_{\text{depl}}$, and molecular gas fractions, $\mu_{\text{gas}}$, in connection with cosmic time (or redshift), stellar mass, and specific star formation rate (sSFR).
• Data and Method: Utilizing observations from different methodologies (CO lines, FIR dust SEDs, and 1mm dust photometry), the study reconciles these varying datasets by adjusting for zero-point offsets, ultimately achieving a unified model. The parameter dependencies are characterized using power-law functions in redshift, stellar mass, and deviation from the star-formation main sequence (MS).
• Redshift Dependency: For main-sequence galaxies, the depletion time scales as $(1+z)^{-0.62 \pm 0.13}$. A notable point of interest is the shallow evolution of this relation, suggesting that the processes governing star formation efficiency are relatively stable across cosmic time, albeit with nuanced redshift dependence.
• Mass and Size Dependency: The study examines the impact of stellar mass and optical size on gas depletion and identifies a minimal effect after controlling for sSFR and redshift. However, potential subtle dependencies could be masked due to observational uncertainties.

Implications

The findings have both practical and theoretical implications. Practically, the integration of gas mass scaling relations improves the robustness of molecular gas content predictions for distant galaxies, aiding in the design of future observational campaigns. Theoretically, the results emphasize a coherent picture of galaxy evolution where the molecular gas reservoir and star formation processes are intricately linked to the cosmic accretion of baryons. The study's conclusions challenge models that posit significant evolution in star formation efficiency over cosmic time, leaning towards models where internal processes within galaxies play a dominant role.

Future Directions

While the study's comprehensive integration of multiple datasets offers a consistent view of the molecular gas properties in galaxies, it highlights the need for further refinement in the gas mass determination techniques and calls for high-resolution mapping of molecular gas at various redshifts. Future advancements in sensitivity and spatial resolution of radio interferometry, like ALMA, will be essential to capture the details of gas dynamics and distribution within high-redshift galaxies.

Overall, this paper solidifies a framework for understanding the evolution of molecular gas reservoirs and star formation efficiency in galaxies throughout cosmic time, presenting a model that correlates well with multi-wavelength observational data and offers predictions for galaxy properties in the uncharted high-redshift Universe.