Making the circumgalactic-atmosphere regulator framework quantitative: contraction-triggered black-hole feedback, stability of contracted atmospheres, total feedback-energy measurement, phase-plane diagnostics, and the redshift evolution of the star-formation-efficiency peak

Voit et al. (2024) propose a 'minimalist regulator' framework in which the circumgalactic medium (CGM) of a galaxy is a galactic atmosphere whose equilibrium between cosmological accretion and feedback-driven outflow sets the galaxy's star-formation efficiency. They find that as mass loading declines with halo mass, atmospheres of halos above roughly $10^{12}\,M_\odot$ contract, raising the possibility that black-hole accretion is triggered by that contraction, and they propose a CGM specific-energy phase-plane diagnostic distinguishing contracted from expanded atmospheres. The paper's future-work discussion identifies five issues that must be resolved for this picture to become a quantitatively tested framework: (1) the model omits black-hole accretion energetics, so the contraction-trigger hypothesis cannot yet be tested quantitatively; (2) the stability and evolution of contracted equilibria under realistic time-varying CGM structural parameters are unknown, including when contraction runs away; (3) the total feedback specific energy $\varepsilon_{\rm fb}$ , dominated by a diffuse hot component, has never been measured in full for simulated or real outflows, which is required to distinguish preventative from ejective feedback empirically; (4) rigorous, reproducible algorithms for identifying a halo's CGM baryons and computing the CGM energy $E_{\rm CGM}$ in grid and particle simulations do not yet exist; and (5) the conjecture that opposing redshift trends of circular velocity $v_c(z)$ and star-formation surface density $\Sigma_{\rm SFR}(z)$ keep the star-formation-efficiency peak near $10^{12}\,M_\odot$ is untested.

Background

Galaxies form at the centers of dark-matter halos, yet only a small fraction of the cosmic baryons associated with a halo condense into stars. The star-formation efficiency $f_* = M_*/(f_{\rm b} M_{\rm halo})$ , the ratio of stellar mass to the baryon mass the halo should contain ( $f_{\rm b}$ is the cosmic baryon fraction), peaks at only $\sim 20\%$ for halos near $10^{12}\,M_\odot$ and falls off steeply on either side. Explaining this peak is a central problem of galaxy formation, and the standard invoked mechanism is feedback: energy and momentum injected by star formation (supernovae, stellar winds, radiation) and by accretion onto the central supermassive black hole heat or eject gas that would otherwise cool and form stars. Feedback is called preventative if it keeps gas hot and extended in the circumgalactic medium (CGM, the $\sim 10^6$ K diffuse gas extending to the halo's virial radius $R_{\rm halo}$ ), and ejective if it expels gas from the halo entirely. In the widely used 'regulator' or bathtub picture, a galaxy's interstellar medium reaches a quasi-steady state between cosmological inflow and feedback-driven outflow, with outflows characterized by mass loading $\eta_{\rm M}$ (outflow rate divided by star-formation rate) and energy loading $\eta_{\rm E}$ (fraction of supernova energy carried by the outflow). Voit et al. (2024, Papers I and II) extend this equilibrium regulator picture from the interstellar medium to the entire CGM, treating the CGM as a 'galactic atmosphere' in hydrostatic-like equilibrium whose structure is set by the balance between atmospheric heating (feedback plus cosmological accretion) and radiative cooling. Paper I ('The Flip Side of Mass Loading') shows that mass loading has a flip side: because the specific energy of a supernova-driven outflow, $\varepsilon_{\rm fb}$ (the energy carried per unit mass of outflowing gas), is diluted by mass loading, it can keep pace with the specific energy of gas accreting onto the halo, $\varepsilon_{\rm acc} \approx 4v_c^2$ (with $v_c$ the halo's circular velocity), only if mass loading declines steeply with halo mass; above the resulting borderline near $10^{12}\,M_\odot$ it cannot, and the atmosphere responds to rising energy input not by expanding but by contracting: less gas is expelled, and the remaining atmosphere becomes denser and more centrally concentrated. Paper II ('Interpretation and Implications') works out the consequences: a denser, contracted atmosphere feeds the central galaxy more rapidly and risks runaway star formation — a 'star-formation crisis' that supernova feedback alone cannot prevent beyond $\sim 10^{12}\,M_\odot$ — and it proposes that atmospheric contraction is what triggers the onset of strong black-hole feedback near $10^{12}\,M_\odot$ , which then intervenes to prevent that crisis and terminate star formation, thereby linking the fall of $f_*$ at high halo mass to the same physics that produces quiescent galaxies and active galactic nuclei. To make this picture testable, Paper II introduces a phase-plane diagnostic in which each halo's CGM is placed according to its baryon fraction $f_{\rm CGM} = M_{\rm CGM}/(f_{\rm b}M_{\rm halo})$ and mean specific energy $\varepsilon_{\rm CGM} = E_{\rm CGM}/M_{\rm CGM}$ , where the total CGM energy $E_{\rm CGM}$ sums gravitational potential energy (usually the dominant term, with the potential's zero point placed at the central galaxy), thermal energy, and kinetic energy (bulk flows plus turbulence), and the CGM mass $M_{\rm CGM}$ comprehensively accounts for the halo's accreted baryons that are neither in stars nor in the interstellar medium, including baryons pushed beyond the virial radius $R_{\rm halo}$ (a related diagnostic is the 'closure radius', the smallest radius within which the enclosed baryon fraction equals the cosmic value $f_{\rm b}$ ): the position of a halo's CGM in this plane relative to the accretion specific energy $\varepsilon_{\rm acc} \approx 4v_c^2$ distinguishes halos whose atmospheres have expanded ( $\varepsilon_{\rm CGM} > \varepsilon_{\rm acc}$ ) from halos whose atmospheres have contracted ( $\varepsilon_{\rm CGM} < \varepsilon_{\rm acc}$ ). Distinguishing ejective from preventative feedback instead relies on comparing $\varepsilon_{\rm fb}$ with $\varepsilon_{\rm acc}$ : values of $\varepsilon_{\rm fb}$ consistently exceeding $\varepsilon_{\rm acc} \approx 4v_c^2$ would signify feedback modes that need to be preventative in order to be effective, while a strong correlation between $\varepsilon_{\rm fb}$ and $v_c^2$ would favor ejective modes. The framework also explains the $f_*$ peak: below $10^{12}\,M_\odot$ halos, atmospheres expand and mass loading limits star formation; above it, contraction and black-hole feedback do. The peak's observed weak evolution with redshift $z$ is conjectured to arise from two countervailing trends — halo circular velocities $v_c(z)$ at fixed mass rise toward higher $z$ , so that a fixed borderline circular velocity for contraction would be reached at lower halo mass, pushing the peak down in mass, while star-formation surface densities $\Sigma_{\rm SFR}(z)$ also rise, raising the ratio $\eta_{\rm E}/\eta_{\rm M}$ and hence the borderline $v_c$ itself, pushing the peak back up toward $10^{12}\,M_\odot$ . The five open issues are exactly the gaps the authors identify between this conjectural picture and a quantitative, testable theory; they share one objective, converting the minimalist regulator framework from a plausible interpretation into a predictive and observationally constrained model of how galaxies are throttled near the critical halo mass $10^{12}\,M_\odot$ .

Problem Statement

The uniting objective, as stated by Voit et al. (2024, Paper II), is to convert the minimalist CGM-regulator picture — in which declining mass loading makes galactic atmospheres contract for $M_{\rm halo} \gtrsim 10^{12}\,M_\odot$ , and black-hole accretion triggered by that contraction terminates star formation — from a conjecture into a quantitatively tested framework. The paper's future-work discussion identifies five linked issues that must be resolved: (1) Extend the minimalist regulator model to include black-hole accretion energetics, predicting how accretion-powered feedback couples to the CGM, so that the hypothesis that black-hole feedback is triggered by atmospheric contraction can be tested quantitatively. (2) Determine the stability and evolution of the contracted atmospheric equilibria under realistic time-dependent variations of the CGM structural parameters $\mathbf{q}$ that set the regulator model's gas-supply rate (they fluctuate with cosmological accretion, cooling enhancements from metal enrichment, and structural changes in the CGM): in particular, under what conditions atmospheric contraction leads to a runaway. (3) Measure the total feedback specific energy $\varepsilon_{\rm fb}$ , including the diffuse hot component that carries most of the energy, for both simulated and real galactic outflows, so that preventative and ejective feedback modes can be distinguished empirically rather than by assumption. (4) Develop rigorous, reproducible algorithms for identifying a halo's CGM baryons and for computing $E_{\rm CGM}$ — fixing the gravitational-potential zero point and the treatment of baryons ejected far beyond $R_{\rm halo}$ — and implement them in both grid-based and particle-based simulations, so the phase-plane diagnostic becomes a standardized tool. (5) Quantitatively test the conjecture that the opposing redshift trends of circular velocity $v_c(z)$ and star-formation surface density $\Sigma_{\rm SFR}(z)$ combine to keep the peak of the star-formation efficiency $f_*$ near $M_{\rm halo} \sim 10^{12}\,M_\odot$ , producing the observed weak redshift evolution of that peak. Each of (1)–(5) is an independently open sub-question: resolving any one of them on its own constitutes a valid resolution of this task, with the remaining issues left open.

References

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