Gas Scale Height Research Articles

Toward Implementation of the Pressure-regulated, Feedback-modulated Model of Star Formation in Cosmological Simulations: Methods and Application to TNG

Traditional star formation subgrid models implemented in cosmological galaxy formation simulations, such as that of V. Springel & L. Hernquist (hereafter SH03), employ adjustable parameters to satisfy constraints measured in the local Universe. In recent years, however, theory and spatially resolved simulations of the turbulent, multiphase, star-forming interstellar medium (ISM) have begun to produce new first-principles models, which when fully developed can replace traditional subgrid prescriptions. This approach has advantages of being physically motivated and predictive rather than empirically tuned, and allowing for varying environmental conditions rather than being tied to local-Universe conditions. As a prototype of this new approach, by combining calibrations from the TIGRESS numerical framework with the pressure-regulated feedback-modulated (PRFM) theory, simple formulae can be obtained for both the gas depletion time and an effective equation of state. Considering galaxies in TNG50, we compare the “native” simulation outputs with postprocessed predictions from PRFM. At TNG50 resolution, the total midplane pressure is nearly equal to the total ISM weight, indicating that galaxies in TNG50 are close to satisfying vertical equilibrium. The measured gas scale height is also close to theoretical equilibrium predictions. The slopes of the effective equations of states are similar, but with effective velocity dispersion normalization from SH03 slightly larger than that from current TIGRESS simulations. Because of this and the decrease in PRFM feedback yield at high pressure, the PRFM model predicts shorter gas depletion times than the SH03 model at high densities and redshift. Our results represent a first step toward implementing new, numerically calibrated subgrid algorithms in cosmological galaxy formation simulations.

Thousands of planetesimals: Simulating the streaming instability in very large computational domains

The streaming instability is a mechanism whereby pebble-sized particles in protoplanetary discs spontaneously come together in dense filaments, which collapse gravitationally to form planetesimals upon reaching the Roche density. The extent of the filaments along the orbital direction is nevertheless poorly characterised, due to a focus in the literature on small simulation domains where the behaviour of the streaming instability on large scales cannot be determined. We present here computer simulations of the streaming instability in boxes with side lengths up to $6.4$ scale heights in the plane. This is $32$ times larger than typically considered simulation domains and nearly a factor $1,000$ times the volume. We show that the azimuthal extent of filaments in the non-linear state of the streaming instability is limited to approximately one gas scale height. The streaming instability will therefore not transform the pebble density field into axisymmetric rings; rather the non-linear state of the streaming instability appears as a complex structure of loosely connected filaments. Including the self-gravity of the pebbles, our simulations form up to $4,000$ planetesimals. This allows us to probe the high-mass end of the initial mass function of planetesimals with much higher statistical confidence than previously. We find that this end is well-described by a steep exponential tapering. Since the resolution of our simulations is moderate -- a necessary trade-off given the large domains -- the mass distribution is incomplete at the low-mass end. When putting comparatively less weight on the numbers at low masses, at intermediate masses we nevertheless reproduce the power-law shape of the distribution established in previous studies.

Delivery of Dust Particles from Protoplanetary Disks onto Circumplanetary Disks of Giant Planets

The principal regular satellites of gas giants are thought to be formed by the accumulation of solid materials in circumplanetary disks (CPDs). While there has been significant progress in the study of satellite formation in CPDs, details of the supply of satellite building blocks to CPDs remain unclear. We perform the orbital integration of solid particles in the protoplanetary disk (PPD) approaching a planet, considering the gas drag force by using the results of three-dimensional hydrodynamical simulations of a local region around the planet. We investigate the planetary mass dependence of the capture positions and the capture rates of dust particles accreting onto the CPD. We also examine the degree of dust retention in the accreting gas onto the CPD, which is important for determining the ratio of the dust-to-gas inflow rates, a key parameter in satellite formation. We find that the degree of dust retention increases with increasing planetary mass for a given dust scale height in the PPD. In the case of a small planet (M p = 0.2M Jup), most particles with insufficient initial altitudes in the PPD are isolated from the gas in the accreting region. On the other hand, in the case of a massive planet (M p = 1M Jup), dust particles can be coupled to the vertically accreting gas, even when the dust scale height is about 10%–30% of the gas scale height. The results of this study can be used for models of dust delivery and satellite formation in the CPDs of gas giants of various masses, including exoplanets.

Galactic Magnetic Fields. I. Theoretical Model and Scaling Relations

Galactic dynamo models have generally relied on input parameters that are very challenging to constrain. We address this problem by developing a model that uses observable quantities as input: the galaxy rotation curve, the surface densities of the gas, stars and star formation rate, and the gas temperature. The model can be used to estimate parameters of the random and mean components of the magnetic field, as well as the gas scale height, root-mean-square velocity and the correlation length and time of the interstellar turbulence, in terms of the observables. We use our model to derive theoretical scaling relations for the quantities of interest, finding reasonable agreement with empirical scaling relations inferred from observation. We assess the dependence of the results on different assumptions about turbulence driving, finding that agreement with observations is improved by explicitly modeling the expansion and energetics of supernova remnants. The model is flexible enough to include alternative prescriptions for the physical processes involved, and we provide links to two open-source python programs that implement it.

Length and Velocity Scales in Protoplanetary Disk Turbulence

In the theory of protoplanetary disk turbulence, a widely adopted ansatz, or assumption, is that the turnover frequency of the largest turbulent eddy, Ω L , is the local Keplerian frequency Ω K . In terms of the standard dimensionless Shakura–Sunyaev α parameter that quantifies turbulent viscosity or diffusivity, this assumption leads to characteristic length and velocity scales given respectively by αH and αc , in which H and c are the local gas scale height and sound speed. However, this assumption is not applicable in cases when turbulence is forced numerically or driven by some natural processes such as vertical shear instability. Here, we explore the more general case where Ω L ≥ Ω K and show that, under these conditions, the characteristic length and velocity scales are respectively α/R′H and αR′c , where R′≡ΩL/ΩK is twice the Rossby number. It follows that α=α˜/R′ , where α˜c is the root-mean-square average of the turbulent velocities. Properly allowing for this effect naturally explains the reduced particle scale heights produced in shearing box simulations of particles in forced turbulence, and it may help with interpreting recent edge-on disk observations; more general implications for observations are also presented. For R′>1 , the effective particle Stokes numbers are increased, which has implications for particle collision dynamics and growth, as well as for planetesimal formation.

Introducing cuDisc: a 2D code for protoplanetary disc structure and evolution calculations

ABSTRACT We present a new two-dimensional (2D) axisymmetric code, cuDisc, for studying protoplanetary discs, focusing on the self-consistent calculation of dust dynamics, grain-size distribution and disc temperature. Self-consistently studying these physical processes is essential for many disc problems, such as structure formation and dust removal, given that the processes heavily depend on one another. To follow the evolution over substantial fractions of the disc lifetime, cuDisc uses the cuda language and libraries to speed up the code through GPU acceleration. cuDisc employs a second-order finite-volume Godonuv solver for dust dynamics, solves the Smoluchowski equation for dust growth, and calculates radiative transfer using a multifrequency hybrid ray-tracing/flux-limited-diffusion method. We benchmark our code against current state-of-the-art codes. Through studying steady-state problems, we find that including 2D structure reveals that when collisions are important, the dust vertical structure appears to reach a diffusion-settling-coagulation equilibrium that can differ substantially from standard models that ignore coagulation. For low fragmentation velocities, we find an enhancement of intermediate-sized dust grains at heights of ∼1 gas scale height due to the variation in collision rates with height, and for large fragmentation velocities, we find an enhancement of small grains around the disc mid-plane due to collisional ‘sweeping’ of small grains by large grains. These results could be important for the analysis of disc spectral energy distributions or scattered light images, given these observables are sensitive to the vertical grain distribution.

On corrugation mode radial wavelengths of the vertical shear instability

Abstract The vertical shear instability (VSI) is a promising mechanism to drive turbulence in protoplanetary disks. Numerical simulations in the literature demonstrate that the VSI non-linear saturation is predominated by the linear corrugation modes. These modes possess vertical wavelengths crucially longer than radial wavelengths. This paper aims to investigate the natural radial wavelength of corrugation modes upon VSI saturation, by a series of numerical simulations conducted in Athena++ at different grid resolutions, disk aspect ratios, and viscosity parameterized by ν. We find a sign of convergence emerges at 64 cells per gas scale height for fiducial simulations. Below it a continuous reduction of wavelengths with grid resolution is observed. Synthetic ALMA molecular line observations of $^{12}\rm CO(2-1)$ are performed to inspect the observability of the corrugation modes feature, which is significantly diminished with a resolution of 32 cells per scale height or above. Flared and viscous disks exhibiting longer saturation wavelengths may mitigate the observational difficulty.

Observational evidence for local vertical constraining of H i by molecular cloud complexes

ABSTRACT A massive molecular cloud complex represents local gravitational potential that can constrain the vertical distribution of surrounding stars and gas. This pinching effect results in the local corrugation of the scale height of stars and gas which is in addition to the global corrugation of the mid-plane of the disc. For the first time, we report observational evidence for this pinching on the H i vertical structures in the Galactic region (20° < l < 40°), also called W41–W44 region. The H i vertical distribution is modelled by a double Gaussian profile that physically represents a narrow dense gas distribution confined to the mid-plane embedded in a wider diffuse H i. We find that the estimate of the H i scale height distribution of wider components shows corrugated structures at the locations of molecular complexes, as theoretically predicted in literature. While the narrow component is less affected by the pinching, we found a hint of the disc being disrupted by the active dynamics in the local environment of the complex, for example, supernova explosions. Molecular complexes of mass of several $10^6 \rm M_{\odot } $, associated with the mini-starburst region W43 and the supernova remnant W41 show the strongest evidence for the pinching; here a broad trough, with an average width of ∼400 pc and height ∼300 pc, in the disc thickness of the wider component is prominently visible. Searching for similar effect on the stars as well as in the location of other complexes in the Milky Way and other galaxies will be useful to establish this phenomenon more firmly.

Non-linear magnetic buoyancy instability and turbulent dynamo

ABSTRACT Stratified discs with strong horizontal magnetic fields, are susceptible to magnetic buoyancy instability (MBI). Modifying the magnetic field and gas distributions, this can play an important role in galactic evolution. The MBI and the Parker instability, in which MBI is exacerbated by cosmic rays, are often studied using an imposed magnetic field. However, in galaxies and accretion discs, the magnetic field is continuously replenished by a large-scale dynamo action. Using non-ideal MHD equations, we model a section of the galactic disc (we neglect rotation and cosmic rays considered elsewhere), in which the large-scale field is generated by an imposed α-effect of variable intensity to explore the interplay between dynamo instability and MBI. The system evolves through three distinct phases: the linear (kinematic) dynamo stage, the onset of linear MBI when the magnetic field becomes sufficiently strong and the non-linear, statistically steady state. Non-linear effects associated with the MBI introduce oscillations which do not occur when the field is produced by the dynamo alone. The MBI initially accelerates the magnetic field amplification but the growth is quenched by the vertical motions produced by MBI. We construct a 1D model, which replicates all significant features of 3D simulations to confirm that magnetic buoyancy alone can quench the dynamo and is responsible for the magnetic field oscillations. Unlike similar results obtained with an imposed magnetic field, the non-linear interactions do not reduce the gas scale height, so the consequences of the magnetic buoyancy depend on how the magnetic field is maintained.

Dust Enrichment and Grain Growth in a Smooth Disk around the DG Tau Protostar Revealed by ALMA Triple Bands Frequency Observations

Characterizing the physical properties of dust grains in a protoplanetary disk is critical to comprehending the planet formation process. Our study presents Atacama Large Millimeter/submillimeter Array (ALMA) high-resolution observations of the young protoplanetary disk around DG Tau at a 1.3 mm dust continuum. The observations, with a spatial resolution of ≈0.″04, or ≈5 au, revealed a geometrically thin and smooth disk without substantial substructures, suggesting that the disk retains the initial conditions of the planet formation. To further analyze the distributions of dust surface density, temperature, and grain size, we conducted a multiband analysis with several dust models, incorporating ALMA archival data of the 0.87 and 3.1 mm dust polarization. The results showed that the Toomre Q parameter is ≲2 at a 20 au radius, assuming a dust-to-gas mass ratio of 0.01. This implies that a higher dust-to-gas mass ratio is necessary to stabilize the disk. The grain sizes depend on the dust models, and for the DSHARP compact dust, they were found to be smaller than ∼400 μm in the inner region (r ≲ 20 au) while exceeding larger than 3 mm in the outer part. Radiative transfer calculations show that the dust scale height is lower than at least one-third of the gas scale height. These distributions of dust enrichment, grain sizes, and weak turbulence strength may have significant implications for the formation of planetesimals through mechanisms such as streaming instability. We also discuss the CO snowline effect and collisional fragmentation in dust coagulation for the origin of the dust size distribution.

On Secular Gravitational Instability in Vertically Stratified Disks

Secular gravitational instability (GI) is one promising mechanism for explaining planetesimal formation. Previous studies of secular GI utilized a razor-thin disk model and derived the growth condition in terms of vertically integrated physical values such as dust-to-gas surface density ratio. However, in weakly turbulent disks where secular GI can operate, a dust disk can be orders of magnitude thinner than a gas disk, and analyses treating the vertical structures are necessary to clarify the interplay of the midplane dust motion and the upper gas motion. In this work, we perform vertically global linear analyses of secular GI with a vertical domain size of a few gas scale heights. We find that dust grains accumulate radially around the midplane while gas circulates over the whole vertical region. We obtain well-converged growth rates when the outer gas boundary is above two gas scale heights. The growth rates are underestimated if we assume the upper gas to be steady and regard it just as the source of external pressure to the dusty lower layer. Therefore, treating the upper gas motion is important even when the dust disk is much thinner than the gas disk. Conducting a parameter survey, we represent the growth condition in terms of the Toomre Q value for dust and dust-to-gas surface density ratio. The critical dust disk mass for secular GI is ∼10−4 M * for a dust-to-gas surface density ratio of 0.01, a Stokes number of 0.1, and a radial dust diffusivity of 10−4 c s H, where c s is the gas sound speed, and H is the gas scale height.

A new buoyancy instability in galaxy clusters due to streaming cosmic rays

ABSTRACT Active Galactic Nuclei (AGN) are believed to provide the energy that prevents runaway cooling of gas in the cores of galaxy clusters. However, how this energy is transported and thermalized throughout the Intracluster Medium (ICM) remains unclear. In recent work, we showed that streaming cosmic rays (CRs) destabilize sound waves in dilute ICM plasmas. Here, we show that CR streaming in the presence of gravity also destabilizes a pressure-balanced wave. We term this new instability the CR buoyancy instability (CRBI). In stark contrast to standard results without CRs, the pressure-balanced mode is highly compressible at short wavelengths due to CR streaming. Maximal growth rates are of order (pc/pg)β1/2ωff, where pc/pg is the ratio of CR pressure to thermal gas pressure, β is the ratio of thermal to magnetic pressure, and ωff is the free-fall frequency. The CRBI operates alongside buoyancy instabilities driven by background heat fluxes, i.e. the heat-flux-driven buoyancy instability (HBI) and the magneto-thermal instability (MTI). When the thermal mean free path lmfp is ≪ the gas scale height H, the HBI/MTI set the growth rate on large scales, while the CRBI sets the growth rate on small scales. Conversely, when lmfp ∼ H and (pc/pg)β1/2 ≳ 1, CRBI growth rates exceed HBI/MTI growth rates even on large scales. Our results suggest that CR-driven instabilities may be partially responsible for the sound waves/weak shocks and turbulence observed in galaxy clusters. CR-driven instabilities generated near radio bubbles may also play an important role redistributing AGN energy throughout clusters.

Spin of protoplanets generated by pebble accretion: Influences of protoplanet-induced gas flow

Context. In the pebble accretion model, protoplanets accrete millimeter-to-centimeter-sized particles (pebbles). When a protoplanet grows, a dense gas envelope forms around it. The envelope affects accretion of pebbles and, in particular, the spin angular momentum transfer at the collision to the planet. Aims. We aim to investigate the spin state of a protoplanet during the pebble accretion influenced by the gas flow in the gravitational potential of the protoplanet and how it depends on the planetary mass, the headwind speed, the distance from the host star, and the pebble size. Methods. We performed nonisothermal three-dimensional hydrodynamical simulations in a local frame to obtain the gas flow around the planet. We then numerically integrated three-dimensional orbits of pebbles under the obtained gas flow. Finally, assuming uniform spatial distribution of incoming pebbles, we calculated net spin by summing up specific angular momentum that individual pebbles transfer to the protoplanet at impacts. Results. We find that a protoplanet with the envelope acquires prograde net spin rotation regardless of the planetary mass, the pebble size, and the headwind speed of the gas. This is because accreting pebbles are dragged by the envelope that commonly has prograde rotation. As the planetary mass or orbital radius increases, the envelope is thicker and the prograde rotation is faster, resulting in faster net prograde spin. When the dimensionless thermal mass of the planet, m = RBondi/H, where RBondi and H are the Bondi radius and the disk gas scale height, is larger than a certain critical mass (m ≳ 0.3 at 0.1 au or m ≳ 0.1 at 1 au), the spin rotation exceeds the breakup one. Conclusions. The predicted spin frequency reaches the breakup one at the planetary mass miso,rot ~ 0.1 (a/1 au)−1/2 (where a is the orbital radius), suggesting that the protoplanet cannot grow beyond miso,rot. It is consistent with the Earth’s current mass and could help the formation of the Moon with a giant impact on a fast-spinning proto-Earth.

Modest Dust Settling in the IRAS04302+2247 Class I Protoplanetary Disk

We present new Very Large Array observations, between 6.8 and 66 mm, of the edge-on Class I disk IRAS04302+2247. Observations at 6.8 mm and 9.2 mm lead to the detection of thermal emission from the disk, while shallow observations at the other wavelengths are used to correct for emission from other processes. The disk radial brightness profile transitions from broadly extended in previous Atacama Large Millimeter/submillimeter Array 0.9 mm and 2.1 mm observations to much more centrally brightened at 6.8 mm and 9.2 mm, which can be explained by optical depth effects. The radiative transfer modeling of the 0.9 mm, 2.1 mm, and 9.2 mm data suggests that the grains are smaller than 1 cm in the outer regions of the disk, allowing us to obtain the first lower limit for the scale height of grains emitting at millimeter wavelengths in a protoplanetary disk. We find that the millimeter dust scale height is between 1 au and 6 au at a radius 100 au from the central star, while the gas scale height is estimated to be about 7 au, indicating a modest level of settling. The estimated dust height is intermediate between less evolved Class 0 sources, which are found to be vertically thick, and more evolved Class II sources, which show a significant level of settling. This suggests that we are witnessing an intermediate stage of dust settling.

On the Origin of Dust Structures in Protoplanetary Disks: Constraints from the Rossby Wave Instability

High-resolution submillimeter observations of protoplanetary disks with ALMA have revealed that dust rings are common in large, bright disks. The leading explanation for these structures is dust trapping in a local gas pressure maximum, caused by an embedded planet or other dynamical process. Independent of origin, such dust traps should be stable for many orbits to collect significant dust. However, ringlike perturbations in gas disks are also known to trigger the Rossby wave instability (RWI). We investigate whether axisymmetric pressure bumps can simultaneously trap dust and remain stable to the RWI. The answer depends on the thermodynamic properties of pressure bumps. For isothermal bumps, dust traps are RWI stable for widths from ∼1 to several gas scale heights. Adiabatic dust traps are stable over a smaller range of widths. For temperature bumps with no surface density component, however, all dust traps tend to be unstable. Smaller values of disk aspect ratio allow stable dust trapping at lower bump amplitudes and over a larger range of widths. We also report a new approximate criterion for RWI. Instability occurs when the radial oscillation frequency is ≲75% of the Keplerian frequency, which differs from the well-known Lovelace necessary (but not sufficient) criterion for instability. Our results can guide ALMA observations of molecular gas by constraining the resolution and sensitivity needed to identify the pressure bumps thought to be responsible for dust rings.

Two saturated states of the vertical shear instability in protoplanetary disks with vertically varying cooling times

Abstract Turbulence in protoplanetary disks plays an important role in dust evolution and planetesimal formation. The vertical shear instability (VSI) is one of the candidate hydrodynamic mechanisms that can generate turbulence in the outer disk regions. The VSI requires rapid gas cooling in addition to vertical shear. A linear stability analysis suggests that the VSI may not operate around the midplane where gas cooling is inefficient. In this study, we investigate the nonlinear outcome of the VSI in disks with a linearly VSI-stable midplane region. We perform two-dimensional global hydrodynamical simulations of an axisymmetric disk with vertically varying cooling times. The vertical cooling time profile determines the thicknesses of the linearly VSI-stable midplane layer and unstable layers above and below the midplane. We find that the thickness of the midplane stable layer determines the vertical structure of VSI-driven turbulence in the nonlinear saturated state. We identify two types of final saturated state: (i) T states, characterized by vertical turbulent motion penetrating into the VSI-stable midplane layer, and (ii) pT states, characterized by turbulent motion confined in the unstable layers. The pT states are realized when the midplane VSI-stable layer is thicker than two gas scale heights. We also find that the VSI-driven turbulence is largely suppressed at all heights when the VSI-unstable region lying above and below the midplane is thinner than two gas scale heights. We present empirical formulas that predict the strength of VSI-driven turbulence as a function of the thicknesses of the unstable and stable layers. These formulas will be useful for studying how VSI-driven turbulence and dust grains controlling the disk cooling efficiency evolve simultaneously.

MAVEN‐STATIC Observations of Ion Temperature and Initial Ion Acceleration in the Martian Ionosphere

AbstractThough ion escape to space is an important mechanism for atmospheric loss at Mars, the processes that accelerate ions to escape velocity have not been fully identified and quantified. The lowest altitude where suprathermal planetary ions appear is an important source region for ion escape, where electromagnetic forces and waves begin to energize ions to escape velocity. We have conducted a statistical study of distribution functions measured by Mars Atmosphere and Volatile EvolutioN SupraThermal And Thermal Ion Composition in order to identify the region where suprathermal tails appear. At all solar zenith angles, suprathermal ions appear just above the exobase region, where the mean free path between collisions exceeds the neutral gas scale height. temperature profiles are also presented. We also investigate the effects of crustal magnetism, finding that crustal fields protect planetary plasma on the dayside and enhance energization on the nightside.

Dust ring and gap formation by gas flow induced by low-mass planets embedded in protoplanetary disks

Context. Recent high-spatial-resolution observations have revealed dust substructures in protoplanetary disks such as rings and gaps, which do not always correlate with gas. Because radial gas flow induced by low-mass, non-gas-gap-opening planets could affect the radial drift of dust, it potentially forms these dust substructures in disks. Aims. We investigate the potential of gas flow induced by low-mass planets to sculpt the rings and gaps in the dust profiles. Methods. We first perform three-dimensional hydrodynamical simulations, which resolve the local gas flow past a planet. We then calculate the trajectories of dust influenced by the planet-induced gas flow. Finally, we compute the steady-state dust surface density by incorporating the influences of the planet-induced gas flow into a one-dimensional dust advection-diffusion model. Results. The outflow of the gas toward the outside of the planetary orbit inhibits the radial drift of dust, leading to dust accumulation (the dust ring). The outflow toward the inside of the planetary orbit enhances the inward drift of dust, causing dust depletion around the planetary orbit (the dust gap). Under weak turbulence (αdiff ≲ 10−4, where αdiff is the turbulence strength parameter), the gas flow induced by the planet with ≳1M⊕ (Earth mass) generates the dust ring and gap in the distribution of small dust grains (≲1 cm) with a radial extent of ~1–10 times the gas scale height around the planetary orbit without creating a gas gap and pressure bump. Conclusions. The gas flow induced by low-mass, non-gas-gap-opening planets can be considered a possible origin of the observed dust substructures in disks. Our results may be helpful in explaining the disks whose dust substructures were found not to correlate with those of the gas.

The impact of cosmic rays on dynamical balance and disc–halo interaction in L⋆ disc galaxies

ABSTRACT Cosmic rays (CRs) are an important component in the interstellar medium, but their effect on the dynamics of the disc–halo interface (<10 kpc from the disc) is still unclear. We study the influence of CRs on the gas above the disc with high-resolution FIRE-2 cosmological simulations of late-type L⋆ galaxies at redshift z ∼ 0. We compare runs with and without CR feedback (with constant anisotropic diffusion κ∥ ∼ 3 × 1029 cm2 s−1 and streaming). Our simulations capture the relevant disc–halo interactions, including outflows, inflows, and galactic fountains. Extra-planar gas in all of the runs satisfies dynamical balance, where total pressure balances the weight of the overlying gas. While the kinetic pressure from non-uniform motion (≳1 kpc scale) dominates in the mid-plane, thermal and bulk pressures (or CR pressure if included) take over at large heights. We find that with CR feedback, (1) the warm (∼104 K) gas is slowly accelerated by CRs; (2) the hot (>5 × 105 K) gas scale height is suppressed; (3) the warm-hot (2 × 104–5 × 105 K) medium becomes the most volume-filling phase in the disc–halo interface. We develop a novel conceptual model of the near-disc gas dynamics in low-redshift L⋆ galaxies: with CRs, the disc–halo interface is filled with CR-driven warm winds and hot superbubbles that are propagating into the circumgalactic medium with a small fraction falling back to the disc. Without CRs, most outflows from hot superbubbles are trapped by the existing hot halo and gravity, so typically they form galactic fountains.

Bursting Bubbles: Feedback from Clustered Supernovae and the Trade-off Between Turbulence and Outflows

We present an analytic model for clustered supernovae (SNe) feedback in galaxy disks, incorporating the dynamical evolution of superbubbles formed from spatially overlapping SNe remnants. We propose two realistic outcomes for the evolution of superbubbles in galactic disks: (1) the expansion velocity of the shock front falls below the turbulent velocity dispersion of the interstellar medium in the galaxy disk, whereupon the superbubble stalls and fragments, depositing its momentum entirely within the galaxy disk; or (2) the superbubble grows in size to reach the gas scale height, breaking out of the galaxy disk and driving galactic outflows/fountains. In either case, we find that superbubble breakup/breakout almost always occurs before the last Type II SN (≲40 Myr) in the recently formed star cluster, assuming a standard high-end initial mass function slope, and scalings between stellar lifetimes and masses. The threshold between these two cases implies a break in the effective strength of feedback in driving turbulence within galaxies, and a resulting change in the scalings of, for example, star formation rates with gas surface density (the Kennicutt–Schmidt relation) and the star formation efficiency in galaxy disks.