arXiv subjects

Davide Martizzi

Publications and source records attributed to Davide Martizzi.

At least 19 recordsLinked to original sources

arXiv2022

Supernova-driven turbulent metal mixing in high redshift galactic disks: metallicity fluctuations in the interstellar medium and its imprints on metal poor stars in the Milky Way

The extent to which turbulence mixes gas in the face of recurrent infusions of fresh metals by supernovae (SN) could help provide important constraints on the local star formation conditions. This includes predictions of the metallicity dispersion amongst metal poor stars, which suggests that the interstellar medium was not very well mixed at these early times. The purpose of this {\it Letter} is to help isolate, via a series of numerical experiments, some of the key processes that regulate turbulent mixing of SN elements in galactic disks. We study the gas interactions in small simulated patches of a galaxy disk with the goal of resolving the small-scale mixing effects of metals at pc scales, which enables us to measure the turbulent diffusion coefficient in various galaxy environments. By investigating the statistics of variations of $α$ elements in these simulations, we are able to derive constraints not only on the allowed range of intrinsic yield variations in SN explosions but also on the star formation history of the Milky Way. We argue that the observed dispersion of [Mg/Fe] in metal poor halo stars is compatible with the star-forming conditions expected in dwarf satellites or in an early low star-forming Milky Way progenitor. In particular, metal variations in stars that have not been phase-mixed can be used to infer the star-forming conditions of disrupted dwarf satellites.

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arXiv2022

Testing the Momentum-driven Supernova Feedback Paradigm in M31

Momentum feedback from isolated supernova remnants (SNRs) have been increasingly recognized by modern cosmological simulations as a resolution-independent means to implement the effects of feedback in galaxies, such as turbulence and winds. However, the integrated momentum yield from SNRs is uncertain due to the effects of SN clustering and interstellar medium (ISM) inhomogeneities. In this paper, we use spatially-resolved observations of the prominent 10-kpc star-forming ring of M31 to test models of mass-weighted ISM turbulence driven by momentum feedback from isolated, non-overlapping SNRs. We use a detailed stellar-age distribution (SAD) map from the Panchromatic Hubble Andromeda Treasury (PHAT) survey, observationally-constrained SN delay-time distributions, and maps of the atomic and molecular hydrogen to estimate the mass-weighted velocity dispersion using the Martizzi et al. ISM turbulence model. Our estimates are within a factor of 2 of the observed mass-weighted velocity dispersion in most of the ring, but exceed observations at densities $\lesssim 0.2$ cm$^{-3}$ and SN rates $>2.1\times 10^{-4}$ SN yr$^{-1}$ kpc$^{-2}$, even after accounting for plausible variations in stellar-age distribution models and ISM scale height assumptions. We conclude that at high SN rates the momentum deposited is most likely suppressed by the non-linear effects of SN clustering, while at low densities, SNRs reach pressure equilibrium before the cooling phase. These corrections should be introduced in models of momentum-driven feedback and ISM turbulence.

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arXiv2021

The large-scale distribution of ionized metals in IllustrisTNG

We study the intrinsic large-scale distribution and evolution of seven ionized metals in the IllustrisTNG magneto-hydrodynamical cosmological simulation. We focus on the fractions of C\,\textsc{ii}, C\,\textsc{iv}, Mg\,\textsc{ii}, N\,\textsc{v}, Ne\,\textsc{viii}, O\,\textsc{vi}, and Si\,\textsc{iv} in different cosmic web structures (filaments, haloes, and voids) and gas phases (warm-hot intergalactic medium WHIM, hot, diffuse, and condensed gas) from $z=6$ to $z=0$. Our analysis provides a new perspective to the study of the distribution and evolution of baryons across cosmic time while offering new hints in the context of the well-known missing baryons problem. The cosmic web components are here identified using the local comoving dark matter density, which provides a simple but effective way of mapping baryons on large scales. Our results show that C\,\textsc{ii} and Mg\,\textsc{ii} are mostly located in condensed gas inside haloes in high-density and low-temperature star-forming regions ($ρ_{\rm gas}/\barρ_{\rm bar}\gtrsim10^3$, and ${\rm T}\lesssim10^{5}$~K). C\,\textsc{iv} and Si\,\textsc{iv} present similar evolution of their mass fractions in haloes and filaments across cosmic time. In particular, their mass budgets in haloes in condensed phase ($ρ_{\rm gas}/\barρ_{\rm bar}\gtrsim10^3$, and ${\rm T}\lesssim10^{5}$~K) are driven by gas cooling and star formation with a peak at $z\sim2$. Finally, our results confirm that O\,\textsc{vi}, Ne\,\textsc{viii}, and N\,\textsc{v} are good tracers of warm/hot and low-density gas at low redshift ($ρ_{\rm gas}/\barρ_{\rm bar}\lesssim10^3$, and ${\rm T}\gtrsim10^{5}$~K), regions that are likely to contain most of the missing baryons in the local Universe.

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arXiv2021

The Effects of Metallicity and Abundance Pattern of the ISM on Supernova Feedback

Supernova (SN) feedback plays a vital role in the evolution of galaxies. While modern cosmological simulations capture the leading structures within galaxies, they struggle to provide sufficient resolution to study small-scale stellar feedback, such as the detailed evolution of SN remnants. It is thus common practice to assume subgrid models that are rarely extended to low metallicities, and which routinely use the standard solar abundance pattern. With the aid of 1-d hydrodynamical simulations, we extend these models to consider low metallicities and non-solar abundance patterns as derived from spectra of Milky Way stars. For that purpose, a simple, yet effective framework has been developed to generate non-solar abundance pattern cooling functions. We find that previous treatments markedly over-predict SN feedback at low metallicities and show that non-negligible changes in the evolution of SN remnants of up to $\approx 50\%$ in $cooling\; mass$ and $\approx 27\%$ in $momentum\; injection\; from\; SN\; remnants$ arise from non-solar abundance patterns. We use our simulations to quantify these results as a function of metallicity and abundance pattern variations and present analytic formulae to accurately describe the trends. These formulae have been designed to serve as subgrid models for SN feedback in cosmological hydrodynamical simulations.

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arXiv2020

Estimating the dark matter velocity anisotropy to the cluster edge

Dark matter dominates the properties of large cosmological structures such as galaxy clusters, and the mass profiles of the dark matter have been measured for these equilibrated structures for years using X-rays, lensing or galaxy velocities. A new method has been proposed, which should allow us to estimate a dynamical property of the dark matter, namely the velocity anisotropy. For the gas a similar velocity anisotropy is zero due to frequent collisions, however, the collisionless nature of dark matter allows it to be non-trivial. Numerical simulations have for years found non-zero and radially varying dark matter velocity anisotropies. Here we employ the method proposed by Hansen and Pifaretti (2007), and developed by Host et al. (2009) to estimate the dark matter velocity anisotropy in the bright galaxy cluster Perseus, to near 5 times the radii previously obtained. We find the dark matter velocity anisotropy to be consistent with the results of numerical simulations, however, still with large error-bars. At half the virial radius we find the velocity anisotropy to be non-zero at 1.7 standard deviations, lending support to the collisionless nature of dark matter.

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arXiv2019

Global Simulations of Galactic Discs: Violent Feedback from Clustered Supernovae during Bursts of Star Formation

A suite of idealised, global, gravitationally unstable, star-forming galactic disc simulations with 2 pc spatial resolution, performed with the adaptive mesh refinement code {\sc ramses} is used in this paper to predict the emergent effects of supernova feedback. The simulations include a simplified prescriptions for formation of single stellar populations of mass $\sim 100 \, M_{\odot}$, radiative cooling, photoelectric heating, an external gravitational potential for a dark matter halo and an old stellar disc, self-gravity, and a novel implementation of supernova feedback. The results of these simulations show that gravitationally unstable discs can generate violent supersonic winds with mass loading factors $η\gtrsim 10$, followed by a galactic fountain phase. These violent winds are generated by highly clustered supernovae exploding in dense environments created by gravitational instability, and they are not produced in simulation without self-gravity. The violent winds significantly perturb the vertical structure of the disc, which is later re-established during the galactic fountain phase. Gas resettles into a quasi-steady, highly turbulent disc with volume-weighted velocity dispersion $σ> 50 \, {\rm km/s}$. The new configuration drives weaker galactic winds with mass loading factor $η\leq 0.1$. The whole cycle takes place in $\leq 10$ dynamical times. Such high time variability needs to be taken into account when interpreting observations of galactic winds from starburst and post-starburst galaxies.

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arXiv2019

Baryons in the CosmicWeb of IllustrisTNG -- II: the Connection among Galaxies, Halos, their Formation Time and their Location in the Cosmic Web

The connections among galaxies, the dark matter halos where they form and the properties of the large-scale Cosmic Web still need to be completely disentangled. We use the cosmological hydrodynamical simulation TNG100 of the IllustrisTNG suite to quantify the effects played by the large-scale density field and the Cosmic Web morphology on the relation between halo mass and galaxy stellar mass. We select objects with total dynamical mass in the range $\geq 6.3\times 10^{10} h ^{-1}\, M_{\odot}$ up to a few $10^{14} h^{-1} \, M_{\odot}$ between redshift $z=4$ and redshift $z=0$. A Cosmic Web class (knot, filament, sheet, void) is assigned to each region of the volume using a density field deformation tensor-based method. We find that galaxy stellar mass strongly correlates with total dynamical mass and formation time, and more weakly with large-scale overdensity and Cosmic Web class. The latter two quantities correlate with each other, but are not entirely degenerate. Furthermore, we find that at fixed halo mass, galaxies with stellar mass lower than the median value are more likely to be found in voids and sheets, whereas galaxies with stellar mass higher than the median are more likely to be found in filaments and knots. Finally, we find that the dependence on environment is stronger for satellites than for centrals, and discuss the physical implications of these results.

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arXiv2019

On the mass mismatch between simulations and weak-lensing measurements

The recently discovered discrepancy between galaxy mass measurements from weak lensing and predictions from abundance matching questions our understanding of cosmology, or of the galaxy-halo connection, or of both. We re-examined this tension by considering, as models, different cosmological simulations in the Illustris suite. We produced excess profiles $RΔΣ$ from subhalo snapshots at different redshifts in Illustris-1 and IllustrisTNG (TNG100 and TNG300) simulations, enabling a direct comparison with weak-lensing measurements. We separate the individual contributions of stars, dark matter and gas within $\approx1$ Mpc (comoving length), beyond which correlated two-halo terms dominate. The mismatch between measurements and predictions is more severe than in previous studies: $RΔΣ$ profiles from IllustrisTNG are $\approx2$ times higher than the measured ones. Contrary to abundance matching results, the mismatch is mostly unchanged with increasing redshifts. The contribution of gas to the $RΔΣ$ profiles is $5-10\%$ over the scales dominated by one-halo terms. Different procedures to link stellar and halo masses (abundance matching, cosmological simulations) are still significantly discrepant with weak lensing measurements, but their trends are different. Therefore, the change in cosmological parameters advocated through abundance-matching arguments may not resolve this tension. Also, current criteria to select isolated massive galaxies in simulations are susceptible to resolution issues and may not correspond to observational criteria. The (currently subdominant) contribution of gas is non-negligible, and even if the major discrepancy within stellar and halo masses is resolved, it will be an appreciable source of systematics in the LSST era, when uncertainties on the $RΔΣ$ profiles are expected to be $\approx10$ times smaller.

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arXiv2019

Baryons in the CosmicWeb of IllustrisTNG - I: Gas in Knots, Filaments, Sheets and Voids

We analyze the IllustrisTNG simulations to study the mass, volume fraction and phase distribution of gaseous baryons embedded in the knots, filaments, sheets and voids of the Cosmic Web from redshift $z=8$ to redshift $z=0$. We find that filaments host more star-forming gas than knots, and that filaments also have a higher relative mass fraction of gas in this phase than knots. We also show that the cool, diffuse Intergalactic Medium (IGM; $T<10^5 \, {\rm K}$, $ n_{\rm H}<10^{-4}(1+z) \, {\rm cm^{-3}}$) and the Warm-Hot Intergalactic Medium (WHIM; $ 10^5 \, {\rm K} <T<10^7 \, {\rm K}$, $ n_{\rm H} <10^{-4}(1+z)\, {\rm cm^{-3}}$) constitute $\sim 39\%$ and $\sim 46\%$ of the baryons at redshift $z=0$, respectively. Our results indicate that the WHIM may constitute the largest reservoir of {\it missing} baryons at redshift $z=0$. Using our Cosmic Web classification, we predict the WHIM to be the dominant baryon mass contribution in filaments and knots at redshift $z=0$, but not in sheets and voids where the cool, diffuse IGM dominates. We also characterise the evolution of WHIM and IGM from redshift $z=4$ to redshift $z=0$, and find that the mass fraction of WHIM in filaments and knots evolves only by a factor $\sim 2$ from redshift $z=0$ to $z=1$, but declines faster at higher redshift. The WHIM only occupies $4-11\%$ of the volume at redshift $0\leq z \leq 1$. We predict the existence of a significant number of currently undetected OVII and NeIX absorption systems in cosmic filaments which could be detected by future X-ray telescopes like Athena.

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arXiv2018

Simulations of Jet Heating in Galaxy Clusters: Successes and Challenges

We study how jets driven by active galactic nuclei influence the cooling flow in Perseus-like galaxy cluster cores with idealised, non-relativistic, hydrodynamical simulations performed with the Eulerian code ATHENA using high-resolution Godunov methods with low numerical diffusion. We use novel analysis methods to measure the cooling rate, the heating rate associated to multiple mechanisms, and the power associated with adiabatic compression/expansion. A significant reduction of the cooling rate and cooling flow within 20 kpc from the centre can be achieved with kinetic jets. However, at larger scales and away from the jet axis, the system relaxes to a cooling flow configuration. Jet feedback is anisotropic and is mostly distributed along the jet axis, where the cooling rate is reduced and a significant fraction of the jet power is converted into kinetic power of heated outflowing gas. Away from the jet axis weak shock heating represents the dominant heating source. Turbulent heating is significant only near the cluster centre, but it becomes inefficient at 50 kpc scales where it only represents a few percent of the total heating rate. Several details of the simulations depend on the choice made for the hydro solver, a consequence of the difficulty of achieving proper numerical convergence for this problem: current physics implementations and resolutions do not properly capture multi-phase gas that develops as a consequence of thermal instability. These processes happen at the grid scale and leave numerical solutions sensitive to the properties of the chosen hydro solver.

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arXiv2018

Clustered Supernovae Drive Powerful Galactic Winds After Super-Bubble Breakout

We use three-dimensional hydrodynamic simulations of vertically stratified patches of galactic discs to study how the spatio-temporal clustering of supernovae (SNe) enhances the power of galactic winds. SNe that are randomly distributed throughout a galactic disc drive inefficient galactic winds because most supernova remnants lose their energy radiatively before breaking out of the disc. Accounting for the fact that most star formation is clustered alleviates this problem. Super-bubbles driven by the combined effects of clustered SNe propagate rapidly enough to break out of galactic discs well before the clusters' SNe stop going off. The radiative losses post-breakout are reduced dramatically and a large fraction ($\gtrsim 0.2$) of the energy released by SNe vents into the halo powering a strong galactic wind. These energetic winds are capable of providing strong preventative feedback and eject substantial mass from the galaxy with outflow rates on the order of the star formation rate. The momentum flux in the wind is only of order that injected by the SNe, because the hot gas vents before doing significant work on the surroundings. We show that our conclusions hold for a range of galaxy properties, both in the local Universe (e.g., M82) and at high redshift (e.g., $z \sim 2$ star forming galaxies). We further show that if the efficiency of forming star clusters increases with increasing gas surface density, as suggested by theoretical arguments, the condition for star cluster-driven super-bubbles to break out of galactic discs corresponds to a threshold star formation rate surface density for the onset of galactic winds $\sim 0.03$ M$_\odot$ yr$^{-1}$ kpc$^{-2}$, of order that observed.

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arXiv2018

Chemical pre-processing of cluster galaxies over the past 10 billion years in the IllustrisTNG simulations

We use the IllustrisTNG simulations to investigate the evolution of the mass-metallicity relation (MZR) for star-forming cluster galaxies as a function of the formation history of their cluster host. The simulations predict an enhancement in the gas-phase metallicities of star-forming cluster galaxies (10^9< M_star<10^10 M_sun) at z<1.0 in comparisons to field galaxies. This is qualitatively consistent with observations. We find that the metallicity enhancement of cluster galaxies appears prior to their infall into the central cluster potential, indicating for the first time a systematic "chemical pre-processing" signature for {\it infalling} cluster galaxies. Namely, galaxies which will fall into a cluster by z=0 show a ~0.05 dex enhancement in the MZR compared to field galaxies at z<0.5. Based on the inflow rate of gas into cluster galaxies and its metallicity, we identify that the accretion of pre-enriched gas is the key driver of the chemical evolution of such galaxies, particularly in the stellar mass range (10^9< M_star<10^10 M_sun). We see signatures of an environmental dependence of the ambient/inflowing gas metallicity which extends well outside the nominal virial radius of clusters. Our results motivate future observations looking for pre-enrichment signatures in dense environments.

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arXiv2017

Survival of Massive Star-forming Galaxies in Cluster Cores Drives Gas-Phase Metallicity Gradients : The Effects of Ram Pressure Stripping

Recent observations of galaxies in a cluster at z=0.35 show that their integrated gas-phase metallicities increase with decreasing cluster-centric distance. To test if ram pressure stripping (RPS) is the underlying cause, we use a semi-analytic model to quantify the "observational bias" that RPS introduces into the aperture-based metallicity measurements. We take integral field spectroscopy of local galaxies, remove gas from their outer galactic disks via RPS, and then conduct mock slit observations of cluster galaxies at z=0.35. Our RPS model predicts a typical cluster-scale metallicity gradient of -0.03 dex/Mpc. By removing gas from the outer galactic disks, RPS introduces a mean metallicity enhancement of +0.02 dex at a fixed stellar mass. This gas removal and subsequent quenching of star formation preferentially removes low mass cluster galaxies from the observed star-forming population. As only the more massive star-forming galaxies survive to reach the cluster core, RPS produces a cluster-scale stellar mass gradient of -0.05 log(M_*/M_sun)/Mpc. This mass segregation drives the predicted cluster-scale metallicity gradient of -0.03 dex/Mpc. However, the effects of RPS alone can not explain the higher metallicities measured in cluster galaxies at z=0.35. We hypothesize that additional mechanisms including steep internal metallicity gradients and self-enrichment due to gas strangulation are needed to reproduce our observations at z=0.35.

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arXiv2017

How Supernovae Launch Galactic Winds

We use idealized three-dimensional hydrodynamic simulations of global galactic discs to study the launching of galactic winds by supernovae (SNe). The simulations resolve the cooling radii of the majority of supernova remnants (SNRs) and thus self-consistently capture how SNe drive galactic winds. We find that SNe launch highly supersonic winds with properties that agree reasonably well with expectations from analytic models. The energy loading ($η_E = \dot{E}_{\rm wind} / \dot{E}_{\rm SN}$) of the winds in our simulations are well converged with spatial resolution while the wind mass loading ($η_M = \dot{M}_{\rm wind} / \dot{M}_\star$) decreases with resolution at the resolutions we achieve. We present a simple analytic model based on the concept that SNRs with cooling radii greater than the local scale height breakout of the disc and power the wind. This model successfully explains the dependence (or lack thereof) of $η_E$ (and by extension $η_M$) on the gas surface density, star formation efficiency, disc radius, and the clustering of SNe. The winds in the majority of our simulations are weaker than expected in reality, likely due to the fact that we seed SNe preferentially at density peaks. Clustering SNe in time and space substantially increases the wind power.

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arXiv2016

Mass modeling of galaxy clusters: quantifying hydrostatic bias and contribution from non-thermal pressure

Galaxy cluster mass determinations achieved using X-ray and Sunyaev-Zel'dovich data combined with the assumption of hydrostatic equilibrium are generally biased. The bias exists for two main reasons: non-thermal pressure forces are expected to contribute to the overall pressure balance and deviations from spherical symmetry and hydrostatic equilibrium can be present. In this paper, we use a sample of zoom-in hydrodynamical simulations of galaxy clusters to measure the magnitude of hydrostatic bias and the non-thermal contribution to the total pressure. We propose a new empirical model for non-thermal pressure based on our simulations that can be applied to observations. We show that our model can be successfully applied to remove most of the bias related to neglection of non-thermal pressure, which is usually not included in hydrostatic cluster mass profile reconstructions. The use of this model may significantly improve the calibration of cluster scaling relations that are a key tool for cluster cosmology.

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arXiv2016

Radial Distribution Of ISM Gas-phase Metallicity In CLASH Clusters at z~0.35: A New Outlook On Environmental Impact On Galaxy Evolution

We present the first observation of cluster-scale radial metallicity gradients from star-forming galaxies. We use the DEIMOS spectrograph on the Keck II telescope to observe two CLASH clusters at z~0.35: MACS1115+0129 and RXJ1532+3021. Based on our measured interstellar medium (ISM) properties of star-forming galaxies out to a radius of 2.5 Mpc from the cluster centre, we find that the galaxy metallicity decreases as a function of projected cluster-centric distance (-0.15+/-0.08 dex/Mpc) in MACS1115+01. On the mass-metallicity relation (MZR), star-forming galaxies in MACS1115+01 are offset to higher metallicity (~0.2 dex) than the local SDSS galaxies at a fixed mass range. In contrast, the MZR of RXJ1532+30 is consistent with the local comparison sample. RXJ1532+30 exhibits a bimodal radial metallicity distribution, with one branch showing a similar negative gradient as MACS1115+01 (-0.14+/-0.05 dex/Mpc) and the other branch showing a positive radial gradient. The positive gradient branch in RXJ1532+30 is likely caused by either interloper galaxies or an in-plane merger, indicating that cluster-scale abundance gradients probe cluster substructures and thus the dynamical state of a cluster. Most strikingly, we discover that neither the radial metallicity gradient nor the offset from the MZR is driven by the stellar mass. We compare our observations with Rhapsody-G cosmological hydrodynamical zoom-in simulations of relaxed galaxy clusters and find that the simulated galaxy cluster also exhibits a negative abundance gradient, albeit with a shallower slope (-0.04+/-0.03 dex/Mpc). Our observations suggest that the negative radial gradient originates from ram-pressure stripping and/or strangulation processes in the cluster environments.

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arXiv2016

RHAPSODY-G simulations II - Baryonic growth and metal enrichment in massive galaxy clusters

We study the evolution of the stellar component and the metallicity of both the intracluster medium and of stars in massive ($M_{\rm vir}\approx 6\times 10^{14}$ M$_{\odot}/h$) simulated galaxy clusters from the Rhapsody-G suite in detail and compare them to observational results. The simulations were performed with the AMR code RAMSES and include the effect of AGN feedback at the sub-grid level. AGN feedback is required to produce realistic galaxy and cluster properties and plays a role in mixing material in the central regions and regulating star formation in the central galaxy. In both our low and high resolution runs with fiducial stellar yields, we find that stellar and ICM metallicities are a factor of two lower than in observations. We find that cool core clusters exhibit steeper metallicity gradients than non-cool core clusters, in qualitative agreement with observations. We verify that the ICM metallicities measured in the simulation can be explained by a simple "regulator" model in which the metallicity is set by a balance of stellar yield and gas accretion. It is plausible that a combination of higher resolution and higher metal yield in AMR simulation would allow the metallicity of simulated clusters to match observed values; however this hypothesis needs to be tested with future simulations. Comparison to recent literature highlights that results concerning the metallicity of clusters and cluster galaxies might depend sensitively on the scheme chosen to solve the hydrodynamics.

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arXiv2016

Supernova feedback in a local vertically stratified medium: interstellar turbulence and galactic winds

We use local Cartesian simulations with a vertical gravitational potential to study how supernova (SN) feedback in stratified galactic discs drives turbulence and launches galactic winds. Our analysis includes three disc models with gas surface densities ranging from Milky Way-like galaxies to gas-rich ultra-luminous infrared galaxies (ULIRGs), and two different SN driving schemes (random and correlated with local gas density). In order to isolate the physics of SN feedback, we do not include additional feedback processes. We find that, in these local box calculations, SN feedback excites relatively low mass-weighted gas turbulent velocity dispersions ~3-7 km/s and low wind mass loading factors < 1 in all the cases we study. The low turbulent velocities and wind mass loading factors predicted by our local box calculations are significantly below those suggested by observations of gas-rich and rapidly star-forming galaxies; they are also in tension with global simulations of disc galaxies regulated by stellar feedback. Using a combination of numerical tests and analytic arguments, we argue that local Cartesian boxes cannot predict the properties of galactic winds because they do not capture the correct global geometry and gravitational potential of galaxies. The wind mass loading factors are in fact not well-defined in local simulations because they decline significantly with increasing box height. More physically realistic calculations (e.g., including a global galactic potential and disc rotation) will likely be needed to fully understand disc turbulence and galactic outflows, even for the idealized case of feedback by SNe alone.

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