# Harvard Astronomy 201b

## ARTICLE: Stellar feedback in galaxies and the origin of galaxy-scale winds (Hopkins et al. 2012)

In Journal Club 2013 on April 27, 2013 at 4:21 pm

Summary by Kate Alexander

Link to paper: Hopkins et al. (2012)

## Abstract

Feedback from massive stars is believed to play a critical role in driving galactic super-winds that enrich the intergalactic medium and shape the galaxy mass function, mass–metallicity relation and other global galaxy properties. In previous papers, we have introduced new numerical methods for implementing stellar feedback on sub-giant molecular cloud (sub-GMC) through galactic scales in numerical simulations of galaxies; the key physical processes include radiation pressure in the ultraviolet through infrared, supernovae (Type I and Type II), stellar winds (‘fast’ O star through ‘slow’ asymptotic giant branch winds), and HII photoionization. Here, we showthat these feedback mechanisms drive galactic winds with outflowrates as high as ∼10–20 times the galaxy star formation rate. The mass-loading efficiency (wind mass-loss rate divided by the star formation rate) scales roughly as $\dot{M}_{wind}/\dot{M}_* \propto V_c^{-1}$ (where $V_c$ is the galaxy circular velocity), consistent with simple momentum-conservation expectations. We use our suite of simulations to study the relative contribution of each feedback mechanism to the generation of galactic winds in a range of galaxy models, from Small Magellanic Cloud-like dwarfs and Milky Way (MW) analogues to z ∼ 2 clumpy discs. In massive, gas-rich systems (local starbursts and high-z galaxies), radiation pressure dominates the wind generation. By contrast, for MW-like spirals and dwarf galaxies the gas densities are much lower and sources of shock-heated gas such as supernovae and stellar winds dominate the production of large-scale outflows. In all of our models, however, the winds have a complex multiphase structure that depends on the interaction between multiple feedback mechanisms operating on different spatial scales and time-scales: any single feedback mechanism fails to reproduce the winds observed.We use our simulations to provide fitting functions to the wind mass loading and velocities as a function of galaxy properties, for use in cosmological simulations and semi- analytic models. These differ from typically adopted formulae with an explicit dependence on the gas surface density that can be very important in both low-density dwarf galaxies and high-density gas-rich galaxies.

## Introduction

Galaxy evolution cannot be properly understood without accounting for strong feedback from massive stars. Specifically, in cosmological models that don’t include feedback processes, the star formation rates in simulated galaxies are much too high, as gas quickly cools and collapses. Additionally, these simulations find that the total amount of gas present in galactic disks is too high. Both of these problems can be solved by including local outflows and galactic superwinds that remove baryons from the disks, slowing star formation and bringing simulations in line with observations. Such winds are difficult to include in simulations, however, because they have their origins in stellar feedback processes, which occur on small scales. Most simulations are either too low resolution to properly model these processes, or they make simplifying assumptions about the physics that prevent accurate modeling of winds. Thus, although we have seen observational evidence of such winds in real galaxies (for example, Coil et al. 2011; Hall et al. 2012), until recently simulations have not been able to generate galactic winds from first principles and have instead added them in manually. Hopkins, Quataert, and Murray for the first time present a series of numerical simulations that successfully reproduce galactic winds that are consistent with observations for a wide range of galaxy types. Unlike previous work, their simulations have both sufficiently high resolution to focus on small-scale processes in giant molecular clouds (GMCs) and star forming regions and the physics to account for multiple types of stellar feedback, not just thermal heating from supernovae. These simulations are also discussed in two companion papers (Hopkins et al. 2011 and Hopkins et al. 2012), which focus on the star formation histories and properties of the galactic ISM of simulated galaxies and outline rigorous numerical tests of the models. The 2011 paper was discussed in the 2011 Ay 201b journal club and is summarized nicely here.

## Key Points

1. Simulations designed to study stellar feedback processes have, for the first time, succeeded in reproducing galactic winds capable of removing material from galaxies at several times the star formation rate when multiple feedback mechanisms are included. They also reproduce the observed inverse scaling of wind mass loading with galactic circular velocity, $\dot{M}_{wind}/\dot{M}_* \propto V_c^{-1}$.
2. Radiation pressure is the primary mechanism for the generation of winds in massive, gas-rich galaxies like local starburst galaxies and high redshift galaxies, while supernovae and stellar winds that shock-heat gas are more important in less gas-rich Milky Way-like galaxies and dwarf galaxies.
3. The wind mass loading and velocity are shown to depend on the gas surface density, an effect which has not previously been quantified.

## Models and Methods

The authors used the parallel TreeSPH code GADGET-3 (Springel 2005) to perform their simulations. The simulations include stars, gas, and dark matter and accounts for cooling, star formation, and stellar feedback. The types of stellar feedback mechanisms they include are local deposition of momentum from radiation pressure, supernovae, and stellar winds; long-range radiation pressure from photons that escape star forming regions; shock heating from supernovae and stellar winds; gas recycling; and photoheating of HII regions. The populations of young, massive stars responsible for most of these feedback mechanisms are evolved using standard stellar population models.

These feedback mechanisms are considered for four different standard galaxy models, each containing a bulge, a disk consisting of stars and gas, and a dark matter halo. These four models are:

1. HiZ: a massive, starburst galaxy at a redshift of 2, with properties chosen to resemble those of non-merging submillimeter galaxies.
2. Sbc: a gas-rich spiral galaxy, with properties chosen to resemble those of luminous infrared galaxies (LIRGs).
3. MW: a Milky Way-like spiral galaxy.
4. SMC: a dwarf galaxy, with properties similar to those of the Small Magellanic Cloud.

Simulations were run for each of these models at a range of resolutions (ranging from 10 pc to sub-pc smoothing lengths) to ensure numerical convergence before settling on a standard resolution. The standard simulations include about $10^8$ particles with masses of $500M_{\odot}$ and have smoothing lengths of about 1-5 pc. (For more details, see the companion papers Hopkins et al. 2011 and Hopkins et al. 2012 or the appendix of this paper). The authors then ran a series of simulations with one or more feedback mechanisms turned off, to assess the relative importance of each mechanism to the properties of the winds generated in the standard model containing all of the feedback mechanisms.

## Results

When all feedback mechanisms are included, the simulations produce the galaxy morphologies seen below. The paper also considers what each galaxy would look like in the X-ray, which traces the thermal emission from the outflows.

The range of morphologies produced with all feedback mechanisms active for the four different model galaxies studied (from left to right: HiZ, Sbc, MW, and SMC). The top two rows show mock images of the galaxies in visible light and the bottom two rows show the distribution of gas at different temperatures (blue=cold molecular gas, pink=warm ionized gas, yellow=hot X-ray emitting gas). Taken from figure 1 of the paper.

## Wind properties and dependence on different feedback mechanisms

As shown above, all four galaxy models have clear outflows when all of these feedback mechanisms are included. When individual feedback mechanisms are turned off to study the relative importance of each mechanism in the different models, the strength of the outflows diminishes. For the HiZ and Sbc models, radiation pressure is shown to be the most important contributing process, while for the MW and SMC models gas heating (from supernovae, stellar wind shock heating, and HII photoionization heating) is more important. The winds are found to consist of mostly (mostly ionized) warm (2000 < T < 400000) and (diffuse) hot (T > 400000) gas, with small amounts of (mostly molecular) colder gas (T < 2000K). Particles in the wind have a range of velocities, differing from simple simulations that often assume a wind with a single, constant speed.

For the purpose of studying galaxy formation, the most important property of the wind is the total mass outflow rate, $\dot{M}$. This is often expressed in terms of the galactic wind mass-loading efficiency, defined as $M_{wind}/M_{new} = \int{\dot{M}_{wind}}/\int{\dot{M}_*}$, where $\dot{M}_{wind}$ is the wind outflow rate and $\dot{M}_*$ is the star formation rate. The galactic mass-loading efficiency for each galaxy model is shown below. By comparing the mass-loading efficiency produced by simulations with all feedback mechanisms turned on (the “standard model”) to simulations with some feedback mechanisms turned off, the importance of each mechanism becomes clear. While the standard model cannot be replicated without all of the feedback mechanisms turned on, radiation pressure is clearly much more important than heating for the HiZ case and less important than heating for the MW and SMC cases. The Sbc case is intermediate, with radiation pressure and heating being of comparable importance.

Galactic wind-mass loading efficiency for each of the four galaxy models studied, taken from figure 8 of the paper.

Derivation of a new model for predicting the wind efficiency of a galaxy

After doing some basic plotting of the wind mass-loading efficiency versus global properties of the galaxy models studied (such as star formation rate and total galaxy mass), the authors explore whether there exists a better model for predicting what the wind mass-loading efficiency should be for a given galaxy. After studying the relations between the wind mass loss rate $\dot{M}_{wind}$ and a range of galaxy properties as a function of radius R, time t, and model type, they conclude that the mass loss rate is most directly dependent on the star formation rate $\dot{M}_*$, the circular velocity of the galaxy $V_c(R)$, and the gas surface density $\Sigma_{gas}$. They find that the mass-loading efficiency can be described by:

$\left<\frac{\dot{M}_{wind}}{\dot{M}_*}\right>_R \approx 10\eta_1\left(\frac{V_c(R)}{100 \text{km/s}}\right)^{-(1+\eta_2)}\left(\frac{\Sigma_{gas}(R)}{10 M_{\odot}\text{pc}^{-2}}\right)^{-(0.5+\eta_3)}$

where $\eta_1\sim 0.7-1.5, \eta_2\sim\pm0.3$, and $\eta_3\sim\pm0.15$ are the uncertainties from the fits of individual simulated galaxies to the model. This relationship is plotted below along with instantaneous and time-averaged properties of simulated galaxies. The dependence of the wind mass loss rate on the star formation rate and the circular velocity of the galaxy match previous results and are easily understandable in terms of conservation of momentum, but the dependence on the surface density of the gas initially seems more surprising. Hopkins et al. posit that this is due to the effects of density on supernovae remnants: for low-density galaxies the expanding hot gas from the supernova will sweep up material with little resistance, increasing its momentum over time, while for high-density galaxies radiative cooling of this gas becomes more important, so it will impart less momentum to swept up material. Therefore supernovae in denser environments contribute less to the wind, all other factors being equal, introducing a dependence of the wind mass loss rate on gas surface density.

## Discussion and Caveats

The results from this paper are fairly robust, as the detailed treatment of multiple feedback mechanisms allows the authors to avoid making some of the simplifying assumptions that are often necessary in galaxy simulations (artificially turning off cooling to slow star formation rates, etc). The combination of high resolution simulations and more realistic physics does a good job of confirming previous numerical work and observational results. Needless to say, however, there is still room for improvement.

One major caveat of these results is that all of the model galaxies are assumed to exist in isolation, with no surrounding intergalactic medium (IGM). In reality, galactic outflows will interact with the IGM and hot coronal gas already present in a halo around the galaxy, which affects the structure of the wind. Additionally, feedback effects from black holes and AGN are not discussed, nor are galactic inflows. Comparisons between observations and simulations have shown that AGN-driven winds cannot alone explain the observed star formation rates in real galaxies (Keres et al. 2009), but they may still be an important contributing factor.

Furthermore, the authors note that their method of modeling radiation pressure is “quite approximate” and could be improved. Cosmic rays are not included and the scattering and absorption of UV and IR photons has been simplified. Computational limits (unresolvable processes) also place constraints on the robustness of the results.

Many of the quantities discussed here are easily derivable from high-resolution simulations, but harder to estimate from observations of real galaxies or simulations that have lower resolution. A good discussion of how simulations compare to the observed galaxy population can be found in Keres et al. 2009. Measurements of hydrogen-alpha emission in galaxies can be used to infer their star formation rate and measurements of their X-ray halos can be used to infer the mass-loss rate from galactic winds, but this requires high-quality observational data that becomes increasingly difficult to capture for galaxies at non-zero redshift (Martin 1998). Depending on the resolution of a simulation or telescope, determining quantities like the galactic rotation curve and gas surface density may not be directly possible. When seeking to apply these results to understand the formation history of galaxies in observational data, these limitations should be taken into account.

Hopkins, P. F., Quataert, E., & Murray, N. 2012, MNRAS, 421, 3522

Keres, D. et al., 2009, MNRAS, 396, 2332

Martin, C. L., 1998, ApJ, 513, 156

## ARTICLE: A Theory of the Interstellar Medium: Three Components Regulated by Supernova Explosions in an Inhomogeneous Substrate

In Journal Club 2013 on March 15, 2013 at 11:09 pm

## Abstract (the paper’s, not ours)

Supernova explosions in a cloudy interstellar medium produce a three-component medium in which a large fraction of the volume is filled with hot, tenuous gas.  In the disk of the galaxy the evolution of supernova remnants is altered by evaporation of cool clouds embedded in the hot medium.  Radiative losses are enhanced by the resulting increase in density and by radiation from the conductive interfaces between clouds and hot gas.  Mass balance (cloud evaporation rate = dense shell formation rate) and energy balance (supernova shock input = radiation loss) determine the density and temperature of the hot medium with (n,T) = ($10^{-2.5}$, $10^{5.7}$) being representative values.  Very small clouds will be rapidly evaporated or swept up.  The outer edges of “standard” clouds ionized by the diffuse UV and soft X-ray backgrounds provide the warm (~$10^{4}$ K) ionized and neutral components.  A self-consistent model of the interstellar medium developed herein accounts for the observed pressure of interstellar clouds, the galactic soft X-ray background, the O VI absorption line observations, the ionization and heating of much of the interstellar medium, and the motions of the clouds.  In the halo of the galaxy, where the clouds are relatively unimportant, we estimate (n,T) = ($10^{-3.3}$, $10^{6.0}$) below one pressure scale height.  Energy input from halo supernovae is probably adequate to drive a galactic wind.

## The gist

The paper’s (McKee and Ostriker 1977) main idea is that supernova remnants (SNRs) play an important role in the regulation of the ISM.  Specifically, they argue that these explosions add enough energy that another phase is warranted: a Hot Ionized Medium (HIM)

A basic supernova explosion consists of several phases.  Their characteristic energies are on the order of $10^{51}$ erg, and indeed this is a widely-used unit.  For a fairly well-characterized SNR, see Cas A which exploded in the late 1600s.

Nearby supernova remnant Cassiopeia A, in X-rays from NuSTAR.

1. Free expansion
A supernova explosion begins by ejecting mass with a range of velocities, the rms of which is highly supersonic.  This means that a shock wave propagates into the ISM at nearly constant velocity during the beginning.  Eventually the density decreases and the shocked pressure overpowers the thermal pressure in the ejected material, creating a reverse shock propagating inwards.  This phase lasts for something on the order of several hundred years.  Much of the Cas A ejecta is in the free expansion phase, and the reverse shock is currently located at 60% of the outer shock radius.
2. Sedov-Taylor phase
The reverse shock eventually reaches the SNR center, the pressure of which is now extremely high compared to its surroundings.  This is called the “blast wave” portion, in which the shock propagates outwards and sweeps up material into the ISM.  The remnant’s time evolution now follows the Sedov-Taylor solution, which finds $R_s \propto t^{2/5}$.  This phase ends when the radiative losses (from hot gas interior to the shock front) become important.  We expect this phase to last about $10^3$ years.
3. Snowplow phase
When the age of the SNR approaches the radiative cooling timescale, cooling causes thermal pressure behind the shock to drop, stalling it.  This phase features a shell of cool gas around a hot volume, the mass of which increases as it sweeps up the surrounding gas like a gasplow.  For typical SNRs, this phase ends at an age of about $10^6$ yr, leading into the next phase:
Eventually the shock speed approaches the sound speed in the gas, and turns into a sound wave.  The “fadeaway time” is on the order of $10^{6}$ years.

## So why are they important?

To constitute an integral part of a model of the ISM, SNRs must occur fairly often and overlap.  In the Milky Way, observations indicate a supernova every 40 years.  Given the size of the disk, this yields a supernova rate of $10^{-13} pc^{-3} yr^{-1}$.

Here we get some justification for an ISM that’s a bit more complicated than the then-standard two-phase model (proposed by Field, Goldsmith, and Habing (1969) consisting mostly of warm HI gas).  Taking into account the typical fadeaway time of a supernova, we can calculate that on average 1 other supernova will explode within a “fadeaway volume” within that original lifetime.  That volume is just the characteristic area swept out by the shock front as it approaches the sound speed in the last phase.  For a fadeaway time of $10^6$ yr and a typical sound speed of the ISM, this volume is about 100 pc.  Thus in just a few million years, this warm neutral medium will be completely overrun by supernova remnants!  The resulting medium would consist of low-density hot gas and dense shells of cold gas.  McKee and Ostriker saw a better way…

## The Three Phase Model

McKee and Ostriker present their model by following the evolution of a supernova remnant, eventually culminating in a consistent picture of the phases of the ISM. Their model consists of a hot ionized medium with cold dense clouds dispersed throughout. The cold dense clouds have surfaces that are heated by hot stars and supernova remnants, making up the warm ionized and neutral media, leaving the unheated interiors as the cold neutral medium. In this picture, supernova remnants are contained by the pressure of the hot ionized medium, and eventually merge with it. In the early phases of their expansion, supernova remnants evaporate the cold clouds, while in the late stages, the supernova remnant material cools by radiative losses and contributes to the mass of cold clouds.

A schematic of the three phase model, showing how supernovae drive the evolution of the interstellar medium.

In the early phases of the supernova remnant, McKee and Ostriker focus on the effects of electron-electron thermal conduction. First, they cite arguments by Chevalier (1975) and Solinger, Rappaport, and Buff (1975) that conduction is efficient enough to make the supernova remnant’s interior almost isothermal. Second, they consider conduction between the supernova remnant and cold clouds that it engulfs. Radiative losses from the supernova remnant are negligible in this stage, so the clouds are evaporated and incorporated into the remnant. Considering this cloud evaporation, McKee and Ostriker modify the Sedov-Taylor solution for this stage of expansion, yielding two substages. In the first substage, the remnant has not swept up much mass from the hot ionized medium, so mass gain from evaporated clouds dominates. They show this mechanism actually modifies the Sedov-Taylor solution to a $t^{3/5}$ dependance. In the second substage, the remnant has cooled somewhat, decreasing the cloud evaporation, making mass sweep-up the dominant effect. The classic $t^{2/5}$ Sedov-Taylor solution is recovered.

The transition to the late stages occurs when the remnant has expanded and cooled enough that radiative cooling becomes important. Here, McKee and Ostriker pause to consider the properties of the remnant at this point (using numbers they calculate in later sections): the remnant has an age of 800 kyr, radius of 180 pc, density of $5 \times 10^{-3} cm^{-3}$, and temperature of 400 000 K. Then, they consider effects that affect the remnant’s evolution at this stage:

• When radiative cooling sets in, a cold, dense shell is formed by runaway cooling: in this regime, radiative losses increase as temperature decreases. This effect is important at a cooling radius where the cooling time equals the age of the remnant.
• When the remnant’s radius is larger than the scale height of the galaxy, it could contribute matter and energy to the halo.
• When the remnant’s pressure is comparable to the pressure of the hot ionized medium, the remnant has merged with the ISM.
• If supernovae happen often enough, two supernova remnants could overlap.
• After the cold shell has developed, when the remnant collides with a cold cloud, it will lose shell material to the cloud.

Frustratingly, they find that these effects become important at about the same remnant radius. However, they find that radiative cooling sets in slightly before the other effects, and continue to follow the remnant’s evolution.

The mean free path of the remnant’s cold shell against cold clouds is very short, making the last effect important once radiative cooling has set in. The shell condenses mass onto the cloud since the cloud is more dense, creating a hole in the shell. The density left behind in the remnant is insufficient to reform the shell around this hole. The radius at which supernova remnants are expected to overlap is about the same as the radius where the remnant is expected to collide with its first cloud after having formed a shell. Then, McKee and Ostriker state that little energy loss occurs when remnants overlap, and so the remnant must merge with the ISM here.

At this point, McKee and Ostriker consider equilibrium in the ISM as a whole to estimate the properties of the hot ionized medium in their model. First, they state that when remnants overlap, they must also be in pressure equilibrium with the hot ionized medium. Second, the remnants have added mass to the hot ionized medium by evaporating clouds and removed mass from the hot ionized medium by forming shells – but there must be a mass balance. This condition implies that the density of the hot ionized medium must be the same as the density of the interior of the remnants on overlap. Third, they state that the supernova injected energy that must be dissipated in order for equilibrium to hold. This energy is lost by radiative cooling, which is possible as long as cooling occurs before remnant overlap. Using supernovae energy and occurrence rate as well as cold cloud size, filling factor, and evaporation rate, they calculate the equilibrium properties of the hot ionized medium. They then continue to calculate “typical” (median) and “average” (mean) properties, using the argument that the hot ionized medium has some volume in equilibrium, and some volume in expanding remnants. They obtain a typical density of $3.5 \times 10^{-3} cm^{-3}$, pressure of $5.0 \times 10^{-13} cm^{-2} dyn$, and temperature of 460 000 K.

McKee and Ostriker also use their model to predict different properties in the galactic halo. There are fewer clouds, so a remnant off the plane would not gain as much mass from evaporating clouds. Since the remnant is not as dense, radiative cooling sets in later – and in fact, the remnant comes into pressure equilibrium in the halo before cooling sets in. Supernova thus heat the halo, which they predict would dissipate this energy by radiative cooling and a galactic wind.

Finally, McKee and Ostriker find the properties of the cold clouds in their model, starting from assuming a spectrum of cloud sizes. They use Hobbs’s (1974) observations that the number of clouds with certain column density falls with the column density squared, adding an upper mass limit from when the cloud exceeds the Jeans mass and gravitationally collapses. A lower mass limit is added from considering when a cloud would be optically thin to ionizing radiation. Then, they argue that the majority of the ISM’s mass lies in the cold clouds. Then using the mean density of the ISM and the production rate of ionizing radiation, they can find the number density of clouds and how ionized they are.

## Parker Instability

The three-phase model gives little prominence to magnetic fields and giant molecular clouds. As a tangent from McKee and Ostriker’s model, the Parker model (Parker 1966) will be presented briefly to showcase the variety of considerations that can go into modelling the ISM.

The primary motivation for Parker’s model are observations (from Faraday rotation) that the magnetic field of the Galaxy is parallel to the Galactic plane. He also assumes that the intergalactic magnetic field is weak compared to the galactic magnetic field: that is, the galactic magnetic field is confined to the galaxy. Then, Parker suggests what is now known as the Parker instability: that instabilities in the magnetic field cause molecular cloud formation.

Parker’s argument relies on the virial theorem: in particular, that thermal pressure and magnetic pressure must be balanced by gravitational attraction. Put another way, field lines must be “weighed down” by the weight of gas they penetrate: if gravity is too weak, the magnetic fields will expand the gas it penetrates. Then, he rules out topologies where all field lines pass through the center of the galaxy and are weighed down only there: the magnetic field would rise rapidly towards the center, disagreeing with many observations. Thus, if the magnetic field is confined to the galaxy, it must be weighed down by gas throughout the disk.

He then considers a part of the disk, and assumes a uniform magnetic field, and shows that it is unstable to transverse waves in the magnetic field. If the magnetic field is perturbed to rise above the galactic plane, the gas it penetrates will slide down the field line towards the disk because of gravity. Then, the field line has less weight at the location of the perturbation, allowing magnetic pressure to grow the perturbation. Using examples of other magnetic field topologies, he argues that this instability is general as long as gravity is the force balancing magnetic pressure. By this instability, he finds that the end state of the gas is in pockets spaced on the order of the galaxy’s scale height. He suggests that this instability explains giant molecular cloud formation. The spacing between giant molecular clouds is of the right order of magnitude. Also, giant molecular clouds are too diffuse to have formed by gravitational collapse, whereas the Parker instability provides a plausible mode of formation.

In today’s perspective, it is thought that the Parker instability is indeed part of giant molecular cloud formation, but it is unclear how important it is. Kim, Ryu, Hong, Lee, and Franco (2004) collected three arguments against Parker instability being the sole cause:

• The formation time predicted by the Parker instability is ~10 Myr. However, looking at giant molecular clouds as the product of turbulent flows gives very short lifetimes (Ballesteros-Paredes et al. 1999). Also, ~10 Myr post T Tauri stars are not found in giant molecular clouds, suggesting that they are young (Elmegreen 2000).
• Adding a random component to the galactic magnetic field can stabilize the Parker instability (Parker & Jokipii 2000, Kim & Ryu 2001).
• Simulations suggest that the density enhancement from Parker instability is too small to explain GMC formation (Kim et al. 1998, 2001).

## Does it hold up to observations?

The paper offers several key observations justifying the model.  First, of course, is the observed supernova rate which argues that a warm intercloud medium would self-destruct in a few Myr.  Other model inputs include the energy per supernova, the mean density of the ISM, and the mean production rate of UV photons.

They also cite O VI absorption lines and soft X-ray emission as evidence of the three-phase model.  The observed oxygen line widths are a factor of 4 smaller than what would be expected if they originated in shocks or the Hot Ionized Medium, and they attribute this to the idea that the lines are generated in the conductive surfaces of clouds — a key finding of their model above.  If one observes soft X-ray emission across the sky, a hot component of T ~ $10^{6.3}$ K can be seen in data at 0.4-0.85 keV, which cannot be well explained just with SNRs of this temperature (due to their small filling factor).  This is interpreted as evidence for large-scale hot gas.

## So can it actually predict anything?

Sure!  Most importantly, with just the above inputs — the supernova rate, the energy per supernova, and the cooling function — they are able to derive the mean pressure of the ISM (which they predict to be $3700 K cm^-3$, very close to the observed thermal pressures).

## Are there any weaknesses?

The most glaring omission of the three-phase model is that the existence of large amounts of warm HI gas, seen through 21cm emission, is not well explained; they underpredict the fraction of hydrogen in this phase by a factor of 15!  In addition, observed cold clouds are not well accounted for; they should disperse very quickly even at temperatures far below that of the ISM that they predict.