Harvard Astronomy 201b

Posts Tagged ‘winds and jets evidence and effects’

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

Handout: Download Here

Link to paper: Hopkins et al. (2012)


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.


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.


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 for the four different types of galaxies studied (from left to right: HiZ, Sbc, MW, and SMC). Taken from figure 1 of the paper.

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.

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.

new model

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.

References and Further Reading

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

Hopkins, P. F., Quataert, E., & Murray, N. 2011, MNRAS, 417, 950 (Paper I)

Hopkins, P. F., Quataert, E., & Murray, N. 2012, MNRAS, 421, 3488 (Paper II)

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

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

ARTICLE: An L1551 Extravaganza: Three Articles

In Journal Club 2013 on April 1, 2013 at 11:55 am

Wide-Field Near-Infrared Imaging of the L1551 Dark Cloud by Masahiko Hayashi and Tae-Soo Pyo

Observations of CO in L1551 – Evidence for stellar wind driven shocks by Ronald L. Snell, Robert B. Loren & Richard L. Plambeck

Multiple Bipolar Molecular Outflows from the L1551 IRS5 Protostellar System by Po-Feng Wu, Shigehisa Takakuwa, and Jeremy Lim

Summary by Fernando Becerra, Lauren Woolsey, and Walker Lu


Young Stellar Objects and Outflows

In the early stages of star formation, Young Stellar Objects (YSOs) produce outflows that perturb the surrounding medium, including their parental gas cloud. The current picture of star formation indicates that once gravity has overcome pressure support, a central protostar is formed surrounded by an infalling and self-supported gas disk. In this context outflows are powered by the release of gravitational potential energy liberated by matter accreting onto the protostar. Outflows are highly energetic and often spatially extended phenomena, and are observable over a wide range of wavelengths from x-ray to the radio. Early studies of molecular outflows (predominantly traced by CO emission lines, e.g. Snell et al. 1980, see below) have shown that most of their momentum is deposited in the surrounding medium and so provide a mass loss history of the protostar. In contrast, the optical and near-infrared (NIR) emission trace active hot shocked gas in the flow.

Interactions with the surrounding medium: Herbig-Haro objects, bow shocks and knots

When outflows interact with the medium surrounding a protostar, emission can often be produced. One example of this is emission from Herbig-Haro (HH) objects, which can be defined as “small nebulae in star-forming regions as manifestations of outflow activity from newborn stars”. The most common pictures show a HH object as a well-collimated jet ending in a symmetric bow shock. Bow shocks are regions where the jet accelerates the ambient material. The shock strength should be greatest at the apex of the bow, where the shock is normal to the outflow, and should decline in the wings, where the shocks become increasingly oblique. Another interesting feature we can distinguish are knots. Their origin is still unknown but a few theories have been developed over the years. They can formed due to the protostar producing bursts of emission periodically in time, or producing emission of varying intensity. They can also form due to interactions between the jet and the surrounding Interstellar Medium (ISM), or due to different regions of the jet having different velocities.

An exceptional case: The L1551 region

The L1551 system is an example of a region in which multiple protostars exhibiting outflows are seen, along with several HH objects and knots. This system has been catalogued for over fifty years (Lyons 1962), but ongoing studies of the star formation and dynamical processes continue to the present day (e.g. Hayashi and Pyo 2009; Wu et al. 2009). L1551 is a dark cloud with a diameter of ~20′ (~1 pc) located at the south end of the Taurus molecular cloud complex. The dark cloud is associated with many young stellar objects. These YSOs show various outflow activities and characteristics such as optical and radio jets, Herbig-Haro objects, molecular outflows, and infrared reflection nebulae. We will start by giving a broad view of the region based on Hayashi and Pyo 2009, and then we will focus on a subregion called L1551 IRS 5 following Snell et al. 1980 and Wu et al. 2009.

Paper I: An overview of the L1551 Region (Hayashi and Pyo 2009)

The L1551 region is very rich in YSOs, outflows and their interaction with the ISM. The most prominent of the YSOs in this region are HL Tau, XZ Tau, LkHα 358, HH 30, L1551 NE, and L1551 IRS 5 (see Fig. 1), arrayed roughly north to south and concentrated in the densest part (diameter ~10′) of the cloud. The authors based their study on observations using two narrowband filters [Fe II] (\lambda_c = 1.6444 μm, \Delta\lambda = 0.026 μm), H_2 (\lambda_c = 2.116 μm, \Delta\lambda = 0.021 μm) and two broad-band filters: H (\lambda_c = 1.64 μm, \Delta\lambda = 0.28 μm) K_s (\lambda_c = 2.14 μm, \Delta\lambda = 0.31 μm). The choice of [Fe II] and H_2 is motivated by previous studies suggesting that the [Fe II] line has higher velocity than the H_2, and thus arises in jet ejecta directly accelerated near the central object, while H_2 emission may originate in shocked regions. In the particular case of bow shocks, regions of higher excitation near the apex are traced by [Fe II], while H_2 is preferentially found along bow wings. The broadband filters were chosen for comparison with NIR narrowband filters and comparison with previous studies. The total sky coverage was 168 arcmin2, focused on 4 regions of the densest part of the L1551 dark cloud, including HL/XZ Tau, HH30, L1551 IRS5, some HH objects to the west, L1551 NE, and part of HH 262 (see Fig. 1).


Figure 1: An overview of L1551 (Figure 1 of Hayashi and Pyo 2009)

HL/XZ Region

Some of the features the authors identify in this region are:

  • A faint [Fe II] jet emanating from HL Tau to its northeast and southwest. The H_2 emission is hard to identify in the northeast part, but significant H_2 emission blobs are detected in the southwest part (denoted “H2 jet” in Fig. 2)
  • A diffuse feature is also distinguished to the north-northeast of XZ Tau, which may be related to the outflow from one member of the XZ Tau binary.
  • A continuum arc from HL Tau to the north and then bending to the east (“cont arc” in Fig. 2) is also identified. This arc may be a dust density discontinuity where enhanced scattering is observed. Although it is not clear if this arc is related to activities at HL Tau or XZ Tau.
  • Another arc feature to the south from HL Tau curving to the southeast can be identified. Two H_2 features are located in the arc and indicated by arrows in Fig. 2. This may be shocked regions in the density discontinuity.
  • Other H_2 features can be distinguished: “A” (interpreted as a limb-brightened edge of the XZ Tau counter-outflow) and “B”, “C”, “a” (blobs driven by the LkH\alpha 358 outflow and interacting with the southern outflow bubble of XZ Tau).

Figure 2: HL/XZ Region (Figure 2 of Hayashi and Pyo 2009)

HH 30 Region

HH 30 is a Herbig-Haro (HH) object including its central star, which is embedded in an almost edge-on flared disk. Although this object doesn’t have clear signs of large-scale [Fe II] or H_2 emission (see Fig. 3), a spectacular jet was detected in the [S II] emission line in previous studies. Despite that, the authors identify two faint small-scale features based on the [Fe II] frame: one to the northeast (corresponding to the brightest part of the [S II] jet) and one to the south-southeast (corresponding to a reflection nebula)


Figure 3: HH 30 Region (Figure 3 of Hayashi and Pyo 2009)

L1551 NE

L1551 NE is a deeply embedded object associated with a fan-shaped infrared reflection nebula opening toward the west-southwest seen in the broad-band Ks continuum emission. It has an opening angle of 60^o. The most important features in this region are:

  • A needle-like feature connecting L1551 NE and HP2 is distinguished from the continuum-substracted [Fe II] image, associated with an [Fe II] jet emanating from L1551 NE.
  • A diffuse red patch at the southwest end of the nebula (denoted as HP1) is dominated by H_2 emission
  • Five isolated compact features are detected in the far-side reflection nebula: HP3 and HP3E ([Fe II] emission), HP4 (both [Fe II] and H_2 emission) and HP5 and HP6 (H_2 emission). All of them are aligned on a straight line that is extrapolated from the jet connecting NE and HP2, naturally assigned to features on the counter-jet.
  • Comparing this data to previous observations in [S II] and radio we can deduce radial velocities of 160-190 km/s for HP2, and 140-190 km/s for HP4 and HP5. With radial velocities in the range 100-130 km/s for these knots, the inclination of the jet axis is estimated to be 45^o60^o.

L1551 IRS-5

L1551 IRS 5 is a protostellar binary system with a spectacular molecular outflow (Snell et al. 1980; see below) and a pair of jets emanating from each of the binary protostars. A conspicuous fan-shaped infrared reflection nebula is seen in Fig. 4, widening from IRS 5 toward the southwest. At the center of this nebula, the two [Fe II] jets appear as two filaments elongated from IRS 5 to its west-southwest; the northern jet is the brighter of the two. Knots A, B and C located farther west and west-southwest of PHK3 (associated with H_2 line emission) have significant [Fe II] emission.


Figure 4: A close-up of IRS-5 (Figure 5 of Hayashi and Pyo 2009)

A counter-jet only seen in the [Fe II] frame can be distinguished to the northeast of IRS 5. Considering its good alignment with the northern jet, it can be interpreted as the receding part of the jet. Based on brightness comparison between the both jets, and transforming H-band extinction to visual extinction the authors deduce a total visual extinction of Av=20-30 mag. Besides the counter-jet, the authors also detect the northern and southern edge of the reflection nebula that delineate the receding-side outflow cone of IRS5.

A brief summary of the HH objects detected in the IRS5 region:

  • HH29: Consistent with a bow shock, its [Fe II] emission features are compact, while the H_2 emission is diffuse. Both emissions are relatively separate.
  • HH260: Consisted with a bow shock with compact [Fe II] emission knot located at the apex of a parabolic H_2 emission feature.
  • HP7: Its [Fe II] and H_2 emission suggest it is also a bow shock driven by an outflow either from L1551 IRS5 or NE.
  • HH264: It is a prominent H_2 emission loop located in the overlapping molecular outflow lobes of L1551 IRS5 and NE. Its velocity gradients are consistent with the slower material surrounding a high-velocity (~ -200 km/s in radial velocity) wind axis from L1551 IRS 5 (or that from L1551 NE)
  • HH 102: Loop feature dominated by H_2 emission (and no [Fe II] emission) similar to HH264. Considering that the major axes of the two elliptical features are consisted with extrapolated axis of the HL Tau jet, it is suggested that they might be holes with wakes on L1551 IRS5 and/or NE outflow lobe(s) that were bored by the collimated flow from HL Tau.

Comparison of Observations

Near-infrared [Fe II] and H_2 emission show different spatial distributions in most of the objects analyzed here. On one hand the [Fe II] emission is confined in narrow jets or relatively compact knots. On the other hand, the H_2 emission is generally diffuse or extended compared with the [Fe II] emission, with none of the H_2 features showing the well collimated morphology as seen in [Fe II].
These differences can be understood based on the conditions that produce different combinations of [Fe II] and H_2 emission:

  • Case of spatially associated [Fe II] and H_2 emissions: Generally requires fast dissociative J shocks (Hollenbach & McKee 1989; Smith 1994; Reipurth et al. 2000).
  • Case of a strong H_2 emission without detectable [Fe II] emission: Better explained by non-dissociative C shocks

The interpretation of differences in [Fe II] and H_2 emission as a result of distinct types shocks is supported by observational evidence showing that the [Fe II] emission usually has a much higher radial velocity than the H_2 emission. In the case of HH 29, HH 260 and HP 7 the [Fe II] emission arises in the bow tips where the shock velocity is fast (~50 km/s) and dissociative whereas H_2 emission occurs along the trailing edges where the shock is slower (~20 km/s)

Paper II: Landmark Observations of Snell et al. 1980

One of the original papers in the study of L1551 was written by Snell, Loren and Plambeck (1980). In this paper, the authors use 12CO to map what they find to be a double-lobed structure extending from the infrared source IRS-5 (see Figures 1, 4). This system is also associated with several Herbig-Haro objects, which are small dense patches that are created in the first few thousands of years after a star is formed. This star is consistent with a B star reddened by 20 magnitudes of dust extinction along the line of sight, through a distance of 160 pc (Snell 1979). By studying these outflows, we are able to better understand the evolution of YSOs.


Snell et al. (1980) made their observations using the 4.9 meter antenna at Millimeter Wave Observatory in Texas. Specifically, they considered the J = 1-0 and J = 2-1 transitions of ^{12}CO and ^{13}CO. Additionally, they made J = 1-0 observations with the NRAO 11 meter antenna. They found asymmetries in the spectral lines, shown below in Figure 5. To the northeast of IRS-5, the high-velocity side of the line has a broad feature, and the southwest of IRS-5 presents a similar broad feature on the low-velocity side of the spectral line. No such features were found to the NW, SE, or in the central position of IRS-5.

Snell et al. 1980, figure 4

Figure 5: 12CO and 13CO 1-0 transition lines; top is NE of central source, bottom is SW of source (Figure 4 of Snell et al. 1980)

The J = 2-1 ^{12}CO transition is enhanced relative to the J = 1-0 transition of ^{12}CO, suggesting that the ^{12}CO emission is not optically thick. If the emission was optically thick, the J = 1-0 line would be the expected dominant transition as it is a lower level transition. The observations also suggest an excitation temperature for the 2-1 transition of T_{ex} ~ 8-35 K. This would only relate to the gas temperature if the environment is in local thermal equilibrium, but it does set a rough minimum temperature. The ^{13}CO emission for the 1-0 transition is roughly 40 times weaker than the same transition for ^{12}CO, which further suggests both isotopes are optically thin in this region (if the ^{12}CO is already optically thin, the weaker transition means ^{13}CO is even more so). The geometry of the asymmetries in the line profiles seen to the NE and SW combined with the distance to L1551 suggest lobes that extend out 0.5 pc in both directions.


Column density

The authors make a rough estimate of the column density of the gas in these broad velocity features by making the following assumptions:

  • the ^{12}CO emission observed is optically thin
  • the excitation temperature is 15 K
  • the ratio of CO to H2 is a constant 5 \times 10^{-5}

With these assumptions, the authors find a column density of 10^{20} cm^{-2}. This is much lower than the region’s extinction measurement of A_{v} = 20 magnitudes by Snell (1979), as the outflow is sweeping out material around the star(s).

Stellar wind and bow shocks

The model of the wind that Snell et al. (1980) suggest is a bimodal wind that sweeps out material in two “bubble-like” lobes, creating a dense shell and possible ionization front that shocks the gas (More on shocks). The physical proximity of the Herbig-Haro (HH) objects in the southwest lobe coming from IRS-5 suggests a causal relationship. Previous work found that the optical spectra of the HH objects resemble spectra expected of shocked gas (Dopita 1978; Raymond 1979).

There is evidence that the CO lobes are the result of a strong stellar wind, the authors clarify this with the schematic shown in Figure 6. They suggest that the wind is creating a bow shock and a shell of swept-up material (More on outflows in star-forming regions). The broad velocity features on the CO emission line wings reach up to 15 km/s, suggesting the shell is moving out at that speed. The Herbig-Haro objects HH29 and HH102 have radial velocities of approximately 50 km/s in the same direction as the SW lobe is expanding (Strom, Grasdalen and Strom 1974). Additionally, Cudworth and Herbig (1979) measured the transverse velocities of HH28 and HH29, and found that the objects were moving at a speed of 150 to 170 km/s away from IRS-5. To have reached these velocities, the HH objects must have been accelerated, most likely by a strong stellar wind at speeds above 200 km/s. The bimodal outflow suggests a thick accretion disk around the young star.

Snell et al. 1980, figure 5

Figure 6: Schematic drawing of stellar outflow (Figure 5 of Snell et al. 1980)

Mass-loss rate

The average density in the region away from the central core is 10^{3} {\rm ~cm}^{-3} (Snell 1979), so the extent and density of the shell implies a swept-up mass of 0.3 to 0.7 solar masses. With the measured velocity of ~15 km/s assumed to be constant during the lifetime of the shell and at the measured distance of 0.5 pc from the star, the shell was created 30,000 years ago. With this age, the authors determined a mass loss using the lower end of the assumed swept-up mass and the observed volume of the shell. They found a mass-loss rate of 8 \times 10^{-7} {\rm ~M}_{Sun}{\rm ~yr}^{-1}, which can be compared to other stars using a chart like that shown in Figure 7. This is not meant to present constraints on the processes that produce the mass loss in the IRS-5 system, but rather to simply provide context for the stellar wind observed. The low-mass main sequence star(s) that will eventually arise from the IRS-5 system will be characterized by much lower mass loss rates, and studies of mass loss rates from other YSOs suggest that this source is at the high end of the range of expected rates.

Cranmer - Ay201a - Stellar Winds

Figure 7: A representative plot of the different types of stellar wind, presented by Steve Cranmer in lectures for Ay201a, Fall 2012

Snell et al. (1980) suggest observational tests of this wind-driven shock model:

  • H2 emission from directly behind the shock
  • FIR emission from dust swept up in the shell; this is a possibly significant source of cooling
  • radio emission from the ionized gas in the wind itself near to IRS-5 with the VLA or similar; an upper limit of 21 mJy at 6 cm for this region was determined by Gilmore (1978), which suggests the wind is completely ionized

The results of some newer observations that support this wind model are presented in the following section.

Paper III: A new look at IRS-5 by Wu et al. 2009

Wu et al. (2009) focus on the outflows in L1551 IRS5, the same region studied by Snell et al. (1980), but at a higher angular resolution (~3 arcsec; <1000 AU) and much smaller field of view (~1 arcmin; ~0.05 pc or 10,000 AU). Using the sub-millimeter array (SMA) right after it was formally dedicated, the authors detected CO(2-1) line and millimeter continuum in this low-mass star formation system. The mm continuum, which comes mostly from thermal dust emission, is used to estimate the dust mass. The CO(2-1) spectral line is used to trace the outflows around the binary or triple protostellar system at the center, revealing complex kinematics that suggest the presence of three possible bipolar outflows. The authors construct a cone-shaped outflow cavity model to explain the X-shaped component, and a precessing outflow or a winding outflow due to orbital motion model to explain the S-shaped component. The third component, the compact central one, is interpreted as newly entrained material by high-velocity jets.

Important concepts

There are several concepts related to radio interferometry that merit some discussion:

1. Extended emission filtered out by the interferometer
This is the well-known ‘missing flux problem’ unique in interferometry. There is a maximum scale over which structure cannot be detected by an interferometer, and this scale is set by the minimum projected baseline (i.e. projected distance between a pair of antennas) in the array. In the channel maps (Fig. 3 of Wu et al. 2009), there is a big gap between 5.8 km/s and 7.1 km/s. It does not indicate that there is no CO gas at these velocities, but rather is the result of very extended and homogenous CO distribution which is unfortunately filtered out. This effect applies to all channels.

2. Visibility vs. image
The data directly obtained from the interferometers are called visibility data, in which the amplitude and phase are stored for each baseline. The amplitude, as it literally means, measures the flux; and the phase derives the relative location with respect to the phase center (a reference position on the antenna). We need to convolve the visibility data with a point spreading function, also called ‘dirty beam’, to get the image we need. Mathematically, visibility and image are related through a Fourier transform. For more information, see this online course.

3. Channel maps and P-V diagram
In radio observations, velocity of spectral lines plays an important role by providing kinematic information inside ISM. Normally, the radio data has (at least) three dimensions, two in spatial (e.g. R.A. and Decl.) and one in frequency or velocity. Velocity itself can be used to identity outflows, turbulence or infall by the analysis of line profile, or it can be combined with spatial distribution of emission, if the spatial resolution allowed as in this paper, in the form of channel maps or P-V diagram, to show the three-dimensional structure. In terms of outflows, we expect to see gas at velocities much different from the systematic velocity, and a symmetric pattern both in red- and blue-shifted sides will be even more persuasive. For the efforts in visualizing the 3-d datacube in a fancier way, see this astrobite.

The classical image of low-mass star formation

Fig. 8 shows a diagram of a simplified four-step model of star formation (Fig. 7 of Shu et al. 1987). First, the dense gas collapses to form a core; second, a disk forms because of conservation of angular momentum; third, a pair of outflows emerge along the rotational axis; finally, a stellar system comes into place. During this process, bipolar outflows are naturally formed when the wind breaks through surrounding gas. Therefore, bipolar outflows are useful tools to indirectly probe the properties of protostellar systems.

Shu et al. 1987, figure 7

Figure 8: The formation of a low-mass star (see Shu et al. 1987)

Protostar candidates in L1551 IRS5

Two protostellar components as well as their own ionized jets and circumstellar disks have been found in this source. In addition, Lim & Takakuwa (2006) found a third protostellar candidate, as seen in Fig. 9. In this paper the authors investigated the possible connection between these protostars and the outflows.

Lim and Takakuwa 2006

Figure 9: Two 7mm continuum peaks in the north and south represent the binary system in IRS 5. Arrows show the direction of jets from each of the protostars. A third protostellar candidate is found close to the northern protostar, marked by a white cross. (see Lim and Takakuwa 2006)

Three outflow components

Based on CO(2-1) emission, the authors found three distinct structures. Here the identification was not only based on morphology, but also on the velocity (see Fig. 5 and Fig. 9 of Wu et al. 2009). In other words, it is based on information in the 3-d datacube, as shown in 3 dimensions by the visualization below.


Figure 10: 3-D Datacube of the observations. Arrows mark the outflows identified in this paper. Red/blue colors indicate the red/blue-shifted components. The solid arrows mark the X-shaped component; the broad arrows are the S-shaped component; the narrow arrows are the compact central component. There is an axes indicator at the lower-left corner (x – R.A., y – Decl., z- velocity). (visualization by Walker Lu)

  • The X-shaped component

The first one is an X-shaped structure, with its morphology and velocity shown in the paper. Four arms comprise an hour-glass like structure, with an opening angle of ~90 degree. The northwest and southwest arms are blue-shifted with respect to the systematic velocity, and the northeast and southeast arms are red-shifted. This velocity trend is the same with the large-scale bipolar outflow (Snell et al. 1980, Fig. 6 above). However the two blue-shifted arms, i.e. the NW and SW arms, are far from perfect: the SW arm is barely seen, while the NW arm consists of two components, and presents a different velocity pattern. This component coincides well the U-shaped infrared emission found to the SW of IRS5 (see Hayashi & Pyo 2009, or Fig. 4 above).

Outflow components

Figure 11: Components of the Outflow. Coordinates are offset from the pointing center. (Figure 7 of Wu et al. 2009)

  • The S-shaped component

The second component is an S-shaped structure. It extends along the symmetry axis of the X-shaped component as well as the large scale outflow, but in an opposite orientation. As it literally means, this component is twisted like an ‘S’, although the western arm is not so prominent.

  • The compact central component

The third component is a compact, high-velocity outflow very close to the protostars. The authors fitted a 2-d Gaussian structure to this component and made a integrated blue/red-shifted intensity map, which shows a likely outflow feature in the same projected orientation with the X-shaped component and the large scale outflow.

Modeling the outflows

  • A Cone-shaped cavity model for the X-shaped component

The authors then move on to construct outflow models for these components. For the X-shaped component, a cone-shaped outflow cavity model is proposed (see Fig. 12 and compare with Fig. 11). By carefully selecting the opening angle of the cone and position angle of the axis, plus assuming a Hubble-like radial expansion, this model can reproduce the X-shaped morphology and the velocity pattern. The origin of this cone is related to a high-velocity and well collimated wind, followed by a low-velocity and wide-angle wind that excavates the cone-shaped cavity. Therefore, what we see as X-shaped structure is actually the inner walls of the cavity. However, this model cannot incorporate the NW arm into the picture.

Outflow Models

Figure 12: Models from the paper (Figure 10 of Wu et al. 2009)

  • Entrained material model of the compact central component

For the compact central component, the authors argue that it is material that has been entrained recently by the jets. After comparing the momentum of this component and that of the optical jets, they found that the jets are able to drive this component. Moreover, the X-ray emission around this component indicates strong shocks, which could be produced by the high-velocity jets as well. Finally, the possibility of infalling motion instead of outflow is excluded, because the velocity gradient is larger than the typical value and rotation should dominate over infall at this scale.

  • Three models of the X-shaped component

For the S-shaped component, the authors present the boldest idea in this paper. They present three possible explanations at one go, then analyze their pros and cons in four pages. But before we proceed, do we need to consider other possibilities, such as that this S-shaped component is not interconnected at all, but instead contains two separate outflows from different objects, or that the western arm of the component is not actually part of the outflow but some background or foreground emission? Although the model can reproduce the velocity pattern, it has so many adjustable parameters that we could use it to reproduce anything we like (which reminds me of the story of ‘drawing an elephant with four parameters‘). Anyway, let’s consider the three explanations individually.

  1. Near and far sides of outflow cavity walls? This possibility is excluded because it cannot be incorporated into the cone-shaped cavity model aforementioned, and cannot explain the S-shaped morphology.
  2. A precessing outflow? The outflow should be driven by a jet. Then if the jet is precessing, the outflow will also be twisted. The authors considered two scenarios: a straight jet and a bent jet, and found with finely tuned precessing angle and period, the bent jet model can best reproduce the velocity pattern along the symmetry axis. Therefore, the orbital motion between the third protostellar component, which is thought to be the driving source of this jet, and northern protostellar component, is proposed to cause the precession of the jet thus the outflow. A schematic image is shown in Fig 12.
  3. A winding outflow due to orbital motion? The difference between this explanation and the previous one is that in a precessing outflow the driving source itself is swung by its companion protostar, so the outflow is point symmetric, while in a winding outflow the driving source is unaffected but the outflow is dragged by the gravity of its companion as it proceeds, so it has mirror symmetry with respect to the circumstellar disk plain. Again, if we fine-tune the parameters in this model, we can reproduce the velocity pattern.
S-shaped component

Figure 13: The best-fit model for the S-shaped component, a bent precessing jet. Note the velocity patterns for red/blue lobes are not symmetric (Figure 11 of Wu et al. 2009)

A problem here, however, is although either the precessing jet or the winding outflow model is assumed to be symmetric, the authors use asymmetric velocity patterns to fit the two arms of the S-shaped component (see Fig. 12 and 13 in the paper). In the winding outflow model for instance, in order to best fit the observed velocities, the authors fit the eastern arm starting at a net velocity of 2 km/s at the center, while they fit the western arm starting at ~1.2 km/s. This means the two arms start at different velocities at the center.


The nature of X-shaped and S-shaped structures interpreted in this paper is based on the analysis of kinematics and comparison with toy models. However, the robustness of their conclusion suffers from several questions: for example, how to explain the uniqueness of the NW arm in the X-shaped structure? Is the X-shaped structure really a bipolar outflow system, or just two crossing outflows? Why is the compact central component filtered out around the systematic velocity? Is the S-shaped structure really a twisted outflow, or it is two outflow lobes from two separated protostars?

All these questions might be caused by the missing flux problem discussed above. Observations from a single-dish telescope could be  combined with the interferometric data to: 1) find the front and back walls of the outflow cavity, given sufficient sensitivity, to confirm that the X-shaped component is interconnected; 2) detect the extended structure around the systematic velocity, thus verify the nature of the compact central component; 3) recover at least part of the flux in the SW arm of the X-shaped component and the west arm of the S-shaped component, and better constrain the models.


Using radio and infrared observations, these three papers together provide a integrated view of jets and outflows around YSOs in L1551. The near infrared observations of Hayashi & Pyo (2009) searched for [Fe II] and H2 features introduced by shocks, and found quite different configurations among the YSOs in this region. Some have complicated IR emission, such as HL/XZ Tau, while others like L1551 NE and IRS5 have well-collimated jets traced by [Fe II]. Among them, L1551 IRS5 is particularly interesting because it shows two parallel jets. The pilot work of Snell et al. (1980) revealed a bipolar molecular outflow traced by 12CO from IRS 5, which is interpreted to be created by a strong stellar wind from the young star. High angular resolution observation by Wu et al. (2009) confirms this outflow component, as well as the presence of another two bipolar outflows originating from the binary, or triple system in IRS 5. All these observations show us that jets and outflows are essential in star formation, no only by transporting the angular momentum so that YSOs can continue accreting, but also by stirring up ambient gas and feeding turbulence into the ISM, which might determine the core mass function as mentioned in Alves et al. 2007.


Cudworth, K. M. and Herbig, G. 1979, AJ, 84, 548.
Dopita, M. 1978, ApJ Supp., 37, 117.
Gilmore, W. S. 1978, Ph.D Thesis, University of Maryland
Hayashi, M. and Pyo, T.-S. 2009, ApJ, 694, 582-592.
Hollenback, D. and McKee, C. F. 1989, ApJ, 342, 306-336.
Lim, J. and Takakuwa, S. 2006, ApJ, 653, 1.
Lyons, B. T. 1962, ApJ Supp., 7, 1.
Raymond, J. C. 1979, ApJ Supp., 39, 1.
Reipurth, B., et al. 2000, AJ, 120, 3.
Pineda, J. et al. 2011, ApJ Lett., 739, 1.
Shu, F. H., Adams, F. C., Lizano, S. 1987, ARA&A, 25, 23-81.
Smith, M. D. 1994, A&A, 289, 1.
Snell, R. L. 1979, Ph.D Thesis, University of Texas.
Strom, S. E., Grasdalen, G. L. and Strom, K. M. 1974, ApJ, 191, 111.
Vrba, F. J., Strom, S. E. and Strom, K. M., 1976, AJ, 81, 958.
Wu, P.-F., Takakuwa, S., and Lim, J. 2009, 698, 184-197. Read the rest of this entry »

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 Bit About SNRs…

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.

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:
  4. Fadeaway
    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.

McKee and Ostriker Three Phase Model
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.