In this section, we briefly discuss results from theoretical studies of accretion processes of Milky Way-type galaxies based on hydrodynamical simulations. Although theses studies will also be discussed in a more general context in other chapters in the second part of this book, they are particularly important for our understanding of gas accretion in the Milky Way and thus need to be considered in this review.
3.1. Hydrodynamical simulations of gas infall
Whatever the initial conditions of an infalling gas structure at a given distance to the Galaxy might be, the gas will interact with the ambient hot coronal medium that fills the galaxy's dark-matter potential. Modeling these interaction processes are of fundamental importance to understand origin and fate of accreted material and to explain the observations discussed in the previous sections.
As mentioned earlier, one plausible scenario for gas accretion in Milky-Way size gaseous halos with Mhalo ∼ 1012 M⊙ and Rvir ∼ 250 kpc is the cooling and fragmentation of hot (T ∼ 106 K) halo gas that falls towards the Galactic disk in the form of overdense clouds (Maller & Bullock 2004). Support for this scenario comes from early SPH simulations (Kaufmann et al. 2006, 2009; Sommer-Larsen 2006). In these simulations, cool pockets of gas condense out from the hot coronal gas from thermal instabilities, mimicing the properties of the Galactic 21 cm HVCs that have d < 20 kpc (Peek, Putman & Sommer-Larsen 2008). More recent studies indicate, however, that these early studies may draw a too simplistic picture of the HVC condensation process. One problem lies in the buoyancy of thermally unstable gas, which is expected to disrupt condensing seed structures before they can cool efficiently (Burkert & Lin 2000). Thus, linear isobaric perturbations in a homogeneous, hot coronal gas are expected to be inefficient to develop cool gas patches in the halo, unless the entropy gradient is very small. An alternative scenario is offered by Joung, Bryan & Putman (2012), who study the condensation process in Galactic coronal gas from non-linear perturbations that might be generated from either infalling intergalactic gas (e.g., Kereš & Hernquist 2009; Kereš et al. 2005; Brooks et al. 2009) or from the gaseous leftovers of satellite accretion (Bland-Hawthorn et al. 2007; Grcevich & Putman 2009; Nichols & Bland-Hawthorn 2011; see below). Joung, Bryan & Putman (2012) find from their high-resolution adaptive mesh refinement (AMR) hydrodynamical simulations that the efficiency for condensing out cool gas patches from non-linear perturbations depends critically on the ratio between the cooling time and the acceleration time (to reach the sound speed) in the gas. If cooling is efficient (such as in clumpy gas and/or in gas with a high-metallicity), cool patches can condense out in a Milky Way-type halo before being disrupted and may show up as 21 cm HVCs. The mixing of outflowing, metal-enriched fountain material and infalling coronal material possibly represents a key process that determines the net accretion through the disk-halo interface, as it regulates the cooling efficiency of the gas (Armilotta, Fraternali & Marinacci 2016; Marinacci et al. 2010).
Cosmologically “cold” (T < Tvir) streams of intergalactic gas are expected to feed the halos of Milky Way-type galaxies (e.g., van de Voort et al. 2011) and such streams may penetrate deep into the hot halo before they are being disrupted. From their AMR simulations, Fernandez, Joung & Putman (2012) find that cold streams from the IGM may continuously bring up to ∼ 108 M⊙ of H i into the Milky Way halo and this amount of neutral gas appears to be fairly constant over time (at least for the last 5 Gyr, or z = 0−0.45). The H i gas accretion rate for a Milky Way-type galaxy in these simulations comes out to 0.2 M⊙ yr−1, thus very similar to what has been derived for the Galactic HVC population at d < 20 kpc, i.e., without the contribution of the MS (see Sect. 2.4).
Next to the cloud-condensation scheme and the cold streams, the interaction of Milky-Way type galaxies with dwarf satellites can transport large amounts of relatively cool gas in the halos of MW-type galaxies directly. From their study of a Milky-Way type galaxy and its satellite-galaxy environment Fernandez, Joung & Putman (2012) derive a median mass-loss rate of H i of ∼ 3 × 10−3 M⊙ yr−1, suggesting that satellites add ∼ 3 × 106 M⊙ of neutral gas to the host galaxy within a Gyr. Based on their overall results, this H i mass flow represents a significant albeit not dominating contribution to the neutral gas accretion rate of the host galaxy. In the light of these results, the observed neutral gas supply from Magellanic Stream for the Milky Way (MHI,MS ∼ 2.5 × 108 M⊙ within 0.5−1.0 Gyr); see Sect. 2.1) is huge, underlining that the MS represents a rather extreme (and atypical) example for gas accretion by satellite interactions.
As suggested by Peek (2009), the specific angular momentum of the gas might be a key parameter to discriminate between the various scenarios for the origin of the HVCs. Gas that is accreted from dwarf satellites by either ram-pressure stripping or tidal interactions enters the halo with a large initial angular momentum (L ∼ 3 × 104 km s−1 kpc), while the angular momentum of the cooling halo clouds is one order of magnitude less (see, e.g., Peek et al. 2008; Kaufmann et al. 2009). Thus, gas accretion from mergers with Milky Way satellites takes place predominantly in the outer regions (R > 15 kpc) of the Galactic disk. In fact, observations indicate that part of the MS (i.e., the Leading Arm) might already be close to the outer disk of the Milky Way, where it possibly already interacts with the underlying interstellar gas (McClure-Griffiths et al. 2008; Casetti-Dinescu et al. 2014), thus providing support for this scenario. Following Peek (2009), the HVCs at small galactocentric distances (R < 15 kpc), in contrast, are more likely to be produced by the condensed halo clouds and it is this process that appears to dominate the feeding of the inner-disk regions where most of the star formation takes place.
Independently of the origin of the infalling gas, how much of it makes it into the disk? To answer this crucial question for the Milky Way and other galaxies of similar mass and type, the initial conditions for the gas infall (e.g., infall velocities, individual cloud masses, density profile of the ambient coronal gas) turn out to be particularly important, as we will discuss in the following.
At T = 106 K in the coronal gas, the infall velocity of the HVCs is close to the sound speed in ambient hot medium (vs ∼ 150 km s−1), so that infalling material moves either in the subsonic, or transonic, or supersonic regime, leading to different ablation scenarios of infalling gas structures (Kwak et al. 2011). Using a grid-based hydrodynamical 3D code, Heitsch & Putman (2009) simulated the fate of H i clouds moving through the hot coronal gas to explore the characteristic morphologies of the infalling structures, such as head-tail structures, infall velocities, disruption path lengths, and timescales. In Fig. 6 we highlight some of their results. From their study it follows that H i clouds with relatively low initial masses of Mcloud < 104.5 M⊙ lose basically all their neutral gas content when infalling from d = 10−12 kpc. Thus, wherever such cloudlets might be formed in the halo, i.e., either from condensing out of the coronal gas or from dissolving infalling tidal or cosmological gas streams at much larger distances, their gas content will not reach the disk in neutral form. However, if the density contrast between the break-up material and the surrounding medium is large enough, the cloud remnants might reach the disk as warm ionized material (e.g., Shull et al. 2009; Heitsch & Putman 2009; Bland-Hawthorn 2009; Joung et al. 2012) or will otherwise fuel the Galactic Corona.
 |
Figure 6. Time sequences of cloud survival-times (left panel) and disruption length-scale (right panel) of neutral halo clouds of different mass that move through hot coronal gas in a Milky-Way type galaxy (Heitsch & Putman 2009). In these models, H i clouds with masses < 104.5 M⊙ do not survive their passage through the halo when infalling from d = 10−12 kpc. Figure adopted from Heitsch & Putman (2009). |
At the high-mass end, Kwak et al. (2011) predict that for cloud masses Mcloud > 105 M⊙ up to 70 percent of the H i mass remains cool at T < 104, even after a possible break-up of the initial infalling cloud. Such massive structures may even survive the trip from larger distances, as they can move several hundred Myr through the hot halo before being destroyed completely. A similar conclusion was drawn from Joung, Bryan & Putman (2012) from their high-resolution AMR simulations (see above). This result is relevant for the Magellanic Stream at d = 50−100 kpc. Although observations suggest that the MS is further braking up into smaller gas clumps as it moves towards the Milky Way disk (e.g., Stanimirovic et al. 2002, 2008; Westmeier & Koribalski 2008; see also Tepper-Garcia et al. 2015), some dense cores with masses Mcloud > 105 M⊙ may survive and these clumps could enter the disk in the form of neutral gas clouds.
Note that a certain fraction of the halo clouds that condense out of the coronal gas may also reach the disk before the gas cools efficiently, i.e., in the form of warm, ionized gas that never becomes neutral and visible in 21 cm emission. Those structures possibly explain some of the isolated high-velocity UV absorber that have no 21 cm counterparts (Collins, Shull & Giroux 2003; Collins et al. 2009; Shull et al. 2009; Richter et al. 2009; Fraternali et al. 2013; Marasco, Marinacci & Fraternali 2013; R17).
Even with the most advanced hydrodynamical simulations at hand, the exact role of many of the involved physical processes in the time evolution of accreted gas remains unclear. For instance, thermal conduction can suppress shear instabilities and thus stabilize clouds from evaporation by smoothing out steep density/temperature gradients between the cool infalling gas and the hot ambient medium (e.g., Vieser & Hensler 2007). However, such steep gradients appear to be unimportant for the cool/warm gas clouds in the Milky Way halo (e.g., Kwak et al. 2011) and also the diffusion by thermal conduction possibly is small compared to turbulent diffusion processes. Not all of the possibly relevant processes can be included simultaneously in the simulations. In particular, the role of magnetic fields (and resulting magnetohydrodynamical effects) have been mostly ignored so far. Also, the spatial (or mass) resolution of many of the simulations discussed above still is very limited. Since early SPH simulation codes, for instance, had problems in resolving Kelvin-Helmholtz instabilities, cool circumgalactic gas clumps are artificially stabilized by SPH particle effects (Agertz et al. 2007), probably leading to misleading results.
In summary, hydrodynamical simulations predict that the life-time, the morphology, and the mass distribution of infalling gas clouds in the Milky Way halo depend strongly on the local boundary conditions under which the gas is generated and moving through the hot halo. Whether or not an infalling cool/warm gas cloud reaches the Milky Way disk in a region where its supplements star formation depends on its initial distance to the disk, its mass and density, its infall velocity, its angular momentum, and other parameters.
3.2. Cosmological hydrodynamical simulations
Given the complexity of the physics of gas accretion outlined above and the strong dependence of the gas-accretion rate on the local boundary conditions, additional large-scale simulations are desired that also consider a realistic cosmological environment of the Milky Way. In particular, the role of a second nearby spiral galaxy (M31), the gas motions within the super-ordinate galaxy group environment (Local Group), as well as the streaming of intergalactic gas within the local cosmic web that connects the Local Group with its surrounding large-scale structure (e.g., the Virgo cluster) should be studied in such a context.
In a recent paper, N14 have studied the large-scale distribution and overall physical properties of gas in the Local Group and around Milky Way and M31 based on simulation data from the Constrained Local UniversE Simulations (CLUES) project (www.clues-project.org). In their study, the authors separate the circumgalactic and intragroup gas into three different phases: neutral gas, cold/warm ionized gas with T < 105 K, and hot gas with T ≥ 105 K, similar as done here. The total neutral gas mass in the simulated Milky Way at galactocentric distances d < 50 kpc comes out to MHI ≈ 3 × 108 M⊙, thus in excellent agreement with the observations (Sect. 2.1). The total mass of the cold/warm ionized gas component is as large as MHII ≈ 3 × 1010 M⊙ for the entire halo out to the virial radius, but reduces to MHII ≈ 2 × 108 M⊙ for d ≤ 10 kpc, where the bulk of UV absorption of warm-ionized gas is observed in the Milky Way (Lehner & Howk 2011; Sect. 2.2). The mass of the Milky Way's hot coronal gas in the simulation is MCorona ≈ 4 × 1010 M⊙ for d ≤ Rvir and ≈ 1010 M⊙ for d ≤ 100 kpc, the latter value being consistent with the estimates from X-ray observations (Sect. 2.3). The Milky Way's neutral gas-accretion rate from gas at d ≤ 50 kpc is estimated as MHI ≈ 0.3 M⊙ yr−1, which is only ∼ 40 percent of the value derived from the 21 cm observations (Richter 2012), but more in line with what is expected for the neutral HVCs without the Magellanic Stream (Sect. 2.4). For larger distances to the disk, the neutral gas-accretion rate quickly falls below 10−2 M⊙ yr−1 in the simulations (N14; their Fig. 14). The accretion rate of cold/warm gas instead is fairly independent of the distance for d > 15 kpc at a level of MHI ≈ 5 M⊙ yr−1, thus in line with the estimate from the UV observations (Fox et al. 2014; R17). Finally, the simulations imply that only for very large distances d > 100 kpc the accretion rate of hot (T > 106 K) gas dominates the mass inflow of gas for the Milky Way.
The influence of the Local Group environment in the simulations is reflected particularly in the anisotropic distribution of gas near the viral radius of the MW, because the gas follows the large-scale matter distribution in the elongated cosmological filament that forms the Local Group (N14). To visualize this, we show in Fig. 7 the gas distribution and gas kinematics around the simulated Milky Way and M31 galaxies from the CLUES simulations. The two galaxies move towards the LG barycenter while the ambient gas is circulating around MW and M31 within the elongated filament in a complex pattern of infall and outflow channels. There is a significant gas excess between the two galaxies, as compared to any other direction, resulting from the overlap of their gaseous halos. Because of the Milky Way's flow towards LG barycenter, a velocity dipole pattern for high-ion absorption from LG gas/M31 halo gas is expected from a perspective within the Milky Way (R17). Such a dipole pattern is indeed observed in UV absorption in the direction of M31 and its antipode on the sky (Sect. 2.2). This possibly implies that warm/hot LG gas/M31 halo gas is pushed into the Milky Way halo due to the large-scale motion of both galaxies in their group environment. If true, this effect might cause a major boost in the Milky Way's future gas-accretion rate.
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Figure 7. Projected distribution and bulk motions of gas in and around the Milky Way (dashed circle, indicating the virial radius of the MW) and M31 (solid circle, indicating the virial radius of the M31) based on constrained cosmological simulations from the CLUES project (N14). Coordinates and velocities of the gas are given with respect to the Local Group barycenter in the x / y, x / z, and y / z planes, respectively. The white arrows show the velocity field of the gas, with the longest arrows representing a velocity of 130 km s−1. The black arrows indicate the velocities of the MW and M31 galaxies. Their absolute space velocities are 67 and 76 km s−1, respectively. Maps kindly provided by Sebastián Nuza. |
3.3. Comparison with observations
For a better understanding of the gas-accretion processes in the Milky Way, the comparison between observational data and predictions from simulations are essential. Next to the gas masses in the individual phases and the accretion rates (see above), the spatial distribution of the various gas phases in the simulations and their kinematics can be compared (in a statistical sense) with the observational constraints from 21 cm data and UV absorption spectra.
Combining 21 cm data from the Milky Way and M31, Richter (2012) predicted that the volume-filling factor of neutral gas in the halo of Milky-Way/M31 type galaxies declines exponentially with radius, leading to an exponential decline of the observed (projected) H i covering fraction. The study suggests that the covering fraction fc(H i) drops below 0.05 for d > 50 kpc. A similar trend indeed has also been found in the recent CGM simulations of Milky-Way type galaxies (Fernandez, Joung & Putman 2012; N14), indicating that basically all neutral gas in MW-type galaxies is concentrated in the inner halo region. This conclusion is supported by the observed cosmological cross-section of neutral gas around low-redshift galaxies (Zwaan et al. 2005; Richter et al. 2011).
Also the apparent interaction between the MS and the surrounding coronal gas as well as the Hα emission from the Stream have been investigated in simulations to reproduce the observational results. Bland-Hawthorn et al. (2007) and Tepper-Garcia et al. (2015) modeled the Hα emission from the MS based on a shock-cascade model. Tepper-Garcia et al. (2015) conclude that the Hα emission from the Stream can only be reproduced if the density of the ambient medium is nH = 2−4 × 10−4 cm−3, indicating that Hα emitting regions in the MS must be within d ≤ 75 kpc from the Galactic center.
Next to these examples, there are several other studies that have addressed these and other aspects by comparing observational results with simulations. Describing all of these unfortunately is beyond the scope of this review. Clearly, with future, more detailed simulations and additional constraints from multi-wavelength observations the systematic combination of simulations and observations will provide crucial new insights into the properties of the Milky Way's CGM.