ARlogo Annu. Rev. Astron. Astrophys. 2012. 50: 491-529
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The amount, metallicity, and ionization state of the halo gas has consequences on a galaxy's resulting star formation. Star formation rates of spiral galaxies at low redshift are approximately 0.5 - 5 Modot / yr, and Galactic chemical evolution models find that at least half this amount needs to be continuously accreted, low metallicity fuel (Chiappini 2009, Chiappini et al. 2001). Without accretion, the SFRs indicate the star formation fuel currently in the disk will last for another few Gyrs at most. In this section, potential sources to maintain a galaxy's star formation over time are discussed. This includes a calculation of the accretion rate for Milky Way halo gas, a discussion of gas at the disk-halo interface, and a brief mention of some often neglected disk sources.

6.1. Halo Sources

The mass inflow rate to the Galactic disk is a crucial parameter to derive from the physical properties of the HVC complexes outlined in Section 2.1.1. Many studies estimate the HVC contribution to the accretion rate using some form of the equation,

Equation 1 (1)

where Mi is the mass of a given complex, vi is the observed radial velocity and Di is the distance (Thom et al. 2008, Wakker et al. 2007). The largest difficulty with this method is that the observed radial velocity of a HVC complex is the sum of the velocity of the complex toward the disk (or more generally a poloidal component), and the azimuthal speed of the cloud around the disk (toroidal component), projected along the line of sight. This observed velocity may be very different from the true radial velocity of the gas toward the Galaxy, and the cloud may be accelerated in the future by MW gravity and/or decelerated by ram pressure. Additionally, the distance to the gas is not the same as the distance from the cloud to where it will eventually impact the disk.

Now that most of the complexes have direct distance constraints, we can construct a very simple model of the HI accretion process that takes into account the bulk of the accretion onto the Galaxy from known HVCs in the next ~ Gyr. We only consider the 13 complexes with relatively well-known distances, excluding the Magellanic Stream and Leading Arm complexes as they are unlikely to accrete within the Gyr. We calculate their mass as outlined in Section 2.1.1, which includes the clouds' HI, He, and ionized gas detected in Halpha, and use the angular position of each complex's flux weighted center. The 23% of the HVCs (by flux) that do not have a direct distance constraint are not included here, but this gas would not substantially increase the calculated accretion rates. We ascribe a radial velocity, vr, obs, to the complex equal to its flux-weighted radial velocity in GSR. We then construct a very simple model for the 3-space velocity of the system of all HVC complexes. All complexes are given an identical azimuthal velocity, vtheta, and accretion velocity toward the Galactic center, vG. Then, for a given vtheta and vG, each complex has some minimum additional velocity to make up the difference between the observed radial velocity and modeled radial velocity. The best fit parameters for the model are those that minimize these differences. We note that our results are qualitatively unchanged if the accretion vector is assumed to be toward the disk instead of the Galactic Center.

The complexes are best fit by [vtheta, vG] = [77, -40] km s-1. We note that the azimuthal velocity, 77 km s-1 in the direction of Galactic rotation, is roughly consistent with the vr gradient of -20 km s-1 kpc-1 above the disk noted in Section 2.5, and that the accretion velocity of -40 km s-1 is roughly consistent with the average radial velocity of all HVCs (~ -50 km s-1). We show the accretion of complexes as a function of time given this best fit velocity in Figure 9, as well as a `maximal' accretion rate using the highest vG allowable with twice the residual in the fit, -200 km s-1. The fit and maximal accretion rates are 0.08 and 0.4 Modot / yr, respectively. The maximal value approaches that required by chemical evolution models for the Milky Way (at least 0.45 Modot / yr; Chiappini 2009), but the fit is far below that required. These values are consistent with accretion rates of neutral gas from simulations (Peek et al. 2008, Fernández et al.2012), and the Complex C accretion model in Thom et al. (2008).

Figure 9

Figure 9. The accretion of HVC complex mass with time for the fit (dark shades) and maximal (light shades) accretion velocities vG. Dashed lines indicate accretion rates of 0.08 Modot / yr and 0.4 Modot / yr, respectively. Several specific HVC complexes are noted for reference. The gap at recent times may be due to selection effects for HVCs close to the disk.

Based on Figures 1 and 2 and the discussion at the end of Section 2.2, the ionized component of the HVCs extends beyond the immediate vicinity of the HI component. The calculation above includes only a factor of two on the HI mass for the warm ionized component directly around HVCs detected in Halpha emission. Observations of ionized HVCs in absorption find an additional mass in more diffuse, warm material on the order of 108 Modot (Lehner & Howk 2011). The ionized HVCs are at similar distances to the HI HVCs and also generally have a similar kinematic and spatial distribution, so to roughly account for the diffuse ionized gas the above best fit accretion rate can be scaled up by approximately a factor of two. Even with this additional ionized component, the accretion rate is still well below that needed by our Galaxy to maintain its current SFR over the next few Gyrs. Our Galaxy may go through a low point in its gas content, and/or decrease its SFR until the arrival of the gas from the Magellanic System.

For other galaxies, the amount of HI halo gas is generally between 107.5-9 Modot, but this includes a combination of halo and disk-halo gas (within a few kpc). Some galaxies show very limited amounts of halo gas and substantial amounts at the disk-halo interface (e.g., Zschaechner et al. 2011, Heald et al. 2011). If accretion rates are estimated from the gas most akin to HVCs, Sancisi et al. (2008) calculates values of 0.1-0.2 Modot / yr for several galaxies from the HI component alone. Large covering fractions of ionized gas are detected through absorption line observations, and so more mass is certainly present in warm and warm-hot halo gas similar to the Milky Way. Including similar percentages of ionized gas as found for the Milky Way still leaves the accretion rates low compared to each galaxies SFR. The sources discussed below will provide additional fuel, but low redshift spiral galaxies may also gradually decrease their SFR's (e.g., Madau et al. 1998, Hopkins 2004).

6.2. Disk-Halo Interface

Halo gas sources need to cool and integrate into the disk in order to become star formation fuel. Cooling and accretion at the disk-halo interface would be difficult to observe for galaxies beyond z ~ 0 (i.e., no significant spatial and kinematic offset from the galaxy), and can be called 'quiet accretion'. This quiet accretion could explain observations at higher redshifts that show substantial SFRs and outflows with little, if any, evidence for accretion (e.g., Erb 2008, Shapley 2011, Steidel et al. 2010). Cooling at the disk-halo interface also potentially explains the relatively constant amount of HI in the universe since z = 3, despite the ongoing star formation (e.g., Prochaska & Wolfe 2009, Putman et al. 2009a, Hopkins et al. 2008). Finally, quiet accretion may be linked to the fact that HI-rich galaxies show quiescent disks (Wang et al. 2011).

There is observational evidence for infalling structures at the disk-halo interface at low redshift. There are large HI features directly connected to galaxy disks in position-velocity space and the IVCs of the Milky Way have a clear bias towards negative velocities. In addition, the WIM layer of our Galaxy detected in Halpha shows a net inflow as one examines the regions toward both poles (Haffner et al. 2003, Putman et al. 2009b). A combination of infalling fuel and feedback can successfully model the lagging rotation with z-height found for numerous galaxies (Fraternali & Binney 2008, Marinacci et al. 2011). The gradient of increasing temperature with increasing z-height (Section 2.2 & Section 3.2) may also be a combination of the gradual cooling of halo gas, and the hot gas from the disk rising to larger z-heights than the cool gas. Given stellar metallicity constraints, the ratio of feedback material to fresh gas throughout time requires a full assessment.

The interaction of inflowing clouds with existing halo gas is likely to be important for cooling to occur at the disk-halo interface (Marinacci et al. 2010, Heitsch & Putman 2009). As clouds move through the halo medium, they are gradually disrupted and slowed. In simulations of Heitsch & Putman (2009), the leftover warm over-densities of the HI clouds become buoyant as they approach the disk and are able to re-cool as they are compressed by the surrounding disk-halo medium. The small clouds that form in this process should be moving similarly to the gas surrounding it at this stage and may be the small cold clouds detected throughout the disk-halo interface of the Galaxy (Section 2.5). When the clouds begin to fall towards the disk again they will be moving through the surrounding diffuse medium and are likely to resemble the small warm intermediate velocity clouds that show net infall (Saul et al. 2012), or the filaments/worms that emanate from the HI disk gas (e.g., Kang & Koo 2007).

The rate of accretion of different gaseous components at the disk-halo interface can be measured through a comparison of observations to high-resolution simulations. Preliminary examination of the MW simulation shows a significant amount of accretion of multiphase gas at this interface (Joung et al. 2012a; see also Murante et al. 2012). This may indicate that quiet accretion at the disk-halo interface is an important fueling source for spiral galaxy disks.

6.3. Disk Sources

Obviously the gas in a galaxy's disk fuels its star formation, however there are two particular fuel reservoirs in the disk for which there is much left to learn. The first is the gas fed back into the ISM from evolved stars, and the second is outer disk gas that is transported to the inner star forming regions. AGB stars lose on the order of 30-50% of their mass back to the ISM according to stellar evolution models (Wachter et al. 2002). These evolved stars have been observed feeding star formation fuel back into the ISM with CO (e.g., Neri et al. 1998, Castro-Carrizo et al. 2010) and HI observations (e.g., Gérard & Le Bertre 2006, Matthews & Reid 2007, Putman et al. 2011a). Leitner & Kravtsov (2011) propose this type of stellar feedback may have provided a significant fraction of a spiral galaxy's fuel over the past few Gyrs. Galactic stellar metallicities and the deuterium abundance require the feedback material is supplemented with a source of lower metallicity gas. Understanding the methods with which the feedback material is fed back into the ISM, and the quantity, will help to determine the amount we need from external sources to maintain star formation.

Another important question related to disk sources of fuel, is how material from gas-rich outer disks is transported to the inner star forming regions. A large reservoir of fuel is in the outer parts of the disk where few stars are currently forming (Werk et al. 2010a, Thilker et al. 2007), and the flat metallicity gradients in gas disks indicate transport mechanisms are active (Werk et al. 2010b, Werk et al. 2011, Bresolin et al. 2009, Spitoni & Matteucci 2011). The radial flow of gas in the disk would transport this fuel (Sellwood & Binney 2002, Elson et al. 2011), as well as the potential return of material from a galaxy's warp to more central regions (Putman et al. 2009c, Józsa 2011, Kawata et al. 2003). Perturbations by companions will result in mixing (e.g., Torrey et al. 2012) and can warp the gas disks (Binney 1992). This will also create halo and disk-halo gas features and may be an important part of cycling accreted material inward.

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