|Annu. Rev. Astron. Astrophys. 2004. 42:
Copyright © 2004 by Annual Reviews. All rights reserved
The physical processes by which kinetic energy gets converted into turbulence are not well understood for the ISM. The main sources for large-scale motions are: (a) stars, whose energy input is in the form of protostellar winds, expanding H II regions, O star and Wolf-Rayet winds, supernovae, and combinations of these producing superbubbles; (b) galactic rotation in the shocks of spiral arms or bars, in the Balbus-Hawley (1991) instability, and in the gravitational scattering of cloud complexes at different epicyclic phases; (c) gaseous self-gravity through swing-amplified instabilities and cloud collapse; (d) Kelvin-Helmholtz and other fluid instabilities, and (e) galactic gravity during disk-halo circulation, the Parker instability, and galaxy interactions.
Sources for the small-scale turbulence observed by radio scintillation (Interstellar Turbulence II) include sonic reflections of shock waves hitting clouds (Ikeuchi & Spitzer 1984, Ferriere et al. 1988), cosmic ray streaming and other instabilities (Wentzel 1969b, Hall 1980), field star motions (Deiss, Just & Kegel 1990) and winds, and energy cascades from larger scales (Lazarian, Vishniac & Cho 2004). We concentrate on the large-scale sources here.
Van Buren (1985) estimated that winds from massive main-sequence stars and Wolf-Rayet stars contribute comparable amounts, 1 × 10-25 erg cm-3 s-1, supernovae release about twice this, and winds from low-mass stars and planetary nebulae are negligible. Van Buren did not estimate the rate at which this energy goes into turbulence, which requires multiplication by an efficiency factor of ~ 0.01-0.1, depending on the source. Mac Low & Klessen (2004) found that main-sequence winds are negligible except for the highest-mass stars, in which case supernovae dominate all the stellar sources, giving 3 × 10-26 erg cm-3 s-1 for the energy input, after multiplying by an efficiency factor of 0.1. Mac Low & Klessen (2004) also derived an average injection rate from protostellar winds equal to 2 × 10-28 erg cm-3 s-1 including an efficiency factor of ~ 0.05. H II regions are much less important as a general source of motions because most of the stellar Lyman continuum energy goes into ionization and heat (Mac Low & Klessen 2004). Kritsuk & Norman (2002a) suggested that moderate turbulence can be maintained by variations in the background nonionizing UV radiation (Parravano et al. 2003).
These estimates agree well with the more detailed "grand source function" estimated by Norman & Ferrara (1996), who also considered the spatial range for each source. They recognized that most Type II SNe contribute to cluster winds and superbubbles, which dominate the energy input on scales of 100-500 pc (Oey & Clarke 1997). Superbubbles are also the most frequent pressure disturbance for any random disk position (Kornreich & Scalo 2000).
Power rates for turbulence inside molecular clouds may exceed these global averages. For example, Stone, Ostriker & Gammie (1998) suggested that the turbulent heating rate inside a giant molecular cloud (GMC) is ~ 1-6 × 10-27 nH v3 / R erg cm-3 s-1 for velocity dispersion v in km s-1 and size R in pc. For typical nH ~ 102-103 cm-3, v ~ 2 and R ~ 10, this exceeds the global average for the ISM by a factor of ~ 10, even before internal star formation begins (see also Basu & Murali 2001). This suggests that power density is not independent of scale as it is in a simple Kolmogorov cascade. An alternative view was expressed by Falgarone, Hily-Blant & Levrier (2003) who suggested that the power density is about the same for the cool and warm phases, GMCs, and dense cores. In either case, self-gravity contributes to the power density locally, and even without self-gravity, dissipation is intermittent and often concentrated in small regions.
Galactic rotation has a virtually unlimited supply of energy if it can be tapped for turbulence (Fleck 1981). Several mechanisms have been proposed. Magneto-rotational instabilities (Sellwood & Balbus 1999, Kim et al. 2003) pump energy into gas motion at a rate comparable to the magnetic energy density times the angular rotation rate. This was evaluated by Mac Low & Klessen (2004) to be 3 × 10-29 erg cm-3 s-1 for B = 3µG. This is smaller than the estimated stellar input rate by a factor of ~ 1000, but it might be important in the galactic outer regions where stars form slowly (Sellwood & Balbus 1999) and in low-surface brightness galaxies. Piontek & Ostriker (2004) considered how reduced dissipation can enhance the power input to turbulence from magnetorotational instabilities.
Rotational energy also goes into the gas in spiral shocks where the fast-moving interspiral medium hits the slower moving dense gas in a density wave arm (Roberts 1969). Additional input comes from the gravitational potential energy of the arm as the gas accelerates toward it. Some of this energy input will be stored in magnetic compressional energy, some will be converted into gravitational potential energy above the midplane as the gas deflects upward (Martos & Cox 1998), and some will be lost to heat. The fraction that goes into turbulence is not known, but the total power available is 0.5 ism vsdw3 / (2H) ~ 5 × 10-27 erg cm-3 s-1 for interspiral density ism ~ 0.1 mH cm-3, shock speed vsdw ~ 30 km s-1, and half disk thickness H = 100 pc. Zhang et al. (2001) suggest that a spiral wave has driven turbulence in the Carina molecular clouds because the linewidth-size relation is not correlated with distance from the obvious sources of stellar energy input.
Fukunaga & Tosa (1989) proposed that rotational energy goes to clouds that gravitationally scatter off each other during random phases in their epicycles. Gammie et al. (1991) estimated that the cloud velocity dispersion can reach the observed value of ~ 5 km s-1 in this way. Vollmer & Beckert (2002) considered the same mechanism with shorter cloud lifetimes and produced a steady state model of disk accretion. A second paper (Vollmer & Beckert 2003) included supernovae.
The gravitational binding energy in a galaxy disk heats the stellar population during swing-amplified shear instabilities that make flocculent spiral arms (e.g., Fuchs & von Linden 1998). It can also heat the gas (Thomasson, Donner & Elmegreen 1991; Bertin & Lodato 2001; Gammie 2001) and feed turbulence (Huber & Pfenniger 2001; Wada, Meurer & Norman 2002). Continued collapse of the gas may feed more turbulence on smaller scales (Semelin et al. 1999, Chavanis 2002, Huber & Pfenniger 2002). A gravitational source of turbulence is consistent with the observed power spectra of flocculent spiral arms (Elmegreen et al. 2003). The energy input rate for the first e-folding time of the instability is approximately the ISM energy density, 1.5 v2, times the growth rate 2 G H / v for velocity dispersion v. This is ~ 10-27 erg cm-3 s-1 in the Solar neighborhood - less than supernovae by an order of magnitude. However, continued energy input during cloud collapse would increase the power available for turbulence in proportion to 4/3. The efficiency for the conversion of gravitational binding energy into turbulence is unknown, but because gravitational forces act on all of the matter and, unlike stellar explosions, do not require a hot phase of evolution during which energy can radiate, the efficiency might be high.
Conventional fluid instabilities provide other sources of turbulence on the scales over which they act. For example, a cloud hit by a shock front will shed its outer layers and become turbulent downstream (Xu & Stone 1995), and the interior of the cloud can be energized as well (Miesch & Zweibel 1994, Kornreich & Scalo 2000). Cold decelerating shells have a kinematic instability (Vishniac 1994) that can generate turbulence inside the swept-up gas (Blondin & Marks 1996, Walder & Folini 1998). Bending mode and other instabilities in cloud collisions generate a complex filamentary structure (Klein & Woods 1998). It is also possible that the kinetic energy of a shock can be directly converted into turbulent energy behind the shock (Rotman 1991; Andreopoulos, Agui & Briassulis 2000). Kritsuk & Norman (2002a, b) discuss how thermal instabilities can drive turbulence, in which case the underlying power source is stellar radiation rather than kinetic energy. There are many individual sources for turbulence, but the energy usually comes from one of the main categories of sources listed above.
Sources of interstellar turbulence span such a wide range of scales that it is often difficult to identify any particular source for a given cloud or region. Little is known about the behavior of turbulence that is driven like this. The direction and degree of energy transfer and the morphology of the resulting flow could be greatly affected by the type and scale of energy input (see Biferale et al. 2004). However, it appears that for average disk conditions the power input is dominated by cluster winds or superbubbles with an injection scale of ~ 50-500 pc.