Annu. Rev. Astron. Astrophys. 2004. 42: 275-316
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3. EFFECTS OF TURBULENCE ON INTERSTELLAR CHEMISTRY

The coupling of interstellar chemistry to the dynamics of interstellar gas has focused for a long time on collapsing or slowly contracting clouds (e.g., Gerola & Glassgold 1978; Prasad, Heere & Tarafdar 1991; Shematovich et al. 2003) and single shocks or MHD waves (e.g., Hollenbach & McKee 1979, 1989; Draine & Katz 1986; Charnley 1998; Flower & Pineau des Forêts 1998). The collapse models explained why early-time solutions for static chemistry often agreed better with observations than late-time solutions (e.g., Prasad et al. 1991; Nejad & Wagenblast 1999; but see Turner et al. 2000). The result that nondynamical time-dependent abundances agreed with observations for different ages is a strong motivation for the influence of turbulence because turbulent timescales are often smaller than the chemical equilibrium times. Turbulent transport can prevent the chemistry from attaining a steady state (e.g., Phillips & Huggins 1981; Xie, Allen & Langer 1995; Willacy, Langer & Allen 2002).

Turbulence can affect ISM chemistry in three ways: (a) by continually transporting material between regions with different physical conditions, like ambient ultraviolet (UV) radiation flux, temperature, and density, (b) by creating localized heating where temperature-sensitive reactions, especially those involving endothermic reactions, will be enhanced, and (c) by magnetically forcing ions to move faster than the thermal speed where they can enhance the temperature-sensitive ion-neutral reactions. Progress in this field is difficult because of limitations in the dynamical models and because of the large number of nondynamical chemical effects that may occur, like neutral-neutral reactions at low temperature, variable C and O depletion, three-body channels for dissociative recombination, the presence of cosmic-ray-induced UV photons, chemical phase transitions, and many more, as reviewed by Herbst (1999), Hollenbach & Tielens (1999), van Dishoeck & Hogerheijde (1999), and Langer et al. (2000). For more recent work on chemistry covering a variety of applications not necessarily related to turbulence, see Roberts & Herbst (2002), Doty et al. (2002), Stantcheva & Herbst (2003), Shematovich et al. (2003), and Charnley & Markwick (2003).

3.1. Turbulent Transport of Chemical Species

The classic observation that implied turbulent transport was the large amount of carbon in the gas phase of dense molecular cores, considering the short freeze-out time on dust. Boland & deJong (1982) proposed that turbulent circulation could explain this discrepancy by bringing grains to the outer layers for UV desorption. Modern observations (Kramer et al. 1999) show more depletion, however, and photodissociation region (PDR) models suggest carbon comes from clump surfaces at a range of depths (Howe et al. 2000).

Turbulent transport has other applications in modern chemical models. Pijpers (1997) considered a diffusive model of turbulent grain transport and obtained a long migration time. Ragot (1998) pointed out that turbulent transport is probably neither ballistic nor diffusive, and used a model based on Levy flights to return to the smaller timescales. This transport effect is important because the degree to which CO is released from grains into the gas can affect the rest of the chemistry (CO deactivates much chemistry by depleting the H3+ ion; Nejad & Wagenblast 1999).

A detailed study of turbulent transport including 87 species and 1100 reactions was given by Xie et al. (1995), who assumed that radial flux is proportional to the spatial gradient of a species and used a mixing length model for turbulent diffusion. They found that most carbon-bearing species and several other important molecules were strongly affected by turbulence. The model was extended recently by Willacy, Langer & Allen (2002), who showed how the H I / H2 ratio could provide a sensitive signature of turbulent transport. This occurs because H2 forms when H reacts on dust grains. The formation rate depends on the density of atomic H and the total dust cross section, whereas the destruction rate depends on the UV field. If turbulence cycles material between regions with different UV optical depths on a timescale comparable to the formation time, then H will penetrate deeper into the cloud and H2 will be closer to the surface. Because many other simple molecules are formed from H2-based intermediaries (especially H3+), turbulent transport could control the chemistry for many species.

Timescales for reaching chemical equilibrium depend on density, temperature, and ionization fraction, and are typically 105-107 years (van Dishoeck & Hogerheijde 1999). For the atomic part of a photodissociation region, the longest part of the cycle C+ --> CH2+ --> CO --> C --> C+ is the formation time of CH2+ through radiative association (Tielens & Hollenbach 1985) with a timescale ~ 106 n2-1 years for n2 = particle density in units of 102 cm-3. For turbulent transport, the fastest possible timescale is ballistic, L / v, for turbulent speed v and length L. Using the ISM scaling relations for illustration (see Interstellar Turbulence I), this minimum time is 106 / n21/2 years. The chemical and transport timescales are comparable at 102 cm-3, but the transport time becomes larger than the chemical time at higher density and then turbulence would seem to have little effect. Because cosmic ray ionization drives the chemistry, and each ionized H2 molecule eventually forms CO or some other important molecule, the chemical timescale in the cores of dense clouds is the ratio of the relative abundance of CO, ~ 10-4, to the cosmic ray ionization rate, ~ 4 × 10-17 s-1; this gives ~ 105 years (D.J. Hollenbach, private communication).

3.2. Turbulent Heating

Another way in which turbulence may affect chemistry is through localized heating in shocks (Flower & Pineau des Forêts 1998), vortices (Joulain et al. 1998), ambipolar diffusion (Padoan, Zweibel & Nordlund 2000), and magnetic reconnection (Lazarian & Vishniac 1999). There are many reactions that seem to require higher than normal temperatures.

For diffuse clouds, the large abundance of CH+ and molecules like HCO+ that can form from CH+, and the large abundance of OH (Gredel 1997, Lucas & Liszt 1997), all suggest that high temperature (~ 103 K) reactions take place, as in shock fronts (Elitzur & Watson 1980, Draine & Katz 1986). However, the correlation between CH+ and the lower-temperature molecule C2 (Gredel 1999), and the similar radial velocities of CH+ and CH rule out CH+ production in single large shocks or cloud surfaces. Instead, CH+ could be made in numerous unresolved shocks that blend on a line of sight with cooler gas at the same average velocity (Gredel, Pineau des Forêts & Federman 2002). Part of the appeal of turbulence is its great range of scales that can yield such an effect.

Temperature fluctuations of several hundred degrees could play a major role in the chemistry of many species because of the inverse temperature dependence of radiative association and the range of activation energies for collisional dissociation, neutral-neutral reactions, and some ion-molecule reactions. Neutral-neutral reactions may be important even in dark clouds (Bettens et al. 1995). Prasad & Huntress (1980) long ago pointed out the importance of temperature variations in radiative association reactions and some ion-molecule reactions. Also, in dense shielded clouds, warm regions drive most of the O, OH, and O2 to H2O through reactions like O + H2 --> OH+H and OH+H2 --> H2O+H (e.g., Charnley 1998), not only enhancing the H2O abundance, but also preventing the formation of molecules like SO2, which rely on the oxygen species for their formation. The CN abundance should be enhanced because its destruction by reaction with O and O2 is suppressed; this can lead to enhanced production of HC3N through reaction of CN with C2H2.

There have been several attempts to model the effects of local turbulent heating on chemistry. Black & van Dishoeck (1991) pointed out that if turbulence extends down to the collisional mean free path, then the tail of the particle velocity distribution could be enhanced. Reaction rates are averages over the particle relative velocity distribution, so energy-dependent cross-sections could have greatly enhanced rates. Spaans (1996) noted that the distribution of velocity differences in turbulent flows at small scales has a large tail and suggested this could result in non-Maxwellian relative speeds between molecules, especially those involved with CH+ production. This assumption is questionable because the reaction scales are the mean free paths, of order 1AU / n2, and these are smaller than the viscous dissipation scale of incompressible turbulence. The validity of the fluid approximation for neutrals is also questionable at these scales (see Interstellar Turbulence I), although MHD turbulence in the ionic component could enhance the ion-neutral collision rate.

Another approach to the problem was presented in a series of papers by Falgarone and coworkers. Falgarone & Puget (1995), Falgarone et al. (1995), and Joulain et al. (1998) considered the diffuse cloud abundances of CH+ and several other molecules such as OH and HCO+. They focused on the solenoidal part of the velocity field in which molecular viscosity on 10 AU scales produces numerous local hot spots (up to several times 103 K). Falgarone et al. (1995) showed that the resulting chemical column densities were consistent with observations. Joulain et al. (1998) used a Burgers-vortex model for the dissipation to explain other features, such as the similarity of CH and CH+ line centroid velocities, when the number of dissipation regions on the line of sight is large.

Decamp & Le Bourlot (2002) approximated turbulence by a stochastic 1D velocity field correlated in space and time, and solved the continuity equation for the density of each species. For a small reaction network, the abundances developed different patterns on different scales, showing how species segregation can occur in a turbulent flow. Species that do not normally peak at the same time for a nonturbulent model can coexist in a turbulent model, which means that the age of a region cannot be inferred from the abundances. The issue of chemical differentiation is important because it is well-established and unexplained in a number of starless cores such as TMC-1, L134N, and L1544, and observed as 1-10 AU variations in CO, H2CO, and OH relative to H2 toward extragalactic background sources (Marscher, Moore & Bania 1993; Moore & Marscher 1995; for more recent work, see Pan, Federman & Welty 2001; Rollinde et al. 2003; Stanimirovic et al. 2003). Although some of these variations may be attributed to freeze-out of molecules on dust grains (Bergin et al. 2002), most are probably also affected by time-dependent chemistry (Langer et al. 2000). One important timescale is cloud contraction (Shematovich et al. 2003), but another is turbulent cycling between different physical conditions over a range of timescales (Decamp & Le Bourlot 2002). The observed variations at scales so small that gravity is unimportant seem to favor turbulence. The calculations by Decamp & LeBourlet also develop a bistable chemical pattern in which dual equilibria are possible. However, it is not known how many of the effects result from the imposed artificial velocity field, which is not able to react to the changing density field through pressure.

The only truly hydrodynamical turbulence simulation that included a small but relevant chemical reaction subset was by Pavlovski et al. (2002), who generalized previous work by Mac Low and coworkers to include a large number of coolants and a wide range of possible temperatures and densities. The reaction network in Pavlovski et al. included H, C, O, and five molecules formed from them, and it included H2 formation on grains. They followed the decay of hypersonic turbulence without self-gravity in a dense (106 cm-3), small (1016 cm) region. Their surprising result was that after H2 dissociated in a shock, the molecules reformed in a pattern of filaments, clumps, and diffuse gas yet the abundances were fairly uniform after only 100 years.

There are probably other processes that produce localized regions of hot chemistry. For example, ambipolar diffusion heating depends on a high-order derivative of the magnetic field and so can produce heating rates that exceed the average rate by orders of magnitude on very small scales (Padoan, Zweibel, & Nordlund 2000). Magnetic reconnection (Lazarian & Vishniac 1999) is another possibility for localized hot gas. The chemistry induced by these processes has not yet been investigated.

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