The phenomenon of bistability in gas phase chemical models of interstellar clouds is by now well known (Pineau des Forêts et al. 1992, Le Bourlot et al. 1993, 1995a,b, Shalabiea & Greenberg 1995). The term bistability refers to the existence of two stable steady-state chemical solutions - labelled the high ionization phase (HIP) and the low ionization phase (LIP) - over a certain range of gas densities and cosmic ray ionization rates. The two solutions, obtained both by solution of algebraic equations and by following the time dependence of differential equations until no further changes occur, arise from different initial conditions. In addition to a high degree of ionization, the HIP solution is characterized by a high C/CO abundance ratio, while the LIP solution is characterized by a much lower C/CO abundance ratio. Other chemical differences have also been explored (Gerin et al. 1997). When selected results, such as the C/CO abundance ratio, are plotted against density or cosmic ray ionization rate, the nature of bistability emerges (Flower & Pineau des Forêts 1996). Starting, for example, from high density with initial abundances either rich in molecules or rich in atoms (with the exception of H2), and proceeding to lower densities at a fixed ionization rate, one encounters only one solution with relatively low ionization at steady-state until at a certain critical point, a sharp phase transition occurs to the HIP solution for the initial abundances rich in atoms. If initial abundances rich in molecules are used, no sharp transition occurs at this density, and a second solution - the LIP solution - is obtained. At a lower density critical point, the LIP solution reached from molecular initial conditions undergoes a phase transition of its own and merges with the HIP solution. At still lower densities, there exists only one solution, with relatively high ionization.
Although the LIP solution corresponds more closely to the "low metal" solution used most frequently by modellers (Lee et al. 1996; the exact correspondence is explored below), the HIP solution offers a plausible explanation for the high atomic carbon abundances observed towards diverse interstellar sources but more commonly explained in terms of photon dominated regions (Keene 1995). In addition, the existence of bistability might help to explain the large abundance variations often seen on small distance scales. One promising line of research concerns differences in deuteration between the LIP and the HIP (Gerin et al. 1997). Although the inclusion of the element deuterium does not have a global effect on the bistability, the HIP and LIP phases show differing abundances of deuterated species. The relevance of bistability to the actual interstellar medium, however, rests on questions such as whether or not it is an artifact of incomplete models and over how wide a region of parameter space it occurs. Bistability has by now been investigated in both small- and moderately-sized model networks, although it has not been studied in any detail with the largest chemical networks, which might be expected to be the most stable. The dependence of the range of bistability on elemental depletions has also been looked at to some degree (Le Bourlot et al. 1995a). In addition, the effect of grain chemistry on the nature of bistability has been investigated and debated (Shalabiea & Greenberg 1995, Le Bourlot et al. 1995b). There is thus still an element of controversy concerning bistability, and a more thorough investigation of the phenomenon is indicated. In this paper, we report such a thorough investigation with a very large gas-phase chemical network - the so-called "new neutral-neutral" model of Bettens et al. (1995). We have chosen not to study bistability with gas-grain model networks at this time, for reasons given in Sect. 4.
Our investigation has been facilitated by the realization (Lepp & Dalgarno 1996), confirmed by us, that steady-state fractional abundances in gas-phase chemical networks where direct photodestruction by external photons can be ignored depend uniquely on the ratio , where (s-1) is the cosmic ray ionization rate and is the total hydrogen density (). In other words, if both and are changed by a common factor f, then the steady-state fractional abundances remain unchanged. In discussing steady-state results, we are thus able to use the ratio to characterize the range of bistability rather than varying each parameter while fixing the other. For non-steady-state results, however, the simple dependence on the ratio does not pertain, although at the so-called "early time" (where the complex molecule abundances in "low metal" models tend to maximize), the fractional abundances, if not the time taken to reach them, also depend only on the ratio. Mathematically, the condition for unique dependence on the ratio is that the time derivatives of the concentrations be zero. Of course, this argument neglects the thermal balance; a high value of is likely to increase the temperature and so cause a change in the chemistry.
© European Southern Observatory (ESO) 1998
Online publication: June 2, 1998