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Astron. Astrophys. 327, 1262-1270 (1997)

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4. Ionizing pulse as trigger of warm to cool phase transition in a gas with solar abundances

Among the various processes that determine the change of state of the ISM material, phase transitions are expected to play an important role. In particular, warm to cool phase transition has been indicated as a channel to transform diffuse gas ([FORMULA]) into denser states ([FORMULA]) (Field, Goldsmith & Habing 1969; Lepp et al. 1985; Parravano 1987; Lioure & Chièze 1990; Dickey & Brinks 1993). Moreover, it has been proposed (Parravano 1988, 1989) that the large scale star formation rate must be self-regulated because, on one hand the warm gas condensation is inhibited by high enough UV radiation (coming mainly from massive stars), and on the other hand, a gas supply from the diffuse phases is required to feed the large scale star formation process. In this way, the large scale star formation rate is limitated, and the warm gas tends to remains close the critical state for warm to cool phase transition. The fact that large quantities of ISM warm gas remain close to this critical state allows the trigger of condensation by relatively small variations of the ambient conditions. More precisely, the mean "distance" of the warm gas state to the critical state for spontaneous condensation is determined by the amplitude spectrum of the variations of the ambient conditions. In any case, the study of triggered condensation of warm gases close to the critical state can be justified by the self-regulatory hypothesis. It is to be noticed that the scale of the inhibitory process is expected to be much larger than the scale of the triggering processes: a fact that apparently is a common characteristic of many dynamical systems where spiral structures arise (Smolin 1996).

Triggering mechanisms of star formation are usually related to compression and pushing of the ISM gas by high pressure events associated to stars formed previously (reviews on this topic can be found in Elmegreen 1992, Franco 1992). Also, compression of the warm gas by the spiral density wave have been evocated as a main trigger of its condensation (Roberts 1969); however, stimulated condensation by ionizing flashes may also enter as an initiator of the chain of processes that finally results in the formation of stars. As it will be shown bellow, this stimulating mechanism is particularly efficient when the warm gas state is close to its marginal state for spontaneous phase transition. Moreover, variations of the ionizing flux are expected to precede pressure variations if both variations are associated to the same perturbing event. Large local variation of the ionizing rate are expected to be present in the interstellar medium. Sudden appearance and disappearance of ionizing sources occur continuously in the galactic plane. Also, "rapid" variation of the opacity to the ionizing radiation in a line of seeing is expected. Finally, variations of the cosmic ray flux are expected to be present due to variations of the sources (cosmic ray acceleration in shock fronts with oblique B-fields; Blandford and Ostriker 1978), and to variations of the magnetic field topology (i.e. focalization or dis-focalization of the cosmic ray stream in a region). It was also proposed (Ko & Parker 1989; Nozakura 1993) that star formation controls dynamo activities and hence large scale magnetic fields of disk galaxies.

The cooling of the diffuse warm interstellar gas is mainly due to electron collisional excitation of a) fine structure levels and metastable states of the positive ions [FORMULA], [FORMULA], [FORMULA], and [FORMULA], and b) [FORMULA] excitation. Therefore, an increase of the ionizing flux (and the consequent increase of the electron density) tends to reduce the gas temperature if the increase of the cooling efficiency overcomes the associated increase of the heating. In general, this is the case for low equilibrium ionization fractions when the kinetic energy of the electrons that result from the ionization process is small. Depending on the value of the pressure and on the increase of the ionizing flux, the new thermal equilibrium state might be located in the cool neutral branch. That is: sufficiently large variations of the ionizing rate are expected to provoke the warm to cool phase transition. Moreover, if the ionizing flux variation has a flash-like variation, then, after the passing of the flash, the cooling rate remains enhanced due to the inertia of ionization.

In order to illustrate this effect, we consider variations of the primary ionization rate by cosmic rays [FORMULA] which is the accepted main source of ionization of the interstellar warm gas far away from massive stars. Other mechanisms of ionization have been proposed (i.e. OB stars (Reinolds & Cox 1992), the neutrino decay theory (Sciama 1990, 1993)), but for the present analysis the exact mechanism of ionization is not relevant. What is important here is the variation of the ionizing and heating rates due to a change of the considered ionizing flux.

The main changes of the curve of thermo-chemical equilibrium (TCE) when [FORMULA] is changed are summarized in Fig. 5, where the maximal ([FORMULA]) and the minimal ([FORMULA]) pressures of the TCE curve are plotted as a function of [FORMULA]. All the results in this section correspond to the standard solar neighborhood far UV energy density and gas composition. The labels are used to remind that if [FORMULA] (or [FORMULA]) then there is only one possible state of TCE in the diffuse and warm phase (or in the dense and cool phase). If [FORMULA] then the gas may reach any of the two stable branches (the warm or the cool branch). If the gas is initially in TCE at the warm branch (for example with the external conditions ([FORMULA]) corresponding to the point (A) in Fig. 5, then, the gas could be forced to evolve toward the cool branch if the external conditions are changed, for example, to ([FORMULA]) corresponding to the point (B). The typical time for the transition from the warm to the cool branch is [FORMULA] yr. Once the gas reaches the cool phase, the external conditions can change again to ([FORMULA]) but the gas will remain in the cool branch. To drive the gas to the warm phase again, the external conditions must be changed, for example, to ([FORMULA]) corresponding to the point (C) in Fig. 5. Now, the gas could return to the initial state if the external conditions change to the initial conditions ([FORMULA]).

[FIGURE] Fig. 5. The maximal ([FORMULA]) and the minimal ([FORMULA]) pressures of the thermo-chemical equilibrium curve plotted as a function of [FORMULA] (see text).

The phase transitions described above assume that the time between the consecutive changes of [FORMULA] are long enough to reach TCE. If the variation of [FORMULA] occurs before TCE is achieved, then, the phase transition does not necessarily occur. Here we will consider the effect of flash-like variations of [FORMULA] at constant pressure. That is, at the beginning we assume that the gas is in the warm branch in the equilibrium state corresponding to the external conditions ([FORMULA]). Then, [FORMULA] is increased abruptly by a factor [FORMULA] during a lapse of time [FORMULA], after which the primary ionization rate by cosmic rays returns to the initial value [FORMULA]. As mentioned above, a fact that favors the phase transition is that the recombination time is much larger than the cooling time; then after the end of an ionizing pulse, the cooling rate remains enhanced due to the non-equilibrium excess of electrons.

In this simple analysis we neglect non-local processes as thermal conduction, cosmic ray attenuation, radiative transfer, and gas dynamics. Only local processes of radiative cooling, heating, H ionization and recombination are considered (Parravano 1987), assuming that the pressure remains constant during evolution. The neglected non-local processes may play an important role in the local evolution of the gas and it should determine the spatial variations of the physical variables. However, here we are interested in showing that the inertia of ionization (after the passing of the ionizing pulse) can, in many cases, enhance sufficiently the cooling efficiency to produce a phase transition from the warm gas phase to the cool phase. The evolution of the temperature and the ionization degree is calculated by solving simultaneously the energy conservation Eq. (2), and the kinetic Eq. (1) restricted to the hydrogen ionization-recombination processes.

In order to show the effect of ionizing pulses, Fig. 6 shows the evolution at constant pressure of a warm gas initially in thermo-chemical equilibrium close to the critical state for spontaneous condensation. The pressure [FORMULA] is bellow [FORMULA] by a factor [FORMULA], when the pre-flash primary ionization rate is [FORMULA]. The three curves in Fig. 6 correspond to the evolution for three different values of the pulse duration [FORMULA], 0.8, and 2.0 Myr, when the flash is initiated at [FORMULA] yr and the factor of increment of [FORMULA] is [FORMULA]. Note in Fig. 6 that there is a critical value of [FORMULA] bellow which condensation does not occur (in this case [FORMULA] Myr). Note also that the time required to complete the phase transition decreases as [FORMULA] increases, but the time required for the temperature drop from [FORMULA] to [FORMULA] is insensitive to [FORMULA]. The kink at the bottom of the [FORMULA] and 2.0 curves, and the smooth dip in the [FORMULA] curve are due to the inertia of the ionization fraction (the recombination time is much longer for the conditions corresponding to the upper curve).

[FIGURE] Fig. 6. The temperature evolution of the warm gas initially in thermo-chemical equilibrium close to the critical state for spontaneous condensation. The three curves correspond to the evolution for three labeled values of the pulse duration when [FORMULA].

In Fig. 7 the critical values of [FORMULA] are plotted as function of [FORMULA] for the three labeled values of [FORMULA]. These curves divide the plane [FORMULA] in two regions: above the curves the flash is capable of inducing phase transition, and bellow the curve the gas returns to its initial state after the passing of the flash. Note that a cosmic ray pulse with a factor of increment [FORMULA] of the order of 10, and a duration of about one Myr can induce the condensation of the warm gas in TCE at [FORMULA].

[FIGURE] Fig. 7. The critical values of [FORMULA] as function of [FORMULA] for the three labeled values of [FORMULA].

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© European Southern Observatory (ESO) 1997

Online publication: April 6, 1998
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