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Early-type stars produce a prodigious amount of ionizing radiation and are capable of ionizing gas well above the midplane of the Galaxy. But does this stellar radiation explain all of the observed H+? For example, do some of the O star photons completely escape the Galaxy to account for the ionized gas observed in the high velocity H I clouds (HVCs) and the Magellanic Stream, located up to 50000 pc from the Galaxy (Weiner and Williams 1996, Tufte et al. 1998, Putman et al. 2003)? If so, then the Halpha surface brightness of these clouds provides a direct measurement of the flux of Lyman continuum radiation that completely escapes the Galaxy (e.g., Tufte et al. 1998). However, because these cooler clouds appear to be immersed in a much hotter plasma (e.g., Savage et al. 2003), we must at least consider the fact that hot gas-cool gas interfaces are also a source of ionizing radiation. Such radiation may even play an important role in the ionization of a very local H I cloud in the vicinity of the sun.

Observations of O+5 and detections of other ions in high states of ionization (Savage et al. 2000, Sembach et al. 2003, Sembach and Savage 1992) show that interfaces between hot (~ 106 K) gas and cooler (ltapprox 104 K) gas are widespread throughout the interstellar medium and Galactic halo. The resulting intermediate temperature (~ 105 K) gas at these interfaces produces extreme ultraviolet ionizing radiation. Thus, even though O star photons can leak through a clumpy interstellar medium and/or through superbubble chimneys, interfaces have the advantage that they exist wherever the hot gas and cooler clouds do, including places where ionizing radiation from O stars does not reach. Although significantly weaker than the flux from hot stars, interface radiation may be more widely distributed, and because the emission is generated in a thin layer adjacent to the absorbing cloud, interface radiation is efficiently used for ionizing that cloud as well as being a source of ionization for other more distant clouds.

6.1. Types of interfaces

A variety of different types of interfaces may exist, depending on the physical processes operating and dynamical state of the boundary region between the hot and cooler gas. These include: evaporative boundaries (e.g., Cowie and McKee 1977), cooling/condensation fronts (Shapiro and Benjamin 1991), and turbulent mixing layers (Slavin et al. 1993, Begelman and Fabian 1990). In evaporative boundaries, thermal conduction heats the cool cloud and produces an outflow. This requires that the magnetic field topology is such that the warm gas is not shielded too thoroughly from the hot gas. In cooling/condensation fronts, slow accretion of hot gas onto the cool gas occurs as the hot gas cools radiatively. A turbulent mixing layer (TML) can develop in regions where there is shear flow at the hot/cool boundary that leads to hydrodynamical instabilities and mixing of the hot and cool gas. The mixed gas in a TML cools rapidly due to its temperature and non-equilibrium ionization state. Although all these types of interfaces share some characteristics, the ionization state of the gas can be radically different for different types of interfaces. For example, relative to collisional ionization equilibrium the gas can be highly underionized in evaporative outflows, overionized in cooling/condensation fronts, or a combination of both overionized and underionized as in a TML, wherein the formerly cool gas is underionized and the formerly hot gas is overionized. In Fig. 18 we show the results of preliminary numerical hydrodynamic simulations of a TML. Other possibilities exist for hot gas/cool gas interfaces involving various combinations of cooling, conduction and mixing, but those have yet to be explored.

Figure 18

Figure 18. Temperature in a shear layer between hot and warm gas. The hot gas (top, T = 106 K) flows to the left at 10 km s-1 while the warm gas (bottom, T = 8000 K) flows to the right at 10 km s-1. Cooling is not included in this 2-D calculation.

The flux and spectrum of ionizing radiation emitted, is determined by the ionization-temperature-density profile in the interface. In general, underionized gas radiates more strongly than overionized gas, because ions that are being ionized up will generally be excited several times before being ionized. In Fig. 19 we show a comparison of the EUV/soft X-ray spectrum generated in an example evaporating cloud boundary and TML. In this calculation the hydrogen ionizing photon production rate between 14 eV and 24 eV is approximately 2 × 104 photons cm-2 s-1. This is only about 10% the ionizing flux that appears to be incident on high velocity clouds in the Galactic halo (e.g., Tufte et al. 1998, Tufte et al. 2002), for example; however, the uncertainty in the properties and morphology of actual cloud interfaces (e.g., the number of interfaces a line of sight through a cloud intersects; see Fig. 18) leaves open the possibility that the Halpha produced by interface radiation could be significant in regions where stellar ionizing photons do not reach.

Figure 19

Figure 19. Comparison of ionizing flux generated in evaporating cloud with that generated in a turbulent mixing layer.

6.2. A test case

The Local Interstellar Cloud (LIC) that surrounds the Solar System appears to be an excellent candidate for exploring interstellar interfaces. It is inside the Local Bubble (Cox and Reynolds 1987), and thus probably surrounded by hot gas. There is no direct Lyman continuum radiations from O stars and the nearest B star (epsilon CMa) is more than 100 pc away. The ionization of the LIC is very well characterized (it is best observed interstellar cloud in the Universe), and its ionization state is somewhat unexpected, that is, quite different from the WIM. In the LIC, the hydrogen is only moderately ionized at ~ 20-40%, and He is more ionized than H.

Models that include ionizing radiation from an evaporative interface (Slavin and Frisch 2002, Frisch and Slavin 2003), are generally successful in matching the myriad of data available and indicate that a diffuse EUV source above the weak ionizing flux provided by nearby stars is necessary to explain the ionization. Problems remain, however, in explaining the relatively low column densities of O+5 and C+3 as well as the high column of Si+2 that have been observed (Gry and Jenkins 2001, Oegerle et al. 20050. These discrepancies would seem to point to a different type of interface surrounding the LIC. The existence of the LIC does raise the question of how common such partially ionized clouds are and how much they contribute to the diffuse interstellar H+ (e.g., Reynolds 2004). While the density and temperature of the LIC are very close to what is found in the WIM, the low values of [O I] / Halpha observed by WHAM imply that H+ / H for most of the diffuse ionized gas in the solar neighborhood is much closer to unity than the lower value found for the LIC (although He+ / He may be similar).

In summary, while many aspects of the physics of interfaces are yet to be explored, the fluxes produced by such interfaces are probably weaker than the ionizing fluxes require to produce the WIM (Section 2). Also, the ionization state of the LIC cloud suggests that such clouds can account for only a small portion of the ionization associated with the WIM. Nonetheless, there are several conclusions we can draw from existing observations and theory that are relevant to the WIM:

  1. Hot-cool gas interfaces appear to be widespread through the interstellar medium. Wherever interfaces with intermediate temperature gas (T ~ 105 - 105.5 K) exist there will be ionizing radiation generated, producing diffuse ionization. The fact that the spectra peak in the EUV and that a large fraction of the generated flux should be captured by the cool cloud gas makes interface radiation a potentially significant source of ionizing radiation in regions shielded from direct O-star Lyman continuum photons. For example, if the interface is very convoluted, a typical line of sight through a cloud may pass through many hot-cool surfaces, resulting in a total Halpha intensity for the cloud that is comparable to what is observed for the HVCs. Interface radiation appears to be require to explain the properties of the local cloud near the sun.

  2. The theoretical spectra from evaporating clouds and turbulent mixing layers are harder than that of the O stars, which could result in the presence of some ions in the WIM that O stars cannot produce.

  3. The type of interface that exists at the boundary of a cloud depends (at least) on the dynamics of the boundary, the geometry of the cloud and the degree to which thermal conduction occurs. Thus refinements in theory and observations of good candidate clouds are needed to determine the extent to which interfaces contribute to ionization in our Galaxy and others.

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