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Astron. Astrophys. 355, 333-346 (2000)

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4. A broad, underlying Galactic component
of molecular absorption

The HCO+ profiles in Figs. 1 and 2 toward B0355+508, B0415+379, and B1730-130 have a weak, broad underlying component which we have chosen not to ascribe to the individual clouds which provide the few strong features. Figs. 6 and 7 show why this is so. In each case, but most spectacularly the low-latitude object B0355+508, the HCO+ is contiguous with the velocity ranges where HI absorption is prominent. The broad wings seem galactic in origin, from gas which is widely dispersed.

[FIGURE] Fig. 6. Comparison of HCO+ absorption with HI absorption and emission. HI absorption spectra are from (Dickey et al. 1983; Garwood and Dickey 1989). Emission data are the nearest profile from the all-sky survey of (Hartmann and Burton 1997). The absorption spectra are in the form of line/continuum - 1, the (scaled) emission spectra have units of Kelvins

[FIGURE] Fig. 7. Comparison of HCO+ absorption with HI absorption and emission, as in Fig. 6

4.1. Equilibrium models of the gas

To understand the presence of this interesting new component of interstellar absorption profiles, we constructed a model of the H-[FORMULA] and C+-CO transitions in diffuse/translucent gas of small-to-moderate density, since these are the conditions under which the lines appear to form.

The calculations were initially begun as models of dense inclusions in diffuse clouds, such as might be called upon to explain the observed fluctuations in our HCO+ profiles; the consequences of these models for just such a circumstance are explored later, in Sect. 5. We divided a model gas sphere of constant total density of H-nuclei into 64 radial zones and iteratively determined the H and [FORMULA] abundances using the dust and self-shielding factors and the free-space photodissociation rate of (Lee et al. 1996), and a cosmic-ray ionization rate [FORMULA]. The anisotropy of the model's internal photon field is taken into account by a numerical integration over solid angle for each zone, and the model was assumed to be illuminated isotropically at its periphery. The interstellar radiation field scales with G0, G0 = 1 being the standard value. We took G0 = 0.65 for the calculations here because that leads to a thermal pressure (density-temperature product) near [FORMULA] K in purely atomic gas, with our chosen carbon depletion of a factor 2.5 with respect to the Solar value (see the annotations on the larger plot in Fig. 11).

Because the rate constant for the formation of [FORMULA] on grains varies as [FORMULA]cm3 s-1 (Spitzer 1978), even a calculation of the H-[FORMULA] transition makes it necessary to do the ionization, heating, cooling, and chemical calculations which simultaneously and self-consistently determine [FORMULA] and the relative abundances of CI, C+, CO, HI, [FORMULA] and electrons. For the heating, we included terms corresponding to: cosmic ray ionization of hydrogen, releasing 6.6 eV of heat per event; photoionization of CI, releasing 1.16 eV; heating due to photoelectrons ejected from grains (Bakes and Tielens 1994); and heating due to the formation of [FORMULA] on grains, releasing 3.4 eV per event. The cooling included: H-[FORMULA] interactions (Martin et al. 1996); excitation of the fine-structure lines of CI, OI, and C+ by electrons and H-atoms (Hollenbach and McKee 1989) and [FORMULA] (Monteiro and Flower 1987; Schroeder et al. 1991; Jaquet et al. 1992); and cooling due to CO including levels up to J=9. Of the cooling transitions, even the CO lines are not thick enough in diffuse clouds to require much attention to the radiative transfer. After some experimentation with more sophisticated methods, we finally did this rather crudely, calculating the local source function using an LVG code and forming the emergent line brightness by integrating the source function along the line of sight. The shielding factors needed to calculate the local abundance of CO were also taken from the work of (Lee et al. 1996).

The results shown here are for the mean (area-weighted) line of sight through the model cloud, intersecting it at an impact parameter equal to two-thirds of the radius. In comparing these models with the direct results of a simple LVG calculation for a bit of gas at constant density and temperature, we find that the non-uniform construct is substantially better at providing for the observed line ratios well up the rotation ladder.

The observed abundance of CO in gas threaded by a largely unattenuated interstellar radiation field cannot be reproduced by standard models of interstellar chemistry at low-to-moderate extinction and density: because they fail by one or two orders of magnitude to reproduce the observed abundances of polyatomics like HCO+ which are the chemical antecedents of CO, standard models underproduce CO in like degree (Liszt and Lucas 1994). Current attempts to explain the observed high molecular abundances in thin gas columns invoke shocks which do not seem to reproduce the profiles we observe (Sect. 3.3) or take the form of somewhat esoteric-seeming discussions of energy dissipation in turbulent microstructures (Joulain et al. 1998) which we could not figure out how to adapt to this work. Here, the microscopic chemistry of CO formation is represented by a single reaction [FORMULA] CO + H proceeding with a rate constant [FORMULA]/[FORMULA]  [FORMULA] (as in the UMIST database), and with the relative abundance n(HCO+)/n([FORMULA]) assumed fixed at the observed value of [FORMULA] (Liszt and Lucas 1996). This simple ansatz produces CO in the proper amount to explain the observations of CO emission, absorption, excitation, and isotopic fractionation discussed by (Liszt and Lucas 1998).

4.2. Weak Galactic HCO+ absorption and the H-H2 transition in diffuse clouds

As Fig. 8 shows, molecular hydrogen can achieve high abundance in clouds of rather low number density if N(H) [FORMULA], [FORMULA], when the column density is above that of the `standard' atomic hydrogen cloud (Spitzer 1978). Although the existence of an abrupt H-[FORMULA] transition is due to dust and self-shielding, the high [FORMULA] abundance comes about in part because the temperature is higher in more diffuse gas, the formation rate increases as [FORMULA], and [FORMULA] formation can be an important source of heating. Of course this cannot continue indefinitely since (for example) the residence time of H-atoms on grains declines at higher temperature (as pointed out to us by the referee, Dr. John Black), but it is quite important within the context of the present models, over the range of temperatures inferred for clouds observed in [FORMULA]21cm hydrogen absorption. The molecular hydrogen fractions shown here are noticeably higher than would have been the case had we approximated the [FORMULA] formation rate by its value at, say, 60 K.

[FIGURE] Fig. 8. Outer frame: Variation of computed [FORMULA] column density with total hydrogen column density. The curves are for model gas spheres of various density, as indicated, with mean equilibrium kinetic temperatures noted. The Copernicus data of (Savage et al. 1977) are shown as open squares. Inset: Calculated CO column density [FORMULA] N([FORMULA]) for number densities n(H) = 8, 16, 32...512 [FORMULA] as indicated. UV absorption measurements summarized in an updated version of the summary in (Federman et al. 1994), mostly from Copernicus, and our [FORMULA]2.6mm absorption line data (Liszt and Lucas 1998) are shown as filled and open symbols, respectively. Both the models and the mm-wave data assume that [FORMULA]. Mean kinetic temperatures weighted by N(CO) are shown. The data toward the star [FORMULA] Oph are shown outlined

If HCO+ forms along with [FORMULA] itself, its weak underlying absorption would be a new diagnostic for the presence of [FORMULA] in the ISM. So we would like to know how large a fraction of molecular gas and what HCO+ abundance are required in order to explain the HCO+ we see. To do this, we compare properties derived from the profile integrals of HCO+ and HI. Toward B0355+508, for instance, the HI absorption may be said to occur in four ranges; [FORMULA] km s-1 where there is no accompanying HCO+; [FORMULA] km s-1 and [FORMULA] km s-1 where HCO+ is weak; and [FORMULA] km s-1 where HCO+ is strong. In Table 4 we show properties of the HCO+ and HI spectra integrated over these ranges. The HCO+ optical depth integral is converted into an equivalent column of H-nuclei assuming HCO+/[FORMULA] = [FORMULA] and N(HCO+) = 1.03 [FORMULA][FORMULA], applicable in the limit of no collisional excitation. The HI optical depth integral is converted into a column density N(HI) by calculating a spin temperature at each velocity, [FORMULA] (v) = [FORMULA] (v)/[FORMULA] and integrating [FORMULA] [FORMULA] over the line profile. For the more opaque regions of the spectrum, this HI column density is 70-80% higher than the optically thin limit N(HI) = [FORMULA]. The table gives the mean [FORMULA] (weighted by optical depth) and shows results for various velocity ranges toward B0415+379 and B1730-130. The last column is the molecular fraction of the gas, given the assumptions.


Table 4. Molecular and atomic column densities toward three sources

Estimates for the molecular fraction in the ISM locally are 25% - 50%. The usually-quoted value for the local density of neutral gas at z = 0 is 1.2 [FORMULA] from surveys of extinction (Spitzer 1978) and no consistent interpretation of the 21 cm line will allow a local average of more than 0.6-0.7 [FORMULA] (Liszt 1983; Dickey and Lockman 1990). In any case, it follows from the table entries that the molecular fractions needed to reproduce the weak broad HCO+ are at or below the local average. Of course the gas in question is not all local and the molecular gas fraction is declining at the Solar Circle but it seems that our observations really demand only one new thing of the interstellar medium: that the relative abundance of HCO+ generally be of order [FORMULA] wherever the fractional abundance of [FORMULA] is appreciable. Given this, the entire distributed molecular absorption component toward B0355+508 may be explained by gas associated with less than 0.25 magnitude of visual extinction.

Lack of detailed knowledge of the Galactic velocity field is a substantial barrier to calculating obvious quantities such as the mean density along the line of sight. A flat rotation curve viewed toward B0355+508 reaches -10 km s-1 at about 1 kpc distance, -20 km s-1 at 2.2 kpc, and -40 at 5.5 kpc (R = 13.5 kpc), for R0 = 8.5 kpc. Roughly speaking, the mean density of molecular material associated with the strong HCO+ absorption from 0 to -20 km s-1 is then just 0.90 (H-nuclei) [FORMULA], and that of the atomic gas perhaps 0.67 [FORMULA]. For the negative-velocity region of weak HCO+ absorption the mean densities are 0.47 [FORMULA] and 0.04 [FORMULA] for the atomic and molecular components, respectively.

4.3. What forms the carbon monoxide we see in diffuse clouds?

There is an implication of ubiquitous HCO+ which deserves to be noted. Inset in Fig. 8 is a plot of predicted and observed CO column densities as a function of N([FORMULA]). The observed values of N(CO) from UV absorption measurements, summarized in an updated version of the summary in (Federman et al. 1994), are shown as filled symbols and are labelled Copernicus. The open symbols are our measurements from the Plateau de Bure (Liszt and Lucas 1998) of N(CO)/N(HCO+), adjusted along the horizontal axis so that [FORMULA], similar to what we derived in our prior discussion of OH and the OH-HCO+ correlation (Liszt and Lucas 1996). The mm-wave data overlap with the UV absorption measurements at their high end, and extend the range of empirically-determined behaviour by about one order of magnitude in N(CO).

Shown are the predictions of our models at various number densities, with the self-consistently determined, CO abundance-weighted kinetic temperatures shown as numbers at some locations in the plane, again for a constant abundance ratio [FORMULA]. It is the case, that with only one assumption - this ubuiquitous, high abundance of HCO+ relative to [FORMULA] - the run of N(CO) [FORMULA] N([FORMULA]) can be explained over a factor of more than 104 in N(CO). A proportionality N(CO) [FORMULA] N[FORMULA] occurs naturally around N(CO) = [FORMULA]

We view this as a confirmation of the claim made earlier (Liszt and Lucas 1994), that the formation problem for CO in conventional models of the diffuse cloud chemistry is a problem of supply - a too-low formation rate - not any gross overestimation of the photodestruction rate. When HCO+ is present at its observed abundance, it follows without further assumptions that the observed quantities of CO form by electron-HCO+ recombination, even in the presence of a high CO photodestruction rate.

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© European Southern Observatory (ESO) 2000

Online publication: March 17, 2000