4 Discussion

The absence of circumstellar material around No. 12 was inferred from direct near-infrared photometry of the star, carried out using a multi-filter Ge bolometer (Persi & Ferrari-Toniolo 1982; Leitherer et al. 1982). No. 12 has been identified, however, as the optical counterpart of an IRAS source (Parthasarathy et al. 1992). Parthasarathy et al. (1992) interpreted their mid-infrared IRAS observations to indicate the presence of warm (T=900 K) and cold dust (T=80 K) around the star. From an analysis of the wavelength dependence of the polarisation, McMillan & Tapia (1977) concluded that the reddening arises in two uniformly polarising slabs, one of them possibly located within the Cyg OB2 association. Massey & Thompson (1991) have suggested that the high luminosity of the star coupled with its high extinction is in fact not a coincidence, but may provide evidence of a previous episode of mass loss, and that the large visual extinction of the star is mainly circumstellar. If so, the detection of unusual isotope ratios may provide an observational test. We have searched our spectra for the presence of ¹²C¹³C absorption lines. We use mass-scaled rotational constants and the molecular parameters of Amiot & Verges (1983) to obtain wavelengths of ¹²C¹³C. The R-branch bandhead of the (2,0) band of the ¹²C¹³C Phillips system is located near 8792 $\rm\AA$, and the Q(1)-Q(10) lines of the (2,0) band are located in the 8808-8830 Å region. Our spectrum shown in Fig. 1 does not contain absorption features which may be associated with ¹²C¹³C. Upper limits are $W_{\lambda} < 0.5$ m$\rm\AA$. The vibrational transition probabilities of ¹²C¹³C are similar than those of C₂ (Halmann & Laulicht 1966). ¹²C¹³C is a hetero-nuclear molecule and all rotational levels in the various electronic states are present. Consequently, the ¹²C¹³C population density is spread over twice as many rotational levels as for C₂. The ratio of the equivalent widths of the say Q(2) absorption lines from C₂ and ¹²C¹³C is >54. This value leads to an estimate of N(C₂)/N(¹²C¹³C) > 27. Assuming that N(C₂)/N(¹²C¹³C ) = a²/2a where a is the ¹²C/¹³C isotope ratio, we obtain a value of a > 54 towards Cyg OB2 No. 12, which is consistent with the interstellar value of a=65 and which agrees within a factor of two with the terrestrial value of a=89. This finding provides little evidence that the extinction towards No. 12 is largely circumstellar.

   
4.1 C₂ and CN formation in quiescent translucent clouds

Observed molecular column densities towards No. 12 are N(H $_3^+) = 3.8\times 10^{14}$ cm^-2 and N(CO $) = 2.6\times 10^{16}$ cm^-2(McCall et al. 1998; Geballe et al. 1999), N(C $_2) = 2\times 10^{14}$ cm^-2 and N(CN $) = (0.8{-}1.3)\times 10^{14}$ cm^-2 (present work), N(CH $) = 4.1\times 10^{13}$ cm^-2, and N(HCO ⁺) = 10¹¹ cm^-2 (Scappini et al. 2000). The CH column density is inferred from an emission line near $V_{\rm {hel}} = -$4.7 km s^-1 (Willson 1984). Note that McCall et al. (1998) do not include saturation corrections when inferring CO column densities. The CO column density may be significantly larger than cited. The presence of strong interstellar absorption lines from CH and CH⁺ was reported by Souza & Lutz (1980), but neither equivalent widths nor molecular column densities are given. Because of the large reddening of Cyg OB2 No. 12, the signal to noise ratio in the blue wavelength region of our spectrum is very low, and neither the CH⁺ (4232 $\rm\AA$) nor the CH (4300 $\rm\AA$) absorption lines are detected.

The visual extinction of A_V = 10 mag towards No. 12 corresponds to a total hydrogen column density of N(H $) = 1.6 \times 10^{22}$ cm^-2. The observed molecular column densities are converted to fractional abundances f(X) = N(X) / N(H) of f(H $_3^+) = 2.4\times 10^{-8}$, f(C $_2)= 1.25\times 10^{-8}$, f(CN $) = (5{-}8)\times 10^{-9}$, f(CO $) = 1.6\times 10^{-6}$, f(CH $) = 2.6\times 10^{-9}$, and f(HCO $^+)= 6.25\times 10^{-12}$.

The models of McCall et al. (1998) and Geballe et al. (1999) reproduce the observed column density of H₃⁺ by assuming that the molecular material along the line of sight towards Cyg OB2 is dominated by diffuse material of average density n = 10 cm^-3spread over pathlengths of some 400-1200 parsec. The authors note that the model does not produce the observed abundances of C₂ and CO. The presence of clumps of molecular gas with densities of $n_{\rm c} = (300 \pm 50)$ cm^-3, or $n = (600 \pm 100)$ cm^-3, towards Cyg OB2 No. 12, is demonstrated from the C₂ observations presented above.

A model by Cecchi-Pestellini & Dalgarno (2000) avoids the assumption of long pathlength and produces the observed abundance of H₃⁺ from a nested structure for the clouds. In their model, H₃⁺ is formed in low density clouds of n = 50-100 cm^-3, C₂ is formed in embedded cloudlets at temperatures T = 35 K and $n=7\times 10^3$ cm^-3, and CO is formed in high density cores of n = 10⁵ cm^-3or greater. The model also predicts a HCO⁺ column density of N(HCO $^+) = 9\times 10^{9}$ cm^-2. The recent detection of HCO⁺towards No. 12 by Scappini et al. (2000) provides further and strong support to a model with dense cores embedded in lower density material.

The gas-kinetic temperature of the C₂-containing cloudlets inferred from the present observations agree very well with the prediction of the model of Cecchi-Pestellini & Dalgarno (2000). The densities inferred from C₂ are significantly lower though, unless a value of I=11 is adopted as the scaling factor of the radiation field of the general background starlight. We have modeled the radiation field from the 44 most luminous stars in the association (cf. Sect. 4.2). We find that the molecular gas will have to be closer than 100 pc to the association in order for it to dominate the radiation field, which we consider unlikely. We conclude that the C₂ observations do indicate a low gas density, rather than a grossly enhanced radiation field.

   
4.2 X-ray induced chemistry towards Cyg OB2

Figure 9: Fractional abundances of H2O+plotted versus X-ray energy deposition rate H/n calculated for a model of n= 600 cm-3 and N(H $) = 1.6 \times 10^{22}$ cm-2. The shaded region corresponds to ionisation rates of $\zeta = (0.6{-}3) \times 10^{-15}$ s-1.

The stars Cyg OB2 Nos. 5, 8A, 9, and 12, are all very powerful X-ray emitters (Kitamoto & Mukai 1996; Waldron et al. 1998). If molecular gas is exposed to X-rays, its chemistry will be modified by increased photoionisation rates caused by X-ray absorptions. In order to estimate whether X-rays may affect the chemical composition of the translucent cloud towards Cyg OB2, we have modeled the radiation field of the 44 most luminous stars with M_V < -4 mag of Massey & Thompson (1991). We obtain a total luminosity of $7\times 10^{50}$ s^-1 ionising photons and a total of $3\times 10^{45}$ s^-1 of X-ray photons. Note that these are lower limits as the Cygnus OB2 region may contain up to 2600 OB stars (Knödlseder 2000). We use the radio observations of Downes & Rinehart (1966) to estimate an emission measure of ${\it EM}= 6450$ cm^-6 pc and an electron density of $n_{\rm e} = 34$ cm^-3 towards No. 12. The large number of ionising photons will support a Strömgren sphere of 104 pc at an electron density of $n_{\rm e} = 34$ cm^-3. This is roughly the size of the 5 GHz free-free emission region seen in the radio map of Downes & Rinehart (1966). The stellar winds may have evacuated such a large region already that the nebula is density-bounded, and thus leaking photons into the neighboring neutral gas. We conclude that an X-ray driven chemistry may very well provide an alternative scenario for the formation of molecules towards the Cygnus OB2 region.

The effects of X-rays on the chemistry of translucent molecular clouds have been modeled by Lepp & Dalgarno (1996). They presented steady-state abundances of various interstellar molecules as a function of $\zeta /n$, where $\zeta$ is the X-ray ionisation rate in units of s^-1. The observed fractional abundances of CO, CH, HCO⁺, and CN, are all well reproduced for ionisation rates per density of $\zeta / n = (\mbox{1$-$ 3})\times 10^{-17}$ s^-1 cm³, or $\zeta = (1{-}2)\times 10^{-15}$ s^-1 for densities of n = 600 cm^-3. The fractional abundance of CH and CN is also reproduced with the lower ionisation rate of $\zeta = 6\times 10^{-18}$ s^-1, but that of the other molecules is not. The lower ionisation rate is close to the cosmic ray ionisation rate of dark clouds.

Maloney et al. (1996) showed that the physics and the chemistry of an X-ray irradiated gas are predominantly determined by the local X-ray energy deposition rate per particle H divided by the particle density n. Comprehensive models of the energy deposition of X-rays in atomic and molecular gas and the effects of the X-rays on the chemistry were developed by Yan (1996), who calculated fractional molecular abundances as a function of H/n. A full discussion of the models and the chemical network used will be presented elsewhere. The parameter H, expressed in units of erg s^-1 per hydrogen nucleus, is related to the X-ray ionisation rate $\zeta$ in units of s^-1 per hydrogen molecule by $\zeta = 3\times 10^{10} H$ (Yan 1996). Here we use the models of Yan (1996) to calculate the fractional abundances of H₃⁺, CO, C₂, CN, CH, and HCO⁺. In all simulations, the total hydrogen density is fixed to a value of $N_{\rm H} = 1.6\times 10^{22}$ cm^-2 and the density is n = 600 cm^-3. Figure 8 contains the calculated fractional molecular abundances as a function of H/n. Filled dots are fractional abundances inferred from the observations. The shaded region corresponds to values of $\zeta = (0.6{-}3) \times 10^{-15}$ s^-1. The observed fractional abundances of CO, C₂, CN, and CH, are well reproduced for this range of X-ray ionisation rates. The inferred ionisation rates agree with those suggested by the models of Lepp & Dalgarno (1996). The modeled fractional H₃⁺ abundance is $f({\rm H}_3^+) = 5\times 10^{-8}$, which corresponds to a column density of N(H $_3^+) = 8\times 10^{14}$ cm^-2. Thus, our model falls short by a factor of two to reproduce the H₃⁺ column density towards Cyg OB2 No. 12.

The models of Yan (1996) determine the gas temperature and the grain temperature by solving the heating and cooling balance equations. The equilibrium temperatures which result for ionisation rates of $\zeta = (0.6{-}3) \times 10^{-15}$ s^-1 are 25-50 K, which agree perfectly with the gas-kinetic temperature derived from the C₂observations.

We derive large abundances of H₂O⁺ in our model. Figure 9 contains a plot of the fractional H₂O⁺abundance as a function of H/n. At the ionisation rates inferred above, again represented by the shaded region, f(H₂O⁺) is of the order of 10^-10. H₂O⁺ peaks with f(H₂O $^+) = 6\times 10^{-9}$at high ionisation rates of $\zeta \approx 6\times 10^{-14}$ s^-1. We predict that towards Cyg OB2 No. 12, H₂O⁺ absorption lines which arise from the $\tilde {\rm A} ^2A_1 - \tilde{\rm X} ^2B_1$system are detectable in the optical wavelength region. We use the molecular parameters of Lew (1976) to calculate the air wavelengths given in Table 7. Oscillator strengths are from Lutz (1987). Towards Cyg OB2 No. 12, the predicted H₂O⁺ fractional abundance corresponds to a column density of N(H₂O $^+) = 2\times 10^{12}$ cm^-2. The strongest lines, such as the $1_{10}\! -\! 0_{00}$ transition of the (0,4,0) - (0,0,0) band near 8057.7 Å (cf. Table 7), will have equivalent widths of some $W_{\lambda} \approx 0.5$ m$\rm\AA$. The H₂O⁺ absorption lines are strong enough to be detectable by optical absorption line techniques. Our spectrum towards Cyg OB2 No. 12 covers all H₂O⁺ lines given in Table 7, but it is not of sufficient quality to unequivocally identify H₂O⁺. At the resolution adopted here, H₂O⁺ will be detectable in spectra with S/N > 1000.

 

 

Table 7: Predicted air wavelengths of H₂O⁺.

band	transition	$\bar{\nu}$	$\lambda_{\rm air}$	f
		cm-1	$\lambda$
(0,4,0)-(0,0,0)	1 10-000	12407.079	8057.698	$4.0 \times 10^{-4}$
		12423.239	8047.217
	211-101	12424.403	8046.463	$2.0 \times 10^{-4}$
		12434.249	8040.091
	111-101	12385.413	8071.794	$2.0 \times 10^{-4}$
		12401.999	8060.999
(0,6,0)-(0,0,0)	110-000	14335.600	6973.717	$4.5 \times 10^{-4}$
		14342.930	6970.153
	211-101	14352.573	6965.470	$2.25 \times 10^{-4}$
		14356.980	6963.332
	111-101	14313.203	6984.629	$2.25 \times 10^{-4}$
		14320.860	6980.895