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Up: Interstellar C and CN


Subsections

3 Analysis

3.1 Adopted molecular parameters

The measured equivalent widths $W_{\lambda}$ of the C2 lines were converted into column densities N using

\begin{displaymath}N = 1.13\times 10^{20} W_{\lambda}/ (f_{J'J''} \lambda^2)
\end{displaymath} (1)

with $W_{\lambda}$ and $\lambda$ in units of Å and N in units of cm-2. Line oscillator strengths fJ'J'' were calculated from the (2,0) band oscillator strength f20 from the relation fJ'J'' = f20 c SJ'J''/(2 (2J''+1)), with $c = \nu_{J'J''}/\nu_{\rm band}$ and Hönl-London factors SJ'J'' of (J''+2), (2J''+1), and (J''-1) for the R, Q, and P lines, respectively. We used $f_{20} = 1.7\times 10^{-3}$ which is obtained from an ab initio calculation by van Dishoeck (1983). The value is close to a theoretical value of $f_{20} = 1.44\times 10^{-3}$ given by Langhoff et al. (1990), and to a measurement by Erman & Iwamae (1995) who infer $f_{20} = (1.36\pm0.15)\times 10^{-3}$. It is larger than $f_{20} = 1.2\times 10^{-3}$ suggested by Lambert et al. (1995). For a recent discussion of discrepancies between theoretical and experimental f-values see Erman & Iwamae (1995) and Lambert et al. (1995). The band oscillator strength for the (3,0) band was derived from f20using the theoretical ratio of f20 / f30 = 2.2 (van Dishoeck & Black 1982).


  \begin{figure}
\par\includegraphics[width=15cm,clip]{12spec.ps}\end{figure} Figure 1: Spectrum covering the (2,0) band of the C2 Phillips System towards Cyg OB2 No. 12. Detected rotational lines are identified and marked by filled triangles. Open triangles indicate the expected positions of rotational lines which are used to infer upper limits in the populations.

In the models of van Dishoeck & Black (1982) the distribution of populations of the levels J'' of C2 is determined by the ratio $n_{\rm c} \sigma_0/I$ where $n_{\rm c}$ is the density of the collision partners of C2, $\sigma_0 = 2\times 10^{-16}$ cm-2 is the cross section for collision induced transitions for level J'' to rotational level (J''-2) and I is a scaling factor for the incident radiation field in the near-infrared. If a C2 absorption oscillator strength different from the one used here is adopted, the parameter $n_{\rm c} \sigma_0/I$ should be scaled by the ratio of the oscillator strengths (cf. note added in proof in van Dishoeck & Black 1982). For a gas of H2, $n_{\rm c} = n$(H2) and $N_{\rm H}=2N$(H2) is the total column density of hydrogen nuclei. The density of hydrogen nuclei is $n_{\rm H} = 2n_{\rm c}$. We take I=1 corresponding to the standard interstellar radiation field (see discussion in Sect. 4.1).

For the CN A $^2\Pi _{\rm u}$ - X ${^2\Sigma ^+}$ system, the experimental band oscillator strengths of Davis et al. (1986) of $f_{10} = 1.5\times 10^{-3}$and $f_{20} = 7.6\times 10^{-4}$ were adopted for the (1,0) and (2,0) bands, respectively. Heliocentric velocities of CN were inferred from the rest wavelengths given by van Dishoeck & Black (1989).

3.2 The C2 (2,0) and (3,0) Phillips bands

The spectrum covering the (2,0) band of the C2 Phillips system towards Cyg OB2 No. 12 is shown in Fig. 1. The spectrum of the star is dominated by a strong stellar H I Paschen 12 line near 8752 Å and the 3p3P - 9d3D He I line near 8777 Å. Superimposed on the stellar continuum are interstellar C2 absorption lines, which are identified. The broad absorption feature near 8763 Å is a blend of the C2 Q(4) line and of a diffuse interstellar band (cf. Sect. 3.4). The sharp absorption features near 8799.75 Å, 8803.23 Å, 8811.51 Å, 8820.05 Å, 8831.2 Å, and 8835.5 Å, arise from telluric H2O absorption. The C2 measurements are summarised in Table 1, where Cols. 1-5 contain the line designation, the heliocentric wavelength $\lambda_{\rm hel}$in Å, the derived heliocentric velocity $V_{\rm {hel}}$ in km s-1, the measured equivalent width $W_{\lambda}$ in mÅ with uncertainties in parenthesis, and the derived column densities N(J'') in units of 1013 cm-2, with uncertainties in parenthesis. The colon in Col. 2 of Table 1, and in Tables 2, 3, and 6, indicates an uncertain wavelength, either because it is inferred from a line blend, or because the wavelength is indicative only in cases were upper limits in $W_{\lambda}$  are given.

Uncertainties in $W_{\lambda}$ are largely governed by uncertainties in the placement of the local continuum, particularly near the strong stellar H I Paschen 12 absorption line. For equivalent widths obtained from a decomposition of unresolved line blends, such as the (2,0) band R(2)+R(10) blend, uncertainties are of the order of 2-3 mÅ. In general, the uncertainties are larger than 3 standard deviations of the noise in the stellar continuum. The C2 column densities adopted here are inferred in the limit of C2 Doppler values $b \rightarrow \infty$ (cf. Eq. (1)). A curve of growth analysis shows that deviations from the linear relation of Eq. (1) exceed values of 10% for $W_\lambda/\lambda \ge 1.7\times 10^{-6}b$ for b in km s-1for the absorption lines in the C2 (2,0) band. Assuming a typical value of b = 1 km s-1 for C2, the C2 lines suffer from saturation for equivalent widths of $\ge$15 mÅ. The strongest C2 absorption lines have equivalent widths of $W_{\lambda} = 27$ m$\rm\AA$. We nevertheless ignore saturation corrections for the following two reasons. Firstly, the observations of GM94 indicate the presence of two main C2 velocity components separated by 3.7 km s-1. Assuming an equal distribution of the population density in both velocity components, the C2 lines are not saturated unless $W_{\lambda} > 15$ mÅ per velocity component or $W_{\lambda} > 30$ mÅ per absorption line. Secondly, the C2 Doppler parameter may be larger than 1 km s-1. The doublet ratio method applied by Chaffee & White (1982) in their analysis of K I absorption lines towards Cyg OB2 No. 12 indicates a Doppler value of b(K) = 6.4 km s-1 towards No. 12, with a range of b(K) = 0.7-10.5 km s-1 allowed by the measurement uncertainties. For b(C2) = b(KI), the C2 lines are not saturated unless $W_{\lambda} > 100$ m$\rm\AA$.

The spectra of stars Nos. 5, 9, 8A, 7, and 11 are shown in Fig. 2, normalised to unity and shifted by values of 0, -0.1, -0.2, -0.3, -0.4, and -0.5, respectively, along the ordinate. The scale of the ordinate applies to star No. 5. The C2 lines detected towards Cyg OB2 No. 5 and No. 9 are summarised in Tables 2 and 3, respectively. C2 absorption lines are marginally detected towards Cyg OB2 No. 8A. Absorption features, which may be assigned to the Q(2), Q(6), and Q(8) lines, appear near heliocentric wavelengths of 8761.038, 8767.640, and 8773.043 Å, respectively, with equivalent widths of $W_{\lambda} \approx
3$ mÅ or 1-2 standard deviations. A weak diffuse interstellar band near 8763 Å is present in all five spectra.

  
Table 1: Summary of C2 measurements towards Cyg OB2 No. 12.
\begin{table}\par\begin{displaymath}
\begin{array}[h]{p{0.25\linewidth}llrrr}
...
...\rm Affected\ by\ cosmic-ray\ hit.}} \\
\end{array}\end{displaymath}\end{table}


  \begin{figure}
\par\includegraphics[width=17cm,clip]{5spec.ps}\end{figure} Figure 2: Stellar spectra covering the (2,0) Phillips band towards stars Cyg OB2 Nos. 5, 9, 8A, 7, and 11. All spectra are normalised to unity and shifted along the ordinate (see text). C2 lines detected in Cyg OB2 No. 5 are marked by filled triangles. Open triangles indicate the expected positions of rotational lines which are used to infer upper limits in the populations.


  
Table 2: Cyg OB2 No. 5, C2 (2,0) Phillips band.
\begin{table}\par\begin{displaymath}
\begin{array}[h]{p{0.25\linewidth}llrrr}
...
...icolumn{2}{l}{^a {\rm Line\ blend.}} \\
\end{array}\end{displaymath}\end{table}


  
Table 3: Cyg OB2 No. 9, C2 (2,0) Phillips band.
\begin{table}\par\begin{displaymath}
\begin{array}[h]{p{0.25\linewidth}llrrr}
...
...icolumn{2}{l}{^a {\rm Line\ blend.}} \\
\end{array}\end{displaymath}\end{table}

3.3 Rotational excitation of C2

In order to obtain average column densities $\rm <N(J'')\!\!>$in rotational levels J'', the column densities inferred from the individual measurements in the R, P, and Q lines of the (2,0) and (3,0) bands, when available, were combined by weighting with the corresponding oscillator strengths. The gas-kinetic temperature T was determined from the rotational excitation temperature $T_{\rm {ex}}$ of the lowest rotational levels, because the population density in these levels is not significantly affected by radiative effects. Total C2 column densities $N_{\rm {tot}}$ and densities $n_{\rm c}$ were obtained from theoretical fits to the population distribution, with forced agreement for N(2) (cf. van Dishoeck & Black 1982). Total observed column densities were derived from the sum $N_{\rm {obs}} = \Sigma_{J''} N(J'')$over the observed rotational levels.

3.3.1 Cyg OB2 No. 12

The signal to noise ratio (S/N) of the spectral region covering the (2,0) Phillips band is very high and reaches values of S/N > 600. Figure 3 contains an excitation diagram constructed from the detected lines, with values of $-\ln \{5N(J'')/(2J''+1)/N(2)\}$plotted versus excitation energy E(J'') of rotational level J''. Individual measurements are represented by filled triangles and upper limits by open triangles. The squares correspond to the averages $\rm <N(J'')\!\!>$. The five lines drawn in the diagram represent theoretical population distributions calculated for a temperature of T = 35 K and densities of collision partners of $n_{\rm c} = 250$, 300, 350, 400, 450 cm-3. The large number of rotational lines detected towards Cyg OB2 No. 12 sharply constrains the density $n_{\rm c}$. The theoretical population distribution predicted for T = 35 K and $n_{\rm c} = (300~ \pm~ 50)$ cm-3 agrees with the measurements. The total density of hydrogen is $n = (600 \pm 100)$ cm-3. The theoretical total C2 column density derived from N(2) and T and $n_{\rm c}$is $N_{\rm {tot}} = (20^{+4}_{-2})\times 10^{13}$ cm-2. The total observed column density is $N_{\rm {obs}} = 21\times 10^{13}$ cm-2. The average C2velocity, derived by weighting individual velocities with the absorption oscillator strengths of the corresponding absorption lines, is $V_{\rm {hel}}$ (C 2) = -5.5 km s-1.


  \begin{figure}
\par\includegraphics[width=8.5cm,clip]{12exc.ps}\end{figure} Figure 3: C2 excitation diagram of Cyg OB2 No. 12, with rotational population densities plotted versus excitation energies E(J''). Filled triangles correspond to individual line detections, open triangles are upper limits. Open squares are averages for individual rotational levels. The five lines drawn in the diagram represent theoretical population distributions obtained at gas-kinetic temperatures of T = 35 K and densities of collision partners of $n_{\rm c}$/I = 250, 300, 350, 400, 450 cm-3.

3.3.2 Cyg OB2 Nos. 5, 7, 8A, 9, 11

The excitation diagrams constructed for Cyg OB2 No. 5 and No. 9 are shown in Figs. 4 and 5. The observed population distribution towards No. 5 is reproduced well by T = 50 K and $n_{\rm c}=300 \pm 100$ cm-3. The parameters indicate a total C2 column density $N_{\rm {tot}} = (10.3^{+3.5}_{-1.5})\times 10^{13}$ cm-2. The total observed column density is $N_{\rm {obs}} = 10.3\times 10^{13}$ cm-2. The average heliocentric velocity is $V_{\rm {hel}}$ (C 2) = -7.9 km s-1.

The excitation diagram constructed for No. 9 is less constraining than that for No. 12 or No. 5. The population density in the J''=0 - 8 rotational levels may be described by a thermal population distribution at T = 100 K. The fit to the population densities in $J''=0\!-\!8$ yields $N(2)= 0.95\times 10^{13}$ cm-2 which is adopted in the following as N(2). The population density in J''=10 and the upper limit in J'' = 12 suggest $n_{\rm c} > 400$ cm-3. For T = 100 K, $n_{\rm c} > 400$ cm-3, and N(2), the modeled total C2 column density is $N_{\rm {tot}} = (5.2 \pm 1)\times 10^{13}$ cm-2. The observations yield N(C $_2) = 5.1\times 10^{13}$ cm-2. The average heliocentric velocity is $V_{\rm {hel}}$ (C 2) = -10.2 km s-1.


  \begin{figure}
\par\includegraphics[width=8.3cm,clip]{5exc.ps}\end{figure} Figure 4: Rotational excitation diagram for Cyg OB2 No. 5. Symbols as in Fig. 3. The five lines correspond to theoretical population distributions obtained at T = 50 K and densities of $n_{\rm c}/I = 200$, 300, 400, 600, 800 cm-3.


  \begin{figure}
\par\includegraphics[width=8.5cm,clip]{9exc.ps}\end{figure} Figure 5: Rotational excitation diagram for Cyg OB2 No. 9. Symbols as in Fig. 3. The five lines correspond to densities of $n_{\rm c}/I = 200$, 400, 800, 1600 cm-3, and a thermal distribution at T = 100 K.

The marginal detections of a few Q-branch lines towards Cyg OB2 No. 8A yield column densities of about $N(J'') \approx 0.5\times 10^{13}$ cm-2 in each of J'' = 2, 6, and 8. The total observed column density is $N_{\rm {obs}} \approx 1.5\times 10^{13}$ cm-2. The population distribution in rotational levels J'' = 2, 6, and 8 indicates a rotational excitation temperature of $T_{\rm {ex}} = 100$ K. Assuming the kinetic temperature T = 100 K and a thermal distribution, we obtain a value of $N_{\rm {tot}} = 3.3\times 10^{13}$ cm-2. The mean heliocentric velocity of the three absorption lines is $V_{\rm {hel}}$ (C 2) = -5.2 km s-1. Towards Cyg OB2 No. 7 and Cyg OB2 No. 11, the upper limits on the Q(2) line correspond to $N(2) < 0.5\times 10^{13}$ cm-2, or $N_{\rm {tot}} \le 3.3\times 10^{13}$ cm-2 towards both stars, for a thermal population distribution at T = 100 K. The C2 column density is $N_{\rm {tot}} \le 2.5\times 10^{13}$ if T were less than 50 K.


  
Table 4: Summary of C2 measurements in Cyg OB2.
\begin{table}\par\begin{displaymath}
\begin{array}[h]{p{0.25\linewidth}lrrrrrr...
...\ldots \\
\noalign{\smallskip }
\hline
\end{array}\end{displaymath}
\end{table}

3.3.3 Comparison with previous results

Our C2 measurements are consistent with previous results. The first detection of C2 towards Cyg OB2 No. 12 (Souza & Lutz 1977) yielded a column density in the J''=2 level of $N(2) = 4.6\times 10^{13}$ cm-2, rescaled to the absorption oscillator strength adopted here. Our value is $4.85\times 10^{13}$ cm-2. The column densities of GM94, in units of 1013 cm-2, are N(0) = 1.1, N(2) = 5.1, and N(4) = 4.2, respectively, again rescaled to the absorption oscillator strength of van Dishoeck (1983). Our values are N(0) = 1.4, N(2) = 4.85, N(4) = 4.3. Towards No. 5, GM94 measured N(0) = 0.5, N(2) = 2.4, and N(4) = 1.6, all in units of 1013 cm-2, which compares with our data of N(0) = 0.5, N(2) = 2.1, and N(4) = 2.1. In general, our measured equivalent widths are consistent with those of Lutz & Crutcher (1983). Exceptions occur for the P(4)+Q(8) line blend, where Lutz & Crutcher (1983) obtain $22 \pm 3$ m$\rm\AA$, compared to our value of $30.5 \pm 3$ m$\rm\AA$, and the R(0) line, where Lutz & Crutcher (1983) give $19.1 \pm 3.2$ m$\rm\AA$, compared to our value of $14 \pm 1$ m$\rm\AA$.

The observations of GM94 were taken at the higher spectral resolution of R=65 000 and indicate a total of four absorption components towards No. 12, two unresolved components at $V_{\rm {hel}} = -$5.7 and -2.5 km s-1, and two weaker components near -10.6 km s-1 and +13.6 km s-1. This agrees reasonably well with our detection of a single, unresolved absorption line near $V_{\rm {hel}} = -$5.5 km s-1. The absorption components near -10.6 km s-1 and +13.6 km s-1 of GM94 are not present in our spectrum, which has a significantly higher S/N compared to the spectra of GM94. They may thus not be real.

Table 4 summarises the C2 measurements towards the Cyg OB2 association. It contains, in Cols. 1-8, respectively, the star and its spectral type, its visual extinction AV as given by Humphreys (1978), the gas-kinetic temperature T, the density $n_{\rm c}$, the column density in rotational level J''=2, the total C2 column density $N_{\rm {tot}}$ inferred from T, $n_{\rm c}$ and N(2), the total observed column density $N_{\rm obs}$, and the average heliocentric velocity $V_{\rm {hel}}$. In the discussion of Sect. 4, theoretical C2 column densities $N_{\rm {tot}}$ are used in the comparison with chemical models, rather than $N_{\rm obs}$, because the theoretical column densities include the population densities in the unobserved levels as well.


  \begin{figure}
\par\includegraphics[width=13.4cm,clip]{12cn.ps}\end{figure} Figure 6: Normalised spectra covering the (2,0) band and (1,0) bands of the CN A $^2\Pi _{\rm u}$ - X ${^2\Sigma ^+}$ red system towards Cyg OB2 No. 12 (bold lines). Comparison spectra of $\eta $ Tau are represented by dotted lines. The locations of various CN lines (cf. Table 6) are given by triangles.

   
3.4 Diffuse interstellar bands near 7721 Å and 8763 Å

The spectra of all six stars in Cyg OB2 observed here are affected by absorption bands near 7721 Å and near 8763 Å which are broader than the interstellar C2 lines. These bands were previously identified as new diffuse interstellar bands (DIBs) (Herbig & Leka 1991; Gredel & Münch 1986). A complete discussion of the DIBs will be presented elsewhere. Table 4 summarises the measurements of the band near 8763 $\rm\AA$, with the star, the wavelength, the full width at half maximum (FWHM), and the equivalent width of the band, listed in Cols. 1-4, respectively. It has been suggested that DIBs form largely in low-density, diffuse material (Herbig 1995). We note here that the DIB towards Cyg OB2 No. 12 is relatively weak compared with the other stars in Cyg OB2. Such is not expected if the line of sight towards No. 12 passes through a high column density of low density material spread over a pathlength of some 1000 pc (cf. discussion in Sect. 4.1).


  
Table 5: The 8763 Å diffuse interstellar band towards Cyg OB2.
\begin{table}\par\begin{displaymath}
\begin{array}[t]{p{0.3\linewidth}lcr}
\hl...
...0 & 13 \\
\noalign{\smallskip }
\hline
\end{array}\end{displaymath}
\end{table}

3.5 The CN (2,0) and (1,0) A ${^2\Pi _{u}}$ - X ${^2\Sigma ^+}$ red system

The spectral region which covers the absorption lines of the (1,0) and (2,0) bands of the CN red system is heavily contaminated by telluric absorption lines. However, a few lines in the (1,0) and (2,0) bands are well isolated and accurate equivalent widths can be determined.

Figure 6 contains the normalised spectra towards Cyg OB2 No. 12. The position of the detected CN lines is indicated by filled triangles. Open triangles mark the expected positions of CN absorption lines which are blended with atmospheric features. The (2,0) SR21(0) (7871.5 $\rm\AA$), (2,0) [ RQ21(1)+R2(1)] (7873.9 $\rm\AA$), (2,0) RQ21(0) (7874.7 $\rm\AA$), (2,0) R1(0) (7906.5 $\rm\AA$), (1,0) [ QP21(1) + Q2(1)] (9146.9 $\rm\AA$), and (1,0) R1(0) (9186.8 $\rm\AA$) lines or line blends, are clearly detected. The measurements allow the determination the column density N(0) in the rotational level N''=0. The lack of clear detections of absorption lines arising from the rotational level N''=1 constrains the column density N(1). In order to judge what the maximum CN abundance is towards Cyg OB2 No. 12, upper limits are estimated for the (2,0) R1(1) (7903.6 $\rm\AA$), (1,0) SR21(0) (9139.6 $\rm\AA$), and (1,0) R1(1) (9183.3 $\rm\AA$) lines. The estimate was obtained from a comparison of the relative strengths of the telluric lines in Cyg OB2 No. 12 and in $\eta $ Tau. The spectrum of $\eta $ Tau is represented in Fig. 6 by the dotted line. CN is not detected towards $\eta $ Tau. Upper limits estimated for the column density in N''=1 agree reasonably well with the column density inferred from the marginally detected (1,0)[ QP21(1)+Q2(1)] line blend near 9147 $\rm\AA$.

The CN measurements are summarised in Table 6. It gives, in Cols. 1-6, the line designation, the measured heliocentric wavelength $\lambda_{\rm hel}$ and the heliocentric velocity $V_{\rm {hel}}$, the measured equivalent width $W_{\lambda}$, and the inferred column densities N(0) and N(1) in the N''=0 and N''=1 rotational levels, respectively. Uncertainties are given in parentheses. The last row contains in Cols. 5 and 6, respectively, the average column density N(0) inferred from the observations and the column density N(1) in the limit where the CN excitation temperature T10 is close to the cosmic microwave background radiation temperature of 2.7 K. The row above contains the value N(1) estimated from the observations, and the corresponding CN excitation temperature in Col. 7. A firm lower limit to the total CN column density towards Cyg OB2 No. 12 is N(CN $) > 8\times 10^{13}$ cm-2, and the upper limit is N(CN $) < 13\times 10^{13}$ cm-2. The average heliocentric velocity of CN is -4.3 km s-1 which is consistent with the velocity of C2.


  
Table 6: Summary of CN absorption lines towards Cyg OB2 No. 12.
\begin{table}\par\begin{displaymath}
\begin{array}[h]{ccccccc}
\hline
\noal...
...\
\par\noalign{\smallskip }
\hline
\end{array} \end{displaymath}
\end{table}

3.6 Interstellar Rubidium towards Cyg OB2 No. 12 and No. 5


  \begin{figure}
\par\includegraphics[width=8.8cm,clip]{Rb.ps}\end{figure} Figure 7: Detection of the interstellar line of Rb I 5s 2S1/2 - 5p2P3/2 towards Cyg OB2 No. 12 and No. 5. The spectrum of No. 5 is shifted by 0.03 units along the ordinate.

We report the detection of the interstellar Rb I $\rm 5$s 2S1/2 - 5p2P3/2 resonance line near 7800 Å towards Cyg OB2 No. 12 and towards No. 5. This presents the first firm detection of rubidium in the interstellar medium. The significance of an earlier Rb I measurement by Jura & Smith (1981) towards $\zeta$ Oph has been questioned by Federman et al. (1985), who did not detect Rb I in their high quality spectra towards $\zeta$ Oph and towards two other lines of sight.

Our spectra are shown in Fig. 7. The Rb I line is detected at 10 standard deviations towards Cyg OB2 No. 12. We use the formalism and the atomic data of Morton (2000) to transfer measured equivalent widths of $(5 \pm 0.5)$ mÅ and $(2.7 \pm 0.5)$ mÅ towards No. 12 and No. 5, respectively, into column densities of N(Rb I $) = (13\pm 2)\times 10^{9}$ cm-2 and N(Rb I $) = (7 \pm 2)\times 10^{9}$ cm-2. Heliocentric velocities are $V_{\rm {hel}} = -$6.4 km s-1 for No. 12 and -8.1 km s-1 towards No. 5, respectively. The Rb I velocities agree with those of C2 within the errors.

Neutral rubidium has an ionisation potential of 4.77 eV, thus interstellar rubidium is mostly ionised. The ionisation potential is similar to that of potassium, and relative abundances of N(Rb+)/N(K+) may be related to measured ratios N(Rb)/N(K) (Federman et al. 1985). Column densities of N(K $) = 3.3\times 10^{12}$ cm-2 towards No. 12 and N(K $) = 2.2\times 10^{12}$ cm-2 towards No. 5 were inferred by Chaffee & White (1982). The K I 7664 Å and 7698 Å absorption lines are also present in our spectra. The K I 7698 Å line is well separated from a telluric O2 absorption line but the K I 7664 Å line is not. Equivalent widths of the K I 7698 Å lines are $382 \pm 10$ mÅ and $275 \pm 10$ m$\rm\AA$, respectively, towards No. 12 and No. 5. The measured equivalent widths are consistent with those inferred by Chaffee & White (1982), who give $323 \pm 59$ towards No. 12 and $294 \pm 48$ towards No. 5. Using the atomic parameters of Morton (1991), we infer N(K $) =
2\times 10^{12}$ cm-2 towards No. 12 and N(K $) = 1.5\times 10^{12}$ cm-2 towards No. 5. These values, calculated in the limit of unsaturated lines, are close to the neutral K column densities derived Chaffee & White (1982) who used the doublet ratio to estimate saturation corrections.

The K I column densities inferred by Chaffee & White (1982) and the Rb I column densities inferred here suggest values of N(Rb+)/N(K $^+) = (0.8{-}1)\times 10^{-3}$ towards Cyg OB2. This ratio compares with upper limits of N(Rb+)/N(K $^+) \le 1.5\times 10^{-3}$ inferred by Federman et al. (1985) towards o Per, $\zeta$ Per, and $\zeta$ Oph. The Rb+/K+ ratio towards No. 12 is about a factor of three lower than the solar ratio of N(Rb+)/N(K $^+)
= 2.9\times 10^{-3}$ (as given in Federman et al. 1985).


  \begin{figure}
\par\includegraphics[width=8.8cm,clip]{mod600.ps}\end{figure} Figure 8: Fractional molecular abundances f(X) 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. Dots are fractional molecular abundances towards Cyg OB2 No. 12 inferred from observations. The shaded region corresponds to X-ray ionisation rates of $\zeta = (0.6{-}3) \times 10^{-15}$ s-1.


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