RUBIDIUM IN THE INTERSTELLAR MEDIUM

The starting input values for χ Oph were taken from the K i and ⁷Li i values of Knauth et al. (2003). The input velocity and b-value were 0.20 and 1.00 km s⁻¹, respectively. Because the lines are so weak, the input column density was derived from the ratio of equivalent width to column density for ρ Oph A using the simple equation

$$\begin{equation} \frac{W{_\lambda }({\rm \rho \ Oph\ A})}{{\it N}({\rm \rho \ Oph\ A})} = \frac{W{_\lambda }({\rm \chi \ Oph})}{{\it N}({\rm \chi \ Oph})}, \end{equation} \tag{ 1 }$$

where W_λ(X) is the equivalent width of the Rb i line and N is the total column density of ⁸⁷Rb and ⁸⁵Rb combined. Once the total column density was determined, it was divided so that the isotope ratio would be similar to that of the solar system. Thus, 67% of N(χ Oph) was ⁸⁵Rb and 33% of it was ⁸⁷Rb, using a ratio of 2:1 that is midway between the results for ρ Oph A (Federman et al. 2004) and the solar system (Lodders 2003). These were the column densities used for the starting point in RbFits. χ Oph has the highest reduced χ², but the synthesized profile fits the data well. This "ratio" technique was also used for HD 147889.

The profile for ζ Per was synthesized in three steps, following the above procedure. The starting values were taken from Knauth et al. (2000). During the second step, however, instead of using the velocity output from ⁸⁷Rb i, the velocity of ⁸⁵Rb i was more similar to that of K i and ⁷Li i from Knauth et al. (2000). After using the velocity and b value from the solution of ⁸⁵Rb i, the rest of the synthesis was performed as described above. Figure 1 displays the fitted spectra toward ζ Per, χ Oph, and HD 147889.

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The profiles of the four lines of sight with two components were more difficult to synthesize. The starting values did not affect the outcome of the one-component fits, whereas the simple "ratio" technique of dividing equivalent widths by column densities was no longer valid because the profiles were more complex, each having eight components (two hyperfine components for each isotope for each cloud). The program needed better starting values from other data (velocity separations, etc.), especially for the column densities. There are two ways to solve this problem.

For the first way, a list of abundances of Rb i and K i was created from lines of sight with one component: χ Oph, ζ Per, HD 147889, ρ Oph A, and the two lines of sight from Gredel et al. (2001), and Cyg OB No. 5 and No. 12. The K i column densities were obtained from Knauth et al. (2000; ζ Per), Knauth et al. (2003; χ Oph), Federman et al. (2004; ρ Oph A, Cyg OB Nos. 5 and 12), and derived from unpublished observations (HD 147889). An average of the N(Rb i)/N(K i) ratios for each line of sight yielded 9.5 × 10⁻⁴. At this preliminary stage of the analysis for AE Aur, the component structure and N(K i) come from the synthesis of λ7699 from unpublished data. For all other directions, N(K i) is obtained from the weak line at λ4044. Using the above average and knowing K i for the four lines of sight in the current study, one could work backwards to find N(Rb i). Then using N(Rb i) as the total column density for a given line of sight and the cloud fractions from Knauth et al. (2003) for o Per, ζ Oph, and 20 Aql as well as our results for AE Aur, the column densities for each cloud were obtained.

For example, o Per has a total K i column density of 1.04 × 10¹² cm⁻². Then, according to Federman et al. (2004) and assuming equal depletion of Rb and K although the elements have somewhat different condensation temperatures (Lodders 2003),

$$\begin{equation} {\Bigg [}\frac{A{_g}({\rm Rb})}{A{_g}({\rm K})}{\Bigg ]} = {\Bigg [}\frac{{\it N}({\rm Rb\ {\mathsc {i}}})}{{\it N}({\rm K\ {\mathsc {i}}})}{\Bigg ]} {\Bigg [}\frac{G({\rm Rb\ {\mathsc {i}}})}{G({\rm K\ {\mathsc {i}}})}{\Bigg ]} {\Bigg [}\frac{\alpha ({\rm K\ {\mathsc {i}}})}{\alpha ({\rm Rb\ {\mathsc {i}}})}{\Bigg ]}, \end{equation} \tag{ 2 }$$

where A_g(Rb)/A_g(K) is the elemental abundance ratio, G(X) is the photoionization rate corrected for grain attenuation, and α(X) is the rate coefficient for radiative recombination. We adopted the same sources for the atomic data used by Federman et al. (2004) to infer photoionization rates for Rb i of 3.42 × 10⁻¹² s⁻¹ and for K i of 8.67 × 10⁻¹² s⁻¹. For Rb i, the theoretical calculations of Weisheit (1972) give cross sections for 1150–1250 Å, which were scaled to the measurements of Marr & Creek (1968) at longer wavelengths. The cross sections for K i are taken from the measurements of Hudson & Carter (1965), Hudson & Carter (1967), Marr & Creek (1968), and Sandner et al. (1981). For wavelengths below 1150 Å, there is no differential attenuation because the ionization potentials are similar (4.18 eV for Rb i and 4.34 eV for K i). Based on these cross sections, a 13% correction was applied to G(Rb i) for λ< 1150 Å. The rate coefficients for radiative electron recombination are similar, within 10% of one another (Wane 1985; Péquignot & Aldrovandi 1986; Wane & Aymar 1987), and so the ratio of the rate coefficients is ∼1. The ratio of the photoionization rates is 0.394.

For o Per, we can solve for N(Rb i), which is 2.51 × 10⁹ cm⁻². Then, we multiplied this column density by the percentage in each cloud (taken from Knauth et al. 2003), 14% and 86% for the clouds at 3.96 and 6.98 km s⁻¹, respectively. Assuming the ratio in each component would be similar to the solar system value, the relative amounts of the isotopes were separated. The result was that four starting column densities were created.

The second way to obtain starting column densities was to perform a one component fit on the data, as in the case of ζ Oph. This one component fit provided a coarse estimate of a weighted velocity, b value, and column density for each isotope. The isotopes were then split into their resultant components according to Knauth et al. (2003). The resulting spectra with two components are shown in Figure 2.

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The Rb isotope ratio is expected to be independent of the two principal effects that hamper the extraction of the Rb/H ratio from the Rb i equivalent widths, namely, the large degree of ionization of Rb to Rb⁺, and the loss of Rb onto grains. Table 4 shows the final solutions for the lines of sight in our survey. It lists the resulting velocities, column densities, b-values, ⁸⁵Rb/⁸⁷Rb ratios, and reduced χ²s, calculated from the RbFits program. The b-values range from 0.45 to 1.46 km s⁻¹; while the larger values may indicate the presence of unresolved structure, similar values have been reported previously (e.g., Knauth et al. 2003). The reduced χ²s are all around 1.0. The uncertainties for each cloud were calculated using the FWHM, derived from the b value, and S/N of each spectrum. For such weak lines, the same fractional uncertainty applies to the column densities also. These were propagated in the usual way to place uncertainties on the inferred isotope ratios. When 2σ was greater than the equivalent widths for the ⁸⁷Rb line, only lower limits to the ratio are possible. All lines of sight are consistent with the solar system value, 2.59, as determined from meteorites, except for HD 147889 and the previously measured ρ Oph A (Federman et al. 2004).

We investigated the sensitivity of our results for HD 147889 by attempting to fit the Rb i profile with the solar system ratio. Various combinations of keeping V_LSR and b-value fixed were attempted. All gave similar results, with reduced χ²s from 1.62 to 1.81 compared to our preferred synthesis with 1.44. We performed analyses of the Rb isotope ratio toward HD 147889 of a single component fit in two additional ways. In the first analysis, all profile synthesis parameters were allowed to vary. For the second analysis only the ⁸⁵Rb and ⁸⁷Rb column densities were allowed to vary. For the second synthesis, the velocity and the Doppler broadening parameters were fixed to those determined from the profile fit to the measured interstellar K i line. This led to an improved reduced χ² over that of the freely varying profile synthesis. Application of an F-test (Lupton 1993, p. 100) shows the improvement in χ² is justified to the 68% confidence level. In order to test whether our single component fit of the Rb isotope ratio is potentially two components, a subsequent analysis was performed. This analysis led to an overall improvement in the reduced χ². An F-test shows that a second component is justified at the 80% confidence level. The synthesis based on changing V_LSR appears in the lower right panel of Figure 1. The fit on the blue side is poorer and below the data points, which is evidenced by the residuals within the left side of the profile not appearing random.

Neutral Rb is expected to follow the spatial trend of neutral K in interstellar clouds because they have similar ionization potentials and chemical properties, and so a determination of the interstellar elemental Rb/K ratio from Equation (2) compared to the meteoritic value may provide new insights into the production of neutron capture elements. High-resolution surveys have been performed for interstellar Li i (Knauth et al. 2003), Na i (Welty et al. 1994), and K i (Welty & Hobbs 2001) absorption. Knauth et al. (2003) conclude that the elemental Li/K abundance ratio is consistent with the solar system value, and Welty & Hobbs (2001) also confirm the essentially linear relationship between the total column densities of Li i, Na i, and K i. It seems that Li, Na, and K are likely depleted by comparable amounts in the relatively cool, dense regions where the neutral species are concentrated (Welty & Hobbs 2001). Thus, we apply Equation (2) with confidence.

Using this equation Rb/K, as well as ⁸⁵Rb/K and ⁸⁷Rb/K, were determined and the results are presented in Table 5. The results for ρ Oph A (Federman et al. 2004) and the solar system values (Lodders 2003) are shown for comparison. The K i column densities were obtained from the weak line at 4044 Å, except for AE Aur, where we adopted the unpublished λ4047 results of P. Boissé. The K i value for HD 147889 comes from Welty & Hobbs (2001).

The seven new lines of sight given in Table 5 all show a deficit in the ratios relative to potassium, with the possible exception of ⁸⁷Rb/K toward ρ Oph A. Relative to the meteoritic ratios, we find Rb/K = 34%, ⁸⁵Rb/K = 32%, and ⁸⁷Rb/K = 36%. These ratios are inferred from Equation (2), which does not allow for different depletions onto grains. As mentioned below, the condensation temperature for Rb is lower than that for K; if only depletion mattered, one would expect a higher Rb/K ratio, contrary to the observational results. Note that ⁸⁵Rb/K toward o Per seems to be larger than the other ratios, and that the anomalously large ratios of ⁸⁷Rb/K (HD 147889 and ρ Oph A) are not included in the above averages.

The first limits on interstellar N(Rb i) come from Federman et al. (1985), who searched for absorption toward the stars o Per, ζ Per, and ζ Oph, but did not detect any to a 3σ limit of ⩽1.5 mÅ. The resulting limits on N(Rb i) and Rb/K are found to be typically ⩽5 × 10⁹ cm⁻² and ⩽1.5 × 10 ⁻³ (Federman et al. 2004). In all cases, our detections yield values 30%–50% of the upper limits.

Gredel et al. (2001) found column densities toward Cyg OB2 Nos. 5 and 12 of N(Rb i) = (7 ± 2) × 10⁹ cm⁻² and N(Rb i) = (13 ± 2) × 10⁹ cm⁻², respectively. Combining these results with the high-resolution K i λ7699 spectra of McCall et al. (2002), Federman et al. (2004) derived values for N(K i) of the three main molecular components to be 9.4(7.7) × 10¹¹, 8.1(12) × 10¹¹, and 6.9(16) × 10¹¹ cm⁻² for the gas toward Cyg OB2 No. 5(12). Thus, Rb/K is 14 × 10⁻⁴ for No. 5 and 12 × 10⁻⁴ for No. 12. Rb/K for ρ Oph A is (13 ± 3) × 10⁻⁴ (Federman et al. 2004). These three lines of sight appear to have Rb/K values about a factor of 2 higher than the average of our 11 clouds, (6.1 ± 1.2) × 10⁻⁴. However, significant uncertainty remains in extracting elemental abundances toward the stars in Cyg OB2 because a blended, optically thick line was used to obtain the K i column density. Our analyses, and those of Snow et al. (2008), for HD 147889 indicate that the weaker line at 4044 Å yields a higher K i column density, leading to a smaller Rb/K ratio. Furthermore, the difference for the gas toward ρ Oph A is within ∼2σ of the results for our other lines of sight. Thus, all interstellar results appear smaller than the solar system value of (18 ± 4) × 10⁻⁴.

From the Rb i detection toward ρ Oph A, Federman et al. (2004) suggested that there was a deficit of r-processed material because ⁸⁷Rb/K seemed to have the meteoritic value, while ⁸⁵Rb/K was considerably less than the solar system value. This is also true toward HD 147889. These two lines of sight are near one another; the anomalously low ⁸⁵Rb/⁸⁷Rb ratios seem to arise from sampling the Rho Ophiuchus Molecular Cloud. For the other lines of sight, our sample indicates that both ⁸⁵Rb and ⁸⁷Rb have a deficit relative to K in the ISM of ∼66%. However, the gas in the Rho Ophiuchus Molecular Cloud appears to be enriched in ⁸⁷Rb.

Kawanomoto et al. (2009) recently published results for the direction toward HD 169454. Their isotope ratio (⁸⁵Rb/⁸⁷Rb > 2.4) is consistent with the meteoritic value, which again highlights the unusual values that we found for the Rho Ophiuchus Molecular Cloud. Their Rb/K ratio also reveals a deficit compared to the meteoritic ratio. It is worth noting that Kawanomoto et al. make comparisons with a solar system ratio at its formation by accounting for the decay of ⁸⁷Rb over 4.55 Gyr. Their estimate of the original ratio is 2.43.

The elemental abundances of Ge, Kr, Cd, and Sn seen in our sample of diffuse clouds, for which sufficient data exist, may provide an answer, because they are also synthesized through neutron capture. For each of these elements, the dominant ion is observed. In the solar system about 10% of Ge, 20% of Kr, 50% of Cd, and 70% of Sn are produced via the main s-process (Beer et al. 1992; Raiteri et al. 1993; Arlandini et al. 1999; Heil et al. 2008); massive stars through a combination of weak s-process and r-process are responsible for the remaining fractions. When corrected for the f-value adopted by Cartledge et al. (2006), Cardelli et al. (1991) obtain N(Ge)/N(H) of (4.9 ± 0.5) × 10⁻¹⁰ for ζ Oph, while Lodders (2003) gives (4.2 ± 0.5) × 10⁻⁹ for the solar system. Cartledge et al. (2003) find N(Kr)/N(H) to be (9.33 ± 1.14) × 10⁻¹⁰ for ζ Per and (7.94 ± 0.97) × 10⁻¹⁰ for ζ Oph, whereas the theoretical solar system abundance from Lodders (2003) is (19.05 ± 3.81) × 10⁻¹⁰. Sn was measured by Sofia et al. (1999), who found N(Sn)/N(H) of (7.41 ± 3.18) × 10⁻¹¹ for ζ Per, (8.13 ± 0.98) × 10⁻¹¹ for χ Oph, (9.12 ± 2.65) × 10⁻¹¹ for ζ Oph, and (5.75 ± 0.95) × 10⁻¹¹ for ρ Oph A. The solar system abundance is (12.88 ± 1.24) × 10⁻¹¹ (Lodders 2003). Finally, there is one line of sight among our sample that has measured Cd, ζ Oph, where N(Cd)/N(H) is (5.50 ± 1.60) × 10⁻¹¹ (Sofia et al. 1999). The solar system value for this element is (5.50 ± 0.38) × 10⁻¹¹ (Lodders 2003). Taking into account the uncertainties, all these values are likely to be lower than the solar system values.

For these relatively dense lines of sight, depletion onto grains, not nucleosynthetic processes, could be the cause for the deficits. It is better to consider the gas phase abundances for low density, warm gas. The condensation temperatures for Ge, Kr, Cd, Sn, and Rb are 734, 52, 652, 704, and 800 K, respectively (Lodders 2003). The survey by Cartledge et al. (2006) indicates an interstellar Ge abundance that is 25% the meteoritic value. With such a low condensation temperature, Kr should not be depleted toward any line of sight. However, the average abundance of Kr found by Cartledge et al. (2003) is ∼50% of the solar system value. The results on Cd and Sn (Sofia et al. 1999) reveal a different trend. For low-density lines of sight, neither element shows any depletion onto grains. There is even a hint that the Sn abundance for these directions is greater than the solar system value. The deficit of Rb relative to K cannot be explained by depletion onto grains resulting from a higher condensation temperature, because Li, Na, and K have even higher values (1135, 953, and 1001 K) according to Lodders (2003), and the Li/K and Na/K elemental ratios are similar to meteoritic values (Welty & Hobbs 2001; Knauth et al. 2003).

The depletion patterns of Ge, Kr, and Rb on the one hand, and Cd and Sn on the other, cannot be attributed to imprecise oscillator strengths. According to Morton (2003), the f-values used to study interstellar Kr i, Rb i, and Cd ii are well known from laboratory measurements. The same applies to Sn ii as a result of the experimental results of Schectman et al. (2000). Morton (2003) recommends the theoretical value of Biémont et al. (1998) for the Ge ii line at 1237 Å. While no more recent theoretical or experimental determinations are available at the present time, the dichotomy noted above would still be present if the results on interstellar Ge were not included.

A summary of the depletion patterns for the five elements appears in the top panel of Figure 3. Observational results for the amount of depletion onto grains both for low and high density clouds is shown. Each survey used to construct this figure (Cartledge et al. 2003 for Kr; Cartledge et al. 2006 for Ge; our results for Rb; Sofia et al. 1999 for Cd and Sn) indicate typical observational scatter of about 0.1 dex in the quoted depletion. Although T_cond is similar for Ge, Rb, Cd, and Sn, the depletion patterns for Cd and Sn are strikingly different than those for Ge and Rb, even when the intrinsic scatter in plots of depletion versus T_cond are considered. Furthermore, there is less depletion for Cd and Sn than for Kr, a noble gas.

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A closer look at the production routes for these n-capture nuclides offers a promising solution. This is highlighted in the bottom panel of Figure 3, where the white bar indicates production by low-mass stars and the shaded bar indicates massive stars. The solar system abundances for the elements Cd and Sn are believed to arise predominantly by the main s-process involving low-mass AGB stars (Beer et al. 1992; Raiteri et al. 1993; Arlandini et al. 1999), and they have reduced levels of depletion in the ISM. On the other hand, elements synthesized by the weak s-process and the r-process that occur in massive stars (Beer et al. 1992; Raiteri et al. 1993; Arlandini et al. 1999; The et al. 2007; Heil et al. 2008) appear to show interstellar abundances significantly lower than seen in the solar system. This possible reduction in the contribution of massive stars to interstellar abundances for n-capture elements contrasts with recent results for lighter elements. For instance, Przybilla et al. (2008) provide abundances for several elements in unevolved, early-type B stars that are indistinguishable from those found for the Orion Nebula (Esteban et al. 2004) and the sun (Asplund et al. 2005). The enhancement of ⁸⁷Rb in the Rho Ophiuchus Molecular Cloud remains puzzling. Our inferences may not be appropriate if Galactic chemical evolution altered the mix of s- and r-processed material from 4.5 Gyr ago when the solar system formed to the ISM of today. While we are not aware of predictions of the evolution of Rb and its isotopes, the weak s-process and r-process from Type II SN might be tied to the evolution of O or Mg or Si, while the main s-process to products of AGB stars such as Y or Ba.

Further efforts in a number of areas will likely improve our understanding. Data on interstellar Ga, As, and Pb—other n-capture nuclides—are available, but as of now it is more difficult to disentangle the effects of nucleosynthesis from depletion onto grains for them. Once this is accomplished, the unexpected results on Rb and its isotopes will likely be clarified. A more complete set of theoretical results, covering all isotopes of interest and based on modern stellar codes (e.g., The et al. 2007; Heil et al. 2008), are needed as well. We also see a need for theoretical studies into the evolution of these elements and their isotopes.