Rotational spectroscopy of AlO

O. Launila; D. P. K. Banerjee

doi:10.1051/0004-6361/200913274

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Volume 508 / No 2 (December III 2009)

A&A, 508 2 (2009) 1067-1072

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Issue		A&A Volume 508, Number 2, December III 2009


Page(s)		1067 - 1072
Section		Atomic, molecular, and nuclear data
DOI		https://doi.org/10.1051/0004-6361/200913274
Published online		21 October 2009

A&A 508, 1067-1072 (2009)

Low-N transitions of astronomical interest in the $X^{2}\Sigma ^{+}$ state

O. Launila¹ - D. P. K. Banerjee²

1 - KTH AlbaNova University Center, Department of Applied Physics, 106 91 Stockholm, Sweden
2 - Astronomy and Astrophysics Division, Physical Research Laboratory, Ahmedabad 380009, Gujarat, India

Received 9 September 2009 / Accepted 9 October 2009

Abstract
Aims. The detection of rotational transitions of the AlO radical at millimeter wavelengths from an astronomical source has recently been reported. In view of this, rotational transitions in the ground $X^{2}\Sigma ^{+}$ state of AlO have been reinvestigated.
Methods. Comparisons between Fourier transform and microwave data indicate a discrepancy regarding the derived value of $\gamma _{\rm D}$ in the v = 0 level of the ground state. This discrepancy is discussed in the light of comparisons between experimental data and synthesized rotational spectra in the v = 0, 1 and 2 levels of $X^{2}\Sigma ^{+}$ .
Results. A list of calculated rotational lines in v = 0, 1 and 2 of the ground state up to N' = 11 is presented which should aid astronomers in analysis and interpretation of observed AlO data and also facilitate future searches for this radical.

Key words: molecular data - molecular processes - ISM: molecules - radio lines: stars

1 Introduction

The ground $X^{2}\Sigma ^{+}$ state of the AlO radical has been studied with microwave spectroscopy in the v = 0, 1 and 2 levels. Törring et al. (1989) recorded the $N = 1 \rightarrow2$ transition near 76 GHz. In their Table 1, frequencies for several $\Delta F = \Delta N$ and $\Delta F \neq \Delta N$ transitions are shown. Yamada et al. (1990) and Goto et al. (1994) recorded several $\Delta F = \Delta N$ rotational transitions, resulting in a set of accurate molecular constants, including $\gamma$ and $\gamma _{\rm D}$ .

Launila et al. (1994) have performed a Fourier transform study of the $A^{2}\Pi _{i} \rightarrow X^{2}\Sigma ^{+}$ transition of AlO in the 2 $\mu$ m region. In that work, some discrepancies were pointed out regarding their derived $\gamma _{\rm D}$ values, as compared to those found in the microwave work. While Yamada et al. (1990) had given a positive value for $\gamma _{\rm D}$ for v = 0, the sign was in fact found to be negative in the light of high-N data of Launila et al. (1994). One of the aims of the present paper is to reinvestigate this discrepancy more closely. The work by Goto et al. (1994), dealing with the v = 1, 2 vibrational levels of the ground state of AlO, does not show the same discrepancy, however.

In a theoretical work, Ito et al. (1994) have discussed and explained the observed vibrational anomalies in the spin-rotation constants of the ground state in the light of spin-orbit interaction with the $A^{2}\Pi_{i}$ and $C^{2}\Pi$ states.

Recently, Tenenbaum & Ziurys (2009) reported three rotational transitions of AlO from the supergiant star VY Canis Majoris. In order to facilitate future millimeter-wave search for rotational transitions of AlO, tables containing expected frequencies in the v = 0, 1 and 2 levels of the ground state are useful. In the present work, such tables are presented.

2 Analysis and results

The $X^{2}\Sigma ^{+}$ ground state of the AlO radical represents a good example of a Hund's case ( $b\beta_{\rm S}$ ) coupling. Here, the nuclear and molecular spins ${\vec I}$ and ${\vec S}$ couple to form an intermediate vector ${\vec G}$ , which subsequently couples with ${\vec N}$ to form ${\vec F}$ . Although the energy levels can be calculated with a standard hyperfine Hamiltonian based on ${\vec J} = {\vec N}+{\vec S}$ formalism, the J quantum number is to be considered as a bookkeeping device only. This is the case in Table I of Yamada et al. (1990), where both J' and J'' have been included. Goto et al. (1994) only specify the ``good'' quantum numbers N and F in their Tables 1 and 2.

In the work of Launila et al. (1994) it was found that the positive sign of $\gamma _{\rm D}$ for v = 0 was in conflict with the high-N behavior of the spin doubling of the ground state, as shown in Figs. 3 and 4 of their study. We have plotted in the present work the observed $^{\rm R}Q_{21}$ and R₂ branches in the (2, 0) band of the $A^{2}\Pi _{i} \rightarrow X^{2}\Sigma ^{+}$ transition from N = 3 to N = 104 (Fig. 1). Here, we are using standard spectroscopic notations, where superscripts in branch designations refer to N-numbered branch types, while subscripts refer to the spin components. For instance, $^{\rm R}Q_{21}$ denotes a Q-branch of R-type, going from the upper state spin component 2 to the lower state component 1. Vibrational bands are denoted as ( $v_{\rm upper}$ , $v_{\rm lower}$ ). From the plot in Fig. 1 we can see that the spin doubling of the ground state v = 0 level increases with N, up to about 0.1 cm^-1 for N = 50, after which it starts to decrease until it finally reaches the value of about 0.07 cm^-1 for N = 104. According to the constants of Yamada et al. (1990), the spin doubling would have to increase monotonically to about 0.3 cm^-1, which is in contrast with the observations.

$\begin{figure} \par\includegraphics[width=9cm,clip]{13274fg1.eps} \end{figure}$	Figure 1: The $^{\rm R}Q_{21}$ and R₂ branches in the (2, 0) band of the $A^{2}\Pi _{i} \rightarrow X^{2}\Sigma ^{+}$ transition of AlO. The traces show a series of 0.3 cm^-1 intervals, cut directly from the FT spectrum. The $^{\rm R}Q_{21}$ lines have been arranged so that their reduced wavenumbers coincide. Some lines belonging to other branches are also visible in the plot.
Open with DEXTER

We have also recalculated the rotational transition $N = 10 \leftarrow 9$ shown in Fig. 2 of Yamada et al. (1990), using the constants given by them ( $\gamma = 51.660$ MHz, $\gamma_{\rm D} = 0.00343$ MHz), and also using the same constants, but with a reversed sign of $\gamma _{\rm D}$ . The Hamiltonian used was the same as in Launila et al. (1994). The results are presented in Fig. 2.

$\begin{figure} \par\includegraphics[width=9cm,clip]{13274fg2.eps} \vspace*{3.5mm} \end{figure}$	Figure 2: The $N = 10 \leftarrow 9$ rotational transition in the $X^{2}\Sigma ^{+}$ (v=0) ground state of AlO from Yamada et al. (1990), as compared with calculated spectra convoluted with a Gaussian line profile of 0.75 MHz FWHM.
Open with DEXTER

The uppermost trace of Fig. 2 shows the experimental data, while the middle one shows the recalculated rotational spectrum using the constants of Yamada et al. (1990). The lower trace shows the same spectrum calculated with reversed sign of $\gamma _{\rm D}$ . The calculated spectra have been convoluted with a Gaussian profile of 0.75 MHz FWHM. It is clear from this comparison that the reversed sign of $\gamma _{\rm D}$ results in an almost perfect agreement with the experimental data, while the unaltered constants by Yamada et al. (1990) give rise to deviations of up to $\pm$ 1 MHz. Our conclusion is that the data fit in the work of Yamada et al. (1990) is essentially correct, although the sign of $\gamma _{\rm D}$ has to be changed. This sign change alone results in overall deviations of less than $\pm$ 0.1 MHz. However, no new least-squares fit of the data in Yamada et al. (1990) has been performed in the present work. The intensities in the calculated spectra were derived using an intensity formula (B1) from Bacis et al. (1973). Although this formula had actually been written for a Hund's case $(b\beta _{J})-(b\beta _{J})$ transition, the agreement with experimental data is surprisingly good.

The calculated frequencies and relative intensities (at 230 K) for all $\Delta N = \Delta F$ rotational transitions in v = 0, 1 and 2 up to N' = 11 are given in Tables 1-3.

Table 1: Calculated frequencies and intensities of $\Delta F = \Delta N$ rotational transitions in the $X^{2}\Sigma ^{+}$ (v=0) ground state of AlO. The constants from Yamada et al. (1990) have been used, with the exception that the sign of $\gamma _{\rm D}$ has been reversed. The intensities are calculated according to a Hund's case $(b\beta _{J})-(b\beta _{J})$ formula (B1) from Bacis et al. (1973), at a temperature of 230 K.

Table 2: Calculated frequencies and intensities of $\Delta F = \Delta N$ rotational transitions in the $X^{2}\Sigma ^{+}$ (v=1) ground state of AlO. The constants from Goto et al. (1994) have been used. The intensities are calculated according to a Hund's case $(b\beta _{J})-(b\beta _{J})$ formula (B1) from Bacis et al. (1973), at a temperature of 230 K.

Table 3: Calculated frequencies and intensities of $\Delta F = \Delta N$ rotational transitions in the $X^{2}\Sigma ^{+}$ (v=2) ground state of AlO. The constants from Goto et al. (1994) have been used. The intensities are calculated according to a Hund's case $(b\beta _{J})-(b\beta _{J})$ formula (B1) from Bacis et al. (1973), at a temperature of 230 K.

3 Discussion

The determination of the correct constants for a molecule/radical has its own intrinsic value. Additionally, the present study is also relevant in an astronomical context. Tenenbaum & Ziurys (2009) have recently made the first radio/mm detection of the AlO ( $X^{2}\Sigma ^{+}$ ) radical toward the envelope of the oxygen rich supergiant star VY Canis Majoris (VY CMa). They observed the $N = 7\rightarrow6$ and $6\rightarrow5$ rotational transitions of AlO at 268 and 230 GHz and the $N = 4\rightarrow3$ line at 153 GHz. While their search for the $N = 7\rightarrow6$ hyperfine transitions was based on direct laboratory measured frequencies by Yamada et al. (1990), the search for the $N = 6\rightarrow5$ and $N = 4\rightarrow3$ transitions was based on frequencies calculated from spectroscopic constants of those authors. As has been pointed out, an error is present in one of these constants ( $\gamma _{\rm D}$ in the v = 0 level of the ground state), which leads to deviations between the calculated and true frequencies. While these deviations are small and may not affect the final result of a line search too seriously, it is still desirable to have accurate frequencies to facilitate future millimeter-wave searches for rotational transitions of AlO. It is planned for several such searches to be taken place in the near future as a consequence of the recent detection in VY CMa. AlO is slowly emerging as a molecule which could attract a fair deal of interest among astronomers. In the VY CMa detection for example it is shown how its study could lead to a better understanding of the gas-phase refractory chemistry in oxygen-rich envelopes. AlO has also been proposed to be a potential molecule in the formation of alumina, which is one of the earliest and most vital dust condensates in oxygen rich circumstellar environments (Banerjee et al. 2007). The mineralogical dust condensation sequence and processes involved are issues of considerable interest to astronomers. The AlO radical also received considerable attention after the strong detection of several $A \rightarrow X$ bands in the near-infrared (1-2.5 microns) in the eruptive variables V4332 Sgr and V838 Mon (Banerjee et al. 2003; Evans et al. 2003). Other IR detections of AlO include IRAS 08182-6000 and IRAS 18530+0817 (Walker et al. 1997). In the optical, the $B \rightarrow X$ bands have been prominently detected in U Equulei (Barnbaum et al. 1996) and in several cool stars and Mira variables including Mira itself (Keenan et al. 1969; Garrison 1997).

The line lists presented here should also aid in analysis of mm line data for aspects related to kinematics. Since the rotational levels of AlO species are split by both fine and hyperfine interactions, each rotational transition consists of several closely spaced hyperfine components. Figure 2 exemplifies this. If line broadening is small and the spectral resolution of the observations is adequate to resolve these components, then different components will yield different Doppler velocities if the corresponding reference or rest frequencies are in error. This could lead to ambiguity in interpreting the data. Even if the hyperfine components are not distinctly resolved but rather blended to give a composite line profile (as in the observed profiles in VY CMa), modelling of such composite profiles using wrong rest frequencies could lead to errors in estimating the composite line centre, half width of the composite profile and half-widths of the individual hyperfine components. Proper estimates of such kinematic parameters are important as they help determine the size and site of origin of a molecular species. The detailed discussion by Tenenbaum & Ziurys (2009) in the case of VY CMa, which has three distinctly different kinematic flows in the system, illustrates this.

4 Summary

Rotational transitions of AlO have been reinvestigated. The discrepancy regarding the derived value of $\gamma _{\rm D}$ of the $X^{2}\Sigma ^{+}$ ground state v = 0 level has been shown to be due to a sign error in the microwave work by Yamada et al. (1990). A list of calculated rotational lines in v = 0, 1 and 2 of the ground state up to N' = 11 has been presented.

References

Bacis, R., Collomb, R., & Bessis, N. 1973, Phys. Rev. A, 8(5), 2255
Banerjee, D. P. K., Misselt, K. A., Su, K. Y. L., Ashok, N. M., & Smith, P. S. 2007, ApJ, 666, L25 [NASA ADS] [CrossRef]
Banerjee, D. P. K., Varricatt, W. P., Ashok, N. M., & Launila, O. 2003, ApJ, 598, L31 [NASA ADS] [CrossRef]
Barnbaum, C., Omont, A., & Morris, M. 1996, A&A, 310, 259 [NASA ADS]
Evans, A., Geballe, T. R., Rushton, M. T., et al. 2003, MNRAS, 343, 1054 [NASA ADS] [CrossRef]
Garrison, R. F. 1997, JAAVSO, 25, 70 [NASA ADS]
Goto, M., Takano, S., Yamamoto, S., Ito, H., & Saito, S. 1994, Chem. Phys. Lett., 227, 287 [NASA ADS] [CrossRef]
Ito, H., & Goto, M. 1994, Chem. Phys. Lett., 227, 293 [NASA ADS] [CrossRef]
Keenan, P. C., Deutsch, A. J., & Garrison, R. F. 1969, ApJ, 158, 261 [NASA ADS] [CrossRef]
Launila, O., & Jonsson, J. 1994, J. Mol. Spectrosc., 168, 1 [NASA ADS] [CrossRef]
Tenenbaum, E. D., & Ziurys, L. M. 2009, ApJ, 694, L59 [NASA ADS] [CrossRef]
Törring, T., & Herrmann, R. 1989, Mol. Phys., 68(6), 1379
Walker, H. J., Tsikoudi, V., Clayton, C. A., et al. 1997, A&A, 323, 442 [NASA ADS]
Yamada, C., Cohen, E. A., Fujitake, M., & Hirota, E. 1990, J. Chem. Phys., 92(4), 2146

All Tables

Table 1: Calculated frequencies and intensities of $\Delta F = \Delta N$ rotational transitions in the $X^{2}\Sigma ^{+}$ (v=0) ground state of AlO. The constants from Yamada et al. (1990) have been used, with the exception that the sign of $\gamma _{\rm D}$ has been reversed. The intensities are calculated according to a Hund's case $(b\beta _{J})-(b\beta _{J})$ formula (B1) from Bacis et al. (1973), at a temperature of 230 K.

Table 2: Calculated frequencies and intensities of $\Delta F = \Delta N$ rotational transitions in the $X^{2}\Sigma ^{+}$ (v=1) ground state of AlO. The constants from Goto et al. (1994) have been used. The intensities are calculated according to a Hund's case $(b\beta _{J})-(b\beta _{J})$ formula (B1) from Bacis et al. (1973), at a temperature of 230 K.

Table 3: Calculated frequencies and intensities of $\Delta F = \Delta N$ rotational transitions in the $X^{2}\Sigma ^{+}$ (v=2) ground state of AlO. The constants from Goto et al. (1994) have been used. The intensities are calculated according to a Hund's case $(b\beta _{J})-(b\beta _{J})$ formula (B1) from Bacis et al. (1973), at a temperature of 230 K.

All Figures

$\begin{figure} \par\includegraphics[width=9cm,clip]{13274fg1.eps} \end{figure}$	Figure 1: The $^{\rm R}Q_{21}$ and R₂ branches in the (2, 0) band of the $A^{2}\Pi _{i} \rightarrow X^{2}\Sigma ^{+}$ transition of AlO. The traces show a series of 0.3 cm^-1 intervals, cut directly from the FT spectrum. The $^{\rm R}Q_{21}$ lines have been arranged so that their reduced wavenumbers coincide. Some lines belonging to other branches are also visible in the plot.
Open with DEXTER
In the text

$\begin{figure} \par\includegraphics[width=9cm,clip]{13274fg2.eps} \vspace*{3.5mm} \end{figure}$	Figure 2: The $N = 10 \leftarrow 9$ rotational transition in the $X^{2}\Sigma ^{+}$ (v=0) ground state of AlO from Yamada et al. (1990), as compared with calculated spectra convoluted with a Gaussian line profile of 0.75 MHz FWHM.
Open with DEXTER
In the text

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