A&A 376, 333-335 (2001)
DOI: 10.1051/0004-6361:20010873

Suggestions for an interstellar cyclopropene search[*]

A. K. Sharma[*] - S. Chandra[*]

School of Physical Sciences, Swami Ramanand Teerth Marathwada University, Nanded 431 606, India

Received 13 December 1999 / Accepted 25 May 2001

Abstract
Following tentative detection of cyclopropene (C3H4) in Sgr B2 through its transition 3 22-221, several attempts to confirm the presence of cyclopropene in astronomical objects (including Sgr B2 itself) have been made. We suggest that cyclopropene may be observed in astronomical objects through its transition 2 20-221 at 3.67218 GHz, in absorption, even against the cosmic 2.7 K background, in a region having low density and low kinetic temperature.

Key words: ISM: molecules - molecular data


With the discovery of cyclopropenylidene (C3H2) in a large number of astronomical objects (see, e.g., Madden et al. 1989), cyclopropene (C3H4) has become a plausible candidate for detection in astronomical objects. A weak line at 106.86 GHz in Sgr B2 observed by Thaddeus et al. (1985) coincided with one of the predicted strongest lines, the 3 22-221 transition, of C3H4. Following this tentative detection of cyclopropene in Sgr B2, several attempts have been made to confirm its presence in astronomical objects (including Sgr B2 itself).

In order to provide rotational frequencies of cyclopropene throughout the radio spectrum to an accuracy sufficient for astronomical purposes, Vrtilek et al. (1987) reported the radio spectrum of cyclopropene. In Sgr B2, a search with the Bell Laboratories 7 m telescope for the 5 15- 414 and 5 05- 404 ortho-para line pair at 149.279 GHz and 149.549 GHz, respectively, resulted in an upper limit of column density $5 \times 10^{14}$ cm-2, assuming a line width of 24 km s-1 and a rotational temperature of 11 K (Vrtilek et al. 1987). This upper limit was found to lie below the tentative detection (which implied the column density of C3H4 to be $1.3 \times 10^{15}$ cm-2), but is still somewhat above the measurement for C3H2 ( $6 \times 10^{13}$ cm-2).

  \begin{figure} \par\includegraphics[width=8.8cm,clip]{aa9485f1.eps} \end{figure} Figure 1: Rotational energy levels in the ground vibrational state of para-C3H4, accounted for in the present investigation.
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 \begin{figure} \par\includegraphics[width=6.7cm,clip]{aa9485f2.eps} \end{figure} Figure 2: The iso-lines for intensity against the cosmic 2.7 K background, in the unit of Planck's function at the kinetic temperature of T (K), i.e., $(I_\nu - I_{\nu ,{\rm bg}})/B_\nu (T)$, for the 2 20-221 transition at 3.67218 GHz of para-C3H4. Only negative values for the kinetic temperatures T = 10, 20, and 30 K are plotted. For large molecular hydrogen densities (where the iso-lines are not plotted), the value becomes positive.
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Cyclopropene is a cyclic, asymmetric top molecule with the electric dipole moment of 0.45 D (Kasai et al. 1958) along the a-axis of inertia. In the present investigation, the NLTE occupation numbers of the C3H4 molecules are calculated in an on-the-spot approximation, by using the escape probability method (see, e.g., Rausch et al. 1996), where the external radiation field, impinging on the volume element emitting the line(s), is the cosmic 2.7 K background only.

The molecular data required as input for the present investigation are: (i) Einstein coefficients for various radiative transitions between the rotational energy levels accounted for, and (ii) the rate coefficients for collisional transitions between the levels due to collisions with H2 molecules. The details for calculation of Einstein A-coefficients for a-type rotational transitions in an asymmetric top molecule have been discussed by Chandra & Rashmi (1998). These transitions are governed by the selection rules:

J: $\triangle$ J = 0, $\pm$ 1  
ka, kc: odd, odd $\longleftrightarrow$ odd, even ortho-transitions
  even, even $\longleftrightarrow$ even, odd para-transitions.
The Einstein A-coefficients for the rotational transitions between the levels up to 70 cm-1 have been calculated by using the molecular and distortional constants derived by Vrtilek et al. (1987), and have been reported in Tables 1a and b, for ortho- and para-C3H4, respectively, which are available in electronic form via anonymous ftp 130.79.128.5 at the CDS. (Though Vrtilek et al. 1987 reported line-intensities for a number of lines of C3H4, for a complete and consistent set of radiative transition probabilities, the Einstein A-coefficients are calculated in the present investigation.)

As of today, knowledge of the collisional transitions, particularly in asymmetric top molecules, is very poor. Furthermore, there are no data for the collisional rates for cyclopropene available in the literature. In the absence of any knowledge of collisional rates, we assumed that the collisional rate coefficient for a downward transition $J' k_a' k_c' \rightarrow J k_a k_c$ at temperature T (K) is given by

$\displaystyle C(J' k_a' k_c' \rightarrow J k_a k_c) = [1 \times 10^{-11}/(2 J' + 1)] \sqrt{T/30}.$     (1)

The rate coefficient for the corresponding upward transition $J k_a k_c \rightarrow J' k_a' k_c'$ has been calculated with the help of the detailed equilibrium equation.

In order to include a large number of astronomical objects where the molecule may be observed, numerical calculations are carried out for wide ranges of physical parameters. The molecular hydrogen density has been varied over the range from 103 cm-3 to 106 cm-3, and the calculations are performed for the kinetic temperatures of 10, 20 and 30 K. The transition 2 20- 221 at 3.67218 GHz, proposed for detection in astronomical objects, belongs to para-C3H4. For para-C3H4, we accounted for 52 rotational energy levels, shown in Fig. 1. These levels are connected through 217 radiative transitions for which the Einstein A-coefficients are given in Table 1b. In the calculations, the free parameters are hydrogen density $n_{\rm H_2}$, and $\gamma \equiv n_{{\rm C}_3{\rm H}_4}/({\rm d}v_{\rm r}/{\rm d}r)$, where $n_{{\rm C}_3{\rm H}_4}$ is the density of C3H4, and $({\rm d}v_{\rm r}/{\rm d}r)$ is the velocity gradient. The intensity, $I_\nu$, of a line generated in an interstellar cloud, with homogeneous excitation conditions, is given by

$\displaystyle I_\nu - I_{\nu,{\rm bg}} = (S_\nu - I_{\nu,{\rm bg}}) (1 - {\rm e}^{-\tau_\nu})$      

where $I_{\nu,{\rm bg}}$ is the intensity of the continuum against which the line is observed, $\tau_\nu$ the optical depth of the line, and $S_\nu$ the source function, which is the Planck's function at the excitation temperature $T_{\rm ex}$, i.e., $S_\nu = B_\nu(T_{\rm ex}$).

Figure 2 shows the iso-lines of intensity for the transition 2 20- 221, in the units of Planck's function [ $(I_\nu - I_{\nu ,{\rm bg}})/B_\nu (T)$], for the kinetic temperatures T = 10, 20, and 30 K. In the figure, we have plotted only negative intensities; in the large density region (on the right-side of iso-lines), the intensity becomes positive. Thus, the absorption and emission nature of the line may play a significant role in providing information about the limiting value of the density in the region. For the low density region, the line 2 20- 221 shows absorption, even against the cosmic 2.7 K background, whereas in the large density region, the transition shows an emission against the cosmic 2.7 K background. (If there is a source in the background of the object, the line would show absorption against the background source.) The negative value of $(I_\nu - I_{\nu ,{\rm bg}})/B_\nu (T)$ increases with the decrease of the molecular hydrogen density. Further, it increases with the decrease of the kinetic temperature T. Thus, cyclopropene has a large probability of detection through its transition 2 20- 221 in cosmic objects having low density and low kinetic temperature.

Acknowledgements
We are grateful to Prof. Dr. W. H. Kegel of the University of Frankfurt/Main, Germany for his encouragement. Financial support from the D.S.T., New Delhi is gratefully acknowledged. Thanks are due to Mr. Harshal Hayatnagarkar for his valuable help.

References

 
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