Emission molecular bands

Absorptional bands of several molecules (${\rm C_2}$, CN, TiO, etc.) are often present in the spectra of post-AGB stars (see, for example, Hrivnak 1995; Bakker et al. 1997). However, molecular emission features are only very rarely observed in the optical spectra of PPNe. One such example is RAFGL2688 (the Egg Nebula) for which Crampton et al. (1975) observed emission features of the ${\rm C_2}$ molecule in a medium resolution spectrum. On the other hand, it is well known that cometary nuclei spectra show prominent Swan band emission.

In both spectra of IRAS04296 we have discovered strong emission in the (0;0) and (0;1) bands of the Swan system of the ${\rm C_2}$ molecule. On Figs. 2-4 we present a comparison between the spectrum of IRAS04296 (observed on February, 26, 1997) and that of the Hale-Bopp comet (observed on March 30, 1997 with the same spectrometer) around bands (0;1), (0;0) and (1;0), respectively. From Figs. 2-4 it is clear that emission band (1;0) at 4735Å is absent in the spectrum of IRAS04296 while the bands (0;1) at 5635Å and (0;0) at 5165Å are reliably measured. Hrivnak (1995) obtained the spectrum of IRAS04296 inside the blue spectral region, 3872-4870ÅÅ, therefore he could not observe emission features of ${\rm C_2}$ at 5165 and 5635ÅÅ.

  

Figure: Comparison of the IRAS04296+3429 ${\rm C_2}$ Swan band head (0;1) at ${\rm \lambda}$=5635Å with that for the Hale-Bopp comet nuclei

  

Figure: The same as Fig.2 but for ${\rm C_2}$ Swan band head (0;0) at ${\rm \lambda}$=5165Å

  

Figure: The same as Fig.2 but for ${\rm C_2}$ Swan band head (1;0) at ${\rm \lambda}$=4735Å

To understand the observed ratios between different bands, we have estimated the temperature function for monochromatic coefficient of absorption per molecule ($\sigma_{\lambda}$) for the Swan bands in the ``just overlapping'' approximation (JOA, Golden 1967). For the microturbulent velocity ${\rm \xi_t\,=\,7\,km/sec}$ this approximation works well near the band heads. Values of $\sigma_{\lambda}$ for band heads of (0;0) at 5165Å and (1;0) at 4735Å coincide within 0.2dex for the temperatures range 3000-7000K, while $\sigma_{\lambda}$ for the band (0;1) at 5635Å is systemically lower by about 0.6dex. Taking into account these relations between $\sigma_{\lambda}$'s for different band heads and since we do not observe the 4735Å band in RAFGL2688 and IRAS04296, we can conclude that it is impossible to describe the intensity ratios of ${\rm C_2}$ emission bands for these objects by means of the equilibrium vibrational temperature in the 3000-7000K range.

To explain emission bands intensities for comets the mechanism of resonance fluorescence has been proposed (Zanstra 1928, Swings 1941). In that case population of vibration-rotational levels for the molecule is described by the Boltzmann approximation, however the value of T in the exponent no longer has the meaning of equilibrium temperature but it is a distribution parameter only. We suggest that the same mechanism could be responsible for the observed emission bands of IRAS04296. However, it is clear from Figs. 2-4 that there are significant differences in the equivalent widths of the emission bands in the spectra of our supergiant and of the Hale-Bopp comet nucleus. They could be explained by a difference of radiation fluxes which illuminate ${\rm C_2}$ molecules in these objects. The temperature of IRAS04296 ( around 6300K) is sufficiently higher than that for the Sun, therefore the band (1,0) at 4735Å for IRAS04296 should be stronger than that for the Hale-Bopp comet nuclei. However, Fig.4 shows the opposite behaviour. It could mean that radiation field of IRAS04296 which excite the ${\rm C_2}$ molecules is strongly reddened by matter located between its photosphere and the region which produces the ${\rm C_2}$ emission.

Together with the emission bands of the Swan system (Klochkova et al., 1997b) absorption bands of the Phillips system (1:0), (2;0), (3;0)have been revealed in the spectrum of IRAS04296 (Bakker et al., 1997). Let us try to explain this phenomenon within the resonance fluorescence mechanism ordinary used to interpret comets' spectra. At first approximation, we can adopt that the vibrational distribution has to be corresponding to the effective temperature of a star illuminating a circumstellar envelope if vibrational transitions in the low triplet state of a homonuclear molecule are strictly forbidden. But even when interpreting comets' spectra such an approach appears to be too poor. The intensity distributions for different systems of bands and for bands of individual systems of the resonance fluorescence of the ${\rm C_2}$ molecule have been considered in papers by Krishna Swamy, O'Dell (1977, 1979, 1981). The intensities of bands have been calculated taking into account the excitation of the Swan, Ballick-Ramsay and Fox-Herzberg triplet systems, Phillips and Milliken singlet systems as well as singlet-triplet transitions in low states. It has been shown, in particular, that at the value of the moment of singlet-triplet transitions ${\rm \vert R_e\vert^{2}=10^{-5}}$ and at the heliocentric distance of a comet d=1a.u. the ratios of intensities of sequences ${\rm \Delta\nu=0,\,1,\,-1}$ in the Phillips system to the intensity of sequence ${\rm \Delta\nu=0}$ of the Swan system is equal to 0.094, 0.11 and 0.04, correspondingly (Krishna Swamy, O'Dell, 1981). This agrees well with results of measurement of comets' spectra. Using these results of Krishna Swamy, O'Dell (1981), we may suppose that the intensity of main bands of the Swan system is ten times higher than that in the Phillips system.

Now consider the case of IRAS04296. Let us add such an emission spectrum of the ${\rm C_2}$ on the stellar continuum. In order to observe the emission bands of both the Swan and the Phillips systems over the continuum in such a combined spectrum, the stellar flux at ${\rm \lambda}$ = 5165Å must be at least 10 times higher than near ${\rm \lambda}$ = 7720Å. From Kurucz's (1979) tables it follows that the ratio of the fluxes near these wavelenghts for the Sun (the emitter in the case of comets) is equal to ${\rm F_{\lambda 5175} / F_{\lambda 7750} = 1.5}$. For the model with = 6300K this ratio is equal to ${\rm F_{\lambda 5175} / F_{\lambda 7750} = 1.9}$. From the real spectral energy distrubution observed for IRAS04296 (Kwok 1993) the ratio of the fluxes is essentially smaller: ${\rm F_{\lambda 5165} / F_{\lambda 7720} = 0.1}$. Therefore, the conditions to observe the absorption bands of the Phillips system and the emission bands of the Swan system may arise inside the circumstellar envelope of IRAS04296.