Astron. Astrophys. 343, 466–476 (1999) ASTRONOMY AND ASTROPHYSICS Modelling the spectral energy distribution and SED variability of the Carbon Mira R Fornacis? A. Lobel1, J.G. Doyle1, and S. Bagnulo2 1 Armagh Observatory, College Hill, Armagh BT61 9DG, Ireland 2 Institut fur¨ Astronomie, Universitat¨ Wien, Turkenschanzstrasse¨ 17, A-1180 Wien, Austria Received 2 July 1998 / Accepted 2 December 1998 Abstract. We have developed a new method to determine the carbide (SiC) grains around stars with carbon-rich atmospheres, physical properties and the local circumstances of dust shells whereas a feature seen near 9.7 µm is ascribed to silicate grains surrounding Carbon- and Oxygen-rich stars for a given pulsa- in the environments of O-rich stars. Low resolution spectra of tion phase. The observed mid-IR dust emission feature(s), in Asymptotic Giant Branch (AGB) stars observed by IRAS in conjunction with IRAS BB photometry and coeval optical and the mid-1980 s enabled a classification of these features (Little- near-IR BB photometry, are modelled from radiative transport Marenin & Little 1988) and to attempt the modelling of their for- calculations through the dust shell using a grid of detailed syn- mation conditions. To that end various sophisticated numerical thetic model input spectra for M-S-C giants. From its application codes have been developed since. A brief review of their gradual to the optical Carbon Mira R For we find that the temperature improvements over the years and a performance comparison of of the inner shell boundary exceeds 1000 K, ranging between three modern codes was discussed by Ivezic´ et al. (1997), cur- 1200 K and 1400 K. The optical depth of the shell at 11.3 µm rently including direct solutions for the pure scattering problem is determined at τ11 µm=0.105 with Teff =3200±200 K for the in their publicly available Dusty code. Their method is based central star in the considered phase of variability. By-products on exact solutions of a self-consistent equation for the radia- of the analysis are the shell composition of 90% amorphous car- tive energy density, including dust scattering, absorption and bon and only 10% SiC grains with rather small average radii of emission in spherical shell geometry (Ivezic´ et al. 1996). From 0.05±0.02 µm. The dust density distribution assumes a power an application to IRAS Low Resolution Spectrograph (LRS) law of r−2 for a steady-state wind with a geometrical thickness spectra and colours of late-type stars they computed mass-loss ranging between 104 and 5104 times the inner boundary shell rates by radiatively-driven outflows which are in agreement with −6 −1 radius and with a high gas mass-loss rate of 3–4 10 M y other methods within a factor of two, and emphasised that the derived by radiation pressure onto the dust. We show that the SiC (and silicate) features are formed at the inner parts of the optical and near-IR light curves are strongly affected by small dust envelopes for SiC abundances below 20%-30% in mixtures changes of Teff and of the shell optical depth with pulsation. with amorphous carbon (Ivezic´ & Elitzur 1995). Bagnulo et al. A comparison of high resolution optical spectra of R For and (1998) have modelled the SED of 12 carbon stars with optically medium/low resolution spectra of other carbon stars with the thin dust shells from optical, near-IR and IRAS broadband (BB) selected model input spectrum is also provided. photometry and UKIRT mid-IR spectro-photometry of the dust emission. They applied an adapted radiative transfer code origi- Key words: stars: AGB and post-AGB – stars: mass-loss – stars: nally due to Haisch (1979), however without the self-consistent individual: R For – stars: carbon coupling with the equation of motion as incorporated in Dusty (Netzer & Elitzur 1993). Nevertheless, all the dust- and SED- modelling available to date from these numerical codes, which 1. Introduction do account for this coupling, is based on an assumption of a blackbody distribution of the stellar radiation. For these cool The presence of grain shells around C- and O-rich stars is stud- atmospheres strong flux differences between the stellar contin- ied already for several decades, and early spectroscopic and uum and the emerging atmospherical flux occur from molecular photometric detections of excess emission from optically thin opacity sources (H, C, N, O compounds). These differences of circumstellar dust near these evolved variables date back to the the flux distribution from the central star, after being repro- late 1960 s (Treffers & Cohen 1974). These spectral ‘features’, cessed through the dust shell, strongly affect the resulting SED often observed for instance at 11.3 µm, are attributed to silicon- from which the shell properties are to be derived. Therefore we presently determine the shell conditions for one target C-star, R Send offprint requests to: A. Lobel ([email protected]) ? Based on observations taken at UKIRT, CST, JCMT, SAAO, AAO Fornacis, using a grid of available synthetic input spectra to the Dusty and the IRAS Pointsource Catalogue code. A. Lobel et al.: Modelling the SED and variability of R Fornacis 467 wise, several objects like V Hya and CIT 6, having rather weak dust emission features, display no apparent changes in shape with changing intensity (Monnier et al. 1998). In Sect. 3 we describe the new modelling method of the SED of R For by means of the optical and near-IR BB photometric data of Sept. ’95, together with the dust emission spectra ob- served in Jul.-Aug. ’95. The SED variability during this phase is discussed in Sect. 4 using BB photometric data observed by Whitelock et al. (1997) between Aug. ’95 and Jan. ’96. This pe- riod follows a particular deep minimum about 1100 days earlier with clearly redder colours. Whitelock (1997) suggested RCB- type fadings, possibly linked with dust formation events. They however stress that there is no clear sign of periodicity in the ob- scuration events of R For and that the pre-whitened (removing the dominant period from the data) light curves are not periodic. Fig. 1. The high-resolution spectrum of R For (C4) (thin line) strongly matches a medium-resolution spectrum of HD 223392 (C3) (bold line), 3. Modelling results indicating Teff ≥ 3000 K 3.1. Selection of the atmospherical model The input model to the Dusty code was selected from a grid of 2. R Fornacis (AFGL 337) cool giant atmospherical models with 2200 K ≤ Teff ≤ 3800 K, From a study of mid-IR light curves Le Bertre (1992) observed a −1.0 ≤ log(g) ≤ 0.5, 0.27 ≤ C/O ≤ 1.02 (by number) for decreasing amplitude of variations with wavelength from about L∗=10000 L , which was released by Allard et al. (1995). The 1m.26 in the J band to 0m.57 in the N filter, further levelling resolution up to 2.5 µmis2A˚ and 5 Aupto5˚ µm. The resolu- off to 0m.32 in Q0. Barthes` et al. (1996) studied light curves tion then lowers to 0.1 µmupto15µm and is only 0.5–1 µm of this long period variable (P =388 d.) and found decreasing up to 90 µm. The models include opacities from important di- amplitudes of the Fourier components from the visible to the atomic absorbers like CO, C2, C3, CN, CH, NH, MgH, butalso near-IR and proposed a modulation of the light curves by the compounds like HCN, C2H2, TiO, SiO, SiH. For a description dust shell. Its average visual magnitudes at minimum and maxi- of the equation of state and the radiative transfer in spherical mum brightness are 8m.9 and 12m.2, with occasionally extreme geometry and hydrostatic equilibrium with the Phoenix code values of 7m.5 and 13m.0. see Hauschildt et al. (1997) and Allard & Hauschildt (1995). Earlier studies of R For by Feast et al. (1984) and by Le R For has been classified as C4,3e, but this information is Bertre (1988) showed that an increased obscuration could result insufficient to determine its atmospherical parameters, since the from condensation of grains in the inner portion of a circum- problem of spectral classification of C stars is to be considered stellar dust shell. In a study of 23 carbon-rich stars Le Bertre still open. For instance, Alksne & Ikaunieks (1981, and refer- (1997) modelled the SED of R For from IRAS BB photometry ences therein) give Teff values of 4500 K for subclass C0 which and coeval optical and near-IR BB photometry. He adopted a fall to 3000 K for subclass C5. By contrast, Cohen (1979) gives blackbody temperature for the central star of 2600 K and ob- 2900 K for a C4 star. In order to estimate the stellar parame- tained good fits to the IRAS photometry, but which clearly over- ters of R For, we have used high-resolution spectra offered in estimated the optical photometry. Barnbaum (1994). These echelle spectra only provide relative R For displays a rather weak SiC emission feature at 11.3 µm fluxes and can therefore not easily be compared with the abso- as observed by IRAS (’83) and by Speck et al. (1997) at UKIRT in lute fluxes of the model spectra over a broad wavelength range. ’93. Our UKIRT spectrum between 16 and 24 µm was obtained However, a comparison with a medium-resolution spectrum of on Aug. 22 ’95 and the optical BVRI photometry at SAAO on another carbon star HD 223392 (C3,2), kindly provided by Dr. Sept. 25 ’95. The near-IR JHKL0 photometry was obtained at Andrews (1998, priv.