1 Introduction

R Doradus is one of the brightest stars in the infrared. Its flux distribution peaks in the 1 $\mu$m range, the spectral type being M8III. R Dor is classified as a semi-regular variable (SRb; Kholopov 1988), or more precisely a red SRV (for a definition, see Kerschbaum & Hron 1992), but is closely related to the Mira variables in the sense that it probably lies near the edge of a Mira instability strip (Bedding et al. 1997). R Dor has, however, a longer period than expected for SRVs, but this fact could be due to irregularities in the periods (Kerschbaum & Hron 1992) or could be telling us that SRVs with long periods represent a sub-group of Mira stars (Bedding et al. 1998).

Semi-regular variables are most likely evolved stars on the Asymptotic Giant Branch (AGB) in the HR diagram, see for example Habing (1996). AGB stars are low-initial-mass stars with electron-degenerate, carbon-oxygen cores on their way from the main sequence towards the white-dwarf/planetary-nebula phase. Approximately 95% of all stars will eventually pass this stage of evolution (Habing 1996). In general, there seems to be an evolutionary sequence on the AGB from the blue SRVs to the long-period Mira stars, passing through the red SRV phase (Kerschbaum & Hron 1992; Lebzelter & Hron 1999). The blue SRVs are supposed to be on the early AGB, the red SRVs are suggested to be experiencing the first thermal pulses, and finally the Miras are associated with the thermal pulses and are supposed to be pulsating in the fundamental mode, showing large amplitudes in the visual brightness.

A key feature of AGB stars is their massive but slow stellar winds, creating an extensive circumstellar envelope. AGB stars and their circumstellar envelopes in general present spherical symmetry (see for example Olofsson 1996). In combination with the thermal pulses and the subsequent third dredge-up, which drags up newly synthesised elements into the atmosphere, the wind causes an enrichment of the interstellar medium in elements synthesised in the AGB star, thus making these stars important actors in the chemical evolution of galaxies (see for example Gustafsson & Ryde 2000). R Dor has a mass-loss rate of $7\times10^{-8}~\mbox{$M_\odot$ ~yr$^{-1}$ }$, which is at the lower end of what is typical for AGB stars, and a wind velocity of $6~\mbox{km~s$^{-1}$ }$ (Loup et al. 1993). R Dor shows some circumstellar dust emission (see discussions in Bedding et al. 1998; Kerschbaum & Hron 1992) and also molecular circumstellar emission from regions close to the star (see for example Ryde et al. 1999).

Thanks to the Infrared Space Observatory (ISO), launched in 1995, it has become possible to study the atmospheres of red giants in detail at low and medium resolution, also at wavelengths obscured by the Earth's atmosphere, for example the interesting region between the K- and L-bands studied here.

Here we present the 2.60- $3.66~\mbox{$\mu$ m}$medium-resolution ( $R \sim 2500$) spectrum of R Dor, observed by the ISO-SWS, and model it by generating a synthetic spectrum from the photosphere only. This results in a good agreement. The photosphere is modeled with the latest version of the MARCS model photosphere code, generating hydrostatic photospheres. The study of infrared (IR) spectra of red giants provides a test of the adequacy of hydrostatic model photospheres, their input data and their constraints, for the modeling of red giants.

In their unmasking of the warm molecular-envelopes surrounding AGB stars Tsuji et al. (1997) model the $3~\mbox{$\mu$ m}$ spectrum of the M 6 giant g Her and the M 7 giant SW Vir observed by the Short-Wavelength Spectrometer (SWS) on board ISO. Markwick & Millar (2000) model the same wavelength region of ISO-SWS observations of the Mira star R Cas (M7III). They suggest that the absorption spectrum originates from the inner regions of the circumstellar envelope, and model it with two circumstellar components, one warm and one cold.