1 Introduction

Cool giants and supergiants typically experience phases of mass loss, sometimes at very high rates, which may strongly affect the evolution of the star. In the case of asymptotic giant branch (AGB) stars, the rate of mass loss exceeds the rate of core growth, so that mass loss is the most important process controlling the evolution of these stars from the AGB to the planetary nebula phase. For M-supergiants, mass loss rates up to $\sim$10^-4 $M_{\odot}$ y^-1 are inferred for timescales of order 10⁵ years, which implies that the evolutionary consequences may be substantial also for these massive stars (M > 10 $M_{\odot}$).

The physical mechanisms which drive mass loss are not yet well-understood, though there has been progress very recently with detailed hydrodynamic calculations of models for pulsating AGB stars (Fleischer et al. 1992; Bessell et al. 1996; Winters et al. 1997, 2000; Höfner et al. 1998; Loidl et al. 1999). These models show that the structure of the atmospheres in large-amplitude pulsators is strongly dependent on hydrodynamic processes which include pulsation-driven shocks, non-equilibrium chemistry, and formation of dust grains. Particularly important are the model predictions for time-dependent structure not only over single pulsation cycles but also temporal variations predicted over multiple cycles. The atmospheric structure and its changes with time determine the rate and velocity at which matter is lost, and the amount of dust which is formed and ejected. To understand the mass loss process, then, it is crucially important to compare predictions of the hydrodynamic models with all possible observable properties of such stars to assess the validity of the models.

Comparisons between hydrodynamic model predictions and selected observational properties have been made in several recent papers. Winters et al. (1997) successfully predicted the spectral energy distribution (SED) and light curve at several wavelengths for the extreme carbon star AFGL 3068, using a self-consistent time-dependent model incorporating hydrodynamics, chemistry, and dust formation. Hron et al. (1998) compared low-resolution ISO-SWS 2-15 $\mu$m spectra of the carbon star R Scl at two phases with both hydrostatic and dynamic atmosphere models. They find moderately good agreement with the dynamic models, and note that the observed time variations require a dynamic treatment of the model atmosphere. Loidl et al. (1999) calculated synthetic spectra from 0.5 to 12 $\mu$m for AGB carbon stars using an opacity sampling method, with the atmospheric structure from dynamical models. They include 7 major carbon-bearing molecules in the opacities, and explore the different time dependencies of various spectral features as a result of the different layers in which molecules form. They note that their synthetic spectra reproduce qualitatively the spectra of cool carbon stars, but that higher spectral resolution is needed in the models to compare with data from the ISO-SWS, for example.

Bessell et al. (1996) and Scholz & Wood (2000) made hydrodynamical models of M-type Miras and calculated detailed absorption line profiles of CO 1st overtone lines (among others). They compared their model spectra with the velocity results of Hinkle et al. (1982, 1984) to estimate the true pulsational velocities of observed Miras. They find that the CO absorption line profiles exhibit complex variability not only over one pulsational cycle, but also from cycle to cycle. They note the scarcity of observational data at present to compare with their predictions.

Aringer et al. (1999) studied the 4 $\mu$m first overtone ro-vibrational bands of SiO in oxygen-rich AGB stars, and compared their observed spectra with hydrostatic and dynamic atmosphere models. They confirm the strong variability of the SiO band strengths with light phase for Miras, and show that this variation is consistent with pulsationally driven hydrodynamic models. In contrast, hydrostatic models cannot explain the observed SiO band strengths in cool giants, a shortcoming which emphasizes the need for dynamical models.

In a high resolution study of molecular hydrogen absorption lines at $\sim$2.2 $\mu$m in 30 Miras and semiregular AGB stars, Hinkle et al. (2000) find a wide range of line intensities. For a few stars, they have time-series spectra which show large changes in the H₂ 1-0 S(1) line intensity over the light cycles, probably reflecting dissociation and re-formation of H₂ with the passage of pulsational shocks. Such behavior is in fact predicted in the dynamical atmosphere models of Höfner (1999).

Finally, in the most detailed calculation published to date, Winters et al. (2000) compare velocity-resolved model spectra with high-resolution observations of the CO v = 1-0 fundamental and v = 2-0 first overtone bands in the carbon star IRC+10216. They find that dynamical models for the atmosphere can produce line profiles which are in good agreement with the observations for reasonable model parameters. Even the temporal variations, reflecting the formation and expansion of dust shells, are in rather good agreement with the observed spectra. In other details such as mass loss rate, however, there are discrepancies which suggest that further refinements to the models and more extensive observations are needed.

The CO molecule offers several advantages as a diagnostic probe of the structure of cool stellar atmospheres. It has a stable, closed-shell structure and a high dissociation energy, so it is predicted to form readily in cool giant and supergiant atmospheres, with an abundance close to the chemical thermodynamic equilibrium (TE) value. Even if the gas is being shocked periodically by stellar pulsations, shock chemistry models predict that the CO abundance is scarcely altered from the TE value (Willacy & Cherchneff 1998; Duari et al. 1999). CO should take up almost all available carbon or oxygen, whichever is less abundant, so the CO molecular abundance can be reliably estimated from atomic abundances. The CO ro-vibrational spectrum has bands in the near-IR which are not too seriously affected by telluric absorption. With modern IR detector arrays, the CO bands are accessible to sensitive spectrometers at the fundamental and overtone wavelengths. The molecular constants are well-determined so that line wavelengths and transition strengths can be calculated reliably.

The detailed spectral models for IRC+10216 by Winters et al. (2000) show that lines of the CO fundamental band at 4.6 $\mu$m are optically thick at least in the core, while the first overtone lines, in particular the v = 2-0 band, are not optically thick, even in models with large mass loss rates and dense extended atmospheres. Since CO should form deep in the photosphere and exist essentially unchanged in abundance out to large distances above the photosphere, this predicted lack of saturation in the first overtone lines suggests that they should be very useful probes for the entire extended atmosphere. The energy level structure of the CO molecule places within a relatively small spectral window ro-vibrational lines originating from a wide range in energy levels. Specifically, the intensities of absorption lines across the v = 2-0 band at 2.3 $\mu$m probe energies ranging from the ground state to $E/k > 20\,000$ K within a spectral range <0.1 $\mu$m.

For all these reasons, the CO first overtone bands at 2.3 $\mu$m should be useful diagnostics of stellar atmospheres models for cool giants and supergiants. In this paper, we present spectra of selected AGB and post-AGB stars and late-type supergiants, from 2.28 to 2.36 $\mu$m. This wavelength range covers the main part of the v = 2-0 and 3-1 CO bands, and parts of the v = 4-2 and the ¹³CO v = 2-0 bands. The spectral resolution is sufficient to separate a large number of the R- and P-branch lines, which span a wide range in energy levels. The spectra should be of value for making comparisons with the predictions of current hydrodynamic models for cool giant and supergiant atmospheres.