Synthetic photometry for carbon rich giants I. Hydrostatic dust-free models

Context: Carbon rich objects represent an important phase during the late stages of evolution of low and intermediate mass stars. They contribute significantly to the chemical enrichment and to the infrared light of galaxies. A proper description of their atmospheres is crucial for the determination of fundamental parameters such as effective temperature or mass loss rate. Aims: We study the spectroscopic and photometric properties of carbon stars. In the first paper of this series we focus on objects that can be described by hydrostatic models neglecting dynamical phenomena like pulsation and mass loss. As a consequence, the reddening due to circumstellar dust is not included. Our results are collected in a database, which can be used in conjunction with stellar evolution and population synthesis calculations involving the AGB. Methods: We have computed a grid of 746 spherically symmetric COMARCS atmospheres covering effective temperatures between 2400 and 4000 K, surface gravities from log(g [cm/s^2]) = 0.0 to -1.0, metallicities ranging from the solar value down to one tenth of it and C/O ratios in the interval between 1.05 and 5.0. Subsequently, we used these models to create synthetic low resolution spectra and photometric data for a large number of filter systems. The tables including the results are electronically available. First tests of the application on stellar evolution calculations are shown. Results: We have selected some of the most commonly used colours in order to discuss their behaviour as a function of the stellar parameters. A comparison with measured data shows that down to 2800 K the agreement between predictions and observations of carbon stars is good and our results may be used to determine quantities like the effective temperature. Below this limit the synthetic colours are much too blue. The obvious reason for these problems is the neglect of circumstellar reddening and structural changes due to pulsation and mass loss. Conclusions: The warmer carbon stars with weak pulsation can be successfully described by our hydrostatic models. In order to include also the cooler objects with intense variations, at least a proper treatment of the reddening caused by the dusty envelopes is needed. This will be the topic of the second paper of this series.