8 Conclusions

The lack of observational constraints is one of the most severe deficiencies that stellar models for the lower main sequence have to face. Eclipsing binaries are thus crucial because they yield simultaneous determinations of masses and radii (and also temperatures) upon which the stellar models can be checked. We have therefore acquired and analysed high-quality R and I light curves with very dense phase coverage (over 2100 observations) of the low-mass eclipsing binary CU Cnc. In the light curve analysis, carried out with the W-D program, we resolved an inherent indeterminacy of the ratio of radii of the components (caused by the partial eclipses) by fixing the luminosity ratio to the value obtained from a high-resolution spectrum. Also, special care has been put in modelling the conspicuous out-of-eclipse variations through surface inhomogeities. The orbital and physical properties resulting from the light curves were combined with the spectroscopic parameters from D99 to achieve precisions better than 2% in the absolute dimensions of CU Cnc components. As a result of this, CU Cnc is the third system (together with YY Gem and CM Dra) to reach sufficient accuracy in its absolute dimensions so that critical tests of stellar models can be performed.

To make the comparison with models more stringent, we made use of further observational constraints. For example, the mean effective temperature of CU Cnc was determined from multi-band photometry (optical through infrared) and synthetic colours resulting from state-of-the-art atmosphere models. Additionally, the space motions of CU Cnc strongly suggest membership of the Castor moving group. This allowed us to infer rough values for the age of the star ($\sim$320 Myr) and its chemical composition ( $Z\approx0.018$). With this host of observational information - quite uncommon for most eclipsing binaries -, we carried out a detailed comparison with all of the recent low-mass stellar models. First, the most reliable check is in the mass-radius diagram because these are two quantities empirically determined from our analysis. The comparison indicates that, whereas some of the models provide radius values that are in reasonable agreement with the observations, the most sophisticated models by Siess et al. (1997) and Baraffe et al. (1998) yield radii that are some 10% smaller than observed. The study of three additional observational planes indicates that CU Cnc's components are also significantly cooler ($\sim$15%) and fainter in the V band ($\sim$1.5 mag) than predicted by most models.

A matter of some concern arises when comparing CU Cnc with other stars of similar mass. The comparison indicates that CU Cnc is some 1.4 mag fainter in the V band and 0.35 mag fainter in the K band. We have analysed a number of possible scenarios to explain the discrepancy and ruled out most of them on the basis of the available observational information. For example, we have discarded the effect of stellar activity, an error in the distance, a different age or an extreme chemical composition. Only two scenarios appear to succeed in explaining the observed differences in the mass-magnitude diagrams: 1) CU Cnc's components are, for a yet unknown reason, about 10% cooler than other stars of the same mass, and 2) there is a certain amount of (circumstellar) dust absorption that is responsible for the reddening of the spectral energy distribution. If the latter turns out to be the correct scenario, this is a very exciting result. Given the almost edge-on configuration of the eclipsing binary, we could be observing CU Cnc through a coplanar dusty disk. Definite proof of this should come from submillimeter observations where the thermal emission of the dust could be detected. Note that CU Cnc belongs in the same moving group and probably has similar age to Vega and Fomalhaut (Barrado y Navascués 1998), both stars with bona-fide circumstellar dust disks (Holland et al. 1998). With the tentative detection of a Vega-like edge-on dust disk and its relatively low mass and surface brightness, CU Cnc also becomes a very interesting target for planet searches through radial velocity studies or the transit method.

In our comparative study, we have concluded that the evolutionary models of Swenson et al. (1994) clearly stand out among all because they achieve the best performance in reproducing all of the observed properties of CU Cnc and even the relative position of the components (much better constrained from the light curves). However, these models cannot obviously fit the position of other 0.4-$M_{\odot }$ stars in the mass-absolute magnitude diagrams, whereas models such as Siess et al. (1997) and especially Baraffe et al. (1998) provide more reasonable fits. Unfortunately, until the discrepancy between the radiative properties of CU Cnc and stars of similar mass is resolved, no strong constraints on the models can be set in the temperature and absolute magnitude diagrams. A better determination of the parallax and an empirical estimation of the metal abundance would surely help to clarify the situation.

Regardless of the issue with the temperature, the comparison of CU Cnc's absolute dimensions (empirically-measured masses and radii) with stellar model predictions clearly confirms the trend seen by TR02 for YY Gem and V818 Tau. The systematic underestimation of the radii of the stars can lead to severely underestimated stellar ages when using the H-R diagram diagnostics. In spite of recent advances, it seems clear that further adjustments are needed in evolution models for the lower main sequence to achieve a good description of the observed stellar physical properties.

Note added in proofs: Forveille (2002, priv. comm.) has recently pointed out that adaptative optics observations reveal a faint close companion to CU Cnc at a distance of 0 $.\!\!^{\prime\prime}$68. The measurements by Beuzit at al. (2001, [astro-ph/0106277]) yield a magnitude difference in the K band of 3.2 mag between the CU Cnc system and the companion. This detection has an impact, albeit limited, on the results presented in this paper. Firstly, an unresolved companion could very well be responsible for a poor parallax determination by Hipparcos, thus explaining the discrepancies discussed in Sect. 4. Secondly, new calculations indicate that the increase in the third light contribution turns out to be negligible (below 1%) and the physical parameters of the stars in Tables 3 and 4 remain untained. And finally, the relative faintness of the CU Cnc's components when compared with other stars of similar mass is somewhat enhanced if the light from the close companion is subtracted. However, the magnitude differences in the V and K bands discussed in Sect. 7 increase by only $\approx$0.02-0.04 mag.

Acknowledgements

Thanks are due to M. I. Andersen & R. J. Irgens who kindly prepared and performed CCD observations of CU Cnc with the Nordic Optical Telescope at La Palma. I am most grateful to E. F. Guinan, G. Torres, A. Giménez, C. Jordi, J. V. Clausen, D. Fernández, F. Arenou, and R. Estalella for their invaluable help and fruitful discussions during the course of this work. The photoelectric observations in this publication have been obtained with the Four College APT, which is supported by NSF grants AST95-28506 and AST-0071260. The ING support astronomers are thanked for carrying out the spectroscopic service observations used in this study. The William Herschel Telescope is operated on the island of La Palma by the Isaac Newton Group in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias. This publication makes use of data products from the Two Micron All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation. This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France. This research has made use of NASA's Astrophysics Data System.