5 Other observational information

5.1 Age and chemical composition

One of the goals of the present study is to carry out a critical analysis of low-mass stellar models similar to that in TR02. Thus, to make the test as stringent as possible, one has to keep the number of degrees of freedom at a minimum. Two of the key parameters that determine the observable physical properties of a star are its age and chemical composition (to simplify, metallicity). The metallicity of a star is generally determined through high-resolution spectroscopy and comparison with synthetic spectra. Unfortunately, this is virtually impossible for M stars because of the huge quantity of spectral features and the shortcomings of the atmosphere models. In turn, the age (and eventually the metallicity) can only be derived if the star belongs in a well-studied cluster. Field M stars are, thus, not ideally suited for reliable estimations of age and metallicity.

One possible way to obtain a rough estimation of the age and chemical composition of a field M star such as CU Cnc is through the analysis of its space velocities. High velocity would likely indicate an (old) halo population and low velocity a (young) star in the galactic disk. The space velocities (U,V,W) of a star are readily computed from its position, proper motions, radial velocity and distance. In the case of CU Cnc, we have adopted the Hipparcos position, proper motion and distance, and the radial velocity has been taken from D99. The resulting space velocities are U=-10.7 km s^-1, V=-4.9 km s^-1, and W=-10.6 km s^-1. Note that we have followed the convention where positive values of U, V, and W indicate velocities towards the galactic center, galactic rotation and galactic North Pole, respectively.

The low values of these velocities are an indication of a disk population and thus a relatively young star. A closer look at the values revealed that these are strikingly similar to the velocities of the Castor moving group (see Anosova & Orlov 1991; Barrado y Navascués 1998) of which YY Gem is a likely member. Ribas (2003) utilised various criteria (isochrones, rotation-activity relationships, etc.) to estimate an age of $320\pm80$ Myr and a metal content of $Z=Z_{\odot}$ for the moving group members. The mean space velocities of the moving group have been recently re-determined by Ribas (2003) to be ${<U>}=-10.6\pm3.7$ km s^-1, ${<V>}=-6.8\pm2.3$ km s^-1, and ${<W>}=-9.4\pm2.1$ km s^-1. These are indeed very similar to the values found for CU Cnc, which strongly suggests its membership of the Castor moving group. Thus, it is sensible to assume that CU Cnc has the same age and chemical composition as the rest of the group members - similarly to what is routinely done in stellar cluster studies. As it happened with YY Gem (TR02) the fortunate fact that CU Cnc belongs in the moving group and has a well-determined age and metal content greatly enhances the value of the star since it allows for an unusually stringent test of the theoretical models.

5.2 Lithium abundance

As it has been known for some time, the measured abundance of lithium in the stellar atmosphere can be used as an age indicator for young cool stars, particularly in clusters (e.g., Duncan 1981; Soderblom et al. 1990). Theoretical studies demonstrate that the ⁷Li nuclei are destroyed by proton collisions at temperatures above $\sim$2.5 MK (Bodenheimer 1965; D'Antona & Mazzitelli 1984). In low mass stars, mixing through convection processes is so efficient that Li is depleted at a very rapid pace. We have inspected our high-resolution spectrum described in Sect. 3 and we report a tentative detection of weak Li  I $\lambda$6708 features at the expected wavelengths for both the primary and secondary components. The equivalent width measurement (corrected for light dilution) yields a value of $\sim$50 mÅ for both stars. From this and the theoretical study of Pavlenko et al. (1995), one can roughly estimate the Li abundance to be $\log N(\mbox{Li})\approx -1.1$ (in the scale in which $\log N(\mbox{H})=12$), and $\log [n({\rm Li})/n_{\circ}({\rm Li})]=-4.1$. Thus, the initial Li content of CU Cnc's components appears to have been mostly destroyed, yet not completely. This is in apparent contradiction with Li destruction sequences in clusters and associations (Barrado y Navascués et al. 1999; Stauffer et al. 1999), which indicate that mid-M type stars fully deplete their initial Li abundance in as little as a few times 10⁷ years. (Recall that the estimated age for CU Cnc is $\sim$320 Myr.) Barrado y Navascués et al. (1997) observed a similar discrepancy with the observed Li abundance ( $\log N(\mbox{Li})=0.0$) for the eclipsing binary YY Gem. In this case, Li also appears to be severely depleted but not fully destroyed, as would be expected for YY Gem's age of $\sim$320 Myr. If we rely on the ages determined for these binaries, the two results seem to indicate that Li depletion for M stars in binary systems might be not as efficient as for single stars. For example, orbital synchronization due to tidal forces could be responsible for inhibiting turbulent mixing, thus slowing down Li depletion (Barrado y Navascués et al. 1997). The tentative detection of Li in the spectrum of CU Cnc is a puzzle yet to be resolved a detailed discussion of this topic is left for an upcoming work.

5.3 Stellar activity

Other observational information for CU Cnc can be inferred from the high-resolution spectrum described in Sect. 3. An inspection of the spectrum reveals very strong H$\alpha$ and H$\beta$ emission features (double lines). The measurements yield (continuum-corrected) H$\alpha$equivalent widths of 3.85 Å and 4.05 Å for the primary and secondary components, respectively. For comparison, Young et al. (1989) report an excess equivalent width of $\approx$2 Å for the presumably coeval but more massive system YY Gem. The H$\alpha$ equivalent widths of both CU Cnc and YY Gem are rather large but not unreasonable when compared with young M-type stars (see, e.g., Soderblom et al. 1991). Note, however, that the strong H$\alpha$ emission in these binary systems is more related to the spin-up caused by orbital synchronization rather than age.

In addition to displaying H$\alpha$ chromospheric emission, CU Cnc is also both and EUV and X-ray source. From the observations in the ROSAT All-Sky Bright Source Catalogue (Voges et al. 1999) and the calibration in Schmitt et al. (1995) one obtains an integrated X-ray luminosity of $\log L_{\rm X} \mbox{(erg s$^{-1}$ })=29.03$ for CU Cnc. Again, this value can be compared with YY Gem's, which was estimated to be $\log L_{\rm X} \mbox{(erg s$^{-1}$ })=29.61$ (Güdel et al. 1993). One must keep in mind that the size of the stars in CU Cnc is significantly smaller than those of YY Gem. Thus, the ratio $L_{\rm X}/L_{\rm bol}$ is a more realistic measure of the stellar activity or, in other words, of the efficiency in producing high energy emissions. The calculations of $L_{\rm X}/L_{\rm bol}$ yield a value very close to 10^-3 for both CU Cnc and YY Gem, thus indicating very similar activity levels. Numerous studies (see, e.g., Jeffries & Tolley 1998; Gagne et al. 1995) suggest that this value of $L_{\rm X}/L_{\rm bol}=10^{-3}$indeed marks a saturation limit in the stellar activity.