7 Is CU Cnc akin to other stars of similar mass?

The comparison discussed above leaves no doubt that most of current stellar models fail in reproducing the observed physical properties of CU Cnc. Only the models by Swenson et al. (1994) yield reasonably good (even excellent) isochrone fits to the data. Even though CU Cnc is the only object with a mass around 0.4 $M_{\odot }$ with fully characterised physical properties, there are other stars in this regime whose masses have been spectroscopically determined to good accuracy. This is the case of Gl 570C, Gl 623A, Gl 644A, Gl 644Ba, Gl 661A, and Gl 661B, all with masses between 0.34 and 0.42 $M_{\odot }$ (see Forveille et al. 1999; Ségransan et al. 2000; Delfosse et al. 2000; Martin et al. 1998; Mazeh et al. 2001). We have compiled V and Kabsolute magnitudes for these stars from Delfosse et al. (2000). Two mass-absolute magnitude plots are shown in Fig. 5, one for the V magnitude and one for the K magnitude. The results are quite striking as CU Cnc appears to be fainter in both plots than other stars of the same mass. The magnitude difference is about 1.4 mag in the V band and 0.35 mag in the K band. The apparent faintness of CU Cnc in the V band had already been pointed out by D99, Delfosse et al. (2000) and Mazeh et al. (2001). Note that the isochrones computed with the models of Baraffe et al. (1998) and Siess et al. (1997) plotted in the figure produce a reasonably close fit to the stars other than CU Cnc in both observational diagrams. On the other hand, the isochrone by Swenson et al. (1994) - only available in $M_{\rm V}$ -, which closely matches CU Cnc, fails in reproducing the observed absolute magnitudes of the other stars.

Figure 5: Mass-absolute magnitude diagrams in the V and K bands for the lower main sequence. CU Cnc is shown together with YY Gem and other stars with spectroscopically-determined masses (see text). The lines represent isochrones for the estimated age of CU Cnc computed with different models.

Let us carefully analyse possible reasons for the discrepancy. One scenario to explain the disagreement is the effect of enhanced stellar activity in CU Cnc due to binarity (higher rotational velocity). This would cause the appearance of large spots on the surface of the stars and also an increase of the TiO absorption. It is well known that the V passband is strongly affected by TiO absorption whereas the K band is mostly free from TiO bands. This might cause the star to appear especially faint in the V band. There are, however, evidences that argue against this scenario. All observational data (X-ray luminosity, H$\alpha$emission) indicate that CU Cnc is not especially active when compared with YY Gem, which is quite closely matched by the models. At CU Cnc's mass range, the ROSAT All-Sky Bright Source Catalogue (Voges et al. 1999) yields an estimated X-ray luminosity for the stars in the Gliese 644 system (plotted in Fig. 5) of $\log L_{\rm X} \mbox{(erg s$^{-1}$ })=29.14$, thus indicating an activity level very similar to CU Cnc's. In addition, the available multi-band photometry (see Table 5) refutes the idea that the apparent faintness of CU Cnc is only restricted to the V band. The spectral energy distribution deduced from the photometric data is internally consistent, i.e. all photometric indices yield the same effective temperature. Thus, it is the temperature of CU Cnc and not the photometry the source of the discrepancy. Using (V-K) indices and the calibrations in Sect. 4, we estimate that CU Cnc is some 300 K cooler than other stars of about 0.4 $M_{\odot }$. That the mean photospheric temperature is reduced by as much as 10% due to enhanced stellar activity in CU Cnc seems, in principle, quite unlikely. More so if we take into account that stellar activity produces photospheric plages in addition to dark spots that would (partly or totally) compensate for the temperature reduction.

The distance to CU Cnc is another possible source for discrepancies since, as we have discussed in Sect. 4, it might be subject to systematic errors. However, a magnitude differential in the distance modulus of the star would be constant over wavelength and affect identically both V and K bands. This is a strong argument against this scenario because we observe a much larger deviation in M_V than in M_K. Nonetheless, a problem with the distance could still be responsible for a fraction of the discrepancy.

Our estimate for the metal abundance for CU Cnc comes from its likely membership of the Castor moving group. The possibility for a different chemical composition can be not completely discarded because the star might not belong in the group after all or have different abundances than other group members. A very high metal abundance of $[\mbox{Fe/H}]=+0.5$was put forward by D99 as a possible explanation for the anomalous location of CU Cnc in the mass-absolute magnitude diagram. This was proposed on the basis of the isochrone behaviour in the mass-M_Vdiagram for metal abundances of $[\mbox{Fe/H}]=0$ and $[\mbox{Fe/H}]=-0.5$. We have carried out this analysis again with the new parameters for CU Cnc and the models of Baraffe et al. (1998). If, as assumed by D99, the absolute magnitude changes are supposed to scale linearly with metallicity, a value even higher than +0.5 is necessary since the V magnitude difference between $[\mbox{Fe/H}]=0$ and $[\mbox{Fe/H}]=-0.5$ at a mass of 0.4 $M_{\odot }$ is only 0.8 mag. We recall that CU Cnc appears to be dimmer by as much as 1.4 mag. Furthermore, this scenario does not explain the discrepancy in the K band because the different metallicity isochrones run virtually on top of one another. An additional argument against the high-metallicity hypothesis is the lack of other stars in the solar neighbourhood with such high metal abundance. In the thorough study of Edvardsson et al. (1993) the highest metallicity found was $[\mbox{Fe/H}]=+0.24$. The catalog of Cayrel de Strobel et al. (2001) lists only a handful of stars with $[\mbox{Fe/H}]>+0.4$ and most of them appear to be misclassified. The high metallicity proposed to resolve the issue with the location of CU Cnc in the mass-M_V diagram seems, at this point, quite unlikely.

A younger age than estimated for CU Cnc from its membership of the Castor moving group would neither explain the discrepancy. A low mass star becomes dimmer as it evolves from the pre-main sequence phase towards the ZAMS, where the minimum luminosity is reached. CU Cnc is already fainter than the other stars in the same mass range. Alternatively, it could be that the stars used for comparison with CU Cnc (Gl 570, Gl 623, Gl 644, Gl 661) were all much younger ($\sim$10-20 Myr) and contracting towards the ZAMS. Once again, this hypothetical situation is not in agreement with the observed mass-magnitude diagrams because the magnitude change in the Vand K bands are predicted by the models to be very similar (actually, a somewhat larger magnitude variation in the K band).

Thus far, there are no plausible scenarios to account for the observed magnitude differences between CU Cnc and similar mass stars. Even though it might appear as improbable, the presence of a certain amount of dust absorption could reproduce the observed behaviour. Indeed, according to Fitzpatrick (1999), the relationship between A_V and A_K for interstellar dust is $A_{V}\approx 8\; A_{\rm K}$. Thus, 1.4 mag of extinction in V would roughly correspond to 0.2 mag in K. Such magnitude corrections would bring the two mass-magnitude plots into fair agreement. At a distance of only $\sim$13 pc, it can be definitely ruled out that line-of-sight interstellar dust could account for over 1 mag of extinction in the V band ( E(B-V)=0.42). The alternative is therefore circumstellar dust. Disks of circumstellar dust have been directly detected in a number of nearby stars (see, e.g., Greaves et al. 1998 and references therein) and some of them have estimated ages similar to CU Cnc's. If the disk was coplanar with the binary's orbit, as it might likely be assumed, we could be observing the stars through a line of sight with enhanced dust absorption. There are no observational grounds to support such hypothesis yet but, at this point, this is the only scenario that explains the observations.

If the disk hypothesis is proven to be correct, our temperature estimate (which is based on multi-colour photometry) and thus the comparison with stellar models in the temperature and absolute magnitude diagrams would have to be revised accordingly. A rough estimate made by correcting for the differences of 1.4 mag in V and 0.35 mag in K raises the temperature of the components to ${T_{\rm eff}}_{\rm A}=3440\pm150$ K and ${T_{\rm eff}}_{\rm B}=3400\pm150$ K. Also, the effective temperatures obtained from the radii, the corrected apparent magnitudes and the Hipparcos parallax (see Sect. 4) are ${T_{\rm eff}}_{\rm A}=3290\pm140$ K and ${T_{\rm eff}}_{\rm B}=3240\pm140$ K, thus achieving a remarkable 1 sigma agreement with the photometric values.