4 Determination of fundamental parameters

  The advent of new or vastly improved parallaxes from the Hipparcos satellite (ESA 1997) has enabled us to calculate significantly improved fundamental parameters for our 10 systems. Such values clearly supersede those given in Table 5 of the CABS catalog (Strassmeier et al. 1993). The literature was searched for the brightest known magnitude of each system, which was assumed to be the unspotted V magnitude of each primary. For the two double-lined systems, LN Peg and HD 81410 (Fig. 2), we converted the equivalent-width ratio of the primary to secondary spectral lines into a brightness difference and corrected the combined magnitude. For LN Peg the secondary's contribution is approximately 0$.\!\!^{\rm m}$25 in V and for HD 81410, 0$.\!\!^{\rm m}$1. Then an M_V was computed from the Hipparcos parallax. For the eight systems closer than 160 pc no interstellar reddening was assumed. However, because of their much greater distances, a reddening of 0$.\!\!^{\rm m}$2 was assumed for HD 136901 and 0$.\!\!^{\rm m}$4 was assumed for HD 152178. Except for HD 136901 and HD 152178, whose B-V values were revised with R=3.2 and the above reddening, the Hipparcos B-V values given in Table 1 were used in conjunction with Table 3 of Flower (1996) to obtain a bolometric correction, B.C., and effective temperature, $T_{\rm eff}$, for each primary. An $M_{\rm bol}$ was computed for each star and converted into units of solar luminosity assuming $M_{\rm bol}$ = +4$.\!\!^{\rm m}$64 for the Sun (Schmidt-Kaler 1982). Finally, a radius, called $R_{\rm Hip}$, was determined for each star from the $T_{\rm eff}$ and $L/L_\odot$ values. It was assumed that the errors in the computed quantities are dominated by errors in the parallax, given in the Hipparcos catalog, and to a lesser extent by the $T_{\rm eff}$, with the latter error estimated to be $\pm 100$ K.

For each active primary a value of $R\sin i$, which is independent of the $R_{\rm Hip}$ value, was computed from its rotational period and $v\sin i$ value listed in Table 1. For $R\sin i$ the error is dominated by the uncertainty in $v\sin i$. Table 3 summarizes the fundamental parameters for our stars.

The values of $R\sin i$, of course, should be smaller than the corresponding values of $R_{\rm Hip}$, but this is not the case for the computed values of the majority of our stars (Table 3). Within the errors, however, agreement between $R\sin i$ and $R_{\rm Hip}$ is acceptable for eight of the 10 stars. For two stars, UZ Lib and HD 106225, the $R_{\rm Hip}$ values are significantly smaller than those computed for $R\sin i$. Their Hipparcos distances result in M_V and $R_{\rm Hip}$ values that indicate that the stars are subgiants, while the minimum radii suggest that both stars have at least begun to ascend the red-giant branch. Note that if we increase the error in $T_{\rm eff}$ from $\pm 100$ K to $\pm 200$ K, the error in $R_{\rm Hip}$ increases by $15-20\%$ but is still only 30% the error from the parallax.

For UZ Lib the Hipparcos distance is nearly a factor of four smaller than the value used by Grewing et al. (1989), which led to contradictory results described by Strassmeier (1996) as the dilemma of big leg Emma (Zappa 1974). However, as a result of the improved distance, we have not extricated ourselves from the dilemma. Instead, it has reversed itself with the radius now being too small compared to the minimum radius.

Systematic trends between $R\sin i$ and $R_{\rm Hip}$, and in particular the problems with the values for UZ Lib and HD 106225, are likely the result of several different factors. One obvious contributor is our assumption that the brightest known magnitude of each system is equal to its unspotted magnitude. For example, for the very active star II Peg, O'Neal et al. (1996) compared photometric and spectroscopic results and found "a substantial symmetric spotted component,'' which they attributed to either a polar spot or spots evenly distributed in longitude. Thus, our assumed unspotted magnitudes listed in Table 3 are almost certainly too faint. For II Peg, O'Neal et al. (1996) computed V = 6$.\!\!^{\rm m}$8 compared with the historically observed $V_{\rm max} = 7$$.\!\!^{\rm m}$2 (Strassmeier et al. 1993). In the cases of UZ Lib and HD 106225, if the unspotted magnitude were 0$.\!\!^{\rm m}$5 brighter than our assumed value, the $R_{\rm Hip}$ values would be increased by 0.9 $R_\odot$.

 

Table 3: Fundamental parameters 

 

Figure 2: The cross-correlation functions (CCFs) for the two double-lined systems, LN Peg (solid line) and HD 81410 (dashed line). Arrows indicate the primary (P) and the secondary (S) CCF for each system