(2) |

(3) |

In the following, two sets of data are considered: the first one (Fig. 2) concerns the objects studied in the present paper (excluding the 6 revised stars taken from Paper II), while the second one includes also all the results obtained in our previous work (Figs. 3, 4 and 5). For the first three plots the components with relative error of the mass larger than 25% have been discarded. This limit is reduced to 13% in the case of the last plot, Fig. 5. There are 30 components belonging to 17 systems in the first set and 99 components belonging to 52 systems in the second group, including the non-main sequence objects and the stars lying outside of the main distribution, called "outliers".

The size of each dot in Figs. 2, 3, 4 and 5 is a visual indication of the relative quality of the mass: the bigger dots correspond to the better results () and so on to the smaller dots by steps of 5%, up to 25%. The error bars in both and absolute magnitude are only represented on the last two plots.

The fits are based on a cleaned sample obtained after the removal of
every non-main sequence
object, identified by their assumed spectral class (SIMBAD
database, Hipparcos
catalogue, literature), an exception being made for the intermediate
class IV-V objects. The
rejected systems are listed in Table 13. When the composite
spectral class of the
pair is the only available information, we assume the components
belong to the same class,
and thus probably reject more stars than needed. The outliers are
naturally also removed and
we are left with 75 components of 42 systems when (Fig. 4), or just
32 components of 18 systems if the restriction is pushed to 13%
(Fig. 5).

Figure 3:
Same as Fig. 2 for the whole set of binaries: 99 components
belonging to 52 systems (compilation of the stars contained in this
paper and the previous one) |

It is well known that a single linear relation cannot fit all mass ranges at a time. The M-L relations for the very high or very low mass stars differ from that concerning the central part of the diagram (see for example Cester et al. 1983, or Söderhjelm et al. 1997). In the present case, the components with masses larger than 2 or smaller than 0.6 were not taken into account in the fit of the central part. These limits are materialized on the plots by two vertical dotted lines. An additional restriction was applied to the absolute magnitude, namely , in order to rule out any ambiguous object. Due to the very small number of objects in the extreme ranges of the diagram, we did not try to fit a relation in these two areas. Thus, the number of stars used in the fit is respectively 54 and 23 in Figs. 4 and 5.

The linear regression was computed in a very classic way, already used by Cester (1983). Briefly, It consists of fitting the data with two different straight lines by minimizing a function estimated in two orthogonal directions, and by taking the line which intercepts the two previous ones and whose slope is the average of the two slopes. In each case the weights of the data points have been set to , representing the standard deviation of the point in or in absolute magnitude, depending on the direction considered. The errors of each coefficient of the solution and the correlation coefficient between the two parameters and are also determined.

This gives for the first case (Fig. 4),

(4) | ||

(5) | ||

(6) | ||

(7) | ||

Figure 5:
Same as Fig. 4 (the previous remarks still hold here) with a
stronger restriction in mass quality:
13%. Over the 32 visible components, 23 are effectively
participating to the fit |

The slopes of the mass-luminosity relation are signifcantly different
according to the
selection threshold. This may indicate that the formal errors in the
linear fit are
underestimated. One must notice that the procedure to allow for the
absence of an
independent and perfectly controlled variable in the model fitting, is
rather ad-hoc
and lacks statistical rigor. Given the precision of the masses, it is
however an
acceptable approach. The value
*K* = 3.7 found in the second and more reliable solution agrees well
with recent
determinations on similar material (Lampens et al. 1997). A more refined
solution and
thoughtful discussion would not only require an improved knowledge of
the masses, but
that of the spectral type and luminosity class for every component and
was beyond
the main scope of this paper.

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