With the previous calibrations, the stars whose effective temperature lies
between 8500 and about 10500 K could not be properly dealt with. This is why
we have defined new photometric parameters we call pT and pG, which are
sensitive to effective temperature and surface gravity respectively. These
parameters have been defined in a similar way as the 
and r ones of the
photometry, and have about the same sensitivity to the corresponding
physical parameters. However, pT and pG are not reddening-free,
contrary to 
and r, because the Geneva system lacks an equivalent to
the 
index for the intermediate and cool stars. Therefore, the
interstellar reddening must be either negligible or known and corrected to
make the calibration meaningful. These parameters are defined by:
which is equivalent to:
and their values for solar-composition Kurucz models (not corrected by standard
stars) are represented in Fig. 6 (click here). This figure can be compared with Fig. 4 (click here)
of Moon & Dworetsky (1985). If the colour excess E(B2-V1) is
known, the correction of the pT and pG parameters has to be done through the
relations
Figure 5: Inverted and corrected grid with solar metallicity for the hot
stars. Roughly horizontal lines are those of constant values of the Y
photometric parameter, while the vertical ones are lines of constant X
parameter. The iso-X lines are separated by an interval of 0.05 magnitudes,
while the iso-Y lines are separated by 0.025. For clarity, not all lines are
labelled
Figure 6: Direct, usual grid showing the (uncorrected) iso-
and
iso-log g lines in the pG vs. pT diagram. These lines are nicely
orthogonal, apart from a small region at high gravity and small 
.
This diagram is quite similar to the 
vs. 
one of the 
photometry
The standard stars used to correct the grid for 
are listed in
Table 4 (click here) while those used to correct log g are listed in Table 5 (click here)-8 (click here).
The standard stars for 
are taken from essentially the same sources
as for the B stars. Table 5 (click here) lists the eclipsing binaries already used by
Moon & Dworetsky (1985) while Tables 6 (click here)-8 (click here) give the members of the
Orion association, of the Pleiades and of IC 2391 respectively. The colour excess
of the stars in Orion was determined from the intrinsic colours of Cramer
(1982), and the pT and pG parameters were corrected for it.
For the
Pleiades, the pT and pG parameters have been
corrected for a mean colour
excess E(B2-V1) = 0.052 (Nicolet 1981) and for IC 2391, they have
been corrected for E(B2-V1) = 0.005 (North & Cramer 1981). For
the Pleiades and IC 2391, the fundamental log g values were deduced from the
estimated effective temperatures using the isochrones at log
and 7.7
respectively. The differences between the fundamental 
and log
and their values interpolated in the (uncorrected) inverted grids from the
observed Geneva colours of the standard stars are shown in Figs. 7 and 8
respectively. For effective temperatures, we obtain:
and for log
:
Figure 7: Difference between interpolated and fundamental 
values vs. fundamental 
for the intermediate stars. The regression
line is shown. See Table 4 for the key to the symbols
The inverted and corrected grids themselves are
represented for the three metallicities
[M/H] = -1, 0, +1 in Figs. 9 (click here)-11 (click here). We show these three diagrams, just
to make clear the effect of the metallicity on the 
and log
estimates. As in the case of the X and Y
parameters, we represent the physical parameters log
vs. 
with the lines of constant pT and pG parameters, rather than the reverse.
Note that for these stars, the metallicity is assumed to be known a priori
so that the most relevant grid can be used; the colours are not sensitive enough
to metallicity to give a significant estimate of it, except perhaps for a few
hot Am stars.
Figure 8: Difference between interpolated and fundamental log
values
vs. photometric 
for the intermediate stars. The line is the
fitted least-squares parabola
The comparison between the fundamental and photometrically determined
and log
is shown in Figs. 12 (click here) and 13 (click here) respectively. The
residual rms scatter is 
K
for the effective temperature, and 
dex (c.g.s.)
for the logarithmic surface gravity respectively. As for the hot stars, 
is mostly due to errors in the fondamental data and in the same proportion. This scatter represents the
uncertainty in the determination of these physical parameters, but we insist
that interstellar reddening must be negligible or corrected for.