Astron. Astrophys. 319, 435-449 (1997)

## 4. Type dependence in the inverse magnitude TF relation

As will be discussed in Sect. 7.4, the type effect in the diameter TF relation implies also a type effect in the magnitude relation, though with a decreased amplitude. We checked this prediction with those 4311 galaxies of our sample which also have B -magnitude; with the other restrictions (see Sect. 2) this number becomes 3214. The slope and the zero-points corresponding to different types were derived similarly as for the diameter relation in Sect. 3.

For the common slope the value of 0.1 was adopted (Fig. 4, top panel). Bottom panels in Fig. 4 show the zero-points for the separate regressions and for the fixed slope. The latter ones we take as giving the actual zero-point shifts. It is satisfying to see that these, while following the shifts in the diameter relation, have a smaller amplitude as expected from the simple model of Sect. 7.4. We shall discuss the magnitude relation (both direct and inverse) in more detail elsewhere. Here it is sufficient to note that the slope 0.1 is also expected from the disc+bulge model similarly as the slope 0.5 for the diameter iTF relation.

 Fig. 4. Same as Fig. 2, now for inverse magnitude relation. A fixed common slope a'=0.1 was used in the bottom panel.

The discussion above utilized galaxies at very different distances (radial velocities). It is interesting to see if the type effect is equally well seen for different radial velocities. To this end we have calculated the cumulative averages of for each type in restricted radial velocity ranges, where is normalized using the inverse slope as follows (D and M are calculated linear diameters and absolute magnitudes):

for diameters,

for magnitudes

The cumulative averages plotted in Fig. 5 reveal clearly the zero-point shifts in the inverse relations all along the velocity axis (note that the ordinate has been put to zero for the complete sample for T = 8). At small radial velocities the scatter naturally increases due to the small number of galaxies there, though the types keep well separated almost down to 1000 km s-1. The fact that there is no clear trend away from horizontality in the diagrams also lends support to the slope adopted. This pair of diagrams also shows quite nicely the expected smaller type effect for magnitudes.

 Fig. 5. The type effect as seen in the (i.e. relative zero-point shift ) vs. radial velocity diagram for both diameter and magnitude inverse relations. Different symbols refer to types ranging from 1 to 8: for , black triangle, , black square, , , and for 2-8 respectively.

© European Southern Observatory (ESO) 1997

Online publication: July 3, 1998