The central velocity dispersion in elliptical and lenticular galaxies as an extragalactic distance indicator

Abstract

The Faber-Jackson relation between absolute magnitude M<SUB>T</SUB><SUP>0</SUP> and central velocity dispersion σ<SUB>υ</SUB> is reexamined for a sample of 157 normal, noninteracting galaxies, 82 ellipticals (T = -5, -4), and 75 lenticulars (T = - 3, - 2, -1). The values of σ<SUB>υ</SUB> are weighted means from various sources reduced to a uniform system (Table 1). <P />Absolute magnitudes are calculated from corrected apparent magnitudes B<SUB>T</SUB><SUP>0</SUP> and distance moduli μ<SUB>0</SUB> which are weighted means of a variety of independent determinations (from optical tertiary indicators and from revised versions of the Tully-Fisher relation) for spirals associated with ellipticals or lenticulars in our sample; group distance moduli derived from redshifts were also used in some cases. The slope and zero point of the one-parameter F-J relation, M<SUB>T</SUB><SUP>0</SUP> (log σ<SUB>υ</SUB>), were derived by Jefferys's generalized least-squares technique for different<SUB>samples</SUB> (E vs. L, lower vs. higher redshifts, Virgo cluster). <P />The best-fit slope (8-9) is generally less than the canonical value (10) and varies slightly with wavelength from ∼8.5 in the U, B, and V bands to ∼10 in the infrared (Appendix A). The zero point is not significantly different for the E and L classes in the red and infrared, but lenticulars are ∼0.2-0.3 mag brighter in the U and B bands. Alternative expressions in the B and V bands are approximately <P />-M<SUB>T</SUB><SUP>0</SUP>(B) =A+9(logσ<SUB>υ</SUB>-2.3), <P />with A = 19.4 (E) or 19.6 (L), and, more precisely, <P />-M<SUB>T</SUB><SUP>0</SUP>(V) = 20.35+8.5(logσ<SUB>υ</SUB>-2.3) <P />for both classes. These expressions give absolute magnitudes with mean errors of∼ 0.5 mag (E) and ∼0.6-0.7 mag (L). The effects of second-order parameters including color index, surface brightness, and apparent axis ratio are investigated. Small but significant effects of the first two are indicated. Generalized expressions of the F-J relation including such terms are given. Weighted mean distance moduli in the range 29 ≤ μ<SUP>w</SUP><SUB>0</SUB> (σ<SUB>υ</SUB>) ≤ 35 calculated by one-, two-, and three-parameter expressions are given for the 157 galaxies in our sample. The mean errors of these distance moduli from all sources are of the order ∼0.5 mag (E) and ∼0.6 mag (L), depending on the precision of the input parameters. Comparison of the distance moduli derived from σ<SUB>υ</SUB> for E, L galaxies and from other indicators for spirals in the same groups indicates no appreciable systematic scale difference in the range 29 &lt; μ<SUB>0</SUB> lt; 35 and, possibly, 24 &amp;lt μ<SUB>0</SUB> &lt; 35.