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8. Maximum velocity rotation and central velocity dispersion

We published compilations of HI-data in 1982 and 1990 (Bottinelli et al. 1982; Bottinelli et al. 1990) but the data are regularly updated from literature. The reduction of raw measurements is the same. The 21-cm line widths are reduced to two standard levels (20% and 50% of the peak) and to zero-velocity resolution using the following formula:
where ws(l,r=0) is the standard 21-cm line width at level l=20 or l=50, while w(l',r) is a raw measurement at a level l' made with a velocity resolution of r tex2html_wrap_inline2131. The constants a, b and c are (Bottinelli et al. 1990): a=0.014, b= -0.83, c= -0.56.

The resulting standard 21-cm line widths ws(l=20,r=0) and ws(l=50,r=0) are corrected for systematic errors by intercomparison reference by reference (program INTERCOMP, Bottinelli et al. 1982) leading to standard widths w20 and w50 and their actual uncertainties sw20 and sw50 respectively.

w20 and w50 are used to calculate the log of the maximum velocity rotation following the expression.
where incl is the inclination (in degrees) between the polar axis and the line of sight calculated from the classical formula (Hubble 1926):
where logro = 0.43+0.053.t, if tex2html_wrap_inline2161 (or logro=0.38 if t>7), has been obtained from the most flattened galaxies.

tex2html_wrap_inline2167 is the weighted mean of the logarithm of the line widths w20 and w50 corrected for internal velocity dispersion. The adopted weight of level 20% is twice the weight of level 50% because it is less sensitive to the definition of the maximum and also because it corresponds to larger fraction of the disk. The correction for internal velocity dispersion is taken according to Tully & Fouqué (1985).
where w is either w20 or w50 and tex2html_wrap_inline2179, assuming an isotropic distribution of the non-circular motions tex2html_wrap_inline2181 and a nearly Gaussian velocity distribution (i.e. k(20)=1.96 and k(50)=1.13).

Mean maximum velocity rotation logvm is available for 6415 galaxies, from 34 436 individual measurements w20 or w50.

The actual uncertainty on logvm can be approximated by (For the detailed calculation see Bottinelli et al. 1983):
where sw and w are used for (sw20 or sw50) and (w20 or w50), respectively. The histogram of slogvm is presented in Fig. 9 (click here).

Figure 9: Histogram of the actual uncertainty on maximum velocity rotation logvm

A preliminary compilation of central velocity dispersions logs was published in 1985 (Davoust et al. 1985) and included in our database. This compilation has been regularly updated from literature (including compilations made by Whitmore et al. 1985; McElroy 1995; Prugniel & Simien 1995). Measurements from various references have been homogeneized using the INTERCOMP program (Bottinelli et al. 1982). The mean central velocity dispersion logs is available for 1816 galaxies resulting from 3402 individual measurements. The actual uncertainty slogs in log scale is shown in Fig. 10 (click here).

Figure 10: Histogram of the actual uncertainty on central velocity dispersion logs

In Fig. 11 (click here) we present the completeness of kinematical parameters logvm or logs in comparison with the total completeness curve. The completeness is fulfilled up to about m=12.0 mag.

Figure 11: Completeness curve for m. The completeness is satisfied up to the limit tex2html_wrap_inline2229 (solid line). This limit drop to tex2html_wrap_inline2231 if we impose that the radial velocity is known (dashed line), and to m=12.0 if we impose that either the maximum velocity rotation or the central velocity dispersion is known (dotted line)

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