2 The sample and statistics

Table 1 presents extraction from the Southern Extention of FGC (Karachentsev et al. 1993, FGCE) for the galaxies with large S-type warps. The sample is limited by coordinates ${\rm 0\hbox{$.\!\!^{\rm h}$}0}~\leq~\alpha({\rm 1950})~\leq~{\rm 14\hbox{$.\!\!^{\rm h}$}0}$,$\delta({\rm 1950})~\leq~{\rm -17\hbox{$.\!\!^\circ$}5}$.The columns are as follows: galaxy FGCE, PGC and ESO number; right ascension and declination for the epoch 1950.0; B magnitude (NED); heliocentric radial velocity (NED); major and minor diameters measured on blue films (in arcmin); morphological type; warp angle $\psi$ - angle measured from the galaxy centre, between the plane and average line from centre to tips of outer isophotes (see Reshetnikov & Combes 1998); position angle of average line passing through the tips of outer contour (measured from N to E) - PA; direction of warp: clockwise (+) or counter-clockwise (-).

  

Table 1: General characteristics of the sample galaxies

 

Table 1: continued

In the Appendix, we present the DSS images of all galaxies (in the $B_{\rm J}$passband), rotated to horizontal.

  

Figure 1: Distribution of the observed warp angles. Dashed line shows $\psi^{-5}$ law

  

Figure 2: Comparison between position angles measurements (in degrees) in our work (PA) and FGCE - PA (FGCE). The solid line shows equality

  

Figure 3: Distribution of the warped galaxies on the sky: top - S-shaped warps, bottom - U-shaped warps. Plots of declinations (in degrees) versus right ascension (hours). The position angles of the galaxies (PA) are indicated by dashes (the length of each dash is 12$^{\rm o}$). Thick dashes show galaxies with counter-clockwise warp, thin dashes - clockwise warps (for S-shape warped galaxies)

Figure 1 presents the distribution of the sample galaxies according to warp angle $\psi$. The distribution is truncated for $\psi~\leq$ 4$^{\rm o}$since we selected only galaxies with clearest warps to avoid selection effects. The mean value of $\psi$ is $4\hbox{$.\!\!^\circ$}8\pm1\hbox{$.\!\!^\circ$}3(\sigma)$ that is comparable with the amplitudes of optical warps found by Sanchez-Saavedra et al. (1990); Reshetnikov (1995), and de Grijs (1997). Dashed line in Fig. 1 shows the $\psi^{-5}$law proposed by Reshetnikov & Combes (1998) to fit the observed distribution. A naive extrapolation of this law to $\psi=0^{\rm o}$ suggested that outer parts of all disk galaxies are warped with typical amplitudes of a few degrees.

In Fig. 2 we compare our measurements of the position angles of the sample galaxies with the FGCE data. The agreement is quite good. The mean difference is $<{\rm PA}-{\rm PA~(FGCE)}\gt\ = -0\hbox{$.\!\!^\circ$}6\pm1\hbox{$.\!\!^\circ$}8$ (s.e.m.). Excluding two most deviating galaxies (FGCE 333, 981) we have $<{\rm PA}-{\rm PA~(FGCE)}\gt\ =+0\hbox{$.\!\!^\circ$}6\pm0\hbox{$.\!\!^\circ$}4$ (s.e.m.).

It is evident in Figs. 3 that the projected spatial distribution of strongly warped galaxies and the distribution of their position angles are quite homogeneous (at least in the first order approximation). The large "void'' in Figs. 3 is due to absorption in the plane of Milky Way. Comparison of the distributions for the galaxies with S-shaped and U-shaped warps shows that both distributions are statistically undistinguishable. There is no evidence of any significant large-scale alignment effect.

The number of galaxies with clockwise warps (18) is smaller than counter-clockwise galaxies (42). But, within our relatively poor statistics, the difference is not significant (both numbers are consistent within 3$\sigma$).

Reshetnikov (1995) found that disks of more massive and luminous galaxies are somewhat less warped. Our present data do not show any significant correlation (see Fig. 4).

  

Figure 4: Warp angle versus blue absolute magnitude for the S-shape warped galaxies (H0=75 km s-1/Mpc)