The general results of our analysis are presented in Table 1.
Table 1. Statistics of the sample galaxies (all numbers in %)
About a quarter of the sample objects are classified as isolated galaxies (without significant neighbours within 5 optical diameters). This fraction depends on the angular size of galaxies: 18%3% of the galaxies with angular diameter between and , and 34%6% of those with diameters between and are found isolated. This correlation was also found by Karachentseva (1973) as a function of apparent magnitude: the fraction of isolated galaxies is higher for brighter objects. This is certainly related to the isolation criterion itself, since the companion should be at least 20% the size of the primary, and large galaxies are rarer.
The relative fraction of interacting galaxies - 6% - is compatible with independent earlier estimations (for example, Arp & Madore 1977, Dostal 1979) based on the presence of morphological signs of interaction.
As can be seen in Table 1 and Fig. 3, a significant fraction of isolated objects (40-50%) does not show measurable warps while among interacting galaxies non-warped objects are relatively rare - 10-20%. On the contrary, the relative fraction of S-shaped warps among isolated galaxies is about 20% only, while among interacting galaxies such objects constitute 40-50%. Non-isolated objects (with close companions but without obvious signs of interaction) are intermediate between isolated and interacting galaxies. The relative fraction of U-shaped warps is the same - 30-40% - for all considered subsamples of galaxies.
In order to check possible observational selection biases leading to an easier detection of warps among nearby and large galaxies, we divided our sample into three parts, according to the angular diameters: from to , from to , and from to . All these samples are of comparable volumes. It is evident in Table 1 that the general observational trends described above do not depend on the angular size of the galaxy.
Fig. 4 presents the relation between the relative fraction of U- and S-shaped warps and the asymmetry index. This index correlates statistically with galaxy inclination - larger values correspond to less inclined disks. As one can see, the detection fraction of S-shaped warps is constant (about 40%) for edge-on galaxies and decreases significantly with decreasing inclination. This reflects obviously an observational bias - difficulty to detect a small optical warp for non edge-on galaxy. On the contrary, the relative fraction of galaxies with U-shaped warps increases systematically with decreasing inclination. We can speculate, therefore, that the U-shaped appearance can be related in many cases to non edge-on orientation (for instance, due to dust influence on the brightness distribution). Anyway, it is evident in Fig. 4 that among edge-on warped galaxies dominate objects with S-shaped warps.
The distribution of observed warp angles is peaked at (Fig. 5). This value is somewhat smaller than reported by Reshetnikov (1995) (). This difference is quite natural since the present study is based on less deep (in the sense of surface brightness level) material. The right wing of Fig. 5 distribution (for ) may be approximated by law. The observed distribution shown in Fig. 5 is strongly affected by our detection limit () for the angles . We detected small warps with in very thin, symmetric and nearly edge-on galaxies only.
Fig. 6 presents the distribution of the sample objects according to morphological type given by Karachentsev et al (1993). The figure demonstrates clearly that the morphological classification in the FGCE depends strongly on the angular size of the galaxy: larger galaxies show a flatter distribution, while smaller concentrate near Sc (T5) type. This is a natural observational bias: a detailed classification is much easier for larger objects.
In Fig. 7 we plot the relative fraction of S-shaped galaxies as a function of their morphological type. The present statistics do not show any significant correlation between the frequency of warps and the morphological type.
De Grijs (1997) has recently made a deep study of edge-on galaxies, and on a sample of 44 galaxies determined a warp fraction of 64%. This appears somewhat higher than the previous estimations, which could be due to several factors. First his study was made on deeper images, down to blue surface brightness of 27 mag (compared to 25 mag for the other surveys), but this does not seem the essential point, since his detected warps begin at a surface brightness level of between 20 and 24 mag . Second, his sample does not contain only very flat galaxies, since the selection criterion is the blue axis ratio at least 3.1. Although the cataloged inclination is high (), the latter is not well determined; the simulations of the next section have shown that the apparent axis ratio can vary from 9 to 4, at a given inclination between 80 and 85, only through variation of the position angle of the spiral arms with respect to the line of sight. For galaxies that are not very flat, the risk to find artificial warps is high (cf fig 10).
To compare our estimation of the warp fraction to that of de Grijs (1997), we have tried to repeat our study on his sample, chosing only the DSS isophotes, as we described in Sect. 2. We find indeed a higher fraction of warps than in the present sample: 7 U-shaped, and 18 S-shaped, i.e. a total fraction of 56%. One of the reasons could be the small number statistics, and another the selection criteria, in particular concerning the axis ratio. Note that de Grijs (1997) selected non-interacting and unperturbed galaxies, so that no conclusion about environment can be drawn. To better disentangle the effects of dust and spiral features on determined warps, it is interesting to examine the near-infrared images. The latter, however, often do not go as far out in radius as the B-band images; but when it is possible to compare, there is no warp in the K-band (cf Grijs 1997). This is related to the statistical results of Sanchez-Saavedra et al (1990) who find almost half of the edge-on galaxies warped in the blue POSS sky survey, while only one third of them is warped in the red POSS plates (see also Florido et al 1991).
About 40% of spiral galaxies with reveal S-shaped optical warps in their outer parts () with typical amplitudes . This high observable percentage would suggest that a large fraction, more than a half, of all spiral galaxies are warped.
The probability of optical warp detection does not depend on galaxy morphology (for objects later than Sab).
Disks of more massive, large and luminous galaxies are somewhat less warped (from a complete sample of 120 northern spirals with known magnitudes, diameters and maximum rotational velocities according to Reshetnikov 1995).
The detection fraction of S-shaped warps depends on galaxy environment: warped galaxies dominate among interacting galaxies, are very frequent among galaxies with close companions, and relatively rare among isolated objects.
© European Southern Observatory (ESO) 1998
Online publication: August 6, 1998