3 Derivation of the global orientation parameters

In order to determine the disk and bulge profiles we need to estimate the orientations of the galaxies, defined by the position angle PA and inclination i. The problems related to determination of these parameters have been discussed for example by Considere & Athanassoula ([1982]). Both kinematic and photometric determinations are faced with problems: motions of gas in the outer parts are affected by galaxy interactions, while the inner parts might have bars or oval distortions. Also the shapes of the spiral arms might have been distorted by the interaction. Even in the case of a very detailed set of observations, like for the weakly barred galaxy IC 4214 (Buta et al. [1999]), kinematic and photometric orientations may deviate by even about $10^\circ$ both in PA and i; these large deviations can be explained by numerical modeling (Salo et al. [1999]). In the current study two methods were used, based on visual inspection of the disk morphology:

1.

Deprojection of the galaxies to face-on orientation;

2.

Ellipticity of the outer contours.

Deprojection of galaxies from the plane of the sky to the face-on orientation was performed by applying an IDL routine and an example for one of the galaxies, Kar 302 A, is shown in Fig. 1. The inclination $i \ = \ 55^\circ$ clearly is an overestimation, while $i \ = \ 45^\circ$ is too small. The uncertainties were estimated by making deprojections with small increments in i. For some of the galaxies only an upper limit for inclination could be estimated.

Figure 1: Kar 302 A (I-band) deprojected to the face-on orientation using the position angle ${\rm PA} \ = \ 170^\circ$ and inclinations $i \ = \ 35^\circ , \ 40^\circ , \ 45^\circ , \ 50^\circ , \ 55^\circ$ and $60^\circ$. The galaxy brightness is shown in the logarithmic scale

Elliptical shapes of the outer isophotes were determined by fitting visually the position angle and the inclination. The fitting level was taken to be the outermost contour not showing any clear signs of perturbation by the nearby galaxy. The formal measurement errors both for the position angle and the inclination were estimated to be about $5^\circ$. As for Arp 86, also the logarithmic form of the spiral arms was used to estimate the inclination. This method gave similar or slightly smaller values than the other two methods, but it could be applied only for a few galaxies. Note that we also measured the isophotal shapes as a function of radius (see the next Sect.). However, we prefer the above subjective method in estimation of orientation, since visual inspection enables to account the effects of spiral arms and tidal deformations better than any automatic method. The inclinations were corrected for the thickness of the disk. We used the Hubble formula for oblate spheroids and an intrinsic axis ratio of 0.2 (Aaronson et al. [1980]):

$$i = \cos^{-1} \ \sqrt{1.024 \ b^2 / a^2 \ - 0.042},$$

where a and b are the major and minor axis. Note that Aaronson et al. applied the additional correction term of $3^\circ$ to compensate for any kinematical opening along the spiral arms: due to the reasons given by Schommer et al. ([1993]) the correction term was not applied here.

The estimated orientations are shown in Table 1, where the values given by De Vaucouleurs et al. ([1991], hereafter RC3) are also indicated. All inclinations in the table were corrected by the above Hubble formula.

The position angles and inclinations measured at the fixed B-band surface brightness level of $25\rm\ mag \ arcsec^{-2}$ can be compared with the values given in RC3. The agreement was generally good except for some galaxies. For example, we measured ${\rm PA} \ = \ 116^\circ$ for Arp 298 B, while RC3 gives ${\rm PA} \ = \ 54^\circ$. However, our measurement is in agreement with ${\rm PA} \ = \ 120^\circ$ obtained by Marquez & Moles (1994) who used deep CCD images. For Kar 179 A a superposition of field objects has probably affected the position angle given in RC3. We also suppose that the high inclination $i \ = \ 74^\circ$ given in RC3 for Arp 70 A may not reflect the real inclination of the disk, because the outer disk is probably strongly distorted. Our lower value $i \ = \ 50^\circ$ for the inner regions might therefore be more realistic.