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7.2.1 Inclination Estimates

Although there has been some success at estimating the inclination of spiral galaxies by fitting the spiral structure to logarithmic templates (e.g., Danver 1942), there are clearly problems with this approach due to the nonuniformities in spiral galaxies. The approach suggested by Holmberg (1958) assumed that disk galaxies can be adequately represented as oblate spheroids such that

Equation 11 (11)

where i is the inclination, (b/a) is the observed axial ratio, and alpha is the axial ratio for an edge-on system. We can also allow alpha to be a function of morphological type (e.g., Heidmann et al. 1972; Bottinelli et al. 1983; Fouqué et al. 1990). This approach assumes that galaxies have circular isophotes, to which there are clearly counter examples (e.g., M101). Fortunately, the most severe cases are obvious and can be excluded. Less obvious cases increase the uncertainty in i, particularly at low i, but the effect due to variations in alpha may be equally important. Historically, axial ratios have been estimated by eye using the Sky Survey or larger scale plates. This is an uncertain procedure, particularly when applied to systems whose inner (higher surface brightness) isophotes are not circular (cf. van den Bergh 1988). Pierce (1988) and Pierce and Tully (1988) have advocated the use of ellipse fitting to CCD images in order to estimate axial ratios and hence inclinations. They found that deep images reveal an apparent underlying old-disk population in dwarf systems which can be used to improve the accuracy of the inclination estimates for these systems. Even for bright galaxies, fitting ellipses to isophotes is more quantitative and objective than are eye estimates using photographic plates. Nevertheless, some personal judgement is still required as significant variations in ellipticity with radius are often present in typical galaxies.

An alternative, and promising technique makes use of the two dimensional velocity field of the galaxy to constrain its inclination. This approach requires an extensive map of the velocity field of the galaxy, using either Fabry-Perot imaging at Halpha or aperture synthesis techniques at 21-cm. While this requires considerably more effort, the technique offers real promise for improving inclination estimates. In this approach the gas is assumed to be rotating in circular motion and the velocity field defines the inclination. However, the gas is also subject to noncircular motions originating from non-axisymmetric mass distributions (e.g., bars, ovals, spiral structure), and so inclination estimates will be somewhat model dependent, although independent of the photometric estimates. Work currently underway by Schommer et al. (1989) should clarify some of these concerns and provide sufficient data to access the technique more fully. Initial results indicate good agreement between the kinematic and photometric inclination estimates.

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