In this paper, we have used the density wave theory to deduce an approximate analytical expression which takes into account the contribution of spiral arms to the surface brightness distribution in disk galaxies (Eq. 29). Since the physics involved by the spiral structure of a galaxy is relatively complex, our expression introduces several additional parameters in the law of total luminosity. Fortunately, most of these constants are related to dynamical parameters which can be measured by using independent techniques. For example, the parameters related to the disk rotation can be directly extracted from the galactic rotation curve and, hence, they are not free constants. In the same way, other parameters can be directly measured (as the pitch angle) or used to limit the freedom in the value of constants appearing in our expression. Reciprocally, the fitting of surface brightness profiles can be used to obtain a rough estimate of several dynamical parameters.
The application of our expression to some observed profiles gives excellent fits even when the surface brightness distribution is considerably affected by the irregularities produced by spiral arms. Much more encouraging for us is the fact that the dynamical parameters implied by such fits coincide reasonably with those measured by using other techniques. Because of the approximations involved in our expression, and the uncertainties inherent to any non-linear fitting, we cannot however consider the outputs of this procedure as an accurate measure of such parameters, but just as a rough estimate.
As a consequence of considering the spiral arms as a third important component in the surface brightness distribution of disk galaxies, the relative importance attributed to the bulge can significantly differ from that obtained from a simple double decomposition. Such values have been used in several statistical studies analyzing problems as a possible universality in the central surface brightness of the bulge (Freeman 1970, Kormendy 1977), the analogies among bulges and elliptical galaxies (Jablonka, Martin & Arimoto 1996), etc. In a forthcoming paper, we will apply the expression obtained in this work to describe the surface brightness distribution of a large number of galaxies. We will be then able to analyze, from a statistical point of view, the full implications of our procedure.
© European Southern Observatory (ESO) 1997
Online publication: July 3, 1998