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1. Introduction

1.1. Brief review of previous work and outline of this

Since the pioneer work of Freeman (1970), the analysis of galaxies in terms of their bulge and disk components has been a fashionable exercise. Reviews of these topics have been given by Capaccioli & Caon (1990), and by Simien (1991).

Most of the effort has been devoted to bulge/disk decompositions based upon the fitting of ad hoc analytical formulae to the 1D or 2D surface brightness (SuBr) distribution. Recent publications of this kind include those by de Jong & van der Kruit (1994), Andredakis & Sanders (1994), Byun & Freeman (1995). Some authors however, have tried other approaches with less stringent a priori constraints. It was then necessary to consider objects projected at such inclinations to the line of sight, that the forms of the isophotes convey information about the two-components structure.

As an aid to derive bulge+disk models from detailed isophotal analysis, a popular approximation has been the Oblique Thin Disk, adopted by Simien & Michard (1990), and by Scorza & Bender (1990) and (1995). A thin disk with circular symmetry will project as a series of concentric ellipses of constant axis ratio, independently of complexities in the radial SuBr distribution of the disk, such as ring or lenses. This constraint will greatly help to derive the bulge and disk models. The Oblique Thin Disk approximation will possibly not remain valid if the inclination becomes so large that the intrinsic thickness of the disk, i.e. its vertical light distribution, contributes to the geometry of the isophotal contours.

Another approximation, here termed the Edge-on Very Thin Disk case, has been introduced by Capaccioli et al. (1987), and again used by Caon et al. (1990). This approach has been technically improved by Seifert & Scorza (1996). It is then assumed that the disk is so thin, and the inclination so close to 90 degrees, that the disk does not contribute to the SuBr near the minor axis of the isophotes but only near their major axis. Then the bulge SuBr and ellipticity distributions may be recovered by fitting ellipses to limited isophotal arcs surrounding the minor axis. A bulge model is thus obtained, and the disk will be simply found by substracting this bulge model from the image. This method might give satisfactory results if the underlying hypothesis are valid, but unfortunately this validity cannot be tested. On the other hand, the existence of thick disks seems to be well established. According to the "quantitative morphology" of Michard & Marchal (1993, 1994a, b) and Michard (1994), thick disks not unfrequently dominate the outer envelopes of S0's galaxies. This makes the Edge-on Very Thin Disk hypothesis quite uncertain for disk dominated lenticulars.

In the present contribution, the bulge and disk models of disky E and S0 galaxies are derived from image analysis within the assumption that both components have concentric and coaxial elliptical isophotes, with arbitrary ellipticity profiles and SuBr distributions. The Oblique Thin Disk approximation, or the one adopted by Kent (1986) (i.e. constant bulge and disk ellipticities) are special cases of our assumptions. Since our techniques provide complete bulge and disk models, the results can be checked by synthesising these models, adding the two corresponding images, and comparing the sum to the input galaxian image. The contribution of bulge and disk to the SuBr at the minor axis of an isophote can also be calculated, and the Edge-on Very Thin Disk hypothesis thus tested.

It should be emphasized however, that real galaxies do not necessarily comply with the assumptions adopted here. Even neglecting such complications as dust lanes or isophotal twists, and considering only images with two orthogonal axis of symmetry, these will not necessarily be well represented by the sum of two families of concentric and coaxials ellipses. This approximation is most likely to break in the case of edge-on, disk dominated objects.

In Sect. 2.1 are given the equations relating observable quantities to the corresponding ones, as calculated from the two-components model. These quantities are the mean value and low order even harmonics of the SuBr distribution along suitable reference ellipses. The important simplification occuring when these ellipses are the bulge isophotes is pointed out. In Sect. 2.2 is discussed the derivation of "external exponential models": the solution of this "restricted" problem is very useful for the derivation of an asymptotic disk model, which is a necessary ingredient of the complete solution. In the following sections are outlined our techniques for deriving and checking the complete solution: the inwards unconstrained continuation of the asymptotic model in Sect. 2.3; the improvement of the solution by introducing ad hoc constraints upon the ellipticities in Sect. 2.4; and finally the control of the solution from the 2D relative residuals tex2html_wrap_inline1158.

In Sect. 3 the results of the analysis are given for 9 test galaxies covering a large range of possible inlinations and D/B ratios. The derived models are shown graphically and commented upon in individual notes.

Finally Sect. 4 offers some comparisons with the results of other authors. A rather good agreement is found between our models and those obtained by Scorza & Bender (1995) with the Inclined Thin Disk approximation. On the other hand the Edge-on Very Thin Disk approximation, as used by Seifert & Scorza (1996), give disk profiles in strong disagreement with our solutions, except for galaxies with an intrinsically faint disk.

1.2. Notations and abbreviations

It may be useful to collect here the notations and abbreviations currently used below.

. SuBr surface brightness.

. MajA major axis; MinA minor axis.

a, c major and minor axis of a Reference Ellipse, i.e. the one used in Carter's representation of isophotal contours.

ei, fi coefficients of cosine and sine terms in Carter's harmonic representation of deviations from the Reference Ellipse. Note that this ellipse is defined by its MajA a and the conditions e1=f1=e2=f2=0.

q axis ratio.

tex2html_wrap_inline1174 ellipticity.

diE, boE, unE subclassification of ellipticals as disky, boxy or undeterminate; p added for peculiar envelopes.

spH, thD, exD classification of envelopes, as spheroidal haloes, thick disks, extended disks respectively.

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