Since the early work of Hubble (1926, ApJ, 64, 321) many attempts have been made to derive the distribution of intrinsic shapes of galaxies from the distribution of their apparent shapes, under the assumption of random orientations.

In the case of elliptical galaxies this inverse problem has formally an unique solution if ellipticals belong to a one parameter family (i.e. oblate or prolate), but the problem is statistically undetermined if ellipticals are triaxial. For this reason several studies have tried to check the consistency of either the oblate, prolate or triaxial hypothesis with the observed distribution of ellipticals (Lambas, Maddox & Loveday 1992, MNRAS, 258, 404; Ryden 1992, ApJ, 396, 445; Ryden Lauer & Postman 1993, ApJ, 410, 515; Tremblay & Merrit 1995, AJ, 110, 1039; Ryden 1996, ApJ, 461, 146).

Thanks to the possibility of obtaining accurate geometrical parameters for elliptical galaxies in a completely automated manner, all the above studies did concentrate on ellipticals, indeed, whereas the intrinsic shape of bulges has not properly explored, as yet. The biggest problem arising in the determination of the intrinsic shape of bulges lies in performing accurate disk-bulge decompositions, especially taking into account that, when one imposes a simultaneous best-fit of the geometrical parameters of the bulge and the disk profile, at some extent, they affect each other.

A measure of the intrinsic shape of a sample of bulges has been attempted only by Bertola Vietri & Zeilinger (1991, ApJ, 374, L13), so far. Though they confine their analysis to a limited sample of spirals (32) and derive the parameters of the bulge by simply subtracting from each galaxy a parametric (exponential) disk, they are able to derive an estimate of the true distribution function of the bulges axial ratios, indeed.

However, as stressed also in the pioneering work by Kent (1986, AJ, 93, 1301), the classic, parametric (exponential, r^1/4) bulge-disk decomposition has to be considered just as a crude representation of the two main galaxy components and specific algorithms have been since then developed to perform fully non-parametric photometric decompositions (e.g. Andredakis, Peletier & Balcells 1995, MNRAS, 275, 874; Moriondo, Giovanardi, Hunt 1998, A&AS, 130, 81).

With this work we study the geometric properties of bulges, by observing a large statistically selected (all non-barred S0-Sa galaxies [-2.5 < T < 1.5] with B_T < 13 in a selected area of the sky) uniform sample of early-type, disk galaxies. We then perform bidimensional non-parametric and parametric disk-bulge photometric decomposition and determine the observed distribution function of the disk-bulge misalignment and ellipticities. The misalignment and the ellipticities of the two components will be later used to derive the distribution of intrinsic shapes of bulges.

The distribution function of the axial ratios of bulges will constitute an important test for recent semi-analytical modeling techniques of galaxy formation, where disks accrete around bare spheroids (Kauffmann 1996, MNRAS, 281, 487), or from the merging of pre-existing, disk proto-galaxies (Baugh, Cole & Frenk 1996, MNRAS, 283, 1361).

Observations have been performed at the 1.5-m VATT telescope in May 1999. All galaxies have been observed in the R-band with a seeing, measured on the final images, between 1 and 2 arcsec. Images have been cross-correlated to align different exposures, cosmic ray cleaned and finally coadded using standard procedures.

We first manually masked region of the images containing stars or dust patches. To apply the parametric and non-parametric disk-bulge decomposition we developed an automated procedure, which consists of the following steps:

Although to derive the distribution of the intrinsic shape of bulges we still need to complete the analysis of the whole sample, a few comments can be given also for this preliminar random subset of galaxies.

We make the reasonable assumption that the disks are perpendicular to one of the principal axis of the bulge. We note that there are few clear signs of misalignments between the disk and bulge apparent major axes, in particular in the galaxies seen at intermediate inclination, where this effect should be more clearly visible. This indicates that bulges cannot be axisymmetric but can be only slightly triaxial. Moreover we do not observe any bulge having the apparent major axis perpendicular to the apparent disk major axis, in particular in galaxies at high inclination (close to edge on) where this effect should be more noticeable. This fact indicates that the fraction of bulges (if any) having the intrinsic major axis orthogonal to the plane of the disk cannot be significant.

We stress the importance of an accurate modeling of the disk surface brightness, which cannot be assumed to be simply exponential, to extract reasonable geometrical parameters for the bulges. An example of how the modeling of the disk can affect the measurement of the bulge parameters is presented in Figure 2 and 3.

Figure 1: For each galaxy presented the left panel shows the bets fit photometric bulge-disk model. The thick solid ellipse has a position angle and ellipticity given by the values for the bulge and a semi-major axis is equal to the effective radius r_e of the bulge. The dashed line ellipse represents the same quantities relative to the disk. The semi-major axis is given by the scale length r_d of the disk. The right panel presents the observed galaxy with superimposed the moment ellipse of the surface brightness. The semi-major axis of this ellipse is given by , while the semi-minor axis of the ellipse is . This ellipse roughly corresponds to the region of galaxy pixels lying above the  level of the background. Only the pixels inside this region have been considered in the fits.

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Figure 2: The R-band image of NGC 4698 upper panel left is compared to the best fitting parametric model (r^1/n bulge and exponential disk) right upper panel. It is apparent that this model cannot reproduce the main features of the photometry of this galaxy. In the bottom panel are shown two cuts along the major and minor axis of the observed galaxy (thin noisy line) and of the model (thick dashed line). The exponential disk is shown with a thick solid line.

Figure 3: The R-band image of NGC 4698, rotated and folded along the major axis of the disk (to avoid the effects of the dust lanes) left upper panel is compared to the best fitting non-parametric model right upper panel. The disk and the bulge are constrained to have elliptical isophotes with constant ellipticity and position angle, but no functional form is imposed. In the bottom panel are shown two cuts along the major and minor axis of the observed galaxy (thin noisy line) and of the model (thick dashed line). The non-parametric disk is shown with a thick solid line.