3. Models for 9 test galaxies

3.1. The data

Defering the application of the present techniques to such a sample of galaxies that would be needed for deriving astrophysical results, a few objects have been selected to test the method and compare its results to previous similar studies.

4.6 4.8

NGC	Typ	Env	Tel	Psf			mean
2549	S0	exD	CFH	0.59	35	-	-	-
id	id	id	OHP	2.06	132	82	+2.7
3098	S0	thD	CFH	0.61	50	47	-7.3	10.0
3115	S0	spH	CFH	0.55	37	-	-	-
id	id	id	OHP	3.10	150	109	+3.1
3245	S0	thD	CFH	0.60	35	-	-	-
id	id	id	OHP	2.49	110	71	+3.5	4.2
3377	diE	spH	CFH	0.59	25	-	-	-
id	id	id	CFH	-	40	-	-	-
id	id	id	OHP	2.35	140	30	+0.2	1.4
3585	diE	spH	CFH	1.07	43	37	-1.5	2.2
4350	S0	spH	TBL	1.38	86	66	-3.2	4.2
5308	S0	thD	TBL	0.95	90	71	-4.0	6.5
5422	S0	thD	TBL	0.81	99	95	-4.0	7.2

Table 1: Studied galaxies: frames and models characteristics

Table 1 (click here) lists these objects with relevant information about the used observations, and the quality of the model. All the frames were obtained in the R band (Cousin's definition).

Column 1: NGC number of the object.
Column 2: Morphological type from Michard & Marchal (1994b).
Column 3: Classification of the envelope from the same source.
Column 4: Telescope, either CFH for the 3.5 m Canada-France-Hawai telescope; TBL for the 2 m Bernard Lyot Pic du Midi telescope; OHP for the 120 cm instrument of Observatoire de Haute-Provence.
Column 5: FWHM of the frame PSF in arcsec.
Column 6: Major axis of the outermost measured isophote.
Column 7: Major axis of the valid range of the two-component model.
Column 8: Mean value of the model residuals in %.
Column 9: Standard deviation of the same.

As may be seen from the table, the CFHT frames have a resolution of about 0.6 arcsec but a small field. The low resolution and large field frames from the OHP were used only to obtain synthetic frames by merging with the CFHT frames (see below): this is done only if the frames have a large enough range of good agreement in their respective Carter-like analysis. For edge-on disk galaxies, the OHP frames are so badly affected by seeing that the merging of data is to be avoided. The Pic du Midi frames have a resolution of circa 1 arcsec and a sufficient field. When a mixed synthetic image was used, the figures in the last three columns refer to this image.

3.2. The use of synthetic images

To represent a galaxy with two systems of concentric and coaxial ellipses, it is advantageous to get rid of the features in the original image that cannot comply with such a model: this includes asymmetries resulting from dust, low contrast bar or spiral structure, and isophotal twists (such as the kind described by Michard & Marchal 1990). For this purpose, the image is analysed in terms of the representation first introduced by Carter (1978): each isophote is described by a reference mean ellipse and harmonics coefficients e_i, f_i describing deviations from this ellipse. Then a modified synthetic image is built from the results of this analysis, forcing all isophotes to a common center and orientation, discarding the sine harmonics f_i and the odd cosine harmonics e_2i+1.

Such a synthetic image retain the essential features of the real galaxy as far as our problem is concerned, and has the advantage to be nearly devoid of noise, making more efficients the algorithms designed for its solution.

Finally if we have two images of complementary qualities for a given object, for instance a high resolution but small field image, and a lower resolution but large field one, both can be separately analysed along Carter's principles, then the resulting files intercompared and eventually mixed if they show a large enough range of good agreement. Then a synthetic image can be obtained from the mixed file, keeping the resolution of the best frame and the field of the other.

3.3. Results

In Fig. 1 (click here) are presented the main relevant data and the run of the bulge and disk models for the test galaxy NGC 2549. Similar figures for the 8 other test galaxies are displayed with the same captions. The data and results for each galaxy will now be commented upon.

Figure 1: The adopted abscissae are a^1/4 in arcsec. In the three upper windows are shown the c/a ratio, the e₄ and e₆ parameters from our analysis according to Carter. The lower window gives the run of the and parameters. The intermediate one gives the profiles of the total SuBr (full squares), the bulge SuBr (circles) and the disk SuBr (spades)

NGC 2549 The data from one CFHT and one OHP frame were successfully merged to produce a synthetic "observed frame". The and e₄ coeeficients have 3 maxima, at a circa 7, 33 and 80 arcsec as regards . Correspondingly our solution shows a disk with two bright rings and a dip in between. The bulge nearly obeys a a^1/4 law. In the outer range, the values decreases while the values increases to form a thick disk envelope. The residuals of this solution are rather small.
NGC 3098 It is the difficult case of an edge-on, disk dominated galaxy! The and e₄ coefficients show maxima near a = 1, 10 and 27 arcsec (the latter two almost merging). Accordingly we find a small inner disk peaking above the main one. The range of the model is limited by the field of the CFHT frame, but the envelope has been classified spH so that the strength of the bulge component is expected to increase in the envelope. The residuals of the solution are large, possibly because the assumptions made in our technique do not well apply.
NGC 3115 It was studied from a synthetic frame, merging data from the CFHT and OHP frames (the merging leaves a small defect in the run of e₆). This object has an spH envelope. The bulge follows the a^1/4 law. As a result of the two maxima in the e₄ coefficient, we find a bright inner disk; the main disk has a bright ring near a = 16 arcsec, and a cut-off near a = 100. The solution has low residuals.
NGC 3245 This galaxy of relatively low inclination and small Carter coefficients, was studied from a synthetic mixed frame. Approximate values of and were derived from local models and the complete solution was obtained with constant axis ratio for both components. The solution has low residuals, but the bulge component shows a surprising SuBr profile.
NGC 3377 This well known diE and spH object was studied from a synthetic mixed frame, involving the analysis of two CFHT and one OHP frame. In agreement with Scorza (1992) the disk has an inner bright and high gradient range, followed by a much lower gradient range and a cut-off near a = 35 arcsec. In the high gradient range, the disk has a transverse scale height below 1 arcsec. The bulge follows the a^1/4 law with an inner cusp. The residuals of the solution are very small.
NGC 3585 This diE was studied from a CFHT frame only. The bulge follows the a^1/4 law. The disk has a low contrast bright ring. Our solution has very small residuals.
NGC 4350 is an S0 with a spH envelope. The bulge is in two parts, both following the a^1/4 law, but with different effective scales and values. It is clear that the spheroidal envelope is not simply a continuation of the inner bulge. The disk thickens prior to its cut-off near a = 70 arcsec. The residuals for our model are small.
NGC 5308 is an edge-on S0 with a thD envelope: as explained in Sect. 2.2 (click here) there are ambiguities in the choice of the asymptotic model. The solution was guided by assuming an outer bulge with constant and a thickening disk. An inner disk well above the main disk is again found (compare with NGC 3098, NGC 3115). The residuals of our solution are relatively large.
NGC 5422 is a very inclined S0 with a thD envelope (although there are hints of spiral structure in our unpublished maps). The and e₄ profiles show 3 maxima as in NGC 2549. In our solution, the inner bulge follows the a^1/4 law but its SuBr shows an uncertain tendency to level off in the outermost range. There is a bright inner disk, followed outwards by a bright ring, a lens...and a cut-off. As for other nearly edge-on disk galaxies, the residuals from our model are relatively large.

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