4.5 Model's Validity and Verifications

As it was stressed at various times in this Chapter, a model such as that here described cannot accurately describe the properties of any given galaxy. However, it is expected to hold on average, i.e. when the average properties of a representative sample of galaxies are considered. Given the several rough approximations introduced, the question as to which extent the model is quantitatively reliable for the purpose of mission planning cannot be answered without a direct comparison between predicted and observed profiles. Before carrying out such a comparison, we will however make a few, essentially qualitative considerations about the model's general validity.

Roughly speaking, it is expected that our statistical model will reliably describe the surface brightness radial profiles of faint galaxies, while the brightest galaxies will display a stronger individuality and thus will require more realistic surface brightness distribution functions to be considered. This latter class of galaxies may tentatively be estimated to include all the galaxies in the Shapley-Ames Catalog ([Shapley and Ames 1932]), so about a thousand galaxies. These galaxies can display a very complex structure and be of very large angular extent, e.g. about 10 deg for the Large Magellanic Cloud. Most bright stars or HII regions will be smaller in angular size than the width of GAIA PSF, and thus will be detected as apparent points. Besides, these point-like structures will be superimposed on a complex background, where surface brightness can vary by magnitudes on small scales, depending on bars, spiral arms and dust lanes. Most of these galaxies will therefore require individual consideration, but conversely will allow particularly detailed scientific investigation. At fainter magnitudes, only the overall structure of galaxies will be relevant, and the typical properties predicted by our model will be useful.

As for a quantitative evaluation of model's reliability, a comparison between its predictions and some ground-based surface photometry of bright galaxies taken from the literature was carried out. Even though, owing to seeing, ground-based observations do not allow an accurate determination of the profiles in the galaxy innermost regions, they have the advantages of being available in substantial amounts and of frequenly following the brightness profiles to very large radii. Conversely, space observations such as the HST WFPC2 images which in Chapter 6 will be used for the simulation of GAIA observations, cover a small field of view, have mostly low exposure times and are still very limited. In much the same way, the large availability in the literature of $B$-band profiles extending down to large radii suggested the use of these for model's verification. The conversions between $B$ and $I$ was carried out using the constant color index $B-I=2.0$, and correspondingly $\mu_B-\mu_I=2.0$, which is the average value for bright galaxies according to [Prugniel and Héraudeau 1998]. Thus, in order to obtain the predicted $B$-band brightness profile against which observations could be compared, the measured total $B$ magnitude of the galaxy is transformed to $I$ through the $I=B-2.0$. Then the predicted $I$-band profile can be derived as described in Sections 4.4.1 and 4.4.2, for Es and Ds respectively. Finally, the predicted $B$-band brightnes profile is derived through the $\mu_B=\mu_I+2.0$.

For elliptical galaxies, the model's predictions were compared with the composite CCD-photographic brightness profiles obtained by [Capaccioli et al. 1988]. for 9 galaxies in the ranges $10.5<B<12.7$ and $18<\mu_B<28$ and down to radii of about 250 arcsec. These are typically found to agree with our model within 0.2 mag/arcsec$^2$ outside an inner circular area of radius about 1 arcsec. Within this area, the observed profiles show a sharp flattening which our model does not describe properly so that the predicted profile is systematically brighter than the observations. This is clearly due to the phenomenon of seeing, whose effects on galaxy surface photometry were described in Subsection 3.2.3, and is compensated by the observed profiles being systematically brighter than predicted at radii just above 1 arcsec.

For disk galaxies, the model's predictions were compared with the photographic surface photometry obtained by [Boroson 1981] for 26 galaxies in the ranges $8.5<B<12.5$ and $18<\mu_B<26$ and down to radii of 120-240 arcsec. In this case, the observations are typically found to agree with the predicted profiles within 0.3 mag/arcsec$^2$ outside the 1-arcsec radius circular area where seeing flattens the observed profiles as observed in the ellipticals.

On the whole, it can be concluded that our model predicts the galaxy surface brightness radial profiles in the range of radii relevant for our purposes with an accuracy of about 30% for most galaxies. Such an accuracy in the model's predictions is considered satisfactory in view of its application to the planning of galaxy observation.