Tests

The notes below refer to the first version of the code, without models for bar and central source. The routine inside BUDDA to find the best model has been improved in the new version which means that its reliability is now higher. Concerning seeing effects the new version has a much better treatment of it so that the retrieval of the correct bulge Sérsic index is much more accurate. In fact we have done tests (not shown here) and checked that BUDDA can work fine even for galaxies 20 pixels accross, convolved with a seeing with an FWHM of 4 pixels. Now that the code have many more parameters to fit, the parameter space got incredibly complicated. This forces one to be even more careful when running the code. In addition, fixing some parameters might be very useful, like, e.g., the center, position angles, ellipticities and ellipse indexes.

To attest the reliability of the results obtained from BUDDA we have made several series of tests, all of them thoroughly described in the main paper. Firstly, we have checked that both the Linux and Unix versions of the code give identical results. Then we have run GMODEL with 41 synthetic galaxies, whose structural parameters are of course known, to verify how well it retrieves these input parameters, starting from first guesses randomly chosen. Interestingly, no matter how far from the right value the first guess for a parameter may be, the code gradually tends to converge to the right value. The figures below summarize the results.
 


Figure 1. Comparison between the parameters of the 41 synthetic galaxies as retrieved by BUDDA: (a) central surface brightness of the disk and effective surface brightness of the bulge in arbitrary magnitudes; (b) characteristic radius of the disk and effective radius of the bulge in arbitrary units (but similar to arcsec in nearby observed galaxies); (c) position angle, and (d) ellipticity. Circles are for the disc and squares are for the bulge parameters. The Pearson correlation coefficient R of each test is also indicated.
 


Figure 2. Same as Figure 1 but for (a) Sérsic index, and (b) the bulge/disk ratios in luminosity (circles) and size (squares).
 

It is worth to note that in these tests there was no user intervention, which should be the case with real galaxies, when some actions are very useful and recommended to maximize the code efficiency in retrieving accurate data. For instance, GMODEL should be applied several times, with different initial values, to search for the best result (which can be done through the chi square value). This avoids that the solution found is not only a local minimum. In some cases, one may initially fix some geometric parameters very well determined by other means, like the position angle with the ELLIPSE task from IRAF. After the first solution is found, one may use these parameters free in a second run, in which the input values are those of the solution of the first run. This is the case, for instance, when the ellipticity is too small (around 0.1) that it's hard to determine the position angle. None of these actions were done in the tests, so their results are actually a lower limit for the code's accuracy. Poissonic noise was added in some of the synthetic images but we found it to be a minor source of error.

These figures show that the reliability of the code is excellent. Two points are worth to note. Firstly, the ellipticity of the most eccentric bulges may be underestimated, but this may be easily corrected with the actions discussed in the above paragraph. Secondly, even with our treatment of the seeing it can disturb the Sérsic index but this should be important only for n larger than around 7, which is not the case for the large majority of galaxies, including ellipticals. Moreover, Figure 3 shows that the discrepancy between an original synthetic galaxy and the model retrieved by BUDDA is restricted to the central region, which has a size of the order of the seeing.
 


Figure 3. Examples of the discrepancy between a synthetic galaxy built with BMODEL and the one retrieved by GMODEL within BUDDA. The differences are restricted to the central region, since the entire original galaxy occupies the whole frame.