2D: Two disk fits on artificial galaxies

The fitting function and the fitting method were tested on their ability to reproduce the input parameters on three artifical galaxies. For two galaxies the two 2D Two Disk models, with the exponential function and the Bessel function to describe the radial behaviour, were tested on a truncated and an untruncated version. The two selected galaxies describe a strong and a weak thick disk component similar to the parameters we found for our sample galaxies. In total four different fits were done on each galaxy. A third galaxy with thick disk parameters comparable to the more distinct thick disk cases from Yoachim & Dalcanton (2006) was only tested with the Bessel function 2D Two Disk model, as this was the model we used for our sample galaxies. In all cases $\mu_0-\mu_\textrm{\scriptsize cut}$ was set at 7.4 mag arcsec$^{-2}$ so that they represent the quality of our own sample galaxies.
The results of the tests of the 2D Two Disk model on artificial galaxies are shown in Table 16. $\mu_{n-k}$ is given to describe the effects of the fits on this value. The $\chi^{2}_{\nu,1}/\chi^{2}_{\nu,2}$ value is added to show how much the fitting method fits the thick disk component more clearly in an artificial galaxy than in our sample galaxies.
Considering the scalelengths the Bessel function returns the original values quite accurately for the untruncated case while the exponential fits badly, but this was expected as the 3D galaxies were created with a Bessel function to describe the line-of-sight integration of the disk over the radius. The differences on the truncated case between the Bessel function and exponential fit however, are small, especially considering the scalelength parameters, where one would again expect the Bessel function to perform better.
For the artificial galaxy with a high $f_z$, the fits return the input accurately. This is not the case for the case with a low $f_z$, which gives overrations in the range of +13-20%. The same can be said for $\mu_{n-k}$. Although it is higher for the $f_z$ = 6 galaxy, the deviations are considerable, but acceptable, while the $f_z$ = 2 galaxy underrates it heavily, ranging from -28-48%. That one overrates and the other underrates is also notable, showing varying possible behaviour.
Neither of the two fitting function are well adjusted to a truncation and over all parameters they perform similar. The exponential overrates the scalelength while the Bessel function underrates it. In the case of the Bessel function we see the line-of-site integration fails, even when cutting at a $R_{\textrm{\scriptsize min}}$ and a $R_{\textrm{\scriptsize max}}$ in the case of radial truncation.
The third galaxy, representing one of the more typical thick disk parameters from Yoachim & Dalcanton (2006), gives very different results. We do not see the similar underrating of the other two galaxies to the scale lenght of the thin disk, which is odd compared to the clear different and expected behaviour of the first two sets of fits. All the parameters are fitted quite well, but strangely enough not $\mu_{n-k}$, which it overrates strongly. The cause for this lies at the thick disk component. The overrating is quite surprising, as the $\mu_{n-k}$ values of Yoachim & Dalcanton (2006) are typically much smaller than our fitted result.
What we can see is that the less truncated a galaxy the better the Bessel model fits will return the input parameters. Truncation however, is a common radial feature (Kregel et. al. 2000, Pohlen & Trujillo 2006). The tests on our artifical galaxies show that the conversion to a Bessel function to keep the correct scalelength will not be able to do so in most cases. The difference between exponential and Bessel function is neglectable for truncated galaxies.
The importance of the tests on artificial galaxies is that they give an indication of the error of our fit results for the 2D Two Disk fit as it is not possible to obtain clear error margins for the six parameter values except for the speed and accuracy of the convergence of the Downhill Simplex method as it only produces one final result.