4.4.2 Disk Galaxies

where is the central surface brightness and is the so called disk scale length. Equation 4.9 can be rewritten in a form similar to the one used for the law as

(4.10) |

where

(4.11) |

Since the first systematic study of [Freeman 1970], this law has been known to fit the profiles of the outer regions of a large class of disk galaxies and has, in fact, come to define the typical surface brightness profile of the intrinsically flat component of disk galaxies, to the extent that deviations from these profile are generally ascribed to the existence of other components or to the effects of dust. Assuming this analytical form for the profile of the disk component, one can then try to disentangle the contributions of the bulge and disk components by means of fitting techniques. The methods for doing this have in time undergone a great development, from the simple one-dimensional fitting procedure along the galaxy major axis first adopted by [Freeman 1970] to the bidimensional decomposition techniques currently being developed, which are applied to whole galaxy images (see e.g. [Byun and Freeman 1995]). In this study, a bulge+disk profile will be considered, combining an law with an exponential law, thus not considering contributions from components such as spiral arms, bars, rings, lenses, or the photometric effcts of dust. The most general form of such a profile

depends on two pairs of parameters characterizing the bulge and disk components, respectively. The only independent variable we have so far introduced in our model is the total magnitude, which however determines also the effective radius through Equation 4.3. Therefore, the values of two other parameters must be given in order to completely determine the form of Equation 4.12. A convenient choice are two quantities derived from bulge/disk decompositions and frequently reported in the literature, namely the bulge/bulge+disk ratio , or the ratio between the brightness contributed by the bulge component and the total brightness, and the ratio between the effective radii of the bulge and disk components. As shown in Appendix D, these two parameters completely determine the bulge+disk profile. As for , [Kent 1985] found that in intrinsically luminous D galaxies this is tightly correlated with the morphological type, falling from a mean value of 0.65 for S0 to a mean value of 0.15 for Sc and later types. Recently, [Ratnatunga et al. 1999] found a mean of 0.4 from the bulge/disk decomposition of the MDS galaxies. The same two references then agree in fixing to about 0.5 the mean value of . Such an excellent agreement between parameters obtained from galaxies of largely different magnitudes suggested to consider the two parameters as fixed, without introducing in the model the complications of other free parameters. Values of , corresponding to a bulge/disk ratio , and were therefore assumed. With our choices for and the bulge+disk profile becomes

In general, the bulge and disk components dominate the profile at small and large radii, respectively. Note, however, that due to the analytical form of the two profiles, at very large radii the bulge contribution eventually exceeds that of the disk. In fact, practically all (99%) of the brightness predicted by the disk profile falls within 4 effective radii, but for the bulge profile only 85% of the light is within 4 effective radii, and the model needs to extend out to about 19 effective radii to contain 99% of it. Shifting to a magnitude scale, the analytical expression for is not as simple as that derived for ellipticals and is

The total brightness emitted by the galaxy and the effective surface brightness can be written as

(4.15) |

and

Table 4.5 reports the values of , and for different total magnitudes. The values therein listed in the second column will be used in Chapter 5 to estimate the number of galaxies that could be detected by GAIA ASM. On the other hand, the values listed in the third and fourth column will be used to estimate the standard error of GAIA broad-band photometry at the effective radius of a galaxy.

mag | mag/arcsec | mag/arcsec | mag/arcsec |

10 | 20.2481 | 21.6410 | 21.2490 |

11 | 20.2800 | 21.6730 | 21.2809 |

12 | 20.3067 | 21.6996 | 21.3076 |

13 | 20.3321 | 21.7250 | 21.3330 |

14 | 20.3616 | 21.7545 | 21.3625 |

15 | 20.4023 | 21.7952 | 21.4032 |

16 | 20.4628 | 21.8557 | 21.4637 |

17 | 20.5531 | 21.9461 | 21.5540 |

18 | 20.6851 | 22.0780 | 21.6860 |

19 | 20.8718 | 22.2648 | 21.8727 |

20 | 21.1281 | 22.5210 | 22.1290 |

21 | 21.4702 | 22.8632 | 22.4711 |

22 | 21.9161 | 23.3090 | 22.9170 |

23 | 22.4851 | 23.8780 | 23.4860 |

24 | 23.1981 | 24.5911 | 24.1991 |