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2.7. The core-Sérsic model

Due to the presence of partially depleted cores in luminous (MB < - 20.5 mag, H0 = 70 km s-1 Mpc-1) elliptical galaxies 6, a `core-Sérsic' model (Graham et al. 2003a, b) has been developed in order to describe and connect the nuclear (typically less than a few hundred parsecs) and the remaining outer stellar distribution. This model consists of an inner power-law and an outer Sérsic function, and has proven essential for modeling the HST-resolved light-profiles of luminous early-type galaxies (Trujillo et al. 2004). As suggested in Graham et al. (2003b), the lower-luminosity `power-law' galaxies have been shown to be described by the Sérsic model over their entire radial extent (Trujillo et al. 2004).

Although the reader is referred to the above papers, especially the Appendix of Trujillo et al. (2004), the core-Sérsic model is given as 7:

Equation 33 (33)

where Rb is the break-radius separating the inner power-law having logarithmic slope gamma from the outer Sérsic function. The intensity Ib at the break-radius Rb can be evaluated from the expression

Equation 34 (34)

The final parameter, alpha, controls the sharpness of the transition between the inner (power-law) and outer (Sérsic) regimes -- higher values of alpha indicating sharper transitions. In practice (e.g., Figure 11) we find that a sharp transition is adequate and recommend setting alpha to a suitably large constant value (typically anything greater than 3 is fine), leaving one with a 5-parameter core-Sérsic model.

Figure 11

Figure 11. Major-axis, R-band light-profile of NGC 3348. The solid line is the best-fitting core-Sérsic model while the dashed line is the best-fitting Sérsic model to the data beyond the HST-resolved break radius (Graham et al. 2003a, b; Trujillo et al. 2004).

6 The luminous `core galaxies' likely correspond to the `bright' family of galaxies identified in Capaccioli, Caon, & D'Onofrio et al. (1992) and Caon et al. (1993). They tend to have boxy rather than disky isophotes (Nieto et al. 1991), and Sérsic indices greater than ~ 4. They are commonly understood to be the product of (elliptical) galaxy mergers (e.g., Capaccioli, Caon, & D'Onofrio 1992, 1994; Graham 2004) Back.

7 The alpha and gamma terms shown here should not be confused with those given earlier in the paper, they are different quantities. Back.

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