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2.2. Same Halo

As an alternative to DD, I have investigated the class of theories which I generically label ``same halo'' (SH; McGaugh & de Blok 1998a). The basic idea here is that there is no distribution in Rh. Simulations of halo formation (e.g., Navarro et al. 1997; hereafter NFW) indicate a strong correlation between halo parameters, consistent with this picture. At a given mass, the halo is the same regardless of the scale length of the optical galaxy. This yields the desired TF relation, by construction.

Since there is now no distribution in Rh, we must invoke some other mechanism to give the observed distribution of optical surface brightnesses. This is usually assumed to follow from the initial angular momentum. In terms of Peebles's spin parameter lambda, the scale length of the luminous disk is h approx lambda Rh. The precise equation can be more complicated (Dalcanton et al. 1997 (2); Mo et al. 1998), but this encapsulates the basic idea. Baryons in a halo with low initial spin collapse a long way before rotational support is achieved, forming an HSB galaxy with a short scale length. A high spin halo of the same mass forms an LSB galaxy with a much larger disk scale length. This makes the rather dubious assumption that there is no interaction between disk and halo which can transfer angular momentum between the two.

The surface brightness distribution is now determined by the initial distribution of lambda rather than delta, causing a different problem to arise. In fixing the failings of DD with regards to the TF relation, we lose its success in predicting the shift in the correlation function. Simulations show no correlation between spin and environment (e.g., Barnes & Efstathiou 1987). Therefore there should be no shift in the correlation function with surface brightness as is observed. This is as much a problem for the SH picture as the TF relation is for DD. We might or might not be able to fix it (cf. Mihos et al. 1997; Moore et al. 1999), but whatever we come up with is a patch after and against the original fact.

2 Given the emphasis placed on a priori predictions, it is worth noting that the original version of the scenario described by Dalcanton et al. (astro-ph/9503093) predicted a shift in the TF relation with surface brightness. The observed lack of such a shift was reported at about this time. Zero shift is ``predicted'' in the published version.

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