**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 *R _{h}*.
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 *R _{h}*, 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 , the scale length of the luminous
disk is

The surface brightness distribution is now determined by the initial
distribution of rather than
, 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.