3.3. Physics of the LSP ?

The LSP may have the potential to connect key observables (luminosity and size) to the fundamental underlying physical properties of bulge and disk systems (mass and angular momentum). In various studies of the formation of disk systems, (e.g., Fall & Efstathiou 1980, Dalcanton et al. 1997, Mo et al. 1998) the dimensionless spin parameter ( = J | E^1/2| G^-1 M_halo^-5/2, Peebles 1969) is directly related to the scale-length of the disk. The spin parameter reflects how close the halo is to a rotationally supported system and is a key parameter monitored by the numerical simulations (see Steinmetz & Bartelmann 1995; Cole & Lacey 1996; Vitvitska et al. 2002; Maller, Dekel & Sommerville 2002 for example). The pivotal idea (here echoing the toy model of de Jong & Lacey 2000) starts with the premise that the baryons are coupled to the dark matter halo, because of this the luminosity (generated by the baryons in the form of stars) can be related to the systemic mass and the rotation of the stars/gas can be related to the systemic angular momentum. Given this premise, which is intimated by the Tully-Fisher relation, one can analytically relate to luminosity and surface brightness (or size): _eff^-1/2 L^{-/3 + 1/2} (from de Jong & Lacey 2000), where _eff is the effective surface brightness, L is the intrinsic luminosity in some filter and is the dependence of luminosity on the mass-to-light ratio (equal to 0.69 in B or 1.00 in H Gavazzi, Pierrini & Boselli 1996). Numerical simulations consistently find that the distribution of the spin parameter is a log Normal distribution which is globally preserved through hierarchical merging (see for example Vitvitska et al. 2002) this yields: _eff = L_B^0.54 or µ_eff = 0.54 M_B. Hence the gradient of any luminosity-surface brightness relation bears upon the relation between mass and light and the dispersion upon the breadth of the spin distribution. Fig. 7 shows the B-band LSP for a variety of samples as indicated (LG, Mateo 1998; HDF, Driver 1999; MGC, Driver et al. 2004; MW GCs, Harris et al. (priv. comm); Local Sphere of Influence, Jerjen, Binggeli & Freeman 2000; LSBGs, de Blok, van der Hulst & Bothun 1995). The solid lines show the approximate expectation as argued above and show remarkable agreement with the data - in detail the observed size distribution is marginally narrower than simulations predict (see Driver et al. 2004). It is also worth noting that systems which form via merging (i.e., bulges) and via accretion (i.e., disks) are also predicted to show distinct distributions (see for example Vitvitska et al. 2002; Maller et al. 2002). At the moment far more data and detailed simulations are required however this connection is clearly promising and could ultimately result in a galaxy equivalent to the Hertzsprung-Russell diagram, allowing a meeting ground between numerical simulations and survey observations.

Figure 7. A summary of available LSP data drawn from a variety of sources. The red line marks the credibly mapped area and the cyan line shows the expectation from de Jong & Lacey (2000). This appears to follow the data remarkably well.