2. Halo models
In Paper I constraints on the halo fraction in clustered and unclustered low-mass stars are derived assuming the stars have zero metallicity and that the halo density varies with Galactocentric cylindrical coordinates () as
where, in Paper I, the local density pc-3, the Solar Galactocentric distance kpc, and the halo core radius kpc.
The assumption of zero metallicity is maintained in the present analysis since one expects the halo to be perhaps the oldest of the Galactic components, and hence its constituents to have more or less primordial metallicity. The expected absolute magnitude in various photometric bands for such stars between the hydrogen-burning limit mass () and has been calculated by Saumon et al. (1994) and their results are employed here as in Paper I.
The model dependency of the conclusions in Paper I is assessed by re-calculating the constraints for a number of different, but plausible, halo models. For ease of comparison the models selected are 5 of the reference halo models used by the MACHO collaboration (Alcock et al. 1996) in its analysis. (MACHO considers a total of 8 Galactic models, though only 5 of the halo models have distinct functional forms.) All halo models assume kpc and kpc. The 5 models are denoted by MACHO as models A-D and S (for `standard'), and this labelling is maintained here.
The standard model S has the same functional form as the halo investigated in Paper I (i.e. it is described by Eq. 1) but uses the slightly larger IAU value for above and assumes a lower local density pc-3. Models A-D are drawn from the self-consistent family of power-law models (Evans 1994), having density profiles
where is the velocity normalisation, q describes the flattening of equipotentials, determines the power-law slope of the density profile at large radii, and and G have their usual meanings. For a flat rotation curve at large radii , where as for a rising curve and for a falling one .
The particular parameters for models A-D, along with those of model S are listed in Table 1. Model A is the closest analogy to model S within the power-law family of models, whilst model B has a rising rotation curve at large radii, model C a falling rotation curve, and model D a flattening equivalent to an E6 halo. When combined with the MACHO canonical Galactic disc (Alcock et al. 1996), the models give values for the local Galactic rotation speed within 15% of the IAU standard value of 220 km s-1 and have rotation curves that are consistent with observations.
Table 1. Parameter values for the 5 MACHO reference halo models A-D and S (Alcock et al. 1996). kpc and kpc is assumed for all models. For models A-D the local density is derived from the parameters in columns 2-4. The local rotation speed is computed from the combined halo and disc mass within .
© European Southern Observatory (ESO) 1997
Online publication: March 24, 1998