The system of mass tracers applied in this section is given in Table 5.4. The system is based on the one used by P-96, with the following exceptions. Dwarf galaxies closer to the MW/M31 galaxy pair than 500 kpc are not considered due to the considerable increase in non-linear behavior. This results in the omission of Fornax, Leo I, and Leo II compared with Table 1 in Peebles' paper. The number of LG galaxies is then five, assuming the membership criteria to the LG proposed by Bergh.
In the outer fringes of the LG, i.e. the LN, there have in the last few years been discoveries of galaxies of rather substantial sizes, which, most probably, had an effect on the dynamical evolution of our immediate galactic neighbourhood. Two of these ``new'' galaxies have been included here: Antlia and Dwingeloo 1. Antlia was discovered as a galaxy by Whit, after an inspection of the UK Schmidt Telescope plates covering the entire southern sky. A closer observation by these authors revealed the galaxy completely, resolving it into stars. This dwarf spheroidal is positioned close to NGC 3109, at least going by the projection on the sky. The distance estimate given by Apar, 1.32 Mpc, indicates that Antlia may not only be visually close to NGC 3109, but even gravitationally bound to it. The reason for including the Antlia in these calculations is precisely to try to determine the relationship between these two dwarf galaxies. Antlia will most probably have no effect on the evolution of the rest of the galaxies in the system due to its small size, with the possible exception of NGC 3109. But, on the other hand, the inclusion of a galaxy that is so close to another mass tracer, may result in an increase of possible solutions for the system. This, and the possible companionship between the Antlia and the NGC 3109 galaxy, will be discussed in Subsection 5.4.3.
Dwingeloo 1 (Dw1 hereafter) may, contrary to the Antlia galaxy, very well had a substantial influence on the dynamical evolution of the LG and the LN. It was discovered independently by Kra and
Table: A system of 22 galaxies in the the LG and the LN. The columns
are: (1) name, (2,3) galactic coordinates (1950), (4) distance from the MW, (5) mass
relative to the mass of M31, (6) mass when the mass of M31 is 
, (7) observed radial velocities referred to the MW, (8) radial velocities given
by one solution to the AVP given in Figure 5.4(a) and 5.5(a), and (9)
adjusted distances from the MW (Subsection 5.4.3).
[referred to as Cas 2]Huch in the zone of avoidance (ZOA); i.e. behind
the disk of the MW. Apart from the celestial coordinates, little definite is known about
this galaxy. It is thought to be a rather large barred spiral at a distance roughly
estimated to be 
Mpc Phil, which most likely makes it a member of the IC
342/Maffei group. The size of the galaxy is probably comparable to Maffei 1 and IC
342--these three galaxies are therefore here given the same mass, namely 
.
Several other galaxies have later been discovered in the ZOA, but are of such
insignificant size that they will not be considered here.
The system has, compared to [Peebles1996], not only been extended by recently discovered galaxies. In order to get a substantial number of dimensions to test the optimizing methods for, the system was also enlarged by five previously well known mass tracers. The Sculptor group was broken up into separate galaxies, NGC 253, NGC 247, and NGC 7793; and the NGC 45 galaxy was added together with the NGC 5326 and M101 groups. The distance to the Sculptor galaxies and NGC 45 were taken from the paper by Pu, while the distance to the M101 and NGC 5326 group, or rather, the distance to NGC 5326 itself, were taken from the papers by Stet and Schm, respectively. The complete set of distances to the mass tracers is given in column (4) of Table 5.4.
The radial velocities of most of these additional galaxies and groups are taken from the publications by Kara and KM, where the groups M101 and NGC 5326 are given a collective flow based on the radial velocity of their constituents. KM gave the radial velocities in the heliocentric reference system, and we therefore have to correct for the rotation of our galaxy, using the following formula:
(cf. equation (8) in Kara). NGC 7793 and NGC 45 were not included by either Kara or KM, so the radial velocities given by Pu were used. The radial velocities are given in column (7) of Table 5.4.
The masses of the Sculptor galaxies and NGC 45 were determined by comparing the mass given to the Sculptor group by [Peebles1996] with their relative masses given by Pu. The masses of the groups M101 and NGC 5326 were determined in a similar way, by comparing the mass given to the Centaurus group by [Peebles1996] with the mass given to these two groups by Kara. The resulting scaled mass estimates are given in column (5) of Table 5.4.
The mass of the system is determined in a somewhat different manner here than previously.
Rather than determining it from reaching the observed radial velocity of M31 of -123 km
s 
, it is decided by getting the best overall fit of the resultant model
velocities to the observed values for the four neighbouring galaxies in the LG
(Table 5.4). The reason for this is the poor quality of the input data,
especially the rather rough mass and distance estimates of most of the mass tracers in
the LN. An accurate adjustment of the mass to fit the observed radial velocity of M31
would be at the cost of the accuracy of the radial velocity of the more distant galaxies.
In Subsection 5.4.3, the distances to these outlying galaxies will be adjusted
to get a better fit to the observed radial velocities, but for the time being, the
distances given in column (4) of Table 5.4 applies. With this system, the best
fit was reached by giving M31 a mass of 
. The
resulting mass of each galaxy is given in column (6) of Table 5.4. But, this
mass estimate does not give the best fit for all the different solutions of the
action; it gives best fit on average for several solutions, located from a hundred
different starting points.
Having determined the system of mass tracers, we need to decide on the cosmological
model. As mentioned earlier, AVP is based on the assumption that galaxies trace mass,
which, from dynamical observations clearly puts the density parameter 
well
below the Einstein-de Sitter value Pad. The most common value used in treaties
concerning the AVP is 
, which also will be applied here. There have been
some discussions about this ruling out of the Einstein-de Sitter model and closed models.
P-90,P-95 showed that the Einstein-de Sitter model results in the LG being a
local void, which is contradictory to observations. B-C and D-L95 on the
other hand, argued against this exclusions of the Einstein-de Sitter universe based on
results from CDM N-body simulations. More on this dispute in the next chapter.
A density parameter being less than unity usually implies that the space is curved. This
can be avoided by having a cosmological constant, making the universe flat. A large
cosmological constant, 
, has here been preferred over space
curvature, a model which is being supported by recent observations of high-redshift
supernovas by the Supernova Cosmology Project SCP.
The next parameter to be determined is the age of the universe, or more correctly, the Hubble age. Here, as in most of the treaties concerning the AVP, h=0.75 has been used, resulting in an age of the model universe of about 17 billion years.
In addition to the enlargement of the mass tracer system in order to get a large number
of dimensions, the number of parameterizations in the orbits (3.21) was
increased to N=10. The resulting number of unknown coefficients is then 660. Other
parameters needed by the calculations were chosen as follows: The cutoff 
,
the termination 
, and the number of abscissas in the
integration (4.3) was n=15. The trial functions from (3.23) were
used.
