An all-sky sample of essentially all the radio galaxies within 30000 kms⁻¹ down to a
flux-density limit of about 0.5 Jy at 1.4 GHz is assembled from the Parkes, Bologna,
Jodrell Bank and Bonn surveys. The ease and uniformity with which this class of object
can be selected render them as excellent statistical probes of the large-scale structure.
This thesis is concerned with an application of the sample to study clustering and
streaming motions in the universe on 10 - 100h⁻¹ Mpc scales.
The observational database acquired the radio galaxies com prise spectroscopic
redshifts and I band CCD frames, with additional ß frames for a few of the galaxies.
These allow a simple distance indicator relation for the radio galaxies to be derived by
fitting deVaucouleurs empirical r ¹/⁴ law to the azimuthally-averaged surface brightness
profiles of the galaxies. This yields an effective size parameter rₑ and a distanceindependent surface-brightness /x for calibrating the ‘stan d ard ro d s’. In term s of rms
scatte r, the μ-rₑ relation yields relative distance accurate to about 28%. This compares
favourably with other distance indicators which incorporate velocity dispersions, yet it
has the advantage that the photometric parameters μ and rₑ are very straightforward
A useful parameter describing the richness of the environments of radio galaxies
is the amplitude of the spatial cross-correlation function ßgr. Its calculation in the
past has involved using full sets of galaxy counts, notably the Lick counts to do the
cross-correlation. In the absence of such a set of galaxy counts, for declinations south
of -23°, it is shown that the Abell cluster catalogue can be used to obtain a reasonable
estimate of ß₉ᵣ. Considering the all-sky sample as a whole it is found that, on average,
radio galaxies reside in systems of A bell richness R ≃ 0. A search for correlations
between radio luminosity and ß₉ᵣ for the radio galaxies is performed but none are
found. Similarly, no evidence is found for correlations between optical luminosity and
T he 3-d correlation function for radio galaxies is calculated here for the first time.
A strong signal is detected, although not as strong as some reports in the past of the
cluster-cluster correlation function would have suggested. There is no trend for the
clustering signal to show a systematic increase or decrease if radio galaxies in bands
of radio luminosity are considered separately. No evidence is found to support the
claim by Tully that rich clusters are aligned along the supergalactic plane and exhibit
correlated structure on a scale 0.1c.
Peculiar velocities are derived for the radio galaxies using the μ- rₑ relation and
these are analysed in term s of simple dipole and quadrupole models for the motion of
the Local Group. Large error bars on the dipole solution are traced to significant of diagonal elements in the error covariance matrix which tells us how the errors in each
of the 6 free parameters in the non-linear least squares fit of the model to the data are
coupled together. Monte-carlo simulations for an isotropised sky-distribution suggests
that the large errors are a consequence of an anisotropic sky coverage - notably the
sparse number of galaxies that were observed in the southern hemisphere relative to
the north . A different technique for analysing peculiar velocities is to use the velocity
autocorrelation tensor. Improvements are shown to exist over previous calculations -
principally a better weighting function can be computed from the data itself and then
fed iteratively back in to the calculation. These improvements are implemented here,
although the overall effects they make to the solution are slight.
A simple model for biased galaxy formation is considered in which the non-linear
dark matter clumps are identified as sites for galaxy formation and their luminosity is
assumed to be proportional to the product of some power of their mass and a power
of the collapse redshift of the system . The implications of subjecting these systems
to a long-wavelength density perturbation are examined. It turns out that the Faber-Jackson relation for elliptical galaxies should exhibit systematic offsets which correlate
with the richness of their environments. This is a testable prediction. A large sample
of elliptical galaxies with photometric and kinematic data are employed. No systematic
offsets are found for either the Faber-Jackson relation or the Dn - δᵥ relation. Offsets
are shown to exist for systems which typically inhabit extremely poor environments,
such such as spiral bulges, and extremely rich environments such as radio galaxies and
Brightest Cluster Members. Offsets are found and they are in the right sense for them
to be attributed to the operation of bias. However, other more likely explanations
are possible. At face value the data examined here seem to suggest that the distance
indicator relations are effectively unbiased.