We present a new method of analyzing galaxy alignments in clusters originaly proposed by Godowski 2012 and now improved.

The luminosity function is an important quantity for analysis of large scale structure statistics, interpretation of galaxy counts (Lin & Kirshner 1996). We investigate the luminosity function of galaxy clusters. This is performed by counting the brightness of galaxies belonging to clusters in PF Catalogue. The obtained luminosity function is significantly different than that obtained both for optical and radiogalaxies (Machalski & Godowski 2000). The implications of this result for theories of galaxy formation are discussed as well.

Magnetohydrodynamic devices that can accelerate plasmas to speeds of the order of hundreds of kilometres per second have been designed and built for nearly forty years. Up to the time of writing, however, the theory for such devices has been exclusively non-relativistic. In this paper we derive the special relativistic magnetohydrodynamic (SRMHD) equations and use them to obtain the relativistic, magnetic nozzle equation which describes the production of jet flows with speeds approaching the speed of light.We obtain analytic solutions to this equation and show that, in principle, magnetic field gradients can accelerate a plasma to highly relativistic speeds. We also show that the exit kinetic energy, EK, of a particle is given by the equation EK = m0C2FR, where m0 is the rest mass of the particle and CFR is the fast magnetosonic speed at the start of the flow.

The relativistic nozzle differs in a number of ways from the non-relativistic case.A non-relativistic nozzle has a relatively symmetric converging/diverging shape, while a highly relativistic nozzle converges in the usual manner, but diverges, in an abrupt fashion, at the very end of the nozzle. The gentle divergence of non-relativistic nozzles causes the exit plasma densities and magnetic fields of the flow to have values that are small relative to their values at the start of the nozzle. The abrupt divergence of a highly relativistic nozzle implies that, for a less than perfect nozzle, the exit values of the mass density and the magnetic field strength are comparable to their initial values. This unexpected dichotomy in behaviour may have future application in understanding the ‘radio-loud’ and ‘radio-quiet’ relativistic jets that are produced from astrophysical sources.

Alignments in the angular momentum vectors of galaxies can induce large scale correlations in their projected orientations. Such alignments arise from the tidal torques exerted on neighboring protogalaxies by the smoothly varying shear field. Weak gravitational lensing can also induce ellipticity correlations since the images of neighboring galaxies will be distorted coherently by the intervening mass distribution. Comparing these two sources of shape correlations, it is found that for current weak lensing surveys with a median redshift of zm = 1, the intrinsic signal is a contaminant on the order of 1–10% of the measured signal. However, for shallower surveys with zm ≤ 0.3, the intrinsic correlations dominate over the lensing signal. The distortions induced by lensing are curl-free, whereas those resulting from intrinsic alignments are not. This difference can be used to disentangle these two sources of ellipticity correlations. When the distortions are dominated by lensing, as occurs at high redshifts, the decomposition provides a valuable tool for understanding properties of the noise and systematic errors.

We investigate the photographic-magnitude (mp) scale of Volume I of the Catalogue of Galaxies and of Clusters of Galaxies for galaxies in the Virgo direction. It is found that for 11.5 ≤ Bt < 14.5, the mp values listed correspond very closely (with a scatter of only 0.16 magnitude) to blue magnitudes measured to the B = 24.4 isophote. If mp values need to be used as estimates of total blue magnitude the scatter is 0.27 magnitude over the same range in Bt and the mean offset is mp – Bt = 0.28 magnitude. However, a serious scale error at the bright end causes both the isophotal and total luminosities of galaxies brighter than Bt ~ 11.5 to be severely underestimated. At the faint end there also appears to be a significant scale error. This causes galaxy luminosities to be seriously overestimated faintward of Bt ~ 14.5.We demonstrate that this is a real effect based on a detailed galaxy-by-galaxy study of the catalogue’s completeness down to Bt = 17.0. The catalogue is found only to be complete to Bt ~ 14.7 whilst its degree of incompleteness is found to be relatively constant at the 30% level over the range 14.75 ≤ Bt < 15.75. Most of the missing objects are found to be elliptical galaxies and so late-type objects are over-represented at the faint end.

We present evidence for an anti-correlation between faint QSOs and B < 23 galaxies.A sample of 192 QSOs in a 2.5 deg2 area has been imaged using the Isaac Newton Telescope Wide-Field Camera. The cross-correlation signal is of a similar amplitude to the galaxy auto-correlation function at the limit of B < 23, but is negative in sign. As fainter galaxies are selected the negative correlation signal becomes less significant, until the signal is effectively zero at B < 26. We propose two alternate explanations for the observed effect. The first is gravitational lensing of the faint background QSOs, which have a flat number count slope. However, the lensing signal is significantly higher than expected in conventional models. The second possibility is that inter-galactic dust absorption is responsible. A reddening of only E(B - V) ≃ 0.02 is required to produce the observed correlation. The large 2dF and SDSS QSO surveys should allow a definitive solution to the question of QSO–galaxy correlations.

The main objectives of this series of papers are: (1) to demonstrate the existence of serious mutual disagreements between established total (and other integrated) magnitude scales forVirgo galaxies; (2) to attempt to quantify both the systematic and random errors present within these magnitude scales; (3) to investigate the origins of any large error uncovered; and thereby (4) to encourage the general adoption of rigorous total-magnitude measurement procedures by the astronomical community. The ramifications of the findings presented in this series of papers will be discussed in detail at a later date.

In this paper, the first in the series, a self-consistent dataset of trustworthy total-magnitude measurements is compiled for a sample of Virgo galaxies spanning a range of 10 000 in apparent brightness, based on only the most reliable measurements and photometry currently available. This reference dataset, which includes luminosity profile shape information, will be used in subsequent papers as one of the bases for assessing existing magnitude scales forVirgo galaxies. As most published magnitudes are based on B–band observations, this series of papers will also focus primarily on B–bnd measurements.

Recently, the OGLE team have reported a clear quasar microlensing signal in Q2237+0305. I have analyzed the microlens event of ‘image C’ by using their finely and densely sampled light curves. From light curve fitting, I unambiguously set the source size of ≤0.98 Einstein-Ring radius as a conservative limit. This limit corresponds to 2000 AU, if I adopt Mlens ~ 0.1M obtained by a recent statistical study of the mean mass of the lens object. This gives clear evidence for the existence of an accretion disk in the central region of the quasar.