The extreme infrared luminosities of some Seyfert galaxies place severe requirements on the efficiency of the energy source. It is attractive to suggest that matter-antimatter annihilation supplies the necessary energy source; efficiencies of up to ∼50% are, in principle, obtainable. However, there is a price to pay for such an explanation: gamma rays and neutrinos.

In a typical nucleon-antinucleon annihilation roughly ⅓ Mc2 is released in electron-positron pairs, ∼⅔ Mc2 in ∼3 gamma rays and ∼Mc2 in ∼3 electron-neutrinos and ∼6 muon-neutrinos. As a result, if the observed infra-red power is to be derived from the energy in electron-positron pairs, then the flux of gamma rays would be 102-103 times the upper limits to the gamma ray flux. It is, of course, possible to account for the absence of the gamma rays by insisting that they be absorbed in the source. The neutrinos, however, will not be stopped and hence provide the possibility of testing the annihilation hypothesis.

We have computed the spectrum of neutrinos produced in annihilation. Assuming the product of the space density and infrared luminosity of Seyfert galaxies varies with redshift (z) as: L (z) n (z) = L0n0 (1 + z)m we have computed the flux of μ-neutrinos contributed by all Seyfert galaxies out to a given red-shift for m = 3 and m = 6.5 (strong evolution). Further, assuming the “3K” and “0.3 mm” background radiation fields to be caused by a burst of “Seyfert type” objects at appropriate redshifts, we have again computed the expected μ-neutrino flux. When these results are compared with present limits on the flux of μ-neutrinos at the Earth, as determined from experiments performed by several groups deep underground, it emerges that the predicted flux is comparable to or greater than present upper limits. Thus, annihilation probably does not supply the infrared sources in Seyfert galaxies with the energy they require.

The explosive events going on in the central parts of some galaxies are related to a very high mass concentration. As an explosion is actually a drastic rearrangement of the concerned masses with energy release, the binding energy of the central core will change and, correspondingly, its effective gravitational mass. A test particle far from the nuclear region, although within the galaxy, will be moving accordingly in a variable-mass Newtonian gravitational field.

On the other hand the observations suggest that explosions in galaxies have axial symmetry, so we are concerned with the global properties of the motion of a particle in a variable mass axisymmetric gravitational field. In order to get rid of the mass variation a space-time conformal transformation is made, which, after imposing some not very restrictive conditions, leads to a conservative potential in the new variables. This new potential has additional terms due to the elimination of the variable mass. The equations of motion in the new variables provide the motion of the test particle relative to an expanding or contracting background which depends on the choice of the transformation and the law of the mass variability. The problem is, at this point, formally similar to Hill's. It is possible to write an equation for the relative energy (a generalization of Jacobi's integral) and also to define surfaces of zero relative velocity for the infinitesimal particle. The general topological properties of these surfaces require singular points along the symmetry axis (analogous to the collinear Eulerian points) and also a dense set in a circumference on a plane perpendicular to the symmetry axis (analogous to the Lagrangian points). The latter one is the main feature characterizing the topology of the zero relative velocity surfaces. Even when we lift some of the restrictive conditions, the Lagrangian ring preserves its properties, as for example, the one of being the only region where zero-velocity curves and equi-potentials coincide when the configuration evolves in time (in the transformed space-time).

It is easy to understand that the topology of the surfaces is kept when we reverse the transformation and go back to physical space-time. If the dust, gas or stars in the system has definite upper limits for its Jacobian constants, spatial segregation of them will arise, as is the case in radio-galaxies such as NGC 5128, NGC 1316, etc. where ringlike dust structures are observed.

An account is given of recent developments in the derivation of the value of the Hubble parameter applicable to regions beyond the local anisotropy. Recent observations relevant to interpretations of the magnitude-redshift diagram for cluster galaxies are discussed, in an attempt to assess uncertainties in the value of the deceleration parameter.

The use of the brightest members of galaxy clusters as distance indicators is questioned because of a possible correlation between the absolute magnitude of the brightest galaxy and the richness of the cluster. Comparison of the clusters' luminosity functions is considered to be more appropriate. The difference between the two approaches is substantial when a comparison is made between the Coma and Virgo clusters. The value of the Hubble parameter may well be less than 50 km s−1 Mpc−1.

The distances of about 100 nearby groups, clouds and clusters of galaxies (δ < 52 Mpc) have been derived from the apparent magnitudes and diameters of the 3 to 5 major members. The linearity of the distance scale was verified for δ < 40 Mpc by comparison with luminosity classifications and diameters of ring structures. The velocity-distance relation of these groups is apparently non-linear for δ < 30 Mpc. The velocity/distance ratio increases from H ≃ 50 to 150 km s−1 Mpc−1 when δ increases from δ ≃ 5 to δ ≃ 25 Mpc. Such local departures from linearity are predicted in condensed regions of an inhomogeneous ‘big bang’ hierarchical model obeying the universal density-radius relation. The galactic apex varies with the apparent magnitude of galaxies used for reference in a manner generally consistent with a model of the Local Supercluster in differential rotation and expansion. The best-fit rotation-expansion constants are ω1R1 = 400 ± 50 km s−1, ε1R1 = 1250 ± 50 km s−1, ż = −250 ± 50 km s−1. The velocity-magnitude relation corrected for solar motion is linear with slope 0.2 in 9 < m < 14, confirming that apart from local departures reflecting the supercluster kinematics the underlying Hubble flow is linear and isotropic. If the distance modulus of the Virgo Cluster is (m - M)0 = 30.5 ± 0.2 the Hubble constant derived from the survey of groups is H0 = (100 ± 10) km s−1 Mpc−1.

An evolutionary sequence is suggested for Virgo cluster galaxies, in a radial velocity-nuclear magnitude diagram. This evolution, on a time scale of about 108 yr, is discussed in terms of the morphology and radial color variations of the galaxies, nuclear size and radio emission. An area scan and profiles of nuclei, obtained with image dissector equipment, are presented.

Radial velocity determinations for galaxies in the vicinity of NGC 7331, including the members of ‘Stephan's Quintet’, show clearly a superposition of at least two distinct physical systems. One includes NGC 7331, NGC 7320 (a Quintet member), and NGC 7343, while the other - seven or eight times more distant - contains the four remaining ‘Quintet’ constituents and six of the seven optical ‘companions’ of NGC 7331.

Recent observational evidence is discussed, showing that (1) Galaxies eject matter; (2) Ejection of matter tends to take place in approximately opposite directions; (3) When the ejected matter is in the form of a smaller, companion galaxy, that galaxy tends to have a relatively high surface brightness and small diameter; and (4) Compact companion galaxies generally have higher redshifts than the galaxies from which they were ejected.

An observational investigation of the angular diameter-redshift relation for galaxies is described, using results from a ‘photographic galaxy synthesizer’. The observations give a value q0 = + 0.3 for the deceleration parameter.

In this paper, we compare the magnitude-redshift data for brightest cluster galaxies with cosmological models of general relativity, including non-zero cosmological constant. Our study is parallel to that by Peach (1970). We use the same data but an independent method, and obtain somewhat different results. We also consider possible effects of evolution.

I shall report the result of a combined cosmological test, including both galaxies in clusters and blue objects of different types. The test is performed on uniform models and the result is a high density, ever expanding model.

The present short notes on cosmology start with two conclusions based on observational data. The first of them is the well-known conclusion that the Universe from the global point of view is at the present epoch of its evolution in a uniform and isotropic expansion. If we accept the very convincing arguments of Bondi (1962) that the geometry of the cosmic space is Riemannian, its properties are described at the present epoch of the cosmic evolution by the well-known Robertson-Walker metric expressing the cosmological principle (Robertson, 1935, 1936; Walker, 1936). The form of the geodesical lines depends on the assumed theory of gravitation. For instance, in the closed Friedman world model they are cycloids with a singularity at the start of the expansion.

Cosmological evidence provided by counts of radio and optical objects, and additional evidence yielded by QSO redshifts, are discussed. The nature of the QSO redshifts is considered, as are the evolutionary properties of these and other objects, and possibly important cosmological investigations using QSOs and radio sources are mentioned.

The number-flux density relation for radio sources selected at 1400 MHz is discussed, the exponent of the counts being given for two flux density ranges. The accuracy of the exponents is limited only by the statistical size of the sample. The completeness of the catalogue is estimated. Results are compared with other flux density measurements.

The results of a survey of selected regions of sky made at a frequency of 5 GHz, and of measurements of the spectral index distributions for sources selected from low frequency surveys are presented. The source counts and spectral distribution at 5 GHz are in excellent agreement with those expected from surveys made at lower frequencies. There is no significant dependence of the spectral distribution on flux density in any of the surveys we have investigated, implying either a low redshift for the sources, or a systematic change in their properties with redshift.

Counts of quasi-stellar objects selected by their optical properties imply evolutionary properties similar to those found by examining the radio-selected objects. The optical luminosity functions of the 3CR and optically-selected quasi-stellar objects are compared. Data on the radio emission and optical variability of the optically-selected sample are presented.

A review is given of the cosmological implications of radio source-counts.

The evolution of QSOs and the reality of their apparent cutoff for z > 2.3 is determined using their large scale redshift distribution. The contributions of QSRs to radio source counts are calculated on the basis of possible evolution of QSOs having z > 2.2.

(Abstract of a paper by M. S. Longair and P. A. G. Scheuer (1971))

It is assumed that the QSOs are at cosmological distances as indicated by their emission-line redshifts. It is further assumed, as indicated by present evidence, that none of the 21 QSOs with emission-line redshifts, ze, of 2.0 ± 0.1 (or of the 30 with ze = 2.0 ± 0.2) is screened by an intervening normal galaxy. The simplest conclusion from these data is, then, that the screening probability must be less than 0.08 (or 0.06) at ze = 2.0. This, in turn, restricts allowable cosmological models in the (σ0, q0) diagram by providing lower limits for ß0 as a function of q0. One can also rank cosmological models in order of the probability that there be no screening of the 21 (or 30) objects. In either case the steady state model ranks higher than the general relativity models found by Peach to give the best fit in the (m – z) diagram.