David F. Crawford

Maximum-likelihood estimation of the number-flux-density distribution of radio sources in the presence of noise and confusion

The application of the method of maximum likelinood to the determination of the slope of the number- flux-density relationship is extended to include the presence of experimental errors in the flux-density measurements. It is shown that these experimental errors have a significant effect on the number counts at higher natios of flux density to error than is often recognized. The case of noise-limited fiux-density measurements is treated in some detail, and it is found that, provided the lower limit of a survey is chosen to be at least five times the rms noise, the enhancement in the source density as a function of fiux density can be readily calculated. For the case of significart confusion errors in the flux-density measurements the importance of a Monte Carlo approach is emphasized. Several methods that have been used previously are discussed and a number of shortcomings noted. (auth)

RADIO SUPERNOVA 1987A AT 843 MHz

We report here the —ux densities of the evolving radio source SN 1987A at 843 MHz measured from observations made with the Molonglo Observatory Synthesis Telescope between 1994 September and 2000 May. The radio light curve shows that the rate of increase of the —ux density jumped markedly around days 2800¨3000 (i.e., in the —rst half of 1995) and that since then the radio evolution has been remarkably well —tted by a simple linear increase of 62.7 ^ 0.5 kJy day~1. We discuss in detail the relationship between the radio light curve and the recent brightening of the system at optical wavelengths.

Curvature pressure in a cosmology with a tired-light redshift

A hypothesis is presented that electromagnetic forces that prevent ions from following geodesics result in a curvature pressure that is very important in astrophysics. It may partly explain the solar neutrino deficiency and it may be the engine that drives astrophysical jets. However, the most important consequence is that, under general relativity without a cosmological constant, it leads to a static and stable cosmology. Combining an earlier hypothesis of a gravitational interaction of photons and particles with curved spacetime, a static cosmology is developed that predicts a Hubble constant of H = 60 . 2 km s− 1 Mpc− 1 and a microwave background radiation with a temperature of 3 . 0 K. The background X-ray radiation is explained, and observations of the quasar luminosity function and the angular distribution of radio sources have a better fit with this cosmology than they do with standard big-bang models. Although recent results (Pahre et al . 1996) for the Tolman surface brightness test favour the standard big-bang cosmology, they are not completely inconsistent with a static tired-light model. Most observations that imply the existence of dark matter measure redshift, interpret them as velocities, and invoke the virial theorem to predict masses that are much greater than those deduced from luminosities. If, however, most of these redshifts are due to the gravitational interaction in intervening clouds, no dark matter is required. Observations of quasar absorption lines, a microwave background temperature at a redshift of z = 1 . 9731, type 1a supernovae light curves and the Butcher–Oemler effect are discussed. The evidence is not strong enough to completely eliminate a non-evolving cosmology. The result is a static and stable cosmological model that agrees with most of the current observations.

The quasar distribution in a static universe

A crucial test of any cosmological model is the distribution of distant objects such as quasars. Because of well defined selection criteria quasars found by a ultraviolet excess (UVX) survey are ideal candidates for testing the model out to a redshift of z = 2.2. The static cosmology proposed by Crawford (1993) is used to analyse a recent quasar survey (BOYLE et al MNRAS 227, 717 1990). It is shown that the distribution of number of quasars from the survey as a function of redshift is in excellent agreement with the predictions of the model. A V/V_m test on 351 confirmed quasars with defined redshifts has a mean value of 0.568\pm 0.015 with the discrepancy being most likely due to incompleteness of the catalogue at low redshifts. For the redshift range

A static stable universe

1.5 < z < 2.2

Angular Size in a Static Universe

where the accuracy of the cosmological model is critical V/V_m was 0.51 \pm 0.02. A well defined quasar luminosity function is derived that has a peak at M_B = -21.16 mag and is well fitted by a Gaussian distribution in absolute magnitude with a standard deviation of 1.52 magnitudes.

The Molonglo Reference Catalogue of Radio Sources

A static and stable solution to a Newtonian cosmological model is described where the centripetal acceleration of high-temperature particles moving in a three-sphere embedded in a four-dimensional Euclidian space balances the gravitational acceleration. This model is used to show a possible deficiency in the equations of general relativity in that the Newtonian model contains a term corresponding to centripetal accelerations that is not present in Friedmanns equations. Together with a gravitational interaction that can explain the Hubble redshift it provides a viable cosmological model

MAXIMUM-LIKELIHOOD ESTIMATION OF THE SLOPE FROM NUMBER-FLUX-DENSITY COUNTS OF RADIO SOURCES.

In principle the geometry of the universe can be investigated by measuring the angular size of known objects as a function of distance. Thus the distribution of angular sizes provides a critical test of the stable and static model of the universe described by Crawford (1991,1993) that has a simple and explicit relationship between the angular size of an object and its redshift. The result is that the agreement with observations of galactic diameters and the size of double radio sources with the static model is much better than the standard (Big Bang) theory without evolution. However there is still a small discrepancy at large redshifts that could be due to selection effects.