Searching for Planetary Eclipses in Open Clusters: NGC 7086

In an attempt to discover planetary eclipses, we observed the open cluster NGC 7086. On one night we observed the cluster and standard stars through the B and V filters, enabling us to make a colour-magnitude diagram. Plots of the differential magnitudes were inspected for variability, but no planetary eclipses were found. New variable stars were discovered and their light curves show some of them to be eclipsing binary stars. The location on the colour-magnitude diagram of some of the variable stars is consistent with cluster membership.     

Swimming with…Devonian fish

Armoured jawless fish, or 'ostracoderms', lived 450–360 million years ago, and display unusual morphologies, unlike any modern fish group. Since they left no living descendants, their mode of swimming has, until recently, remained speculative, although this is a crucial question as the first true pectoral fins evolved within the 'ostracoderms'. The discovery of the oldest-known fish trails, from the Early Devonian (400 million year old) 'Lower Old Red Sandstone' of south-east Wales offers new insights into the swimming behaviour of these early fish, notably the osteostracan 'ostracoderms' (or cephalaspids), whose horseshoe-shaped head and paddle-shaped pectoral fins have remained a functional riddle.     

A model of an exploding,radiating star in general relativity

In a previous paper Adams, Cary and Cohen (1994) presented a model of a supernova. In that paper the equations of General Relativity describing the evolution of a spherically symmetric, radiating star were solved analytically. The evolution of the star was determined by the application of boundary conditions at the center and at the edge. Due to lmitations in the presupernova model, only the very slow inward motion of an unstable, degenerate core could be considered. The solution was also limited by the need to exclude a runaway term, one that increased exponentially with time. Without the exclusion of the runaway, the luminosity would have increased without bound and the mass would have become negative.This paper presents a completely analytic solution to the equations of General Relativity describing the evolution of a Type II supernova. Professor S.E. Woosley kindly gave us data on the physical variables of a 12M ₀ presupernova star. In our model the core collapses within 1 s, leaving a 1.3M ₀ remnant. Shortly afterward 10.6M ₀ is ejected to infinity, and 0.17M ₀ is radiated away in the form of neutrinos. The distance of the edge from the center increases proportionally to the two-thirds power of the time. The luminosity decreases proportionally to the inverse four-thirds power.Although the runaway solution was modified by the exploding rather than a static envelope, it must still be excluded by adjusting initial conditions. Its character is changed from an exponential to a very large power (55) of time. The removal of a degree of freedom by this exclusion leads to physically non-sensical results such as negative luminosity. The inclusion of a term describing motion of the mantle due to neutrino interactions provides the additional degree of freedom necessary for physically reasonable results.     

Non-radial stellar oscillations: a perspective from potential scattering (I)

This article is the first in a series designed to gain insight into the stellar oscillation problem from a somewhat novel point of view: that of potential scattering, well-known in the quantum mechanical literature. In this paper the known theoretical foundations are developed and applied in the context of the astrophysical problem, wherein the star itself (rather than any portion of it) is the potential which scatters waves and traps them. The basis for the identification of a precisely defined scattering problem is the existence of a linear Schrödinger equation associated both globally (Section 2) and locally (Section 8) with the nonlinear eigenvalue equation for nonradial stellar pulsations. The paper is also designed to be a fairly complete account of the relevant mathematical topics that are germane to a study of this kind. This paper is dedicated to the memory of Professor Zdenèk Kopal, who was a great source of professional encouragement to me during the last fifteen years of his life.