On the coplanar eccentric non-restricted co-orbital dynamics

We study the phase space of eccentric coplanar co-orbitals in the non-restricted case. Departing from the quasi-circular case, we describe the evolution of the phase space as the eccentricities increase. We find that over a given value of the eccentricity, around 0.5 for equal mass co-orbitals, important topological changes occur in the phase space. These changes lead to the emergence of new co-orbital configurations and open a continuous path between the previously distinct trojan domains near the L_4 and L_5 eccentric Lagrangian equilibria. These topological changes are shown to be linked with the reconnection of families of quasi-periodic orbits of non-maximal dimension.publishe

Shedding Light on the Galaxy Luminosity Function

From as early as the 1930s, astronomers have tried to quantify the statistical nature of the evolution and large-scale structure of galaxies by studying their luminosity distribution as a function of redshift - known as the galaxy luminosity function (LF). Accurately constructing the LF remains a popular and yet tricky pursuit in modern observational cosmology where the presence of observational selection effects due to e.g. detection thresholds in apparent magnitude, colour, surface brightness or some combination thereof can render any given galaxy survey incomplete and thus introduce bias into the LF. Over the last seventy years there have been numerous sophisticated statistical approaches devised to tackle these issues; all have advantages -- but not one is perfect. This review takes a broad historical look at the key statistical tools that have been developed over this period, discussing their relative merits and highlighting any significant extensions and modifications. In addition, the more generalised methods that have emerged within the last few years are examined. These methods propose a more rigorous statistical framework within which to determine the LF compared to some of the more traditional methods. I also look at how photometric redshift estimations are being incorporated into the LF methodology as well as considering the construction of bivariate LFs. Finally, I review the ongoing development of completeness estimators which test some of the fundamental assumptions going into LF estimators and can be powerful probes of any residual systematic effects inherent magnitude-redshift data.Comment: 95 pages, 23 figures, 3 tables. Now published in The Astronomy & Astrophysics Review. This version: bring in line with A&AR format requirements, also minor typo corrections made, additional citations and higher rez images adde

Relativistic Fractal Cosmologies

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