Bifurcations in the Space of Exponential Maps

This article investigates the parameter space of the exponential family $z\mapsto \exp(z)+\kappa$. We prove that the boundary (in \C) of every hyperbolic component is a Jordan arc, as conjectured by Eremenko and Lyubich as well as Baker and Rippon. In fact, we prove the stronger statement that the exponential bifurcation locus is connected in \C, which is an analog of Douady and Hubbard's celebrated theorem that the Mandelbrot set is connected. We show furthermore that $\infty$ is not accessible through any nonhyperbolic ("queer") stable component. The main part of the argument consists of demonstrating a general "Squeezing Lemma", which controls the structure of parameter space near infinity. We also prove a second conjecture of Eremenko and Lyubich concerning bifurcation trees of hyperbolic components.Comment: 29 pages, 3 figures. The main change in the new version is the introduction of Theorem 1.1 on the connectivity of the bifurcation locus, which follows from the results of the original version but was not explicitly stated. Also, some small revisions have been made and references update

Interagency report - Astrogeology 18. A proposed scheme for lunar geologic description

Method for lunar geologic descriptio

The Applegate mechanism in Post-Common-Envelope Binaries: Investigating the role of rotation

Eclipsing time variations (ETVs) are observed in many close binary systems. In particular, for several post-common-envelope binaries (PCEBs) that consist of a white dwarf and a main sequence star, the O-C diagram suggests that real or apparent orbital period variations are driven by Jupiter-mass planets or as a result of magnetic activity, the so-called Applegate mechanism. The latter explains orbital period variations as a result of changes in the stellar quadrupole moment due to magnetic activity. We explore the feasibility of driving ETVs via the Applegate mechanism for a sample of PCEB systems, including a range of different rotations. Using the MESA code we evolve 12 stars with different masses and rotation rates. We apply a simple dynamo model to their radial profiles to investigate on which scale the predicted activity cycle matches the observed modulation period, and quantify the uncertainty, and further calculate the required energies to drive que Applegate mechanism. We show that the Applegate mechanism is energetically feasible in 5 PCEB systems, and note that these are the systems with the highest rotation rate compared to the critical rotation rate of the main-sequence star. The results suggest that the ratio of physical to critical rotation in the main sequence star is an important indicator for the feasibility of Applegate's mechanism, but exploring larger samples will be necessary to probe this hypothesis.Comment: 9 pages, 5 figures. Accepted for publication in A&

A high resolution solar atlas for fluorescence calculations

The characteristics required of a solar atlas to be used for studying the fluorescence process in comets are examined. Several sources of low resolution data were combined to provide an absolutely calibrated spectrum from 2250 A to 7000A. Three different sources of high resolution data were also used to cover this same spectral range. The low resolution data were then used to put each high resolution spectrum on an absolute scale. The three high resolution spectra were then combined in their overlap regions to produce a single, absolutely calibrated high resolution spectrum over the entire spectral range

The physics of the Applegate mechanism: Eclipsing time variations from magnetic activity

Since its proposal in 1992, the Applegate mechanism has been discussed as a potential intrinsical mechanism to explain transit timing variations in various kinds of close binary systems. Most analytical arguments presented so far focused on the energetic feasibility of the mechanism, while applying rather crude one- or two-zone prescriptions to describe the exchange of angular momentum within the star. In this paper, we present the most detailed approach to date to describe the physics giving rise to the modulation period from kinetic and magnetic fluctuations. Assuming moderate levels of stellar parameter fluctuations, we find that the resulting binary period variations are one or two orders of magnitude lower than the observed values in RS-CVn like systems, supporting the conclusion of existing theoretical work that the Applegate mechanism may not suffice to produce the observed variations in these systems. The most promising Applegate candidates are low-mass post-common-envelope binaries (PCEBs) with binary separations $\lesssim 1~\mathrm{R}_\odot$ and secondary masses in the range of $0.30~\mathrm{M}_\odot$ and $0.36~\mathrm{M}_\odot$.Comment: 10 pages, 8 figures. Accepted for publication in A&

Low-metallicity star formation: Relative impact of metals and magnetic fields

Low-metallicity star formation poses a central problem of cosmology, as it determines the characteristic mass scale and distribution for the first and second generations of stars forming in our Universe. Here, we present a comprehensive investigation assessing the relative impact of metals and magnetic fields, which may both be present during low-metallicity star formation. We show that the presence of magnetic fields generated via the small-scale dynamo stabilises the protostellar disc and provides some degree of support against fragmentation. In the absence of magnetic fields, the fragmentation timescale in our model decreases by a factor of ~10 at the transition from Z=0 to Z>0, with subsequently only a weak dependence on metallicity. Similarly, the accretion timescale of the cluster is set by the large-scale dynamics rather than the local thermodynamics. In the presence of magnetic fields, the primordial disc can become completely stable, therefore forming only one central fragment. At Z>0, the number of fragments is somewhat reduced in the presence of magnetic fields, though the shape of the mass spectrum is not strongly affected in the limits of the statistical uncertainties. The fragmentation timescale, however, increases by roughly a factor of 3 in the presence of magnetic fields. Indeed, our results indicate comparable fragmentation timescales in primordial runs without magnetic fields and Z>0 runs with magnetic fields.Comment: MNRAS in pres