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

The Highly Unusual Outgassing of Comet 103P/Hartley 2 from Narrowband Photometry and Imaging of the Coma

We report on photometry and imaging of Comet 103P/Hartley 2 obtained at Lowell Observatory from 1991 through 2011. We acquired photoelectric photometry on two nights in 1991, four nights in 1997/98, and 13 nights in 2010/11. We observed a strong secular decrease in water and all other observed species production in 2010/11 from the 1991 and 1997/98 levels. We see evidence for a strong asymmetry with respect to perihelion in the production rates of our usual bandpasses, with peak production occurring ~10 days post-perihelion and production rates considerably higher post-perihelion. The composition was "typical", in agreement with the findings of other investigators. We obtained imaging on 39 nights from 2010 July until 2011 January. We find that, after accounting for their varying parentage and lifetimes, the C2 and C3 coma morphology resemble the CN morphology we reported previously. These species exhibited an hourglass shape in October and November, and the morphology changed with rotation and evolved over time. The OH and NH coma morphology showed hints of an hourglass shape near the nucleus, but was also enhanced in the anti-sunward hemisphere. This tailward brightness enhancement did not vary significantly with rotation and evolved with the viewing geometry. We conclude that all five gas species likely originate from the same source regions on the nucleus, but that OH and NH were derived from small grains of water and ammonia ice that survived long enough to be affected by radiation pressure and driven in the anti-sunward direction. We detected the faint, sunward facing dust jet reported by other authors, and did not detect a corresponding gas feature. This jet varied little during a night but exhibited some variations from night to night, suggesting it is located near the total angular momentum vector.Comment: Accepted by Icarus; 20 pages of text (preprint style), 5 tables, 7 figure

Model Averaging in Risk Management with an Application to Futures Markets

This paper considers the problem of model uncertainty in the case of multi-asset volatility models and discusses the use of model averaging techniques as a way of dealing with the risk of inadvertently using false models in portfolio management. Evaluation of volatility models is then considered and a simple Value-at-Risk (VaR) diagnostic test is proposed for individual as well as ‘average ’ models. The asymptotic as well as the exact finite-sample distribution of the test statistic, dealing with the possibility of parameter uncertainty, are established. The model averaging idea and the VaR diagnostic tests are illustrated by an application to portfolios of daily returns on six currencies, four equity indices, four ten year government bonds and four commodities over the period 1991-2007. The empirical evidence supports the use of ‘thick’ model averaging strategies over single models or Bayesian type model averaging procedures

The formation of supermassive black holes in rapidly rotating disks

Massive primordial halos exposed to moderate UV backgrounds are the potential birthplaces of supermassive black holes. In such a halo, an initially isothermal collapse will occur, leading to high accretion rates of $\sim0.1$~M$_\odot$~yr$^{-1}$. During the collapse, the gas in the interior will turn into a molecular state, and form an accretion disk due to the conservation of angular momentum. We consider here the structure of such an accretion disk and the role of viscous heating in the presence of high accretion rates for a central star of $10$, $100$ and $10^4$~M$_\odot$. Our results show that the temperature in the disk increases considerably due to viscous heating, leading to a transition from the molecular to the atomic cooling phase. We found that the atomic cooling regime may extend out to several $100$~AU for a $10^4$~M$_\odot$ central star and provides substantial support to stabilize the disk. It therefore favors the formation of a massive central object. The comparison of clump migration and contraction time scales shows that stellar feedback from these clumps may occur during the later stages of the evolution. Overall, viscous heating provides an important pathway to obtain an atomic gas phase within the center of the halo, and helps in the formation of very massive objects. The latter may collapse to form a massive black hole of about $\geq 10^4$~M$_\odot$.Comment: Accepted for publication in Astronomy & Astrophysics, comments are still welcom

The Nucleus of Comet 10P/Tempel 2 in 2013 and Consequences Regarding Its Rotational State: Early Science from the Discovery Channel Telescope

We present new lightcurve measurements of Comet 10P/Tempel 2 carried out with Lowell Observatory's Discovery Channel Telescope in early 2013 when the comet was at aphelion. These data represent some of the first science obtained with this new 4.3-m facility. With Tempel 2 having been observed to exhibit a small but ongoing spin-down in its rotation period for over two decades, our primary goals at this time were two-fold. First, to determine its current rotation period and compare it to that measured shortly after its most recent perihelion passage in 2010, and second, to disentangle the spin-down from synodic effects due to the solar day and the Earth's orbital motion and to determine the sense of rotation, i.e. prograde or retrograde. At our midpoint of 2013 Feb 24, the observed synodic period is 8.948+/-0.001 hr, exactly matching the predicted prograde rotation solution based on 2010 results, and yields a sidereal period of the identical value due to the solar and Earth synodic components just canceling out during the interval of the 2013 observations. The retrograde solution is ruled out because the associated sidereal periods in 2010 and 2013 are quite different even though we know that extremely little outgassing, needed to produce torques, occurred in this interval. With a definitive sense of rotation, the specific amounts of spin-down to the sidereal period could be assessed. The nominal values imply that the rate of spin-down has decreased over time, consistent with the secular drop in water production since 1988. Our data also exhibited an unexpectedly small lightcurve amplitude which appears to be associated with viewing from a large, negative sub-Earth latitude, and a lightcurve shape deviating from a simple sinusoid implying a highly irregularly shaped nucleus.Comment: Accepted by AJ; 12 pages of text (pre-print style), 3 tables, 2 figure

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&