An Analysis of Jitter and Transit Timing Variations in the HAT-P-13 System

If the two planets in the HAT-P-13 system are coplanar, the orbital states provide a probe of the internal planetary structure. Previous analyses of radial velocity and transit timing data of the system suggested that the observational constraints on the orbital states were rather small. We reanalyze the available data, treating the jitter as an unknown MCMC parameter, and find that a wide range of jitter values are plausible, hence the system parameters are less well constrained than previously suggested. For slightly increased levels of jitter ($\sim 4.5\,m\,s^{-1}$) the eccentricity of the inner planet can be in the range $0<e_{inner}<0.07$, the period and eccentricity of the outer planet can be $440<P_{outer}<470$ days and $0.55<e_{outer}<0.85$ respectively, while the relative pericenter alignment, $\eta$, of the planets can take essentially any value $-180^{\circ}<\eta<+180^{\circ}$. It is therefore difficult to determine whether $e_{inner}$ and $\eta$ have evolved to a fixed-point state or a limit cycle, or to use $e_{inner}$ to probe the internal planetary structure. We perform various transit timing variation (TTV) analyses, demonstrating that current constraints merely restrict $e_{outer}<0.85$, and rule out relative planetary inclinations within $\sim 2^{\circ}$ of $i_{rel}=90^{\circ}$, but that future observations could significantly tighten the restriction on both these parameters. We demonstrate that TTV profiles can readily distinguish the theoretically favored inclinations of i_{rel}=0^{\circ}\,&\,45^{\circ}, provided that sufficiently precise and frequent transit timing observations of HAT-P-13b can be made close to the pericenter passage of HAT-P-13c. We note the relatively high probability that HAT-P-13c transits and suggest observational dates and strategies.Comment: Published in Ap

Using Transit Timing Observations to Search for Trojans of Transiting Extrasolar Planets

Theoretical studies predict that Trojans are likely a frequent byproduct of planet formation and evolution. We examine the sensitivity of transit timing observations for detecting Trojan companions to transiting extrasolar planets. We demonstrate that this method offers the potential to detect terrestrial-mass Trojans using existing ground-based observatories. We compare the transit timing variation (TTV) method with other techniques for detecting extrasolar Trojans and outline the future prospects for this method.Comment: submitted to ApJL, 12 pages, 2 figure

For the love of God: An analysis of the hermeneutical principles, and practices, and their development, in Augustine's On Christian Teaching, The Spirit and the Letter, The Literal Meaning of Genesis and The Enchiridion

In the history of western thought, few people are more influential than Augustine. His thought continues to impact theology, philosophy and politics, amongst other subjects, some sixteen hundred years after his death. It has been said that all western theology is a footnote to Augustine, and this is difficult to argue with. He is a man of great intellect and influence, who spoke of Scripture as the “supreme authority” (The Literal Meaning of Genesis, 4.14.25). That is why it is of interest to study how this great thinker interpreted Scripture. Augustine was not a biblical specialist like his contemporaries, Jerome or Origen. But the theological concern in his exegesis has made him a popular resource for recent biblical theologians. When asking any question of hermeneutics, the appeal of Augustine is that he reads Scripture primarily as a theologian, raising important theological questions

The Effect of Uterine Environment on Meishan and Yorkshire Fetal Development and Placental Size and Vascularity

When Meishan (M) and Yorkshire (Y) embryos were cotransferred to Y recipients that were then allowed to farrow, it was observed that the birth weights of M and Y littermates were similar averaging 1.15 ± .06 kg. In contrast, placentae matched to M piglets were markedly smaller (.70% lighter) and more vascular (.two-fold) than Y placentae. To investigate the effect of uterine environment on conceptus development to term, M and Y embryos were cotransferred to M recipients (n=3) that were slaughtered one day before expected parturition (day 113). Fetal weight, placental weight, and placental surface area were recorded. Additionally, a section of the intact maternal placental interface was excised, fixed, embedded, sectioned, and stained to allow quantitation of the placental vascular density (PVD). As observed when M and Y fetuses were cogestated by Y recipients, littermate M and Y fetuses gestated in M uteri were similar in weight (1.04 ± .03 vs. 1.03 ± .05 kg) at term. Further, M conceptuses exhibited markedly reduced (P\u3c.03) placental weights (170 ± 19 vs. 249 ± 10 g) and surface areas (1017 ± 70 vs. 1506 ± 96 cm 2 ) compared with their Y littermates. As was the case for conceptuses gestated in Y uteri, the similarity in fetal weight between the two breeds with very different placental sizes appears to result from an increased (P\u3c.09) M PVD compared with littermate Y fetuses (2.5 ± .3 vs. 1.4 ± .4%). These data indicate that in both the M and Y uterine environment, the reduced size of the M compared with Y placenta is compensated for by an increase in PVD. Currently it is unknown whether M placentae contain a greater amount of vasculature (total volume) or a similar amount of vasculature simply squeezed into a smaller space. To investigate breed differences in total placental vasculature we have perfused placentae of M and Y conceptuses cogestated in M uteri on d 113 of gestation with vascular casting material and will compare the volumes of the corrosion casts

Correction to:A Multi-stage Representation of Cell Proliferation as a Markov Process

The original version of this article unfortunately contained a mistake. It has been corrected with this correction. Equations (9) and (10) were transcribed incorrectly. Equation (9) originally read (Formula Presented.) In fact, we should first have introduced scaled variables m j = Mj ekt/C, for j = 1, . . . , k. Equation (9) should then have read (Formula Presented.).</p

Efficient choice of coloured noises in stochastic dynamics of open quantum systems

The Stochastic Liouville-von Neumann (SLN) equation describes the dynamics of an open quantum system reduced density matrix coupled to a non-Markovian harmonic environment. The interaction with the environment is represented by complex coloured noises which drive the system, and whose correlation functions are set by the properties of the environment. We present a number of schemes capable of generating coloured noises of this kind that are built on a noise amplitude reduction procedure [Imai et al, Chem. Phys. 446, 134 (2015)], including two analytically optimised schemes. In doing so, we pay close attention to the properties of the correlation functions in Fourier space, which we derive in full. For some schemes the method of Wiener filtering for deconvolutions leads to the realisation that weakening causality in one of the noise correlation functions improves numerical convergence considerably, allowing us to introduce a well controlled method for doing so. We compare the ability of these schemes, along with an alternative optimised scheme [Schmitz and Stockburger, Eur. Phys. J.: Spec. Top. 227, 1929 (2019)], to reduce the growth in the mean and variance of the trace of the reduced density matrix, and their ability to extend the region in which the dynamics is stable and well converged for a range of temperatures. By numerically optimising an additional noise scaling freedom, we identify the scheme which performs best for the parameters used, improving convergence by orders of magnitude and increasing the time accessible by simulation.Comment: 23 pages, 7 figure

An Empirically Derived Three-Dimensional Laplace Resonance in the Gliese 876 Planetary System

We report constraints on the three-dimensional orbital architecture for all four planets known to orbit the nearby M dwarf Gliese 876 based solely on Doppler measurements and demanding long-term orbital stability. Our dataset incorporates publicly available radial velocities taken with the ELODIE and CORALIE spectrographs, HARPS, and Keck HIRES as well as previously unpublished HIRES velocities. We first quantitatively assess the validity of the planets thought to orbit GJ 876 by computing the Bayes factors for a variety of different coplanar models using an importance sampling algorithm. We find that a four-planet model is preferred over a three-planet model. Next, we apply a Newtonian MCMC algorithm to perform a Bayesian analysis of the planet masses and orbits using an n-body model in three-dimensional space. Based on the radial velocities alone, we find that a 99% credible interval provides upper limits on the mutual inclinations for the three resonant planets ($\Phi_{cb}<6.20^\circ$ for the "c" and "b" pair and $\Phi_{be}<28.5^\circ$ for the "b" and "e" pair). Subsequent dynamical integrations of our posterior sample find that the GJ 876 planets must be roughly coplanar ($\Phi_{cb}<2.60^\circ$ and $\Phi_{be}<7.87^\circ$), suggesting the amount of planet-planet scattering in the system has been low. We investigate the distribution of the respective resonant arguments of each planet pair and find that at least one argument for each planet pair and the Laplace argument librate. The libration amplitudes in our three-dimensional orbital model supports the idea of the outer-three planets having undergone significant past disk migration.Comment: 19 pages, 11 figures, 8 tables. Accepted to MNRAS. Posterior samples available at https://github.com/benelson/GJ87