On the Inference of Thermal Inversions in Hot Jupiter Atmospheres

Several studies in the recent past have inferred the existence of thermal inversions in some transiting hot Jupiter atmospheres. Given the limited data available, the inference of a thermal inversion depends critically on the chemical composition assumed for the atmosphere. In this study, we explore the degeneracies between thermal inversions and molecular abundances in four highly irradiated hot Jupiter atmospheres, day-side observations of which were previously reported to be consistent with thermal inversions based on Spitzer photometry. The four systems are: HD 209458b, HAT-P-7b, TrES-4, and TrES-2. For each system, we explore the model parameter space with ~ 10^6 models using a Markov chain Monte Carlo routine. Our results primarily suggest that a thorough exploration of the model parameter space is necessary to identify thermal inversions in hot Jupiter atmospheres. We find that existing observations of TrES-4 and TrES-2 can both be fit very precisely with models with and without thermal inversions, and with a wide range in chemical composition. On the other hand, observations of HD 209458b and HAT-P-7b are better fit with thermal inversions than without, as has been reported before. We do not see a correlation between irradiation levels and thermal inversions, given current data. Before JWST becomes available, near-IR observations from ground and with HST, along with existing Spitzer observations, can potentially resolve thermal inversions in some systems.Comment: 16 pages in emulate ApJ format, 6 figures, 3 tables (Accepted in ApJ

The number of inversions of permutations with fixed shape

The Robinson-Schensted correspondence can be viewed as a map from permutations to partitions. In this work, we study the number of inversions of permutations corresponding to a fixed partition $\lambda$ under this map. Hohlweg characterized permutations having shape $\lambda$ with the minimum number of inversions. Here, we give the first results in this direction for higher numbers of inversions. We give explicit conjectures for both the structure and the number of permutations associated to $\lambda$ where the extra number of inversions is less than the length of the smallest column of $\lambda$. We prove the result when $\lambda$ has two columns.Comment: 19 pages, 2 figure

Do Some Stakeholders in Publicly Traded Firms Benefit at the Expense of Others as a Result of Corporate Inversions?

This report examines corporate inversions to determine whether this practice benefits the majority of stakeholders or merely a select few. A sample of firms previously incorporated in the United States that have since undergone inversions is examined to answer this question. Annual stock price returns, stock price volatility, and earnings per share changes from the sample of inversion firms are the main sources of data examined. These results are compared to the S&P 500 and peer firms to determine whether the changes can be attributed to the inversions, or are merely a result of general economic conditions. Supporting topics addressed in this paper include an overview of legislation related to inversions and suggestions to mitigate the negative consequences of inversions. This study shows that there are no observable benefits to shareholder wealth arising from corporate inversions. While there were changes in the data from pre to post inversion, they were not unique to the inversion firms as the same changes were observed in the peer firms. However, the study showed that there is a fundamental difference between inversion firms when compared to the S&P 500

On Quasi-inversions

Given a bounded domain $D \subset {\mathbb R}^n$ strictly starlike with respect to $0 \in D\,,$ we define a quasi-inversion w.r.t. the boundary $\partial D \,.$ We show that the quasi-inversion is bi-Lipschitz w.r.t. the chordal metric if and only if every "tangent line" of $\partial D$ is far away from the origin. Moreover, the bi-Lipschitz constant tends to $1,$ when $\partial D$ approaches the unit sphere in a suitable way. For the formulation of our results we use the concept of the $\alpha$-tangent condition due to F. W. Gehring and J. V\"ais\"al\"a (Acta Math. 1965). This condition is shown to be equivalent to the bi-Lipschitz and quasiconformal extension property of what we call the polar parametrization of $\partial D$. In addition, we show that the polar parametrization, which is a mapping of the unit sphere onto $\partial D\,,$ is bi-Lipschitz if and only if $D$ satisfies the $\alpha$-tangent condition.Comment: 22 pages; 5 figure

Inclinations of small quiet-Sun magnetic features based on a new geometric approach

High levels of horizontal magnetic flux have been reported in the quiet-Sun internetwork, often based on Stokes profile inversions. Here we introduce a new method for deducing the inclination of magnetic elements and use it to test magnetic field inclinations from inversions. We determine accurate positions of a set of small, bright magnetic elements in high spatial resolution images sampling different photospheric heights obtained by the Sunrise balloon-borne solar observatory. Together with estimates of the formation heights of the employed spectral bands, these provide us with the inclinations of the magnetic features. We also compute the magnetic inclination angle of the same magnetic features from the inversion of simultaneously recorded Stokes parameters. Our new, geometric method returns nearly vertical fields (average inclination of around 14 deg with a relatively narrow distribution having a standard deviation of 6 deg). In strong contrast to this, the traditionally used inversions give almost horizontal fields (average inclination of 75+-8 deg) for the same small magnetic features, whose linearly polarised Stokes profiles are adversely affected by noise. The almost vertical field of bright magnetic features from our geometric method is clearly incompatible with the nearly horizontal magnetic fields obtained from the inversions. This indicates that the amount of magnetic flux in horizontal fields deduced from inversions is overestimated in the presence of weak Stokes signals, in particular if Stokes Q and U are close to or under the noise level. By combining the proposed method with inversions we are not just improving the inclination, but also the field strength. This technique allows us to analyse features that are not reliably treated by inversions, thus greatly extending our capability to study the complete magnetic field of the quiet Sun.Comment: 12 pages, 9 figures, 1 table; Accepted for publication in Astronomy & Astrophysic

The stability of late-type stars close to the Eddington limit

Super-Eddington luminosities in hydrostatic model atmospheres manifest themselves by the presence of gas pressure inversions. Such inversions are not an artifact of the assumption of hydrostatic equilibrium but can also be present in hydrodynamical model atmospheres. Only for very large mass loss rates hardly realized in supergiants will the inversions be removed. Instabilities may, however, still be present in such inversions, which is investigated for both H-rich and H-deficient late-type supergiant model atmospheres. A local, non-adiabatic, linear stability analysis reveals that sound waves can be amplified due to the strong radiative forces. However, despite the super-Eddington luminosities, the efficiency of the radiative instabilities is fairly low compared to for early-type stars with growth rates of $10^{-5} s^{-1}$.Comment: 11 pages; accepted for publication in Astronomy & Astrophysic

Discovery of large genomic inversions using long range information.

BackgroundAlthough many algorithms are now available that aim to characterize different classes of structural variation, discovery of balanced rearrangements such as inversions remains an open problem. This is mainly due to the fact that breakpoints of such events typically lie within segmental duplications or common repeats, which reduces the mappability of short reads. The algorithms developed within the 1000 Genomes Project to identify inversions are limited to relatively short inversions, and there are currently no available algorithms to discover large inversions using high throughput sequencing technologies.ResultsHere we propose a novel algorithm, VALOR, to discover large inversions using new sequencing methods that provide long range information such as 10X Genomics linked-read sequencing, pooled clone sequencing, or other similar technologies that we commonly refer to as long range sequencing. We demonstrate the utility of VALOR using both pooled clone sequencing and 10X Genomics linked-read sequencing generated from the genome of an individual from the HapMap project (NA12878). We also provide a comprehensive comparison of VALOR against several state-of-the-art structural variation discovery algorithms that use whole genome shotgun sequencing data.ConclusionsIn this paper, we show that VALOR is able to accurately discover all previously identified and experimentally validated large inversions in the same genome with a low false discovery rate. Using VALOR, we also predicted a novel inversion, which we validated using fluorescent in situ hybridization. VALOR is available at https://github.com/BilkentCompGen/VALOR

Principles of genome evolution in the Drosophila melanogaster species group.

That closely related species often differ by chromosomal inversions was discovered by Sturtevant and Plunkett in 1926. Our knowledge of how these inversions originate is still very limited, although a prevailing view is that they are facilitated by ectopic recombination events between inverted repetitive sequences. The availability of genome sequences of related species now allows us to study in detail the mechanisms that generate interspecific inversions. We have analyzed the breakpoint regions of the 29 inversions that differentiate the chromosomes of Drosophila melanogaster and two closely related species, D. simulans and D. yakuba, and reconstructed the molecular events that underlie their origin. Experimental and computational analysis revealed that the breakpoint regions of 59% of the inversions (17/29) are associated with inverted duplications of genes or other nonrepetitive sequences. In only two cases do we find evidence for inverted repetitive sequences in inversion breakpoints. We propose that the presence of inverted duplications associated with inversion breakpoint regions is the result of staggered breaks, either isochromatid or chromatid, and that this, rather than ectopic exchange between inverted repetitive sequences, is the prevalent mechanism for the generation of inversions in the melanogaster species group. Outgroup analysis also revealed evidence for widespread breakpoint recycling. Lastly, we have found that expression domains in D. melanogaster may be disrupted in D. yakuba, bringing into question their potential adaptive significance