The Transit Light Source Effect: False Spectral Features and Incorrect Densities for M-dwarf Transiting Planets

Transmission spectra are differential measurements that utilize stellar illumination to probe transiting exoplanet atmospheres. Any spectral difference between the illuminating light source and the disk-integrated stellar spectrum due to starspots and faculae will be imprinted in the observed transmission spectrum. However, few constraints exist for the extent of photospheric heterogeneities in M dwarfs. Here, we model spot and faculae covering fractions consistent with observed photometric variabilities for M dwarfs and the associated 0.3-5.5 $\mu$m stellar contamination spectra. We find that large ranges of spot and faculae covering fractions are consistent with observations and corrections assuming a linear relation between variability amplitude and covering fractions generally underestimate the stellar contamination. Using realistic estimates for spot and faculae covering fractions, we find stellar contamination can be more than $10 \times$ larger than transit depth changes expected for atmospheric features in rocky exoplanets. We also find that stellar spectral contamination can lead to systematic errors in radius and therefore the derived density of small planets. In the case of the TRAPPIST-1 system, we show that TRAPPIST-1's rotational variability is consistent with spot covering fractions $f_{spot} = 8^{+18}_{-7}\%$ and faculae covering fractions $f_{fac} = 54^{+16}_{-46}\%$. The associated stellar contamination signals alter transit depths of the TRAPPIST-1 planets at wavelengths of interest for planetary atmospheric species by roughly 1-15 $\times$ the strength of planetary features, significantly complicating $JWST$ follow-up observations of this system. Similarly, we find stellar contamination can lead to underestimates of bulk densities of the TRAPPIST-1 planets of $\Delta(\rho) = -3^{+3}_{-8} \%$, thus leading to overestimates of their volatile contents.Comment: accepted for publication in Ap

Quantum chaos in one dimension?

In this work we investigate the inverse of the celebrated Bohigas-Giannoni-Schmit conjecture. Using two inversion methods we compute a one-dimensional potential whose lowest N eigenvalues obey random matrix statistics. Our numerical results indicate that in the asymptotic limit, N->infinity, the solution is nowhere differentiable and most probably nowhere continuous. Thus such a counterexample does not exist.Comment: 7 pages, 10 figures, minor correction, references extende

Methods for easy recognition of isostructurality – lab jack-like crystal structures of halogenated 2-phenylbenzimidazoles

Easy recognition and numerical description of isostructurality; how different the similar structures can be; supramolecular aspects of isostructurality

Xylan-Degrading Catalytic Flagellar Nanorods

Flagellin, the main component of flagellar filaments, is a protein possessing polymerization ability. In this work, a novel fusion construct of xylanase A from B. subtilis and Salmonella flagellin was created which is applicable to build xylan-degrading catalytic nanorods of high stability. The FliC-XynA chimera when overexpressed in a flagellin deficient Salmonella host strain was secreted into the culture medium by the flagellum-specific export machinery allowing easy purification. Filamentous assemblies displaying high surface density of catalytic sites were produced by ammonium sulfate-induced polymerization. FliC-XynA nanorods were resistant to proteolytic degradation and preserved their enzymatic activity for a long period of time. Furnishing enzymes with self-assembling ability to build catalytic nanorods offers a promising alternative approach to enzyme immobilization onto nanostructured synthetic scaffolds

Subexponential Parameterized Algorithms for Planar and Apex-Minor-Free Graphs via Low Treewidth Pattern Covering

We prove the following theorem. Given a planar graph $G$ and an integer $k$, it is possible in polynomial time to randomly sample a subset $A$ of vertices of $G$ with the following properties: (i) $A$ induces a subgraph of $G$ of treewidth $\mathcal{O}(\sqrt{k}\log k)$, and (ii) for every connected subgraph $H$ of $G$ on at most $k$ vertices, the probability that $A$ covers the whole vertex set of $H$ is at least $(2^{\mathcal{O}(\sqrt{k}\log^2 k)}\cdot n^{\mathcal{O}(1)})^{-1}$, where $n$ is the number of vertices of $G$. Together with standard dynamic programming techniques for graphs of bounded treewidth, this result gives a versatile technique for obtaining (randomized) subexponential parameterized algorithms for problems on planar graphs, usually with running time bound $2^{\mathcal{O}(\sqrt{k} \log^2 k)} n^{\mathcal{O}(1)}$. The technique can be applied to problems expressible as searching for a small, connected pattern with a prescribed property in a large host graph, examples of such problems include Directed $k$-Path, Weighted $k$-Path, Vertex Cover Local Search, and Subgraph Isomorphism, among others. Up to this point, it was open whether these problems can be solved in subexponential parameterized time on planar graphs, because they are not amenable to the classic technique of bidimensionality. Furthermore, all our results hold in fact on any class of graphs that exclude a fixed apex graph as a minor, in particular on graphs embeddable in any fixed surface