Characterization of Knots and Links Arising From Site-specific Recombination on Twist Knots

We develop a model characterizing all possible knots and links arising from recombination starting with a twist knot substrate, extending previous work of Buck and Flapan. We show that all knot or link products fall into three well-understood families of knots and links, and prove that given a positive integer $n$, the number of product knots and links with minimal crossing number equal to $n$ grows proportionally to $n^5$. In the (common) case of twist knot substrates whose products have minimal crossing number one more than the substrate, we prove that the types of products are tightly prescribed. Finally, we give two simple examples to illustrate how this model can help determine previously uncharacterized experimental data.Comment: 32 pages, 7 tables, 27 figures, revised: figures re-arranged, and minor corrections. To appear in Journal of Physics

Knots, Braids and BPS States in M-Theory

In previous work we considered M-theory five branes wrapped on elliptic Calabi-Yau threefold near the smooth part of the discriminant curve. In this paper, we extend that work to compute the light states on the worldvolume of five-branes wrapped on fibers near certain singular loci of the discriminant. We regulate the singular behavior near these loci by deforming the discriminant curve and expressing the singularity in terms of knots and their associated braids. There braids allow us to compute the appropriate string junction lattice for the singularity and,hence to determine the spectrum of light BPS states. We find that these techniques are valid near singular points with N=2 supersymmetry.Comment: 38 page

Three Small Planets Transiting a Hyades Star

We present the discovery of three small planets transiting K2-136 (LP 358 348, EPIC 247589423), a late K dwarf in the Hyades. The planets have orbital periods of $7.9757 \pm 0.0011$, $17.30681^{+0.00034}_{-0.00036}$, and $25.5715^{+0.0038}_{-0.0040}$ days, and radii of $1.05 \pm 0.16$, $3.14 \pm 0.36$, and $1.55^{+0.24}_{-0.21}$ $R_\oplus$, respectively. With an age of 600-800 Myr, these planets are some of the smallest and youngest transiting planets known. Due to the relatively bright (J=9.1) host star, the planets are compelling targets for future characterization via radial velocity mass measurements and transmission spectroscopy. As the first known star with multiple transiting planets in a cluster, the system should be helpful for testing theories of planet formation and migration.Comment: Accepted to The Astronomical Journa

Is the orbit of the exoplanet WASP-43b really decaying? TESS and MuSCAT2 observations confirm no detection

We thank Dr. S. Hoyer from the Laboratoire d'Astrophysique de Marseille (LAM) in France for the helpful discussions. We also thank the anonymous reviewer for the helpful comments and suggestions. This work was supported by the Erasmus+ grant number 2017-1-CZ01-KA203-035562, by the VEGA grant of the Slovak Academy of Sciences number 2/0031/18, by an ESA PRODEX grant under contracting with the ELTE University, by the GINOP number 2.3.2-15-2016-00003 of the Hungarian National Research, Development and Innovation Office, and by the City of Szombathely under agreement number 67.177-21/2016. This paper includes data collected with the TESS mission, obtained from the MAST data archive at the Space Telescope Science Institute (STScI). Funding for the TESS mission is provided by the NASA Explorer Program. STScI is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555. This work has made use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC, https://www.cosmos.esa.int/web/gaia/dpac/consortium).Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement. This article is based on observations made with the MuSCAT2 instrument, developed by ABC, at Telescopio Carlos Sanchez operated on the island of Tenerife by the IAC in the Spanish Observatorio del Teide. This work was partly financed by the Spanish Ministry of Economics and Competitiveness through grant number PGC2018098153-B-C31. This work was partly supported by JSPS KAKENHI grant numbers JP17H04574, JP18H01265 and JP18H05439, and JST PRESTO grant number JPMJPR1775. This work was partly supported by Grant-in-Aid for JSPS Fellows, grant number JP20J21872. TP acknowledges support from the Slovak Research and Development Agency - the contract No. APVV-20-0148. MT was supported by MEXT/JSPS KAKENHI grant numbers 18H05442, 15H02063, and 22000005. AC acknowledges financial support from the State Agency for Research of the Spanish MCIU through the `Center of Excellence Severo Ochoa' award for the Instituto de Astrophysics of Andalusia (SEV-2017-0709). We acknowledge funding from the European Research Council under the European Union's Horizon 2020 research and innovation program under grant agreement number 694513.Up to now, WASP-12b is the only hot Jupiter confirmed to have a decaying orbit. The case of WASP-43b is still under debate. Recent studies preferred or ruled out the orbital decay scenario, but further precise transit timing observations are needed to definitively confirm or refute the period change of WASP-43b. This possibility is given by the Transiting Exoplanet Survey Satellite (TESS) space telescope. In this work, we used the available TESS data, multicolour photometry data obtained with the Multicolor Simultaneous Camera for studying Atmospheres of Transiting exoplanets 2 (MuSCAT2) and literature data to calculate the period change rate of WASP-43b and to improve its precision, and to refine the parameters of the WASP-43 planetary system. Based on the observed-minus-calculated data of 129 mid-transit times in total, covering a time baseline of about 10 yr, we obtained an improved period change rate of (P)over dot = -0.6 +/- 1.2 ms yr(-1) that is consistent with a constant period well within 1 sigma. We conclude that new TESS and MuSCAT2 observations confirm no detection of WASP-43b orbital decay.Erasmus+ grant 2017-1-CZ01-KA203-035562VEGA grant of the Slovak Academy of Sciences 2/0031/18ESA PRODEX grantELTE UniversityNational Research, Development & Innovation Office (NRDIO) - Hungary 2.3.2-15-2016-00003City of Szombathely 67.177-21/2016National Aeronautics & Space Administration (NASA) NAS 5-26555Gaia Multilateral AgreementSpanish Ministry of Economics and Competitiveness PGC2018098153-B-C31Ministry of Education, Culture, Sports, Science and Technology, Japan (MEXT) Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research (KAKENHI) JP17H04574 JP18H01265 JP18H05439JST PRESTO grant JPMJPR1775Ministry of Education, Culture, Sports, Science and Technology, Japan (MEXT) Japan Society for the Promotion of Science JP20J21872Slovak Research and Development Agency APVV-20-0148Ministry of Education, Culture, Sports, Science and Technology, Japan (MEXT) Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research (KAKENHI) 18H05442 15H02063 22000005State Agency for Research of the Spanish MCIU through the 'Center of Excellence Severo Ochoa' award for the Instituto de Astrophysics of Andalusia SEV-2017-0709European Research Council under the European Union's Horizon 2020 research and innovation program 69451

Obliquity measurement and atmospheric characterization of the WASP-74 planetary system

We present new transit observations of the hot Jupiter WASP-74 b ($T_\mathrm{eq} \sim$ 1860 K) using the high-resolution spectrograph HARPS-N and the multi-colour simultaneous imager MuSCAT2. We refine the orbital properties of the planet and its host star, and measure its obliquity for the first time. The measured sky-projected angle between the stellar spin-axis and the planet's orbital axis is compatible with an orbit well-aligned with the equator of the host star ($\lambda = 0.77\pm0.99 \mathrm{deg}$). We are not able to detect any absorption feature of H$\alpha$, or any other atomic spectral features, in its high-resolution transmission spectra due to low S/N at the line cores. Despite previous claims regarding the presence of strong optical absorbers such TiO and VO gases in the atmosphere of WASP-74 b, the new ground-based photometry combined with a reanalysis of previously reported observations from the literature shows a slope in the low-resolution transmission spectrum steeper than expected from Rayleigh scattering alone.Comment: Accepted for publication in Astronomy & Astrophysics. 12 pages, 8 figures, 5 table

Describing semigroups with defining relations of the form xy=yz xy and yx=zy and connections with knot theory

We introduce a knot semigroup as a cancellative semigroup whose defining relations are produced from crossings on a knot diagram in a way similar to the Wirtinger presentation of the knot group; to be more precise, a knot semigroup as we define it is closely related to such tools of knot theory as the twofold branched cyclic cover space of a knot and the involutory quandle of a knot. We describe knot semigroups of several standard classes of knot diagrams, including torus knots and torus links T(2, n) and twist knots. The description includes a solution of the word problem. To produce this description, we introduce alternating sum semigroups as certain naturally defined factor semigroups of free semigroups over cyclic groups. We formulate several conjectures for future research

Nodal precession of WASP-33b for 11 yr by Doppler tomographic and transit photometric observations

Stars and planetary system

Carbenic nitrile imines: Properties and reactivity

Structures and properties of nitrile imines were investigated computationally at B3LYP and CCSD(T) levels. Whereas NBO analysis at the B3LYP DFT level invariably predicts a propargylic electronic structure, CCSD(T) calculations permit a clear distinction between propargylic, allenic, and carbenic structures. Nitrile imines with strong IR absorptions above ca. 2150 cm-1 have propargylic structures with a CN triple bond (RCNNSiMe 3 and R2BCNNBR2), and those with IR absorptions below ca. 2150 cm-1 are allenic (HCNNH, PhCNNH, and HCNNPh). Nitrile imines lacking significant cumulenic IR absorptions at 1900-2200 cm -1 are carbenic (R-(C:)-N=N-R′). Electronegative but lone pair-donating groups NR2, OR, and F stabilize the carbenic form of nitrile imines in the same way they stabilize "normal" singlet carbenes, including N-heterocyclic carbenes. NBO analyses at the CCSD(T) level confirm the classification into propargylic, allenic, and carbenic reactivity types. Carbenic nitrile imines are predicted to form azoketenes 21 with CO, to form [2+2] and [2+4] cycloadducts and borane adducts, and to cyclize to 1H-diazirenes of the type 24 in mildly exothermic reactions with activation energies in the range 29-38 kcal/mol. Such reactions will be readily accessible photochemically and thermally, e.g., under the conditions of matrix photolysis and flash vacuum thermolysis

A hot sub-Neptune in the desert and a temperate super-Earth around faint M dwarfs: Color validation of TOI-4479b and TOI-2081b

We report the discovery and validation of two TESS exoplanets orbiting faint M dwarfs: TOI-4479b and TOI-2081b. We have jointly analyzed space (TESS mission) and ground based (MuSCAT2, MuSCAT3 and SINISTRO instruments) lightcurves using our multi-color photometry transit analysis pipeline. This allowed us to compute contamination limits for both candidates and validate them as planet-sized companions. We found TOI-4479b to be a sub-Neptune-sized planet ($R_{p}=2.82^{+0.65}_{-0.63}~\rm R_{\oplus}$) and TOI-2081b to be a super-Earth-sized planet ($R_{p}=2.04^{+0.50}_{-0.54}~\rm R_{\oplus}$). Furthermore, we obtained that TOI-4479b, with a short orbital period of $1.15890^{+0.00002}_{-0.00001}~\rm days$, lies within the Neptune desert and is in fact the largest nearly ultra-short period planet around an M dwarf known to date. These results make TOI-4479b rare among the currently known exoplanet population around M dwarf stars, and an especially interesting target for spectroscopic follow-up and future studies of planet formation and evolution.Comment: Accepted for publication in Astronomy&Astrophysic