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Planetary systems in mean motion resonances hold a special place among the planetary population. They allow us to study planet formation in great detail as dissipative processes are thought to have played an important role in their existence. Additionally, planetary masses in bright resonant systems may be independently measured both by radial velocities (RVs) and transit timing variations (TTVs). In principle, they also allow us to quickly determine the inclination of all planets in the system, as for the system to be stable, they are likely all in coplanar orbits. To describe the full dynamical state of the system, we also need the stellar obliquity that provides the orbital alignment of a planet with respect to the spin of their host star and can be measured thanks to the Rossiter-McLaughlin effect. It was recently discovered that HD 110067 harbours a system of six sub-Neptunes in resonant chain orbits. We here analyze an ESPRESSO high-resolution spectroscopic time series of HD 110067 during the transit of planet c. We find the orbit of HD 110067 c to be well aligned with sky projected obliquity $\lambda =6^{+24}_{-26}$ deg. This result is indicative that the current architecture of the system has been reached through convergent migration without any major disruptive events. Finally, we report transit-timing variation in this system as we find a significant offset of 19 $\pm$ 4 minutes in the center of the transit compared to the published ephemeris., Comment: Accepted to A&A

One can infer the orbital alignment of exoplanets with respect to the spin of their host stars using the Rossiter-McLaughlin effect, thereby giving us the chance to test planet formation and migration theories and improve our understanding of the currently observed population. We analyze archival HARPS and HARPS-N spectroscopic transit time series of six gas giant exoplanets on short orbits, namely WASP-77 Ab, WASP-101b, WASP-103b, WASP-105b, WASP-120b and WASP-131b. We find a moderately misaligned orbit for WASP-101b ($\lambda =34\degree\ \pm$ 3) and a highly misaligned orbit for WASP-131b ($\lambda =161\degree\ \pm$ 5), while the four remaining ones appear aligned: WASP-77 Ab ($\lambda =-8\degree\ ^{+19}_{-18}$), WASP-103b ($\lambda =2\degree\ ^{+35}_{-36}$), WASP-105b ($\lambda =-14\degree\ ^{+28}_{-24}$), and WASP-120b ($\lambda =-2\degree\ \pm$ 4). For WASP-77 Ab, we were able to infer its true orbital obliquity ($\Psi =48\degree\ ^{+22}_{-21}$). We additionally perform transmission spectroscopy of the targets in search of strong atomic absorbers in the exoatmospheres, but are unable to detect any features, most likely due to the presence of high-altitude clouds or Rayleigh scattering muting the strength of the features. Finally, we comment on future perspectives for studying these targets with the upcoming space missions to investigate the evolution and migration histories of these planets., Comment: Accepted to A&A

The quest for quiet or dormant black holes has been ongoing since several decades. Ellipsoidal variables possibly indicate the existence of a very high-mass invisible companion and are thought to be one of the best ways to find such dormant black holes. This, however, is not a panacea as we show here with one example. We indeed report the discovery of a new semi-detached interacting binary, V1315 Cas, discovered as an ellipsoidal variable. Using data from photometric surveys (ASAS-SN, TESS) and high-resolution spectroscopy, we derived a nearly circular orbit with an orbital period of $P_{\rm{orb}}$=34.54 d. The binary system consists of an evolved F-type star primary that is likely still filling its Roche lobe and a B-type star secondary. Using \textsc{phoebe}2, we derived the following masses and radii: for the primary, $M_p =0.84 \pm 0.03 \, M_\odot$ and $R_p =18.51^{+0.12}_{-0.07} \, R_\odot$; for the secondary, $M_s =7.3 \pm 0.3 \,M_\odot$ and $R_s =4.02^{+2.3}_{-2.0}\,R_\odot$. Modeling the evolution of the system with MESA, we found an age of $\sim$7.7e7 years. The system is at the end of a period of rapid non-conservative mass transfer that reversed its mass ratio, while significantly widening its orbit. The primary shows carbon depletion and nitrogen overabundance, indicative of CNO processed material being exposed due to mass transfer. An infrared excess as well as stationary H$\alpha$ emission suggest the presence of a circumstellar or circumbinary disc. V1315 Cas will likely become a detached stripped star binary., Comment: Accepted in MNRAS

The goal of our study is to provide a reliable classification of variability of A-F stars brighter than 11 mag located in the northern TESS continuous viewing zone. We also aim at thorough discussion about issues in the classification related to the data characteristics and the issues arising from the similar light curve shape generated by different physical mechanisms. We used TESS long- and short-cadence photometric data and corresponding Fourier transform to classify the variability type of the stars. We present a clear and concise classification system that is demonstrated on many examples. We found clear signs of variability in 3025 of 5923 studied stars (51 %). For 1813 of these 3025 stars, we provide a classification. From the classified stars, 64.5 % are pulsating stars of GDOR and DSCT types and their hybrids. We realised that the long- and short-cadence PDCSAP data can differ significantly not only in amplitudes but also in the content of instrumental/data reduction artifacts making the long-cadence data less reliable. We identified a new group of stars showing stable light curves and characteristic frequency spectra pattern (8.5 % of the classified stars). According to the position in the Hertzsprung-Russell diagram, these stars are likely GDOR stars but are about 200 K cooler than GDORs on average and have smaller amplitudes and longer periods in average. We show that without spectroscopic observations, it can be impossible to unambiguously distinguish between ellipsoidal variability and rotational variability. We also apply our methodology to three previous studies and found significant discrepancies in the classification. We demonstrate how difficult the classification of variable A-F stars can be when using only photometric data., Comment: Accepted for publication in A&A, 23 pages, 17 figures, 5 tables

We report the discovery of TOI-1268b, a transiting Saturn-mass planet from the TESS space mission. With an age of less than one Gyr, derived from various age indicators, TOI-1268b is the youngest Saturn-mass planet known to date and contributes to the small sample of well characterised young planets. It has an orbital period of $P\,=\,8.1577080\pm0.0000044$ days, and transits an early K dwarf star with a mass of $M_\star$ = $ 0.96 \pm 0.04$ $M_{\odot}$, a radius of $R_\star$ = $ 0.92 \pm 0.06$ $R_{\odot}$, an effective temperature of $T_\mathrm{eff}\,=\,5300\pm100$ K, and a metallicity of $0.36\pm0.06$ dex. By combining TESS photometry with high-resolution spectra acquired with the Tull spectrograph at McDonald observatory, and the high-resolution spectrographs at Tautenburg and Ondrejov observatories, we measured a planetary mass of $M_\mathrm{p}\,=\,96.4 \pm 8.3\,M_{\oplus}$ and a radius of $R_\mathrm{p}\,=\,9.1 \pm 0.6\,R_{\oplus}$. TOI-1268 is an ideal system to study the role of star-planet tidal interactions for non-inflated Saturn-mass planets. We used system parameters derived in this paper to constrain the planet tidal quality factor to the range of $10^{4.5-5.3}$. When compared with the sample of other non-inflated Saturn-mass planets, TOI-1268b is one of the best candidates for transmission spectroscopy studies., Comment: 21 pages, 17 figures, accepted for publication in Astronomy & Astrophysics; see independent work by Dong et al. for Rossiter-McLaughlin measurement of TOI-1268b

We report the discovery of the third tidally tilted pulsator, TIC 63328020. Observations with the TESS satellite reveal binary eclipses with an orbital period of 1.1057 d, and $\delta$ Scuti-type pulsations with a mode frequency of 21.09533 d$^{-1}$. This pulsation exhibits a septuplet of orbital sidelobes as well as a harmonic quintuplet. Using the oblique pulsator model, the primary oscillation is identified as a sectoral dipole mode with $l = 1, |m| = 1$. We find the pulsating star to have $M_1 \simeq 2.5\, {\rm M}_\odot$, $R_1 \simeq 3 \, {\rm R}_\odot$, and $T_{\rm eff,1} \simeq 8000$ K, while the secondary has $M_2 \simeq 1.1 \, {\rm M}_\odot$, $R_2 \simeq 2 \, {\rm R}_\odot$, and $T_{\rm eff,2} \simeq 5600$ K. Both stars appear to be close to filling their respective Roche lobes. The properties of this binary as well as the tidally tilted pulsations differ from the previous two tidally tilted pulsators, HD74423 and CO Cam, in important ways. We also study the prior history of this system with binary evolution models and conclude that extensive mass transfer has occurred from the current secondary to the primary., Comment: 16 pages, 12 figures, and 8 tables

Transmission spectroscopy is an important technique to probe the atmospheres of exoplanets. With the advent of TESS and, in the future, of PLATO, more and more transiting planets around bright stars will be found and the observing time at large telescopes currently used to apply these techniques will not suffice. We demonstrate here that 2-m class telescopes equipped with spectrographs with high resolving power may be used for a certain number of potential targets. We obtained a time series of high-resolution FEROS spectra at the 2.2-m telescope at La Silla of the very hot Jupiter hosting planet WASP-18b and show that our upper limit is consistent with the expectations. This is the first analysis of its kind using 2-m class telescopes, and serves to highlight their potential. In this context, we then proceed to discuss the suitability of this class of telescopes for the upcoming flood of scientifically interesting targets from TESS space mission, and propose a methodology to select the most promising targets. This is of particular significance given that observing time on 2-m class telescopes is more readily available than on large 8-m class facilities., Comment: accepted PASP

Pt electrocatalytic nanoparticles were deposited onto hybrid carriers composed of reduced graphene oxide (rGO)-transition metal hexacyanoferrate (Prussian Blue-PB) and the resulting system's electrochemical activity was investigated during oxygen reduction reaction in acidic solution. The Prussian Blue -utilizing and Pt nanoparticle-containing materials were characterized using transmission electron microscopy, X-ray diffraction and electrochemical diagnostic techniques such as cyclic voltammetry and rotating ring-disk voltammetry. Application of rGO carriers modified with Prussian Blue as matrices (supports) for Pt catalytic centers does not change practically the potential of electroreduction of oxygen in 0.5 mol dm-3 H2SO4 (under rotating disk voltammetric conditions) relative to the behavior of the analogous PB-free system. What is even more important that, due to the presence of the polynuclear cyanoferrate modifier, the amounts of the undesirable hydrogen peroxide intermediate are significantly decreased (at ring in the rotating ring-disk voltammetry). The results are consistent with the bifunctional mechanism in which oxygen reduction is initiated at Pt centers and the hydrogen peroxide intermediate is reductively decomposed at reactive PB-modified rGO supports.

In 1960 Schwinger [J. Schwinger, Proc.Natl.Acad.Sci. 46 (1960) 570- 579] proposed the algorithm for factorization of unitary operators in the finite M dimensional Hilbert space according to a coprime decomposition of M. Using a special permutation operator A we generalize the Schwinger factorization to every decomposition of M. We obtain the factorized pairs of unitary operators and show that they obey the same commutation relations as Schwinger's. We apply the new factorization to two problems. First, we show how to generate two kq-like mutually unbiased bases for any composite dimension. Then, using a Harper-like Hamiltonian model in the finite dimension M = M1M2, we show how to design a physical system with M1 energy levels, each having degeneracy M2., Comment: 17 pages

It is shown that on a finite phase plane the $kq$-coordinates and the sites of a von Neumann lattice are conjugate to one another. This elementary result holds when the number $M$ defining the size of the phase plane can be expressed as a product, $M=M_{1}M_{2}$, with $M_{1}$ and $M_{2}$ being relatively prime. As a consequence of this result a hitherto unknown wave function is defined giving the probability of simultaneously measuring the momentum and coordinate on the von Neumann lattice., Comment: Published in EPL 83 (2008) 10007

A Hilbert space in M dimensions is shown explicitly to accommodate representations that reflect the prime numbers decomposition of M. Representations that exhibit the factorization of M into two relatively prime numbers: the kq representation (J. Zak, Phys. Today, {\bf 23} (2), 51 (1970)), and related representations termed $q_{1}q_{2}$ representations (together with their conjugates) are analysed, as well as a representation that exhibits the complete factorization of M. In this latter representation each quantum number varies in a subspace that is associated with one of the prime numbers that make up M.

The N distinct prime numbers that make up a composite number M allow $2^{N-1}$ bi partioning into two relatively prime factors. Each such pair defines a pair of conjugate representations. These pairs of conjugate representations, each of which spans the M dimensional space are the familiar complete sets of Zak transforms (J. Zak, Phys. Rev. Let.{\bf 19}, 1385 (1967)) which are the most natural representations for periodic systems. Here we show their relevance to factorizations. An example is provided for the manifestation of the factorization.

Based on the recently introduced averaging procedure in phase space, a new type of entropy is defined on the von Neumann lattice. This quantity can be interpreted as a measure of uncertainty associated with simultaneous measurement of the position and momentum observables in the discrete subset of the phase space. Evaluating for a class of the coherent states, it is shown that this entropy takes a stationary value for the ground state, modulo a unit cell of the lattice in such a class. This value for the ground state depends on the ratio of the position lattice spacing and the momentum lattice spacing. It is found that its minimum is realized for the perfect square lattice, i.e., absence of squeezing. Numerical evaluation of this minimum gives 1.386...., Comment: 14 pages, no figures; J. Phys. A, in press