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Anti-solar differential rotation (DR) profiles are characterized by a slow equator and fast rotating poles (reversed with respect to the Sun). They have been reported in numerous 3D numerical simulations over the last decades for slowly rotating solar-like models experiencing high Rossby numbers. However, unambiguous observation of anti-solar DR profiles is still pending for solar-type stars on the main-sequence, although it has been reported for later evolutionary stages. During their main-sequence, stars spin-down, which increases their Rossby number and could induce a transition toward an anti-solar DR state. Such a rotational transition would have an impact on the large-scale dynamo process, activity and angular momentum evolution for old solar-type stars. We show in this work the development of a new theoretical formula in order to estimate the effective fluid Rossby number Rof of solar-type stars. We express it as a function of observational quantities such as Teff and Prot, while considering several aspects, such as structure, evolutionary stage, and metallicity. We then quantify the fluid Rossby number of the most recent Kepler catalog of rotational periods by Santos et al. (2019, 2021). After sanity checks, we obtain 22 targets experiencing high Rossby numbers and being promising candidates to host anti-solar differential rotation. The method can then be applied to future PLATO observations in order to extend this sample, whose future characterization would increase our understanding of magnetic and rotational evolution of solar-type stars. For that purpose, the formula we developed here will be implemented in the mission analysis pipeline.

The existence of super-massive (> 10^4M⊙) Pop III stars has been theorized, but never observed. If such stars were to have existed during early galaxy formation, it has long been thought that in absence of heavy metals (A > 4), they would have collapsed due to instabilities caused by general relativity. Such a collapse would have resulted in the creation of a super- massive black hole, possibly emitting gravitational waves if accompanied by an anisotropic neutrino burst. Super-massive black holes have been detected very early on in galaxy formation (red shift: z ≈ 7), and their origin remains unknown. Gravitational waves created by such a collapse may be detectable by next generation gravitational wave detectors.Recent simulations have suggested that a narrow range of super-massive stars with masses around 5 × 10^4M⊙ may have exploded due to simultaneously reaching the general relativistic instability and the ignition of triple-α fusion. If such explosions were to have occurred, depending on their frequency of occurrence, they may have left behind a measurable elemental signature of heavy elements in an otherwise primordial elemental composition during early galaxy formation.This dissertation details the investigation of post-instability energetics, both from a theoretical stand point as well as via simulations using the KEPLER stellar evolution code. Previous research has found that for a small range of stars with masses around 5 × 10^4M⊙, due to the extreme temperature sensitivity of the triple-α process at its ignition point (~2 × 10^8 K), there is a theoretical basis for accelerated nuclear energy production to possibly reverse the collapse before too much energy is lost in electron-positron pair annihilation neutrinos combined with in-falling kinetic energy. However, complimentary findings via simulations were not found to be satisfactory. Future three dimensional simulations with high precision accounting of nuclear energy production as well as energy losses and kinematics would be necessary to definitively conclude whether such explosions are energetically possible.

TIC137608661/TYC4544-2658-1/FBS0938+788 is a new sdBV+dM reflection-effect binary discovered by the TESS space mission with an orbital period of 7.21 hours. In addition to the orbital frequency and its harmonics, the Fourier transform of TIC137608661 shows many g-mode pulsation frequencies from the sdB star. The amplitude spectrum is particularly simple to interpret as we immediately see several rotational triplets of equally spaced frequencies. The central frequencies of these triplets are equally spaced in period with a mean period spacing of 270.12 s, corresponding to consecutive l=1 modes. From the mean frequency spacing of 1.25 {\mu}Hz we derive a rotation period of 4.6 days in the deep layers of the sdB star, significantly longer than the orbital period. Among the handful of sdB+dM binaries for which the sdB rotation was measured through asteroseismology, TIC137608661 is the non-synchronized system with both the shortest orbital period and the shortest core rotation period. Only NY Vir has a shorter orbital period but it is synchronized. From a spectroscopic follow-up of TIC137608661 we measure the radial velocities of the sdB star, determine its atmospheric parameters, and estimate the rotation rate at the surface of the star. This measurement allows us to exclude synchronized rotation also in the outer layers and suggests a differential rotation, with the surface rotating faster than the core, as found in few other similar systems. Furthermore, an analysis of the spectral energy distribution of TIC137608661, together with a comparison between sdB pulsation properties and asteroseismic models, gives us further elements to constrain the system., Comment: Accepted for publication in MNRAS Main Journal

One of the key concepts in modern science is force (F). In present studies on the history of dynamics, Patricius is either completely omitted or only cursorily mentioned. The aim of this text is to show that Patricius’ concept of the soul, as he developed it in his Nova de universis philosophia from 1591, comes close to the modern (i.e. Newtonian) understanding of force. This should support the more general position that one of the most intriguing aspects of Patricius’ philosophy is his contribution to the emergence of modern science.

Asteroseismology, the study of intrinsic oscillations in stars, can reveal fundamental properties of cool stars critical in our understanding of stellar rotational evolution. Through space missions such as Kepler and TESS, asteroseismology has seen a surge of new data and research in the past decade. These data have contributed to important results in the field of stellar braking particularly for F, G and K stars, thanks to estimates of stellar age for rotating field stars, and the measurement of stellar rotation through oscillation spectra as important comparisons for estimates from star-spots. In this talk, I will provide an introduction to asteroseismology how it can provide important results for your research. This will be followed by a breakdown of how asteroseismologists have used these techniques to establish the presence of weakened magnetic braking on the main sequence using asteroseismic data, and what we should be looking forward to from these techniques with the TESS mission., {"references":["Hall, Oliver et al. (2021), Nature Astronomy, Volume 5, p. 707-714","Nielsen, Martin et al. (2015), Astronomy & Astrophysics, Volume 582, id.A10, 5 pp.","Davies, Guy et al. (2015), Monthly Notices of the Royal Astronomical Society, Volume 446, Issue 3, p.2959-2966","Benomar, Othman et al. (2018), Science, Volume 361, Issue 6408, pp. 1231-1234","Silva Aguirre, Victor et al. (2015), Monthly Notices of the Royal Astronomical Society, Volume 452, Issue 2, p.2127-2148","Davies, Guy et al. (2016), Monthly Notices of the Royal Astronomical Society, Volume 456, Issue 2, p.2183-2195","Lund, Mikkel et al. (2017), The Astrophysical Journal, Volume 835, Issue 2, article id. 172, 31 pp.","Silva Aguirre, Victor et al. (2017), The Astrophysical Journal, Volume 835, Issue 2, article id. 173, 18 pp.","Lund, Mikkel et al. (2014), The Astrophysical Journal, Volume 790, Issue 2, article id. 121, 28 pp.","David, Trevor et al. (2022), The Astrophysical Journal, Volume 933, Issue 1, id.114, 22 pp."]}

The fundamental concepts and principles of mechanics, or dynamics, were established in the 17th century. Copernicus gave the notion of reference system in 1543, and Galileo stated the principle of inertia in 1638 in his important work Discorsi e dimostrazioni mathematiche intorno a due nove scienze alla meccanica ed i movimenti locali.1 A particle on which no force is exerted has a constant velocity. Linear uniform motion is a state relative to the observer, and not a process. It is the variation of the velocity that is a process resulting from an external action. Many scientists participated in this evolution, such as Tycho Brahe, Kepler, Descartes, and Christiaan Huygens, to name a few.

We present a comparative analysis of observations of the selected exoplanet transits obtained at the Kyiv Comet station with the database of the TESS (Transiting Exoplanet Survey Satellite) and Kepler space telescopes. The light curves obtained by the TESS and Kepler orbital telescopes were processed using a program based on the Python package Lightcurve 2.3v which is freely available in the MUST archive (Barbara A. Mikulski Archive for Space Telescopes). The ground based observations were carried out with the 70-cm telescope AZT- 8 (Lisnyky). Photometric processing of the ground based observation was performed by using the Muniwin program. The light curves and parameters of the observed transits as well as the exoplanet orbital parameters obtained from ground based observations were published in the ETD (Exoplanet Transit Database). Determined transit parameters were compared with the results of the TESS command, which are stored in the MUST archive. Here we presents a comparison of the parameters of transit phenomena (period, depth, transit duration) and some orbital parameters obtained from two independent sets of observations, terrestrial and orbital, performed in different epochs., Ми презентуємо порiвняльний аналiз спостережень транзитiв вибраних екзопла нет, отриманих на кометнiй станцiї Лiсники, з кривими блиску їх батькiвських зiр, з бази даних космiчних телескопiв TESS (Transiting Exoplanet Survey Satellite) i Kepler. Криавi блиску, отриманi орбiтальними телескопами TESS i Kepler, були обробленi за допомогою програми, розробленої на основi Python пакету Lightcurve 2.3, який є у вiльному доступi в архiвi MUST (Barbara A. Mikulski Archive for Space Telescopes). Спостере- ження також проводились на 70-ти сантиметровому телескопi-рефлекторi АЗТ-8 (Лiсники). Фотомет- рична обробка цих результатiв проводилась за допомогою програми Munivin. Отриманi нами з наземних спостережень кривi блиску та оцiнки параметрiв спостережених транзитiв та орбiтальнi параметри екзопланет опублiкованi в базi даних ETD (Exoplanet Transit Database). Визначенi нами параметри транзитiв порiвнювались з результатами команди TESS, якi зберiгаються в архiвi MUST. В роботi представлено порiвняння параметрiв транзитних явищ (перiод, глибина, тривалiсть транзиту), а також орбiтальних параметрiв вибра- них екзопланет, отриманих з двох незалежних наборiв спостережень, наземних та орбiтальних, виконаних в рiзнi епохи.

Gyrochronology, the empirical relation between rotation and age, can provide important leverage on important astrophysical questions ranging from basic stellar evolution models, to the timescale for the development of habitable planets, to the structural and chemical history of the Galaxy. Key to gyrochronology’s usefulness is the determination of reliable rotation rates. We present the rotational characteristics of a sample of several thousand main sequence pairs observed by NASA’s Transiting Earth Survey Satellite (TESS) and the Kepler K2 extended missions. Essentially open clusters with only two components, such pairs may help break the degeneracies in the rotation-activity-metallicity vs. age relations for main sequence stars. Support from NSF grants AST-1910396, AST-2108975 and NASA grants 80NSSC22K0622, 80NSSC21K0245, NNX16AB76G is gratefully acknowledged., Poster presented at The Cambridge Workshop on Cool Stars, Stellar Systems, and the Sun (CSW 21), 4-9 July, 2022, Toulouse, France, {"references":["Angus, R., Aigrain, S., Foreman-Mackey, D., McQuillan, A. 2015, \"Calibrating Gyrochronology Using Kepler Asteroseismic Targets,\" MNRAS 450, 1787","Avallone, E., et al. (8 coauthors) 2022, \"Rotation Distributions around the Kraft Break with TESS and Kepler: The Influences of Age, Metallicity, and Binarity,\" ApJ 930, 7","Barnes, S. 2007, \"Ages for Illustrative Field Stars Using Gyrochronology: Viability, Limitations and Error\" ApJ, 669, 1167","Mamajek, E., Hillenbrand, L. 2008, \"Improved Age Estimation for Solar-Type Dwarfs Using Activity-Rotation Diagnostics,\" ApJ 687, 1264","Meibom, S. et al. (21 coauthors) 2011, \"The Kepler Cluster Study: Stellar Rotation in NGC 6811,\" ApJ 733 L9","Oswalt, T., Otani, T., Buzasi, D., von Hippel T. 2021, \"Testing the Gyrochronology Paradigm Using Wide Binary Stars,\" BAAS 53 141.02","Otani, T., von Hippel, T., Buzasi, D., Oswalt, T., Stone-Martinez, A., Majewski, P. 2022, \"A Monte Carlo Method for Evaluating Empirical Gyrochronology Models and Its Application to Wide Binary Benchmarks,\" ApJ 930, 36","Spada, F., Lanzafame, A. 2020, \"Competing Effect of Wind Braking and Interior Coupling in the Rotational Evolution of Solar-Like Stars,\" A&A 363, A76","Zavada, P., Piska, K. 2020, \"Statistical Analysis of Binary Stars from the Gaia Catalog Data Release 2,\" AJ 159 33"]}

The study of detached eclipsing binaries in open clusters can provide powerful tests of theoretical stellar evolutionary models. These models must simultaneously fit the masses, radii, and radiative properties of the eclipsing stars with essentially the same distance, age, and initial composition. In this way, clusters are ideal test benches for verification of the stellar evolution theory. To fully exploit this potential, we present a detailed analysis of three spectroscopic binaries that are members of NGC 6791. Measurements of the radial velocities were combined with Kepler photometry, to provide a full set of orbital and physical parameters. We applied a standard analysis to disentangle the spectra of each binary system and to determine the temperatures and metallicities for each component in binaries. High-precision analysis affords us the opportunity to define the evolutionary status of the components. We also derived the distances to the systems. Finally, we report on the detection of solar-like oscillation signals in a member in data from the Kepler mission., Scientific and Technological Research Council of Turkey [119F216]; ESO [091.D0125(A), 081.D-0091(A)]; NASA's Science Mission Directorate; National Aeronautics and Space Administration; National Science Foundation, We are grateful to the anonymous referee for her/his valuable suggestions. This study is supported by Scientific and Technological Research Council of Turkey under project number 119F216. This research made use of data collected at ESO under programmes 091.D0125(A) (PI: Brogaard, K.) and 081.D-0091(A) (PI: Grundahl, F.). The following internet-based resources were used in research for this paper: the NASA Astrophysics Data System and the SIMBAD data base operated at CDS, Strasbourg, France. This work is based on data from the Kepler mission. Kepler was competitively selected as the tenth Discovery mission. Funding for this mission is provided by NASA's Science Mission Directorate. The photometric data were obtained from the Mikulski Archive for Space Telescopes. This work has also made use of data from the European Space Agency mission Gaia (http://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (http://www.cosmos.esa.int/web/gaia/dpac/consortium).This research made use of LIGHTKURVE, a Python package for Kepler and TESS data analysis (Lightkurve Collaboration et al. 2018). This publication makes use of data products from the Two Micron All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation.

Kepler’s laws are an appropriate topic to highlight the significance of the pedal equation in physics. There are several articles that obtain Kepler’s laws through conservation and gravitation laws. This can be shown more easily and ingeniously if one uses the pedal equation of an ellipse. In fact, the complete kinematics of a particle in an attractive central force field can be derived from one single pedal form. Though many articles use the pedal equation, the classical procedure (without proof) for obtaining the pedal equation is mentioned only in a few because the classical derivations can sometimes be lengthier and are not simple. In this paper, using elementary physics, we derive the pedal equation for all conic sections in a unique, short, and pedagogical way. Later, from the dynamics of a particle in the attractive central force field, we deduce the single pedal form, which elegantly describes all the possible trajectories. Also, for the purpose of completeness, we derive Kepler’s laws.

We present the findings for the magnetic activities seen on V1130 Cyg and V461 Lyr. In the case of V1130 Cyg, the secondary component's temperature was found to be 3891 +/- 50 K, while the mass ratio was computed as 0.689 +/- 0.001, and the orbital inclination as 90 degrees.00 +/- 0 degrees.01. The temperature of V461 Lyr's secondary component was found to be 4206 +/- 50 K, and the mass ratio was calculated as 0.999 +/- 0.001 with 89 degrees.58 +/- 0 degrees.01 of orbital inclination. The analyses exhibit the effects of the stellar spots on the light curves. The models indicate that there are two types of flares in the case of V1130 Cyg, and three types of flares for V461 Lyr. The Plateau parameters have been found as 2.1997 s for Group 1 and 1.0068 s for Group 2 in the case of V1130 Lyr. They have been computed as 1.9015 s for Group 1, 2.7943 s for Group 2, and 3.4324 s for Group 3 of V461 Lyr., Turkish Scientific and Tech-nical Research Council (TdUBITAK) [116F213], We thank the referee for useful comments that contributed to the improvement of the paper. We also wish to thank the Turkish Scientific and Tech-nical Research Council (TdUBITAK) for supporting this work through Grant No. 116F213.

Melville, en tant que marin, a souvent exprimé son goût pour l’astronomie, les éphémérides et leurs ressources narratologiques : cette fascination se manifeste dans le système métaphorique qui sous-tend toute la structure de Mardi et le monde qu’il parcourt : ce périple prend sens si l’on considère que le héros voyage dans l’orbite des étoiles. Melville avait lu de nombreux « voyages dans la lune », et son roman pourrait être directement inspiré des œuvres de Cyrano de Bergerac, Kepler ou Godwin. En outre, au moment où il écrit ses romans polynésiens, les questions astronomiques sont d’actualité avec le passage de la comète de Halley en particulier, ce nom étant le palindrome presque parfait du nom de l’héroïne Yillah—ce qui permet de lire l’ensemble du roman comme une vaste métaphore astronomique touchant le sens du roman dans son ensemble, à interpréter comme un voyage dans les astres, en particulier dans le monde planétaire de Mardi et de l’anneau de ses îles. Melville as a sailor expressed his fascination for astronomy, ephemerides and their creative potential, which is evidenced in the metaphorical setting that structures the whole argument of Mardi ’s confusing world. Indeed, the hero sails on the orbit of stars. Melville had read many “travels to the moon,” and his novel might be directly inspired by Cyrano de Bergerac, Kepler or Godwin. Moreover, at the time he was writing his Polynesian novels, Melville could not ignore astronomical topics such as the passage of Halley’s comet. Its name is the nearly perfect palindrome of Yillah, which imparts a major metaphorical and celestial dimension to the topography of Mardi and its rings of islands. Instead of being a travelogue-satire, the entire novel operates as an astronomical metaphor.

Machine learning algorithms play an impressive role in modern technology and address automation problems in many fields as these techniques can be used to identify features with high sensitivity, which humans or other programming techniques aren’t capable of detecting. In addition, the growth of the availability of the data demands the need of faster, accurate, and more reliable automating methods of extracting information, reforming, and preprocessing, and analyzing them in the world of science. The development of machine learning techniques to automate complex manual programs is a time relevant research in astrophysics as it’s a field where, experts are dealing with large sets of data every day. In this study, an automated classification was built for 6 types of star classes Beta Cephei, Delta Scuti, Gamma Doradus, Red Giants, RR Lyrae and RV Tarui with widely varying properties, features extracted from training dataset of stellar light curves obtained from Kepler mission. The Random Forest classification model was used as the Machine Learning model and both periodic and non-periodic features extracted from light curves were used as the inputs to the model. Our implementation achieved an accuracy of 86.5%, an average precision level of 0.86, an average recall value of 0.87, and average F1-Score of 0.86 for the testing dataset obtained from the Kepler mission.

Johannes Kepler is often cited as a witness to scholars’ resistance to the shift from Latin to vernacular languages in the scientific literature in the early 17th century. Allegedly he was unable to read Italian, and reacted to Galileo's transition from Latin to Italian by accusing him of committing a crimen laesae humanitatis, with the double sense of “crime against humanity” and “crime against classical scholarship”. The paper shows that this claim is groundless. The arguments are as follows: 1. Kepler's alledged remark about Galileo is not documented in Kepler's works. 2. Kepler was very well able to read Italian books. 3. The expression crimen laesae humanitatis is not attested in the neo‐Latin literature of the 17th century 4. All the references of this statement can be traced back to a book by the Heidelberg professor of Romance Studies Leonardo Olschki of 1922, who did not mark the expression as a quotation and who did not give any source reference. 5. Kepler himself published scientific texts in his native German and contributed to the development of a German astronomical terminology.

We present the first short-duration candidate microlensing events from the Kepler K2 mission. From late April to early July 2016, Campaign 9 of K2 obtained high temporal cadence observations over a 3.7 square degree region of the Galactic bulge. Its primary objectives were to look for evidence of a free-floating planet (FFP) population using microlensing, and demonstrate the feasibility of space-based planetary microlensing surveys. Though Kepler K2 is far from optimal for microlensing, the recently developed MCPM photometric pipeline enables us to identify and model microlensing events. We describe our blind event-selection pipeline in detail and use it to recover 22 short-duration events with effective timescales of less than 10 days previously announced by the OGLE and KMTNet ground-based surveys. We also announce five new candidate events. One of these is a caustic-crossing binary event, consistent with a bound planet and modelled as such in a companion study. The other four have very short durations (effective timescales less than 0.1 days) typical of an Earth-mass FFP population. Whilst Kepler was not designed for crowded-field photometry, the K2C9 dataset clearly demonstrates the feasibility of conducting blind space-based microlensing surveys towards the Galactic bulge., Comment: 25 pages including appendices, published MNRAS

Physics textbooks generally present the equation for universal gravitation as if it sprang fully formed from the head of Isaac Newton, which it most certainly did not. This analysis traces the development of Classical/Newtonian gravity as it evolved from Aristotle to Copernicus to Kepler, Horrocks, Roberval, Boulliau, Baliani, Borelli, Hooke, Halley, Wren, Newton, and Cavendish, and then finally on to C. V. Boys and J. H. Poynting. By focusing on the evolution of the underlying physics, we unfold a fascinating story that has never quite been told before, one we hope will provide insights useful in the classroom.

In this paper, the determination of eccentric anomaly (E) for Kepler’s satellite orbit using Perturbation-Based Seeded Secant (PBSS) iteration algorithm is presented. The solution is meant for Kepler’s orbit with the value of eccentricity (e) in the range 0 ≤ e ≤ 1. Such orbits are either circular or elliptical. The demonstration of the applicability of the PBSS iteration is presented using sample numerical examples with different values of mean anomaly (M) and eccentricity (e). The summary of the results of E for M = 30° and e in the range 0.001 ≤ e ≤1 showed that the convergence cycle (n) increases as e increases. Particularly, n increased from 2 at e = 0.01 to n = 8 at e =1. The implication is that it takes more iterations to arrive at the value of E with the desired accuracy or error performance (which in this case is set to 10^(-12)). Another implication is that a good choice of the initial value of E is essential especially as the value of e increases. As such, effort should be made to develop a means of estimating the initial value of E which will reduce the convergence cycle for higher values of e.

The multiscale entropy assesses the complexity of a signal across different timescales. It originates from the biomedical domain and was recently successfully used to characterize light curves as part of a supervised machine learning framework to classify stellar variability. We explore the behavior of the multiscale entropy in detail by studying its algorithmic properties in a stellar variability context and by linking it with traditional astronomical time series analysis methods. We subsequently use the multiscale entropy as the basis for an interpretable clustering framework that can distinguish hybrid pulsators with both p- and g-modes from stars with only p-mode pulsations, such as $\delta$ Sct stars, or from stars with only g-mode pulsations, such as $\gamma$ Dor stars. We find that the multiscale entropy is a powerful tool for capturing variability patterns in stellar light curves. The multiscale entropy provides insights into the pulsation structure of a star and reveals how short- and long-term variability interact with each other based on time-domain information only. We also show that the multiscale entropy is correlated to the frequency content of a stellar signal and in particular to the near-core rotation rates of g-mode pulsators. We find that our new clustering framework can successfully identify the hybrid pulsators with both p- and g-modes in sets of $\delta$ Sct and $\gamma$ Dor stars, respectively. The benefit of our clustering framework is that it is unsupervised. It therefore does not require previously labeled data and hence is not biased by previous knowledge., Comment: 14 pages, 15 figures, 2 tables, Accepted for publication in Astronomy & Astrophysics

From the determination of the first occurrence rates by the Kepler Mission, small planets (< 4 Earth radii) have garnered outsize interest. Early Kepler occurrence rates showed that small planets are more abundant than their larger counterparts, but these analyses were limited by the precision of stellar radii. As a result, the planet radius gap – a relative minimum in occurrence separating super-Earths (< 1.8 Earth radii) from sub-Neptunes (>1.8 Earth radii) — was confirmed when the California-Kepler Survey precisely determined the properties of >1000 host stars hosting >2000 planets. Today, in the era of Gaiaphotometry and parallaxes and all-sky exoplanet transit surveys, homogeneous, precise stellar properties are possible for thousands of host stars enabling detailed studies of the gap. In this talk, I will present the discovery and subsequent Gaia-Era investigations of the exoplanet radius gap. I will discuss the gap’s potential origins and proposed formation mechanisms’ ability to explain the current observational data. Finally, I will discuss the prospects for differentiating between the various gap formation mechanisms, so that we may further understand planet formation and evolution for planets similar to our own.

Full list of authors: Turtelboom, Emma V.; Weiss, Lauren M.; Dressing, Courtney D.; Nowak, Grzegorz; Pallé, Enric; Beard, Corey; Blunt, Sarah; Brinkman, Casey; Chontos, Ashley; Claytor, Zachary R.; Dai, Fei; Dalba, Paul A.; Giacalone, Steven; Gonzales, Erica; Harada, Caleb K.; Hill, Michelle L.; Holcomb, Rae; Korth, Judith; Lubin, Jack; Masseron, Thomas; MacDougall, Mason; Mayo, Andrew W.; Močnik, Teo; Akana Murphy, Joseph M.; Polanski, Alex S.; Rice, Malena; Rubenzahl, Ryan A.; Scarsdale, Nicholas; Stassun, Keivan G.; Tyler, Dakotah B.; Zandt, Judah Van; Crossfield, Ian J. M.; Deeg, Hans J.; Fulton, Benjamin; Gandolfi, Davide; Howard, Andrew W.; Huber, Dan; Isaacson, Howard; Kane, Stephen R.; Lam, Kristine W. F.; Luque, Rafael; Martín, Eduardo L.; Morello, Giuseppe; Orell-Miquel, Jaume; Petigura, Erik A.; Robertson, Paul; Roy, Arpita; Van Eylen, Vincent; Baker, David; Belinski, Alexander A.; Bieryla, Allyson; Ciardi, David R.; Collins, Karen A.; Cutting, Neil; Della-Rose, Devin J.; Ellingsen, Taylor B.; Furlan, E.; Gan, Tianjun; Gnilka, Crystal L.; Guerra, Pere; Howell, Steve B.; Jimenez, Mary; Latham, David W.; Larivière, Maude; Lester, Kathryn V.; Lillo-Box, Jorge; Luker, Lindy; Mann, Christopher R.; Plavchan, Peter P.; Safonov, Boris; Skinner, Brett; Strakhov, Ivan A.; Wittrock, Justin M.; Caldwell, Douglas A.; Essack, Zahra; Jenkins, Jon M.; Quintana, Elisa V.; Ricker, George R.; Vanderspek, Roland; Seager, S.; Winn, Joshua N.-- This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited., Multiplanet systems are valuable arenas for investigating exoplanet architectures and comparing planetary siblings. TOI-1246 is one such system, with a moderately bright K dwarf (V = 11.6, K = 9.9) and four transiting sub-Neptunes identified by TESS with orbital periods of 4.31, 5.90, 18.66, and 37.92 days. We collected 130 radial velocity observations with Keck/HIRES and TNG/HARPS-N to measure planet masses. We refit the 14 sectors of TESS photometry to refine planet radii (2.97 ± 0.06 R⊕, 2.47 ± 0.08 R⊕, 3.46 ± 0.09 R⊕, and 3.72 ± 0.16 R⊕) and confirm the four planets. We find that TOI-1246 e is substantially more massive than the three inner planets (8.1 ± 1.1 M⊕, 8.8 ± 1.2 M⊕, 5.3 ± 1.7 M⊕, and 14.8 ± 2.3 M⊕). The two outer planets, TOI-1246 d and TOI-1246 e, lie near to the 2:1 resonance (Pe/Pd = 2.03) and exhibit transit-timing variations. TOI-1246 is one of the brightest four-planet systems, making it amenable for continued observations. It is one of only five systems with measured masses and radii for all four transiting planets. The planet densities range from 0.70 ± 0.24 to 3.21 ± 0.44 g cm−3, implying a range of bulk and atmospheric compositions. We also report a fifth planet candidate found in the RV data with a minimum mass of 25.6 ± 3.6 M⊕. This planet candidate is exterior to TOI-1246 e, with a candidate period of 93.8 days, and we discuss the implications if it is confirmed to be planetary in nature. © 2022. The Author(s). Published by the American Astronomical Society., We thank the time assignment committees of the University of California, the California Institute of Technology, NASA, and the University of Hawaii for supporting the TESS-Keck Survey with observing time at Keck Observatory. We thank NASA for funding associated with our Key Strategic Mission Support project. We gratefully acknowledge the efforts and dedication of the Keck Observatory staff for support of HIRES and remote observing. We recognize and acknowledge the very significant cultural role and reverence that the summit of Maunakea has within the indigenous Hawaiian community. We are deeply grateful to have the opportunity to conduct observations from this mountain. We thank Ken and Gloria Levy, who supported the construction of the Levy Spectrometer on the Automated Planet Finder. We thank the University of California and Google for supporting Lick Observatory, and the UCO staff for their dedicated work scheduling and operating the telescopes of Lick Observatory. This paper is based on data collected by the TESS mission. Funding for the TESS mission is provided by the NASA Explorer Program. C.D. gratefully acknowledges support from the David & Lucile Packard Foundation and the Alfred P. Sloan Foundation. A.A.B., B.S.S., and I.A.S. acknowledge the support of the Ministry of Science and Higher Education of the Russian Federation under the grant 075-15-2020-780(N13.1902.21.0039). J.K. gratefully acknowledges the support of the Swedish National Space Agency (SNSA; DNR 2020-00104). A.W.M. is supported by the NSF Graduate Research Fellowship grant No. DGE 1752814. J.M.A.M. is supported by the National Science Foundation Graduate Research Fellowship Program under grant No. DGE-1842400. J.M.A.M. acknowledges the LSSTC Data Science Fellowship Program, which is funded by LSSTC, NSF Cybertraining grant No. 1829740, the Brinson Foundation, and the Moore Foundation; his participation in the program has benefited this work. C.K.H. acknowledges support from the National Science Foundation Graduate Research Fellowship Program under grant No. DGE 2146752. M.R. is supported by the National Science Foundation Graduate Research Fellowship Program under grant No. DGE-1752134. R.A.R. is supported by an NSF Graduate Research Fellowship, grant No. DGE 1745301. P.D. is supported by a National Science Foundation (NSF) Astronomy and Astrophysics Postdoctoral Fellowship under award AST-1903811. R.L. acknowledges financial support from the Centre of Excellence "Severo Ochoa" award to the Instituto de Astrofísica de Andalucía (SEV-2017-0709). D.H. acknowledges support from the Alfred P. Sloan Foundation and the National Aeronautics and Space Administration (80NSSC20K0593, 80NSSC21K0652). T.M. acknowledges financial support from the Spanish Ministry of Science and Innovation (MICINN) through the Spanish State Research Agency, under the Severo Ochoa Program 2020-2023 (CEX2019-000920-S). K.W.F.L. acknowledges support by DFG grants RA714/14-1 within the DFG Schwerpunkt SPP 1992, "Exploring the Diversity of Extrasolar Planets."

With recent advances in modelling stars using high-precision asteroseismology, the systematic effects associated with our assumptions of stellar helium abundance ($Y$) and the mixing-length theory parameter ($\alpha_\mathrm{MLT}$) are becoming more important. We apply a new method to improve the inference of stellar parameters for a sample of Kepler dwarfs and subgiants across a narrow mass range ($0.8 < M < 1.2\,\mathrm{M_\odot}$). In this method, we include a statistical treatment of $Y$ and the $\alpha_\mathrm{MLT}$. We develop a hierarchical Bayesian model to encode information about the distribution of $Y$ and $\alpha_\mathrm{MLT}$ in the population, fitting a linear helium enrichment law including an intrinsic spread around this relation and normal distribution in $\alpha_\mathrm{MLT}$. We test various levels of pooling parameters, with and without solar data as a calibrator. When including the Sun as a star, we find the gradient for the enrichment law, $\Delta Y / \Delta Z = 1.05^{+0.28}_{-0.25}$ and the mean $\alpha_\mathrm{MLT}$ in the population, $\mu_\alpha = 1.90^{+0.10}_{-0.09}$. While accounting for the uncertainty in $Y$ and $\alpha_\mathrm{MLT}$, we are still able to report statistical uncertainties of 2.5 per cent in mass, 1.2 per cent in radius, and 12 per cent in age. Our method can also be applied to larger samples which will lead to improved constraints on both the population level inference and the star-by-star fundamental parameters., Comment: 21 pages, 15 figures, 12 tables. Accepted for publication in Monthly Notices of the Royal Astronomical Society

In Chapter 16 of Astronomia nova, Kepler describes and applies a method for finding the parameters of what he will call the vicarious hypothesis: a model that still assumes circular orbits and an equant point, but does not assume the bisection of the eccentricity, that is, that the center of the orbit is halfway between the equant point and the Sun. The method allows Kepler to find independently both centers in a very elegant way, but its application is tedious. He confesses that he had to apply it seventy times over a period of 5 years to obtain trustable results. Years earlier, when Kepler arrived to work with Tycho, he found that Tycho and Longomontanus had rejected bisection and somehow had obtained a ratio between eccentricities that, as Kepler himself highlights, happened to be very close to the one Kepler would later find after so much effort. Kepler does not say how Tycho and Longomontanus obtained their parameters and, to the best of my knowledge, there is no single published work that attempts to answer this question. Still, it is a very interesting question to ask how they arrived at values so close to those that took so much pain for Kepler to obtain. Recently, I published a paper describing a method Tycho used for finding Saturn’s parameters. In this paper, I show that by applying this method to the data of Tychonic observations of oppositions, it is possible to arrive at parameters very close to those that we know Tycho found. In this way, I argue that this is the method Tycho applied for obtaining Mars’s parameters. The simplicity of the Tychonic method contrasts with the complexity of Kepler’s.