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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.

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.

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.

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.

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.

In the present work, in order to estimate the semi-amplitude of the radial velocity, we evaluate the contribution of the Doppler beaming effect to the phase curves of the all confirmed extrasolar planets (2776, September 2019), observed so far by the Kepler telescope. By modeling the tiny photometric variations (reflection, ellipsoidal and Doppler beaming effects) of the light curves, we found that the best observational data are in close agreement with the theoretical and published values of the amplitudes only for exoplanets: KOI-13b and TrES-2b. The derived values for the radial velocity also are in good agreement with those published by some authors. Furthermore, we found it necessary to introduce a third harmonic (3Φ) contribution into the KOI-13b and HAT-P7b light curve models, in order to decrease the residuals.

This paper deals with the integrations of homogeneous quasi-Keplerian Hamiltonians, that is, perturbed Kepler Hamiltonians which perturbation is of the form ∑ j = 2 N A j ∕ r j with A j constant. Although there are many applications of these Hamiltonians in Physics, Astronomy and Astrodynamics, we focus our interest on a particular case in the core of Artificial Satellite Theory, the Cid’s radial intermediary. For this problem, we integrate the equations of motion in two different ways, by means of the elliptic P -Weierstrass function and by using the Krylov–Bogoliubov averaging method to integrate a perturbed harmonic oscillator. In this case, the resulting solution is given in terms of the classical Kepler’s equation, with no need of introducing more complex generalized Kepler’s equation.

We present the results of a search for stellar flares from stars neighbouring the target sources in the Kepler short cadence data. These flares have been discarded as contaminants in previous surveys and therefore provide an unexplored resource of flare events, in particular high energy events from faint stars. We have measured M dwarf flare energies up to 1.5$\times$10^35 erg, pushing the limit for flare energies measured using Kepler data. We have used our sample to study theflaring activity of wide binaries, finding that the lower mass counterpart in a wide binary flares more often at a given energy. Of the 4430 flares detected in our original search, 298 came from a neighbouring star, a rate of 6.7$\pm$0.4 per cent for the Kepler short cadence lightcurves. We have used our sample to estimate a 5.8$\pm$0.1 per cent rate of false positive flare events in studies using TESS short cadence data., 10 pages, 2 figures, 2 tables. Accepted for publication in the Monthly Notices of the Royal Astronomical Society

We examine the origins of the Kepler 36 planetary system, which features two very different planets: Kepler 36b ($\rm \rho = 7.46$ $\rm g$ $\rm cm^{-3}$) and Kepler 36c ($\rm \rho = 0.89$ $\rm g$ $\rm cm^{-3}$). The planets lie extremely close to one another, separated by just 0.01 au, and they orbit just a tenth of an au from the host star. In our origin scenario, Kepler 36b starts with far less mass than Kepler 36c, a gaseous giant planet that forms outside the ice line and quickly migrates inwards, capturing its neighbour into its 2:1 mean-motion resonance while continuing to move inwards through a swarm of planetesimals and protoplanets. Subsequent collisions with these smaller bodies knock Kepler 36b out of resonance and raise its mass and density (via self-compression). We find that our scenario can yield planets whose period ratio matches that of Kepler 36b and c, although these successes are rare, occurring in just 1.2 per cent of cases. However, since systems like Kepler 36 are themselves rare, this is not necessarily a drawback.

If a transiting exoplanet has a moon, that moon could be detected directly from the transit it produces itself, or indirectly via the transit timing variations it produces in its parent planet. There is a range of parameter space where the Kepler Space Telescope is sensitive to the TTVs exomoons might produce, though the moons themselves would be too small to detect photometrically via their own transits. The Earth's Moon, for example, produces TTVs of 2.6 minutes amplitude by causing our planet to move around their mutual centre of mass. This is more than Kepler's short-cadence interval of 1 minute and so nominally detectable (if transit timings can be measured with comparable accuracy), even though the Moon's transit signature is only 7% that of Earth's, well below Kepler's nominal photometric threshold. Here we examine several Kepler systems, exploring the hypothesis that an exomoon could be detected solely from the TTVs it induces on its host planet. We compare this with the alternate hypothesis that the TTVs are caused by an non-transiting planet in the system. We examine 13 Kepler systems and find 8 where both hypotheses explain the observed TTVs equally well. Though no definitive exomoon detection can be claimed on this basis, the observations are nevertheless completely consistent with a dynamically stable moon small enough to fall below Kepler's photometric threshold for transit detection, and these systems warrant further observation and analysis., 17 pages. 15 figures. Accepted for publication on November 26, 2020, by the Monthly Notices of the Royal Astronomical Society

An algorithm for the numerical solution of Kepler’s equation with machine precision is presented. The convergence of the iterative sequence of Newton’s method is proved for the indicated initial approximation. The problem of finding a numerical solution to Kepler’s equation as a floating point number is formulated. Aspects related to computations near machine zero are taken into account. We analyzed the accuracy of the possible result. A problem is identified that arises when tending for the highest possible accuracy and a solution is proposed. An estimate is given of the computer time required to solve Kepler’s equation by this method.

We discuss the current state of problems associated with the discovery and study of exocomets, i.e objects of extrasolar systems, that are in many aspects similar to the solar system comets. Thus far, more than 4,300 exoplanetary systems have been discovered, but little is known about the populations of subplanetary bodies in these systems, in particular comets. Existing theories of planet formation suggest that populations of small bodies in the planetary systems should be numerous, especially at the early stages of their formation. Currently, most of the stars observed with the confirmed transit exoplanets and candidate stars with exoplanetary systems have been collected in the Kepler and TESS space mi- ssion databases. These databases can be used for a search and study of the exocomet transit signatures in extrasolar systems. So far, the number of observed cases of exocomet transits has been small, only about 20 events. Due to the rapid accumulation of data, new researches aimed to identify the specific transit events and study the physical characteristics of small bodies in the extrasolar systems are of great importance.Worth considering is the concept of “falling evaporating bodies”, massive enough bodies surrounded by mini- atmospheres, which fall on the parent star. The events might produce the variable, short-time red-shifts of some spectral features in their spectra. Alternative evidence of exocomet transits can be obtained by detection of the cometary emissions in CO, C, and O lines in the millimeter region of the spectra of debris disks by the ALMA and APEX telescopes. We discuss the known detection methods based on the analysis of the photometric and spectral series of observational data of space missions and ground- based complexes. Some results of experimental studi- es of the exocometary transit signatures obtained by other authors are presented and discussed.

Dedicated transiting surveys, such as the Kepler space telescope, have provided the astronomy community with a rich data set resulting in many new discoveries. In this paper, we look at eight Kepler objects identified by Wheeler & Kipping with a periodic, broad increase in flux, that look distinctly different from intrinsic star variability. We consider two physical phenomena as explanations for these observed Kepler light curves; the first being the classical explanation while the second being an alternative scenario: (i) tidal interactions in a binary star system, and (ii) forward scattering from an optically thin cloud around an exoplanet. We investigate the likelihood of each model by modelling and fitting to the observed data. The binary system qualitatively does a good job of reproducing the shape of the observed light curves due to the tidal interaction of the two stars. We do, however, see a mismatch in flux right before or after the peak brightness. We find that six out of the eight systems require an F-type primary star with a K-type companion with large eccentricities. At the same time, we find that optically thin discs, modelled using a Henyey–Greenstein phase function are also able to generate these broad brightening events. Five of the eight observed objects can be described with this new hypothesis in the absence of RV observations. As the other three are not well-described by the disc model, we conclude that they are indeed heartbeat stars.

Approximately half of the planets discovered by NASA's Kepler mission are in systems where just a single planet transits its host star, and the remaining planets are observed to be in multi-planet systems. Recent analyses have reported a dichotomy in the eccentricity distribution displayed by systems where a single planet transits compared with that displayed by the multi-planet systems. Using $N$-body simulations, we examine the hypothesis that this dichotomy has arisen because inner systems of super-Earths are frequently accompanied by outer systems of giant planets that can become dynamically unstable and perturb the inner systems. Our initial conditions are constructed using a subset of the known Kepler five-planet systems as templates for the inner systems, and systems of outer giant planets with masses between those of Neptune and Saturn that are centred on orbital radii $2 \le a_{\rm p} \le 10$ au. The parameters of the outer systems are chosen so that they are always below an assumed radial velocity detection threshold of 3 ms$^{-1}$. The results show an inverse relation between the mean eccentricities and the multiplicites of the systems. Performing synthetic transit observation of the final systems reveals dichotomies in both the eccentricity and multiplicity distributions that are close to being in agreement with the Kepler data. Hence, understanding the observed orbital and physical properties of the compact systems of super-Earths discovered by Kepler may require holistic modelling that couples the dynamics of both inner and outer systems of planets during and after the epoch of formation., 19 pages, 24 figures, accepted to MNRAS

The ratio of small-to-large separations r010 has been widely used in helioseismology and asteroseismology to investigate the internal structure of a star, as it is approximately independent of the structure of the outer layers. Several studies have used this tool to constrain the convective-core overshooting of main-sequence stars (i.e. 0.0 ≤ δov ≤ 0.2). This is consistent with the generally accepted values. However, Yang et al. have proposed that there is large convective-core overshooting in the Kepler targets KIC 2837475 and 11081729: 1.2 ≤ δov ≤ 1.6 and 1.7 ≤ δov ≤ 1.8, respectively. These are much larger than the normal values. Thus, the aim of this study is to re-investigate the ratios of the two stars using a model-independent method with the latest p-mode observations. Our results indicate that there is no robustness for including such a large convective-core overshooting while modelling these two stars. In fact, this leads to over-fitting, and the observational constraints of r010 prefer models with a normal convective-core overshooting (i.e. 0.0 ≤ δov ≤ 0.2) as the candidates for the best-fitting model of KIC 2837475 and 11081729.

The K2 mission of the Kepler Space Telescope offers a unique possibility to examine sources of both Galactic and Extra-galactic origin with high cadence photometry. Alongside the multitude of supernovae and quasars detected within targeted galaxies, it is likely that Kepler has serendipitously observed many transients throughout K2. Such events will likely have occurred in background pixels, coincidentally surrounding science targets. Analysing the background pixels presents the possibility to conduct a high cadence survey with areas of a few square degrees per campaign. We demonstrate the capacity to independently recover key K2 transients such as KSN 2015K and SN 2018oh. With this survey, we expect to detect numerous transients and determine the first comprehensive rates for transients with lifetimes $\leq1$ day., 13 pages, 10 figures, 4 tables

In this work, we investigate configuration formation of two inner terrestrial planets near mean motion resonance (MMRs) induced by the perturbation of a distant gas-giant for the Kepler-68 system, by conducting thousands of numerical simulations. The results show that the formation of terrestrial planets is relevant to the speed of Type I migration, the mass of planets, and the existence of giant planet. The mass and eccentricity of the giant planet may play a crucial role in shaping the final configuration of the system. The inner planet pair can be trapped in 5:3 or 7:4 MMRs if the giant planet revolves the central star with an eccentric orbit, which is similar to the observed configuration of Kepler-68. Moreover, we find that the eccentricity of the middle planet can be excited to roughly 0.2 if the giant planet is more massive than 5 $M_J$,otherwise the terrestrial planets are inclined to remain near-circular orbits. Our study may provide a likely formation scenario for the planetary systems that harbor several terrestrial planets near MMRs inside and one gas-giant exterior to them., Comment: 13 pages, 8 figures, accepted for publication in MNRAS

According to statistics of planetary period ratios in multi-planet extrasolar systems, evident excesses appear just over the exact integral ratios 2 : 1 and 3 : 2 , while deficits exist on the near left side. There are various dynamical explanations for the phenomenon. For three observed planets in Kepler-9 system, the period ratio of the planet b and c approximately equals to 2.03, which cause this planet pair as a typical sample close to the 2:1 resonance. For two situations where secular interactions are considered only and resonance perturbations are added in, we applied Hamiltonian functions with second-order eccentricity terms to provide positions of current orbital configurations located in the level curves of energy as well as surfaces of section, then discussed the probable near resonance configurations of the two planets.

Solar-type stars in eclipsing binaries are proving to be a remarkable resource of knowledge for testing models of stellar evolution, as spectroscopic and photometric studies have opened up a window into their interiors. Until recently, many cases have been worked out with Kepler data. in an ongoing effort to elucidate this research, we examine five detached eclipsing binaries, selected from the Kepler catalogue. There is a well-known stellar parameter discrepancy for low-mass stars, in that the observed radii and masses are often larger and stars overluminous than predicted by theory by several per cent. in our samples, we found five double-lined binaries, with solar-type stars dominating the spectrum. the orbital and light-curve solutions were found for them, and compared with isochrones, in order to estimate absolute physical parameters and evolutionary status of the components. An important aspect of this work is that the calculated stellar radii and masses are consistent with theoretical models within the uncertainties, whereas the estimated temperatures from the disentangled spectra of the components are no different than predicted., ESO [089.D-0097(B), 091.D-0145(B), 094.A-9029(R), 098.D-0076(A), 0100.D-0339(B), 0100.D-0273(A)]; NASA's Science Mission Directorate; National Aeronautics and Space AdministrationNational Aeronautics & Space Administration (NASA); National Science FoundationNational Science Foundation (NSF); Ege University Research FoundationEge University [FDK-2019-20215], This research made use of data collected at ESO under programmes 089.D-0097(B) and 091.D-0145(B) (by K. Helminiak), 094.A-9029(R) (by R. Gredel), 098.D-0076(A) (by J. Southworth), 0100.D-0339(B) (by G. Pietrzynski), 0100.D-0273(A) (by W. Gieren). 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 (MAST). This work has also made use of data from the European Space Agency (ESA) mission Gaia (http://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC, http://www.cosmos.esa.int/web/gaia/dpac/consortium).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 andAnalysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation. We thank Ege University Research Foundation (Project No. FDK-2019-20215) for supporting this study. the authors express their sincere thanks to an anonymous referee whose valuable comments led to an improvement of the paper. This article is a part of the PhD thesis of B. Hoyman. the following internet-based resources were used in research for this paper: the NASA Astrophysics Data System; the SIMBAD data base operated at CDS, Strasbourg, France.

This work deals with the full reduction of the spatial Kepler system for bounded and unbounded motions. Precisely, we consider the four-dimensional oscillator associated to the Kepler system and ca...

On August 12, 2018, NASA launched the Parker Solar Probe (PSP) to explore regions very near the Sun. Losing enough energy and angular momentum to approach the Sun requires either an impractical amount of fuel or a maneuver called a gravity assist. A gravity assist is essentially an elastic collision with a massive, moving target—Rutherford scattering from a planet. Gravity assists are often used to gain energy in missions destined for the outer solar system, but they can also be used to lose energy. Reaching an orbit sufficiently close to the Sun requires that PSP undergoes not one but seven successive gravity assists off the planet Venus. This simple description poses several conceptual challenges to the curious physics student. Why is it so much more challenging to get to the Sun than to leave the Solar System? Why does it take more than one gravity assist to achieve this, and why does it require seven? Would it be more effective to use Mercury instead of Venus? These questions can be answered using the basic physics principles of Kepler's laws and Rutherford scattering. The reasoning can be presented in an illuminating graphical format to show that these and other seemingly arcane aspects of interplanetary exploration can be understood at the undergraduate level.

International audience; We present the analysis of the multi-planetary system Kepler-117, which is part of our program of observations of Kepler planets. This system is composed of a ~ 30 MEarth planet in a ~ 19 days orbit and a ~ 2 MJ planet orbiting in ~ 51 days. Both the orbits have low eccentricity. The planets are not close to an exact low-order mean motion resonance, but exhibit significant transit timing variations (TTVs) nevertheless. We perform a combined Markov Chain Monte Carlo fit on all the available data: the Kepler photometry, the TTVs, the radial velocities we obtained with SOPHIE/OHP and the stellar parameters. The prime result is that the modelling of the TTVs allows to increase the precision on the system parameters which are not constrained by the radial velocities alone.

No presente trabalho são apresentados dados coletados na literatura científica em relação ao afélio e ao periélio de alguns corpos celestes, e com base na primeira lei de Kepler, são determinadas as equações elípticas que descrevem suas trajetórias ao redor do Sol. Utilizando o binômio de Newton, e conceitos básicos de conservação de energia e do momento angular de um sistema físico, pode ser obtida a velocidade máxima orbital de cada corpo celeste aqui analisado em função da excentricidade de sua órbita elíptica e de seu eixo. Obtido o tempo orbital de cada um desses corpos celestes e o comprimento de suas trajetórias em torno do Sol, sua velocidade média orbital foi calculada usando a cinemática do movimento. Os resultados obtidos usando essa metodologia simplificada encontram-se em boa concordância com os divulgados pelos astrônomos.

In the first chapter of his Astronomia Nova, Kepler introduced a diagram that, he claimed, represents the path of Mars between 1580 and 1596, assuming a resting Earth. In the words of Willi...

Taking advantage of the unparalleled quantity and quality of high-cadence Kepler light curves of several dwarf novae, the strength of the flickering and the high-frequency spectral index of their power spectra are investigated as a function of magnitude around the outburst cycle of these systems. Previous work suggesting that the flickering strength (on a magnitude scale) is practically constant above a given brightness threshold and only rises at fainter magnitudes is confirmed for most of the investigated systems. As a new feature, a hysteresis in the flickering strength is seen in the sense that at the same magnitude level flickering is stronger during decline from outburst than during the rise. A similar hysteresis is also seen in the spectral index. In both cases, it can qualitatively be explained under plausible assumptions within the disc instability model model for dwarf nova outbursts.

Data from the Transiting Exoplanet Survey Satellite (TESS) has produced of order one million light curves at cadences of 120 s and especially 1800 s for every ~27-day observing sector during its two-year nominal mission. These data constitute a treasure trove for the study of stellar variability and exoplanets. However, to fully utilize the data in such studies a proper removal of systematic noise sources must be performed before any analysis. The TESS Data for Asteroseismology (T'DA) group is tasked with providing analysis-ready data for the TESS Asteroseismic Science Consortium, which covers the full spectrum of stellar variability types, including stellar oscillations and pulsations, spanning a wide range of variability timescales and amplitudes. We present here the two current implementations for co-trending of raw photometric light curves from TESS, which cover different regimes of variability to serve the entire seismic community. We find performance in terms of commonly used noise statistics to meet expectations and to be applicable to a wide range of different intrinsic variability types. Further, we find that the correction of light curves from a full sector of data can be completed well within a few days, meaning that when running in steady-state our routines are able to process one sector before data from the next arrives. Our pipeline is open-source and all processed data will be made available on TASOC and MAST., 27 pages, 15 figures, accepted for publication in The Astrophysical Journal Supplement Series

The anomalously large radii of highly-irradiated gaseous exoplanets has long been a mystery. One mechanism suggested as a solution for hot Jupiters is the heating of the deep atmosphere via the vertical advection of potential temperature resulting in an increased internal entropy. Here we intend to explore if this mechanism can also explain the observed brown dwarf radii trend: a general increase in radius with irradiation, with an exception for highly-irradiated brown dwarfs orbiting white dwarfs. We use a 3D GCM, DYNAMICO, to run a series of long-timescale models of the atmospheres of Kepler-13Ab, KELT-1b, and SDSS1411B. These models allow us to explore not only if a stable advective adiabat can develop, but also the associated dynamics. We find that our models fall into two distinct regimes: Kepler-13Ab and KELT-1b both show signs of significant deep heating and hence maintain adiabats that are hotter than 1D models predict. On the other hand, SDSS1411B exhibits a much weaker downward heating profile which not only struggles to heat the interior under ideal conditions, but is highly sensitive to the presence of deep radiative dynamics. We find that the vertical advection of potential temperature by large-scale atmospheric circulations represents a robust mechanism to explain the trend of increasing inflation with irradiation, including the exception for highly irradiated brown dwarfs orbiting white dwarfs. This can be understood as occurring due to the role that increasing rotational influence plays on mid- to-high latitude advective dynamics. Furthermore, when paired with a suitable parametrisation of the outer atmosphere irradiation profile, this mechanism alone could potentially provide a complete explanation for the observed levels of inflation in our brown dwarfs., 20 pages, 11 figures. Accepted for publication in A&A. Updated version with a fixed typo in the vertical enthalpy flux equation

The NASA Transiting Exoplanet Survey Satellite (TESS) is observing tens of millions of stars with time spans ranging from $\sim$ 27 days to about 1 year of continuous observations. This vast amount of data contains a wealth of information for variability, exoplanet, and stellar astrophysics studies but requires a number of processing steps before it can be fully utilized. In order to efficiently process all the TESS data and make it available to the wider scientific community, the TESS Data for Asteroseismology working group, as part of the TESS Asteroseismic Science Consortium, has created an automated open-source processing pipeline to produce light curves corrected for systematics from the short- and long-cadence raw photometry data and to classify these according to stellar variability type. We will process all stars down to a TESS magnitude of 15. This paper is the next in a series detailing how the pipeline works. Here, we present our methodology for the automatic variability classification of TESS photometry using an ensemble of supervised learners that are combined into a metaclassifier. We successfully validate our method using a carefully constructed labelled sample of Kepler Q9 light curves with a 27.4 days time span mimicking single-sector TESS observations, on which we obtain an overall accuracy of 94.9%. We demonstrate that our methodology can successfully classify stars outside of our labeled sample by applying it to all $\sim$ 167,000 stars observed in Q9 of the Kepler space mission., 35 pages, 17 figures, 6 tables, Accepted for publication in The Astronomical Journal

Many fundamental physical processes regarding planetary formation in protoplanetary disks are still imperfectly understood, with an elusive phenomenon being turbulence in such disks. Observations are available of planetary systems and of some protoplanetary disks, which can serve as a starting point for these investigations. Detected systems reveal different architectures of planets. One particularly interesting case to consider is the Kepler-223 system, which contains a rare configuration of four planets in a resonance chain, implying a certain migration history. We aim to use the orbital configuration of Kepler-223's planets to constrain the parameters of the protoplanetary disk that allow for the formation of a chain of mean-motion resonances that resembles the one of Kepler-223. The parameters we aim to investigate are primarily the disk viscosity and surface density. We use the swift_symba N-body integrator with additional dissipative forces to mimic planet-disk interactions. We constrain the surface densities and viscosities that allow the formation of a resonant chain like that of Kepler-223. We find that surface densities of up to a few minimum mass solar nebula (MMSN) surface densities and disk viscosity parameters $\alpha$ of a few $10^{-3}$ up to $10^{-2}$ are most successful at reproducing the architecture of this particular planetary system. We describe how these two quantities are linked to each other considering the success of reproducing the chain and find that higher disk surface densities in turn require lower viscosities to build the chain. Our results show that well characterized observed planetary systems hold information about their formation conditions in the protoplanetary disks and that it is possible to extract this information, namely the initial disk surface density and viscosity, helping to constrain planet formation., Comment: 12 pages, 7 figues, accepted for publication in A&A

A supernova close enough to the Earth is a spectacular event: it can appear as a \new star" as luminous as Venus, or even more, visible for several days. The rate of Galactic supernovae is expected to be of about one in 30 years, with a fraction visible at naked eye; however in all the history of human civilization only seven supernovae in the Milky Way have been reported, the last two (1572 and 1604) during Galilei's life. The supernova of 1604, today called Kepler's Supernova, was observed by Galilei, Kepler and other astronomers in Europe, Korea, and China. Like the supernova SN1572, today called Tycho's supernova, it has been the subject of extensive studies, and inspired observational measurements and philosophical considerations on the nature of the heavens. The remnant of SN1604 has been indicated by recent X- and gamma-ray data to be a likely site of cosmic ray acceleration. The first recorded data of optical observations, together with new data, can still tell us a lot about the early evolution of this supernova.

Unlike the conventional design of aspheric shaping systems, in order to provide a laser source for applications such as multi-beam laser interference, which can maintain evenly distributed power over a large distance, the influence of shape parameter and aperture on long-distance propagation performance of Kepler refractive beam shaping system is studied. Current work describes the lens, designed automatically by using ZEMAX programming language (ZPL), and simulations of Kepler refractive shaping systems of flattened Lorenz (FL) beams with different shape parameters and apertures.

The spectroscopic class of subdwarf A-type (sdA) stars has come into focus in recent years because of their possible link to extremely low-mass white dwarfs, a rare class of objects resulting from binary evolution. Although most sdA stars are consistent with metal-poor halo main-sequence stars, the formation and evolution of a fraction of these stars are still matters of debate. The identification of photometric variability can help to put further constraints on the evolutionary status of sdA stars, in particular through the analysis of pulsations. Moreover, the binary ratio, which can be deduced from eclipsing binaries and ellipsoidal variables, is important as input for stellar models. In order to search for variability due to either binarity or pulsations in objects of the spectroscopic sdA class, we have extracted all available high precision light curves from the Kepler K2 mission. We have performed a thorough time series analysis on all available light curves, employing three different methods. Frequencies with a signal-to-noise ratio higher than four have been used for further analysis. From the 25 targets, 13 turned out to be variables of different kinds (i.e. classical pulsating stars, ellipsoidal and cataclysmic variables, eclipsing binaries, and rotationally induced variables). For the remaining 12 objects, a variability threshold was determined., 11 pages, 11 figures, 3 tables, accepted for publication in Astronomy & Astrophysics

We report on precise Doppler measurements of L231-32 (TOI-270), a nearby M dwarf ($d=22$ pc, $M_\star = 0.39$ M$_\odot$, $R_\star = 0.38$ R$_\odot$), which hosts three transiting planets that were recently discovered using data from the Transiting Exoplanet Survey Satellite (TESS). The three planets are 1.2, 2.4, and 2.1 times the size of Earth and have orbital periods of 3.4, 5.7, and 11.4 days. We obtained 29 high-resolution optical spectra with the newly commissioned Echelle Spectrograph for Rocky Exoplanet and Stable Spectroscopic Observations (ESPRESSO) and 58 spectra using the High Accuracy Radial velocity Planet Searcher (HARPS). From these observations, we find the masses of the planets to be $1.58 \pm 0.26$, $6.15 \pm 0.37$, and $4.78 \pm 0.43$ M$_\oplus$, respectively. The combination of radius and mass measurements suggests that the innermost planet has a rocky composition similar to that of Earth, while the outer two planets have lower densities. Thus, the inner planet and the outer planets are on opposite sides of the `radius valley' -- a region in the radius-period diagram with relatively few members, which has been interpreted as a consequence of atmospheric photo-evaporation. We place these findings into the context of other small close-in planets orbiting M dwarf stars, and use support vector machines to determine the location and slope of the M dwarf ($T_\mathrm{eff} < 4000$ K) radius valley as a function of orbital period. We compare the location of the M dwarf radius valley to the radius valley observed for FGK stars, and find that its location is a good match to photo-evaporation and core-powered mass loss models. Finally, we show that planets below the M dwarf radius valley have compositions consistent with stripped rocky cores, whereas most planets above have a lower density consistent with the presence of a H-He atmosphere., Accepted for publication in MNRAS

During the survey phase of the Kepler mission, several thousands of stars were observed in short cadence, allowing the detection of solar-like oscillations in more than 500 main-sequence and sub-giant stars. Later, the Kepler Science Office discovered an issue in the calibration that affected half of the short-cadence data, leading to a new data release (DR25) with improved corrections. We re-analyze the one-month time series of the Kepler survey phase to search for new solar-like oscillations. We study the seismic parameters of 99 stars (46 targets with new reported solar-like oscillations) increasing by around 8% the known sample of solar-like stars with asteroseismic analysis of the short-cadence data from Kepler. We compute the masses and radii using seismic scaling relations and find that this new sample populates the massive stars (above 1.2Ms and up to 2Ms) and subgiant phase. We determine the granulation parameters and amplitude of the modes, which agree with previously derived scaling relations. The stars studied here are slightly fainter than the previously known sample of main-sequence and subgiants with asteroseismic detections. We also study the surface rotation and magnetic activity levels of those stars. Our sample of has similar levels of activity compared to the previously known sample and in the same range as the Sun between the minimum and maximum of its activity cycle. We find that for 7 stars, a possible blend could be the reason for the previous non detection. We compare the radii obtained from the scaling relations with the Gaia ones and find that the Gaia radii are overestimated by 4.4% on average compared to the seismic radii and a decreasing trend with evolutionary stage. We re-analyze the DR25 of the main-sequence and sub-giant stars with solar-like oscillations previously detected and provide their global seismic parameters for a total of 526 stars., 18 pages, 21 figures. Accepted for publication in A&A

Targeted observations of possible exomoon host systems will remain difficult to obtain and time-consuming to analyze in the foreseeable future. As such, time-domain surveys such as Kepler, K2 and TESS will continue to play a critical role as the first step in identifying candidate exomoon systems, which may then be followed-up with premier ground- or space-based telescopes. In this work, we train an ensemble of convolutional neural networks (CNNs) to identify candidate exomoon signals in single-transit events observed by Kepler. Our training set consists of ${\sim}$27,000 examples of synthetic, planet-only and planet+moon single transits, injected into Kepler light curves. We achieve up to 88\% classification accuracy with individual CNN architectures and 97\% precision in identifying the moons in the validation set when the CNN ensemble is in total agreement. We then apply the CNN ensemble to light curves from 1880 Kepler Objects of Interest with periods $>10$ days ($\sim$57,000 individual transits), and further test the accuracy of the CNN classifier by injecting planet transits into each light curve, thus quantifying the extent to which residual stellar activity may result in false positive classifications. We find a small fraction of these transits contain moon-like signals, though we caution against strong inferences of the exomoon occurrence rate from this result. We conclude by discussing some ongoing challenges to utilizing neural networks for the exomoon search., 14 pages, 13 figures, 1 table. Accepted for publication in Monthly Notices of the Royal Astronomical Society, 15 September 2021

Integrals of motion are constructed from noncommutative (NC ) Kepler dynamics, generating $$\mathrm{SO}(3)$$ , $$\mathrm{SO}(4)$$ , and $$\mathrm{SO}(1,3)$$ dynamical symmetry groups. The Hamiltonian vector field is derived in action–angle coordinates, and the existence of a hierarchy of bi-Hamiltonian structures is highlighted. Then, a family of Nijenhuis recursion operators is computed and discussed.

We present the second results of an ensemble and systematic survey of oscillation mode variability in compact pulsators observed with the original {\sl Kepler} mission. Two types of flux calibrations, raw and corrected, collected on two hot B subdwarf stars, KIC\,2438324 and KIC\,11179657, are thoroughly examined with the goal to evaluate the difference of patterns when oscillation modes modulate in amplitude (AM) and frequency (FM). We concentrate on AMs and FMs occurring in seven multiplet components in each star as representative frequencies. The analysis shows that FM measurements are independent of the flux calibration we choose. However, if flux contamination by nearby stars is large, AMs may be significantly different between raw and corrected flux. In addition, AMs suffer, to some extent, from systematic modulation pattern which is most likely induced by instrumental effects {and} differs from one star to another. Our results indicate that stars with no contamination are better candidates to quantitatively compare modulation patterns with theory and should be given a higher priority for such studies, since light contamination will destroy real amplitude modulation patterns., 17 pages, 12 figures, 3 tables, ApJ in press

The planetary systems detected so far already exhibit a wide diversity of architectures, and various methods are proposed to study quantitatively this diversity. Straightforward ways to quantify the difference between two systems and more generally, two sets of multiplanetary systems, are useful tools in the study of this diversity. In this work we present a novel approach, using a Weighted extension of the Energy Distance (WED) metric, to quantify the difference between planetary systems on the logarithmic period-radius plane. We demonstrate the use of this metric and its relation to previously introduced descriptive measures to characterise the arrangements of Kepler planetary systems. By applying exploratory machine learning tools, we attempt to find whether there is some order that can be ascribed to the set of Kepler multiplanet system architectures. Based on WED, the 'Sequencer', which is such an automatic tool, identifies a progression from small and compact planetary systems to systems with distant giant planets. It is reassuring to see that a WED-based tool indeed identifies this progression. Next, we extend WED to define the Inter-Catalogue Energy Distance (ICED) - a distance metric between sets of multiplanetary systems. We have made the specific implementation presented in the paper available to the community through a public repository. We suggest to use these metrics as complementary tools in attempting to compare between architectures of planetary system, and in general, catalogues of planetary systems., Comment: 8 pages, 5 figures, accepted for publication in A&A, usage examples at: https://github.com/dolevbas/PASSta

Over the course of the last two decades, traditional models of planet formation have been repeatedly challenged by the emerging census of extrasolar planets. Key among them is the orbital architecture problem: while standard models of orbital migration predict resonant orbits for short-period objects, most planets do not appear to lie in orbital resonances. Here, we show that the four-planet system Kepler-221, not previously recognized to have active orbital resonances, has a three-body commensurability relation unique within the Kepler sample. Using a suite of numerical experiments as well as a perturbative analysis, we demonstrate that this system likely began as a resonant chain and proceeded to undergo large-scale divergence away from resonance, under the action of tidal dissipation. Our results further indicate that obliquity tides, driven by a secular spin–orbit resonance and mutual inclination, are an excellent candidate for driving this orbital divergence, and that the high tidal luminosity may also explain the anomalous size of planet b, which lies within the Fulton radius gap.

Early analyses of exoplanet statistics from the Kepler Mission revealed that a model population of multiple-planet systems with low mutual inclinations (${\sim1^{\circ}-2^{\circ}}$) adequately describes the multiple-transiting systems but underpredicts the number of single-transiting systems. This so-called "Kepler dichotomy" signals the existence of a sub-population of multi-planet systems possessing larger mutual inclinations. However, the details of these inclinations remain uncertain. In this work, we derive constraints on the intrinsic mutual inclination distribution by statistically exploiting Transit Duration Variations (TDVs) of the Kepler planet population. When planetary orbits are mutually inclined, planet-planet interactions cause orbital precession, which can lead to detectable long-term changes in transit durations. These TDV signals are inclination-sensitive and have been detected for roughly two dozen Kepler planets. We compare the properties of the Kepler observed TDV detections to TDV detections of simulated planetary systems constructed from two population models with differing assumptions about the mutual inclination distribution. We find strong evidence for a continuous distribution of relatively low mutual inclinations that is well-characterized by a power law relationship between the median mutual inclination ($\tilde{\mu}_{i,n}$) and the intrinsic multiplicity ($n$): $\tilde{\mu}_{i,n} = \tilde{\mu}_{i,5}(n/5)^{\alpha}$, where $\tilde{\mu}_{i,5} = 1.10^{+0.15}_{-0.11}$ and $\alpha = -1.73^{+0.09}_{-0.08}$. These results suggest that late-stage planet assembly and possibly stellar oblateness are the dominant physical origins for the excitation of Kepler planet mutual inclinations., Comment: Accepted to AJ, 19 pages, 10 figures (excluding appendix)