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GJ 1148 is an M-dwarf star, which has two well-separated Saturn mass planets with an orbital period ratio of around 13 and eccentricities of around 0.375 at the current epoch. A plausible scenario for producing the orbital architecture of the GJ 1148 system is planet-planet scattering. To test this scenario, we perform scattering experiments, assuming the third planet of 0.1 MJ (Jupiter’s mass) in the initial GJ 1148 system with initial orbital separations set to 3.5, 4, and 4.5 mutual Hill radii Rm,H respectively and initial semi-major axis of the innermost planet ai,1 in the range of 0.10-0.50 AU. The majority of scattering results in planet-planet collisions, followed by planet ejections, and planet removals as its distance to the star are smaller than a critical value of 0.02 AU. Among them, only the post-ejection two-planet systems have similar properties to the GJ 1148 system, and when ai,1 is around 0.21 AU, the semi-major axis of the inner planet GJ 1148 b can be reproduced. We further perform simulations with ai,1 in a narrower range between 0.16 and 0.30 AU, and found one system with similar orbital properties to the GJ 1148 system. Therefore, the simulation results suggest that the GJ 1148 system may have lost a giant planet. The two-sample Kolmogorov–Smirnov (KS) test on simulations with and without GR apsidal precession shows that it does not affect the ejection outcomes. When setting the mass of the third planet to 0.227 MJ of GJ1148 c, the optimal ai,1 move to about 0.29 AU.

A parameter to quantify macroscale (i.e., systemwide) asymmetry of tropical cyclones (TC) in infrared satellite images, galaxy asymmetry (GASYM), which is adopted from astronomy, is described. In addition, an alternative approach to identify TC cloud clusters that is based on a density-based spatial clustering algorithm, cluster identification (CI), is presented in this study. Although a commonly used approach in TC study, the predefined radius of calculation (ROC), can be used to identify the TC region in the calculation of GASYM, this approach is not optimal because the size of the TC cloud cluster is often unknown in the calculation. The area specified by the ROC often includes pixels that do not belong to the TC cloud cluster and excludes pixels that belong to the TC cloud cluster. The CI approach addresses this issue by identifying TC cloud clusters of any size with any shape, because it depends solely on the threshold brightness temperature that corresponds to the upper bound of the brightness temperature of the specific cloud types. This study shows that the CI approach can be integrated into the GASYM calculation as an objective measure of TC symmetry. Although GASYM-CI and intensity are correlated, the relationship between GASYM-CI and intensity depends on the size of the TC cloud cluster. Comparison between GASYM and an existing objective method to quantify symmetry of TCs, the deviation angle variance technique, is also presented.

Based on recently-taken and archival HARPS, FEROS and HIRES radial velocities (RVs), we present evidence for a new planet orbiting the first ascent red giant star HD33142 (with an improved mass estimate of 1.52$\pm$0.03 M$_\odot$), already known to host two planets. We confirm the Jovian mass planets HD33142 b and c with periods of $P_{\rm b}$ = 330.0$_{-0.4}^{+0.4}$ d and $P_{\rm c}$ = 810.2$_{-4.2}^{+3.8}$ d and minimum dynamical masses of $m_{\rm b}\sin{i}$ = 1.26$_{-0.05}^{+0.05}$ M$_{\rm Jup}$ and $m_{\rm c}\sin{i}$ = 0.89$_{-0.05}^{+0.06}$ M$_{\rm Jup}$. Furthermore, our periodogram analysis of the precise RVs shows strong evidence for a short-period Doppler signal in the residuals of a two-planet Keplerian fit, which we interpret as a third, Saturn-mass planet with $m_\mathrm{d}\sin{i}$ = 0.20$_{-0.03}^{+0.02}$ M$_{\rm Jup}$ on a close-in orbit with an orbital period of $P_{\rm d}$ =89.9$_{-0.1}^{+0.1}$ d. We study the dynamical behavior of the three-planet system configurations with an N-body integration scheme, finding it long-term stable with the planets alternating between low and moderate eccentricities episodes. We also performed N-body simulations, including stellar evolution and second-order dynamical effects such as planet-stellar tides and stellar mass-loss on the way to the white dwarf phase. We find that planets HD33142 b, c and d are likely to be engulfed near the tip of the red giant branch phase due to tidal migration. These results make the HD33142 system an essential benchmark for the planet population statistics of the multiple-planet systems found around evolved stars., Accepted for publication in AJ

Direct $N$-body simulations of a large number of particles, especially in the study of planetesimal dynamics and planet formation, have been computationally challenging even with modern machines. This work presents the combination of fully parallelized $N^2/2$ interactions and the incorporation of the GENGA code's close encounter pair grouping strategy to enable MIMD parallelization of the Symplectic Massive Body Algorithm (SyMBA) with OpenMP on multi-core CPUs in shared-memory environment. SyMBAp (SyMBA parallelized) preserves the symplectic nature of SyMBA and shows good scalability, with a speedup of 30.8 times with 56 cores in a simulation with 5,000 fully interactive particles., Accepted for publication in Research Notes of the AAS

TOI-2202 b is a transiting warm Jovian-mass planet with an orbital period of P=11.91 days identified from the Full Frame Images data of five different sectors of the TESS mission. Ten TESS transits of TOI-2202 b combined with three follow-up light curves obtained with the CHAT robotic telescope show strong transit timing variations (TTVs) with an amplitude of about 1.2 hours. Radial velocity follow-up with FEROS, HARPS and PFS confirms the planetary nature of the transiting candidate (a$_{\rm b}$ = 0.096 $\pm$ 0.002 au, m$_{\rm b}$ = 0.98 $\pm$ 0.06 M$_{\rm Jup}$), and dynamical analysis of RVs, transit data, and TTVs points to an outer Saturn-mass companion (a$_{\rm c}$ = 0.155 $\pm$ 0.003 au, m$_{\rm c}$= $0.37 \pm 0.10$ M$_{\rm Jup}$) near the 2:1 mean motion resonance. Our stellar modeling indicates that TOI-2202 is an early K-type star with a mass of 0.82 M$_\odot$, a radius of 0.79 R$_\odot$, and solar-like metallicity. The TOI-2202 system is very interesting because of the two warm Jovian-mass planets near the 2:1 MMR, which is a rare configuration, and their formation and dynamical evolution are still not well understood., Accepted for publication in AJ

Using the Hamilton Echelle Spectrograph at Lick Observatory, we have obtained precise radial velocities (RVs) of a sample of 373 G- and K-giant stars over more than 12 years, leading to the discovery of several single and multiple planetary systems. The RVs of the long-period (~53 years) spectroscopic binary $\epsilon$ Cyg (HIP 102488) are found to exhibit additional regular variations with a much shorter period (~291 days). We intend to improve the orbital solution of the $\epsilon$ Cyg system and attempt to identify the cause of the nearly periodic shorter period variations, which might be due to an additional substellar companion. We used precise RV measurements of the K-giant star $\epsilon$ Cyg from Lick Observatory, in combination with a large set of RVs collected more recently with the SONG telescope, as well as archival data sets. Our Keplerian model to the RVs characterizes the orbit of the spectroscopic binary to higher precision than achieved previously, resulting in a semi-major axis of $a = 15.8 \mathrm{AU}$, an eccentricity of $e = 0.93$, and a minimum mass of the secondary of $m \sin i = 0.265 M_\odot$. Additional short-period RV variations closely resemble the signal of a Jupiter-mass planet orbiting the evolved primary component with a period of $291 \mathrm{d}$, but the period and amplitude of the putative orbit change strongly over time. Furthermore, in our stability analysis of the system, no stable orbits could be found in a large region around the best fit. Both of these findings deem a planetary cause of the RV variations unlikely. Most of the investigated alternative scenarios, such as an hierarchical triple or stellar spots, also fail to explain the observed variability convincingly. Due to its very eccentric binary orbit, it seems possible, however, that $\epsilon$ Cyg could be an extreme example of a heartbeat system., Comment: 17 pages, 13 figures, accepted to A&A

Planets and satellites orbiting a binary system exist in the solar system and extrasolar planetary systems. Their orbits can be significantly different from Keplerian orbits, if they are close to the binary and the secondary-to-primary mass ratio is high. A proper description of a circumbinary orbit is in terms of the free eccentricity $e_{\rm free}$ at the epicyclic frequency $\kappa_0$, forced eccentricity $e_{\rm forced}$ at the mean motion $n_0$, and oscillations at higher frequencies forced by the non-axisymmetric components of the binary's potential. We show that accurate numerical values for the amplitudes and frequencies of these terms can be extracted from numerical orbit integrations by applying fast Fourier transformation (FFT) to the cylindrical distance between the circumbinary object and the center of mass of the binary as a function of time. We apply this method to three Kepler circumbinary planets and the satellites of Pluto-Charon. For the satellite Styx of Pluto-Charon, the FFT results for $\kappa_0$ and $e_{\rm free}$ differ significantly from the first-order analytic value and the value reported by Showalter & Hamilton (2015), respectively. We show that the deviation in $\kappa_0$ is likely due to the effect of the 3:1 mean-motion resonance and discuss the implications of the lower value for $e_{\rm free}$., Comment: 17 pages, including 9 figures, accepted for publication in AJ

We present an independent Doppler validation and dynamical orbital analysis of the two-planet system HD 107148, which was recently announced in Rosenthal et al. Our detailed analyses are based on literature HIRES data and newly obtained HARPS and CARMENES radial-velocity (RV) measurements as part of our survey in search for additional planets around single-planet systems. We perform a periodogram analysis of the available HIRES and HARPS precise RVs and stellar activity indicators. We do not find any apparent correlation between the RV measurements and the stellar activity indicators, thus linking the two strong periodicities to a moderately compact multiplanet system. We carry out orbital fitting analysis by testing various one- and two-planet orbital configurations and studying the posterior probability distribution of the fitted parameters. Our results solidify the existence of a Saturn-mass planet (HD 107148b, discovered first) with a period of P b ∼ 77.2 days and a second, eccentric (e c ∼ 0.4), Neptune-mass exoplanet (HD 107148c) with an orbital period of P c ∼ 18.3 days. Finally, we investigate the two-planet system’s long-term stability and overall orbital dynamics with the posterior distribution of our preferred orbital configuration. Our N-body stability simulations show that the system is long-term stable and exhibits large secular osculations in eccentricity but in no particular mean motion resonance configuration. The HD 107148 system, consisting of a solar-type main-sequence star with two giant planets in a rare configuration, features a common proper-motion white dwarf companion and is therefore a valuable target for understanding the formation and evolution of planetary systems.

Open Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Open Access funding provided by Max Planck Society., Context. GJ 1148 is an M-dwarf star hosting a planetary system composed of two Saturn-mass planets in eccentric orbits with periods of 41.38 and 532.02 days. Aims. We reanalyze the orbital configuration and dynamics of the GJ 1148 multi-planetary system based on new precise radial velocity measurements taken with CARMENES. Methods. We combined new and archival precise Doppler measurements from CARMENES with those available from HIRES for GJ 1148 and modeled these data with a self-consistent dynamical model. We studied the orbital dynamics of the system using the secular theory and direct N-body integrations. The prospects of potentially habitable moons around GJ 1148 b were examined. Results. The refined dynamical analyses show that the GJ 1148 system is long-term stable in a large phase-space of orbital parameters with an orbital configuration suggesting apsidal alignment, but not in any particular high-order mean-motion resonant commensurability. GJ 1148 b orbits inside the optimistic habitable zone (HZ). We find only a narrow stability region around the planet where exomoons can exist. However, in this stable region exomoons exhibit quick orbital decay due to tidal interaction with the planet. Conclusions. The GJ 1148 planetary system is a very rare M-dwarf planetary system consisting of a pair of gas giants, the inner of which resides in the HZ. We conclude that habitable exomoons around GJ 1148 b are very unlikely to exist. © 2020 T. Trifonov et al., CARMENES is an instrument for the Centro Astronomico Hispano-Aleman de Calar Alto (CAHA, Almeria, Spain). CARMENES is funded by the German Max-Planck-Gesellschaft (MPG), the Spanish Consejo Superior de Investigaciones Cientificas (CSIC), the European Union through FEDER/ERF FICTS-2011-02 funds, and the members of the CARMENES Consortium (Max-Planck-Institut fur Astronomie, Instituto de Astrofisica de Andalucia, Landessternwarte Konigstuhl, Institut de Ciencies de l'Espai, Insitut fur Astrophysik Gottingen, Universidad Complutense de Madrid, Thuringer Landessternwarte Tautenburg, Instituto de Astrofisica de Canarias, Hamburger Sternwarte, Centro de Astrobiologia and Centro Astronomico Hispano-Aleman), with additional contributions by the Spanish Ministry of Economy, the German Science Foundation (DFG), the Klaus Tschira Stiftung, the states of BadenWurttemberg and Niedersachsen, the DFG Research Unit FOR2544 "Blue Planets around Red Stars, project RE 2694/4-1, and by the Junta de Andalucia. We acknowledge financial support from the Agencia Estatal de Investigacion of the Ministerio de Ciencia, Innovacion y Universidades and the European FEDER/ERF funds through projects AYA2016-79425-C3-1/2/3-P, AYA2015-69350-C3-2-P, ESP2017-87676-C5-2-R, ESP2017-87143-R, and the Centre of Excellence "Severo Ochoa" and "Maria de Maeztu" awards to the Instituto de Astrofisica de Canarias (SEV-2015-0548), Instituto de Astrofisica de Andalucia (SEV-2017-0709), and Centro de Astrobiologia (MDM-2017-0737) This work has made use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC, https://www.cosmos.esa.int/web/gaia/dpac/consortium).Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement. M.H.L. and K.H.W. were supported in part by Hong Kong RGC grant HKU 17305618. R.B. was supported by the NASA Virtual Planetary Laboratory Team through Grant Number 80NSSC18K0829. T.H. acknowledges support from the European Research Council under the Horizon 2020 Framework Program via the ERC Advanced Grant Origins 83 24 28. T.T. thanks Alexandre Correia and Laetitia Rodet for helpful discussions. We thank the anonymous referee for the excellent comments that helped to improve the quality of this paper.

Table B.1 is only available at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/cat/J/A+A/636/A119., Context. The nearby ultra-compact multiplanetary system YZ Ceti consists of at least three planets, and a fourth tentative signal. The orbital period of each planet is the subject of discussion in the literature due to strong aliasing in the radial velocity data. The stellar activity of this M dwarf also hampers significantly the derivation of the planetary parameters. Aims. With an additional 229 radial velocity measurements obtained since the discovery publication, we reanalyze the YZ Ceti system and resolve the alias issues. Methods. We use model comparison in the framework of Bayesian statistics and periodogram simulations based on a method by Dawson and Fabrycky to resolve the aliases. We discuss additional signals in the RV data, and derive the planetary parameters by simultaneously modeling the stellar activity with a Gaussian process regression model. To constrain the planetary parameters further we apply a stability analysis on our ensemble of Keplerian fits. Results. We find no evidence for a fourth possible companion. We resolve the aliases: the three planets orbit the star with periods of 2.02 d, 3.06 d, and 4.66 d. We also investigate an effect of the stellar rotational signal on the derivation of the planetary parameters, in particular the eccentricity of the innermost planet. Using photometry we determine the stellar rotational period to be close to 68 d and we also detect this signal in the residuals of a three-planet fit to the RV data and the spectral activity indicators. From our stability analysis we derive a lower limit on the inclination of the system with the assumption of coplanar orbits which is imin = 0.9 deg. From the absence of a transit event with TESS, we derive an upper limit of the inclination of imax = 87.43 deg. Conclusions. YZ Ceti is a prime example of a system where strong aliasing hindered the determination of the orbital periods of exoplanets. Additionally, stellar activity influences the derivation of planetary parameters and modeling them correctly is important for the reliable estimation of the orbital parameters in this specific compact system. Stability considerations then allow additional constraints to be placed on the planetary parameters. © 2020 ESO., This work was supported by the DFG Research Unit FOR2544 "Blue Planets around Red Stars", project no. RE 2694/4-1. CARMENES is an instrument for the Centro Astronomico Hispano-Aleman de Calar Alto (CAHA, Almeria, Spain). CARMENES is funded by the German Max-Planck-Gesellschaft (MPG), the Spanish Consejo Superior de Investigaciones Cientificas (CSIC), the European Union through FEDER/ERF FICTS -2011 -02 funds, and the members of the CARMENES Consortium (Max-Planck-Institut fur Astronomie, Instituto de Astrofisica de Andalucia, Landessternwarte Konigstuhl, Institut de Ciencies de l'Espai, Insitut fur Astrophysik Gottingen, Universidad Complutense de Madrid, Thuringer Landessternwarte Tautenburg, Instituto de Astrofisica de Canarias, Hamburger Sternwarte, Centro de Astrobiologia and Centro Astronomico Hispano -Aleman), with additional contributions by the Spanish Ministry of Economy, the German Science Foundation through the Major Research Instrumentation Programme and DFG Research Unit FOR2544 "Blue Planets around Red Stars", the Klaus Tschira Stiftung, the states of Baden-Wurttemberg and Niedersachsen, and by the Junta de Andalucia. The authors acknowledge support by the High Performance and Cloud Computing Group at the Zentrum fur Datenverarbeitung of the University of Tubingen, the state of Baden-Wurttemberg through bwHPC and the German Research Foundation (DFG) through grant no. INST 37/935 -1 FUGG. We acknowledge financial support from the Agencia Estatal de Investigacion of the Ministerio de Ciencia, Innovacion y Universidades and the European FEDER/ERF funds through projects AYA2015-69350-C3-2-P, AYA2016-79425-C3-1/2/3-P, ESP2017-87676-C5-2-R, ESP2017-87143-R and the Centre of Excellence "Severo Ochoa" and "Maria de Maeztu" awards to the Instituto de Astrofisica de Canarias (SEV-2015-0548), Instituto de Astrofisica de Andalucia (SEV-2017-0709), and Centro de Astrobiologia (MDM-2017-0737), and the Generalitat de Catalunya/CERCA programme. This work is supported by the Science and Technology Facilities Council [ST/M001008/1 and ST/P000584/1]. J.S.J. acknowledges support by Fondecyt grant 1161218 and partial support by CATA-Basal (PB06, CONICYT). Z.M.B acknowledges funds from CONICYT-FONDECYT/Chile Postdoctorado 3180405. M.H.L. was supported in part by Hong Kong RGC grant HKU 17305618. T.H. acknowledges support from the European Research Council under the Horizon 2020 Framework Program via the ERC Advanced Grant Origins 83 24 28. Data were partly collected with the robotic 40-cm telescope ASH2 at the SPACEOBS observatory (San Pedro de Atacama, Chile) and the 90-cm telescope at Sierra Nevada Observatory (Granada, Spain) both operated by the Instituto de Astrofifica de Andalucia (IAA). This work has made use of the Exo-Striker tool (Trifonov 2019).

We present radial-velocity (RV) measurements for the K giant $\nu$ Oph (= HIP88048, HD163917, HR6698), which reveal two brown dwarf companions with a period ratio close to 6:1. For our orbital analysis we use 150 precise RV measurements taken at Lick Observatory between 2000 and 2011, and we combine them with RV data for this star available in the literature. Using a stellar mass of $M = 2.7\,M_\odot$ for $\nu$ Oph and applying a self-consistent N-body model we estimate the minimum dynamical companion masses to be $m_1\sin i \approx 22.2\,M_{\mathrm{Jup}}$ and $m_2\sin i \approx 24.7\,M_{\mathrm{Jup}}$, with orbital periods $P_1 \approx 530$ d and $P_2 \approx 3185$ d. We study a large set of potential orbital configurations for this system, employing a bootstrap analysis and a systematic $\chi_{\nu}^2$ grid-search coupled with our dynamical fitting model, and we examine their long-term stability. We find that the system is indeed locked in a 6:1 mean motion resonance (MMR), with $\Delta \omega$ and all six resonance angles $\theta_{1}, \ldots, \theta_{6}$ librating around 0$^\circ$. We also test a large set of coplanar inclined configurations, and we find that the system will remain in a stable resonance for most of these configurations. The $\nu$ Oph system is important for probing planetary formation and evolution scenarios. It seems very likely that the two brown dwarf companions of $\nu$ Oph formed like planets in a circumstellar disk around the star and have been trapped in a MMR by smooth migration capture., Comment: 17 pages, 9 figures. New version with corrected number in title. No other changes

We present evidence for a new two-planet system around the giant star HD202696 (= HIP105056, BD+26 4118). The discovery is based on public HIRES radial velocity measurements taken at Keck Observatory between July 2007 and September 2014. We estimate a stellar mass of 1.91$^{+0.09}_{-0.14}M_\odot$ for HD202696, which is located close to the base of the red giant branch. A two-planet self-consistent dynamical modeling MCMC scheme of the radial velocity data followed by a long-term stability test suggests planetary orbital periods of $P_{\rm b}$ = 517.8$_{-3.9}^{+8.9}$ days and $P_{\rm c}$ = 946.6$_{-20.9}^{+20.7}$ days, eccentricities of $e_{\rm b}$ = 0.011$_{-0.011}^{+0.078}$ and $e_{\rm c}$ = 0.028$_{-0.012}^{+0.065}$ , and minimum dynamical masses of $m_{\rm b}$ = 2.00$_{-0.10}^{+0.22}$\,$M_{\mathrm{Jup}}$ and $m_{\rm c}$ = 1.86$_{-0.23}^{+0.18}$,$M_{\mathrm{Jup}}$, respectively. Our stable MCMC samples are consistent with orbital configurations predominantly in a mean period ratio of 11:6 and its close-by high order mean-motion commensurabilities with low eccentricities. For the majority of the stable configurations we find an aligned or anti-aligned apsidal libration (i.e.\ $\Delta\omega$ librating around 0$^\circ$ or 180$^\circ$), suggesting that the HD202696 system is likely dominated by secular perturbations near the high-order 11:6 mean-motion resonance. The HD202696 system is yet another Jovian mass pair around an intermediate mass star with a period ratio below the 2:1 mean motion resonance. Therefore, the HD202696 system is an important discovery, which may shed light on the primordial disk-planet properties needed for giant planets to break the strong 2:1 mean motion resonance and settle in more compact orbits., Comment: Accepted for publication in AJ on 18th December 2018. 15 pages, 11 Figures, 4 Tables (this .v2 is copy corrected and identical with the published paper)

We report the discovery of a second planet orbiting the K giant star 7 CMa based on 166 high-precision radial velocities obtained with Lick, HARPS, UCLES and SONG. The periodogram analysis reveals two periodic signals of approximately 745 and 980 d, associated to planetary companions. A double-Keplerian orbital fit of the data reveals two Jupiter-like planets with minimum masses $m_b\sin i \sim 1.9 \,\mathrm{M_{J}}$ and $m_c\sin i \sim 0.9 \,\mathrm{M_{J}}$, orbiting at semi-major axes of $a_b \sim 1.75\,\mathrm{au}$ and $a_c \sim 2.15\,\mathrm{au}$, respectively. Given the small orbital separation and the large minimum masses of the planets close encounters may occur within the time baseline of the observations, thus, a more accurate N-body dynamical modeling of the available data is performed. The dynamical best-fit solution leads to collision of the planets and we explore the long-term stable configuration of the system in a Bayesian framework, confirming that 13% of the posterior samples are stable for at least 10 Myr. The result from the stability analysis indicates that the two-planets are trapped in a low-eccentricity 4:3 mean-motion resonance. This is only the third discovered system to be inside a 4:3 resonance, making it very valuable for planet formation and orbital evolution models., Comment: Accepted in A&A

Barnard’s star is a red dwarf, and has the largest proper motion (apparent motion across the sky) of all known stars. At a distance of 1.8 parsecs, it is the closest single star to the Sun; only the three stars in the α Centauri system are closer. Barnard’s star is also among the least magnetically active red dwarfs known and has an estimated age older than the Solar System. Its properties make it a prime target for planetary searches; various techniques with different sensitivity limits have been used previously, including radial-velocity imaging, astrometry and direct imaging, but all ultimately led to negative or null results. Here we combine numerous measurements from high-precision radial-velocity instruments, revealing the presence of a low-amplitude periodic signal with a period of 233 days. Independent photometric and spectroscopic monitoring, as well as an analysis of instrumental systematic effects, suggest that this signal is best explained as arising from a planetary companion. The candidate planet around Barnard’s star is a cold super-Earth, with a minimum mass of 3.2 times that of Earth, orbiting near its snow line (the minimum distance from the star at which volatile compounds could condense). The combination of all radial-velocity datasets spanning 20 years of measurements additionally reveals a long-term modulation that could arise from a stellar magnetic-activity cycle or from a more distant planetary object. Because of its proximity to the Sun, the candidate planet has a maximum angular separation of 220 milliarcseconds from Barnard’s star, making it an excellent target for direct imaging and astrometric observations in the future. © 2018, Springer Nature Limited., The results are based on observations made with the CARMENES instrument at the 3.5-m telescope of the Centro Astronomico Hispano-Aleman de Calar Alto (CAHA, Almeria, Spain), funded by the German Max-Planck-Gesellschaft (MPG), the Spanish Consejo Superior de Investigaciones Cientificas (CSIC), the European Union and the CARMENES Consortium members; the 90-cm telescope at the Sierra Nevada Observatory (Granada, Spain) and the 40-cm robotic telescope at the SPACEOBS observatory (San Pedro de Atacama, Chile), both operated by the Instituto de Astrofisica de Andalucia (IAA); and the 80-cm Joan Oro Telescope (TJO) of the Montsec Astronomical Observatory (OAdM), owned by the Generalitat de Catalunya and operated by the Institute of Space Studies of Catalonia (IEEC). This research was supported by the following institutions, grants and fellowships: Spanish MINECO ESP2016-80435-C2-1-R, ESP2016-80435-C2-2-R, AYA2016-79425-C3-1-P, AYA2016-79245-C3-2-P, AYA2016-79425-C3-3-P, AYA2015-69350-C3-2-P, ESP2014-54362-P, AYA2014-56359-P, RYC-2013-14875; Generalitat de Catalunya/CERCA programme; Fondo Europeo de Desarrollo Regional (FEDER); German Science Foundation (DFG) Research Unit FOR2544, project JE 701/3-1; STFC Consolidated Grants ST/P000584/1, ST/P000592/1, ST/M001008/1; NSF AST-0307493; Queen Mary University of London Scholarship; Perren foundation grant; CONICYT-FONDECYT 1161218, 3180405; Swiss National Science Foundation (SNSF); Koshland Foundation and McDonald-Leapman grant; and NASA Hubble Fellowship grant HST-HF2-51399.001. J.T. is a Hubble Fellow.

We present a detailed orbital and stability analysis of the HD~59686 binary-star planet system. HD~59686 is a single-lined moderately close ($a_{B} = 13.6\,$AU) eccentric ($e_{B} = 0.73$) binary, where the primary is an evolved K giant with mass $M = 1.9 M_{\odot}$ and the secondary is a star with a minimum mass of $m_{B} = 0.53 M_{\odot}$. Additionally, on the basis of precise radial velocity (RV) data a Jovian planet with a minimum mass of $m_p = 7 M_{\mathrm{Jup}}$, orbiting the primary on a nearly circular S-type orbit with $e_p = 0.05$ and $a_p = 1.09\,$AU, has recently been announced. We investigate large sets of orbital fits consistent with HD 59686's radial velocity data by applying bootstrap and systematic grid-search techniques coupled with self-consistent dynamical fitting. We perform long-term dynamical integrations of these fits to constrain the permitted orbital configurations. We find that if the binary and the planet in this system have prograde and aligned coplanar orbits, there are narrow regions of stable orbital solutions locked in a secular apsidal alignment with the angle between the periapses, $\Delta \omega$, librating about $0^\circ$. We also test a large number of mutually inclined dynamical models in an attempt to constrain the three-dimensional orbital architecture. We find that for nearly coplanar and retrograde orbits with mutual inclination $145^\circ \lesssim \Delta i \leq 180^\circ$, the system is fully stable for a large range of orbital solutions., Comment: 17 pages, 11 figures, accepted for publication by AJ

For grain growth to proceed effectively and lead to planet formation a number of barriers to growth must be overcome. One such barrier, relevant for compact grains in the inner regions of the disc, is the `bouncing barrier' in which large grains ($\sim$ mm size) tend to bounce off each other rather than sticking. However, by maintaining a population of small grains it has been suggested that cm-size particles may grow rapidly by sweeping up these small grains. We present the first numerically resolved investigation into the conditions under which grains may be lucky enough to grow beyond the bouncing barrier by a series of rare collisions leading to growth (so-called `breakthrough'). Our models support previous results, and show that in simple models breakthrough requires the mass ratio at which high velocity collisions transition to growth instead of causing fragmentation to be low, $\phi \lesssim 50$. However, in models that take into account the dependence of the fragmentation threshold on mass-ratio, we find breakthrough occurs more readily, even if mass transfer is relatively inefficient. This suggests that bouncing may only slow down growth, rather than preventing growth beyond a threshold barrier. However, even when growth beyond the bouncing barrier is possible, radial drift will usually prevent growth to arbitrarily large sizes., This work has been supported by the DISCSIM project, grant agreement 341137 funded by the European Research Council under ERC-2013-ADG and the Hong Kong RGC grant HKU 7030/11P. FM acknowledges support from the Leverhulme Trust Early Career Fellowship and the Isaac Newton Trust. This work used the DIRAC Shared Memory Processing system at the University of Cambridge, operated by the COSMOS Project at the Department of Applied Mathematics and Theoretical Physics on behalf of the STFC DiRAC HPC Facility (www.dirac.ac.uk). This equipment was funded by BIS National E-infrastructure capital grant ST/J005673/1, STFC capital grant ST/H008586/1, and STFC DiRAC Operations grant ST/K00333X/1. DiRAC is part of the National E-Infrastructure.

Aims. Our new program with HARPS aims to detect mean motion resonant planetary systems around stars which were previously reported to have a single bona fide planet, often based only on sparse radial velocity data. Methods. Archival and new HARPS radial velocities for the K2V star HD 27894 were combined and fitted with a three-planet self-consistent dynamical model. The best-fit orbit was tested for long-term stability. Results. We find clear evidence that HD 27894 is hosting at least three massive planets. In addition to the already known Jovian planet with a period $P_{\rm b}$ $\approx$ 18 days we discover a Saturn-mass planet with $P_{\rm c}$ $\approx$ 36 days, likely in a 2:1 mean motion resonance with the first planet, and a cold massive planet ($\approx$ 5.3 $M_{\mathrm{Jup}}$) with a period $P_{\rm d}$ $\approx$ 5170 days on a moderately eccentric orbit ($e_{\rm d}$ = 0.39). Conclusions. HD 27894 is hosting a massive, eccentric giant planet orbiting around a tightly packed inner pair of massive planets likely involved in an asymmetric 2:1 mean motion resonance. HD 27894 may be an important milestone for probing planetary formation and evolution scenarios., 4 pages, 2 tables, 3 figures. Accepted for publication in A&A Letters to the Editor

The orbits of Pluto's four small satellites (Styx, Nix, Kerberos, and Hydra) are nearly circular and coplanar with the orbit of the large satellite Charon, with orbital periods nearly in the ratios 3:1, 4:1, 5:1, and 6:1 with Charon's orbital period. These properties suggest that the small satellites were created during the same impact event that placed Charon in orbit and had been pushed to their current positions by being locked in mean-motion resonances with Charon as Charon's orbit was expanded by tidal interactions with Pluto. Using the Pluto-Charon tidal evolution models developed by Cheng et al. (2014), we show that stable capture and transport of a test particle in multiple resonances at the same mean-motion commensurability is possible at the 5:1, 6:1, and 7:1 commensurabilities, if Pluto's zonal harmonic $J_{2P} = 0$. However, the test particle has significant orbital eccentricity at the end of the tidal evolution of Pluto-Charon in almost all cases, and there are no stable captures and transports at the 3:1 and 4:1 commensurabilities. Furthermore, a non-zero hydrostatic value of $J_{2P}$ destroys the conditions necessary for multiple resonance migration. Simulations with finite but minimal masses of Nix and Hydra also fail to yield any survivors. We conclude that the placing of the small satellites at their current orbital positions by resonant transport is extremely unlikely., Comment: 22 pages, including 7 figures; accepted for publication in Icarus

The multiple-planet systems discovered by the Kepler mission show an excess of planet pairs with period ratios just wide of exact commensurability for first-order resonances like 2:1 and 3:2. In principle, these planet pairs could be in resonance if their orbital eccentricities are sufficiently small, because the width of first-order resonances diverges in the limit of vanishingly small eccentricity. We consider a widely-held scenario in which pairs of planets were captured into first-order resonances by migration due to planet-disk interactions, and subsequently became detached from the resonances, due to tidal dissipation in the planets. In the context of this scenario, we find a constraint on the ratio of the planet's tidal dissipation function and Love number that implies that some of the Kepler planets are likely solid. However, tides are not strong enough to move many of the planet pairs to the observed separations, suggesting that additional processes are at play.

In this paper we present new precise Doppler data of GJ1046 taken between November 2005 and July 2018 with the HARPS and the FEROS high- resolution spectographs. In addition, we provide a new stellar mass estimate of GJ1046 and we update the orbital parameters of the GJ1046 system. These new data and analysis could be used together with the GAIA epoch astrometry, when available, for braking the $\sin i$ degeneracy and revealing the true mass of the GJ1046 system.

We revisit the appropriate energies to be used for computing heat production from 26Al decay. Due to the complexity of the decay scheme of this radioisotope, previous geophysical studies have used values ranging from 1.2 to 4 MeV per decay. The upper bound corresponds to the difference in mass energy between the 26Al and 26Mg ground states. This includes energy carried away by neutrinos, which does not contribute to heating planetary material. The lower bound does not account for the heating caused by the absorption of the γ rays from the excited 26Mg, or for the annihilation energy deposited in the material if the decay occurs inside even small planetesimals. Based on the calculations described by Schramm et al. [Schramm, D., Tera, F., Wasserburg, G.J., 1970. The isotopic abundance of 26Mg and limits on 26Al in the early Solar System. Earth Planet. Sci. Lett. 10, 44–59] updated with the most recent nuclear constants, we recommend using a heat production value of 3.12 MeV per decay, which is the total energy of disintegration minus the energy carried off by the neutrinos. This heat production value is higher than the value used in the modeling of Iapetus by Castillo-Rogez et al. [Castillo-Rogez, J., Matson, D.L., Sotin, C., Johnson, T.V., Lunine, J.I., Thomas, P.C., 2007. Iapetus’ geophysics: Rotation rate, shape, and equatorial ridge. Icarus 190, 179–202] by about a factor 2.5. The resulting estimate of the time of formation of Iapetus is shifted by about 1 Myr, to between ∼3.4 and 5.4 Myr after the production of the calcium–aluminum inclusions (CAIs).

The differential migration of two planets due to planet-disk interaction can result in capture into the 2:1 eccentricity-type mean-motion resonances. Both the sequence of 2:1 eccentricity resonances that the system is driven through by continued migration and the possibility of a subsequent capture into the 4:2 inclination resonances are sensitive to the migration rate within the range expected for type II migration. If the migration rate is fast, the resonant pair can evolve into a family of 2:1 eccentricity resonances different from those found by Lee (2004). This new family has outer orbital eccentricity e_2 > 0.4-0.5, asymmetric librations of both eccentricity resonance variables, and orbits that intersect if they are exactly coplanar. Although this family exists for an inner-to-outer planet mass ratio m_1/m_2 > 0.2, it is possible to evolve into this family by fast migration only for m_1/m_2 > 2. Thommes and Lissauer (2003) have found that a capture into the 4:2 inclination resonances is possible only for m_1/m_2 < 2. We show that this capture is also possible for m_1/m_2 > 2 if the migration rate is slightly slower than that adopted by Thommes and Lissauer. There is significant theoretical uncertainty in both the sign and the magnitude of the net effect of planet-disk interaction on the orbital eccentricity of a planet. If the eccentricity is damped on a timescale comparable to or shorter than the migration timescale, e_2 may not be able to reach the values needed to enter either the new 2:1 eccentricity resonances or the 4:2 inclination resonances. Thus, if future observations of extrasolar planetary systems were to reveal certain combinations of mass ratio and resonant configuration, they would place a constraint on the strength of eccentricity damping during migration, as well as on the migration rate itself., 25 pages, including 12 figures; accepted for publication in ApJ

Tsiganis et al. (2005) have proposed that the current orbital architecture of the outer solar system could have been established if it was initially compact and Jupiter and Saturn crossed the 2:1 orbital resonance by divergent migration. The crossing led to close encounters among the giant planets, but the orbital eccentricities and inclinations were damped to their current values by interactions with planetesimals. Brunini (2006) has presented widely publicized numerical results showing that the close encounters led to the current obliquities of the giant planets. We present a simple analytic argument which shows that the change in the spin direction of a planet relative to an inertial frame during an encounter between the planets is very small and that the change in the obliquity (which is measured from the orbit normal) is due to the change in the orbital inclination. Since the inclinations are damped by planetesimal interactions on timescales much shorter than the timescales on which the spins precess due to the torques from the Sun, especially for Uranus and Neptune, the obliquities should return to small values if they are small before the encounters. We have performed simulations using the symplectic integrator SyMBA, modified to include spin evolution due to the torques from the Sun and mutual planetary interactions. Our numerical results are consistent with the analytic argument for no significant remnant obliquities., Comment: 14 pages, including 2 figures; uses AASTeX; a slightly expanded Section 2; accepted for publication in Icarus

Two small satellites of Pluto, S/2005 P1 (hereafter P1) and S/2005 P2 (hereafter P2), have recently been discovered outside the orbit of Charon, and their orbits are nearly circular and nearly coplanar with that of Charon. Because the mass ratio of Charon–Pluto is ∼0.1, the orbits of P2 and P1 are significantly non-Keplerian even if P2 and P1 have negligible masses. We present an analytic theory, with P2 and P1 treated as test particles, which shows that the motion can be represented by the superposition of the circular motion of a guiding center, the forced oscillations due to the non-axisymmetric components of the potential rotating at the mean motion of Pluto–Charon, the epicyclic motion, and the vertical motion. The analytic theory shows that the azimuthal periods of P2 and P1 are shorter than the Keplerian orbital periods, and this deviation from Kepler's third law is already detected in the unperturbed Keplerian fit of Buie and coworkers. In this analytic theory, the periapse and ascending node of each of the small satellites precess at nearly equal rates in opposite directions. From direct numerical orbit integrations, we show the increasing influence of the proximity of P2 and P1 to the 3:2 mean-motion commensurability on their orbital motion as their masses increase within the ranges allowed by the albedo uncertainties. If the geometric albedos of P2 and P1 are high and of order of that of Charon, the masses of P2 and P1 are sufficiently low that their orbits are well described by the analytic theory. The variation in the orbital radius of P2 due to the forced oscillations is comparable in magnitude to that due to the best-fit Keplerian eccentricity, and there is at present no evidence that P2 has any significant epicyclic eccentricity. However, the orbit of P1 has a significant epicyclic eccentricity, and the prograde precession of its longitude of periapse with a period of 5300 days should be easily detectable. If the albedos of P2 and P1 are as low as that of comets, the large inferred masses induce significant short-term variations in the epicyclic eccentricities and/or periapse longitudes on the 400–500-day timescales due to the proximity to the 3:2 commensurability. In fact, for the maximum inferred masses, P2 and P1 may be in the 3:2 mean-motion resonance, with the resonance variable involving the periapse longitude of P1 librating. Observations that sample the orbits of P2 and P1 well on the 400–500-day timescales should provide strong constraints on the masses of P2 and P1 in the near future.

A diversity of 2 : 1 resonance configurations can be expected in extrasolar planetary systems, and their geometry can provide information about the origin of the resonances. Assembly during planet formation by the differential migration of planets due to planet-disk interaction is one scenario for the origin of mean-motion resonances in extrasolar planetary systems. The stable 2 : 1 resonance configurations that can be reached by differential migration of planets with constant masses and initially coplanar and nearly circular orbits are (1) antisymmetric configurations with the mean-motion resonance variables θ1 = λ1 - 2λ2 + 1 and θ2 = λ1 - 2λ2 + 2 (where λj and j are the mean longitudes and the longitudes of periapse, respectively) librating about 0° and 180°, respectively (as in the Io-Europa pair), (2) symmetric configurations with both θ1 and θ2 librating about 0° (as in the GJ 876 system), and (3) asymmetric configurations with θ1 and θ2 librating about angles far from either 0° or 180°. There are, however, stable 2 : 1 resonance configurations with symmetric (θ1 ≈ θ2 ≈ 0°), asymmetric, and antisymmetric (θ1 ≈ 180° and θ2 ≈ 0°) librations that cannot be reached by differential migration of planets with constant masses and initially coplanar and nearly circular orbits. If real systems with these configurations are ever found, their origin would require (1) a change in the planetary mass ratio m1/m2 during migration, (2) a migration scenario involving inclination resonances, or (3) multiple-planet scattering in crowded planetary systems. We find that the asymmetric configurations with large e2 and the θ1 ≈ 180° and θ2 ≈ 0° configurations have intersecting orbits and that the θ1 ≈ θ2 ≈ 0° configurations with e1 > 0.714 have prograde periapse precessions.

The formation of Pluto's small satellites—Styx, Nix, Keberos, and Hydra—remains a mystery. Their orbits are nearly circular and are near mean-motion resonances and nearly coplanar with Charon's orbit. One scenario suggests that they all formed close to their current locations from a disk of debris that was ejected from the Charon-forming impact before the tidal evolution of Charon. The validity of this scenario is tested by performing N-body simulations with the small satellites treated as test particles and Pluto–Charon evolving tidally from an initial orbit at a few Pluto radii with initial eccentricity e C = 0 or 0.2. After tidal evolution, the free eccentricities e free of the test particles are extracted by applying fast Fourier transformation to the distance between the test particles and the center of mass of the system and compared with the current eccentricities of the four small satellites. The only surviving test particles with e free matching the eccentricities of the current satellites are those not affected by mean-motion resonances during the tidal evolution in a model with Pluto's effective tidal dissipation function Q = 100 and an initial e C = 0.2 that is damped down rapidly. However, these test particles do not have any preference to be in or near 4:1, 5:1, and 6:1 resonances with Charon. An alternative scenario may be needed to explain the formation of Pluto's small satellites.

The discovery by Marcy and coworkers of two planets in 2 : 1 orbital resonance about the star GJ 876 has been supplemented by a dynamical fit to the data by Laughlin & Chambers, which places the planets in coplanar orbits deep in three resonances at the 2 : 1 mean-motion commensurability. The selection of this almost singular state by the dynamical fit means that the resonances are almost certainly real, and with the small amplitudes of libration of the resonance variables, indefinitely stable. Several unusual properties of the 2 : 1 resonances are revealed by the GJ 876 system. The libration of both lowest order mean-motion resonance variables and the secular resonance variable, θ1 = λ1 - 2λ2 + 1, θ2 = λ1 - 2λ2 + 2, and θ3 = 1 - 2, about 0° (where λ1,2 are the mean longitudes of the inner and outer planet and 1,2 are the longitudes of periapse) differs from the familiar geometry of the Io-Europa pair, where θ2 and θ3 librate about 180°. By considering the condition that 1 = 2 for stable simultaneous librations of θ1 and θ2, we show that the GJ 876 geometry results from the large orbital eccentricities ei, whereas the very small eccentricities in the Io-Europa system lead to the latter's geometry. Surprisingly, the GJ 876 configuration, with θ1, θ2, and θ3 all librating, remains stable for e1 up to 0.86 and for amplitude of libration of θ1 approaching 45° with the current eccentricities—further supporting the indefinite stability of the existing system. Any process that drives originally widely separated orbits toward each other could result in capture into the observed resonances at the 2 : 1 commensurability. We find that forced inward migration of the outer planet of the GJ 876 system results in certain capture into the observed resonances if initially e1 0.06 and e2 0.03 and the migration rate |2/a2| 3 × 10-2(a2/AU)-3/2 yr-1. Larger eccentricities lead to likely capture into higher order resonances before the 2 : 1 commensurability is reached. The planets are sufficiently massive to open gaps in the nebular disk surrounding the young GJ 876 and to clear the disk material between them, and the resulting planet-nebular interaction typically forces the outer planet to migrate inward on the disk viscous timescale, whose inverse is about 3 orders of magnitude less than the above upper bound on |2/a2| for certain capture. If there is no eccentricity damping, eccentricity growth is rapid with continued migration within the resonance, with ei exceeding the observed values after a further reduction in the semimajor axes ai of only 7%. With eccentricity damping i/ei = -K|i/ai|, the eccentricities reach equilibrium values that remain constant for arbitrarily long migration within the resonances. The equilibrium eccentricities are close to the observed eccentricities for K ≈ 100 if there is migration and damping of the outer planet only, but for K ≈ 10 if there is also migration and damping of the inner planet. This result is independent of the magnitude or functional form of the migration rate i as long as i/ei = -K|i/ai|. Although existing analytic estimates of the effects of planet-nebula interaction are consistent with this form of eccentricity damping for certain disk parameter values, it is as yet unclear that such interaction can produce the large value of K required to obtain the observed eccentricities. The alternative eccentricity damping by tidal dissipation within the star or the planets is completely negligible, so the observed dynamical properties of the GJ 876 system may require an unlikely fine-tuning of the time of resonance capture to be near the end of the nebula lifetime.

We report the discovery of a new planetary system around the K giant $\eta$ Cet (HIP 5364, HD 6805) based on 118 high-precision optical radial velocities taken at Lick Observatory since July 2000. Since October 2011 an additional nine near-infrared Doppler measurements have been taken using the ESO CRIRES spectrograph (VLT, UT1). The visible data set shows two clear periodicities. Although we cannot completely rule out that the shorter period is due to rotational modulation of stellar features, the infrared data show the same variations as in the optical, which strongly supports that the variations are caused by two planets. Assuming the mass of $\eta$ Cet to be 1.7 $M_\odot$, the best edge-on coplanar dynamical fit to the data is consistent with two massive planets ($m_b\sin i$ = 2.6 $\pm$ 0.2 $M_{\mathrm{Jup}}$, $m_c\sin i$ = 3.3 $\pm$ 0.2 $M_{\mathrm{Jup}}$), with periods of $P_b$ = 407 $\pm$ 3 days and $P_c$ = 740 $\pm$ 5 days and eccentricities of $e_b$ = 0.12 $\pm$ 0.05 and $e_c$ = 0.08 $\pm$ 0.03. We tested a wide variety of edge-on coplanar and inclined planetary configurations for stability, which agree with the derived radial velocities. We find that in certain coplanar orbital configurations with moderate $e_b$ eccentricity, the planets can be effectively trapped in an anti-aligned 2:1 mean motion resonance. A much larger non-resonant stable region exists in low-eccentricity parameter space, although it appears to be much farther from the best fit than the 2:1 resonant region. In all other cases, the system is categorized as unstable or chaotic. Another conclusion from the coplanar inclined dynamical test is that the planets can be at most a factor of $\sim$ 1.4 more massive than their suggested minimum masses. This stability constraint on the inclination excludes the possibility of two brown dwarfs, and strongly favors a planetary system., Comment: 15 pages, 11 figures, accepted for publication in A&A on June 20, 2014

The coagulation equation, which is widely used for modeling growth in planet formation and other astrophysical problems, is the mean-rate equation that describes the evolution of the mass spectrum of a collection of particles due to successive mergers. A numerical code that can yield accurate solutions to the coagulation equation with a reasonable number of mass bins is developed, and it is used to study the properties of solutions to the coagulation equation. We consider limiting cases of the merger rate coefficient A ij for gravitational interaction, with the power-law index of the mass–radius relation β=1/3 (for planetesimals) and 2/3 (for stars). We classify the mass dependence of A ij using the exponent λ for the merger between two particles of comparable mass, and the exponents μ and ν for the merger between a heavy particle and a light particle. For the two cases with λ≤1 and ν≤1, the mass spectrum evolves in an orderly fashion. For the remaining cases, which have ν>1, we find strong numerical and analytical evidence that there are no self-consistent solutions to the coagulation equation at any time. The results for the ν>1 cases are qualitatively different from the well-known example with A ij ∝ ij . For the latter case, which is in the range ν≤1 and λ>1, there is an analytic solution to the coagulation equation that is valid for a finite amount of time t 0 . We discuss a simplified merger problem that illustrates the qualitative differences in the solutions to the coagulation equation for the three classes of A ij . Our results strongly suggest that there are two types of runaway growth. For A ij with ν≤1 and λ>1, runaway growth starts at t crit ≈ t 0 , the time at which the coagulation equation solution becomes invalid. For A ij with ν>1, which include all gravitational interaction cases expected to show runaway growth, the dependence of the time t crit for the onset of runaway growth on the parameters of the problem is not yet well understood, but there are indications that t crit (in units of 1/( n 0 A 11 )) may decrease slowly toward zero with increasing initial total number of particles n 0 .

We present a new symplectic algorithm that has the desirable properties of the sophisticated but highly efficient numerical algorithms known as mixed variable symplectic (MVS) methods and that, in addition, can handle close encounters between objects. This technique is based on a variant of the standard MVS methods, but it handles close encounters by employing a multiple time step technique. When the bodies are well separated, the algorithm has the speed of MVS methods, and whenever two bodies suffer a mutual encounter, the time step for the relevant bodies is recursively subdivided to whatever level is required. We demonstrate the power of this method using several tests of the technique. We believe that this algorithm will be a valuable tool for the study of planetesimal dynamics and planet formation.

Both Pluto and its satellite Charon have rotation rates synchronous with their orbital mean motion. This is the theoretical end point of tidal evolution where transfer of angular momentum has ceased. Here we follow Pluto's tidal evolution from an initial state having the current total angular momentum of the system but with Charon in an eccentric orbit with semimajor axis $a \approx 4R_P$ (where $R_P$ is the radius of Pluto), consistent with its impact origin. Two tidal models are used, where the tidal dissipation function $Q \propto$ 1/frequency and $Q=$ constant, where details of the evolution are strongly model dependent. The inclusion of the gravitational harmonic coefficient $C_{22}$ of both bodies in the analysis allows smooth, self consistent evolution to the dual synchronous state, whereas its omission frustrates successful evolution in some cases. The zonal harmonic $J_2$ can also be included, but does not cause a significant effect on the overall evolution. The ratio of dissipation in Charon to that in Pluto controls the behavior of the orbital eccentricity, where a judicious choice leads to a nearly constant eccentricity until the final approach to dual synchronous rotation. The tidal models are complete in the sense that every nuance of tidal evolution is realized while conserving total angular momentum - including temporary capture into spin-orbit resonances as Charon's spin decreases and damped librations about the same., 36 pages, including 18 figures; accepted for publication in Icarus

We present six years of new radial-velocity data from the Anglo-Australian and Magellan Telescopes on the HD 73526 2:1 resonant planetary system. We investigate both Keplerian and dynamical (interacting) fits to these data, yielding four possible configurations for the system. The new data now show that both resonance angles are librating, with amplitudes of 40 degrees and 60 degrees, respectively. We then perform long-term dynamical stability tests to differentiate these solutions, which only differ significantly in the masses of the planets. We show that while there is no clearly preferred system inclination, the dynamical fit with i=90 degrees provides the best combination of goodness-of-fit and long-term dynamical stability., Accepted for publication in ApJ

We examine the conditions under which the disks of gas and dust orbiting young gas giant planets are sufficiently conducting to experience turbulence driven by the magneto-rotational instability. By modeling the ionization and conductivity in the disk around proto-Jupiter, we find that turbulence is possible if the X-rays emitted near the Sun reach the planet's vicinity and either (1) the gas surface densities are in the range of the minimum-mass models constructed by augmenting Jupiter's satellites to Solar composition, while dust is depleted from the disk atmosphere, or (2) the surface densities are much less, and in the range of gas-starved models fed with material from the Solar nebula, but not so low that ambipolar diffusion decouples the neutral gas from the plasma. The results lend support to both minimum-mass and gas-starved models of the protojovian disk: (1) The dusty minimum-mass models have internal conductivities low enough to prevent angular momentum transfer by magnetic forces, as required for the material to remain in place while the satellites form. (2) The gas-starved models have magnetically-active surface layers and a decoupled interior "dead zone". Similar active layers in the Solar nebula yield accretion stresses in the range assumed in constructing the circumjovian gas-starved models. Our results also point to aspects of both classes of models that can be further developed. Non-turbulent minimum-mass models will lose dust from their atmospheres by settling, enabling gas to accrete through a thin surface layer. For the gas-starved models it is crucial to learn whether enough stellar X-ray and ultraviolet photons reach the circumjovian disk. Additionally the stress-to-pressure ratio ought to increase with distance from the planet, likely leading to episodic accretion outbursts., 35 pages, 8 figures. Chemical network description expanded in sec. 4.1. Turbulent mixing discussion reorganized in secs. 6.3-6.4. Accepted to ApJ

We present an updated analysis of radial velocity data of the HD 82943 planetary system based on 10 years of measurements obtained with the Keck telescope. Previous studies have shown that the HD 82943 system has two planets that are likely in 2:1 mean-motion resonance (MMR), with the orbital periods about 220 and 440 days (Lee et al. 2006). However, alternative fits that are qualitatively different have also been suggested, with two planets in a 1:1 resonance (Gozdziewski & Konacki 2006) or three planets in a Laplace 4:2:1 resonance (Beauge et al. 2008). Here we use \c{hi}2 minimization combined with parameter grid search to investigate the orbital parameters and dynamical states of the qualitatively different types of fits, and we compare the results to those obtained with the differential evolution Markov chain Monte Carlo method. Our results support the coplanar 2:1 MMR configuration for the HD 82943 system, and show no evidence for either the 1:1 or 3-planet Laplace resonance fits. The inclination of the system with respect to the sky plane is well constrained at about 20(+4.9 -5.5) degree, and the system contains two planets with masses of about 4.78 MJ and 4.80 MJ (where MJ is the mass of Jupiter) and orbital periods of about 219 and 442 days for the inner and outer planet, respectively. The best fit is dynamically stable with both eccentricity-type resonant angles {\theta}1 and {\theta}2 librating around 0 degree., Comment: 55 pages, 21 figures. Accepted for publication in ApJ

The multiple-planet systems discovered by the Kepler mission show an excess of planet pairs with period ratios just wide of exact commensurability for first-order resonances like 2:1 and 3:2. In principle, these planet pairs could have both resonance angles associated with the resonance librating if the orbital eccentricities are sufficiently small, because the width of first-order resonances diverges in the limit of vanishingly small eccentricity. We consider a widely-held scenario in which pairs of planets were captured into first-order resonances by migration due to planet-disk interactions, and subsequently became detached from the resonances, due to tidal dissipation in the planets. In the context of this scenario, we find a constraint on the ratio of the planet's tidal dissipation function and Love number that implies that some of the Kepler planets are likely solid. However, tides are not strong enough to move many of the planet pairs to the observed separations, suggesting that additional dissipative processes are at play., Comment: 20 pages, including 7 figures; accepted for publication in ApJ

The formalism developed by Gunn J. E. (1967, Astrophys. J., 150) on the gravitational lensing effect of smooth inhomogeneities in the Universe is reviewed and some new simple analytical expressions for the dispersion in amplification are derived. Two models for the distribution and evolution of density fluctuations are considered, namely a universe dominated by cold dark matter, and a scale-free universe with an initial density fluctuation spectrum corresponding to white noise.

The migration and encounter histories of the giant planets in our Solar System can be constrained by the obliquities of Jupiter and Saturn. We have performed secular simulations with imposed migration and N-body simulations with planetesimals to study the expected obliquity distribution of migrating planets with initial conditions resembling those of the smooth migration model, the resonant Nice model and two models with five giant planets initially in resonance (one compact and one loose configuration). For smooth migration, the secular spin-orbit resonance mechanism can tilt Saturn's spin axis to the current obliquity if the product of the migration time scale and the orbital inclinations is sufficiently large (exceeding 30 Myr deg). For the resonant Nice model with imposed migration, it is difficult to reproduce today's obliquity values, because the compactness of the initial system raises the frequency that tilts Saturn above the spin precession frequency of Jupiter, causing a Jupiter spin-orbit resonance crossing. Migration time scales sufficiently long to tilt Saturn generally suffice to tilt Jupiter more than is observed. The full N-body simulations tell a somewhat different story, with Jupiter generally being tilted as often as Saturn, but on average having a higher obliquity. The main obstacle is the final orbital spacing of the giant planets, coupled with the tail of Neptune's migration. The resonant Nice case is barely able to simultaneously reproduce the {orbital and spin} properties of the giant planets, with a probability ~0.15%. The loose five planet model is unable to match all our constraints (probability, Accepted for publication in the Astronomical Journal

We present an analysis of the HD 82943 planetary system based on a radial velocity data set that combines new measurements obtained with the Keck telescope and the CORALIE measurements published in graphical form. We examine simultaneously the goodness of fit and the dynamical properties of the best-fit double-Keplerian model as a function of the poorly constrained eccentricity and argument of periapse of the outer planet's orbit. The fit with the minimum chi_{nu}^2 is dynamically unstable if the orbits are assumed to be coplanar. However, the minimum is relatively shallow, and there is a wide range of fits outside the minimum with reasonable chi_{nu}^2. For an assumed coplanar inclination i = 30 deg. (sin i = 0.5), only good fits with both of the lowest order, eccentricity-type mean-motion resonance variables at the 2:1 commensurability, theta_1 and theta_2, librating about 0 deg. are stable. For sin i = 1, there are also some good fits with only theta_1 (involving the inner planet's periapse longitude) librating that are stable for at least 10^8 years. The libration semiamplitudes are about 6 deg. for theta_1 and 10 deg. for theta_2 for the stable good fit with the smallest libration amplitudes of both theta_1 and theta_2. We do not find any good fits that are non-resonant and stable. Thus the two planets in the HD 82943 system are almost certainly in 2:1 mean-motion resonance, with at least theta_1 librating, and the observations may even be consistent with small-amplitude librations of both theta_1 and theta_2., 24 pages, including 10 figures; accepted for publication in ApJ

The two planets about the star GJ 876 appear to have undergone extensive migration from their point of origin in the protoplanetary disk -- both because of their close proximity to the star (30 and 60 day orbital periods) and because of their occupying three stable orbital resonances at the 2:1 mean-motion commensurability. The resonances were most likely established by converging differential migration of the planets leading to capture into the resonances. A problem with this scenario is that continued migration of the system while it is trapped in the resonances leads to orbital eccentricities that rapidly exceed the observational upper limits of e_1 = 0.31 and e_2 = 0.05. As seen in forced 3-body simulations, lower eccentricities would persist during migration only for an applied eccentricity damping. Here we explore the evolution of the GJ 876 system using two-dimensional hydrodynamical simulations that include viscous heating and radiative effects. We find that a hydrodynamic evolution within the resonance, where only the outer planet interacts with the disk, always rapidly leads to large values of eccentricities that exceed those observed. Only if mass is removed from the disk on a time scale of the order of the migration time scale (before there has been extensive migration after capture), as might occur for photoevaporation in the late phases of planet formation, can we end up with eccentricities that are consistent with the observations., Comment: Paper accepted by A&A, 17 Pages, 17 Figures

(Abridged) We investigate the dynamical evolution of coplanar hierarchical two-planet systems where the ratio of the orbital semimajor axes alpha=a_1/a_2 is small. The orbital parameters obtained from a multiple Kepler fit to the radial velocity variations of a star are best interpreted as Jacobi coordinates and Jacobi coordinates should be used in any analyses of hierarchical planetary systems. An approximate theory that can be applied to coplanar hierarchical two-planet systems with a wide range of masses m_j and orbital eccentricities e_j is the octupole-level secular perturbation theory (OSPT). The OSPT shows that if the ratio of the maximum orbital angular momenta, lambda \approx (m_1/m_2) alpha^{1/2}, for given a_j is approximately equal to a critical value lambda_{crit}, then libration of the difference in the longitudes of periapse, w_1-w_2, about either 0 or 180 deg. is almost certain, with possibly large amplitude variations of both e_j. We establish that the OSPT is highly accurate for systems with alpha, 32 pages, including 8 figures; uses AASTeX v5.0; accepted for publication in ApJ

Understanding the origin of the orbital resonances of the Galilean satellites of Jupiter will constrain the longevity of the extensive volcanism on Io, may explain a liquid ocean on Europa, and may guide studies of the dissipative properties of stars and Jupiter-like planets. The differential migration of the newly formed Galilean satellites due to interactions with a circumjovian disk can lead to the primordial formation of the Laplace relation n_1 - 3 n_2 + 2 n_3 = 0, where the n_i are the mean orbital angular velocities of Io, Europa, and Ganymede, respectively. This contrasts with the formation of the resonances by differential expansion of the orbits from tidal torques from Jupiter., 13 pages, including 4 figures; uses scicite.sty

We consider the dynamical evolution of bound, hierarchical triples of supermassive black holes that might be formed in the nuclei of galaxies undergoing sequential mergers. The tidal force of the outer black hole on the inner binary produces eccentricity oscillations through the Kozai mechanism, and this can substantially reduce the gravitational wave merger time of the inner binary. We numerically calculate the merger time for a wide range of initial conditions and black hole mass ratios, including the effects of octupole interactions in the triple as well as general relativistic periastron precession in the inner binary. The semimajor axes and the mutual inclination of the inner and outer binaries are the most important factors affecting the merger time. We find that for a random distribution of inclination angles and approximately equal mass black holes, it is possible to reduce the merger time of a near circular inner binary by more than a factor of ten in over fifty percent of all cases. We estimate that a typical exterior quadrupole moment from surrounding matter in the galaxy may also be sufficient to excite eccentricity oscillations in supermassive black hole binaries, and also accelerate black hole mergers., 25 pages, including 12 figures; uses AASTeX v5.0; revised version accepted for publication in ApJ

We present the results of a systematic survey of numerical solutions to the coagulation equation for a rate coefficient of the form A_ij \propto (i^mu j^nu + i^nu j^mu) and monodisperse initial conditions. The results confirm that there are three classes of rate coefficients with qualitatively different solutions. For nu \leq 1 and lambda = mu + nu \leq 1, the numerical solution evolves in an orderly fashion and tends toward a self-similar solution at large time t. The properties of the numerical solution in the scaling limit agree with the analytic predictions of van Dongen and Ernst. In particular, for the subset with mu > 0 and lambda < 1, we disagree with Krivitsky and find that the scaling function approaches the analytically predicted power-law behavior at small mass, but in a damped oscillatory fashion that was not known previously. For nu \leq 1 and lambda > 1, the numerical solution tends toward a self-similar solution as t approaches a finite time t_0. The mass spectrum n_k develops at t_0 a power-law tail n_k \propto k^{-tau} at large mass that violates mass conservation, and runaway growth/gelation is expected to start at t_crit = t_0 in the limit the initial number of particles n_0 -> \infty. The exponent tau is in general less than the analytic prediction (lambda + 3)/2, and t_0 = K/[(lambda - 1) n_0 A_11] with K = 1--2 if lambda > 1.1. For nu > 1, the behaviors of the numerical solution are similar to those found in a previous paper by us. They strongly suggest that there are no self-consistent solutions at any time and that runaway growth is instantaneous in the limit n_0 -> \infty. They also indicate that the time t_crit for the onset of runaway growth decreases slowly toward zero with increasing n_0., 41 pages, including 14 figures; accepted for publication in J. Phys. A

Three transiting circumbinary planets (Kepler-16 b, Kepler-34 b, and Kepler-35 b) have recently been discovered from photometric data taken by the Kepler spacecraft. Their orbits are significantly non-Keplerian because of the large secondary-to-primary mass ratio and orbital eccentricity of the binaries, as well as the proximity of the planets to the binaries. We present an analytic theory, with the planet treated as a test particle, which shows that the planetary motion can be represented by the superposition of the circular motion of a guiding center, the forced oscillations due to the non-axisymmetric components of the binary's potential, the epicyclic motion, and the vertical motion. In this analytic theory, the periapse and ascending node of the planet precess at nearly equal rates in opposite directions. The largest forced oscillation term corresponds to a forced eccentricity (which is an explicit function of the parameters of the binary and of the guiding center radius of the planet), and the amplitude of the epicyclic motion (which is a free parameter of the theory) is the free eccentricity. Comparisons with direct numerical orbit integrations show that this analytic theory gives an accurate description of the planetary motion for all three Kepler systems. We find that all three Kepler circumbinary planets have nonzero free eccentricities., 21 pages, including 8 figures; accepted for publication in ApJ