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The large eccentricities of cold Jupiters and the existence of hot Jupiters have long challenged theories of planet formation. A proposed solution to both of these puzzles is high-eccentricity migration, in which an initially cold Jupiter is excited to high eccentricities before being tidally circularized. Secular perturbations from an inclined stellar companion are a potential source of eccentricity oscillations, a phenomenon known as the Eccentric Kozai-Lidov (EKL) mechanism. Previous studies have found that the cold Jupiter eccentricity distribution produced by EKL is inconsistent with observations. However, these studies assumed all planets start on circular orbits. Here, we revisit this question, considering that an initial period of planet-planet scattering on $\sim$Myr timescales likely places planets on slightly eccentric orbits before being modulated by EKL on $\sim$Myr-Gyr timescales. Small initial eccentricities can have a dramatic effect by enabling EKL to act at lower inclinations. We numerically integrate the secular hierarchical three-body equations of motion, including general relativity and tides, for populations of cold giant planets in stellar binaries with varied initial eccentricity distributions. For populations with modest initial mean eccentricities, the simulated eccentricity distribution produced by EKL is statistically consistent with the observed eccentricities of cold single-planet systems. The lower eccentricities in a multi-planet control sample suggest that planetary companions quench stellar EKL. We show that scattering alone is unlikely to reproduce the present-day eccentricity distribution. We also show that the anisotropic inclination distribution produced by EKL may lead radial velocity measurements to underestimate giant planet masses., Comment: Submitted to ApJL, 15 pages, 6 figures (typo corrected and reference added in v2)

More than half of all main-sequence (MS) stars have one or more companions, and many of those with initial masses <8 M$_\odot$ are born in hierarchical triples. These systems feature two stars in a close orbit (the inner binary) while a tertiary star orbits them on a wider orbit (the outer binary). In hierarchical triples, three-body dynamics combined with stellar evolution drives interactions and, in many cases, merges the inner binary entirely to create a renovated `Post-Merger Binary' (PMB). By leveraging dynamical simulations and tracking binary interactions, we explore the outcomes of merged triples and investigate whether PMBs preserve signatures of their three-body history. Our findings indicate that in 26-54% of wide double WD binaries (s>100 au), the more massive white dwarf (WD) is a merger product, implying that these DWD binaries were previously triples. Overall, we estimate that $44\pm14\%$ of observed wide DWDs originated in triple star systems and thereby have rich dynamical histories. Additionally, our results suggest that the separations of inner and outer binaries are uncorrelated at birth, providing insights into stellar formation processes. We also examine MS+MS and MS+Red Giant mergers manifesting as Blue Straggler stars (BSSs). These PMBs have orbital configurations and ages similar to most observed BSS binaries. While the triple+merger formation channel can explain the observed chemical abundances, moderate eccentricities, and companion masses in BSS binaries, it likely only accounts for $\sim$20-25% of BSSs. Meanwhile, we predict that the majority of observed single BSSs formed as collisions in triples and harbor long-period (>10 yr) companions. Furthermore, both BSS binaries and DWDs exhibit signatures of WD birth kicks., Comment: Accepted for publication to ApJ. Additional comments are welcome

Triple body systems are prevalent in nature, from planetary to stellar to supermassive black hole scales. In a hierarchical triple system, oscillations of the inner orbit's eccentricity and inclination can be induced on secular timescales. Over many cycles, the octupole-level terms in the secular equations of motion can drive the system to extremely high eccentricities via the Eccentric Kozai-Lidov (EKL) mechanism. The overall decrease in the inner orbit's pericenter distance has potentially dramatic effects for realistic systems, such as tidal disruption events. We present an analytical approximation in the test particle limit to describe individual step-wise increases in eccentricity of the inner orbit. A second approximation, also in the test particle limit, is obtained by integrating the equations of motion and calibrating to numerical simulations to estimate the overall octupole-level time evolution of the eccentricity. The latter approach is then extended beyond the test particle to the general case. The three novel analytical approximations are compared to numerical solutions to show that the models accurately describe the form and timescale of the secular descent from large distances to a close-encounter distance (e.g., the Roche limit). By circumventing the need for numerical simulations to obtain the long-term behavior, these approximations can be used to readily estimate properties of close encounters and descent timescales for populations of systems. We demonstrate by calculating rates of EKL-driven migration for Hot Jupiters in stellar binaries., Comment: Accepted to ApJ, 16 pages, 8 figures

Most, if not all, sun-like stars host one or more planets, making multi-planetary systems commonplace in our galaxy. We utilize hundreds of multi-planet simulations to explore the origin of such systems, focusing on their orbital architecture. The first set of simulations assumes in-situ assembly of planetary embryos, while the second explores planetary migration. After applying observational biases to the simulations, we compare them to 250+ observed multi-planetary systems, including 13 systems with planets in the habitable zone. For all of the systems, we calculate two of the so-called statistical measures: the mass concentration ($S_{c}$) and orbital spacing ($S_{s}$). After analytic and empirical analyses, we find that the measures are related to first-order with a power law: $S_{c} \sim S_{s}^\beta$. The in-situ systems exhibit steeper power-law relations relative to the migration systems. We show that different formation scenarios cover different regions in the $S_{s} - S_{c}$ diagram with some overlap. Furthermore, we discover that observed systems with $S_{s} < 30$ are likely dominated by the migration scenario, while those with $S_{s} \geq 30$ are likely dominated by the in-situ scenario. We apply these criteria to determine that a majority (62%) of observed multi-planetary systems formed via migration, whereas most systems with currently observed habitable planets formed via in-situ assembly. This work provides methods of leveraging the statistical measures ($S_{s}$ and $S_{c}$) to disentangle the formation history of observed multi-planetary systems based on their present-day architectures., Comment: Accepted for publication in ApJ Letters

The $Gaia$ mission has detected many white dwarfs (WDs) in binary and triple configurations, and while observations suggest that triple stellar systems are common in our Galaxy, not much attention was devoted to WDs in triples. For stability reasons, these triples must have hierarchical configurations, i.e., two stars are on a tight orbit (the inner binary), with the third companion on a wider orbit about the inner binary. In such a system, the two orbits torque each other via the eccentric Kozai-Lidov mechanism (EKL), which can alter the orbital configuration of the inner binary. We simulate thousands of triple stellar systems for over $10$ Gyr, tracking gravitational interactions, tides, general relativity, and stellar evolution up to their WD fate. As demonstrated here, three-body dynamics coupled with stellar evolution is a critical channel to form tight WD binaries or merge a WD binary. Amongst these triples, we explore their manifestations as cataclysmic variables, Type Ia supernovae, and gravitational-wave events. The simulated systems are then compared to a sample of WD triples selected from the $Gaia$ catalog. We find that including the effect of mass loss-induced kicks is crucial for producing a distribution of the inner binary-tertiary separations that is consistent with $Gaia$ observations. Lastly, we leverage this consistency to estimate that, at minimum, $30\%$ of solar-type stars in the local $200$ parsecs were born in triples., Comment: 18 pages, 7 figures, revised version accepted for publication in ApJ

Irregular satellites are the minor bodies found orbiting all four Solar System giant planets, with large semi-major axes, eccentricities, and inclinations. Previous studies have determined that the Solar System's irregular satellites are extremely collisionally evolved populations today, having lost $\sim$99 per cent of their initial mass over the course of hundreds of Myr. Such an evolution implies that the irregular satellites must have produced a population of dusty collisional debris in the past, which is potentially observable due to the resulting reprocessing of stellar light. In this paper we examine the signatures of the debris discs produced by extrasolar analogues of this process. Radiation pressure, quantified by the parameter $\beta$, is the driving force behind the liberation of dust grains from the planetary Hill sphere, and results in the formation of circumstellar dust rings, even in the absence of an underlying belt of asteroids in the system. Our simulated discs reproduce many of the same features seen in some classes of observed debris discs, such as thin ring morphology, a large blowout size, and azimuthal symmetry. We compare our simulated discs' radial profiles to those of the narrow dust rings observed around Fomalhaut and HR 4796A, and show that they can broadly reproduce the observed radial distribution of dust., Comment: 19 pages, 17 figures

Moons orbiting rocky exoplanets in compact orbits about other stars experience an accelerated tidal evolution, and can either merge with their parent planet or reach the limit of dynamical instability within a Hubble time. We review the parameter space over which moons become unbound, including the effects of atmospheric tides on the planetary spin. We find that such tides can change the final outcome from merger to escape, albeit over a limited parameter space. We also follow the further evolution of unbound moons, and demonstrate that the overwhelmingly most likely long-term outcome is that the unbound moon returns to collide with its original parent planet. The dust released by such a collision is estimated to reach optical depths approximately 0.001, exhibit characteristic temperatures of a few hundred degrees Kelvin, and last for a few thousand years. These properties make such events an attractive model for the emerging class of middle-aged main sequence stars that are observed to show transient clouds of warm dust. Furthermore, a late collision between a planet and a returning moon on a hyperbolic orbit may sterilise an otherwise habitable planet., Comment: to appear in Monthly Notices of the Royal Astronomical Society

The maximum mass of a star that can produce a white dwarf (WD) is an important astrophysical quantity. One of the best approaches to establishing this limit is to search for WDs in young star clusters in which only massive stars have had time to evolve and where the mass of the progenitor can be established from the cooling time of the WD together with the age of the cluster. Searches in young Milky Way clusters have not thus far yielded WD members more massive than about 1.1$~M_{\odot}$, well below the Chandrasekhar mass of $1.38~M_{\odot}$, nor progenitors with masses in excess of about $6~M_{\odot}$. However, the hunt for potentially massive WDs that escaped their cluster environs is yielding interesting candidates. To expand the cluster sample further, we used HST to survey four young and massive star clusters in the Magellanic Clouds for bright WDs that could have evolved from stars as massive as 10$~M_{\odot}$. We located five potential WD candidates in the oldest of the four clusters examined, the first extragalactic single WDs thus far discovered. As these hot WDs are very faint at optical wavelengths, final confirmation will likely have to await spectroscopy with 30-metre class telescopes., Comment: 10 pages, 5 figures, accepted to the Astrophysical Journal Letters

We present a catalog of unbound stellar pairs, within 100 pc of the Sun, that are undergoing close, hyperbolic, encounters. The data are drawn from the GAIA EDR3 catalogue, and the limiting factors are errors in the radial distance and unknown velocities along the line of sight. Such stellar pairs have been suggested (Hansen & Zuckerman 2021) to be possible events associated with the migration of technological civilisations between stars. As such, this sample may represent a finite set of targets for a SETI search based on this hypothesis. Our catalog contains a total of 132 close passage events, featuring stars from across the entire main sequence, with 16 pairs featuring at least one main sequence star of spectral type between K1 and F3. Many of these stars are also in binaries, so that we isolate eight single stars as the most likely candidates to search for an ongoing migration event -- HD 87978, HD 92577, HD 50669, HD 44006, HD 80790, LSPM J2126+5338, LSPM J0646+1829 and HD 192486. Amongst host stars of known planets, the stars GJ 433 and HR 858 are the best candidates., Comment: 25 pages, 10 figures+22 finding charts. to appear in AJ

We study the stationary points of the hierarchical three body problem in the planetary limit (m_2, m_3 << m_1) at both the quadrupole and octupole orders. We demonstrate that the extension to octupole order preserves the principal stationary points of the quadrupole solution in the limit of small outer eccentricity e_2 but that new families of stable fixed points occur in both prograde and retrograde cases. The most important new equilibria are those that branch off from the quadrupolar solutions and extend to large e_2. The apsidal alignment of these families is a function of mass and inner planet eccentricity, and is determined by the relative directions of precession of omega_1 and omega_2 at the quadrupole level. These new equilibria are also the most resilient to the destabilizing effects of relativistic precession. We find additional equilibria that enable libration of the inner planet argument of pericentre in the limit of radial orbits and recover the non-linear analogue of the Laplace-Lagrange solutions in the coplanar limit. Finally, we show that the chaotic diffusion and orbital flips identified with the Eccentric Kozai Lidov mechanism and its variants can be understood in terms of the stationary points discussed here., Comment: 27 pages, 36 figures

The COVID-19 pandemic has highlighted the importance of in-silico epidemiological modelling in predicting the dynamics of infectious diseases to inform health policy and decision makers about suitable prevention and containment strategies. Work in this setting involves solving challenging inference and control problems in individual-based models of ever increasing complexity. Here we discuss recent breakthroughs in machine learning, specifically in simulation-based inference, and explore its potential as a novel venue for model calibration to support the design and evaluation of public health interventions. To further stimulate research, we are developing software interfaces that turn two cornerstone COVID-19 and malaria epidemiology models COVID-sim, (https://github.com/mrc-ide/covid-sim/) and OpenMalaria (https://github.com/SwissTPH/openmalaria) into probabilistic programs, enabling efficient interpretable Bayesian inference within those simulators.

Naive approaches to amortized inference in probabilistic programs with unbounded loops can produce estimators with infinite variance. This is particularly true of importance sampling inference in programs that explicitly include rejection sampling as part of the user-programmed generative procedure. In this paper we develop a new and efficient amortized importance sampling estimator. We prove finite variance of our estimator and empirically demonstrate our method's correctness and efficiency compared to existing alternatives on generative programs containing rejection sampling loops and discuss how to implement our method in a generic probabilistic programming framework., Comment: AISTATS 2022 camera ready

The origin of close-in Jovian planets is still elusive. We examine the in-situ gas accretion scenario as a formation mechanism of these planets. We reconstruct natal disk properties from the occurrence rate distribution of close-in giant planets, under the assumption that the occurrence rate may reflect the gas accretion efficiency onto cores of these planets. We find that the resulting gas surface density profile becomes an increasing function of the distance from the central star with some structure at $r \simeq 0.1$ au. This profile is quite different from the standard minimum-mass solar nebula model, while our profile leads to better reproduction of the population of observed close-in super-Earths based on previous studies. We compute the resulting magnetic field profiles and find that our profiles can be fitted by stellar dipole fields ($\propto r^{-3}$) in the vicinity of the central star and large-scale fields ($\propto r^{-2}$) at the inner disk regions, either if the isothermal assumption breaks down or if nonideal MHD effects become important. For both cases, the transition between these two profiles occurs at $r \simeq 0.1$ au, which corresponds to the period valley of giant exoplanets. Our work provides an opportunity to test the in-situ gas accretion scenario against disk quantities, which may constrain the gas distribution of the minimum-mass {\it extra}solar nebula., Comment: 5 pages, 3 figures, accepted for publication in A&A Letters

Probabilistic programming languages (PPLs) are receiving widespread attention for performing Bayesian inference in complex generative models. However, applications to science remain limited because of the impracticability of rewriting complex scientific simulators in a PPL, the computational cost of inference, and the lack of scalable implementations. To address these, we present a novel PPL framework that couples directly to existing scientific simulators through a cross-platform probabilistic execution protocol and provides Markov chain Monte Carlo (MCMC) and deep-learning-based inference compilation (IC) engines for tractable inference. To guide IC inference, we perform distributed training of a dynamic 3DCNN--LSTM architecture with a PyTorch-MPI-based framework on 1,024 32-core CPU nodes of the Cori supercomputer with a global minibatch size of 128k: achieving a performance of 450 Tflop/s through enhancements to PyTorch. We demonstrate a Large Hadron Collider (LHC) use-case with the C++ Sherpa simulator and achieve the largest-scale posterior inference in a Turing-complete PPL., Comment: 14 pages, 8 figures

Epidemiology simulations have become a fundamental tool in the fight against the epidemics of various infectious diseases like AIDS and malaria. However, the complicated and stochastic nature of these simulators can mean their output is difficult to interpret, which reduces their usefulness to policymakers. In this paper, we introduce an approach that allows one to treat a large class of population-based epidemiology simulators as probabilistic generative models. This is achieved by hijacking the internal random number generator calls, through the use of a universal probabilistic programming system (PPS). In contrast to other methods, our approach can be easily retrofitted to simulators written in popular industrial programming frameworks. We demonstrate that our method can be used for interpretable introspection and inference, thus shedding light on black-box simulators. This reinstates much-needed trust between policymakers and evidence-based methods., Comment: 6 pages, 3 figures, Accepted at the International Conference on Machine Learning AI for Social Good Workshop, Long Beach, United States, 2019

Using the updated exoplanet population parameters of our previous study, which includes the planetary radius updates from Gaia DR2 and an inferred multiplicity distribution, we provide a revised $\eta_{\oplus}$ calculation. This is achieved by sampling planets from our derived population model and determining which planets meet our criterion for habitability. To ensure robust results, we provide probabilities calculated over a range of upper radius limits. Our most optimistic criterion for habitability provides an $\eta_{\oplus}$ value of $0.34\pm 0.02 \frac{\rm planets}{\rm star}$. We also consider the effects of multiplicity and the number of habitable planets each system may contain. Our calculation indicates that $6.4\pm0.5\%$ of GK dwarfs have more than one planet within their habitable zone. This optimistic habitability criterion also suggests that $0.036\pm0.009\%$ of solar-like stars will harbor 5 or more habitable planets. These tightly packed highly habitable system should be extremely rare, but still possible. Even with our most pessimistic criterion we still expect that $1.8\pm0.2\%$ of solar-like stars harbor more than one habitable planet., Comment: 7 pages, 1 figure; Accepted for publication in MNRAS

Identification of the main planet formation site is fundamental to understanding how planets form and migrate to the current locations. We consider the heavy-element content trend of observed exoplanets derived from improved measurements of mass and radius, and explore how this trend can be used as a tracer of their formation sites. Using gas accretion recipes obtained from detailed hydrodynamical simulations, we confirm that the disk-limited gas accretion regime is most important for reproducing the heavy-element content trend. Given that such a regime is specified by two characteristic masses of planets, we compute these masses as a function of the distance ($r$) from the central star, and then examine how the regime appears in the mass-semimajor axis diagram. Our results show that a plausible solid accretion region emerges at $r \simeq 0.6$ au and expands with increasing $r$, using the conventional disk model. Given that exoplanets that possess the heavy-element content trend distribute currently near their central stars, our results imply the importance of planetary migration that would occur after solid accretion onto planets might be nearly completed at $r \geq 0.6$ au. Self-consistent simulations would be needed to verify the predictions herein., Comment: 6 pages, 3 figures, accepted for publication in ApJ Letters

We develop a new Low-level, First-order Probabilistic Programming Language (LF-PPL) suited for models containing a mix of continuous, discrete, and/or piecewise-continuous variables. The key success of this language and its compilation scheme is in its ability to automatically distinguish parameters the density function is discontinuous with respect to, while further providing runtime checks for boundary crossings. This enables the introduction of new inference engines that are able to exploit gradient information, while remaining efficient for models which are not everywhere differentiable. We demonstrate this ability by incorporating a discontinuous Hamiltonian Monte Carlo (DHMC) inference engine that is able to deliver automated and efficient inference for non-differentiable models. Our system is backed up by a mathematical formalism that ensures that any model expressed in this language has a density with measure zero discontinuities to maintain the validity of the inference engine., Comment: Published in the proceedings of the 22nd International Conference on Artificial Intelligence and Statistics (AISTATS)

We present precision 4.5 $\mu$m Spitzer transit photometry of eight planet candidates discovered by the K2 mission: K2-52 b, K2-53 b, EPIC 205084841.01, K2-289 b, K2-174 b, K2-87 b, K2-90 b, and K2-124 b. The sample includes four sub-Neptunes and two sub-Saturns, with radii between 2.6 and 18 $R_\oplus$, and equilibrium temperatures between 440 and 2000 K. In this paper we identify several targets of potential interest for future characterization studies, demonstrate the utility of transit follow-up observations for planet validation and ephemeris refinement, and present new imaging and spectroscopy data. Our simultaneous analysis of the K2 and Spitzer light curves yields improved estimates of the planet radii, and multi-wavelength information which help validate their planetary nature, including the previously un-validated candidate EPIC 205686202.01 (K2-289 b). Our Spitzer observations yield an order of magnitude increase in ephemeris precision, thus paving the way for efficient future study of these interesting systems by reducing the typical transit timing uncertainty in mid-2021 from several hours to a dozen or so minutes. K2-53 b, K2-289 b, K2-174 b, K2-87 b, and K2-90 b are promising radial velocity (RV) targets given the performance of spectrographs available today or in development, and the M3V star K2-124 hosts a temperate sub-Neptune that is potentially a good target for both RV and atmospheric characterization studies., Comment: 21 pages, 8 figures, 9 tables, accepted for publication in AJ

Informal settlements are home to the most socially and economically vulnerable people on the planet. In order to deliver effective economic and social aid, non-government organizations (NGOs), such as the United Nations Children's Fund (UNICEF), require detailed maps of the locations of informal settlements. However, data regarding informal and formal settlements is primarily unavailable and if available is often incomplete. This is due, in part, to the cost and complexity of gathering data on a large scale. To address these challenges, we, in this work, provide three contributions. 1) A brand new machine learning data-set, purposely developed for informal settlement detection. 2) We show that it is possible to detect informal settlements using freely available low-resolution (LR) data, in contrast to previous studies that use very-high resolution (VHR) satellite and aerial imagery, something that is cost-prohibitive for NGOs. 3) We demonstrate two effective classification schemes on our curated data set, one that is cost-efficient for NGOs and another that is cost-prohibitive for NGOs, but has additional utility. We integrate these schemes into a semi-automated pipeline that converts either a LR or VHR satellite image into a binary map that encodes the locations of informal settlements., Comment: Published at the AAAI/ACM Conference on AI, ethics and society. Extended results from our previous workshop: arXiv:1812.00812

We investigate the role that planet detection order plays in the Kepler planet detection pipeline. The Kepler pipeline typically detects planets in order of descending signal strength (MES). We find that the detectability of transits experiences an additional $5.5\%$ and $15.9\%$ efficiency loss, for periods $<200$ days and $>200$ days respectively, when detected after the strongest signal transit in a multiple-planet system. We provide a method for determining the transit probability for multiple-planet systems by marginalizing over the empirical Kepler dataset. Furthermore, because detection efficiency appears to be a function of detection order, we discuss the sorting statistics that affect the radius and period distributions of each detection order. Our occurrence rate dataset includes radius measurement updates from the California Kepler Survey (CKS), Gaia DR2, and asteroseismology. Our population model is consistent with the results of Burke et al. (2015), but now includes an improved estimate of the multiplicity distribution. From our obtained model parameters, we find that only $4.0\pm4.6\%$ of solar-like GK dwarfs harbor one planet. This excess is smaller than prior studies and can be well modeled with a modified Poisson distribution, suggesting that the Kepler Dichotomy can be accounted for by including the effects of multiplicity on detection efficiency. Using our modified Poisson model we expect the average number of planets is $5.86\pm0.18$ planets per GK dwarf within the radius and period parameter space of Kepler., Comment: 17 pages, 8 figures, and 4 tables; accepted for publishing in MNRAS

Detecting and mapping informal settlements encompasses several of the United Nations sustainable development goals. This is because informal settlements are home to the most socially and economically vulnerable people on the planet. Thus, understanding where these settlements are is of paramount importance to both government and non-government organizations (NGOs), such as the United Nations Children's Fund (UNICEF), who can use this information to deliver effective social and economic aid. We propose two effective methods for detecting and mapping the locations of informal settlements. One uses only low-resolution (LR), freely available, Sentinel-2 multispectral satellite imagery with noisy annotations, whilst the other is a deep learning approach that uses only costly very-high-resolution (VHR) satellite imagery. To our knowledge, we are the first to map informal settlements successfully with low-resolution satellite imagery. We extensively evaluate and compare the proposed methods. Please find additional material at https://frontierdevelopmentlab.github.io/informal-settlements/., Comment: arXiv admin note: text overlap with arXiv:1812.00786

Detecting and mapping informal settlements encompasses several of the United Nations sustainable development goals. This is because informal settlements are home to the most socially and economically vulnerable people on the planet. Thus, understanding where these settlements are is of paramount importance to both government and non-government organizations (NGOs), such as the United Nations Children's Fund (UNICEF), who can use this information to deliver effective social and economic aid. We propose a method that detects and maps the locations of informal settlements using only freely available, Sentinel-2 low-resolution satellite spectral data and socio-economic data. This is in contrast to previous studies that only use costly very-high resolution (VHR) satellite and aerial imagery. We show how we can detect informal settlements by combining both domain knowledge and machine learning techniques, to build a classifier that looks for known roofing materials used in informal settlements. Please find additional material at https://frontierdevelopmentlab.github.io/informal-settlements/., Comment: Appeared at the 32nd Conference on Neural Information Processing Systems (NeurlPS 2018) Machine Learning for the Developing World (ML4DW) Workshop

We present a novel probabilistic programming framework that couples directly to existing large-scale simulators through a cross-platform probabilistic execution protocol, which allows general-purpose inference engines to record and control random number draws within simulators in a language-agnostic way. The execution of existing simulators as probabilistic programs enables highly interpretable posterior inference in the structured model defined by the simulator code base. We demonstrate the technique in particle physics, on a scientifically accurate simulation of the tau lepton decay, which is a key ingredient in establishing the properties of the Higgs boson. Inference efficiency is achieved via inference compilation where a deep recurrent neural network is trained to parameterize proposal distributions and control the stochastic simulator in a sequential importance sampling scheme, at a fraction of the computational cost of a Markov chain Monte Carlo baseline., Comment: 20 pages, 9 figures

Hamiltonian Monte Carlo (HMC) is arguably the dominant statistical inference algorithm used in most popular "first-order differentiable" Probabilistic Programming Languages (PPLs). However, the fact that HMC uses derivative information causes complications when the target distribution is non-differentiable with respect to one or more of the latent variables. In this paper, we show how to use extensions to HMC to perform inference in probabilistic programs that contain discontinuities. To do this, we design a Simple first-order Probabilistic Programming Language (SPPL) that contains a sufficient set of language restrictions together with a compilation scheme. This enables us to preserve both the statistical and syntactic interpretation of if-else statements in the probabilistic program, within the scope of first-order PPLs. We also provide a corresponding mathematical formalism that ensures any joint density denoted in such a language has a suitably low measure of discontinuities., Comment: 4 pages, 2 figures

We show that a model in which Mars grows near Earth and Venus but is then scattered out of the terrestrial region yields a natural pathway to explain the low masses of the Martian moons Phobos & Deimos. In this scenario, the last giant impact experienced by Mars is followed by an extended period (tens to hundreds of Myr) of close passages by other planetary embryos. These close passages perturb and dynamically heat any system of forming satellites left over by the giant impact and can substantially reduce the mass in the satellite system (sometimes to zero). The close passage of massive perturbing bodies also offers the opportunity to capture small objects by three-body scattering. Both mechanisms lead to low mass moon systems with a substantially collisional history., Comment: 16 pages, 10 figures, MNRAS in press

We investigate the constraints on the formation of, and tidal dissipation processes in, hot Jupiters (HJs) that can be inferred based on reliable knowledge of the age of a system or population. Particular attention is paid to the role of young systems (such as those in open clusters or star-forming regions) in such studies. For an ensemble of coeval HJ (or proto-HJ) systems, we quantify the effect of age on the distribution of orbital eccentricities with respect to orbital periods as well as the location of the observed "pile-up" feature. We expect the effects of pre-main-sequence stellar evolution to be important only if a substantial fraction of HJs approach their current orbits early in protostellar contraction (ages less than 10 Myr). Application to the HJs presently known in the cluster M67 yields constraints on the dissipation roughly consistent with those gleaned from planets in the field; for those in the Hyades and Praesepe, our results suggest a higher degree of dissipation at early times than that inferred from other populations., Comment: 14 pages, 9 figures. Submitted to MNRAS on 2017 November 27

We examine the effect of secular perturbations by giant planets on systems of multiple, lower mass planets orbiting Sun-like stars. We simulate the effects of forcing both eccentricity and inclination, separately and together. We compare our results to the statistics of the observed Kepler data and examine whether these results can be used to explain the observed excess of single transiting planets. We cannot explain the observed excess by pumping only inclination without driving most systems over the edge of dynamical instability. Thus, we expect the underlying planetary population for systems with a single transitting planet to contain an intrinsically low multiplicity population. We can explain the Kepler statistics and occurrence rates for R< 2 Rearth planets with a perturber population consistent with that inferred from radial velocity surveys, but require too many giant planets if we wish to explain all planets with R < 4 Rearth. These numbers can be brought into agreement if we posit the existence of an equivalent size population of planets below the RV detection limit (of characteristic mass 0.1 Mjupiter). This population would need to be dynamically hot to produce sufficiently strong perturbations and would leave the imprint of high obliquities amongst the surviving planets. Thus, an extensive sample of obliquities for low mass planets can help to indicate the presence of such a population. (...) Some of our simulations also produce planetary systems with planets that survive in the habitable zone but have no planets interior to them -- much as in the case of our Solar System. This suggests that such a configuration may not be altogether rare, but may occur around a few percent of FGK stars., Comment: submitted, 33 pages, 25 figures

We present Hubble Space Telescope observations of the upper part (T_eff> 10 000 K) of the white dwarf cooling sequence in the globular cluster 47 Tucanae and measure a luminosity function of hot white dwarfs. Comparison with previous determinations from large scale field surveys indicates that the previously determined plateau at high effective temperatures is likely a selection effect, as no such feature is seen in this sample. Comparison with theoretical models suggests that the current estimates of white dwarf neutrino emission (primarily by the plasmon channel) are accurate, and variations are restricted to no more than a factor of two globally, at 95% confidence. We use these constraints to place limits on various proposed exotic emission mechanisms, including a non-zero neutrino magnetic moment, formation of axions, and emission of Kaluza-Klein modes into extra dimensions., Comment: 13 pages, 12 figures, to appear in the Astrophysical Journal

We describe the long-term evolution of compact systems of terrestrial planets, using a set of simulations that match the statistical properties of the observed exoplanet distribution. The evolution is driven by tidal dissipation in the planetary interiors, but the systems evolve as a whole due to secular gravitational interactions. We find that, for Earth-like dissipation levels, planetary orbits can be circularised out to periods of order 100 days, an order of magnitude larger than is possible for single planets. The resulting distribution of eccentricities is a qualitative match to that inferred from transit timing variations, with a minority of non-zero eccentricities maintained by particular secular configurations. The coupling of the tidal and secular processes enhance the inward migration of the innermost planets in these systems, and can drive them to short orbital periods. Resonant interactions of both the mean motion and secular variety are observed, although the interactions are not strong enough to drive systemic instability in most cases. However, we demonstrate that these systems can easily be driven unstable if coupled to giant planets on longer period orbits., Comment: 17 pages, 22 figures, 2 tables, submitted to Monthly Notices of the Royal Astronomical Society

We examine the consequences of a model for the circulation of solids in a protoplanetary nebula in which aerodynamic drag is counterbalanced by the recycling of material to the outer disc by a protostellar outflow or a disc wind. This population of circulating dust eventually becomes unstable to the formation of planetesimals by gravitational instability, and results in the ultimate deposition of 30--50 earth masses in planetesimals on scales R< 1 AU. Such a model may provide an appropriate justification for the approximately power law initial conditions needed to reproduce observed planetary systems by in situ assembly., Comment: 13 pages, 14 figures, to appear in Monthly Notices of Royal Astronomical Society

We investigated the probability that an inelastic collision of planetesimals within the Hill sphere of the Jovian planets could explain the presence and orbits of observed irregular satellites. Capture of satellites via this mechanism is highly dependent on not only the mass of the protoplanetary disk, but also the shape of the planetesimal size distribution. We performed 2000 simulations for integrated time intervals $\sim 2$ Myr and found that, given the currently accepted value for the minimum mass solar nebula and planetesimal number density based upon the \citet{Nesvorny2003} and \citet{Charnoz2003} size distribution $dN \sim D^{-3.5} dD$, the collision rates for the different Jovian planets range between $\sim 0.6$ and $\gtrsim 170 \, \Myr^{-1}$ for objects with radii, $1 \, \km \le r \le 10 \, \km$. Additionally, we found that the probability that these collisions remove enough orbital energy to yield a bound orbit was $\lesssim 10^{-5}$ and had very little dependence on the relative size of the planetesimals. Of these collisions, the collision energy between two objects was $\gtrsim 10^3$ times the gravitational binding energy for objects with radii $\sim 100$ km. We find that, capturing irregular satellites via collisions between unbound objects can only account for $\sim 0.1%$ of the observed population, hence can this not be the sole method of producing irregular satellites., Comment: 11 pages 4 figures 1 table; This replaces a prior submission, which contained some minor contradictions within the text accepted by MNRAS in press

We present the results of three body simulations focused on understanding the fates of intermediate mass black holes (IBH) that drift within the central 0.5 pc of the Galaxy. In particular, we modeled the interactions between pairs of $4000 {\rm M}_{\odot}$ black holes as they orbit a central blac k hole of mass $4 \times 10^6 {\rm M}_{\odot}$. The simulations performed assume a Schwarzschild geometry and account for Chandrasekhar dynamical friction as well as acceleration resulting from energy lost due to gravitational radiation. We found the branching ratio for one of the orbiting IBHs to merge with the CBH was 0.95 and is independent of the inner IBH's initial eccentricity as well as the rate of sinking. This, coupled with an infall rate of $\sim 10^7 $ yrs for an IBH to drift into the Galactic center, results in an IBH-CBH merger every $\lesssim 11$ Myrs. Lastly we found that the IBH-IBH-CBH triple body system ``resets'' itself, in the sense that a system with an inner I BH with an initially circular orbit generally left behind an IBH with a large eccentricity, whereas a system in which the inner IBH had a high eccentricity ($e_0 \sim 0.9$) usually left a remnant with low eccentricity. Branching ratios for different outcomes are also similar in the two cases., Comment: Official paper to appear in November 2008 issue of ApJ