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Transiting planets with orbital periods longer than 40 d are extremely rare among the 5000+ planets discovered so far. The lack of discoveries of this population poses a challenge to research into planetary demographics, formation, and evolution. Here, we present the detection and characterization of HD88986b, a potentially transiting sub-Neptune, possessing the longest orbital period among known transiting small planets (< 4 R$_{\oplus}$) with a precise mass measurement ($\sigma_M/M$ > 25%). Additionally, we identified the presence of a massive companion in a wider orbit around HD88986. Our analysis reveals that HD88986b, based on two potential single transits on sector 21 and sector 48 which are both consistent with the predicted transit time from the RV model, is potentially transiting. The joint analysis of RV and photometric data show that HD88986b has a radius of 2.49$\pm$0.18 R$_{\oplus}$, a mass of 17.2$^{+4.0}_{-3.8}$ M$_{\oplus}$, and it orbits every 146.05$^{+0.43}_{-0.40}$ d around a subgiant HD88986 which is one of the closest and brightest exoplanet host stars (G2V type, R=1.543 $\pm$0.065 R$_{\odot}$, V=$6.47\pm 0.01$ mag, distance=33.37$\pm$0.04 pc). The nature of the outer, massive companion is still to be confirmed; a joint analysis of RVs, Hipparcos, and Gaia astrometric data shows that with a 3$\sigma$ confidence interval, its semi-major axis is between 16.7 and 38.8 au and its mass is between 68 and 284 M$_{Jup}$. HD88986b's wide orbit suggests the planet did not undergo significant mass loss due to extreme-ultraviolet radiation from its host star. Therefore, it probably maintained its primordial composition, allowing us to probe its formation scenario. Furthermore, the cold nature of HD88986b (460$\pm$8 K), thanks to its long orbital period, will open up exciting opportunities for future studies of cold atmosphere composition characterization., Comment: 37 pages, accepted to be published in A&A

At Jupiter, part of the auroral radio emissions are induced by the Galilean moons Io, Europa and Ganymede. Until now, except for Ganymede, they have been only remotely detected, using ground-based radio-telescopes or electric antennas aboard spacecraft. The polar trajectory of the Juno orbiter allows the spacecraft to cross the range of magnetic flux tubes which sustain the various Jupiter-satellite interactions, and in turn to sample in situ the associated radio emission regions. In this study, we focus on the detection and the characterization of radio sources associated with Io, Europa and Ganymede. Using electric wave measurements or radio observations (Juno/Waves), in situ electron measurements (Juno/JADE-E), and magnetic field measurements (Juno/MAG) we demonstrate that the Cyclotron Maser Instability (CMI) driven by a loss-cone electron distribution function is responsible for the encountered radio sources. We confirmed that radio emissions are associated with Main (MAW) or Reflected Alfv\'en Wing (RAW), but also show that for Europa and Ganymede, induced radio emissions are associated with Transhemispheric Electron Beam (TEB). For each traversed radio source, we determine the latitudinal extension, the CMI-resonant electron energy, and the bandwidth of the emission. We show that the presence of Alfv\'en perturbations and downward field aligned currents are necessary for the radio emissions to be amplified.

In this paper, we explore different Markovian random walk strategies on networks with transition probabilities between nodes defined in terms of functions of the Laplacian matrix. We generalize random walk strategies with local information in the Laplacian matrix, that describes the connections of a network, to a dynamics determined by functions of this matrix. The resulting processes are non-local allowing transitions of the random walker from one node to nodes beyond its nearest neighbors. We find that only two types of Laplacian functions are admissible with distinct behaviors for long-range steps in the infinite network limit: type (i) functions generate Brownian motions, type (ii) functions L\'evy flights. For this asymptotic long-range step behavior only the lowest non-vanishing order of the Laplacian function is relevant, namely first order for type (i), and fractional order for type (ii) functions. In the first part, we discuss spectral properties of the Laplacian matrix and a series of relations that are maintained by a particular type of functions that allow to define random walks on any type of undirected connected networks. Once described general properties, we explore characteristics of random walk strategies that emerge from particular cases with functions defined in terms of exponentials, logarithms and powers of the Laplacian as well as relations of these dynamics with non-local strategies like L\'evy flights and fractional transport. Finally, we analyze the global capacity of these random walk strategies to explore networks like lattices and trees and different types of random and complex networks., Comment: 33 pages, 5 figures

We analyze a random walk strategy on undirected regular networks involving power matrix functions of the type $L^{\frac{\alpha}{2}}$ where $L$ indicates a `simple' Laplacian matrix. We refer such walks to as `Fractional Random Walks' with admissible interval $0<\alpha \leq 2$. We deduce for the Fractional Random Walk probability generating functions (network Green's functions). From these analytical results we establish a generalization of Polya's recurrence theorem for Fractional Random Walks on $d$-dimensional infinite lattices: The Fractional Random Walk is transient for dimensions $d > \alpha$ (recurrent for $d\leq\alpha$) of the lattice. As a consequence for $0<\alpha< 1$ the Fractional Random Walk is transient for all lattice dimensions $d=1,2,..$ and in the range $1\leq\alpha < 2$ for dimensions $d\geq 2$. Finally, for $\alpha=2$ Polya's classical recurrence theorem is recovered, namely the walk is transient only for lattice dimensions $d\geq 3$. The generalization of Polya's recurrence theorem remains valid for the class of random walks with L\'evy flight asymptotics for long-range steps. We also analyze for the Fractional Random Walk mean first passage probabilities, mean first passage times, and global mean first passage times (Kemeny constant). For the infinite 1D lattice (infinite ring) we obtain for the transient regime $0<\alpha<1$ closed form expressions for the fractional lattice Green's function matrix containing the escape and ever passage probabilities. The ever passage probabilities fulfill Riesz potential power law decay asymptotic behavior for nodes far from the departure node. The non-locality of the Fractional Random Walk is generated by the non-diagonality of the fractional Laplacian matrix with L\'evy type heavy tailed inverse power law decay for the probability of long-range moves., Comment: 28 pages, 5 figures. HAL Id : hal-01543330, version 1

We develop physically admissible lattice models in the harmonic approximation which define by Hamilton's variational principle fractional Laplacian matrices of the forms of power law matrix functions on the n -dimensional periodic and infinite lattice in n=1,2,3,..n=1,2,3,.. dimensions. The present model which is based on Hamilton's variational principle is confined to conservative non-dissipative isolated systems. The present approach yields the discrete analogue of the continuous space fractional Laplacian kernel. As continuous fractional calculus generalizes differential operators such as the Laplacian to non-integer powers of Laplacian operators, the fractional lattice approach developed in this paper generalized difference operators such as second difference operators to their fractional (non-integer) powers. Whereas differential operators and difference operators constitute local operations, their fractional generalizations introduce nonlocal long-range features. This is true for discrete and continuous fractional operators. The nonlocality property of the lattice fractional Laplacian matrix allows to describe numerous anomalous transport phenomena such as anomalous fractional diffusion and random walks on lattices. We deduce explicit results for the fractional Laplacian matrix in 1D for finite periodic and infinite linear chains and their Riesz fractional derivative continuum limit kernels., Comment: arXiv admin note: text overlap with arXiv:1604.01725