We carry out 2D viscous hydrodynamical simulations of circumbinary accretion using the moving-mesh code AREPO. We self-consistently compute the accretion flow over a wide range of spatial scales, from the circumbinary disk (CBD) far from the central binary, through accretion streamers, to the disks around individual binary components, resolving the flow down to 2% of the binary separation. We focus on equal-mass binaries with arbitrary eccentricities. We evolve the flow over long (viscous) timescales until a quasi-steady state is reached, in which the mass supply rate at large distancesṀ 0 (assumed constant) equals the time-averaged mass transfer rate across the disk and the total mass accretion rate onto the binary components. This quasi-steady state allows us to compute the secular angular momentum transfer rate onto the binary, J b , and the resulting orbital evolution. Through direct computation of the gravitational and accretional torques on the binary, we find that J b is consistently positive (i.e., the binary gains angular momentum), with l 0 ≡ J b /Ṁ 0 in the range of (0.4 − 0.8)a 2 b Ω b , depending on the binary eccentricity (where a b , Ω b are the binary semi-major axis and angular frequency); we also find that this J b is equal to the net angular momentum current across the CBD, indicating that global angular momentum balance is achieved in our simulations. In addition, we compute the time-averaged rate of change of the binary orbital energy for eccentric binaries, and thus obtain the secular rates ȧ b and ė b . In all cases, ȧ b is positive, i.e., the binary expands while accreting. We discuss the implications of our results for the merger of supermassive binary black holes and for the formation of close stellar binaries.

We carry out numerical simulations of circumbinary discs, solving the viscous hydrodynamics equations on a polar grid covering an extended disc outside the binary co-orbital region. We use carefully controlled outer boundary conditions and longterm integrations to ensure that the disc reaches a quasi-steady state, in which the time-averaged mass accretion rate onto the binary, Ṁ , matches the mass supply rate at the outer disc. We focus on binaries with comparable masses and a wide range of eccentricities (e B ). For e B 0.05, the mass accretion rate of the binary is modulated at about 5 times the binary period; otherwise it is modulated at the binary period. The inner part of the circumbinary disc (r 6a B ) generally becomes coherently eccentric. For low and high e B , the disc line of apsides precesses around the binary, but for intermediate e B (0.2 − 0.4), it instead becomes locked with that of the binary. By considering the balance of angular momentum transport through the disc by advection, viscous stress, and gravitational torque, we determine the time-averaged net angular momentum transfer rate to the binary, J . The specific angular momentum, l 0 = J / Ṁ , depends non-monotonically on e B . Contrary to previous claims, we find that l 0 is positive for most e B , implying that the binary receives net angular momentum, which may cause its separation to grow with time. The minimum l 0 occurs at intermediate e B (0.2 − 0.4), corresponding to the regime where the inner eccentric disc is apsidally aligned with the binary.

The Lidov-Kozai (LK) mechanism plays an important role in the secular evolution of many hierarchical triple systems. The standard LK mechanism consists of large-amplitude oscillations in eccentricity and inclination of a binary subject to the quadrupole potential from an outer perturber. Recent work has shown that when the octupole terms are included in the potential, the inner binary can reach more extreme eccentricities as well as undergo orientation flips. It is known that pericenter precessions due to short-range effects, such as General Relativity and tidal and rotational distortions, can limit the growth of eccentricity and even suppress standard (quadrupolar) LK oscillations, but their effect on the octupole-level LK mechanism has not been fully explored. In this paper, we systematically study how these short-range forces affect the extreme orbital behaviour found in octupole LK cycles. In general, the influence of the octupole potential is confined to a range of initial mutual inclinations i tot centered around 90• (when the inner binary mass ratio is 1), with this range expanding with increasing octupole strength. We find that, while the short-range forces do not change the width and location of this "window of influence", they impose a strict upper limit on the maximum achievable eccentricity. This limiting eccentricity can be calculated analytically, and its value holds even for strong octupole potential and for the general case of three comparable masses. Short-range forces also affect orbital flips, progressively reducing the range of i tot within which flips are possible as the intensity of these forces increases.

We present numerical simulations of circumbinary accretion onto eccentric and circular binaries using the moving-mesh code AREPO. This is the first set of simulations to tackle the problem of binary accretion using a finite-volume scheme on a freely moving mesh, which allows for accurate measurements of accretion onto individual stars for arbitrary binary eccentricity. While accretion onto a circular binary shows bursts with period of ∼5 times the binary period P b , accretion onto an eccentric binary is predominantly modulated at the period ∼1P b . For an equal-mass circular binary, the accretion rates onto individual stars are quite similar to each other, following the same variable pattern in time. By contrast, for eccentric binaries, one of the stars can accrete at a rate 10-20 times larger than its companion. This "symmetry breaking" between the stars, however, alternates over timescales of order 200P b , and can be attributed to a slowly precessing, eccentric circumbinary disk. Over longer timescales, the net accretion rates onto individual stars are the same, reaching a quasi-steady state with the circumbinary disk. These results have important implications for the accretion behavior of binary T-Tauri stars and supermassive binary black holes.

We carry out 2D viscous hydrodynamics simulations of circumbinary disk (CBD) accretion using AREPO. We resolve the accretion flow from a large-scale CBD down to the streamers and disks around individual binary components. Extending our recent studies (Muñoz et al. 2019), we consider circular binaries with various mass ratios (0.1 ≤ q b ≤ 1) and study accretion from "infinite", steady-supply disks and from finite-sized, viscously spreading tori. For "infinite" disks, a global steady state can be reached, and the accretion variability has a dominant frequency ∼0.2Ω b for q b > 0.5 and Ω b for q b < 0.5, (Ω b is the binary angular frequency). We find that the accretion "eigenvalue" l 0 -the net angular momentum transfer from the disk to the binary per unit accreted mass -is always positive and falls in the range (0.65-0.85)a 2 b Ω b (with a b the binary separation), depending weakly on the mass ratio and viscosity. This leads to binary expansion when q b 0.3. Accretion from a finite torus can be separated into two phases: an initial transient phase, corresponding to the filling of the binary cavity, followed by a viscous pseudo-stationary phase, during which the torus viscously spreads and accretes onto the binary. In the viscous phase, the net torque on the binary per unit accreted mass is close to l 0 , the value derived for "infinite" disks. We conclude that similar-mass binaries accreting from CBDs gain angular momentum and expand over long time scales. This result significantly impacts the coalescence of supermassive binary black holes and newly formed binary stars. We offer a word of caution against conclusions drawn from simulations of transient accretion onto empty circumbinary cavities.

A better understanding of in-game competition demands potentially improves coaching strategy and quality. However, there is very limited information about game patterns in padel, a very modern racket sport born in the 70'. The purpose of this study was therefore to quantify and classify game dynamics during the match in professional padel players through a multivariate decision tree approach including technical, spatial and effectiveness indicators. The results determined three main game styles strongly defined by the court zone (net, middle and baseline). Additionally, particular technical, spatial and effectiveness indicators were identified in each zone. In net and middle areas (offence) stood the use of volleys and over-head strokes on the center lane to both keep a positional advantage and solve the point. Conversely in the baseline (defense), the use of corner side walls and the domain of lobs showed to be relevant. It is also remarkable the high rate of backhand groundstrokes, involving over four out of ten actions. This information may have relevant implications for coaches working in padel by providing a novel hierarchically organization of game dynamics, which helps in designing training and conditioning programs close to real competitive situations.

The presence of a planetary system can shield a planetesimal disk from the secular gravitational perturbations due to distant outer massive objects (planets or stellar companions). As the host star evolves off the main sequence to become a white dwarf, these planets can be engulfed during the giant phase, triggering secular instabilities and leading to the tidal disruptions of small rocky bodies. These disrupted bodies can feed the white dwarfs with rocky material and possibly explain the highmetallicity material in their atmospheres. We illustrate how this mechanism can operate when the gravitational perturbations are due to the KL mechanism from a stellar binary companion, a process that is activated only after the planet has been removed/engulfed. We show that this mechanism can explain the observed accretion rates if: (1) the planetary engulfment happens fast compared to the secular timescale, which is generally the case for wide binaries (> 100 AU) and planetary engulfment during the Asymptotic Giant Branch ; (2) the planetesimal disk has a total mass of ∼ 10 −4 −10 −2 M ⊕ . We show that this new mechanism can provide a steady supply of material throughout the entire life of the white dwarfs for all cooling ages and can account for a large fraction (up to nearly half) of the observed polluted WDs.

We report the first detections of circularly polarized emission at submillimeter wavelengths from the compact radio source and supermassive black hole candidate Sgr A* at a level of 1.2 ± 0.3% at 1.3 mm wavelength (230 GHz) and 1.6 ± 0.3% at 860 µm (345 GHz) with the same handedness, left circular polarization (LCP), as observed at all lower frequencies (1.4-15 GHz). The observations, taken with the Submillimeter Array in multiple epochs, also show simultaneous linear polarization (LP) at both wavelengths of about 6%. These properties differ sharply from those at wavelengths longer than 1 cm (frequencies below 30 GHz), where weak circular polarization (CP) (∼ 0.5%) dominates over LP, which is not detected at similar fractional limits. We describe an extensive set of tests to ensure the accuracy of our measurements. We find no circular polarization (CP) in any other source, including the bright quasar 1924-292, which traces the same path on the sky as Sgr A* and therefore should be subject to identical systematic errors originating in the instrument frame. Since a relativistic synchrotron plasma is expected to produce little CP, the observed CP is probably generated close to the event horizon by the Faraday conversion process. We use a simple approximation to show that the phase shift associated with Faraday conversion can be nearly independent of frequency, a sufficient condition to make the handedness of CP independent of frequency. Because the size of the τ = 1 surface changes by more than an order of magnitude between 1.4 and 345 GHz, the magnetic field must be coherent over such scales to consistently produce LCP. To improve our understanding of the environment of SgrA* critical future measurements include determining whether the Faraday rotation deviates from a λ 2 dependence in wavelength and whether the circular and linear components of the flux density are correlated.

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