This paper investigates integrality properties of perfect matching polytopes, focusing on box-total dual integrality and integer decomposition properties.We begin by characterizing the graphs whose perfect matching polytope is a slice of the nonnegative orthant, identifying these as the solid graphs introduced by de Carvalho et al. (2002) [17]. As a result, perfect matching polytopes of solid graphs admit a compact description. Moreover, we observe that 0,1 polytopes that are slices of the nonnegative orthant have the integer Carathéodory property. Thus, perfect matching polytopes of solid graphs have the integer Carathéodory property. This in particular unveils a new positive case of the generalized Berge-Fulkeron conjecture.We also establish that deciding the box-total dual integrality of a perfect matching polytope can be done in polynomial time. Additionally, we characterize the conditions under which perfect matching polytopes of two fundamental graph classes, namely near-bricks and bicritical graphs, are box-totally dual integral.
Characterizing the mechanisms and galaxy properties conducive to the escape of ionizing (LyC) emission is necessary to accurately model the Epoch of Reionization and identify the sources that powered it. Using Hubble Space Telescope data, the Ly α and Continuum Origins Survey (LaCOS) is the first program to obtain uniform, multiwavelength subkiloparsec imaging for a large sample (42) of galaxies observed in LyC and enable statistically robust studies between LyC and resolved galaxy properties. Here, we characterize the morphology and galaxy merger properties of LaCOS galaxies and investigate their connection with the escape fraction of LyC emission f esc LyC . We find strong anticorrelations between f esc LyC and size ( r 20 , r 50 , and r 80 ) measured in filters containing emission from star-forming regions, and with the asymmetry and clumpiness in F150LP, a filter tracing UV continuum and Ly α . We find that ≥48% of LaCOS galaxies, and ≥41% of LaCOS LyC-emitters are visually classified as galaxy mergers. Galaxies robustly identified as mergers in LaCOS are at advanced stages of interaction, close to coalescence. The f esc LyC properties of robust mergers and low-probability mergers cannot be differentiated statistically, and we only find significant difference between the two populations in terms of their sizes and LyC luminosity: robust mergers having larger values. We conclude that (i) f esc LyC tends to be larger in galaxies with a small number of compact, centrally located, UV-emitting star-forming regions, (ii) mergers at advanced stages of interaction represent a sizable fraction of LyC-emitting samples at z ∼ 0.3, and (iii) mergers can facilitate the escape of LyC photons from galaxies.
Context. The Solar System giant planets harbor a wide variety of moons. Among them, the largest moons have moon-to-planet mass ratios of the order of 10−4. Moons around exoplanets are plausibly similarly abundant, even though most of them are likely too small to be easily detectable with modern instruments. Moons are known to affect the long-term dynamics of the spin of their host planets; however, their influence on warm exoplanets (i.e. with moderately short periods of about 10 to 200 days), which undergo significant star–planet tidal dissipation, is still unclear. Aims. Here, we study the coupled dynamical evolution of exomoons and the spin dynamics of their host planets, focusing on warm exoplanets. Methods. Analytical criteria give the relevant dynamical regimes at play as a function of the system’s parameters. Possible evolution tracks mostly depend on the hierarchy of timescales between the star–planet and the moon-planet tidal dissipations. We illustrate the variety of possible trajectories using self-consistent numerical simulations. Results. We find two principal results: i) Due to star–planet tidal dissipation, a substantial fraction of warm exoplanets naturally evolve through a phase of instability for the moon’s orbit (the ‘Laplace plane’ instability). Many warm exoplanets may have lost their moon(s) through this process. ii) Surviving moons slowly migrate inwards due to the moon-planet tidal dissipation until they are disrupted below the Roche limit. During their last migration stage, moons – even small ones – eject planets from their tidal spin equilibrium. Planets can then converge back to this equilibrium or adopt a new one with a low or high obliquity. Additionally, before their disruption, massive exomoons (with moon-to-planet mass ratios of the order of 10−2) can maintain their planet in a long-lived high-obliquity state. Conclusions. The loss of moons through the Laplace plane instability may contribute to disfavor the detection of moons around close-in exoplanets. Moreover, moons (even those that have been lost) play a critical role in the final obliquities of warm exoplanets. Hence, the existence of exomoons poses a serious challenge in predicting the present-day obliquities of observed exoplanets.
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We present a study of low-temperature electric and thermal transport in RuO2, a metallic oxide which has attracted much recent attention. Careful scrutiny of electric resistivity reveals a quadratic temperature dependence below similar to 20 K undetected in previous studies of electronic transport in this material. The prefactor of this T2 resistivity, given the electronic specific heat, corresponds to what is expected by the Kadowaki-Woods scaling. The variation of its amplitude across four different samples is negligible despite an eightfold variation of residual resistivity. There is also a T 5 resistivity due to scattering by phonons. By measuring thermal conductivity kappa at zero field and at 12 T, we separate its electronic and phononic components and find that the former respects the Wiedemann-Franz law at zero temperature and deviates downward at finite temperature. The latter corresponds to a threefold discrepancy between the prefactors of the two (thermal and electric) T-square resistivities. Our results, establishing RuO2 as a weakly correlated Fermi liquid, provide input for the ongoing theoretical attempt to give a quantitative account of electron-electron scattering in metallic oxides starting from first principles.
