Period Ratio Sculpting near Second-order Mean-motion Resonances

Second-order mean-motion resonances lead to an interesting phenomenon in the sculpting of the period-ratio distribution, due to their shape and width in period-ratio/eccentricity space. As the osculating periods librate in resonance, the time-averaged period ratio approaches the exact commensurability. The width of second-order resonances increases with increasing eccentricity, and thus more eccentric systems have a stronger peak at commensurability when averaged over sufficient time. The libration period is short enough that this time-averaging behavior is expected to appear on the timescale of the Kepler mission. Using N-body integrations of simulated planet pairs near the 5:3 and 3:1 mean-motion resonances, we investigate the eccentricity distribution consistent with the planet pairs observed by Kepler. This analysis, an approach independent from previous studies, shows no statistically significant peak at the 3:1 resonance and a small peak at the 5:3 resonance, placing an upper limit on the Rayleigh scale parameter, σ, of the eccentricity of the observed Kepler planets at σ = 0.245 (3:1) and σ = 0.095 (5:3) at 95% confidence, consistent with previous results from other methods.

Dips and eclipses in the X-ray binary Swift J1858.6–0814 observed with NICER

We present the discovery of eclipses in the X-ray light curves of the X-ray binary Swift J1858.6–0814. From these, we find an orbital period of $P=76841.3_{-1.4}^{+1.3}$ s (≈21.3 hours) and an eclipse duration of $t_{\rm ec}=4098_{-18}^{+17}$ s (≈1.14 hours). We also find several absorption dips during the pre-eclipse phase. From the eclipse duration to orbital period ratio, the inclination of the binary orbit is constrained to i > 70○. The most likely range for the companion mass suggests that the inclination is likely to be closer to this value than 90○. The eclipses are also consistent with earlier data, in which strong variability (‘flares’) and the long orbital period prevent clear detection of the period or eclipses. We also find that the bright flares occurred preferentially in the post-eclipse phase of the orbit, likely due to increased thickness at the disc-accretion stream interface preventing flares being visible during the pre-eclipse phase. This supports the notion that variable obscuration is responsible for the unusually strong variability in Swift J1858.6–0814.

Exploring the Origin and Evolution of the Kepler 36 System

We examine the origins of the Kepler 36 planetary system, which features two very different planets: Kepler 36b, ($\rm \rho = 7.46$ $\rm g$ $\rm cm^{-3}$) and Kepler 36c ($\rm \rho = 0.89$ $\rm g$ $\rm cm^{-3}$). The planets lie extremely close to one another, separated by just 0.01 AU, and they orbit just a tenth of an AU from the host star. In our origin scenario, Kepler 36b starts with far less mass than Kepler 36c, a gaseous giant planet that forms outside the ice line and quickly migrates inward, capturing its neighbour into its 2:1 mean-motion resonance while continuing to move inward through a swarm of planetesimals and protoplanets. Subsequent collisions with these smaller bodies knock Kepler 36b out of resonance and raise its mass and density (via self-compression). We find that our scenario can yield planets whose period ratio matches that of Kepler 36b and c, although these successes are rare, occurring in just 1.2 per cent of cases. However, since systems like Kepler 36 are themselves rare, this is not necessarily a drawback.

Can Healthy Checkout Counters Improve Food Purchases? Two Real-Life Experiments in Dutch Supermarkets

Most snacks displayed at supermarket checkouts do not contribute to a healthy diet. We investigated the effects of introducing healthier snack alternatives at checkouts in supermarkets on purchasing behavior. In Study 1, we investigated the effect of completely substituting less healthy with healthier snacks (one supermarket). In Study 2, we investigated the effect of placing and discounting healthier snacks while the less healthy snacks remain in place (two supermarkets). In both studies, the number of purchased snacks (per 1000 customers) was used as the outcome variable. Results for Study 1 showed that the absolute number of purchased checkout snacks was 2.4 times lower (95% confidence interval (CI): 1.9–2.7) when healthier snacks instead of less healthy snacks were placed at the supermarket checkouts. Results for Study 2 showed that when additional healthier snacks were placed near the checkouts, the absolute number of healthier purchased snacks increased by a factor of 2.1 (95% CI: 1.3–3.3). When additional healthier snacks were placed near the checkouts and discounted, the absolute number of healthier purchased snacks increased by a factor of 2.7 (95% CI: 2.0–3.6), although this was not statistically significant higher than placement only (ratio: 1.1, 95% CI: 0.7–1.9). Purchases of less healthy snacks did not decline, and even slightly increased, during the intervention period (ratio: 1.3, 95% CI: 1.1–1.5). If supermarkets want to promote healthier snack purchases, additional healthier products can be positioned near the checkouts. However, this does not discourages the purchase of less healthy snacks. Therefore, to discourage unhealthy snack purchases at supermarket checkouts, a total substitution of less healthy snacks with healthier alternatives is most effective.

Characteristic of Free-rolling Motion of Twodimensional Rectangular Body in the Regular Wave

his study investigated the characteristics of rolling motion of rectangular body for regular waves with a range of wave periods that are equal to and longer than its natural roll period. Using the volume of fluid (VOF) method based on the finite volume method with standard k-ε turbulence model, twodimensional (2D) incompressible viscous two-phase flow is simulated in a wave tank with the rectangular body. The present study introduces a wave period ratio (Tr=TW/TN) of an incident wave period (TW) to the roll natural period (TN) of body. The wide range of 1≤ Tr ≤2.5 is considered in this study. In the wave periods considered in this study, the roll motion shows two distinct patterns. One is the single oscillatory motion which appears in the period ratio of 1≤ Tr ≤1.7. The other is the double oscillatory motion in 1.8≤ Tr ≤2.5. In these two regimes, flow and the roll motion of the rectangular body, which are induced by the fluid flow-structure interaction for various wave periods, are carefully investigated to reveal the mechanism of two roll modes.

Transit timing variation signature of planet migration: the case of K2-24

The convergent migration of two planets in a gaseous disc can lead to mean motion resonance (MMR) capture. In addition, pairs of planets in or near MMRs are known to produce strong transit timing variations (TTVs). In this paper, we study the impact of disc-induced migrations on the TTV signal of pairs of planets that enter a resonant configuration. We show that disc-induced migration creates a correlation between the amplitude and the period of the TTVs. We study the case of K2-24, a system of two planets whose period ratio indicates that they are in or near the 2:1 MMR, with non-zero eccentricities and large-amplitude TTVs. We show that a simple disc-induced migration cannot reproduce the observed TTVs. Moreover, we propose a formation scenario in which the capture in resonance during migration in a disc with strong eccentricity damping is followed by eccentricity excitation during the dispersal of the disc. This is assisted by a third planet whose presence has been suggested by radial velocity observations. This scenario accounts for the eccentricities of the two planets and their period ratio, and it accurately reproduces the amplitude and period of the TTVs. It allows for a unified view of the formation and evolution history of K2-24, from disc-induced migration to its currently observed properties.

Sub-Neptune formation: the view from resonant planets

ABSTRACT The orbital period ratios of neighbouring sub-Neptunes are distributed asymmetrically near first-order resonances. There are deficits of systems – ‘troughs’ in the period ratio histogram – just short of commensurability, and excesses – ‘peaks’ – just wide of it. We reproduce quantitatively the strongest peak-trough asymmetries, near the 3:2 and 2:1 resonances, using dissipative interactions between planets and their natal discs. Disc eccentricity damping captures bodies into resonance and clears the trough, and when combined with disc-driven convergent migration, draws planets initially wide of commensurability into the peak. The migration implied by the magnitude of the peak is modest; reductions in orbital period are ∼10 per cent, supporting the view that sub-Neptunes complete their formation more-or-less in situ. Once captured into resonance, sub-Neptunes of typical mass $\sim \,$5–15M⊕ stay captured (contrary to an earlier claim), as they are immune to the overstability that afflicts lower mass planets. Driving the limited, short-scale migration is a gas disc depleted in mass relative to a solar-composition disc by three to five orders of magnitude. Such gas-poor but not gas-empty environments are quantitatively consistent with sub-Neptune core formation by giant impacts (and not, e.g. pebble accretion). While disc-planet interactions at the close of the planet formation era adequately explain the 3:2 and 2:1 asymmetries at periods $\gtrsim \, $5–15 d, subsequent modification by stellar tides appears necessary at shorter periods, particularly for the 2:1.