Catching a planet: A tidal capture origin for the exomoon candidate Kepler 1625b I

The (yet-to-be confirmed) discovery of a Neptune-sized moon around the ~3.2 Jupiter-mass planet in Kepler 1625 puts interesting constraints on the formation of the system. In particular, the relatively wide orbit of the moon around the planet, at ~40 planetary radii, is hard to reconcile with planet formation theories. We demonstrate that the observed characteristics of the system can be explained from the tidal capture of a secondary planet in the young system. After a quick phase of tidal circularization, the lunar orbit, initially much tighter than 40 planetary radii, subsequently gradually widened due to tidal synchronization of the spin of the planet with the orbit, resulting in a synchronous planet-moon system. Interestingly, in our scenario the captured object was originally a Neptune-like planet, turned into a moon by its capture.Comment: Accepted for publication in ApJL. 7 pages, 5 figure

On the Balancedness of M-Sequencing Games

This paper studies m-sequencing games that arise from sequencing situations with m parallel and identical machines. These m-sequencing games, which involve n players, give rise to m-machine games, which involve m players. Here, n corresponds to the number of jobs in an m-sequencing situation, and m corresponds to the number of machines in the same m-sequencing situation. We prove that an m-sequening game is balanced if and only if the corresponding m-machine game is balanced. Furthermore, it is shown that m-sequencing games are balanced ifm 2 f1;2g. Finally, ifm 3, balancedness is established for two special classes of m-sequencing games.cooperative games;sequencing situations

Balancedness of Permutation Games and Envy-Free Allocations in Indivisible Good Economies

We present a simple proof of the balancedness of permutation games. In the proof we use the existence of envy-free allocations in economies with indivisible objects, quasi-linear utility functions, and an amount of money.Permutation Games;Balancedness;Envy-free Allocations

On the Convexity of Precedence Sequencing Games

In this paper we study a class of cooperative sequencing games that arise from one-machine sequencing situations in which chain precedence relations are imposed on the jobs.It is shown that these sequencing games are convex.cooperative games;sequencing games

A triple origin for the lack of tight coplanar circumbinary planets around short-period binaries

Transiting circumbinary planets are more easily detected around short-period than long-period binaries, but none have yet been observed by {\it Kepler} orbiting binaries with periods shorter than seven days. In triple systems, secular Kozai-Lidov cycles and tidal friction (KLCTF) have been shown to reduce the inner orbital period from $\sim 10^4$ to a few days. Indeed, the majority of short-period binaries are observed to possess a third stellar companion. Using secular evolution analysis and population synthesis, we show that KLCTF makes it unlikely for circumbinary transiting planets to exist around short-period binaries. We find the following outcomes. (1) Sufficiently massive planets in tight and/or coplanar orbits around the inner binary can quench the KL evolution because they induce precession in the inner binary. The KLCTF process does not take place, preventing the formation of a short-period binary. (2) Secular evolution is not quenched and it drives the planetary orbit into a high eccentricity, giving rise to an unstable configuration, in which the planet is most likely ejected from the system. (3) Secular evolution is not quenched but the planet survives the KLCTF evolution. Its orbit is likely to be much wider than the currently observed inner binary orbit, and is likely to be eccentric and inclined with respect to the inner binary. These outcomes lead to two main conclusions: (1) it is unlikely to find a massive planet on a tight and coplanar orbit around a short-period binary, and (2) the properties of circumbinary planets in short-period binaries are constrained by secular evolution.Comment: Revised to match MNRAS publication. 24 pages, 22 figure

A Cooperative Approach to Queue Allocation of Indivisible Objects

We consider the allocation of a finite number of indivisible objects to the same number of agents according to an exogenously given queue.We assume that the agents collaborate in order to achieve an efficient outcome for society.We allow for side-payments and provide a method for obtaining stable outcomes.game theory;cooperative games;allocation