Multiple star systems in the Orion nebula

This is the author accepted manuscript. The final fersion is available from EDP Sciences via the DOI in this record.This work presents an interferometric study of the massive-binary fraction in the Orion Trapezium cluster with the recently comissioned GRAVITY instrument. We observed a total of 16 stars of mainly OB spectral type. We find three previously unknown companions for θ1 Ori B, θ2 Ori B, and θ2 Ori C. We determined a separation for the previously suspected companion of NU Ori. We confirm four companions for θ1 Ori A, θ1 Ori C, θ1 Ori D, and θ2 Ori A, all with substantially improved astrometry and photometric mass estimates. We refined the orbit of the eccentric high-mass binary θ1 Ori C and we are able to derive a new orbit for θ1 Ori D. We find a system mass of 21.7 M⊙ and a period of 53 days. Together with other previously detected companions seen in spectroscopy or direct imaging, eleven of the 16 high-mass stars are multiple systems. We obtain a total number of 22 companions with separations up to 600 AU. The companion fraction of the early B and O stars in our sample is about two, significantly higher than in earlier studies of mostly OB associations. The separation distribution hints toward a bimodality. Such a bimodality has been previously found in A stars, but rarely in OB binaries, which up to this point have been assumed to be mostly compact with a tail of wider companions. We also do not find a substantial population of equal-mass binaries. The observed distribution of mass ratios declines steeply with mass, and like the direct star counts, indicates that our companions follow a standard power law initial mass function. Again, this is in contrast to earlier findings of flat mass ratio distributions in OB associations. We excluded collision as a dominant formation mechanism but find no clear preference for core accretion or competitive accretion.Marie Skłodowska-Curie Grant AgreementFCT-PortugalERC Starting Gran

The optimal treatment of an infectious disease with two strains

This paper explores the optimal treatment of an infectious disease in a Susceptible-Infected-Susceptible model, where there are two strains of the disease and one strain is more infectious than the other. The strains are perfectly distinguishable, instantly diagnosed and equally costly in terms of social welfare. Treatment is equally costly and effective for both strains. Eradication is not possible, and there is no superinfection. In this model, we characterise two types of fixed points: coexistence equilibria, where both strains prevail, and boundary equilibria, where one strain is asymptotically eradicated and the other prevails at a positive level. We derive regimes of feasibility that determine which equilibria are feasible for which parameter combinations. Numerically, we show that optimal policy exhibits switch points over time, and that the paths to coexistence equilibria exhibit spirals, suggesting that coexistence equilibria are never the end points of optimal paths

Harvesting in an integrated general equilibrium model

Harvesting of prey biomass is analyzed in an integrated ecological-economic system whose submodels, a predator–prey ecosystem and a simple economy, are microfounded dynamic general equilibrium models. These submodels are interdependent because the ecosystem responds to harvesting—through the reactions of optimizing individual organisms—by changing the provision of public ecosystem services to consumers. General analytical results are derived regarding the impact of harvesting policies on short-run equilibria of both submodels, on population dynamics, and on stationary states of the integrated model. A key insight is that prey biomass carries a positive ecosystem price which needs to be added as a tax mark-up to the economic price of harvested biomass to attain allocative efficiency. Further information on the dynamics is gained by resorting to numerical analysis of the policy regimes of zero harvesting, laissez-faire harvesting and efficient harvesting. It “... is a matter of weighing costs and benefits of taking action, whether the action is the “inert” one of leaving resources alone in order to conserve them, or whether it involves exploiting a resource ... for so-called material ends”. Pearce (1976, p. 320) Copyright Springer Science+Business Media, Inc. 2007Predator, Prey, Biomass price, Harvesting, Q20, Q57,