Extreme isolation of WN3/O3 stars and implications for their evolutionary origin as the elusive stripped binaries

Recent surveys of the Magellanic Clouds have revealed a subtype of Wolf-Rayet (WR) star with peculiar properties. WN3/O3 spectra exhibit both WR-like emission and O3 V-like absorption - but at lower luminosity than O3 V or WN stars. We examine the projected spatial distribution of WN3/O3 stars in the LMC as compared to O-type stars. Surprisingly, WN3/O3 stars are among the most isolated of all classes of massive stars; they have a distribution similar to red supergiants dominated by initial masses of 10-15 $M_{\odot}$, and are far more dispersed than classical WR stars or luminous blue variables (LBVs). Their lack of association with clusters of O-type stars suggests strongly that WN3/O3 stars are not the descendants of single massive stars (30 $M_{\odot}$ or above). Instead, they are likely products of interacting binaries at lower initial mass (10-18 $M_{\odot}$). Comparison with binary models suggests a probable origin with primaries in this mass range that were stripped of their H envelopes through non-conservative mass transfer by a low-mass secondary. We show that model spectra and positions on the Hertzsprung-Russell diagram for binary stripped stars are consistent with WN3/O3 stars. Monitoring radial velocities with high-resolution spectra can test for low-mass companions or runaway velocities. With lower initial mass and environments that avoid very massive stars, the WN3/O3 stars fit expectations for progenitors of Type Ib and possibly Type Ibn supernovae.Comment: Accepted for publication in MNRA

Sensitivity analysis of hybrid systems with state jumps with application to trajectory tracking

This paper addresses the sensitivity analysis for hybrid systems with discontinuous (jumping) state trajectories. We consider state-triggered jumps in the state evolution, potentially accompanied by mode switching in the control vector field as well. For a given trajectory with state jumps, we show how to construct an approximation of a nearby perturbed trajectory corresponding to a small variation of the initial condition and input. A major complication in the construction of such an approximation is that, in general, the jump times corresponding to a nearby perturbed trajectory are not equal to those of the nominal one. The main contribution of this work is the development of a notion of error to clarify in which sense the approximate trajectory is, at each instant of time, a firstorder approximation of the perturbed trajectory. This notion of error naturally finds application in the (local) tracking problem of a time-varying reference trajectory of a hybrid system. To illustrate the possible use of this new error definition in the context of trajectory tracking, we outline how the standard linear trajectory tracking control for nonlinear systems -based on linear quadratic regulator (LQR) theory to compute the optimal feedback gain- could be generalized for hybrid systems

On the Effects of Subvirial Initial Conditions and the Birth Temperature of R136

We investigate the effect of different initial virial temperatures, Q, on the dynamics of star clusters. We find that the virial temperature has a strong effect on many aspects of the resulting system, including among others: the fraction of bodies escaping from the system, the depth of the collapse of the system, and the strength of the mass segregation. These differences deem the practice of using "cold" initial conditions no longer a simple choice of convenience. The choice of initial virial temperature must be carefully considered as its impact on the remainder of the simulation can be profound. We discuss the pitfalls and aim to describe the general behavior of the collapse and the resultant system as a function of the virial temperature so that a well reasoned choice of initial virial temperature can be made. We make a correction to the previous theoretical estimate for the minimum radius, $R_{min}$, of the cluster at the deepest moment of collapse to include a Q dependency, $R_{min}\approx Q + N^{(-1/3)}$, where $N$ is the number of particles. We use our numerical results to infer more about the initial conditions of the young cluster R136. Based on our analysis, we find that R136 was likely formed with a rather cool, but not cold, initial virial temperature ($Q\approx 0.13$). Using the same analysis method, we examined 15 other young clusters and found the most common initial virial temperature to be between 0.18 and 0.25.Comment: Accepted for publication in MNRA

Governance Issues for Health Insurance Exchanges

Outlines considerations for states in deciding how to structure a health insurance exchange, as well as issues of funding sources, operational flexibility, political independence and accountability, management structure, and sub-state dimensions