Post-Newtonian Models of Binary Neutron Stars

Using an energy variational method, we calculate quasi-equilibrium configurations of binary neutron stars modeled as compressible triaxial ellipsoids obeying a polytropic equation of state. Our energy functional includes terms both for the internal hydrodynamics of the stars and for the external orbital motion. We add the leading post-Newtonian (PN) corrections to the internal and gravitational energies of the stars, and adopt hybrid orbital terms which are fully relativistic in the test-mass limit and always accurate to PN order. The total energy functional is varied to find quasi-equilibrium sequences for both corotating and irrotational binaries in circular orbits. We examine how the orbital frequency at the innermost stable circular orbit depends on the polytropic index n and the compactness parameter GM/Rc^2. We find that, for a given GM/Rc^2, the innermost stable circular orbit along an irrotational sequence is about 17% larger than the innermost secularly stable circular orbit along the corotating sequence when n=0.5, and 20% larger when n=1. We also examine the dependence of the maximum neutron star mass on the orbital frequency and find that, if PN tidal effects can be neglected, the maximum equilibrium mass increases as the orbital separation decreases.Comment: 53 pages, LaTex, 9 figures as 10 postscript files, accepted by Phys. Rev. D, replaced version contains updated reference

Post-Newtonian SPH calculations of binary neutron star coalescence. I. Method and first results

We present the first results from our Post-Newtonian (PN) Smoothed Particle Hydrodynamics (SPH) code, which has been used to study the coalescence of binary neutron star (NS) systems. The Lagrangian particle-based code incorporates consistently all lowest-order (1PN) relativistic effects, as well as gravitational radiation reaction, the lowest-order dissipative term in general relativity. We test our code on sequences of single NS models of varying compactness, and we discuss ways to make PN simulations more relevant to realistic NS models. We also present a PN SPH relaxation procedure for constructing equilibrium models of synchronized binaries, and we use these equilibrium models as initial conditions for our dynamical calculations of binary coalescence. Though unphysical, since tidal synchronization is not expected in NS binaries, these initial conditions allow us to compare our PN work with previous Newtonian results. We compare calculations with and without 1PN effects, for NS with stiff equations of state, modeled as polytropes with $\Gamma=3$. We find that 1PN effects can play a major role in the coalescence, accelerating the final inspiral and causing a significant misalignment in the binary just prior to final merging. In addition, the character of the gravitational wave signal is altered dramatically, showing strong modulation of the exponentially decaying waveform near the end of the merger. We also discuss briefly the implications of our results for models of gamma-ray bursts at cosmological distances.Comment: RevTeX, 37 pages, 17 figures, to appear in Phys. Rev. D, minor corrections onl

Do compensation plans with performance targets provide better incentives?

YesGuided by academic literature, industry practice and policy recommendations, we analyze a wide range of option and restricted stock plans with exercise and vesting conditions that may be contingent on stock price performance. To assess the effectiveness of these plans at attracting and providing incentives to executives, we create compensation plans with fixed firm cost and executive valuation and calculate their expected total lifetime incentives. We show that performance vesting targets provide the least cost effective incentives, performance exercise targets provide the largest risk incentives, option plans are generally superior to restricted stock plans, and calendar vesting is only efficient up to a maximum of three years. Performance exercise targets can increase the expected total lifetime incentives provided by compensation plans, but in general, standard options with short vesting periods provide the most cost effective pay-for-performance incentives

Why do banks promise to pay par on demand?

We survey the theories of why banks promise to pay par on demand and examine evidence about the conditions under which banks have promised to pay the par value of deposits and banknotes on demand when holding only fractional reserves. The theoretical literature can be broadly divided into four strands: liquidity provision, asymmetric information, legal restrictions, and a medium of exchange. We assume that it is not zero cost to make a promise to redeem a liability at par value on demand. If so, then the conditions in the theories that result in par redemption are possible explanations of why banks promise to pay par on demand. If the explanation based on customers’ demand for liquidity is correct, payment of deposits at par will be promised when banks hold assets that are illiquid in the short run. If the asymmetric-information explanation based on the difficulty of valuing assets is correct, the marketability of banks’ assets determines whether banks promise to pay par. If the legal restrictions explanation of par redemption is correct, banks will not promise to pay par if they are not required to do so. If the transaction explanation is correct, banks will promise to pay par value only if the deposits are used in transactions. After the survey of the theoretical literature, we examine the history of banking in several countries in different eras: fourth-century Athens, medieval Italy, Japan, and free banking and money market mutual funds in the United States. We find that all of the theories can explain some of the observed banking arrangements, and none explain all of them

The Dynamical Evolution of Black Hole-Neutron Star Binaries in General Relativity: Simulations of Tidal Disruption

We calculate the first dynamical evolutions of merging black hole-neutron star binaries that construct the combined black hole-neutron star spacetime in a general relativistic framework. We treat the metric in the conformal flatness approximation, and assume that the black hole mass is sufficiently large compared to that of the neutron star so that the black hole remains fixed in space. Using a spheroidal spectral methods solver, we solve the resulting field equations for a neutron star orbiting a Schwarzschild black hole. The matter is evolved using a relativistic, Lagrangian, smoothed particle hydrodynamics (SPH) treatment. We take as our initial data recent quasiequilibrium models for synchronized neutron star polytropes generated as solutions of the conformal thin-sandwich (CTS) decomposition of the Einstein field equations. We are able to construct from these models relaxed SPH configurations whose profiles show good agreement with CTS solutions. Our adiabatic evolution calculations for neutron stars with low compactness show that mass transfer, when it begins while the neutron star orbit is still outside the innermost stable circular orbit, is more unstable than is typically predicted by analytical formalisms. This dynamical mass loss is found to be the driving force in determining the subsequent evolution of the binary orbit and the neutron star, which typically disrupts completely within a few orbital periods. The majority of the mass transferred onto the black hole is accreted promptly; a significant fraction (~30%) of the mass is shed outward as well, some of which will become gravitationally unbound and ejected completely from the system. The remaining portion forms an accretion disk around the black hole, and could provide the energy source for short-duration gamma ray bursts.Comment: 32 pages, 16 figures, 2 tables, RevTeX, accepted by PR

Stock Options and Chief Executive Officer Compensation

Although stock options are commonly observed in chief executive o±cer (CEO) compensation contracts, there is theoretical controversy about whether stock options are part of the optimal contract. Using a sample of Fortune 500 companies, we solve an agency model calibrated to the company-specific data and we find that stock options are almost always part of the optimal contract. This result is robust to alternative assumptions about the level of CEO risk-aversion and the disutility associated with their effort. In a supplementary analysis, we solve for the optimal contract when there are no restrictions on the contract space. We find that the optimal contract (which is characterized as a state-contingent payoff to the CEO) typically has option-like features over the most probable range of outcomes

Integrated monitoring of mola mola behaviour in space and time

Over the last decade, ocean sunfish movements have been monitored worldwide using various satellite tracking methods. This study reports the near-real time monitoring of finescale (< 10 m) behaviour of sunfish. The study was conducted in southern Portugal in May 2014 and involved satellite tags and underwater and surface robotic vehicles to measure both the movements and the contextual environment of the fish. A total of four individuals were tracked using custom-made GPS satellite tags providing geolocation estimates of fine-scale resolution. These accurate positions further informed sunfish areas of restricted search (ARS), which were directly correlated to steep thermal frontal zones. Simultaneously, and for two different occasions, an Autonomous Underwater Vehicle (AUV) videorecorded the path of the tracked fish and detected buoyant particles in the water column. Importantly, the densities of these particles were also directly correlated to steep thermal gradients. Thus, both sunfish foraging behaviour (ARS) and possibly prey densities, were found to be influenced by analogous environmental conditions. In addition, the dynamic structure of the water transited by the tracked individuals was described by a Lagrangian modelling approach. The model informed the distribution of zooplankton in the region, both horizontally and in the water column, and the resultant simulated densities positively correlated with sunfish ARS behaviour estimator (r(s) = 0.184, p < 0.001). The model also revealed that tracked fish opportunistically displace with respect to subsurface current flow. Thus, we show how physical forcing and current structure provide a rationale for a predator's finescale behaviour observed over a two weeks in May 2014

Relationship between self-reported dietary intake and physical activity levels among adolescents: The HELENA study

Background Evidence suggests possible synergetic effects of multiple lifestyle behaviors on health risks like obesity and other health outcomes. Therefore it is important to investigate associations between dietary and physical activity behavior, the two most important lifestyle behaviors influencing our energy balance and body composition. The objective of the present study is to describe the relationship between energy, nutrient and food intake and the physical activity level among a large group of European adolescents. Methods The study comprised a total of 2176 adolescents (46.2% male) from ten European cities participating in the HELENA (Healthy Lifestyle in Europe by Nutrition in Adolescence) study. Dietary intake and physical activity were assessed using validated 24-h dietary recalls and self-reported questionnaires respectively. Analyses of covariance (ANCOVA) were used to compare the energy and nutrient intake and the food consumption between groups of adolescents with different physical activity levels (1st to 3rd tertile). Results In both sexes no differences were found in energy intake between the levels of physical activity. The most active males showed a higher intake of polysaccharides, protein, water and vitamin C and a lower intake of saccharides compared to less active males. Females with the highest physical activity level consumed more polysaccharides compared to their least active peers. Male and female adolescents with the highest physical activity levels, consumed more fruit and milk products and less cheese compared to the least active adolescents. The most active males showed higher intakes of vegetables and meat, fish, eggs, meat substitutes and vegetarian products compared to the least active ones. The least active males reported the highest consumption of grain products and potatoes. Within the female group, significantly lower intakes of bread and cereal products and spreads were found for those reporting to spend most time in moderate to vigorous physical activity. The consumption of foods from the remaining food groups, did not differ between the physical activity levels in both sexes. Conclusion It can be concluded that dietary habits diverge between adolescents with different self-reported physical activity levels. For some food groups a difference in intake could be found, which were reflected in differences in some nutrient intakes. It can also be concluded that physically active adolescents are not always inclined to eat healthier diets than their less active peers.The HELENA study took place with the financial support of the European Community Sixth RTD Framework Programme (Contract FOOD-CT: 2005-007034). This work was also partially supported by the European Union, in the framework of the Public Health Programme (ALPHA project, Ref: 2006120), the Swedish Council for Working Life and Social Research (FAS), the Spanish Ministry of Education (EX-2007-1124, and EX-2008-0641), and the Spanish Ministry of Health, Maternal, Child Health and Development Network (number RD08/0072) (JPRL, LAM)