DISCUSSION: NEEDED RESEARCH WITH RESPECT TO ENERGY USE IN AGRICULTURAL PRODUCTION

Resource /Energy Economics and Policy,

AN ECONOMIC SIMULATION MODEL FOR ANALYZING NATURAL RESOURCE POLICY

Resource /Energy Economics and Policy,

Can the QCD Effective Charge Be Symmetrical in the Euclidean and the Minkowskian Regions?

We study a possible symmetrical behavior of the effective charges defined in the Euclidean and Minkowskian regions and prove that such symmetry is inconsistent with the causality principle.Comment: 5 pages, REVTe

GRMHD simulations of prompt-collapse neutron star mergers: the absence of jets

Inspiraling and merging binary neutron stars are not only important source of gravitational waves, but also promising candidates for coincident electromagnetic counterparts. These systems are thought to be progenitors of short gamma-ray bursts (sGRBs). We have shown previously that binary neutron star mergers that undergo {\it delayed} collapse to a black hole surrounded by a {\it weighty} magnetized accretion disk can drive magnetically-powered jets. We now perform magnetohydrodynamic simulations in full general relativity of binary neutron stars mergers that undergo {\it prompt} collapse to explore the possibility of jet formation from black hole-{\it light} accretion disk remnants. We find that after $t-t_{\rm BH}\sim 26(M_{\rm NS}/1.8M_\odot)$ms [$M_{\rm NS}$ is the ADM mass] following prompt black hole formation, there is no evidence of mass outflow or magnetic field collimation. The rapid formation of the black hole following merger prevents magnetic energy from approaching force-free values above the magnetic poles, which is required for the launching of a jet by the usual Blandford--Znajek mechanism. Detection of gravitational waves in coincidence with sGRBs may provide constraints on the nuclear equation of state (EOS): the fate of an NSNS merger--delayed or prompt collapse, and hence the appearance or nonappearance of an sGRB--depends on a critical value of the total mass of the binary, and this value is sensitive to the EOS.Comment: 11 pages, 6 figures, matches published versio

Casimir Energies and Pressures for δ\delta-function Potentials

The Casimir energies and pressures for a massless scalar field associated with $\delta$-function potentials in 1+1 and 3+1 dimensions are calculated. For parallel plane surfaces, the results are finite, coincide with the pressures associated with Dirichlet planes in the limit of strong coupling, and for weak coupling do not possess a power-series expansion in 1+1 dimension. The relation between Casimir energies and Casimir pressures is clarified,and the former are shown to involve surface terms. The Casimir energy for a $\delta$-function spherical shell in 3+1 dimensions has an expression that reduces to the familiar result for a Dirichlet shell in the strong-coupling limit. However, the Casimir energy for finite coupling possesses a logarithmic divergence first appearing in third order in the weak-coupling expansion, which seems unremovable. The corresponding energies and pressures for a derivative of a $\delta$-function potential for the same spherical geometry generalizes the TM contributions of electrodynamics. Cancellation of divergences can occur between the TE ($\delta$-function) and TM (derivative of $\delta$-function) Casimir energies. These results clarify recent discussions in the literature.Comment: 16 pages, 1 eps figure, uses REVTeX

Jet launching from binary black hole-neutron star mergers: Dependence on black hole spin, binary mass ratio and magnetic field orientation

Black hole-neutron star (BHNS) mergers are one of the most promising targets for multimessenger astronomy. Using general relativistic magnetohydrodynamic simulations of BHNS undergoing merger we showed that a magnetically--driven jet can be launched by the remnant if the NS is endowed with a dipole B field extending from the interior into the exterior as in a radio pulsar. These self-consistent studies considered a BHNS system with mass ratio $q=3:1$, BH spin $a/M_{BH}=0.75$ aligned with the total orbital angular momentum (OAM), and a NS that is irrotational, threaded by an aligned B field, and modeled by an $\Gamma$--law equation of state with $\Gamma=2$. Here, as a crucial step in establishing BHNS systems as viable progenitors of central engines that power short gamma--ray bursts (sGRBs) and thereby solidify their role as multimessenger sources, we survey different BHNS configurations that differ in BH spin ($a/M_{BH} =-0.5,\,0,\,0.5,\,0.75$), in the mass ratio ($q=3:1$ and $q=5:1$), and in the orientation of the B field (aligned and tilted by $90^\circ$ with respect to the OAM). We find that by $\Delta t\sim 3500M-4000M \sim 88(M_{NS}/1.4M_\odot){\rm ms}-100(M_{NS}/1.4M_\odot)\rm ms$ after the peak gravitational wave signal a jet is launched in the cases where the initial BH spin is $a/M_{BH}= 0.5$ or $0.75$. The lifetime of the jets[$\Delta t\sim 0.5(M_{NS}/1.4M_\odot){\rm s-0.7}(M_{NS}/1.4M_\odot)\rm s$] and their Poynting luminosities [$L_{jet}\sim 10^{51\pm 1}\rm erg/s$] are consistent with sGRBs, as well as with the Blandford--Znajek mechanism. By the time we terminate our simulations, we do not observe either an outflow or a large-scale B field collimation in the other configurations we simulate. These results suggest that future multimessenger detections from BHNSs are more likely produced by binaries with highly spinning BH companions and small tilt-angle B fields.Comment: 17 pages, 14 figures. Added references, matches published versio

Magnetic Braking and Damping of Differential Rotation in Massive Stars

Fragmentation of highly differentially rotating massive stars that undergo collapse has been suggested as a possible channel for binary black hole formation. Such a scenario could explain the formation of the new population of massive black holes detected by the LIGO/VIRGO gravitational wave laser interferometers. We probe that scenario by performing general relativistic magnetohydrodynamic simulations of differentially rotating massive stars supported by thermal radiation pressure plus a gas pressure perturbation. The stars are initially threaded by a dynamically weak, poloidal magnetic field confined to the stellar interior. We find that magnetic braking and turbulent viscous damping via magnetic winding and the magnetorotational instability in the bulk of the star redistribute angular momentum, damp differential rotation and induce the formation of a massive and nearly uniformly rotating inner core surrounded by a Keplerian envelope. The core + disk configuration evolves on a secular timescale and remains in quasi-stationary equilibrium until the termination of our simulations. Our results suggest that the high degree of differential rotation required for $m=2$ seed density perturbations to trigger gas fragmentation and binary black hole formation is likely to be suppressed during the normal lifetime of the star prior to evolving to the point of dynamical instability to collapse. Other cataclysmic events, such as stellar mergers leading to collapse, may therefore be necessary to reestablish sufficient differential rotation and density perturbations to drive nonaxisymmetric modes leading to binary black hole formation.Comment: 11 pages, 5 figures. Minor changes, matches published versio

Relativistic Coulomb Resummation in QCD

A relativistic Coulomb-like resummation factor in QCD is suggested, based on the solution of the quasipotential equation.Comment: 4 pages, 2 eps figures, REVTe

Simulating the Magnetorotational Collapse of Supermassive Stars: Incorporating Gas Pressure Perturbations and Different Rotation Profiles

Collapsing supermassive stars (SMSs) with masses $M \gtrsim 10^{4-6}M_\odot$ have long been speculated to be the seeds that can grow and become supermassive black holes (SMBHs). We previously performed GRMHD simulations of marginally stable magnetized $\Gamma = 4/3$ polytropes uniformly rotating at the mass-shedding limit to model the direct collapse of SMSs. These configurations are supported entirely by thermal radiation pressure and model SMSs with $M \gtrsim 10^{6}M_\odot$. We found that around $90\%$ of the initial stellar mass forms a spinning black hole (BH) surrounded by a massive, hot, magnetized torus, which eventually launches an incipient jet. Here we perform GRMHD simulations of $\Gamma \gtrsim 4/3$, polytropes to account for the perturbative role of gas pressure in SMSs with $M \lesssim 10^{6}M_\odot$. We also consider different initial stellar rotation profiles. The stars are initially seeded with a dynamically weak dipole magnetic field that is either confined to the stellar interior or extended from its interior into the stellar exterior. We find that the mass of the BH remnant is $90\%-99\%$ of the initial stellar mass, depending sharply on $\Gamma -4/3$ as well as on the initial stellar rotation profile. After $t\sim 250-550M\approx 1-2\times 10^3(M/10^6M_\odot)$s following the BH formation, a jet is launched and it lasts for $\sim 10^4-10^5(M/10^6M_\odot)$s, consistent with the duration of long gamma-ray bursts. Our results suggest that the Blandford-Znajek mechanism powers the jet. They are also in agreement with our proposed universal model that estimates accretion rates and luminosities that characterize magnetized BH-disk remnant systems that launch a jet. This model helps explain why the outgoing luminosities for vastly different BH-disk formation scenarios all reside within a narrow range ($\sim 10^{52 \pm 1} \rm erg/s$), roughly independent of $M$.Comment: 16 pages, 7 figures. Added references, matches published versio