Habitable Zone Lifetime of Exoplanets around Main Sequence Stars

Funding: Dean's Scholarship at the University of East Anglia.The potential habitability of newly discovered exoplanets is initially assessed by determining whether their orbits fall within the circumstellar habitable zone of their star. However, the habitable zone (HZ) is not static in time or space, and its boundaries migrate outward at a rate proportional to the increase in luminosity of a star undergoing stellar evolution, possibly including or excluding planets over the course of the star’s main sequence lifetime. We describe the time that a planet spends within the HZ as its ‘‘habitable zone lifetime.’’ The HZ lifetime of a planet has strong astrobiological implications and is especially important when considering the evolution of complex life, which is likely to require a longer residence time within the HZ. Here, we present results from a simple model built to investigate the evolution of the ‘‘classic’’ HZ over time, while also providing estimates for the evolution of stellar luminosity over time in order to develop a ‘‘hybrid’’ HZ model. These models return estimates for the HZ lifetimes of Earth and 7 confirmed HZ exoplanets and 27 unconfirmed Kepler candidates. The HZ lifetime for Earth ranges between 6.29 and 7.79 · 109 years (Gyr). The 7 exoplanets fall in a range between ∼1 and 54.72 Gyr, while the 27 Kepler candidate planets’ HZ lifetimes range between 0.43 and 18.8 Gyr. Our results show that exoplanet HD 85512b is no longer within the HZ, assuming it has an Earth analog atmosphere. The HZ lifetime should be considered in future models of planetary habitability as setting an upper limit on the lifetime of any potential exoplanetary biosphere, and also for identifying planets of high astrobiological potential for continued observational or modeling campaigns.Publisher PDFPeer reviewe

Reports on injurious insects

A short time since Prof. Curtiss informed us that Mr. Dana Reed, of Coon Rapids, had given him some beetles that were eating into the ears of corn, and from his description it was inferred that they were the common Indian Cetonia (Euphoria inda), which has in a few instances heretofore been reported as doing damage of this character. The beetles proved, as suspected, to be this species, and in view of the uncertainty as to the possibility of this species to do damage of this kind it seemed desirable to get as much data as possible and to make some tests of its ability to enter uninjured ears. The cases hitherto recorded where Euphoria inda has attacked corn, eating into the ears, may be summed up as follows, most of the information on the subject, so far as we have noticed, being contained in the first Report on the Insects of New York by Prof. J. A Lintner

Reports of entomological work

On the evening of the twenty-third of May many small dark brown moths were noticed flying about a clover field upon the College Farm. They were resting upon the blossoms and among the leaves and upon being disturbed would fly a few paces and then settle again. These moths proved upon examination to be Grapholitha intersinctana, Clemens, the parent forms of the Clover-Seed Caterpillar mentioned in the Entomologist’s report to the Commissioner of Agriculture in 1880. We had during the past winter received specimens of clover-seed which we suspected of being some of the states east of us in the last year or two, and the moths are remembered as occurring here in numbers some eight or ten years ago, but they were not at that time connected with any damage observed in clover fields

Moyal Quantum Mechanics: The Semiclassical Heisenberg Dynamics

The Moyal--Weyl description of quantum mechanics provides a comprehensive phase space representation of dynamics. The Weyl symbol image of the Heisenberg picture evolution operator is regular in $\hbar$. Its semiclassical expansion `coefficients,' acting on symbols that represent observables, are simple, globally defined differential operators constructed in terms of the classical flow. Two methods of constructing this expansion are discussed. The first introduces a cluster-graph expansion for the symbol of an exponentiated operator, which extends Groenewold's formula for the Weyl product of symbols. This Poisson bracket based cluster expansion determines the Jacobi equations for the semiclassical expansion of `quantum trajectories.' Their Green function solutions construct the regular $\hbar\downarrow0$ asymptotic series for the Heisenberg--Weyl evolution map. The second method directly substitutes such a series into the Moyal equation of motion and determines the $\hbar$ coefficients recursively. The Heisenberg--Weyl description of evolution involves no essential singularity in $\hbar$, no Hamilton--Jacobi equation to solve for the action, and no multiple trajectories, caustics or Maslov indices.Comment: 50, MANIT-94-0

Conformal anomaly of Wilson surface observables - a field theoretical computation

We make an exact field theoretical computation of the conformal anomaly for two-dimensional submanifold observables. By including a scalar field in the definition for the Wilson surface, as appropriate for a spontaneously broken A_1 theory, we get a conformal anomaly which is such that N times it is equal to the anomaly that was computed in hep-th/9901021 in the large N limit and which relied on the AdS-CFT correspondence. We also show how the spherical surface observable can be expressed as a conformal anomaly.Comment: 18 pages, V3: an `i' dropped in the Wilson surface, overall normalization and misprints corrected, V4: overall normalization factor corrected, references adde

Stochastic field theory for a Dirac particle propagating in gauge field disorder

Recent theoretical and numerical developments show analogies between quantum chromodynamics (QCD) and disordered systems in condensed matter physics. We study the spectral fluctuations of a Dirac particle propagating in a finite four dimensional box in the presence of gauge fields. We construct a model which combines Efetov's approach to disordered systems with the principles of chiral symmetry and QCD. To this end, the gauge fields are replaced with a stochastic white noise potential, the gauge field disorder. Effective supersymmetric non-linear sigma-models are obtained. Spontaneous breaking of supersymmetry is found. We rigorously derive the equivalent of the Thouless energy in QCD. Connections to other low-energy effective theories, in particular the Nambu-Jona-Lasinio model and chiral perturbation theory, are found.Comment: 4 pages, 1 figur

Dirac eigenvalues and eigenvectors at finite temperature

We investigate the eigenvalues and eigenvectors of the staggered Dirac operator in the vicinity of the chiral phase transition of quenched SU(3) lattice gauge theory. We consider both the global features of the spectrum and the local correlations. In the chirally symmetric phase, the local correlations in the bulk of the spectrum are still described by random matrix theory, and we investigate the dependence of the bulk Thouless energy on the simulation parameters. At and above the critical point, the properties of the low-lying Dirac eigenvalues depend on the $Z_3$-phase of the Polyakov loop. In the real phase, they are no longer described by chiral random matrix theory. We also investigate the localization properties of the Dirac eigenvectors in the different $Z_3$-phases.Comment: Lattice 2000 (Finite Temperature), 5 page

Renormalization Group and Infinite Algebraic Structure in D-Dimensional Conformal Field Theory

We consider scalar field theory in the D-dimensional space with nontrivial metric and local action functional of most general form. It is possible to construct for this model a generalization of renormalization procedure and RG-equations. In the fixed point the diffeomorphism and Weyl transformations generate an infinite algebraic structure of D-Dimensional conformal field theory models. The Wilson expansion and crossing symmetry enable to obtain sum rules for dimensions of composite operators and Wilson coefficients.Comment: 16 page