Assessment of early-modern observations of comets and supernovae: Focus on pre-telescopic European astrometric and physical data

The two-century period prior to the publication of Newton's Principia (first edition 1687; third edition 1726) was most important in terms of the radical changes that occurred in the observation, perception, and understanding of celestial objects that in turn spurred Newton to deduce his laws of gravitation and motion. Surprisingly, much of the available observational data embedded in contemporary texts from that two-century period has remained unused by modern astronomers, and this thesis (a) describes large amounts of data that were found and reanalyzed during the course of this Ph.D. research project, (b) places these data and their resulting analyses in context with the astronomy of the early-modern era, and (c) shows how modern astronomers and historians benefit from such information. The emphasis is placed here on west-European observations, as observations made elsewhere (eastern Europe, Asia) were isolated (not communicated for convenient rapid use by contemporary astronomers elsewhere) and did not develop or employ the level of precision that was utilized by western European astronomers through the extensive discussions that developed from correspondence and publication in Europe

Controlling Chaos through Compactification in Cosmological Models with a Collapsing Phase

We consider the effect of compactification of extra dimensions on the onset of classical chaotic "Mixmaster" behavior during cosmic contraction. Assuming a universe that is well-approximated as a four-dimensional Friedmann-Robertson--Walker model (with negligible Kaluza-Klein excitations) when the contraction phase begins, we identify compactifications that allow a smooth contraction and delay the onset of chaos until arbitrarily close the big crunch. These compactifications are defined by the de Rham cohomology (Betti numbers) and Killing vectors of the compactification manifold. We find compactifications that control chaos in vacuum Einstein gravity, as well as in string theories with N = 1 supersymmetry and M-theory. In models where chaos is controlled in this way, the universe can remain homogeneous and flat until it enters the quantum gravity regime. At this point, the classical equations leading to chaotic behavior can no longer be trusted, and quantum effects may allow a smooth approach to the big crunch and transition into a subsequent expanding phase. Our results may be useful for constructing cosmological models with contracting phases, such as the ekpyrotic/cyclic and pre-big bang models.Comment: 1 figure. v2/v3: minor typos correcte

Hypermatrix factors for string and membrane junctions

The adjoint representations of the Lie algebras of the classical groups SU(n), SO(n), and Sp(n) are, respectively, tensor, antisymmetric, and symmetric products of two vector spaces, and hence are matrix representations. We consider the analogous products of three vector spaces and study when they appear as summands in Lie algebra decompositions. The Z3-grading of the exceptional Lie algebras provide such summands and provides representations of classical groups on hypermatrices. The main natural application is a formal study of three-junctions of strings and membranes. Generalizations are also considered.Comment: 25 pages, 4 figures, presentation improved, minor correction

Chandra Observations of SDSS J1004+4112: Constraints on the Lensing Cluster and Anomalous X-Ray Flux Ratios of the Quadruply Imaged Quasar

We present results from Chandra observations of SDSS J1004+4112, a strongly lensed quasar system with a maximum image separation of 15". All four bright images of the quasar, as well as resolved X-ray emission originating from the lensing cluster, are clearly detected. The emission from the lensing cluster extends out to approximately 1.5 arcmin. We measure the bolometric X-ray luminosity and temperature of the lensing cluster to be 4.7e44 erg s^-1 and 6.4 keV, consistent with the luminosity-temperature relation for distant clusters. The mass estimated from the X-ray observation shows excellent agreement with the mass derived from gravitational lensing. The X-ray flux ratios of the quasar images differ markedly from the optical flux ratios, and the combined X-ray spectrum of the images possesses an unusually strong Fe Kalpha emission line, both of which are indicative of microlensing.Comment: 9 pages, 5 figures. Accepted for publication in ApJ. Version with high-quality color figures at http://cosmic.riken.jp/ota/publications/index.htm

Probing the Origins of the CIV and Fe Kalpha Baldwin Effect

We use UV/optical and X-ray observations of 272 radio-quiet Type 1 AGNs and quasars to investigate the CIV Baldwin Effect (BEff). The UV/optical spectra are drawn from the Hubble Space Telescope, International Ultraviolet Explorer and Sloan Digital Sky Survey archives. The X-ray spectra are from the Chandra and XMM-Newton archives. We apply correlation and partial-correlation analyses to the equivalent widths, continuum monochromatic luminosities, and alpha_ox, which characterizes the relative X-ray to UV brightness. The equivalent width of the CIV 1549 emission line is correlated with both alpha_ox and luminosity. We find that by regressing l_UV with EW(CIV) and alpha_ox, we can obtain tighter correlations than by regressing l_UV with only EW(CIV). Both correlation and regression analyses imply that l_UV is not the only factor controlling the changes of EW(CIV); alpha_ox (or, equivalently, the soft X-ray emission) plays a fundamental role in the formation and variation of CIV. Variability contributes at least 60% of the scatter of the EW(CIV)-l_UV relation and at least 75% of the scatter of the of the EW(CIV)-alpha_ox relation. In our sample, narrow Fe Kalpha 6.4 keV emission lines are detected in 50 objects. Although narrow Fe Kalpha exhibits a BEff similar to that of CIV, its equivalent width has almost no dependence on either alpha_ox or EW(CIV). This suggests that the majority of narrow Fe Kalpha emission is unlikely to be produced in the broad emission-line region. We do find suggestive correlations between the emission-line luminosities of CIV and Fe Kalpha, which could be potentially used to estimate the detectability of the Fe Kalpha line of quasars from rest-frame UV spectroscopic observations

Fermi surface instabilities at finite Temperature

We present a new method to detect Fermi surface instabilities for interacting systems at finite temperature. We first apply it to a list of cases studied previously, recovering already known results in a very economic way, and obtaining most of the information on the phase diagram analytically. As an example, in the continuum limit we obtain the critical temperature as an implicit function of the magnetic field and the chemical potential $T_c(\mu,h)$. By applying the method to a model proposed to describe reentrant behavior in $Sr_3Ru_2O_7$, we reproduce the phase diagram obtained experimentally and show the presence of a non-Fermi Liquid region at temperatures above the nematic phase.Comment: 10 pages, 10 figure

Kaluza-Klein Induced Gravity Inflation

A D-dimensional induced gravity theory is studied carefully in a $4 + (D-4)$ dimensional Friedmann-Robertson-Walker space-time. We try to extract information of the symmetry breaking potential in search of an inflationary solution with non-expanding internal-space. We find that the induced gravity model imposes strong constraints on the form of symmetry breaking potential in order to generate an acceptable inflationary universe. These constraints are analyzed carefully in this paper.Comment: 10 pages, title changed, corrected some typos, two additional comments adde