High Resolution BIMA Observations of CO, HCN, and 13CO in NGC 1068

We present high-resolution CO, HCN, and 13CO maps of the inner arcminute of NGC 1068 made with the BIMA interferometer. Several features appear in the CO map which have not previously been observed: (1) a firm detection of CO line emission from a compact region centered on the nucleus of the galaxy; (2) the detection of a triplet velocity structure characteristic of kinematically independent regions shown on the spectrum of the unresolved nuclear emission ; and (3) the detection of a molecular bar, the extent and position angle of which are in good agreement with the 2 $\mu$m stellar bar. The most intense CO emission is nonnuclear; the structure and kinematics of this emission imply that this gas is distributed along the inner spiral arms and not in a ring. The bar's kinematic influence on the molecular gas in the spiral arms is modest, with typical ordered noncircular motions of \la\ 30 \kms\ in the plane of the galaxy. Interior to the spiral arms, the bar's influence is more dramatic, as reflected by the twisted isovelocity contours in the CO and HCN velocity fields. The surface density of molecular gas within the central 100 pc radius of NGC 1068 is the same as that in the central 200 pc radius in the Milky Way to within the uncertainties. There is evidence for an $m= 1$ kinematic mode in NGC 1068; we find the kinematic center of rotation to be displaced from the radio continuum center by about 2.9", or 200 pc. The HCN image, in contrast to the CO map, shows a strong concentration of emission centered on the nucleus. The ratio of integrated intensities of the HCN emission to that of CO is about 0.6 and is the highest ratio measured in the central region of any galaxy.Comment: 35 pages of uuencoded, compressed postscript, 20 postscript figures not included but available from [email protected] or from ftp://astro.astro.umd.edu/pub/thelfer/n1068_figs.ps.Z To appear in The Astrophysical Journal, V. 450, Sept. 199

Quaternionic eigenvalue problem

We discuss the (right) eigenvalue equation for $\mathbb{H}$, $\mathbb{C}$ and $\mathbb{R}$ linear quaternionic operators. The possibility to introduce an isomorphism between these operators and real/complex matrices allows to translate the quaternionic problem into an {\em equivalent} real or complex counterpart. Interesting applications are found in solving differential equations within quaternionic formulations of quantum mechanics.Comment: 13 pages, AMS-Te

Quantum decoupling transition in a one-dimensional Feshbach-resonant superfluid

We study a one-dimensional gas of fermionic atoms interacting via an s-wave molecular Feshbach resonance. At low energies the system is characterized by two Josephson-coupled Luttinger liquids, corresponding to paired atomic and molecular superfluids. We show that, in contrast to higher dimensions, the system exhibits a quantum phase transition from a phase in which the two superfluids are locked together to one in which, at low energies, quantum fluctuations suppress the Feshbach resonance (Josephson) coupling, effectively decoupling the molecular and atomic superfluids. Experimental signatures of this quantum transition include the appearance of an out-of-phase gapless mode (in addition to the standard gapless in-phase mode) in the spectrum of the decoupled superfluid phase and a discontinuous change in the molecular momentum distribution function.Comment: 4 RevTeX pages, 1 figure, submitted to PR

Dense Gas in the Milky Way

We present a study of dense gas emission in the Milky Way in order to serve as a basis for comparison with extragalactic results. This study combines new observations of HCN, CS, and CO in individual GMCs and in the Milky Way plane with published studies of emission from these molecules in the inner 500 pc of the Milky Way. We find a strong trend in the fraction of emission from dense gas tracers as a function of location in the Milky Way: in the bulge, I_{HCN}/I_{CO} = 0.081 \pm 0.004, in the plane, I_{HCN}/I_{CO} = 0.026 \pm 0.008 on average, and over the full extent of nearby GMCs, I_{HCN}/I_{CO} = 0.014 \pm 0.020. Similar trends are seen in I_{CS}/I_{CO}. The low intensities of the HCN and CS emission in the plane suggests that these lines are produced by gas at moderate densities; they are thus not like the emission produced by the dense, pc-scale star forming cores in nearby GMCs. The contrast between the bulge and disk ratios in the Milky Way is likely to be caused by a combination of higher kinetic temperatures as well as a higher dense gas fraction in the bulge of the Milky Way.Comment: 34 pages LaTeX, AASTEX macros, includes 11 postscript figures. To appear in ApJ 478, March 199

The octonionic eigenvalue problem

By using a real matrix translation, we propose a coupled eigenvalue problem for octonionic operators. In view of possible applications in quantum mechanics, we also discuss the hermiticity of such operators. Previous difficulties in formulating a consistent octonionic Hilbert space are solved by using the new coupled eigenvalue problem and introducing an appropriate scalar product for the probability amplitudes.Comment: 21 page