Position and momentum observables on R and on R^3

We characterize all position and momentum observables on R and on R^3. We study some of their operational properties and discuss their covariant joint observables.Comment: 18 page

X-ray Emission from Magnetically Torqued Disks of Oe/Be Stars

We focus attention on the Oe/Be stars to test the concept that the disks of these stars form by magnetic channeling of wind material toward the equator. Calculations are made of the X-rays expected from the Magnetically Torqued Disk (MTD) model for Be stars discussed by Cassinelli et al. (2002), by Maheswaran (2003), and by Brown et al. (2004). The dominant parameters in the model are the $\beta$ value of the velocity law, the rotation rate of the star, $S_o$, and the ratio of the magnetic field energy density to the disk gravitational energy density, $\gamma$. The model predictions are compared with the $ROSAT$ observations obtained for an O9.5 star $\zeta$ Oph from \Berghofer et al. (1996) and for 7 Be stars from Cohen et al. (1997). Extra considerations are also given here to the well studied Oe star $\zeta$ Oph for which we have $Chandra$ observations of the X-ray line profiles of the triad of He-like lines from the ion Mg XI.Comment: 28 pages with 6 figures. Accepted for publication in Ap

New Challenges For Wind Shock Models: The Chandra Spectrum Of The Hot Star Delta Orionis

The Chandra spectrum of delta Ori A shows emission lines from hydrogen- and helium-like states of Si, Mg, Ne, and O, along with N VII Lyalpha and lines from ions in the range Fe XVII-Fe XXI In contrast to the broad lines seen in zeta Pup and zeta Ori (850 +/- 40 and 1000 +/- 240 km s(-1) half-width at half-maximum [HWHM], respectively), these lines are broadened to only 430 +/- 60 km s(-1) HWHM. This is much lower than the measured wind terminal velocity of 2000 km s(-1). The forbidden, intercombination, and resonance (fir) lines from He-like ions indicate that the majority of the X-ray line emission does not originate at the base of the wind, in agreement with the standard wind shock models for these objects. However, in that model the X-ray emission is distributed throughout an expanding, X-ray-absorbing wind, and it is therefore surprising that the emission lines appear relatively narrow, unshifted, and symmetric. We compare the observed line profiles to recent detailed models for X-ray line pro le generation in hot stars, but none of them offers a fully satisfactory explanation for the observed line profiles

On the structure of covariant phase observables

We study the mathematical structure of covariant phase observables. Such an observable can alternatively be expressed as a phase matrix, as a sequence of unit vectors, as a sequence of phase states, or as an equivalent class of covariant trace-preserving operations. Covariant generalized operator measures are defined by structure matrices which form a W*-algebra with phase matrices as its subset. The properties of the Radon-Nikodym derivatives of phase probability measures are studied.Comment: 11 page

Highly Accelerated Diamagnetic Plasmoids: A New X-ray Production Mechanism for OB Stellar Winds

The observed X-ray source temperature distributions in OB stellar winds, as determined from high energy resolution Chandra observations, show that the highest temperatures occur near the star, and then steadily decrease outward through the wind. To explain this unexpected behavior, we propose a shock model concept that utilizes a well-known magnetic propulsion mechanism; the surface ejection of "diamagnetic plasmoids" into a diverging external magnetic field. This produces rapidly accelerating self-contained structures that plow through an ambient wind and form bow shocks that generate a range in X-ray temperatures determined by the plasmoid-wind relative velocities. The model free parameters are the plasmoid initial Alfven speed, the initial plasma-beta of the external medium, and the divergence rate of the external field. These are determined by fitting the predicted bow shock temperatures with the observed OB supergiant X-ray temperature distribution. We find that the initial external plasma-beta has a range between 0 and 2, and the assumed radially-decreasing external magnetic field strength that scales as r^{-S} has a value of S lying between 2 and 3. Most importantly, the initial plasmoid Alfven speed is found to be well-constrained at a value of 0.6 times the terminal velocity, which appears to represent an upper limit for all normal OB stars. This intriguing new limit on OB magnetic properties, as derived from Chandra observations, emphasizes the need for further studies of magnetic propulsion mechanisms in these stars.Comment: Accepted for publication in ApJ Letters, 4 pages, 4 figures (color), 1 tabl

The Correlation between X-Ray Line Ionization and Optical Spectral Types of the OB Stars

Marked correlations are reported between the ionization of the X-ray line spectra of normal OB stars, as observed by the Chandra X-Ray Observatory, and their optical spectral types. These correlations include the progressive weakening of the higher ionization relative to the lower ionization X-ray lines with advancing spectral type, and the similarly decreasing intensity ratios of the H-like to He-like lines of the alpha ions. These relationships were not predicted by models, nor have they been clearly evident in astrophysical studies of a few objects; rather, they have emerged from morphological analysis of an adequate (albeit still small) sample, from which known peculiar objects such as magnetic stars and very rapid rotators have been isolated to reveal the normal trends. This process is analogous to that which first demonstrated the strong relationships between the UV wind profiles and the optical spectral types of normal OB stars, which likely bear a physical as well as a historical connection to the present X-ray results. Since the optical spectral types are calibrated in terms of fundamental stellar parameters, it follows that the winds and X-ray spectra are determined by the latter. These observations provide strong guidance for further astrophysical modeling of these phenomena.Comment: 19 pages, 7 figures, 2 tables; ApJ accepte

X-ray line emission from a fragmented stellar wind

We discuss X-ray line formation in dense O star winds. A random distribution of wind shocks is assumed to emit X-rays that are partially absorbed by cooler wind gas. The cool gas resides in highly compressed fragments oriented perpendicular to the radial flow direction. For fully opaque fragments, we find that the blueshifted part of X-ray line profiles remains flat-topped even after severe wind attenuation, whereas the red part shows a steep decline. These box-type, blueshifted profiles resemble recent Chandra observations of the O3 star zeta Pup. For partially transparent fragments, the emission lines become similar to those from a homogeneous wind.Comment: 8 pages, 7 figures, Latex, to be published in A&

Collisionless Damping of Fast MHD Waves in Magneto-rotational Winds

We propose collisionless damping of fast MHD waves as an important mechanism for the heating and acceleration of winds from rotating stars. Stellar rotation causes magnetic field lines anchored at the surface to form a spiral pattern and magneto-rotational winds can be driven. If the structure is a magnetically dominated, fast MHD waves generated at the surface can propagate almost radially outward and cross the field lines. The propagating waves undergo collisionless damping owing to interactions with particles surfing on magnetic mirrors that are formed by the waves themselves. The damping is especially effective where the angle between the wave propagation and the field lines becomes moderately large ($\sim 20$ to $80^{\circ}$). The angle tends naturally to increase into this range because the field in magneto-rotational winds develops an increasingly large azimuthal component. The dissipation of the wave energy produces heating and acceleration of the outflow. We show using specified wind structures that this damping process can be important in both solar-type stars and massive stars that have moderately large rotation rates. This mechanism can play a role in coronae of young solar-type stars which are rapidly rotating and show X-ray luminosities much larger than the sun. The mechanism could also be important for producing the extended X-ray emitting regions inferred to exist in massive stars of spectral type middle B and later.Comment: 12 pages, including 7 figures, accepted for publication in Ap