Mean magnetic field generation in sheared rotators

A generalized mean magnetic field induction equation for differential rotators is derived, including a compressibility, and the anisotropy induced on the turbulent quantities from the mean magnetic field itself and a mean velocity shear. Derivations of the mean field equations often do not emphasize that there must be anisotropy and inhomogeneity in the turbulence for mean field growth. The anisotropy from shear is the source of a term involving the product of the mean velocity gradient and the cross-helicity correlation of the isotropic parts of the fluctuating velocity and magnetic field, \lb{\bfv}\cdot{\bfb}\rb^{(0)}. The full mean field equations are derived to linear order in mean fields, but it is also shown that the cross-helicity term survives to all orders in the velocity shear. This cross-helicity term can obviate the need for a pre-existing seed mean magnetic field for mean field growth: though a fluctuating seed field is necessary for a non-vanishing cross-helicity, the term can produce linear (in time) mean field growth of the toroidal field from zero mean field. After one vertical diffusion time, the cross-helicity term becomes sub-dominant and dynamo exponential amplification/sustenance of the mean field can subsequently ensue. The cross-helicity term should produce odd symmetry in the mean magnetic field, in contrast to the usually favored even modes of the dynamo amplification in sheared discs. This may be important for the observed mean field geometries of spiral galaxies. The strength of the mean seed field provided by the cross- helicity depends linearly on the magnitude of the cross-helicity.Comment: 15 pages, LaTeX, matches version accepted to ApJ, minor revision

Efficiency at optimal work from finite reservoirs: a probabilistic perspective

We revisit the classic thermodynamic problem of maximum work extraction from two arbitrary sized hot and cold reservoirs, modelled as perfect gases. Assuming ignorance about the extent to which the process has advanced, which implies an ignorance about the final temperatures, we quantify the prior information about the process and assign a prior distribution to the unknown temperature(s). This requires that we also take into account the temperature values which are regarded to be unphysical in the standard theory, as they lead to a contradiction with the physical laws. Instead in our formulation, such values appear to be consistent with the given prior information and hence are included in the inference. We derive estimates of the efficiency at optimal work from the expected values of the final temperatures, and show that these values match with the exact expressions in the limit when any one of the reservoirs is very large compared to the other. For other relative sizes of the reservoirs, we suggest a weighting procedure over the estimates from two valid inference procedures, that generalizes the procedure suggested earlier in [J. Phys. A: Math. Theor. {\bf 46}, 365002 (2013)]. Thus a mean estimate for efficiency is obtained which agrees with the optimal performance to a high accuracy.Comment: 14 pages, 6 figure

Probing the causes of thermal hysteresis using tunable N-agg micelles with linear and brush-like thermoresponsive coronas

Self-assembled thermoresponsive polymers in aqueous solution have great potential as smart, switchable materials for use in biomedical applications. In recent years, attention has turned to the reversibility of these polymers’ thermal transitions, which has led to debate over what factors influence discrepancies in the transition temperature when heating the system compared to the temperature obtained when cooling the system, known as the thermal hysteresis. Herein, we synthesize micelles with tunable aggregation numbers (Nagg) whose cores contain poly(n-butyl acrylate-co-N,N-dimethylacrylamide) (p(nBA-co-DMA)) and four different thermoresponsive corona blocks, namely poly(N-isopropylacrylamide) (pNIPAM), poly(N,N-diethylacrylamide) (pDEAm), poly(diethylene glycol monomethyl ether methacrylate) (pDEGMA) and poly(oligo(ethylene glycol) monomethyl ether methacrylate) (pOEGMA). By studying their thermoresponsive behavior, we elucidate the effects of changing numerous important characteristics both in the thermoresponsive chain chemistry and architecture, and in the structure of their self-assemblies. Our findings demonstrate large deviations in the reversibility between the self-assemblies and the corresponding thermoresponsive homopolymers; specifically we find that micelles whose corona consist of polymers with a brush-like architecture (pDEGMA and pOEGMA) exhibit irreversible phase transitions at a critical chain density. These results lead to a deeper understanding of stimuli-responsive self-assemblies and demonstrate the potential of tunable Nagg micelles for uncovering structure–property relationships in responsive polymer systems

Fuel-Supply-Limited Stellar Relaxation Oscillations: Application to Multiple Rings around AGB Stars and Planetary Nebulae

We describe a new mechanism for pulsations in evolved stars: relaxation oscillations driven by a coupling between the luminosity-dependent mass-loss rate and the H fuel abundance in a nuclear-burning shell. When mass loss is included, the outward flow of matter can modulate the flow of fuel into the shell when the stellar luminosity is close to the Eddington luminosity $L_{\rm Edd}$. When the luminosity drops below $L_{\rm Edd}$, the mass outflow declines and the shell is re-supplied with fuel. This process can be repetitive. We demonstrate the existence of such oscillations and discuss the dependence of the results on the stellar parameters. In particular, we show that the oscillation period scales specifically with the mass of the H-burning relaxation shell (HBRS), defined as the part of the H-burning shell above the minimum radius at which the luminosity from below first exceeds the Eddington threshold at the onset of the mass loss phase. For a stellar mass M_*\sim 0.7\Msun, luminosity L_*\sim 10^4\Lsun, and mass loss rate |\dot M|\sim 10^{-5}\Msun yr$^{-1}$, the oscillations have a recurrence time $\sim 1400$ years $\sim 57\tau_{\rm fsm}$, where $\tau_{\rm fsm}$ is the timescale for modulation of the fuel supply in the HBRS by the varying mass-loss rate. This period agrees with the $\sim$ 1400-year period inferred for the spacings between the shells surrounding some planetary nebulae, and the the predictied shell thickness, of order 0.4 times the spacing, also agrees reasonably well.Comment: 15 pages TeX, 1 ps figure submitted to Ap

The divergence of neighboring magnetic field lines and fast-particle diffusion in strong magnetohydrodynamic turbulence, with application to thermal conduction in galaxy clusters

We investigate field-line separation in strong MHD turbulence using direct numerical simulations. We find that in the static-magnetic-field approximation the thermal conductivity in galaxy clusters is reduced by a factor of about 50 relative to the Spitzer thermal conductivity of a non-magnetized plasma. This value is too small for heat conduction to balance radiative cooling in clusters.Comment: Major revision: higher resolution simulations lead to significantly different conclusions. 4 pages, 4 figures, submitted to Physical Review Letter

MHD Stellar and Disk Winds: Application to Planetary Nebulae

MHD winds can emanate from both stars and surrounding accretion disks. It is of interest to know how much wind power is available and which (if either) of the two rotators dominates that power. We investigate this in the context of multi-polar planetary nebulae (PNe) and proto-planetary nebulae (PPNe), for which recent observations have revealed the need for a wind power source in excess of that available from radiation driving, and a possible need for magnetic shaping. We calculate the MHD wind power from a coupled disk and star, where the former results from binary disruption. The resulting wind powers depend only on the accretion rate and stellar properties. We find that if the stellar envelope were initially slowly rotating, the disk wind would dominate throughout the evolution. If the envelope of the star were rapidly rotating, the stellar wind could initially be of comparable power to the disk wind until the stellar wind carries away the star's angular momentum. Since an initially rapidly rotating star can have its spin and magnetic axes misaligned to the disk, multi-polar outflows can result from this disk wind system. For times greater than a spin-down time, the post-AGB stellar wind is slaved to the disk for both slow and rapid initial spin cases and the disk wind luminosity dominates. We find a reasonably large parameter space where a hybrid star+disk MHD driven wind is plausible and where both or either can account for PPNe and PNe powers. We also speculate on the morphologies which may emerge from the coupled system. The coupled winds might help explain the shapes of a number of remarkable multi-shell or multi-polar nebulae. Magnetic activity such as X-ray flares may be associated with the both central star and the disk and would be a valuable diagnostic for the dynamical role of MHD processes in PNe.Comment: ApJ accepted version, incorporating some important revisions. 25 Pages, LaTex, + 5 fig

A Compact X-ray Source and Possible X-ray Jets within the Planetary Nebula Menzel 3

We report the discovery, by the Chandra X-ray Observatory, of X-ray emission from the bipolar planetary nebula Menzel 3. In Chandra CCD imaging, Mz 3 displays hot (3-6x10^6 K) gas within its twin, coaxial bubbles of optical nebulosity, as well as a compact X-ray source at the position of its central star(s). The brightest diffuse X-ray emission lies along the polar axis of the optical nebula, suggesting a jet-like configuration. The observed combination of an X-ray-emitting point source and possible X-ray jet(s) is consistent with models in which accretion disks and, potentially, magnetic fields shape bipolar planetary nebulae via the generation of fast, collimated outflows.Comment: 12 pages, 3 figures; to appear in Astrophysical Journal (Letters