Transition Radius Research Articles

Off-diagonal Goldberger-Treiman relation and its discrepancy

We study the off-diagonal Goldberger-Treiman relation (ODGTR) and its discrepancy (ODGTD) in the N, Delta, pi sector through O(p^2) using heavy baryon chiral perturbation theory. To this order, the ODGTD and axial vector N to Delta transition radius are determined solely by low energy constants. Loop corrections appear at O(p^4). For low-energy constants of natural size, the ODGTD would represent a ~ 2% correction to the ODGTR. We discuss the implications of the ODGTR and ODGTD for lattice and quark model calculations of the transition form factors and for parity-violating electroexcitation of the Delta.

Energetic Argument for Bimodal Black Hole Accretion discs

Based on simple energetic considerations, we show that twocrucial ingredients of bimodal black hole accretion discs, namely thesonic point and the transition radius, can be determined from the discconstant parameters. Thus, we can further justify the model of bimodaldiscs containing thermal instability triggered transition.

Do Modified Newtonian Dynamics Follow from the Cold Dark Matter Paradigm?

In a recent paper, Kaplinghat and Turner (2001) (KT) advertise that MOND can be derived naturally in the CDM paradigm. They actually proceed to produce a more limited result: Every galaxy should have a transition radius, $r_t$, below which baryons dominate, and above which dark matter (DM) takes over; the acceleration at $r_t$ is nearly the same for all galaxies; and due to a coincidences this is of order $a_0\sim cH_0$. This follows from their tacit, intermediate result, whereby CDM halos of galaxies have a very nearly universal acceleration profile $a(r)\approx v^2(r)/r\approx A\hat a(r/\ell)$, where A is universal, and only the scale $\ell$ varies from halo to halo. (This remains so when baryons are added because they assume a universal baryon-collapse factor.) The KT scenario is phenomenologically wrong--observed galaxies are simply not like that. For example, it precludes altogether the existence of LSB galaxies, in which the acceleration is everywhere smaller than $a_0$. The phenomenologically sound outcome--i.e., the role of $a_0$ as a transition acceleration in high-surface-brightness galaxies--pertains to only a small part of the statement of MOND. There are several other, independent roles that $a_0\sim cH_0$ plays in MOND phenomenology, and other predictions of MOND, not related to the value of $a_0$, that are not explainable in the KT scenario. The results of KT also disagree with those of CDM simulations, which, as they now stand, do not reproduce any aspect of MOND phenomenology.

Coronal-temporal correlations in GX 339-4: hysteresis, possible reflection changes and implications for advection-dominated accretion flows

We present spectral fits and timing analysis of Rossi X-ray Timing Explorer observations of GX 339-4. These observations were carried out over a span of more than two years and encompassed both the soft/high and hard/low states. Two observations were simultaneous with Advanced Satellite for Cosmology and Astrophysics observations. Hysteresis in the soft-hard state transition is observed. The hard state exhibits a possible anticorrelation between coronal compactness (i.e. spectral hardness) and the covering fraction of cold, reflecting material. The correlation between 'reflection fraction' and soft X-ray flux, however, appears to be more universal. Furthermore, low-flux, hard-state observations - taken over a decline into quiescence - show that the Fe line, independent of 'reflection fraction', remains broad and at a roughly constant equivalent width, counter to expectations from advection-dominated accretion flow models. All power spectral densities of the hard-state X-ray light curves are describable as the sum of just a few broad, quasi-periodic features with frequencies that roughly scale as coronal compactness, l c , to the - 3/2 power. This is interpretable in a simple, toy model of an efficient spherical corona as variations of l c oc R t , where R t is the 'transition radius' between the corona and an outer thin disc. Similar to observations of Cyg X-1, time lags between soft and hard variability anticorrelate with coronal compactness, and peak shortly after the transition from the soft to the hard state. A stronger correlation is seen between the time lags and the 'reflection fraction'. These latter facts might suggest that the time lags are associated with the known, spatially very extended, synchrotron-emitting outflow.

Fast and Accurate Fourier Series Solutions to Gravitational Lensing by a General Family of Two–Power‐Law Mass Distributions

Fourier series solutions to the deflection and magnification by a family of three-dimensional cusped two-power-law ellipsoidal mass distributions are presented. The cusped two-power-law ellipsoidal mass distributions are characterized by inner and outer power-law radial indices and a break (or transition) radius. The model family includes mass models mimicking Jaffe, Hernquist, and η models and dark matter halo profiles from numerical simulations. The Fourier series solutions for the cusped two-power-law mass distributions are relatively simple and allow a very fast calculation, even for a chosen small fractional calculational error (e.g., 10-5). These results will be particularly useful for studying lensed systems that provide a number of accurate lensing constraints and for systematic analyses of large numbers of lenses. Subroutines employing these results for the two-power-law model and the results by Chae, Khersonsky, & Turnshek for the generalized single-power-law mass model are made publicly available.

Ejection of the inner accretion disk in GRS 1915+105: The magnetic rubber-band effect

We examine theoretically the behaviour of the inner accretion disk in GRS 1915+105 when soft X-ray dips are present in the X-ray light curve. We assume the presence of a radial shock in the accretion disk, as in some of the Two Component Advective Flow (TCAF) solutions. We discuss the behaviour of the flux tubes inside a TCAF (which we name Magnetized TCAF or MTCAF model for brevity) and compare various competing forces on the flux tubes. In this MTCAF model, we find that the magnetic tension is the strongest force in a hot plasma of temperature $\gsim 10^{10}$K and as a result, magnetic flux tubes entering in this region collapse catastrophically, thereby occasionally evacuating the inner disk. We postulate that this magnetic `rubber-band' effect induced evacuated disk matter produces the blobby components of outflows and IR/radio jets. We derive the size of the post-shock region by equating the time scale of the Quasi-Periodic Oscillations to the infall time of accreting matter in the post-shock region and found the shock location to be $\sim 45-66 r_g$. We calculate the transition radius $r_{tr}$, where the Keplerian disk deviates into a sub-Keplerian flow, to be $\sim 320r_g$. Based on the derived X-ray spectral parameters, we calculate the mass of this region to be $\sim10^{18}$g. We conclude that during the X-ray dips the matter in the post-shock region, which manifests itself as the thermal-Compton component in the X-ray spectrum, is ejected, along with some sub-Keplerian matter in the pre-shock region.

Moments of the neutron charge form factor and the N --> Delta quadrupole transition.

Recent data allow a new parametrization of the neutron charge form factor GnE. A parameter-free quark-model relation between GnE and the N-->Delta quadrupole form factor G(N-->Delta)C2 is used to predict G(N-->Delta)C2 from GnE data. In particular, <r2n> is related to N-->Delta quadrupole moment Q(N-->Delta), while <r4n> connects to the N-->Delta quadrupole transition radius <r2(N-->Delta)>. From the latter we derive an experimental value for the charge radius of the light constituent quarks r(gamma(q)) = 0.8 fm. Finally, the C2/M1 ratio in pion electroproduction is predicted from the elastic neutron form factor data.

New Optical Constraints on the Presence of a Compact Central Object in Cassiopeia A

Deep optical imaging at the location of the pointlike X-ray source at the center of the 300 yr old Cassiopeia A supernova remnant discovered in the Chandra first-light observation is presented. R-band images obtained with the Steward Observatory 2.3 m telescope and direct CCD on four nights in 1999 September are used to set a new brightness limit of R 26.3 mag (1 σ) on the presence of any optical object associated with the X-ray source. This new limit implies MR 10.3 mag and LX(0.2-10 keV)/Lopt 800. Accretion models are the most constrained by the optical results. Binary accretion models and scenarios involving very low accretion rates from a disk onto a neutron star or a black hole similar to models for quiescent transient low-mass X-ray binaries are effectively ruled out. Fallback accretion models may be ruled out in some circumstances, but the emitted optical and infrared flux is sensitive to the location of the transition radius, the geometry of the disk, and its inclination to the line of sight.

Prediction of fly-ash size distribution: a correlation between the char transition radius and coal properties

Prediction of fly-ash size distribution: a correlation between the char transition radius and coal properties

Modelling of the flow at the rotor disc in a geothermal turbine of 110 MW

To elucidate an excessive erosion damage produced by solid particles in the fourth stage rotor disc of a 110 MW double flow geothermal turbine, a bi-dimensional modelling investigation has been conducted. The study was based on a set of results from a computational model using a Reynolds stress, RSM, turbulence model. The predicted results confirmed characteristic flow conditions that may play a main role in the serious erosion of the fourth stage rotor disc governor side, which has been detected in periodic overhauls. The results show a jet of vapour that hits the disc transition radius surface at velocities around 112 m/s. These conditions are produced by the flow outgoing from the labyrinth seal, which passes through a drastic cross-section reduction in the last seal strip. The flow was then simulated introducing specific changes to the geometry and the grid in order to modify the flow patterns favourably. Actually, the suggested changes have been envisaged indeed to be practically feasible of being implemented. The new results showed that it is possible to reduce the erosion process up to 86% by increasing the distance from the labyrinth seal to the rotor disc, which produces a 38% velocity reduction of the vapour flow in that zone. The design proposed in this work produces a flow pattern of a lower velocity on disc surface together with a modified angle of flow incidence. Furthermore, the proposed design also reduces a recirculating flow at the exit of the last seal strip. Based on these results, an analysis of erosion against velocity demonstrates that the redesigned rotor disc proposed here leads to the duplication of the time period used at present between maintenance repairs.

Numerical studies of low cycle fatigue in forward extrusion dies

Forward extrusion dies typically fail due to transverse fatigue cracks or wear. Fatigue cracks are initiated in regions where the material is subjected to repeated plastic deformations, e.g. the transition radius in a forward extrusion die. In the present work, a material model capable of describing the elastic–plastic material behaviour under cyclic loadings is used to study the effects of different pre-stressing concepts on the accumulation of plastic strain and the development of fatigue damage. The results show, that the accumulation of plastic strain in the critical region can be controlled by means of the pre-stressing system or the geometry of the die insert.

Bimodal Accretion Disks: Shakura-Sunyaev Disk–Advection-dominated Accretion Flow Transitions

We show that, unlike the results presented previously in the literature, the transition from an outer Shakura-Sunyaev disk (SSD) to an advection-dominated accretion flow (ADAF) is possible for large values of the viscosity parameter α > 0.5. The transition is triggered by the thermal instability of a radiation pressure-supported SSD. The transition radius is close to the central black hole. We confirm our qualitative prediction by actually constructing global bimodal SSD-ADAF solutions.

Transition from Standard Disk to Advection‐dominated Accretion Flow

We studied a global accretion flow model with a radial transition from outer standard disks to inner advection-dominated accretion flows. The height-integrated viscous hydrodynamic equations were solved numerically using radiative transfer equations. We found two kinds of solutions: (1) standard-disk solutions and (2) solutions with transitions from inner advection-dominated accretion flows to outer standard disks, thus confirming the recent results of Honma. We investigated in detail the thermal structure of the transition region, finding a series of transition solutions with a different transition radius for a given set of physical parameters. The transitions occur only when the efficiency of the energy transport by the turbulence is above a minimum value. The physical mechanism of the transition is also discussed.

Hydrodynamic simulations of the Bardeen-Petterson effect

We present SPH simulations of accretion discs in orbit about rotating compact objects, such as black holes and neutron stars, and study the structure of warped discs produced by the Bardeen-Petterson effect. We calculate the transition radius out to which the disc specific angular momentum vector is aligned with that of the black hole. We focus on the parameter regime where the warp dynamics are controlled by bending wave propagation, but also consider models in which warps are subject to diffusion rather than wave transport, and are able to consider the fully non-linear regime. Because of hydrodynamic or pressure effects, for the parameter range investigated, the transition radius is always found to be much smaller than that obtained by Bardeen & Petterson. For discs with mid-plane Mach numbers of ∼10, the transition occurs between 10 and 16R+ (gravitational radii), whereas for a Mach number of ∼30 it occurs at around 30R+. A thicker disc with a Mach number of 5 is found to produce no discernible warped structure. The rate of black hole-disc alignment is found to be consistent with the ideas of Rees, with the alignment torque behaving as if it arises from the accreted material transferring its misaligned component of angular momentum at the larger transition radius of Bardeen & Petterson. The inclusion of Einstein precession in the calculations modified both the warped disc structure and, consistent with linear analysis, produced an increased alignment rate by up to a factor of 4 because of the effect that the non-Keplerian potential has on the propagation of warps.

Prediction of fly-ash size distribution: a correlation between the char transition radius and coal properties

The Random Coalescence (RC) model, predicting the size distributions of the fly-ash produced from coal combustion, is applied to correlate the char transition radius with coal size and the size and volume fraction of the mineral inclusions for different types of coals.

Advection-dominated Inflow/Outflows from Evaporating Accretion Disks.

In this Letter we investigate the properties of advection-dominated accretion flows (ADAFs) fed by the evaporation of a Shakura-Sunyaev accretion disk (SSD). In our picture, the ADAF fills the central cavity evacuated by the SSD and extends beyond the transition radius into a coronal region. We find that, because of global angular momentum conservation, a significant fraction of the hot gas flows away from the black hole, forming a transsonic wind, unless the injection rate depends only weakly on radius (if r2sigma&d2;~r-xi, xi<1&solm0;2). The Bernoulli number of the inflowing gas is negative if the transition radius is less, similar100 Schwarzschild radii, so matter falling into the hole is gravitationally bound. The ratio of inflowing to outflowing mass is approximately 1/2, so in these solutions the accretion rate is of the same order as in standard ADAFs and much larger than in advection-dominated inflow/outflow models. The possible relevance of evaporation-fed solutions to accretion flows in black hole X-ray binaries is briefly discussed.

Broad Emission Line Regions in Active Galactic Nuclei: The Link with the Accretion Power.

We present a model that relates the width of the broad emission lines of active galactic nuclei (AGNs) to the Keplerian velocity of an accretion disk at a critical distance from the central black hole. This critical distance falls in a region bounded on the inward side by the transition radius between the radiation pressure- and the gas pressure-dominated region of the accretion disk and on the outward side by the maximum radius below which a stabilizing, radially accreting and vertically outflowing corona exists. We show that in the framework of this picture, the observed range of Hbeta FWHMs from broad-line to narrow-line type 1 AGNs is well reproduced as a function of the accretion rate. This interval of velocities is the only permitted range and goes from approximately 20,000 km s-1 for sub-Eddington accretion rates to approximately 1000 km s-1 for Eddington accretion rates.

Dynamics of the Transition from a Thin Accretion Disk to an Advection‐dominated Accretion Flow

We consider an optically thin advection-dominated accretion flow (ADAF) that is connected at a finite transition radius to an outer optically thick, geometrically thin disk. We include turbulent energy transport and examine ADAF models that satisfy the following boundary conditions at the transition radius: (1) the temperature of the gas is much lower than the virial temperature, (2) the rotation is super-Keplerian, and (3) the net radial flux of energy is outward. We numerically solve the height-integrated viscous hydrodynamic equations with these boundary conditions. We find that the Bernoulli parameter is positive for a wide range of radius, indicating that outflows may be possible from ADAFs. Turbulent energy transport enhances the Bernoulli parameter. We compare our numerical global solutions with two published analytical solutions. We find that the solution of Honma represents the transition region well, while the self-similar solution of Narayan & Yi works better away from the transition. However, neither analytical solution is able to represent the density or angular momentum profile in the inner region of the ADAF, where the flow makes a sonic transition.

INCREASING THE NATURAL FREQUENCIES OF CIRCULAR DISKS USING INTERNAL CHANNELS

This paper investigates a new design for computer disk drive disks that raises their natural frequencies. In this new design, a pattern of small, dense, internal channels or voids is distributed axisymmetrically about the midplane of the disk. These channels increase the natural frequencies of the disk by removing mass from the midplane of the disk while maintaining the coupling between the deflections of the upper and lower surfaces of the disk. This practice is commonly employed in I-beams and honeycombed sandwich panels, but the channeled geometry proposed here has not been previously considered or studied. This paper presents a detailed analytical model for a channeled disk, specifications for optimal channeled disk design, and experimental corroboration. Numerical results show that the natural frequencies of a properly channeled disk can be 10–100% higher than those of a uniform disk, depending on the size of the channels. The orientation of the channels does not significantly affect the natural frequencies, but, in the optimal design, the channels do not extend through the whole disk. Instead, they begin at an optimal, central, transition radius and radiate outward to the outer edge of the disk. Disks with this optimal channel design may be competitive with uniform thickness disks for disk drive applications in terms of both natural frequency and cost.

Residual Stresses in Weld-Deposited Clad Pressure Vessels and Nozzles

Results of through-thickness residual stress measurements are provided for a variety of samples of weld-deposited 308/309L stainless steel and Alloy 600 cladding on low-alloy pressure vessel ferritic steels. Clad thicknesses between 5 and 9 mm on samples that vary in thickness from 45 to 200 mm were studied. The samples were taken from flat plates, from a spherical head of a pressure vessel, from a ring-segment of a nozzle bore, and from the transition radius between a nozzle and a pressure vessel shell. A layer removal method was used to measure the residual stresses. The effects of uncertainties in elastic constants (Young’s modulus and Poisson’s ratio) as well as experimental error are assessed. All measurements were done at room temperature. The results of this work indicate that curvature plays a significant role in cladding residual stress and that tensile residual stresses as high as the yield stress can be measured in the cladding material. Since the vessel from which the spherical and nozzle corner samples were taken was hydrotested, and the flat plate specimens were taken from specimens used in mechanical fatigue testing, these results suggest that rather high tensile residual stresses can be retained in the cladding material, even after some mechanical loading associated with hydrotesting.