Abstract A steady-state, semi-analytical model of energetic particle acceleration in radio-jet shear flows due to cosmic-ray viscosity obtained by Webb et al. is generalized to take into account more general cosmic-ray boundary spectra. This involves solving a mixed Dirichlet–Von Neumann boundary value problem at the edge of the jet. The energetic particle distribution functionf0(r,p) at cylindrical radiusrfrom the jet axis (assumed to lie along thez-axis) is given by convolving the particle momentum spectrum with the Green’s function , which describes the monoenergetic spectrum solution in which asr→ ∞ . Previous work by Webb et al. studied only the Green’s function solution for . In this paper, we explore for the first time, solutions for more general and realistic forms for . The flow velocityu=u(r)ezis along the axis of the jet (thez-axis).uis independent ofz, andu(r) is a monotonic decreasing function ofr. The scattering time in the shear flow region 0 <r<r2, and , wheres> 0 in the regionr>r2is outside the jet. Other original aspects of the analysis are (i) the use of cosmic ray flow lines in (r,p) space to clarify the particle spatial transport and momentum changes and (ii) the determination of the probability distribution that particles observed at (r,p) originated fromr→ ∞ with momentum . The acceleration of ultrahigh-energy cosmic rays in active galactic nuclei jet sources is discussed. Leaky box models for electron acceleration are described. 
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                            Jets and Rings in Images of Spinning Black Holes
                        
                    
    
            Abstract We develop a “dual-cone” model for millimeter wavelength emission near a spinning black hole. The model consists of optically thin, luminous cones of emission, centered on the spin axis, which are meant to represent jet walls. The resulting image is dominated by a thin ring. We first consider the effect of the black hole’s spin on the image and show that the dominant effect is to displace the ring perpendicular to the projection of the spin axis on the sky by . This effect is lower order ina*than changes in the shape and size of the photon ring itself but is undetectable without a positional reference. We then show that the centerline of the jet can provide a suitable reference: its location is exactly independent of spin if the observer is outside the cone and nearly independent of spin if the observer is inside the cone. If astrophysical uncertainties can be controlled, then spin displacement is large enough to be detectable by future space very long baseline interferometry missions. Finally, we consider ring substructure in the dual-cone model and show that features in total intensity are not universal and depend on the cone-opening angle. 
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                            - PAR ID:
- 10396799
- Publisher / Repository:
- DOI PREFIX: 10.3847
- Date Published:
- Journal Name:
- The Astrophysical Journal
- Volume:
- 944
- Issue:
- 1
- ISSN:
- 0004-637X
- Format(s):
- Medium: X Size: Article No. 55
- Size(s):
- Article No. 55
- Sponsoring Org:
- National Science Foundation
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