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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This content will become publicly available on June 30, 2026
Quantifying the Velocity Anisotropy Profile of Galaxy Clusters Using the Uchuu Cosmological Simulation
Abstract Galaxy clusters are powerful laboratories for studying both cosmic structure formation and galaxy evolution. We present a comprehensive analysis of the velocity anisotropy profile,β(r), in galaxy clusters using the Uchuu-UniverseMachine mock galaxy catalog, which combines the large-volume UchuuN-body simulation with the UniverseMachine galaxy formation model. Focusing on clusters with up to redshiftz= 1.5, we investigate the behavior ofβ(r) as a function of clustercentric radius, mass, and redshift. We find thatβ(r) exhibits a universal shape: it rises from isotropic values near the cluster core, peaks at ∼1.7R200, declines around 3.4R200due to orbital mixing, and increases again in the outskirts, due to the dominance of first-infalling galaxies. Our results show that more massive clusters have higher radial anisotropy and larger peakβvalues. Moreover,β(r) evolves with redshift, with high-redshift clusters displaying more radially dominated orbits and enhanced infall motions. We further derive redshift-dependent power-law scaling relations betweenM200and key physical radii—hydrostatic (Rhs), infall ( ), and turnaround (Rta). These findings offer a robust theoretical framework for interpreting the dynamical properties of observed galaxy clusters and provide key insights into the evolution of their dynamical state over cosmic time.
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- Award ID(s):
- 2347348
- PAR ID:
- 10638723
- Publisher / Repository:
- ApJ
- Date Published:
- Journal Name:
- The Astrophysical Journal
- Volume:
- 987
- Issue:
- 1
- ISSN:
- 0004-637X
- Page Range / eLocation ID:
- 70
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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