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1. Acceleration and Spectral Redistribution of Cosmic Rays in Radio-jet Shear Flows

   https://doi.org/10.3847/1538-4357/acfda9  

   Webb, G. M.; Xu, Y.; Biermann, P. L.; Al-Nussirat, S.; Mostafavi, P.; Li, G.; Barghouty, A. F.; Zank, G. P. (November 2023, The Astrophysical Journal)

   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 $f_0(\infty ,p\prime )$with the Green’s function $G(r,p;p\prime )$, which describes the monoenergetic spectrum solution in which $f_0\to \delta (p-p\prime )$asr→ ∞ . Previous work by Webb et al. studied only the Green’s function solution for $G(r,p;p\prime )$. In this paper, we explore for the first time, solutions for more general and realistic forms for $f_0(\infty ,p\prime )$. The flow velocityu=u(r)e_zis along the axis of the jet (thez-axis).uis independent ofz, andu(r) is a monotonic decreasing function ofr. The scattering time $\tau {(r,p)={\tau }_0\left(p/p_0\right)}^{\alpha }$in the shear flow region 0 <r<r₂, and $\tau {(r,p)={\tau }_0\left(p/p_0\right)}^{\alpha }{\left(r/r_2\right)}^s$, 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 ${\psi }_p(r,p;p\prime )$that particles observed at (r,p) originated fromr→ ∞ with momentum $p\prime$. 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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2. The Kelvin–Helmholtz Instability at the Boundary of Relativistic Magnetized Jets

   https://doi.org/10.3847/2041-8213/acdfcf  

   Chow, Anthony; Davelaar, Jordy; Rowan, Michael E; Sironi, Lorenzo (July 2023, The Astrophysical Journal Letters)

   Abstract We study the linear stability of a planar interface separating two fluids in relative motion, focusing on conditions appropriate for the boundaries of relativistic jets. The jet is magnetically dominated, whereas the ambient wind is gas-pressure-dominated. We derive the most general form of the dispersion relation and provide an analytical approximation of its solution for an ambient sound speed much smaller than the jet Alfvén speedv_A, as appropriate for realistic systems. The stability properties are chiefly determined by the angleψbetween the wavevector and the jet magnetic field. Forψ=π/2, magnetic tension plays no role, and our solution resembles the one of a gas-pressure-dominated jet. Here, only sub-Alfvénic jets are unstable ( $0<M_e\equiv \left(v/v_{\mathrm{A}}\right)\cos \theta <1$, wherevis the shear velocity andθthe angle between the velocity and the wavevector). Forψ= 0, the free energy in the velocity shear needs to overcome the magnetic tension, and only super-Alfvénic jets are unstable ( $1<M_e<\sqrt{{(1+{\mathrm{\Gamma }}_w^2)/[1+(v_{\mathrm{A}}/c)}^2{\mathrm{\Gamma }}_w^2]}$, with Γ_wthe wind adiabatic index). Our results have important implications for the propagation and emission of relativistic magnetized jets. 

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3. Stellar Metallicities and Gradients in the Isolated, Quenched Low-mass Galaxy Tucana

   https://doi.org/10.3847/1538-4357/ad25ed  

   Fu, Sal_Wanying; Weisz, Daniel_R; Starkenburg, Else; Martin, Nicolas; Mercado, Francisco_J; Savino, Alessandro; Boylan-Kolchin, Michael; Côté, Patrick; Dolphin, Andrew_E; Longeard, Nicolas; et al (April 2024, The Astrophysical Journal)

   Abstract We measure the metallicities of 374 red giant branch (RGB) stars in the isolated, quenched dwarf galaxy Tucana using Hubble Space Telescope narrowband (F395N) calcium H and K imaging. Our sample is a factor of ∼7 larger than what is available from previous studies. Our main findings are as follows. (i) A global metallicity distribution function (MDF) with $〈\mathrm{[Fe/H]}〉=-{1.55}_{-0.04}^{+0.04}$and ${\sigma }_{\mathrm{[Fe/H]}}={0.54}_{-0.03}^{+0.03}$. (ii) A metallicity gradient of −0.54 ± 0.07 dex $R_e^{-1}$(−2.1 ± 0.3 dex kpc⁻¹) over the extent of our imaging (∼2.5R_e), which is steeper than literature measurements. Our finding is consistent with predicted gradients from the publicly available FIRE-2 simulations, in which bursty star formation creates stellar population gradients and dark matter cores. (iii) Tucana’s bifurcated RGB has distinct metallicities: a blue RGB with $〈\mathrm{[Fe/H]}〉=-{1.78}_{-0.06}^{+0.06}$and ${\sigma }_{\mathrm{[Fe/H]}}={0.44}_{-0.06}^{+0.07}$and a red RGB with $〈\mathrm{[Fe/H]}〉=-{1.08}_{-0.07}^{+0.07}$and ${\sigma }_{\mathrm{[Fe/H]}}={0.42}_{-0.06}^{+0.06}$. (iv) At fixed stellar mass, Tucana is more metal-rich than Milky Way satellites by ∼0.4 dex, but its blue RGB is chemically comparable to the satellites. Tucana’s MDF appears consistent with star-forming isolated dwarfs, though MDFs of the latter are not as well populated. (v) About 2% of Tucana’s stars have [Fe/H] < −3% and 20% have [Fe/H] > −1. We provide a catalog for community spectroscopic follow-up. 

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4. HSTPROMO Internal Proper-motion Kinematics of Dwarf Spheroidal Galaxies. I. Velocity Anisotropy and Dark Matter Cusp Slope of Draco

   https://doi.org/10.3847/1538-4357/ad571c  

   Vitral, Eduardo; van_der_Marel, Roeland_P; Sohn, Sangmo_Tony; Libralato, Mattia; del_Pino, Andrés; Watkins, Laura_L; Bellini, Andrea; Walker, Matthew_G; Besla, Gurtina; Pawlowski, Marcel_S; et al (July 2024, The Astrophysical Journal)

   Abstract We analyze four epochs of Hubble Space Telescope imaging over 18 yr for the Draco dwarf spheroidal galaxy. We measure precise proper motions for hundreds of stars and combine these with existing line-of-sight (LOS) velocities. This provides the first radially resolved 3D velocity dispersion profiles for any dwarf galaxy. These constrain the intrinsic velocity anisotropy and resolve the mass–anisotropy degeneracy. We solve the Jeans equations in oblate axisymmetric geometry to infer the mass profile. We find the velocity dispersion to be radially anisotropic along the symmetry axis and tangentially anisotropic in the equatorial plane, with a globally averaged value $\overline{{\beta }_{\mathrm{B}}}=-{0.20}_{-0.53}^{+0.28}$, (where 1 – ${\beta }_{\mathrm{B}}\equiv 〈v_{\tan }^2〉/〈v_{\mathrm{rad}}^2〉$in 3D). The logarithmic dark matter (DM) density slope over the observed radial range, Γ_dark, is $-{0.83}_{-0.37}^{+0.32}$, consistent with the inner cusp predicted in ΛCDM cosmology. As expected given Draco’s low mass and ancient star formation history, it does not appear to have been dissolved by baryonic processes. We rule out cores larger than 487, 717, and 942 pc at 1σ, 2σ, and 3σconfidence, respectively, thus imposing important constraints on the self-interacting DM cross section. Spherical models yield biased estimates for both the velocity anisotropy and the inferred slope. The circular velocity at our outermost data point (900 pc) is ${24.19}_{-2.97}^{+6.31}\mathrm{km}{\mathrm{s}}^{-1}$. We infer a dynamical distance of ${75.37}_{-4.00}^{+4.73}$kpc and show that Draco has a modest LOS rotation, with $\left(v/\sigma \right)=0.22\pm 0.09$. Our results provide a new stringent test of the so-called “cusp–core” problem that can be readily extended to other dwarfs. 

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5. The reduced ring of the 𝑅𝑂(𝐶₂)-graded 𝐶₂-equivariant stable stems

   https://doi.org/10.1090/bproc/203  

   Belmont, Eva; Xu, Zhouli; Zhang, Shangjie (January 2024, Proceedings of the American Mathematical Society, Series B)

   We describe in terms of generators and relations the ring structure of the $RO\left(C_2\right)$-graded $C_2$-equivariant stable stems ${\mathrm{\pi <\#comment/>}}_{\star <\#comment/>}^{C_2}$modulo the ideal of all nilpotent elements. As a consequence, we also record the ring structure of the homotopy groups of the rational $C_2$-equivariant sphere ${\mathrm{\pi <\#comment/>}}_{\star <\#comment/>}^{C_2}\left({\mathbb{S}}_{\mathbb{Q}}\right)$. 

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