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1. Discovery and Spectroscopic Confirmation of Aquarius III: A Low-mass Milky Way Satellite Galaxy

   https://doi.org/10.3847/1538-4357/ad8eba  

   Cerny, W; Chiti, A; Geha, M; Mutlu-Pakdil, B; Drlica-Wagner, A; Tan, C Y; Adamów, M; Pace, A B; Simon, J D; Sand, D J; et al (January 2025, The Astrophysical Journal)

   Abstract We present the discovery of Aquarius III, an ultra-faint Milky Way satellite galaxy identified in the second data release of the DECam Local Volume Exploration survey. Based on deeper follow-up imaging with DECam, we find that Aquarius III is a low-luminosity ( $M_V=-{2.5}_{-0.5}^{+0.3};$ $L_V={850}_{-260}^{+380}{L}_{\odot }$), extended ( $r_{1/2}={41}_{-8}^{+9}$pc) stellar system located in the outer halo (D_⊙= 85 ± 4 kpc). From medium-resolution Keck/DEIMOS spectroscopy, we identify 11 member stars and measure a mean heliocentric radial velocity of $v_{\mathrm{sys}}=-{13.1}_{-0.9}^{+1.0}\mathrm{km}{\mathrm{s}}^{-1}$for the system and place an upper limit ofσ_v< 3.5 km s⁻¹(σ_v< 1.6 km s⁻¹) on its velocity dispersion at the 95% (68%) credible level. Based on calcium-triplet metallicities of the six brightest red giant members, we find that Aquarius III is very metal-poor ([Fe/H]= − 2.61 ± 0.21) with a statistically significant metallicity spread ( ${\sigma }_{\left[\mathrm{Fe}/\mathrm{H}\right]}={0.46}_{-0.14}^{+0.26}$dex). We interpret this metallicity spread as strong evidence that the system is a dwarf galaxy as opposed to a star cluster. Combining our velocity measurement with Gaia proper motions, we find that Aquarius III is currently situated near its orbital pericenter in the outer halo (r_peri= 78 ± 7 kpc) and that it is plausibly on first infall onto the Milky Way. This orbital history likely precludes significant tidal disruption from the Galactic disk, notably unlike other satellites with comparably low velocity dispersion limits in the literature. Thus, if further velocity measurements confirm that its velocity dispersion is truly belowσ_v≲ 2 km s⁻¹, Aquarius III may serve as a useful laboratory for probing galaxy formation physics in low-mass halos. 

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2. KMT-2022-BLG-0086: Another Binary-lens Binary-source Microlensing Event

   https://doi.org/10.3847/1538-3881/ade2e7  

   Chung, Sun-Ju; Hwang, Kyu-Ha; Yee, Jennifer C; Gould, Andrew; Bond, Ian A; Yang, Hongjing; Albrow, Michael D; Jung, Youn Kil; Han, Cheongho; Ryu, Yoon-Hyun; et al (July 2025, The Astronomical Journal)

   Abstract We present the analysis of a microlensing event KMT-2022-BLG-0086 of which the overall light curve is not described by a binary-lens single-source (2L1S) model, which suggests the existence of an extra lens or an extra source. We found that the event is best explained by the binary-lens binary-source (2L2S) model, but the 2L2S model is only favored over the triple-lens single-source (3L1S) model by Δχ² ≃ 9. Although the event has noticeable anomalies around the peak of the light curve, they are not enough covered to constrain the angular Einstein radiusθ_E, thus we only measure the minimum angular Einstein radius ${\theta }_{\mathrm{E},\min }$. From the Bayesian analysis, it is found that that the binary lens system is a binary star with masses of $(m_1,m_2)=(0.46_{-0.25}^{+0.35}{M}_{\odot },0.75_{-0.55}^{+0.67}{M}_{\odot })$at a distance of $D_{\mathrm{L}}=5.87_{-1.79}^{+1.21}$kpc, while the triple lens system is a brown dwarf or a massive giant planet in a low-mass binary-star system with masses of $(m_1,m_2,m_3)=(0.43_{-0.35}^{+0.41}{M}_{\odot },0.056_{-0.047}^{+0.055}{M}_{\odot }$, $20.84_{-17.04}^{+20.20}{M}_{\mathrm{J}})$at a distance of $D_{\mathrm{L}}=4.06_{-3.28}^{+1.39}$kpc, indicating a disk lens system. The 2L2S model yields the relative lens-source proper motion ofμ_rel ≥ 4.6 mas yr⁻¹that is consistent with the Bayesian result, whereas the 3L1S model yieldsμ_rel ≥ 18.9 mas yr⁻¹, which is more than three times larger than that of a typical disk object of ∼6 mas yr⁻¹and thus is not consistent with the Bayesian result. This suggests that the event is likely caused by the binary-lens binary-source model. 

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3. 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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4. Ordinary modules for vertex algebras of 𝔬𝔰𝔭 _1|2𝑛

   https://doi.org/10.1515/crelle-2024-0060  

   Creutzig, Thomas; Genra, Naoki; Linshaw, Andrew (August 2024, Journal für die reine und angewandte Mathematik (Crelles Journal))

   Abstract We show that the affine vertex superalgebra $V^k\left(\mathfrak{o}\mathfrak{s}{\mathfrak{p}}_{1|2n}\right)$V^{k}(\mathfrak{osp}_{1|2n})at generic level 𝑘 embeds in the equivariant 𝒲-algebra of $\mathfrak{s}{\mathfrak{p}}_{2n}$\mathfrak{sp}_{2n}times $4n$4nfree fermions.This has two corollaries:(1) it provides a new proof that, for generic 𝑘, the coset $\mathrm{Com}(V^k\left(\mathfrak{s}{\mathfrak{p}}_{2n}\right),V^k\left(\mathfrak{o}\mathfrak{s}{\mathfrak{p}}_{1|2n}\right))$\operatorname{Com}(V^{k}(\mathfrak{sp}_{2n}),V^{k}(\mathfrak{osp}_{1|2n}))is isomorphic to ${\mathcal{W}}^{\mathrm{\ell }}\left(\mathfrak{s}{\mathfrak{p}}_{2n}\right)$\mathcal{W}^{\ell}(\mathfrak{sp}_{2n})for $\mathrm{\ell }=-\left(n+1\right)+\left(k+n+1\right)/\left(2k+2n+1\right)$\ell=-(n+1)+(k+n+1)/(2k+2n+1), and(2) we obtain the decomposition of ordinary $V^k\left(\mathfrak{o}\mathfrak{s}{\mathfrak{p}}_{1|2n}\right)$V^{k}(\mathfrak{osp}_{1|2n})-modules into $V^k\left(\mathfrak{s}{\mathfrak{p}}_{2n}\right)\otimes {\mathcal{W}}^{\mathrm{\ell }}\left(\mathfrak{s}{\mathfrak{p}}_{2n}\right)$V^{k}(\mathfrak{sp}_{2n})\otimes\mathcal{W}^{\ell}(\mathfrak{sp}_{2n})-modules.Next, if 𝑘 is an admissible level and ℓ is a non-degenerate admissible level for $\mathfrak{s}{\mathfrak{p}}_{2n}$\mathfrak{sp}_{2n}, we show that the simple algebra $L_k\left(\mathfrak{o}\mathfrak{s}{\mathfrak{p}}_{1|2n}\right)$L_{k}(\mathfrak{osp}_{1|2n})is an extension of the simple subalgebra $L_k\left(\mathfrak{s}{\mathfrak{p}}_{2n}\right)\otimes {\mathcal{W}}_{\mathrm{\ell }}\left(\mathfrak{s}{\mathfrak{p}}_{2n}\right)$L_{k}(\mathfrak{sp}_{2n})\otimes{\mathcal{W}}_{\ell}(\mathfrak{sp}_{2n}).Using the theory of vertex superalgebra extensions, we prove that the category of ordinary $L_k\left(\mathfrak{o}\mathfrak{s}{\mathfrak{p}}_{1|2n}\right)$L_{k}(\mathfrak{osp}_{1|2n})-modules is a semisimple, rigid vertex tensor supercategory with only finitely many inequivalent simple objects.It is equivalent to a certain subcategory of ${\mathcal{W}}_{\mathrm{\ell }}\left(\mathfrak{s}{\mathfrak{p}}_{2n}\right)$\mathcal{W}_{\ell}(\mathfrak{sp}_{2n})-modules.A similar result also holds for the category of Ramond twisted modules.Due to a recent theorem of Robert McRae, we get as a corollary that categories of ordinary $L_k\left(\mathfrak{s}{\mathfrak{p}}_{2n}\right)$L_{k}(\mathfrak{sp}_{2n})-modules are rigid. 

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5. Jacobian determinants for nonlinear gradient of planar ∞-harmonic functions and applications

   https://doi.org/10.1515/crelle-2024-0016  

   Dong, Hongjie; Peng, Fa; Zhang, Yi Ru-Ya; Zhou, Yuan (April 2024, Journal für die reine und angewandte Mathematik (Crelles Journal))

   Abstract We introduce a distributional Jacobian determinant $detD{V}_{\beta }\left(Dv\right)$\det DV_{\beta}(Dv)in dimension two for the nonlinear complex gradient $V_{\beta }\left(Dv\right)={\left|Dv\right|}^{\beta }(v_{x_1},-v_{x_2})$V_{\beta}(Dv)=\lvert Dv\rvert^{\beta}(v_{x_{1}},-v_{x_{2}})for any $\beta >-1$\beta>-1, whenever $v\in W_{\mathrm{loc}}^{1,2}$v\in W^{1\smash{,}2}_{\mathrm{loc}}and $\beta {\left|Dv\right|}^{1+\beta }\in W_{\mathrm{loc}}^{1,2}$\beta\lvert Dv\rvert^{1+\beta}\in W^{1\smash{,}2}_{\mathrm{loc}}.This is new when $\beta \ne 0$\beta\neq 0.Given any planar ∞-harmonic function 𝑢, we show that such distributional Jacobian determinant $detD{V}_{\beta }\left(Du\right)$\det DV_{\beta}(Du)is a nonnegative Radon measure with some quantitative local lower and upper bounds.We also give the following two applications. Applying this result with $\beta =0$\beta=0, we develop an approach to build up a Liouville theorem, which improves that of Savin.Precisely, if 𝑢 is an ∞-harmonic function in the whole ${\mathbb{R}}^2$\mathbb{R}^{2}with $\underset{R\to \mathrm{\infty }}{lim\; inf}\underset{c\in \mathbb{R}}{inf}\frac{1}{R}{⨍}_{B(0,R)}\left|u\left(x\right)-c\right|dx<\mathrm{\infty },$\liminf_{R\to\infty}\inf_{c\in\mathbb{R}}\frac{1}{R}\barint_{B(0,R)}\lvert u(x)-c\rvert\,dx<\infty,then $u=b+a\cdot x$u=b+a\cdot xfor some $b\in \mathbb{R}$b\in\mathbb{R}and $a\in {\mathbb{R}}^2$a\in\mathbb{R}^{2}.Denoting by $u_p$u_{p}the 𝑝-harmonic function having the same nonconstant boundary condition as 𝑢, we show that $detD{V}_{\beta }\left(D{u}_p\right)\to detD{V}_{\beta }\left(Du\right)$\det DV_{\beta}(Du_{p})\to\det DV_{\beta}(Du)as $p\to \mathrm{\infty }$p\to\inftyin the weak-⋆ sense in the space of Radon measure.Recall that $V_{\beta }\left(D{u}_p\right)$V_{\beta}(Du_{p})is always quasiregular mappings, but $V_{\beta }\left(Du\right)$V_{\beta}(Du)is not in general. 

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