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1. What Does the Geometry of the Hβ BLR Depend On?

   https://doi.org/10.3847/1538-4357/accc84  

   Villafaña, Lizvette; Williams, Peter R.; Treu, Tommaso; Brewer, Brendon J.; Barth, Aaron J.; U, Vivian; Bennert, Vardha N.; Guo, Hengxiao; Bentz, Misty C.; Canalizo, Gabriela; et al (May 2023, The Astrophysical Journal)

   Abstract We combine our dynamical modeling black-hole mass measurements from the Lick AGN Monitoring Project 2016 sample with measured cross-correlation time lags and line widths to recover individual scale factors,f, used in traditional reverberation-mapping analyses. We extend our sample by including prior results from Code for AGN Reverberation and Modeling of Emission Lines (caramel) studies that have utilized our methods. Aiming to improve the precision of black-hole mass estimates, as well as uncover any regularities in the behavior of the broad-line region (BLR), we search for correlations betweenfand other AGN/BLR parameters. We find (i) evidence for a correlation between the virial coefficient ${\log }_{10}\left(f_{\mathrm{mean},\sigma }\right)$and black-hole mass, (ii) marginal evidence for a similar correlation between ${\log }_{10}\left(f_{\mathrm{rms},\sigma }\right)$and black-hole mass, (iii) marginal evidence for an anticorrelation of BLR disk thickness with ${\log }_{10}\left(f_{\mathrm{mean},\mathrm{FWHM}}\right)$and ${\log }_{10}\left(f_{\mathrm{rms},\mathrm{FWHM}}\right)$, and (iv) marginal evidence for an anticorrelation of inclination angle with ${\log }_{10}\left(f_{\mathrm{mean},\mathrm{FWHM}}\right)$, ${\log }_{10}\left(f_{\mathrm{rms},\sigma }\right)$, and ${\log }_{10}\left(f_{\mathrm{mean},\sigma }\right)$. Last, we find marginal evidence for a correlation between line-profile shape, when using the root-mean-square spectrum, ${\log }_{10}{\left(\mathrm{FWHM}/\sigma \right)}_{\mathrm{rms}}$, and the virial coefficient, ${\log }_{10}\left(f_{\mathrm{rms},\sigma }\right)$, and investigate how BLR properties might be related to line-profile shape usingcaramelmodels. 

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2. COOL-LAMPS. VI. Lens Model and New Constraints on the Properties of COOL J1241+2219, a Bright z = 5 Lyman Break Galaxy and its z = 1 Cluster Lens

   https://doi.org/10.3847/1538-4357/ad22de  

   Klein, Maxwell; Sharon, Keren; Napier, Kate; Gladders, Michael D; Khullar, Gourav; Bayliss, Matthew; Dahle, Håkon; Owens, M Riley; Stark, Antony; Brownsberger, Sasha; et al (February 2024, The Astrophysical Journal)

   Abstract We present a strong lensing analysis of COOL J1241+2219, the brightest known gravitationally lensed galaxy atz≥ 5, based on new multiband Hubble Space Telescope (HST) imaging data. The lensed galaxy has a redshift ofz= 5.043, placing it shortly after the end of the “Epoch of Reionization,” and an AB magnitudez_AB= 20.47 mag (Khullar et al.). As such, it serves as a touchstone for future research of that epoch. The high spatial resolution of HST reveals internal structure in the giant arc, from which we identify 15 constraints and construct a robust lens model. We use the lens model to extract the cluster mass and lensing magnification. We find that the mass enclosed within the Einstein radius of thez= 1.001 cluster lens is $M(<5.″77)={1.079}_{-0.007}^{+0.023}\times {10}^{13}{M}_{☉}$, significantly lower than other known strong lensing clusters at its redshift. The average magnification of the giant arc is 〈μ_arc〉 = ${76}_{-20}^{+40}$, a factor of ${2.4}_{-0.7}^{+1.4}$greater than previously estimated from ground-based data; the flux-weighted average magnification is 〈μ_arc〉 = ${92}_{-31}^{+37}$. We update the current measurements of the stellar mass and star formation rate (SFR) of the source for the revised magnification to $\log \left(M_{\star }/M_{\odot }\right)=$9.7 ± 0.3 and SFR = ${10.3}_{-4.4}^{+7.0}$M_⊙yr⁻¹, respectively. The powerful lensing magnification acting upon COOL J1241+2219 resolves the source and enables future studies of the properties of its star formation on a clump-by-clump basis. The lensing analysis presented here will support upcoming multiwavelength characterization with HST and JWST data of the stellar mass assembly and physical properties of this high-redshift lensed galaxy. 

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3. Quantum group intertwiner space from quantum curved tetrahedron

   https://doi.org/10.1088/1361-6382/ad5f71  

   Han, Muxin; Hsiao, Chen-Hung; Pan, Qiaoyin (July 2024, Classical and Quantum Gravity)

   Abstract In this paper, we develop a quantum theory of homogeneously curved tetrahedron geometry, by applying the combinatorial quantization to the phase space of tetrahedron shapes defined in Haggardet al(2016Ann. Henri Poincaré172001–48). Our method is based on the relation between this phase space and the moduli space of SU(2) flat connections on a 4-punctured sphere. The quantization results in the physical Hilbert space as the solution of the quantum closure constraint, which quantizes the classical closure condition $M_4{M}_3{M}_2{M}_1=1$, $M_{\nu }\in \mathrm{SU}\left(2\right)$, for the homogeneously curved tetrahedron. The quantum group $U_q\left(\mathfrak{su}\right(2\left)\right)$emerges as the gauge symmetry of a quantum tetrahedron. The physical Hilbert space of the quantum tetrahedron coincides with the Hilbert space of 4-valent intertwiners of $U_q\left(\mathfrak{su}\right(2\left)\right)$. In addition, we define the area operators quantizing the face areas of the tetrahedron and compute the spectrum. The resulting spectrum is consistent with the usual Loop-Quantum-Gravity area spectrum in the large spin regime but is different for small spins. This work closely relates to 3+1 dimensional Loop Quantum Gravity in presence of cosmological constant and provides a justification for the emergence of quantum group in the theory. 

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4. Characterizing the fundamental bending vibration of a linear polyatomic molecule for symmetry violation searches

   https://doi.org/10.1088/1367-2630/ace471  

   Jadbabaie, Arian; Takahashi, Yuiki; Pilgram, Nickolas H; Conn, Chandler J; Zeng, Yi; Zhang, Chi; Hutzler, Nicholas R (July 2023, New Journal of Physics)

   Abstract Polyatomic molecules have been identified as sensitive probes of charge-parity violating and parity violating physics beyond the Standard Model (BSM). For example, many linear triatomic molecules are both laser-coolable and have parity doublets in the ground electronic $\tilde{X}{}^2{\mathrm{\Sigma }}^{+}\left(010\right)$state arising from the bending vibration, both features that can greatly aid BSM searches. Understanding the $\tilde{X}{}^2{\mathrm{\Sigma }}^{+}\left(010\right)$state is a crucial prerequisite to precision measurements with linear polyatomic molecules. Here, we characterize the fundamental bending vibration of ${}^{174}$YbOH using high-resolution optical spectroscopy on the nominally forbidden $\tilde{X}{}^2{\mathrm{\Sigma }}^{+}\left(010\right)$ $\to \tilde{A}{}^2{\mathrm{\Pi }}_{1/2}\left(000\right)$transition at 588 nm. We assign 39 transitions originating from the lowest rotational levels of the $\tilde{X}{}^2{\mathrm{\Sigma }}^{+}\left(010\right)$state, and accurately model the state’s structure with an effective Hamiltonian using best-fit parameters. Additionally, we perform Stark and Zeeman spectroscopy on the $\tilde{X}{}^2{\mathrm{\Sigma }}^{+}\left(010\right)$state and fit the molecule-frame dipole moment to $D_{\mathrm{m}\mathrm{o}\mathrm{l}}=2.16\left(1\right)$Dand the effective electrong-factor to $g_S=2.07\left(2\right)$. Further, we use an empirical model to explain observed anomalous line intensities in terms of interference from spin–orbit and vibronic perturbations in the excited $\tilde{A}{}^2{\mathrm{\Pi }}_{1/2}\left(000\right)$state. Our work is an essential step toward searches for BSM physics in YbOH and other linear polyatomic molecules. 

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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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