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1. The metastable Q 3 Δ 2 state of ThO: a new resource for the ACME electron EDM search

   https://doi.org/10.1088/1367-2630/ab6a3a  

   Wu, X. ; Han, Z. ; Chow, J. ; Ang, D. G. ; Meisenhelder, C. ; Panda, C. D. ; West, E. P. ; Gabrielse, G. ; Doyle, J. M. ; DeMille, D. ( February 2020 , New Journal of Physics)

   The best upper limit for the electron electric dipole moment was recently set by the ACME collaboration. This experiment measures an electron spin-precession in a cold beam of ThO molecules in their metastable$H{(}^3{\mathrm{\Delta }}_1)$state. Improvement in the statistical and systematic uncertainties is possible with more efficient use of molecules from the source and better magnetometry in the experiment, respectively. Here, we report measurements of several relevant properties of the long-lived$Q{(}^3{\mathrm{\Delta }}_2)$state of ThO, and show that this state is a very useful resource for both these purposes. TheQstate lifetime is long enough that its decay during the time of flight in the ACME beam experiment is negligible. The large electric dipole moment measured for theQstate, giving rise to a large linear Stark shift, is ideal for an electrostatic lens that increases the fraction of molecules detected downstream. The measured magnetic moment of theQstate is also large enough to be used as a sensitive co-magnetometer in ACME. Finally, we show that theQstate has a large transition dipole moment to the$C{(}^1{\mathrm{\Pi }}_1)$state, which allows for efficient population transfer between the ground state$X{(}^1{\mathrm{\Sigma }}^{+})$and theQstate via$X-C-Q$Stimulated Raman Adiabatic Passage (STIRAP). We demonstrate 90 % STIRAP transfer efficiency. In the course of these measurements, we also determine the magnetic moment ofCstate, the$X\to C$transition dipole moment, and branching ratios of decays from theCstate.

    

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2. Global existence and singularity formation for the generalized Constantin–Lax–Majda equation with dissipation: the real line vs. periodic domains

   https://doi.org/10.1088/1361-6544/ad140c  

   Ambrose, David M ; Lushnikov, Pavel M ; Siegel, Michael ; Silantyev, Denis A ( December 2023 , Nonlinearity)

   The question of global existence versus finite-time singularity formation is considered for the generalized Constantin–Lax–Majda equation with dissipation$-{\mathrm{\Lambda }}^{\sigma }$, where$\widehat{{\mathrm{\Lambda }}^{\sigma }}=|k{|}^{\sigma }$, both for the problem on the circle$x\in [-\pi ,\pi ]$and the real line. In the periodic geometry, two complementary approaches are used to prove global-in-time existence of solutions for$\sigma \text{⩾}1$and all real values of an advection parameterawhen the data is small. We also derive new analytical solutions in both geometries whena = 0, and on the real line when$a=1/2$, for various values ofσ. These solutions exhibit self-similar finite-time singularity formation, and the similarity exponents and conditions for singularity formation are fully characterized. We revisit an analytical solution on the real line due to Schochet fora = 0 andσ = 2, and reinterpret it terms of self-similar finite-time collapse. The analytical solutions on the real line allow finite-time singularity formation for arbitrarily small data, even for values ofσthat are greater than or equal to one, thereby illustrating a critical difference between the problems on the real line and the circle. The analysis is complemented by accurate numerical simulations, which are able to track the formation and motion of singularities in the complex plane. The computations validate and build upon the analytical theory.

    

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3. Analytic genericity of diffusing orbits in a priori unstable Hamiltonian systems

   https://doi.org/10.1088/1361-6544/ac50bb  

   Chen, Qinbo ; de la Llave, Rafael ( March 2022 , Nonlinearity)

   The genericity of Arnold diffusion in the analytic category is an open problem. In this paper, we study this problem in the followinga prioriunstable Hamiltonian system with a time-periodic perturbation${\mathcal{H}}_{\epsilon }(p,q,I,\phi ,t)=h(I)+\sum _{i=1}^n\pm \left(\frac{1}{2}{p}_i^2+V_i(q_i)\right)+\epsilon H_1(p,q,I,\phi ,t),$where$(p,q)\in {\mathbb{R}}^n\times {\mathbb{T}}^n$,$(I,\phi )\in {\mathbb{R}}^d\times {\mathbb{T}}^d$withn,d⩾ 1,V_iare Morse potentials, andɛis a small non-zero parameter. The unperturbed Hamiltonian is not necessarily convex, and the induced inner dynamics does not need to satisfy a twist condition. Using geometric methods we prove that Arnold diffusion occurs for generic analytic perturbationsH₁. Indeed, the set of admissibleH₁isC^ωdense andC³open (a fortiori,C^ωopen). Our perturbative technique for the genericity is valid in theC^ktopology for allk∈ [3, ∞) ∪ {∞,ω}.

    

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4. Toward Astrometric Constraints on a Supermassive Black Hole Binary in the Early-type Galaxy NGC 4472

   https://doi.org/10.3847/1538-4357/ac680b  

   Wrobel, J. M. ; Lazio, T. J. W. ( May 2022 , The Astrophysical Journal)

   The merger of two galaxies, each hosting a supermassive black hole (SMBH) of mass 10⁶M_⊙or more, could yield a bound SMBH binary. For the early-type galaxy NGC 4472, we study how astrometry with a next-generation Very Large Array could be used to monitor the reflex motion of the primary SMBH of massM_pri, as it is tugged on by the secondary SMBH of mass$M_{\sec }$. Casting the orbit of the putative SMBH binary in terms of its periodP, semimajor axisa_bin, and mass ratio$q=M_{\sec }/M_{\mathrm{pri}}\le 1$, we find the following: (1) Orbits with fiducial periods ofP= 4 yr and 40 yr could be spatially resolved and monitored. (2) For a 95% accuracy of 2μas per monitoring epoch, subparsec values ofa_bincould be accessed over a range of mass ratios notionally encompassing major$\left(q>\frac{1}{4}\right)$and minor$\left(q<\frac{1}{4}\right)$galaxy mergers. (3) If no reflex motion is detected forM_priafter 1 (10) yr of monitoring, an SMBH binary with periodP= 4 (40) yr and mass ratioq> 0.01 (0.003) could be excluded. This would suggest no present-day evidence for a past major merger like that recently simulated, where scouring by aq∼ 1 SMBH binary formed a stellar core with kinematic traits like those of NGC 4472. (4) Astrometric monitoring could independently check the upper limits onqfrom searches for continuous gravitational waves from NGC 4472.

    

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5. The Physical Conditions of Emission-line Galaxies at Cosmic Dawn from JWST/NIRSpec Spectroscopy in the SMACS 0723 Early Release Observations

   https://doi.org/10.3847/1538-4357/acba8a  

   Trump, Jonathan R. ; Arrabal Haro, Pablo ; Simons, Raymond C. ; Backhaus, Bren E. ; Amorín, Ricardo O. ; Dickinson, Mark ; Fernández, Vital ; Papovich, Casey ; Nicholls, David C. ; Kewley, Lisa J. ; et al ( March 2023 , The Astrophysical Journal)

   We present rest-frame optical emission-line flux ratio measurements for fivez> 5 galaxies observed by the James Webb Space Telescope Near-Infared Spectrograph (NIRSpec) in the SMACS 0723 Early Release Observations. We add several quality-control and post-processing steps to the NIRSpec pipeline reduction products in order to ensure reliablerelativeflux calibration of emission lines that are closely separated in wavelength, despite the uncertainabsolutespectrophotometry of the current version of the reductions. Compared toz∼ 3 galaxies in the literature, thez> 5 galaxies have similar [Oiii]λ5008/Hβratios, similar [Oiii]λ4364/Hγratios, and higher (∼0.5 dex) [NeIII]λ3870/[OII]λ3728 ratios. We compare the observations to MAPPINGS V photoionization models and find that the measured [NeIII]λ3870/[OII]λ3728, [Oiii]λ4364/Hγ, and [Oiii]λ5008/Hβemission-line ratios are consistent with an interstellar medium (ISM) that has very high ionization ($\log (Q)\simeq 8-9$, units of cm s⁻¹), low metallicity (Z/Z_⊙≲ 0.2), and very high pressure ($\log (P/k)\simeq 8-9$, units of cm⁻³). The combination of [Oiii]λ4364/Hγand [Oiii]λ(4960 + 5008)/Hβline ratios indicate very high electron temperatures of$4.1<\log (T_e/\mathrm{K})<4.4$, further implying metallicities ofZ/Z_⊙≲ 0.2 with the application of low-redshift calibrations for “T_e-based” metallicities. These observations represent a tantalizing new view of the physical conditions of the ISM in galaxies at cosmic dawn.

    

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