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1. Bounded projections to the Z$$\mathcal {Z}$$‐factor graph

   https://doi.org/10.1112/topo.70024  

   Clay, Matt; Uyanik, Caglar (June 2025, Journal of Topology)

   Abstract Suppose that is a free product , where each of the groups is torsion‐free and is a free group of rank . Let be the deformation space associated to this free product decomposition. We show that the diameter of the projection of the subset of where a given element has bounded length to the ‐factor graph is bounded, where the diameter bound depends only on the length bound. This relies on an analysis of the boundary of as a hyperbolic group relative to the collection of subgroups together with a given nonperipheral cyclic subgroup. The main theorem is new even in the case that , in which case is the Culler–Vogtmann outer space. In a future paper, we will apply this theorem to study the geometry of free group extensions. 

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2. The Pan-STARRS1 z > 5.6 Quasar Survey. III. The z ≈ 6 Quasar Luminosity Function

   https://doi.org/10.3847/1538-4357/aca7ca  

   Schindler, Jan-Torge; Bañados, Eduardo; Connor, Thomas; Decarli, Roberto; Fan, Xiaohui; Farina, Emanuele Paolo; Mazzucchelli, Chiara; Nanni, Riccardo; Rix, Hans-Walter; Stern, Daniel; et al (January 2023, The Astrophysical Journal)

   Abstract We present thez≈ 6 type-1 quasar luminosity function (QLF), based on the Pan-STARRS1 (PS1) quasar survey. The PS1 sample includes 125 quasars atz≈ 5.7–6.2, with −28 ≲M₁₄₅₀≲ −25. With the addition of 48 fainter quasars from the SHELLQs survey, we evaluate thez≈ 6 QLF over −28 ≲M₁₄₅₀≲ −22. Adopting a double power law with an exponential evolution of the quasar density (Φ(z) ∝ 10^k(z−6);k= −0.7), we use a maximum likelihood method to model our data. We find a break magnitude of $M^{*}=-{26.38}_{-0.60}^{+0.79}\mathrm{mag}$, a faint-end slope of $\alpha =-{1.70}_{-0.19}^{+0.29}$, and a steep bright-end slope of $\beta =-{3.84}_{-1.21}^{+0.63}$. Based on our new QLF model, we determine the quasar comoving spatial density atz≈ 6 to be $n(M_{1450}<-26)={1.16}_{-0.12}^{+0.13}{\mathrm{cGpc}}^{-3}$. In comparison with the literature, we find the quasar density to evolve with a constant value ofk≈ −0.7, fromz≈ 7 toz≈ 4. Additionally, we derive an ionizing emissivity of ${ϵ}_{912}(z=6)={7.23}_{-1.02}^{+1.65}\times {10}^{22}\mathrm{erg}{\mathrm{s}}^{-1}{\mathrm{Hz}}^{-1}{\mathrm{cMpc}}^{-3}$, based on the QLF measurement. Given standard assumptions, and the recent measurement of the mean free path by Becker et al. atz≈ 6, we calculate an Hiphotoionizing rate of Γ_{H I}(z= 6) ≈ 6 × 10⁻¹⁶s⁻¹, strongly disfavoring a dominant role of quasars in hydrogen reionization. 

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3. Properties of the Lowest-metallicity Galaxies over the Redshift Range z = 0.2 to z = 1

   https://doi.org/10.3847/1538-4357/ac81c7  

   Laseter, Isaac H.; Barger, Amy J.; Cowie, Lennox L.; Taylor, Anthony J. (August 2022, The Astrophysical Journal)

   Abstract Low-metallicity galaxies may provide key insights into the evolutionary history of galaxies. Galaxies with strong emission lines and high equivalent widths (rest-frame EW(H β ) ≳ 30 Å) are ideal candidates for the lowest-metallicity galaxies to z ∼ 1. Using a Keck/DEIMOS spectral database of about 18,000 galaxies between z = 0.2 and z = 1, we search for such extreme emission-line galaxies with the goal of determining their metallicities. Using the robust direct T e method, we identify eight new extremely metal-poor galaxies (XMPGs) with 12 + log O/H ≤7.65, including one at 6.949 ± 0.091, making it the lowest-metallicity galaxy reported to date at these redshifts. We also improve upon the metallicities for two other XMPGs from previous work. We investigate the evolution of H β using both instantaneous and continuous starburst models, finding that XMPGs are best characterized by continuous starburst models. Finally, we study the dependence on age of the buildup of metals and the emission-line strength. 

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4. The Evolution of Lyα Emitter Line Widths from z = 5.7 to z = 6.6

   https://doi.org/10.3847/1538-4357/ac8051  

   Songaila, A.; Barger, A. J.; Cowie, L. L.; Hu, E. M.; Taylor, A. J. (August 2022, The Astrophysical Journal)

   Abstract Recent evidence suggests that high-redshift Ly α emitting galaxies (LAEs) with log L ( Ly α ) > 43.5 erg s − 1 , referred to as ultraluminous LAEs (ULLAEs), may show less evolution than lower-luminosity LAEs in the redshift range z = 5.7–6.6. Here we explore the redshift evolution of the velocity widths of the Ly α emission lines in LAEs over this redshift interval. We use new wide-field, narrowband observations from Subaru/Hyper Suprime-Cam to provide a sample of 24 z = 6.6 and 12 z = 5.7 LAEs with log L ( Ly α ) > 43 erg s − 1 , all of which have follow-up spectroscopy from Keck/DEIMOS. Combining with archival lower-luminosity data, we find a significant narrowing of the Ly α lines in LAEs at log L ( Ly α ) < 43.25 erg s − 1 —somewhat lower than the usual ULLAE definition—at z = 6.6 relative to those at z = 5.7, but we do not see this in higher-luminosity LAEs. As we move to higher redshifts, the increasing neutrality of the intergalactic medium should increase the scattering of the Ly α lines, making them narrower. The absence of this effect in the higher-luminosity LAEs suggests they may lie in more highly ionized regions, self-shielding from the scattering effects of the intergalactic medium. 

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5. Structure and Formation of Z-DNA and Z-RNA

   https://doi.org/10.3390/molecules28020843  

   Krall, Jeffrey B.; Nichols, Parker J.; Henen, Morkos A.; Vicens, Quentin; Vögeli, Beat (January 2023, Molecules)

   Despite structural differences between the right-handed conformations of A-RNA and B-DNA, both nucleic acids adopt very similar, left-handed Z-conformations. In contrast to their structural similarities and sequence preferences, RNA and DNA exhibit differences in their ability to adopt the Z-conformation regarding their hydration shells, the chemical modifications that promote the Z-conformation, and the structure of junctions connecting them to right-handed segments. In this review, we highlight the structural and chemical properties of both Z-DNA and Z-RNA and delve into the potential factors that contribute to both their similarities and differences. While Z-DNA has been extensively studied, there is a gap of knowledge when it comes to Z-RNA. Where such information is lacking, we try and extend the principles of Z-DNA stability and formation to Z-RNA, considering the inherent differences of the nucleic acids. 

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