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1. SN 2023ixf in Messier 101: A Variable Red Supergiant as the Progenitor Candidate to a Type II Supernova

   https://doi.org/10.3847/2041-8213/ace4ca  

   Kilpatrick, Charles D.; Foley, Ryan J.; Jacobson-Galán, Wynn V.; Piro, Anthony L.; Smartt, Stephen J.; Drout, Maria R.; Gagliano, Alexander; Gall, Christa; Hjorth, Jens; Jones, David O.; et al (July 2023, The Astrophysical Journal Letters)

   Abstract We present preexplosion optical and infrared (IR) imaging at the site of the type II supernova (SN II) 2023ixf in Messier 101 at 6.9 Mpc. We astrometrically registered a ground-based image of SN 2023ixf to archival Hubble Space Telescope (HST), Spitzer Space Telescope (Spitzer), and ground-based near-IR images. A single point source is detected at a position consistent with the SN at wavelengths ranging from HSTRband to Spitzer 4.5μm. Fitting with blackbody and red supergiant (RSG) spectral energy distributions (SEDs), we find that the source is anomalously cool with a significant mid-IR excess. We interpret this SED as reprocessed emission in a 8600R_⊙circumstellar shell of dusty material with a mass ∼5 × 10⁻⁵M_⊙surrounding a $\log \left(L/L_{\odot }\right)=4.74\pm 0.07$and $T_{\mathrm{eff}}={3920}_{-160}^{+200}$K RSG. This luminosity is consistent with RSG models of initial mass 11M_⊙, depending on assumptions of rotation and overshooting. In addition, the counterpart was significantly variable in preexplosion Spitzer 3.6 and 4.5μm imaging, exhibiting ∼70% variability in both bands correlated across 9 yr and 29 epochs of imaging. The variations appear to have a timescale of 2.8 yr, which is consistent withκ-mechanism pulsations observed in RSGs, albeit with a much larger amplitude than RSGs such asαOrionis (Betelgeuse). 

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2. The Preexplosion Environments and the Progenitor of SN 2023ixf from the Hobby–Eberly Telescope Dark Energy Experiment (HETDEX)

   https://doi.org/10.3847/2041-8213/ad0da8  

   Liu, Chenxu; Chen, Xinlei; Er, Xinzhong; Zeimann, Gregory R; Vinkó, József; Wheeler, J Craig; Cooper, Erin Mentuch; Davis, Dustin; Farrow, Daniel J; Gebhardt, Karl; et al (November 2023, The Astrophysical Journal Letters)

   Abstract Supernova (SN) 2023ixf was discovered on 2023 May 19. The host galaxy, M101, was observed by the Hobby–Eberly Telescope Dark Energy Experiment collaboration over the period 2020 April 30–2020 July 10, using the Visible Integral-field Replicable Unit Spectrograph (3470 ≲λ≲ 5540 Å) on the 10 m Hobby–Eberly Telescope. The fiber filling factor within ±30″ of SN 2023ixf is 80% with a spatial resolution of 1″. Ther< 5.″5 surroundings are 100% covered. This allows us to analyze the spatially resolved preexplosion local environments of SN 2023ixf with nebular emission lines. The two-dimensional maps of the extinction and the star formation rate (SFR) surface density (Σ_SFR) show weak increasing trends in the radial distributions within ther< 5.″5 regions, suggesting lower values of extinction and SFR in the vicinity of the progenitor of SN 2023ixf. The median extinction and that of the surface density of SFR withinr< 3″ areE(B−V) = 0.06 ± 0.14, and ${\mathrm{\Sigma }}_{\mathrm{SFR}}={10}^{-5.44\pm 0.66}{M}_{☉}{\mathrm{yr}}^{-1}{\mathrm{arcsec}}^{-2}.$There is no significant change in extinction before and after the explosion. The gas metallicity does not change significantly with the separation from SN 2023ixf. The metal-rich branch of theR₂₃calculations indicates that the gas metallicity around SN 2023ixf is similar to the solar metallicity (∼Z_☉). The archival deep images from the Canada–France–Hawaii Telescope Legacy Survey (CFHTLS) show a clear detection of the progenitor of SN 2023ixf in thezband at 22.778 ± 0.063 mag, but nondetections in the remaining four bands of CFHTLS (u,g,r,i). The results suggest a massive progenitor of ≈22M_☉. 

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3. SN 2023ixf in Messier 101: Photo-ionization of Dense, Close-in Circumstellar Material in a Nearby Type II Supernova

   https://doi.org/10.3847/2041-8213/acf2ec  

   Jacobson-Galán, W. V.; Dessart, L.; Margutti, R.; Chornock, R.; Foley, R. J.; Kilpatrick, C. D.; Jones, D. O.; Taggart, K.; Angus, C. R.; Bhattacharjee, S.; et al (September 2023, The Astrophysical Journal Letters)

   Abstract We present UV and/or optical observations and models of SN 2023ixf, a type II supernova (SN) located in Messier 101 at 6.9 Mpc. Early time (flash) spectroscopy of SN 2023ixf, obtained primarily at Lick Observatory, reveals emission lines of Hi, Hei/ii, Civ, and Niii/iv/vwith a narrow core and broad, symmetric wings arising from the photoionization of dense, close-in circumstellar material (CSM) located around the progenitor star prior to shock breakout. These electron-scattering broadened line profiles persist for ∼8 days with respect to first light, at which time Doppler broadened the features from the fastest SN ejecta form, suggesting a reduction in CSM density atr≳ 10¹⁵cm. The early time light curve of SN 2023ixf shows peak absolute magnitudes (e.g.,M_u= −18.6 mag,M_g= −18.4 mag) that are ≳2 mag brighter than typical type II SNe, this photometric boost also being consistent with the shock power supplied from CSM interaction. Comparison of SN 2023ixf to a grid of light-curve and multiepoch spectral models from the non-LTE radiative transfer codeCMFGENand the radiation-hydrodynamics codeHERACLESsuggests dense, solar-metallicity CSM confined tor= (0.5–1) × 10¹⁵cm, and a progenitor mass-loss rate of $\dot{M}={10}^{-2}{M}_{\odot }$yr⁻¹. For the assumed progenitor wind velocity ofv_w= 50 km s⁻¹, this corresponds to enhanced mass loss (i.e.,superwindphase) during the last ∼3–6 yr before explosion. 

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4. SN 2024ggi in NGC 3621: Rising Ionization in a Nearby, Circumstellar-material-interacting Type II Supernova

   https://doi.org/10.3847/1538-4357/ad5c64  

   Jacobson-Galán, W V; Davis, K W; Kilpatrick, C D; Dessart, L; Margutti, R; Chornock, R; Foley, R J; Arunachalam, P; Auchettl, K; Bom, C R; et al (September 2024, The Astrophysical Journal)

   Abstract We present UV–optical–near-infrared observations and modeling of supernova (SN) 2024ggi, a type II supernova (SN II) located in NGC 3621 at 7.2 Mpc. Early-time (“flash”) spectroscopy of SN 2024ggi within +0.8 days of discovery shows emission lines of Hi, Hei, Ciii, and Niiiwith a narrow core and broad, symmetric wings (i.e., “IIn-like”) arising from the photoionized, optically thick, unshocked circumstellar material (CSM) that surrounded the progenitor star at shock breakout (SBO). By the next spectral epoch at +1.5 days, SN 2024ggi showed a rise in ionization as emission lines of Heii, Civ, Niv/v, and Ovbecame visible. This phenomenon is temporally consistent with a blueward shift in the UV–optical colors, both likely the result of SBO in an extended, dense CSM. The IIn-like features in SN 2024ggi persist on a timescale oft_IIn= 3.8 ± 1.6 days, at which time a reduction in CSM density allows the detection of Doppler-broadened features from the fastest SN material. SN 2024ggi has peak UV–optical absolute magnitudes ofM_w2= −18.7 mag andM_g= −18.1 mag, respectively, that are consistent with the known population of CSM-interacting SNe II. Comparison of SN 2024ggi with a grid of radiation hydrodynamics and non–local thermodynamic equilibrium radiative-transfer simulations suggests a progenitor mass-loss rate of $\dot{M}={10}^{-2}{M}_{\odot }$yr⁻¹(v_w= 50 km s⁻¹), confined to a distance ofr< 5 × 10¹⁴cm. Assuming a wind velocity ofv_w= 50 km s⁻¹, the progenitor star underwent an enhanced mass-loss episode in the last ∼3 yr before explosion. 

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5. On a Traveling Salesman Problem for Points in the Unit Cube

   https://doi.org/10.1007/s00453-024-01257-w  

   Balogh, József; Clemen, Felix Christian; Dumitrescu, Adrian (September 2024, Algorithmica)

   Abstract LetXbe ann-element point set in thek-dimensional unit cube$$[0,1]^k$$ ${[0,1]}^k$where$$k \ge 2$$ $k\ge 2$. According to an old result of Bollobás and Meir (Oper Res Lett 11:19–21, 1992) , there exists a cycle (tour)$$x_1, x_2, \ldots , x_n$$ $x_1,x_2,\dots ,x_n$through thenpoints, such that$$\left( \sum _{i=1}^n |x_i - x_{i+1}|^k \right) ^{1/k} \le c_k$$ ${\left({\sum }_{i=1}^n,{|x_i-x_{i+1}|}^k\right)}^{1/k}\le c_k$, where$$|x-y|$$ $|x-y|$is the Euclidean distance betweenxandy, and$$c_k$$ $c_k$is an absolute constant that depends only onk, where$$x_{n+1} \equiv x_1$$ $x_{n+1}\equiv x_1$. From the other direction, for every$$k \ge 2$$ $k\ge 2$and$$n \ge 2$$ $n\ge 2$, there existnpoints in$$[0,1]^k$$ ${[0,1]}^k$, such that their shortest tour satisfies$$\left( \sum _{i=1}^n |x_i - x_{i+1}|^k \right) ^{1/k} = 2^{1/k} \cdot \sqrt{k}$$ ${\left({\sum }_{i=1}^n,{|x_i-x_{i+1}|}^k\right)}^{1/k}=2^{1/k}·\sqrt{k}$. For the plane, the best constant is$$c_2=2$$ $c_2=2$and this is the only exact value known. Bollobás and Meir showed that one can take$$c_k = 9 \left( \frac{2}{3} \right) ^{1/k} \cdot \sqrt{k}$$ $c_k=9{\left(\frac{2}{3}\right)}^{1/k}·\sqrt{k}$for every$$k \ge 3$$ $k\ge 3$and conjectured that the best constant is$$c_k = 2^{1/k} \cdot \sqrt{k}$$ $c_k=2^{1/k}·\sqrt{k}$, for every$$k \ge 2$$ $k\ge 2$. Here we significantly improve the upper bound and show that one can take$$c_k = 3 \sqrt{5} \left( \frac{2}{3} \right) ^{1/k} \cdot \sqrt{k}$$ $c_k=3\sqrt{5}{\left(\frac{2}{3}\right)}^{1/k}·\sqrt{k}$or$$c_k = 2.91 \sqrt{k} \ (1+o_k(1))$$ $c_k=2.91\sqrt{k}(1+o_k\left(1\right))$. Our bounds are constructive. We also show that$$c_3 \ge 2^{7/6}$$ $c_3\ge 2^{7/6}$, which disproves the conjecture for$$k=3$$ $k=3$. Connections to matching problems, power assignment problems, related problems, including algorithms, are discussed in this context. A slightly revised version of the Bollobás–Meir conjecture is proposed. 

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