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A sizable fraction of the heavy elements synthesized by stars in galaxies condenses into sub-micron-sized solid-state particles, known as dust grains. Dust produces a wavelength-dependent attenuation, $A_\lambda$, of the galaxy emission, thereby significantly altering its observed properties. Locally, $A_\lambda$ is in general the sum of a power-law and a UV feature ('bump') produced by small, carbon-based grains. However, scant information exists regarding its evolution across cosmic time. Here, leveraging data from 173 galaxies observed by the James Webb Space Telescope in the redshift range z = 2 - 12, we report the most distant detection of the UV bump in a z ~ 7.55 galaxy (when the Universe was only ~ 700 Myr old), and show for the first time that the power-law slope and the bump strength decrease towards high redshifts. We propose that the flat $A_\lambda$ shape at early epochs is produced by large grains newly formed in supernova ejecta, which act as the main dust factories at such early epochs. Importantly, these grains have undergone minimal reprocessing in the interstellar medium due to the limited available cosmic time. This discovery opens new perspectives in the study of cosmic dust origin and evolution., Comment: 16 pages, 5 figures

Attenuation curves in galaxies depend on dust chemical composition, content, and grain size distribution. Such parameters are related to intrinsic galaxy properties such as metallicity, star formation rate, and stellar age. Due to the lack of observational constraints at high redshift, dust empirical curves measured in the local Universe (e.g. Calzetti and SMC curves) have been employed to describe the dust attenuation at early epochs. We exploit the high sensitivity and spectral resolution of the JWST to constrain the dust attenuation curves in high-z galaxies. Our goals are to check whether dust attenuation curves evolve with redshift and quantify the dependence of the inferred galaxy properties on the assumed dust attenuation law. We develop a modified version of the SED fitting code BAGPIPES by including a detailed dust attenuation curve parametrization. Dust parameters are derived, along with galaxy properties, from the fit to the data from FUV to mm bands. Once applied to three star-forming galaxies at z = 7-8, we find that their attenuation curves differ from local templates. One out of three galaxies shows a characteristic MW bump, typically associated to the presence of small carbonaceous dust grains such as PAHs. This is one of the first evidences suggesting the presence of PAHs in early galaxies. Galaxy properties such as stellar mass and SFR inferred from SED fitting are strongly affected by the assumed attenuation curve, though the adopted star formation history also plays a major role. Our results highlight the importance of accounting for the potential diversity of dust attenuation laws when analyzing the properties of galaxies at the EoR, whose dust properties are still poorly understood. The application of our method to a larger sample of galaxies observed with JWST can provide us important insights into the properties of dust and galaxies in the early universe., Comment: 19 pages, 10 figures

Recent ALMA large surveys unveiled the presence of significant dust continuum emission in star-forming galaxies at $z>4$. Unfortunately, such large programs -- i.e. ALPINE ($z\sim 5$) and REBELS ($z \sim 7$) -- only provide us with a single Far-Infrared (FIR) continuum data point for their individual targets. Therefore, high-$z$ galaxies FIR spectral energy densities (SEDs) remain mostly unconstrained, hinging on an assumption for their dust temperature ($T_{\rm d}$) in the SED fitting procedure. This introduces uncertainties in the inferred dust masses ($M_{\rm d }$), infrared luminosities ($L_{\rm IR}$), and obscured Star Formation Rate (SFR) fraction at $z > 4$. In this work we use a method that allows us to constrain $T_{\rm d}$ with a single band measurement by combining the $158\ \mathrm{\mu m}$ continuum information with the overlying [CII] emission line. We analyse the $21$ [CII] and FIR continuum detected $z\sim 5$ galaxies in ALPINE, finding a range of $T_{\rm d}=25-60\ \mathrm{K}$ and $M_{\rm d} = 0.6-25.1\ \times 10^{7}\ \mathrm{M_{\odot}}$. Given the measured stellar masses of ALPINE galaxies, the inferred dust yields are around $M_{\rm d}/M_{\star} = (0.2-8) \times 10^{-3}$, consistent with theoretical dust-production constraints. We find that $8$ out of $21$ ALPINE galaxies have $L_{\rm IR} \geq 10^{12}\ \mathrm{L_{\odot}}$, comparable to UltraLuminous IR Galaxies (ULIRGs). Relying on ultraviolet-to-optical SED fitting, the SFR was underestimated by up to $2$ orders of magnitude in $4$ of these $8$ ULIRGs-like galaxies. We conclude that these $4$ peculiar sources should be characterised by a two-phase interstellar medium structure with "spatially-segregated" FIR and ultraviolet emitting regions., Comment: Accepted for publication in MNRAS. 13 pages, 4 figures

In this paper, we identify many important properties and develop criteria for the existence of subquasigroups in finite quasigroups. Based on these results, we propose an effective method that concludes the nonexistence of subquasigroup of a finite quasigroup, otherwise finds its all possible proper subquasigroups. This has an important application in checking the cryptographic suitability of a finite quasigroup. \par Further, we propose a binary operation using arithmetic of finite fields to construct quasigroups of order $p^r$. We develop the criteria under which these quasigroups have desirable cryptographic properties, viz. polynomially completeness and possessing no proper subquasigroups. Then a practical method is given to construct cryptographically suitable quasigroups. We also illustrate these methods by some academic examples and implement all proposed algorithms in the computer algebra system {\sc{Singular}}.