arXiv subjects

Yuxin Lin

Publications and source records attributed to Yuxin Lin.

At least 55 records · Page 3Linked to original sources

arXiv2024

Massive clumps in W43-main: Structure formation in an extensively shocked molecular cloud

W43-main is a massive molecular complex located at the interaction of the Scutum arm and the Galactic bar undergoing starburst activities. We aim to investigate the gas dynamics, in particular, the prevailing shock signatures from the cloud to clump scale and assess the impact of shocks on the formation of dense gas and early-stage cores. We have carried out NOEMA and IRAM-30m observations at 3 mm with an angular resolution of $\sim$0.1 pc towards five massive clumps in W43 main. We use CH$_{3}$CCH and H$_{2}$CS lines to trace the extended gas temperature and CH$_{3}$OH lines to probe the volume density of the dense gas ($\gtrsim$10$^{5}$ cm$^{-3}$). The emission of SiO (2-1) is extensive across the region ($\sim$4 pc) and is mostly contained within a low-velocity regime, hinting at a large-scale origin of the shocks. The position-velocity maps of multiple tracers show systematic spatio-kinematic offsets supporting the cloud-cloud collision/merging scenario. We identify an additional extended velocity component in CCH emission, which coincides with one of the velocity components of the larger scale $^{13}$CO (2-1) emission, likely representing an outer, less dense gas layer in the cloud merging process. We find that the V-shaped, asymmetric SiO wings are tightly correlated with localised gas density enhancements, which is direct evidence of dense gas formation and accumulation in shocks. We resolve two categories of NH$_{2}$D cores: ones exhibiting only subsonic to transonic velocity dispersion, and the others with an additional supersonic velocity dispersion. The centroid velocities of the latter cores are correlated with the shock front seen by SiO. The kinematics of the $\sim$0.1 pc NH$_{2}$D cores are heavily imprinted by shock activities, and may represent a population of early-stage cores forming around the shock interface.

astro-ph.GA↗

arXiv2023

Abelian covers of $\mathbb{P}^1$ of $p$-ordinary Ekedahl-Oort type

Given a family of abelian covers of $\mathbb{P}^1$ and a prime $p$ of good reduction, by considering the associated Deligne--Mostow Shimura variety, we obtain lower bounds for the Ekedahl-Oort type, and the Newton polygon, at $p$ of the curves in the family. In this paper, we investigate whether such lower bounds are sharp. In particular, we prove sharpness when the number of branching points is at most five and $p$ sufficiently large. Our result is a generalization under stricter assumptions of [2, Theorem 6.1] by Bouw, which proves the analogous statement for the $p$-rank, and it relies on the notion of Hasse-Witt triple introduced by Moonen in [9].

math.AG↗

arXiv2023

Initial conditions of star formation at $\lesssim$2000 au: physical structure and NH$_{3}$ depletion of three early-stage cores

Pre-stellar cores represent a critical evolutionary phase in low-mass star formation. We aim to unveil the detailed thermal structure and density distribution of three early-stage cores, starless core L1517B, and prestellar core L694-2 and L429, with the high angular resolution observations of the NH$_{3}$ (1,1) and (2,2) inversion transitions obtained with VLA and GBT. In addition, we explore where/if NH$_{3}$ depletes in the central regions. Applying the mid-infrared extinction method to the $\textit{Spitzer}$ 8$~μ$m map we obtain a high angular resolution hydrogen column density map, and derive the gas density profile to assess the variation of NH$_{3}$ abundance as a function of gas volume density. The measured temperature profiles of L429 and L1517B show a minor decrease towards the core center, dropping from $\sim$9K to below 8K, and $\sim$11 K to 10 K, while L694-2 has a rather uniform temperature distribution around $\sim$9 K. Among the three cores, L429 has the highest central gas density, close to sonic velocity line-width, and largest localised velocity gradient, all indicative of an advanced evolutionary stage. We resolve that the abundance of NH$_{3}$ becomes two times lower in the central region of L429, occurring around a gas density of 4.4$\times$10$^{4}$$~cm^{-3}$. Compared to Ophiuchus/H-MM1 which shows an even stronger drop of the NH$_{3}$ abundance at 2$\times$10$^{5}$$~cm^{-3}$, the abundance variations of the three cores plus Ophiuchus/H-MM1 suggest a progressive NH$_{3}$ depletion with increasing central density of the core.

astro-ph.GA↗

arXiv2023

Simulated observations of star formation regions: infrared evolution of globally collapsing clouds

The direct comparison between hydrodynamical simulations and observations is needed to improve the physics included in the former and test biases in the latter. Post-processing radiative transfer and synthetic observations are now the standard way to do this. We report on the first application of the \texttt{SKIRT} radiative transfer code to simulations of a star-forming cloud. The synthetic observations are then analyzed following traditional observational workflows. We find that in the early stages of the simulation, stellar radiation is inefficient in heating dust to the temperatures observed in Galactic clouds, thus the addition of an interstellar radiation field is necessary. The spectral energy distribution of the cloud settles rather quickly after $\sim3$ Myr of evolution from the onset of star formation, but its morphology continues to evolve for $\sim8$ Myr due to the expansion of \textsc{Hii} regions and the respective creation of cavities, filaments, and ridges. Modeling synthetic \textit{Herschel} fluxes with 1- or 2-component modified black bodies underestimates total dust masses by a factor of $\sim2$. Spatially-resolved fitting recovers up to about $70\%$ of the intrinsic value. This ``missing mass'' is located in a very cold dust component with temperatures below $10$ K, which does not contribute appreciably to the far-infrared flux. This effect could bias real observations if such dust exists in large amounts. Finally, we tested observational calibrations of the SFR based on infrared fluxes and concluded that they are in agreement when compared to the intrinsic SFR of the simulation averaged over $\sim100$ Myr.

astro-ph.GA↗

arXiv2023

Denisty questions in rings of the form $\mathcal{O}_K[γ]\cap K$

We fix a number field $K$ and study statistical properties of the ring $\mathcal{O}_K[γ]\cap K$ as $γ$ varies over algebraic numbers of a fixed degree $n\geq 2$. Given $k\geq 1$, we explicitly compute the density of $γ$ for which $\mathcal{O}_K[γ]\cap K =\mathcal{O}_K[1/k]$ and show that this does not depend on the number field $K$. In particular, we show that the density of $γ$ for which $\mathcal{O}_K[γ]\cap K=\mathcal{O}_K$ is $\frac{ζ(n+1)}{ζ(n)}$. In a recent paper the authors defined $X(K,γ)$ to be a certain finite subset of $\text{Spec}(\mathcal{O}_K)$ and showed that $X(K,γ)$ determines the ring $\mathcal{O}_K[γ]\cap K$. We show that if $\mathfrak{p}_1,\mathfrak{p}_2\in \text{Spec}(\mathcal{O}_K)$ satisfy $\mathfrak{p}_1\cap \mathbb{Z}\neq\mathfrak{p}_2\cap \mathbb{Z}$, then the events $\mathfrak{p}_1\in X(K,γ)$ and $\mathfrak{p}_2\in X(K,γ)$ are independent. As $t\to\infty$, we study the asymptotics of the density of $γ$ for which $|X(K,γ)|=t$.

math.NT↗

arXiv2022

First detection of CHD$_{2}$OH towards pre-stellar cores

The inheritance of material across the star and planet formation process is traced by deuterium fractionation. We report here the first detection of doubly deuterated methanol towards pre-stellar cores. We study the deuterium fractionation of methanol, CH$_{3}$OH, towards two starless and two pre-stellar cores. We derive a D/H ratio of 0.8-1.9$\%$ with CH$_{2}$DOH in pre-stellar cores H-MM1 and L694-2, consistent with measurements in more evolved Class 0/I objects and comet 67P/Churyumov-Gerasimenko, suggesting a direct chemical link arising in the pre-stellar stage. Furthermore, the column density ratios of CHD$_{2}$OH/CH$_{2}$DOH are $\sim$50-80$\%$, consistently high as that towards Class 0/I objects, indicating an efficient formation mechanism of CHD$_{2}$OH, possibly through H atom additions to D$_{2}$CO. The CH$_{2}$DOH/CH$_{3}$OH and CHD$_{2}$OH/CH$_{3}$OH column density ratios in the two pre-stellar cores are larger than that in the two starless cores B68 and L1521E, representing an evolutionary trend of methanol deuteration in early-stage cores.

astro-ph.GA↗

arXiv2022

Primes in denominators of algebraic numbers

Denote the set of algebraic numbers as $\overline{\mathbb{Q}}$ and the set of algebraic integers as $\overline{\mathbb{Z}}$. For $γ\in\overline{\mathbb{Q}}$, consider its irreducible polynomial in $\mathbb{Z}[x]$, $F_γ(x)=a_nx^n+\dots+a_0$. Denote $e(γ)=\gcd(a_{n},a_{n-1},\dots,a_1)$. Drungilas, Dubickas and Jankauskas show in a recent paper that $\mathbb{Z}[γ]\cap \mathbb{Q}=\{α\in\mathbb{Q}\mid \{p\mid v_p(α)<0\}\subseteq \{p\mid p|e(γ)\}\}$. Given a number field $K$ and $γ\in\overline{\mathbb{Q}}$, we show that there is a subset $X(K,γ)\subseteq \text{Spec}(\mathcal{O}_K)$, for which $\mathcal{O}_K[γ]\cap K=\{α\in K\mid \{\mathfrak{p}\mid v_{\mathfrak{p}}(α)<0\}\subseteq X(K,γ)\}$. We prove that $\mathcal{O}_K[γ]\cap K$ is a principal ideal domain if and only if the primes in $X(K,γ)$ generate the class group of $\mathcal{O}_K$. We show that given $γ\in \overline{\mathbb{Q}}$, we can find a finite set $S\subseteq \overline{\mathbb{Z}}$, such that for every number field $K$, we have $X(K,γ)=\{\mathfrak{p}\in\text{Spec}(\mathcal{O}_K)\mid \mathfrak{p}\cap S\neq \emptyset\}$. We study how this set $S$ relates to the ring $\overline{\mathbb{Z}}[γ]$ and the ideal $\mathfrak{D}_γ=\{a\in\overline{\mathbb{Z}}\mid aγ\in\overline{\mathbb{Z}}\}$ of $\overline{\mathbb{Z}}$. We also show that $γ_1,γ_2\in \overline{\mathbb{Q}}$ satisfy $\mathfrak{D}_{γ_1}=\mathfrak{D}_{γ_2}$ if and only if $X(K,γ_1)=X(K,γ_2)$ for all number fields $K$.

math.NT↗

arXiv2022

J-comb: An image fusion algorithm to combine observations covering different spatial frequency ranges

Ground-based, high-resolution bolometric (sub)millimeter continuum mapping observations on spatially extended target sources are often subject to significant missing fluxes. This hampers accurate quantitative analyses. Missing flux can be recovered by fusing high-resolution images with observations that preserve extended structures. However, the commonly adopted image fusion approaches do not maintain the simplicity of the beam response function and do not try to elaborate the details of the yielded beam response functions. These make the comparison of the observations at multiple wavelengths not straightforward. We present a new algorithm, J-comb, which combines the high and low-resolution images linearly. By applying a taper function to the low-pass filtered image and combining it with a high-pass filtered image using proper weights, the beam response functions of our combined images are guaranteed to have near-Gaussian shapes. This makes it easy to convolve the observations at multiple wavelengths to share the same beam response functions. Moreover, we introduce a strategy to tackle the specific problem that the imaging at 850 um from the present-date ground-based bolometric instrument and that taken with the Planck satellite do not overlap in the Fourier domain. We benchmarked our method against two other widely-used image combination algorithms, CASA-feather and MIRIAD-immerge, with mock observations of star-forming molecular clouds. We demonstrate that the performance of the J-comb algorithm is superior to those of the other two algorithms. We applied the J-comb algorithm to real observational data of the Orion A star-forming region. We successfully produced dust temperature and column density maps with ~10" angular resolution, unveiling much greater details than the previous results.

astro-ph.IM↗

arXiv2022

A massive Keplerian protostellar disk with flyby-induced spirals in the Central Molecular Zone

Accretion disks are an essential component in the paradigm of the formation of low-mass stars. Recent observations further identify disks surrounding low-mass pre-main-sequence stars perturbed by flybys. Whether disks around more massive stars evolve in a similar manner becomes an urgent question. We report the discovery of a Keplerian disk of a few solar masses surrounding a 32 solar-mass protostar in the Sagittarius C cloud around the Galactic Center. The disk is gravitationally stable with two embedded spirals. A combined analysis of analytical solutions and numerical simulations demonstrates that the most likely scenario to form the spirals is through external perturbations induced by a close flyby, and one such perturber with the expected parameters is identified. The massive, early O-type star embedded in this disk forms in a similar manner with respect to low-mass stars, in the sense of not only disk-mediated accretion, but also flyby-impacted disk evolution.

astro-ph.GA↗

arXiv2022

Multi-line observations of CH$_{3}$OH, c-C$_{3}$H$_{2}$ and HNCO towards L1544: Dissecting the core structure with chemical differentiation

Pre-stellar cores are the basic unit for the formation of stars and stellar systems. The anatomy of the physical and chemical structures of pre-stellar cores is critical for understanding the star formation process. L1544 is a prototypical pre-stellar core, which shows significant chemical differentiation surrounding the dust peak. We aim to constrain the physical conditions at the different molecular emission peaks. This study allows us to compare the abundance profiles predicted from chemical models together with the classical density structure of Bonnor-Ebert (BE) sphere. We conducted multi-transition pointed observations of CH$_{3}$OH, c-C$_{3}$H$_{2}$ and HNCO with the IRAM 30m telescope, towards the dust peak and the respective molecular peaks of L1544. With non-LTE radiative transfer calculations and a 1-dimensional model, we revisit the physical structure of L1544, and benchmark with the abundance profiles from current chemical models. We find that the HNCO, c-C$_{3}$H$_{2}$ and CH$_{3}$OH lines in L1544 are tracing progressively higher density gas, from $\sim$10$^{4}$ to several times 10$^{5}$ cm$^{-3}$. Particularly, we find that to produce the observed intensities and ratios of the CH$_{3}$OH lines, a local gas density enhancement upon the BE sphere is required. This suggests that the physical structure of an early-stage core may not necessarily follow a smooth decrease of gas density profile locally, but can be intercepted by clumpy substructures surrounding the gravitational center. Multiple transitions of molecular lines from different molecular species can provide a tomographic view of the density structure of pre-stellar cores. The local gas density enhancement deviating from the BE sphere may reflect the impact of accretion flows that appear asymmetric and are enhanced at the meeting point of large-scale cloud structures.

astro-ph.GA↗

arXiv2021

The evolution of temperature and density structures of OB cluster-forming molecular clumps

OB star clusters originate from parsec-scale massive molecular clumps. We aim to understand the evolution of temperature and density structures on the intermediate-scale ($\lesssim$0.1-1 pc) extended gas of massive clumps. We performed $\sim$0.1 pc resolution observations (SMA+APEX) of multiple molecular line tracers (e.g., CH$_{3}$CCH, H$_{2}$CS, CH$_{3}$CN, CH$_{3}$OH) which cover a wide range of excitation conditions, towards a sample of eight massive clumps. Based on various radiative transfer models, we constrain the gas temperature and density structures and establish an evolutionary picture, aided by a spatially-dependent virial analysis and abundance ratios of multiple species. We determine temperature radial profiles varying between 30-200 K over a continuous scale, from the center of the clumps out to 0.3-0.4 pc radii. The clumps' radial gas density profiles, described by radial power-laws with slopes between -0.6 and $\sim$-1.5, are steeper for more evolved sources, as suggested by results based on both dust continuum, representing the bulk of the gas ($\sim$10$^{4}$ cm$^{-3}$), and CH$_{3}$OH lines probing the dense gas ($\gtrsim$10$^{6}$-10$^{8}$ cm$^{-3}$) regime. The density contrast between the dense gas and the bulk gas increases with evolution, and may be indicative of spatially and temporally varying star formation efficiencies. The radial profiles of the virial parameter show a global variation towards a sub-virial state as the clump evolves. The line-widths decline with increasing radius around the central core region and increase in the outer envelope, with a slope shallower than the case of the supersonic turbulence ($\,\propto\,$$r^{0.5}$) and the subsonic Kolmogorov scaling ($\,\propto\,$$r^{0.33}$). In the context of clump evolution, we also find that the abundance ratios of [CCH]/[CH$_{3}$OH] and [CH$_{3}$CN]/[CH$_{3}$OH] show correlations with clump $L/M$.

astro-ph.GA↗

arXiv2021

Frobenius allowable gaps of Generalized Numerical Semigroups

A generalised numerical semigroup (GNS) is a submonoid $S$ of $\mathbb{N}^d$ for which the complement $\mathbb{N}^d\setminus S$ is finite. The points in the complement $\mathbb{N}^d\setminus S$ are called gaps. A gap $F$ is considered Frobenius allowable if there is some relaxed monomial ordering on $\mathbb{N}^d$ with respect to which $F$ is the largest gap. We characterise the Frobenius allowable gaps of a GNS. A GNS that has only one Frobenius allowable gap is called a Frobenius GNS. We estimate the number of Frobenius GNS with a given Frobenius gap $F=(F^{(1)},\dots,F^{(d)})\in\mathbb{N}^d$ and show that it is close to $\sqrt{3}^{(F^{(1)}+1)\cdots (F^{(d)}+1)}$ for large $d$. We define notions of quasi-irreducibility and quasi-symmetry for GNS. While in the case of $d=1$ these notions coincide with irreducibility and symmetry of GNS, they are distinct in higher dimensions.

math.CO↗

arXiv2020

A multiple-relaxation-time lattice Boltzmann model based four-level finite-difference scheme for one-dimensional diffusion equation

In this paper, we first present a multiple-relaxation-time lattice Boltzmann (MRT-LB) model for one-dimensional diffusion equation where the D1Q3 (three discrete velocities in one-dimensional space) lattice structure is considered. Then through the theoretical analysis, we derive an explicit four-level finite-difference scheme from this MRT-LB model. The results show that the four-level finite-difference scheme is unconditionally stable, and through adjusting the weight coefficient $ω_{0}$ and the relaxation parameters $s_1$ and $s_2$ corresponding to the first and second moments, it can also have a sixth-order accuracy in space. Finally, we also test the four-level finite-difference scheme through some numerical simulations, and find that the numerical results are consistent with our theoretical analysis.

math.NA↗

arXiv2020

The limiting spectral measure for an ensemble of generalized checkerboard matrices

Random matrix theory successfully models many systems, from the energy levels of heavy nuclei to zeros of $L$-functions. While most ensembles studied have continuous spectral distribution, Burkhardt et al introduced the ensemble of $k$-checkerboard matrices, a variation of Wigner matrices with entries in generalized checkerboard patterns fixed and constant. In this family, $N-k$ of the eigenvalues are of size $O(\sqrt{N})$ and were called bulk while the rest are tightly contrained around a multiple of $N$ and were called blip. We extend their work by allowing the fixed entries to take different constant values. We can construct ensembles with blip eigenvalues at any multiples of $N$ we want with any multiplicity (thus we can have the blips occur at sequences such as the primes or the Fibonaccis). The presence of multiple blips creates technical challenges to separate them and to look at only one blip at a time. We overcome this by choosing a suitable weight function which allows us to localize at each blip, and then exploiting cancellation to deal with the resulting combinatorics to determine the average moments of the ensemble; we then apply standard methods from probability to prove that almost surely the limiting distributions of the matrices converge to the average behavior as the matrix size tends to infinity. For blips with just one eigenvalue in the limit we have convergence to a Dirac delta spike, while if there are $k$ eigenvalues in a blip we again obtain hollow $k \times k$ GOE behavior.

math.PR↗

arXiv2020

Density of Numerical sets associated to a Numerical semigroup

A numerical set is a co-finite subset of the natural numbers that contains zero. Its Frobenius number is the largest number in its complement. Each numerical set has an associated semigroup $A(T)=\{t\mid t+T\subseteq T\}$, which has the same Frobenius number as $T$. For a fixed Frobenius number $f$ there are $2^{f-1}$ numerical sets. It is known that there is a number $γ$ close to $0.484$ such that the ratio of these numerical sets that are mapped to $N_f=\{0\}\cup(f,\infty)$ is asymptotically $γ$. We identify a collection of families $N(D,f)$ of numerical semigroups such that for a fixed $D$ the ratio of the $2^{f-1}$ numerical sets that are mapped to $N(D,f)$ converges to a positive limit as $f$ goes to infinity. We denote the limit as $γ_D$, these constants sum up to $1$ meaning that they asymptotically account for almost all numerical sets.

math.CO↗

arXiv2020

Data-driven Analytical Models of COVID-2019 for Epidemic Prediction, Clinical Diagnosis, Policy Effectiveness and Contact Tracing: A Survey

The widely spread CoronaVirus Disease (COVID)-19 is one of the worst infectious disease outbreaks in history and has become an emergency of primary international concern. As the pandemic evolves, academic communities have been actively involved in various capacities, including accurate epidemic estimation, fast clinical diagnosis, policy effectiveness evaluation and development of contract tracing technologies. There are more than 23,000 academic papers on the COVID-19 outbreak, and this number is doubling every 20 days while the pandemic is still on-going [1]. The literature, however, at its early stage, lacks a comprehensive survey from a data analytics perspective. In this paper, we review the latest models for analyzing COVID19 related data, conduct post-publication model evaluations and cross-model comparisons, and collect data sources from different projects.

stat.AP↗

arXiv2019

Fragmentation and filaments at the onset of star and cluster formation: SABOCA 350 $μ$m view of ATLASGAL selected massive clumps

The structure formation of the dense interstellar material and the fragmentation of clumps into cores is a fundamental step to understand how stars and stellar clusters form. We aim to establish a statistical view of clump fragmentation at sub-parsec scales based on a large sample of massive clumps selected from the ATLASGAL survey. We used the APEX/SABOCA camera at 350 $μ$m to image clumps at a resolution of 8.$''$5. The majority of the sample consists of massive clumps that are weak or in absorption at 24 $μ$m. We resolve rich filamentary structures and identify the population of compact sources. We use association with mid-infrared 22-24 $μ$m and 70 $μ$m point sources to pin down the star formation activity of the cores. We then statistically assess their physical properties, and the fragmentation characteristics of massive clumps. We find a moderate correlation between the clump fragmentation levels with the clump gas density and the predicted number of fragments with pure Jeans fragmentation scenario; we find a strong correlation between the mass of the most massive fragment and the total clump mass, suggesting that the self-gravity may play an important role in the clumps' small scale structure formation. We identify 27 massive quiescent cores with $M_{\rm core}>100$ M$_{\odot}$ within 5 kpc; these are massive enough to be self-gravitating but do not yet show any sign of star-formation. This sample comprises, therefore, promising candidates of massive pre-stellar cores, or deeply embedded high-mass protostars.

astro-ph.GA↗

arXiv2019

Filamentary Accretion Flows in the Infrared Dark Cloud G14.225-0.506 Revealed by ALMA

Filaments are ubiquitous structures in molecular clouds and play an important role in the mass assembly of stars. We present results of dynamical stability analyses for filaments in the infrared dark cloud G14.225$-$0.506, where a delayed onset of massive star formation was reported in the two hubs at the convergence of multiple filaments of parsec length. Full-synthesis imaging is performed with the Atacama Large Millimeter/submillimeter Array (ALMA) to map the $\mathrm{N_2H^+} \; (1-0)$ emission in two hub-filament systems with a spatial resolution of $\sim 0.034 \; \mathrm{pc}$. Kinematics are derived from sophisticated spectral fitting algorithm that accounts for line blending, large optical depth, and multiple velocity components. We identify five velocity coherent filaments and derive their velocity gradients with principal component analysis. The mass accretion rates along the filaments are up to $10^{-4} \; \mathrm{M_\odot \, \mathrm{yr^{-1}}}$ and are significant enough to affect the hub dynamics within one free-fall time ($\sim 10^5 \; \mathrm{yr}$). The $\mathrm{N_2H^+}$ filaments are in equilibrium with virial parameter $α_\mathrm{vir} \sim 1.2$. We compare $α_\mathrm{vir}$ measured in the $\mathrm{N_2H^+}$ filaments, $\mathrm{NH_3}$ filaments, $870 \; μ\mathrm{m}$ dense clumps, and $3 \; \mathrm{mm}$ dense cores. The decreasing trend in $α_\mathrm{vir}$ with decreasing spatial scales persists, suggesting an increasingly important role of gravity at small scales. Meanwhile, $α_\mathrm{vir}$ also decreases with decreasing non-thermal motions. In combination with the absence of high-mass protostars and massive cores, our results are consistent with the global hierarchical collapse scenario.

astro-ph.GA↗