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Hu and Ye conjectured that for a $k$-th order and $n$-dimensional tensor $\mathcal{A}$ with an eigenvalue $\lambda$ and the corresponding eigenvariety $\mathcal{V}_\lambda(\mathcal{A})$, $$\mathrm{am}(\lambda) \ge \sum_{i=1}^\kappa \mathrm{dim}(V_i)(k-1)^{\mathrm{dim}(V_i)-1},$$ where $\mathrm{am}(\lambda)$ is the algebraic multiplicity of $\lambda$, and $V_1,\ldots,V_\kappa$ are all irreducible components of $\mathcal{V}_\lambda(\mathcal{A})$. In this paper, we prove that if $\mathcal{A}$ is a nonnegative weakly irreducible tensor with spectral radius $\rho$, then $\mathrm{am}(\lambda) \ge |\mathbb{V}_\lambda(\mathcal{A})|$ for all eigenvalues $\lambda$ of $\mathcal{A}$ with modulus $\rho$, where $\mathbb{V}_\lambda(\mathcal{A})$ is the projective eigenvariety of $\mathcal{A}$ associated with $\lambda$. Consequently we confirm Hu-Ye's conjecture for the above eigenvalues $\lambda$ of $\mathcal{A}$ and the least H-eigenvalue of a weakly irreducible $Z$-tensor. We prove the equality case in Hu-Ye's conjecture for some eigenvalues of the adjacency tensor or Laplacian tensor of several classes of hypergraphs.

We investigate the production of axion-like particles (ALPs) in stellar cores, where they interact with electromagnetic fields and electrons, with typical masses between $\mathcal O(0.1)$ and $\mathcal O(10)$ keV. These low-energy ALPs are gravitationally trapped in the orbits of stars and subsequently decay into two photons that we detect as monochromatic X-ray lines. We propose to search for these gravitationally trapped ALPs in the Alpha Centauri binary system, our closest stellar neighbor, using sensitive X-ray detectors like Chandra and eROSITA. Our search for ALP decay signals in the energy range of 0.2 keV to 10 keV yielded null results, thus establishing the most stringent limits on ALP interactions to date. Specifically, if ALPs are mainly produced by Compton or bremsstrahlung processes (ALP-electron coupling $g_{aee}$ being significant), we have improved the limits on the ALP-photon coupling $g_{a\gamma\gamma}$ by two to three orders of magnitude, in ALP mass range between 0.2 keV to 5 keV, compared to previous measurements, including those from GW170817, SN 2023ixf, and other sources., Comment: 8 pages, 3 figures

The precision measurements of the muon magnetic moment and the $W$ boson mass have sparked interest in the potential deviations from standard model (SM) predictions. While it may be premature to attribute any excesses in these precision measurements to new physics, they do offer a valuable indication of potential directions for physics beyond the SM. Additionally, the particle nature of dark matter (DM) remains a crucial enigma. Despite the absence of any definitive DM signal in direct detection and collider experiments, the Galactic Center GeV $\gamma$-ray excess and the AMS-02 antiproton ($\overline{p}$) excess could potentially offer hints related to the evidence of DM. Motivated by these observations, we propose a simple DM model that addresses all these issues. This model extends the SM by incorporating singlet and doublet Dirac fermion fields, along with a doublet complex scalar field. For the viable parameter regions in this model, we find that future upgrades of the Large Hadron Collider and DM direct detection experiments can only partially probe them, while future high-energy muon colliders hold promise for exploring the unexplored parameter space., Comment: 33 pages, 10 figures, 2 tables. Comments are welcome

General criteria on spectral extremal problems for hypergraphs were developed by Keevash, Lenz, and Mubayi in their seminal work (SIAM J. Discrete Math., 2014), in which extremal results on \alpha-spectral radius of hypergraphs for \alpha>1 may be deduced from the corresponding hypergraph Tur\'an problem which has the stability property and whose extremal construction satisfies some continuity assumptions. Using this criterion, we give two general spectral Tur\'an results for hypergraphs with bipartite or mulitpartite pattern, transform corresponding the spectral Tur\'an problems into pure combinatorial problems with respect to degree-stability of a nondegenerate k-graph family. As an application, we determine the maximum \alpha-spectral radius for some classes of hypergraphs and characterize the corresponding extremal hypergraphs, such as the expansion of complete graphs, the generalized Fans, the cancellative hypergraphs, the generalized triangles, and a special book hypergraph.

The origin and evolution of organic molecules represent a pivotal issue in the fields of astrobiology and astrochemistry, potentially shedding light on the origins of life. The James Webb Space Telescope (JWST), with its exceptional sensitivity and spectral resolution, is well suitable to observe molecules such as methane ($\rm CH_4$). Our analysis focused on the distribution of $\rm CH_4$, $\rm CO_2$, $\rm H_2O$, $\rm{CH_3OH+NH_4^+}$ ice and silicate absorption dips at approximately 7.7, 15.0, 6.0, 6.7 and 10.0 micrometres in two protostars: IRAS 16253-2429 and IRAS 23385+6053. We extract the $\rm CH_4$, $\rm CO_2$, $\rm H_2O$, $\rm{CH_3OH+NH_4^+}$ ice equivalent width (EW) maps and silicate extinction maps of the two sources. Our results reveal that the spatial distribution of $\rm CH_4$ in the protostellar system IRAS 16253-2429 closely mirrors that of its $\rm CO_2$ ice, forming a surrounded distribution that encircles the central protostar. This alignment suggests a common formation mechanism and subsequent trapping within the protostellar envelope, which is consistent with the "Classical" dark-cloud chemistry with ion-molecule reaction. In contrast, the spatial distributions of various molecules in the system IRAS 23385+6053 exhibit low similarities, which may be attributed to the dynamic influences of outflows or accretion processes. These discrepancies highlight the complex interplay between physical processes and chemical evolution in protostellar environments., Comment: 5 pages, 2 figures, 1 table

Scalar-tensor gravity, exemplified by Brans-Dicke (BD) gravity, introduces additional scalar polarization modes that contribute scalar radiation alongside tensor modes. We conduct a comprehensive analysis of how gravitational wave generation and propagation effects under Brans-Dicke gravity are encoded into the astrophysical stochastic gravitational wave background (AGWB). We perform end-to-end analyses of realistic populations of simulated coalescing binary systems to generate AGWB mock data with third-generation gravitational wave detectors and conducted a complete Bayesian analysis for the first time. We find the uncertainties in the population properties of binary black holes (BBH) significantly affect the ability to constrain BD gravity. Under the most favorable conditions, the upper limit may suggest $\omega_{\rm BD} > 816$. Furthermore, we explore the detectability of potential scalar backgrounds arising from binary neutron star (BNS) mergers, setting upper limits on scalar backgrounds expected to be two orders of magnitude lower than the total background contributed by both BBH and BNS in one year of observational data. We conclude that for ambiguous populations, employing waveform matching with individual sources provides a more robust approach to constrain Brans-Dicke gravity. However, the future detection of a potential scalar background within the AGWB could provide significant support for gravity theories beyond General Relativity., Comment: 26 pages, 6 figures, and 2 tables

As the largest gravitationally bound objects in the Universe, galaxy clusters have provided the first piece of evidence for the presence of dark matter and may be suitable targets for indirect dark matter searches. Among various signals, the GeV-TeV $\gamma$-ray line has been taken as the smoking-gun signal of the dark matter annihilation/decay since no known astrophysical/physical process(es) could generate such a peculiar spectrum. With 15.5 years of Fermi-LAT P8R3 publicly available data, we search for the $\gamma$-ray line emission in the directions of a group of 13 nearby massive galaxy clusters with an unbinned likelihood analysis. A $\gamma$-ray line signal at $\sim 43.2$ GeV has a net TS value of $\approx 30$ if we only take into account the data in the directions of Virgo, Fornax and Ophiuchus clusters, three massive clusters with the highest J-factors expected to generate the dark matter annihilation signal. The signal still presents when the data of other 10 nearby massive clusters have also been included, though the TS value decreases to $\approx 21$ likely because of their lower signal-to-noise ratios. The absence of this signal in the inner Galaxy disfavors both the instrumental effect and the canonical dark matter annihilation interpretation, and a more sophisticated dark matter model or very peculiar astrophysical scenario might be needed. This $\gamma$-ray line signal, if intrinsic, could be unambiguously verified by the Very Large Area $\gamma$-ray Space Telescope in its first two years of performance., Comment: 9 pages, 7 figures, 1 table. Comments are welcome!

Let $K$ be a simplicial complex, and let $\Delta_i^{up}(K)$ be the $i$-th up normalized Laplacian of $K$. Horak and Jost showed that the largest eigenvalue of $\Delta_i^{up}(K)$ is at most $i+2$, and characterized the equality case by the orientable or non-orientable circuits. In this paper, by using the balancedness of signed graphs, we show that $\Delta_i^{up}(K)$ has an eigenvalue $i+2$ if and only if $K$ has an $(i+1)$-path connected component $K'$ such that the $i$-th signed incidence graph $B_i(K')$ is balanced, which implies Horak and Jost's characterization. We also characterize the multiplicity of $i+2$ as an eigenvalue of $\Delta_i^{up}(K)$, which generalizes the corresponding result in graph case. Finally we gave some classes of infinitely many simplicial complexes $K$ with $\Delta_i^{up}(K)$ having an eigenvalue $i+2$ by using wedge, Cartesian product and duplication of motifs., Comment: arXiv admin note: substantial text overlap with arXiv:2405.19078

This study reanalyzes the detection prospects of dark matter (DM) annihilation signals in the Galactic Center, focusing on velocity-dependent dynamics within a spike density near the supermassive black hole (Sgr~A$^{\star}$). We investigate three annihilation processes -- $p$-wave, resonance, and forbidden annihilation -- under semi-relativistic velocities, leveraging gamma-ray data from Fermi and DAMPE telescopes. Our analysis integrates a fermionic DM model with an electroweak axion-like particle (ALP) portal, exploring annihilation into two or four photons. Employing a comprehensive six-dimensional integration, we precisely calculate DM-induced gamma-ray fluxes near Sgr~A$^{\star}$, incorporating velocity and positional dependencies in the annihilation cross-section and photon yield spectra. Our findings highlight scenarios of resonance and forbidden annihilation, where the larger ALP-DM-DM coupling constant $C_{a\chi\chi}$ can affect spike density, potentially yielding detectable gamma-ray line spectra within Fermi and DAMPE energy resolution. We set upper limits for $C_{a\chi\chi}$ across these scenarios, offering insights into the detectability and spectral characteristics of DM annihilation signals from the Galactic Center., Comment: 24 pages, 13 figures

Superluminous supernovae (SLSNe) are a new class of transients with luminosities $\sim10 -100$ times larger than the usual core-collapse supernovae (SNe). Their origin is still unclear and one widely discussed scenario involves a millisecond magnetar central engine. The GeV-TeV emission of SLSNe has been predicted in the literature but has not been convincingly detected yet. Here we report the search for the $\gamma$-ray emission in the direction of SN 2017egm, one of the closest SLSNe detected so far, with the 15-year {\it Fermi}-LAT Pass 8 data. There is a transient $\gamma$-ray source appearing about 2 months after this event and lasting a few months. Both the peak time and the luminosity of the GeV emission are consistent with the magnetar model prediction, suggesting that such a GeV transient is the high-energy counterpart of SN 2017egm and the central engine of this SLSNe is a young magnetar.

A graph $G$ is factored into graphs $H$ and $K$ via a matrix product if there exist adjacency matrices $A$, $B$, and $C$ of $G$, $H$, and $K$, respectively, such that $A = BC$. In this paper, we study the spectral aspects of the matrix product of graphs, including regularity, bipartiteness, and connectivity. We show that if a graph $G$ is factored into a connected graph $H$ and a graph $K$ with no isolated vertices, then certain properties hold. If $H$ is non-bipartite, then $G$ is connected. If $H$ is bipartite and $G$ is not connected, then $K$ is a regular bipartite graph, and consequently, $n$ is even. Furthermore, we show that trees are not factorizable, which answers a question posed by Maghsoudi et al., Comment: Comments are welcome

The recent measurements of cosmic ray deuteron fluxes by AMS-02 show that the rigidity dependence of deuterons is similar with that of protons but flatter than $^3$He, which has been attributed to the existence of primary deuterons with abundance much higher than that from the Big Bang nucleosynthesis. The requirement of highly deuteron-abundant sources imposes a serious challenge on the modern astrophysics since there is no known process to produce a large amount of deuterons without violating other constraints \citep{1976Natur.263..198E}. In this work we demonstrate that the fragmentation of heavy nuclei up to nickel plays a crucial role in shaping/enhancing the spectrum/flux of the cosmic ray deuterons. Based on the latest cosmic ray data, the predicted secondary fluxes of deuterons and $^3$He are found to be reasonably consistent with the AMS-02 measurements and a primary deuteron component is not needed. The observed differences between the spectra of D and $^3$He, as well as those between the D/$^4$He (D/p) and $^3$He/$^4$He ($^3$He/p) flux ratios, measured in the rigidity space, is probably due to the kinetic-energy-to-rigidity conversion and the solar modulation, given different charge-to-mass ratios of D and $^3$He. More precise measurements of the fragmentation cross sections of various nuclei to produce deuterons, tritons, and $^3$He in a wide energy range will be very helpful in further testing the secondary origin of cosmic ray deuterons., Comment: 14 pages, 8 figures, and 1 table; published in ApJL

The cosmic expansion rate can be directly measured with gravitational waves (GWs) of the compact binary mergers, by jointly constraining the mass function of the population and the cosmological model via the so called spectral sirens. Such a method relies on the features in the mass functions, which may originate from some individual sub-populations, and hence become blurred/indistinct due to the superposition of different sub-populations. In this work we propose a novel approach to constrain the cosmic expansion rate with sub-populations of GW events, named multi-spectral sirens. We illustrate the advantage of the multi-spectral sirens compared to the traditional spectral sirens by simulation with mock data. The application of this approach to the GWTC-3 data yields $H_0=73.25^{+29.87}_{-25.55}~{\rm Mpc}^{-1}~{\rm km}~{\rm s}^{-1}$ (median and symmetric 68.3\% credible level). The incorporation of the bright standard siren GW170817 with a uniform prior in $ [10,200] ~{\rm Mpc}^{-1}~{\rm km}~{\rm s}^{-1}$ gives $H_0=72.38^{+15.03}_{-9.13}~{\rm Mpc}^{-1}~{\rm km}~{\rm s}^{-1}$ (68.3\% confidence level), corresponding to an improvement of $\sim28\%$ with respect to the measurement from sole GW170817., Comment: 14 pages, 8 figures, 1 table; comments are welcome

The spins of binary black holes (BBHs) measured from gravitational waves carry notable information of the formation pathways. Here we propose a quantity "dimensionless net spin" ($\chi_{\rm N}$), which is related to the sum of angular momentum of component black holes in the system, to provide a novel perspective to study the origin(s) of BBHs. By performing hierarchical Bayesian inference on $\chi_{\rm N}$, we find strong evidence that the marginal distribution of this quantity can be better fitted by two Gaussian components rather than one: there is a narrow peak at $\chi_{\rm N} \sim 0.15$ and another extended peak at $\chi_{\rm N} \sim 0.47$. We also find that the rapidly spinning systems likely dominate the high-mass end of the population and they evolve with redshift much quicker. These findings bring new challenges to the field binary scenario, and suggest that dynamical process should plays a key role in forming high total mass BBHs., Comment: Submitted on 25 April 2024

Let $K$ be a simplical complex, and let $\mathcal{L}_i^{up}(K), \mathcal{Q}_i^{up}(K)$ be the $i$-th up Laplacian and signless Laplacian of $K$, respectively. In this paper we proved that the largest eigenvalue of $\mathcal{L}_i^{up}(K)$ is not greater than the largest eigenvalue of $\mathcal{Q}_i^{up}(K)$; furthermore, if $K$ is $(i+1)$-path connected, then the equality holds if and only if the $i$-th incidence signed graph $B_i(K)$ of $K$ is balanced. As an application we provided an upper bound for the largest eigenvalue of the $i$-th up Laplacian of $K$, which improves the bound given by Horak and Jost and generalizes the result of Anderson and Morley on graphs.We characterized the balancedness of simplicial complexes under operations such as wedge sum, join, Cartesian product and duplication of motifs. For each $i \ge 0$, by using wedge sum or duplication of motifs, we can construct an infinitely many $(i+1)$-path connected simplicial complexes $K$ with $B_i(K)$ being balanced.

In this work, we study the implications of GW230529 on gravity theories and the charge of black holes. The GW230529, which was initially released in O4a, is most likely neutron star-black hole (NSBH) mergers. We reanalyze the data from the GW230529 event to obtain bounds on the Einstein-dilation-Gauss-Bonnet (EdGB) gravity parameter $\sqrt{\alpha_{\rm EdGB}}$ and the electric charge of compact binary systems. The event places a $90\%$ credible upper bounds on $\sqrt{\alpha_{\rm EdGB}}$ of $\lesssim 0.298$ km. After including high order corrections of EdGB gravity, the bounds improve to $\sqrt{\alpha_{\rm EdGB}} \lesssim 0.260$ km. Analyses of GW230529 also yield a $90\%$ credible upper bounds on the combination of charge-to-mass ratio of the binary components $\zeta \lesssim 0.024$. The constraints are more stringent than those derived from previously observed single gravitational wave merger event., Comment: 7 pages, 4 figures, PRD accepted

Thanks to the successful performance of the James Webb Space Telescope, our understanding of the epoch of reionization of the Universe has been advanced. The ultraviolet luminosity functions (UV LFs) of galaxies span a wide range of redshift, not only revealing the connection between galaxies and dark matter (DM) halos but also providing the information during reionization. In this work, we develop a model connecting galaxy counts and apparent magnitude based on UV LFs, which incorporates redshift-dependent star formation efficiency (SFE) and corrections for dust attenuation. By synthesizing some observations across the redshift range $4\le z \le 10$ from various galaxy surveys, we discern the evolving SFE with increasing redshift and DM halo mass through model fitting. Subsequent analyses indicate that the Thomson scattering optical depth was $\tau_{\rm e} = 0.054^{+0.001}_{-0.003}$ and the epoch of reionization started (ended) at $z=18.8^{+7.2}_{-6.0}$ ($z=5.3^{+0.8}_{-1.0}$) which is insensitive to the choice of the truncated magnitude of the UV LFs. Incorporating additional dataset and some reasonable constraints, the amplitude of matter perturbation is found to be $\sigma_8=0.80\pm0.05$, which is consistent with the standard $\Lambda$CDM model. Future galaxy surveys and the dynamical simulations of galaxy evolution will break the degeneracy between SFE and cosmological parameters, improving the accuracy and the precision of the UV LF model further., Comment: 18 pages, 11 figures and 4 tables. Accepted for publication in ApJ

Very recently, it has been shown that there is an upper bound on the squared sound speed of nuclear matter from the transport, which reads $c_{\rm s}^2 \leq 0.781$. In this work, we demonstrate that this upper bound is corroborated by the reconstructed equation of state (EOS; modeled with a nonparametric method) for ultradense matter. The reconstruction integrates multimessenger observation for neutron stars, in particular, the latest radius measurements for PSR J0437-4715 ($11.36^{+0.95}_{-0.63}$ km), PSR J0030+0451 ($11.71^{+0.88}_{-0.83}$ km, in the ST+PDT model), and PSR J0740+6620 ($12.49^{+1.28}_{-0.88}$ km) by NICER have been adopted. The result shows in all cases, the $c_{\rm s}^2 \leq 0.781$ upper limit for EOS will naturally yield the properties of matter near the center of the massive neutron star consistent with the causality-driven constraint from pQCD, where, in practice, the density in implementing the pQCD likelihood ($n_{\rm L}$) is applied at $10n_s$ (where $n_s$ is the nuclear saturation density). We also note that there is a strong correlation for the maximum $c_s^2$ with $n_{\rm L}$, and $c_{\rm s}^2 \leq 0.781$ is somehow violated when $n_{\rm L} = n_{\rm c,TOV}$. The result indicates that a higher $n_{\rm L}$, even considering the uncertainties from statistics, is more natural. Moreover, the remarkable agreement between the outcomes derived from these two distinct and independent constraints (i.e., the transport calculation and pQCD boundary) lends strong support to their validity. In addition, the latest joint constraint for $R_{1.4}$, $R_{2.0}$, $R_{1.4}-R_{2.0}$, and $M_{\rm TOV}$ are $11.94_{-0.68}^{+0.77}$ km, $11.99_{-0.67}^{+0.88}$ km, $-0.1_{-0.27}^{+0.42}$ km, and $2.24_{-0.10}^{+0.13}M_\odot$ (at $90\%$ credible level), respectively., Comment: 9 pages, 9 figures, ApJ published

Let $F$ be a graph and let $\mathcal{B}_r(F)$ be the class of $r$-uniform Berge-$F$ hypergraphs. In this paper, by establishing a relationship between the spectral radius of the adjacency tensor of a uniform hypergraph and its local structure via walks, we give a spectral asymptotic bound for $\mathcal{B}_{r}(C_3)$-free linear $r$-uniform hypergraphs and upper bounds for the spectral radii of $\mathcal{B}_{r}(K_{2,t})$-free or $\{\mathcal{B}_{r}(K_{s,t}),\mathcal{B}_{r}(C_{3})\}$-free linear $r$-uniform hypergraphs, where $C_{3}$ and $K_{s,t}$ are respectively the triangle and the complete bipartite graph with one part having $s$ vertices and the other part having $t$ vertices. Our work implies an upper bound for the number of edges of $\{\mathcal{B}_{r}(K_{s,t}),\mathcal{B}_{r}(C_{3})\}$-free linear $r$-uniform hypergraphs, and extends some known work on (spectral) extreme problems of hypergraphs.

We investigate the elastic scattering cross section between dark matter and protons using the DES Year 3 weak lensing data. This scattering induces a dark acoustic oscillation structure in the matter power spectra. To address non-linear effects at low redshift, we utilize principal component analysis alongside a limited set of $N$-body simulations, improving the reliability of our matter power spectrum prediction. We further perform a robust Markov Chain Monte Carlo analysis to derive the upper bounds on the DM-proton elastic scattering cross-section, assuming different velocity dependencies. Our results, presented as the first Frequentist upper limits, are compared with the ones obtained by Bayesian approach. Compared with the upper limits derived from the Planck cosmic microwave background data, our findings from DES Year 3 data exhibit improvements of up to a factor of five. In addition, we forecast the future sensitivities of the China Space Station Telescope, the upcoming capabilities of this telescope could improve the current limits by approximately one order of magnitude., Comment: 24 pages, 11 figures, published in JCAP

A hierarchical triple merger (HTM) constitutes a type of event in which two successive black hole (BH) mergers occur sequentially within the observational window of gravitational wave (GW) detectors, which has important role in testing general relativity and studying BH population. In this work, we conduct an analysis to determine the feasibility of identifying HTMs from a large GW event catalog using the third-generation ground-based GW detectors. By comparing the Bhattacharyya coefficient that measures the overlap between the posterior distributions of the remnant and progenitor BH parameters, we find that the overlap between the event pair can serve as a preliminary filter, which balances between computational demand and the probability of false alarms. Following this initial, time-efficient, yet less accurate screening, a subset of potential HTM candidates will be retained. These candidates will subsequently be subjected to a more precise, albeit time-intensive, method of joint parameter estimation for verification. Ultimately, this process will enable us to robustly identify HTMs., Comment: 13 pages, 8 figures, ApJ accepted

The central engine of a Gamma-Ray Burst (GRB) is widely believed to launch a pair of oppositely moving jets, i.e. the forward jet moving towards us and the counter jet regressing away. The forward jet generates the radiation typically observed in GRBs, while the counter jet has not been detected yet due to its dimness. GRB 170817A, a short burst associated with a binary neutron star merger event, is a nearby event ($z=0.0097$) with an off-axis structured energetic forward jet and hence probably the most suitable target for searching the counter jet radiation. Assuming the same properties for the forward and counter jet components as well as the shock parameters, the fit to the multi-wavelength afterglow emission of GRB 170817A suggests a peak time $\sim {\rm quite~a~few}\times 10^{3}$ day of the counter jet radiation, but the detection prospect of this new component is not promising. Anyhow, if the shock parameters ($\epsilon_{\rm e}$ and $\epsilon_{\rm B}$) of the counter jet component are (a few times) higher than that of the forward shock e.g., the posterior results of the magnetic energy fraction of the forward shock and the counter jet are $\log_{10}\epsilon_{\rm B}=-4.23^{+1.42}_{-0.69}$ and $\log_{10}\epsilon_{\rm B, cj}=-3.65^{+3.06}_{-2.11}$, respectively), as still allowed by the current data, the counter jet afterglow emission will be enhanced and hence may be detected. A few hour exposure by JWST in F356W band will stringently test such a scenario.

Gamma-ray bursts (GRBs) have been proposed as one of promising sources of ultra-high-energy cosmic rays (UHECRs), but observational evidence is still lacking. The nearby B.O.A.T. (brightest of all time) GRB 221009A, an once-in-1000-year event, is able to accelerate protons to $\sim 10^{3}$ EeV. Protons arriving at the Milky Way are dominated by neutron-decay-induced protons. The inter-galactic magnetic fields would not yield a sizable delay of the $\geq 10{\rm~EeV}$ cosmic rays if its strength is $\lesssim 10^{-13}{\rm~G}$, while Galactic magnetic fields would cause a significant time delay. We predict that, an UHECR burst from GRB 221009A would be detectable by the Pierre Auger Observatory and the TA$\times$4, within $\sim$ 10 years. The detection of such an UHECR outburst will provide the direct evidence for UHECR acceleration in GRBs.

Mergers of binary compact objects, accompanied with electromagnetic (EM) counterparts, offer excellent opportunities to explore varied cosmological models, since gravitational waves (GWs) and EM counterparts always carry the information of luminosity distance and redshift, respectively. $f(T)$ gravity, which alters the background evolution and provides a friction term in the propagation of GWs, can be tested by comparing the modified GW luminosity distance with the EM luminosity distance. Considering the third-generation gravitational-wave detectors, Einstein Telescope and two cosmic explorers, we simulate a series of GW events of binary neutron stars and neutron-star-black-hole binaries with EM counterparts. These simulations can be used to constrain $f(T)$ gravity [especially the power-law model $f(T)=T+\alpha(-T)^\beta$ in this work] and other cosmological parameters, such as $\beta$ and the Hubble constant. In addition, combining simulations with current observations of type Ia supernovae and baryon acoustic oscillations, we obtain tighter limitations for $f(T)$ gravity. We find that the estimated precision significantly improved when all three datasets are combined ($\Delta \beta \sim 0.03$), compared to analyzing the current observations alone ($\Delta \beta \sim 0.3$). Simultaneously, the uncertainty of the Hubble constant can be reduced to approximately $1\%$., Comment: 12 pages, 6 figures, 3 tables

In this paper, by the representation theory of symmetric group, we give a decomposition of the Laplace operator (in matrix form) of a covering simplicial complex into the direct sum of some matrices, including the Laplace operator of the underlying simplicial complex. So, the spectrum of a covering simplicial complex can be expressed into a union of the spectrum of the underlying simplicial complex and the spectra of some other matrices, which implies a result of Horak and Jost. In particular, we show that the spectrum of a $2$-fold covering simplicial complex is the union the that of the underlying simplicial complex and that of an incidence-signed simplicial complex, which is an analog of Bilu and Linial's result on graphs. Finally we show that the dimension of the cohomology group of a covering simplicial complex is greater than or equal to that of the underlying simplicial complex.

Recently, an association of GW190425 and FRB 20190425A had been claimed and a highly magnetized neutron star (NS) remnant was speculated. Given the $\sim 2.5$-h delay of the occurrence of FRB 20190425A, a uniformly rotating supramassive magnetar is favored since the differential rotation would have been promptly terminated by the magnetic braking. The required maximum gravitational mass ($M_{\rm TOV}$) of the nonrotating NS is $\approx 2.77M_\odot$, which is strongly in tension with the relatively low $M_{\rm TOV}\approx 2.25M_\odot$ obtained in current equation of state (EOS) constraints incorporating perturbative quantum chromodynamics (pQCD) information. However, the current mass-radius and mass-tidal deformability measurements of NSs alone do not convincingly exclude the high $M_{\rm TOV}$ possibility. By performing EOS constraints with mock measurements, we find that with a $2\%$ determination for the radius of PSR J0740+6620-like NS it is possible to distinguish between the low and high $M_{\rm TOV}$ scenarios. We further explore the prospect to resolve the issue of the appropriate density to impose the pQCD constraints with future massive NS observations or determinations of $M_{\rm TOV}$ and/or $R_{\rm TOV}$. It turns out that measuring the radius of a PSR J0740+6620-like NS is insufficient to probe the EOSs around 5 nuclear saturation density, where the information from pQCD becomes relevant. The additional precise $M_{\rm TOV}$ measurements anyhow could provide insights into the EOS at such a density. Indeed, supposing the central engine of GRB 170817A is a black hole formed via the collapse of a supramassive NS, the resulting $M_{\rm TOV}\approx 2.2M_\odot$ considerably softens the EOS at the center of the most massive NS, which is in favor of imposing the pQCD constraint at density beyond the one achievable in the NSs., Comment: 12 pages, 5 figures, PRD published

In this paper we investigate Ramanujan hypergraphs by using hypergraph coverings. We first show that the spectrum of a $k$-fold covering $\bar{H}$ of a connected hypergraph $H$ contains the spectrum of $H$, and that it is the union of the spectrum of $H$ and the spectrum of an incidence-signed hypergraph with $H$ as underlying hypergraph if $k=2$, which generalizes Bilu-Linial result on graph coverings. We give a lower bound for the second largest eigenvalue of a $d$-regular hypergraph by universal cover, which generalizes Alon-Boppana bound on $d$-regular graphs and Feng-Li bound on $(d,r)$-regular hypergraphs. By using interlacing family of polynomials, we prove that every $(d,r)$-regular hypergraph has a right-sided Ramanujan $2$-covering, and has a left-sided Ramanujan $2$-covering if the roots of the matching polynomial of its incident graph satisfy some condition. By Ramanujan $2$-coverings, we prove the existence of some families of infinite many left-sided or right-sided $(d,r)$-regular Ramanujan hypergraphs under certain conditions on $d$ and $r$.

The mass ($M_{\rm TOV}$) and radius ($R_{\rm TOV}$) of the maximum-mass nonrotating neutron star (NS) play a crucial role in constraining the elusive equation of state of cold dense matter and in predicting the fate of remnants from binary neutron star (BNS) mergers. In this study, we introduce a novel method to deduce these parameters by examining the mergers of second-generation (2G) black holes (BHs) with NSs. These 2G BHs are assumed to originate from supramassive neutron stars (SMNSs) formed in BNS mergers. Since the properties of the remnant BHs arising from the collapse of SMNSs follow a universal relation governed by $M_{\rm TOV}$ and $R_{\rm TOV}$, we anticipate that by analyzing a series ($\sim 100$ detections) of mass and spin measurements of the 2G BHs using the third-generation ground-based gravitational-wave detectors, $M_{\rm TOV}$ and $R_{\rm TOV}$ can be determined with a precision of $\sim 0.01M_\odot$ and $\sim 0.6$ km, respectively., Comment: 11 pages, 5 figures, ApJ published

The maximal gravitational mass of nonrotating neutron stars ($M_{\rm TOV}$) is one of the key parameters of compact objects and only loose bounds can be set based on the first principle. With reliable measurements of the masses and/or radii of the neutron stars, $M_{\rm TOV}$ can be robustly inferred from either the mass distribution of these objects or the reconstruction of the equation of state (EoS) of the very dense matter. For the first time we take the advantages of both two approaches to have a precise inference of $M_{\rm TOV}=2.25^{+0.08}_{-0.07}~M_\odot$ (68.3\% credibility), with the updated neutron star mass measurement sample, the mass-tidal deformability data of GW170817, the mass-radius data of PSR J0030+0451 and PSR J0740+6620, as well as the theoretical information from the chiral effective theory ($\chi$EFT) and perturbative quantum chromodynamics (pQCD) at low and very high energy densities, respectively. This narrow credible range is benefited from the suppression of the high $M_{\rm TOV}$ by the pQCD constraint and the exclusion of the low $M_{\rm TOV}$ by the mass function. Three different EoS reconstruction methods are adopted separately, and the resulting $M_{\rm TOV}$ and $R_{\rm TOV}$ are found to be almost identical, where $R_{\rm TOV}=11.90^{+0.63}_{-0.60}$ km is the radius of the most massive non-rotating NS. This precisely evaluated $M_{\rm TOV}$ suggests that the EoS of neutron star matter is just moderately stiff and the $\sim 2.5-3M_\odot$ compact objects detected by the second generation gravitational wave detectors are most likely the lightest black holes., Comment: 17 pages, 9 figures. The latest mass measurements of the neutron stars up to April 2023 have been summarized in Table 1 of the Appendix. Published in PRD with moderate revision

For bright transients such as Gamma-Ray Bursts (GRBs), the Ultra-Violet/Optical Telescope (UVOT) operates under event mode at early phases, which records incident positions and arrival time for each photon. The event file is able to be screened into many exposures to study the early light curve of GRBs with a high time resolution, including in particular the rapid brightening of the UV/Optical emission. Such a goal, however, is hampered for some extremely bright GRBs by the saturation in UVOT event images. For moderately saturated UVOT sources, in this work we develop the method proposed in Jin et al. (2023) to recover their photometries. The basic idea is to assume a stable point spread function (PSF) of UVOT images, for which the counts in the core region (i.e., an aperture of a radius of 5 arcsec) and the wing region (i.e., an annulus ranging from 15 arcsec to 25 arcsec) should be a constant and the intrinsic flux can be reliably inferred with data in the ring. We demonstrate that in a given band, a tight correlation does hold among the background-removed count rates in the core and the wing. With the new method, the bright limit of measuring range for UVOT V and B bands increases ~ 1.7 mag, while only ~ 0.7 mag for U band due to the lack of bright calibration sources. Systematic uncertainties are ~ 0.2 mag for V, B and U bands., Comment: 27 pages, 19 figures, 3 tables, accepted to ApJS

Early results from the James Webb Space Telescope (JWST) observations have hinted at two traces beyond the standard cosmological framework. One is the extraordinarily high stellar masses and their density at $z=7.5\sim9.1$, another is the unexpected abundance of ultraviolet (UV) bright galaxies at $z\ge10$. Nevertheless, both pieces of evidence are not statistically robust yet. In this work, we construct rest-frame UV luminosity functions (LFs) based on a general formation model for these high-redshift galaxy candidates, since UV LFs always carry the information of stellar formation efficiency (SFE), initial mass function (IMF), dust attenuation, and other crucial elements for galaxy evolution. By updating the massive galaxies candidates with spectroscopic observations and exploring the parameter space of SFE, we are able to reasonably explain the cumulative stellar mass density within the redshift range of $7.5\sim9.1$, with only one galaxy exhibiting unusual characteristics. We also reveal a potential nonmonotonic trend of SFE with the increasing redshift. At higher redshift ($z\sim13$), bright UV LFs can be well fitted with non-dust attenuation or top-heavy IMF for Population III stars. The Population III star scenario can also naturally account for the possible dip of the peak SFE evolution curve at $z\sim9$., Comment: 10 pages, 7 figures, and 2 tables. Published in ApJL

Several Pulsar Timing Array (PTA) collaborations have recently provided strong evidence for a nHz Stochastic Gravitational-Wave Background (SGWB). Here we investigate the implications of a first-order phase transition occurring within the early universe's dark quantum chromodynamics (dQCD) epoch, specifically within the framework of the mirror twin Higgs dark sector model. Our analysis indicates a distinguishable SGWB signal originating from this phase transition, which can explain the measurements obtained by PTAs. Remarkably, a significant portion of the parameter space for the SGWB signal also effectively resolves the existing tensions in both the $H_0$ and $S_8$ measurements in Cosmology. This intriguing correlation suggests a possible common origin of these three phenomena for $0.2 < \Delta N_{\rm eff} < 0.5$, where the mirror dark matter component constitutes about $30\%$ of the total dark matter abundance. Next generation CMB experiment such as CMB-S4 is able to test this parameter region., Comment: 7 pages, 4 figures

The edge blow-up of a graph $G$, denoted by $G^{p+1}$, is obtained by replacing each edge of $G$ with a clique of order $p+1$, where the new vertices of the cliques are all distinct. Yuan [J. Comb. Theory, Ser. B, 152 (2022) 379-398] determined the range of the Tur\'{a}n numbers for edge blow-up of all bipartite graphs and the exact Tur\'{a}n numbers for edge blow-up of all non-bipartite graphs. In this paper we prove that the graphs with the maximum spectral radius in an $n$-vertex graph without any copy of edge blow-up of star forests are the extremal graphs for edge blow-up of star forests when $n$ is sufficiently large., Comment: 22. arXiv admin note: text overlap with arXiv:2208.06550

Neural network quantum state (NNQS) has emerged as a promising candidate for quantum many-body problems, but its practical applications are often hindered by the high cost of sampling and local energy calculation. We develop a high-performance NNQS method for \textit{ab initio} electronic structure calculations. The major innovations include: (1) A transformer based architecture as the quantum wave function ansatz; (2) A data-centric parallelization scheme for the variational Monte Carlo (VMC) algorithm which preserves data locality and well adapts for different computing architectures; (3) A parallel batch sampling strategy which reduces the sampling cost and achieves good load balance; (4) A parallel local energy evaluation scheme which is both memory and computationally efficient; (5) Study of real chemical systems demonstrates both the superior accuracy of our method compared to state-of-the-art and the strong and weak scalability for large molecular systems with up to $120$ spin orbitals., Comment: Accepted by SC'23, fix Table1 CCSD references

Recently, pulsar timing array (PTA) experiments have provided compelling evidence for the existence of the nanohertz stochastic gravitational wave background (SGWB). In this work, we demonstrated that cosmic string loops generated from cosmic global strings offer a viable explanation for the observed nanohertz SGWB data, requiring a cosmic string tension parameter of $\log(G\mu) \sim -12$ and a loop number density of $\log N \sim 4$. Additionally, we revisited the impact of cosmic string loops on the abundance of massive galaxies at high redshifts. However, our analysis revealed challenges in identifying a consistent parameter space that can concurrently explain both the SGWB data and observations from the James Webb Space Telescope. This indicates the necessity for either extending the existing model employed in this research or acknowledging distinct physical origins for these two phenomena., Comment: 7 pages, 4 figures, accepted for publication in Sci. China-Phys. Mech. Astron. (SCPMA)

The origin of interstellar and intergalactic magnetic fields remains largely unknown. One possibility is that they are related to the primordial magnetic fields (PMFs) produced by, for instance, the phase transitions of the early Universe. In this paper, we show that the PMF-induced turbulence generated at around the QCD phase transition epoch--the characteristic magnetic field strength $B_{\rm ch}^* \sim \mathcal{O}(1)~\rm{\mu G}$ and coherent length scale $\ell_{\rm ch}^* \sim \mathcal{O}(1)~\rm{pc}$--can naturally accommodate nanohertz gravitational waves reported by pulsar timing array (PTA) collaborations. Moreover, the evolution of the PMFs to the recombination era with the form of $B_{\rm ch}\sim \ell_{\rm ch}^{-\alpha}$ can induce baryon density inhomogeneities, alter the recombination history, and alleviate the tension of the Hubble parameter $H_0$ and the matter clumpiness parameter $S_8$ between early- and late-time measurements for $0.88\leq \alpha \leq 1.17$ (approximate 95\% credible region based on three PTA likelihoods). The further evolved PMFs may account for the $\sim {\cal O}(10^{-16})$ Gauss extragalactic magnetic field inferred with GRB 221009A., Comment: 7 pages, 3 figures, 1 table

This study investigates the antineutrinos production by $\beta$-decay of $r$-process nuclei in two astrophysical sites that are capable of producing gamma-ray bursts (GRBs): binary neutron star mergers (BNSMs) and collapsars, which are promising sites for heavy element nucleosynthesis. We employ a simplified method to compute the $\beta$-decay $\bar\nu_e$ energy spectrum and consider a number of different representative thermodynamic trajectories for $r$-process simulations, each with four sets of $Y_e$ distribution. The time evolution of the $\bar\nu_e$ spectrum is derived for both the dynamical ejecta and the disk wind for BNSMs and collapsar outflow, based on approximated mass outflow rates. Our results show that the $\bar\nu_e$ has an average energy of approximately 3 to 9~MeV, with a high energy tail of up to 20 MeV. The $\bar\nu_e$ flux evolution is primarily determined by the outflow duration, and can thus remain large for $\mathcal{O}(10)$~s and $\mathcal{O}(100)$~s for BNSMs and collapsars, respectively. For a single merger or collapsar at 40~Mpc, the $\bar\nu_e$ flux is $\mathcal{O}(10-100)$~cm$^{-2}$~s$^{-1}$, indicating a possible detection horizon up to $0.1-1$~Mpc for Hyper-Kamiokande. We also estimate their contributions to the diffuse $\bar\nu_e$ background, and find that both sources should only contribute subdominantly to the diffuse background when compared to that expected from core-collapse supernovae., Comment: 14 pages, 8 figures