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We present new scaling relations for the isotropic phase-space distribution functions (DFs) and energy distributions of simulated dark matter haloes. These relations are inspired by those for the singular isothermal sphere with density profile $\rho(r)\propto r^{-2}$, for which the DF satisfies $f(E) \propto r_{\max}^{-2}(E)$ and the energy distribution satisfies $dM/dE \propto r_{\max}(E)$, with $r_{\max}(E)$ being the radius where the gravitational potential equals energy $E$. For the simulated haloes, we find $f(E)\propto r_{\max}^{-2.08}(E)$ and $dM/dE \propto r_{\max}(E)$ across broad energy ranges. In addition, the proportionality coefficients depend on the gravitational constant and the parameters of the best-fit Navarro-Frenk-White density profile. These scaling relations are satisfied by haloes over a wide mass range and provide an efficient method to approximate their DFs and energy distributions. Understanding the origin of these relations may shed more light on halo formation., Comment: 9 pages, 4 figures, comments are welcome

We introduce the emPDF (Empirical Distribution Function), a novel dynamical modeling method that infers the gravitational potential from kinematic tracers with optimal statistical efficiency under the minimal assumption of steady state. emPDF determines the best-fit potential by maximizing the similarity between instantaneous kinematics and the time-averaged phase-space distribution function (DF), which is empirically constructed from observation upon the theoretical foundation of oPDF (Han et al. 2016). This approach eliminates the need for presumed functional forms of DFs or orbit libraries required by conventional DF- or orbit-based methods. emPDF stands out for its flexibility, efficiency, and capability in handling observational effects, making it preferable to the popular Jeans equation or other minimal assumption methods, especially for the Milky Way (MW) outer halo where tracers often have limited sample size and poor data quality. We apply emPDF to infer the MW mass profile using Gaia DR3 data of satellite galaxies and globular clusters, obtaining consistent measurements with the constraints from simulation-informed DF fitting (Li et al. 2020). While the simulation-informed DF offers superior precision owing to the additional information extracted from simulations, emPDF is independent of such supplementary knowledge and applicable to general tracer populations. We provide tabulated measurements of the mass profile from emPDF, along with updated measurements from simulation-informed DF., Comment: 18 pages, 10 figures. Submitted to MNRAS. Comments are welcome

We study $\nu_\mu$-$\nu_s$ and $\bar\nu_\mu$-$\bar\nu_s$ mixing in the protoneutron star (PNS) created in a core-collapse supernova (CCSN). We point out the importance of the feedback on the general composition of the PNS in addition to the obvious feedback on the $\nu_\mu$ lepton number. We show that for our adopted mixing parameters $\delta m^2\sim 10^2$~keV$^2$ and $\sin^2 2\theta$ consistent with the current constraints, sterile neutrino production is dominated by the Mikheyev-Smirnov-Wolfenstein conversion of $\bar\nu_\mu$ into $\bar\nu_s$ and that the subsequent escape of $\bar\nu_s$ increases the $\nu_\mu$ lepton number, which in turn enhances muonization of the PNS primarily through $\nu_\mu+n\to p+\mu^-$. While these results are qualitatively robust, their quantitative effects on the dynamics and active neutrino emission of CCSNe should be evaluated by including $\nu_\mu$-$\nu_s$ and $\bar\nu_\mu$-$\bar\nu_s$ mixing in the simulations., Comment: v2: 11 pages, 7 figures. Minor clarifications added, conclusion unchanged. Matches version published in PRD

For a spherical dark matter halo with isotropic velocity distribution, the phase space distribution function (DF), the energy distribution, and the density profile form a set of self-consistent description of its equilibrium state, and knowing one is sufficient to determine the other two. The Navarro-Frenk-White density profile (NFW profile) is known to be a good approximation to the spherically-averaged density distribution in simulated haloes. The DARKexp energy distribution is also known to compare well with the simulated energy distribution. We present a quantitative assessment of the NFW and DARKexp fits to the simulated DF and energy distribution for a wide range of haloes in a dark-matter-only simulation from the IllustrisTNG Project. As expected, we find that the NFW fits work well except at low energy when the density at small radii deviates from the NFW profile. Further, the NFW and DARKexp fits have comparable accuracy in the region where both fit well, but the DARKexp fits are better at low energy because they require matching of the central gravitational potential. We also find an approximate relation between the energy scale parameterizing the DARKexp energy distribution and that defined by the characteristic density and radius of the NFW profile. This relation may be linked to the relaxation process during halo formation., Comment: 9 pages, 7 figures, 1 table, accepted for publication in MNRAS

This paper explores core-collapse supernovae as crucial targets for neutrino telescopes, addressing uncertainties in their simulation results. We comprehensively analyze eighteen modern simulations and discriminate among supernova models using realistic detectors and interactions. A significant correlation between the total neutrino energy and cumulative counts, driven by massive lepton neutrinos and oscillations, is identified, particularly noticeable with the DUNE detector. Bayesian techniques indicate strong potential for model differentiation during a Galactic supernova event, with HK excelling in distinguishing models based on equation of state, progenitor mass, and mixing scheme., Comment: 31 pages, 12 Figures

We explore the possibility that high-energy (HE) neutrinos produced from choked jets can be annihilated with low-energy (LE) neutrinos emitted from the accretion disk around a black hole in binary neutron star mergers and rare core-collapse supernovae. For HE neutrinos produced close to the stellar center ($\lesssim 10^{9}-10^{12}$ cm), we find that the emerging all-flavor spectrum for neutrinos of $E\gtrsim 0.1-1$ PeV could be modified by a factor $E^{-n}$ with $n\gtrsim 0.4-0.5$ under realistic conditions. Flavor evolution of LE neutrinos does not affect this result but can change the emerging flavor composition of HE neutrinos. As a consequence, the above annihilation effect may need to be considered for HE neutrinos produced from choked jets at small radii. We briefly discuss the annihilation effects for different HE neutrino production models and point out that such effects could be tested through precise measurements of the diffuse neutrino spectrum and flavor composition., Comment: 11 pages, 4 figures

We present a data-driven model for abundances of Fe, Sr, Ba, and Eu in metal-poor (MP) stars. The production patterns for core-collapse supernovae (CCSNe) and binary neutron star mergers (BNSMs) are derived from the data of Holmbeck et al. (arXiv:2007.00749) on [Sr/Fe], [Ba/Fe], and [Eu/Fe] for 195 stars. Nearly all the data can be accounted for by mixtures of contributions from these two sources. We find that on average, the Sr contribution to an MP star from BNSMs is $\approx 3$ times that from CCSNe. Our model is also consistent with the solar inventory of Fe, Sr, Ba, and Eu. We carry out a parametric $r$-process study to explore the conditions that can give rise to our inferred production patterns and find that such conditions are largely consistent with those from simulations of CCSNe and BNSMs. Our model can be greatly enhanced by accurate abundances of many $r$-process elements in a large number of MP stars, and future results from this approach can be used to probe the conditions in CCSNe and BNSMs in much more detail., Comment: 7 pages, 5 figures, submitted to ApJ Letters

We study the problem of multimodal fusion in this paper. Recent exchanging-based methods have been proposed for vision-vision fusion, which aim to exchange embeddings learned from one modality to the other. However, most of them project inputs of multimodalities into different low-dimensional spaces and cannot be applied to the sequential input data. To solve these issues, in this paper, we propose a novel exchanging-based multimodal fusion model MuSE for text-vision fusion based on Transformer. We first use two encoders to separately map multimodal inputs into different low-dimensional spaces. Then we employ two decoders to regularize the embeddings and pull them into the same space. The two decoders capture the correlations between texts and images with the image captioning task and the text-to-image generation task, respectively. Further, based on the regularized embeddings, we present CrossTransformer, which uses two Transformer encoders with shared parameters as the backbone model to exchange knowledge between multimodalities. Specifically, CrossTransformer first learns the global contextual information of the inputs in the shallow layers. After that, it performs inter-modal exchange by selecting a proportion of tokens in one modality and replacing their embeddings with the average of embeddings in the other modality. We conduct extensive experiments to evaluate the performance of MuSE on the Multimodal Named Entity Recognition task and the Multimodal Sentiment Analysis task. Our results show the superiority of MuSE against other competitors. Our code and data are provided at https://github.com/RecklessRonan/MuSE.

Neutrinos are known to play important roles in many astrophysical scenarios from the early period of the big bang to current stellar evolution being a unique messenger of the fusion reactions occurring in the center of our sun. In particular, neutrinos are crucial in determining the dynamics and the composition evolution in explosive events such as core-collapse supernovae and the merger of two neutron stars. In this paper, we review the current understanding of supernovae and binary neutron star mergers by focusing on the role of neutrinos therein. Several recent improvements on the theoretical modeling of neutrino interaction rates in nuclear matter as well as their impact on the heavy element nucleosynthesis in the supernova neutrino-driven wind are discussed, including the neutrino-nucleon opacity at the mean field level taking into account the relativistic kinematics of nucleons, the effect due to the nucleon-nucleon correlation, and the nucleon-nucleon bremsstrahlung. We also review the framework used to compute the neutrino-nucleus interactions and the up-to-date yield prediction for isotopes from neutrino nucleosynthesis occurring in the outer envelope of the supernova progenitor star during the explosion. Here improved predictions of energy spectra of supernova neutrinos of all flavors have had significant impact on the nucleosynthesis yields. Rapid progresses in modeling the flavor oscillations of neutrinos in these environments, including several novel mechanisms for collective neutrino oscillations and their potential impacts on various nucleosynthesis processes are summarized., Comment: Matches the published version on PPNP

We present an approximate treatment of the mixing between $\nu_{\tau}$ ($\bar\nu_{\tau}$) and a sterile species $\nu_s$ ($\bar\nu_s$) with a vacuum mass-squared difference of $\sim$ 10$^2$-10$^3$ keV$^2$ in protoneutron stars created in core-collapse supernovae. Including production of sterile neutrinos through both resonant flavor conversion and collisions, we track the evolution of the $\nu_{\tau}$ lepton number due to both escape of sterile neutrinos and diffusion. Our approach provides a reasonable treatment of the pertinent processes discussed in previous studies and serves a pedagogical purpose to elucidate the relevant physics. We also discuss refinements needed to study more accurately how flavor mixing with sterile neutrinos affects protoneutron star evolution., Comment: v2: 8 pages, 4 figures. Matches version published in PRD

We identify a geometric symmetry on the two-flavor Bloch sphere for collective flavor oscillations of a homogeneous dense neutrino gas. Based on this symmetry, analytical solutions to the periodic bipolar flavor evolution are derived. Using numerical calculations, we show that for configurations without this symmetry, the flavor evolution displays deviations from the bipolar flavor motion or even exhibits aperiodic patterns. We also discuss the implication of our finding for more general three-flavor and inhomogeneous cases., Comment: 11 pages, 4 figures

If collapsars are sources for both high-energy (HE) neutrinos and $r$-process nuclei, the profuse low-energy antineutrinos from $\beta$-decay of the newly-synthesized nuclei can annihilate the HE neutrinos. Considering HE neutrinos produced at internal shocks induced by intermittent mildly-magnetized jets, we show that such annihilation suppresses the overall HE neutrino spectrum at $\gtrsim 300$~TeV and produces a corresponding flavor composition of $(F_{\nu_e+\bar\nu_e}: F_{\nu_\mu+\bar\nu_\mu}: F_{\nu_\tau+\bar\nu_\tau})_\star \approx (1 : 10 : 1)$ at source. We find that the emergent HE neutrino flux can well fit the diffuse flux observed at IceCube if contributions from all similar sources are taken into account. Our results highlight the unique role of HE neutrinos in supporting collapsars as sources for $r$-process nuclei, and can be tested by accurate measurement of the diffuse HE neutrino flux spectrum and flavor composition, as well as detection of HE neutrinos from individual sources., Comment: 10 pages, 7 figures

The next Galactic core-collapse supernova (SN) should yield a large number of observed neutrinos. Using Bayesian techniques, we show that with an SN at a known distance up to 25 kpc, the neutrino events in a water Cherenkov detector similar to Super-Kamiokande (SK) could be used to distinguish between seven one-dimensional neutrino emission models assuming no flavor oscillations or the standard Mikheyev-Smirnov-Wolfenstein effect. Some of these models could still be differentiated with an SN at a known distance of 50 kpc. We also consider just the relative distributions of neutrino energy and arrival time predicted by the models and find that a detector like SK meets the requirement to distinguish between these distributions with an SN at an unknown distance up to $\sim 10$ kpc., Comment: 12 pages, 2 figures

Metal-poor stars were formed during the early epochs when only massive stars had time to evolve and contribute to the chemical enrichment. Low-mass metal-poor stars survive until the present and provide fossil records of the nucleosynthesis of early massive stars. On the other hand, short-lived radionuclides (SLRs) in the early solar system (ESS) reflect the nucleosynthesis of sources that occurred close to the proto-solar cloud in both space and time. Both the ubiquity of Sr and Ba and the diversity of heavy-element abundance patterns observed in single metal-poor stars suggest that some neutron-capture mechanisms other than the r-process might have operated in early massive stars. Three such mechanisms are discussed: the weak s-process in non-rotating models with initial carbon enhancement, a new s-process induced by rapid rotation in models with normal initial composition, and neutron-capture processes induced by proton ingestion in non-rotating models. In addition, meteoritic data are discussed to constrain the core-collapse supernova (CCSN) that might have triggered the formation of the solar system and provided some of the SLRs in the ESS. If there was a CCSN trigger, the data point to a low-mass CCSN as the most likely candidate. An 11.8 solar mass CCSN trigger is discussed. Its nucleosynthesis, the evolution of its remnant, and the interaction of the remnant with the proto-solar cloud appear to satisfy the meteoritic constraints and can account for the abundances of the SLRs 41Ca, 53Mn, and 60Fe in the ESS., Comment: 5 pages, Proceedings of the 16th International Symposium on Nuclei in the Cosmos