% !TeX root = ../main.tex

% 中英文摘要和关键字

\begin{abstract}
热亚矮星是一类特殊恒星，它质量只有太阳的一半，处于氦核稳定燃烧阶段。它的壳层质量非常低（小于$0.01\,{M}_\odot$），并且恒星表面元素丰度也存在显著差异。观测数据显示，超过一半的热亚矮星处于双星系统中，这一现象表示，双星中的一些机制可能在热亚矮星的形成过程中可能发挥着重要作用。对于热亚矮星的研究，能够帮助我们了解小质量恒星的后期演化，恒星内部的元素扩散，处于双星系统中的热亚矮星则为物质转移机制的观测研究提供了关键数据支持，而部分脉动的热亚矮星可以成为星震学研究的天然探针，为恒星内部结构的研究提供了理想样本。

尽管已有超过6000颗热亚矮星被证认，但只有很少一部分热亚矮星的的质量被精确测定。质量作为恒星演化中的重要参数，其分布特征可揭示不同光谱型热亚矮星的形成机制。目前关于热亚矮星的质量其主要计算方法有三种，分别是星震学、双星动力学、以及光谱能量分布拟合。其中，星震学和双星动力学虽精度较高，但受限于观测条件仅适用于少数特殊样本。相比之下，通过光谱能量分布计算质量的方法应用广泛且可信度较高，成为研究大样本热亚矮星质量分布的主要手段，但也受限于合成光谱能量分布计算的复杂性。

本研究提出了一种深度学习模型SENN（基于卷积神经网络和自注意力机制），利用LAMOST和SDSS光谱数据预测了1025颗已知热亚矮星的合成光谱能量分布（SED）。借助西班牙虚拟天文台的VOSA服务，通过对比预测SED与观测流量，我们获得了这些恒星的高质量参数（包括质量、半径和光度）。相较于以往研究，本研究的大样本统计分析为探索不同光谱型热亚矮星的形成机制提供了更可靠的依据。

结果显示，sdB/sdOB型热亚矮星的质量分布与双星星族合成（BPS）模型预测高度吻合，其两个质量峰（约$0.46\,\mathrm{ M}_\odot$和$0.36\,\mathrm{ M}_\odot$）分别对应公共包层抛射（CE）和稳定洛希瓣物质转移（RLOF）两种形成机制。对于富氦热亚矮星，其质量分布也出现了一个主峰（约$0.56\,\mathrm{ M}_\odot$）和一个次峰（约$0.4\,\mathrm{ M}_\odot$）。与近期BPS模型的对比表明，双氦白矮星（He-WD）合并通道可解释大部分富氦热亚矮星的形成，但双星演化中洛希瓣溢流阶段的物质转移需满足至少部分守恒甚至完全守恒条件。然而，由于本研究中质量参数存在较大不确定性，其他潜在形成通道（如超新星伴星演化）仍不能完全排除。

% 关键词用“英文逗号”分隔
  \xtusetup{
    keywords = {热亚矮星, 双星系统, 恒星演化, 质量分布, 神经网络}
  }
\end{abstract}

\begin{abstract*}
Hot subdwarf stars are a unique class of low-mass stars (typically $0.5\,{M}_\odot$) undergoing stable helium-core burning. Their extremely thin hydrogen-rich envelopes (mass $<0.01\,{M}_\odot$) and diverse surface elemental abundances distinguish them from ordinary main-sequence stars. Observations reveal that over half of these stars reside in binary systems, suggesting that dynamical interactions within binaries play a critical role in their formation. Studying hot subdwarfs provides insights into the late-stage evolution of low-mass stars and the mechanisms of element diffusion within stellar interiors. For binary system members, they offer key observational constraints on mass transfer processes, while pulsating subdwarfs act as natural probes for asteroseismic studies, enabling detailed analysis of internal stellar structures through their oscillation modes.

Despite the identification of over 6,000 hot subdwarf stars, only a small fraction have had their masses accurately determined. As a fundamental parameter in stellar evolution, mass distributions hold clues to the formation pathways of different spectral subtypes. Current mass determination methods include asteroseismology, binary dynamics, and spectral energy distribution (SED) fitting. While asteroseismology and binary dynamics provide high precision, their applicability is restricted to rare cases due to observational limitations. In contrast, SED-based mass estimation is widely adopted for statistical studies of large stellar samples, despite challenges posed by the computational complexity of synthetic SED calculations.

This study introduces a novel deep learning model, SENN (CNN with Squeeze-and-Excitation blocks), to predict synthetic SEDs for 1,025 known hot subdwarf stars using spectra from LAMOST and SDSS. By comparing these synthetic SEDs with observed fluxes via the VOSA service of the Spanish Virtual Observatory, we derived precise physical parameters (mass, radius, and luminosity) for this large sample. This dataset provides a statistically robust foundation for exploring formation mechanisms of different spectral-type subdwarfs.

Results show that the mass distribution of sdB/sdOB stars aligns well with predictions from binary population synthesis (BPS) models. Two distinct mass peaks (around $0.46\,M_\odot$ and $0.36\,M_\odot$) correspond to formation pathways via common envelope ejection (CE) and stable Roche lobe overflow (RLOF), respectively. For helium-rich subdwarfs, a prominent primary peak ($\sim 0.56\,M_\odot$) and a secondary peak ($\sim 0.4\,M_\odot$) are evident. Comparisons with recent BPS models suggest that the merger of two helium white dwarfs (He-WDs) dominates the formation of observed helium-rich subdwarfs. However, the secondary peak’s prevalence implies that mass transfer during RLOF must be at least partially conserved. Despite these findings, uncertainties in mass determinations leave room for alternative formation channels (e.g., supernova companion evolution). Future work requires higher-precision observational data and refined theoretical models to fully characterize the diversity of hot subdwarf formation mechanisms.

  \xtusetup{
    keywords* = {Hot subdwarf, Binary, Star evolution, Mass distribution, Neural network}
  }
\end{abstract*}
