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docs: 修订 AA 论文文字与格式，更新 .gitignore 并整理项目结构 - 修正 AA54562-25.tex 中的拼写错误和零宽字符 - 统一数学符号格式，去除段落多余前导空格和换行 - 更新 .gitignore 忽略 ADS 输出文件和 AI 工具目录
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% aims heading (mandatory)
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{The formation mechanisms of spectrally diverse hot subdwarfs remain unclear. While existing mass distribution analyses suggest additional channels beyond helium white dwarf (He-WD) mergers contribute to He-rich subdwarf formation, these conclusions are constrained by the limited sample sizes of mass-measured He-rich objects.}
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% methods heading (mandatory)
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{We developed a deep leaning model that combines a convolution neural network (CNN) with a squeeze-and-excitation (SE) block to calculate synthetic spectral energy distributions (SEDs) for 1,012 spectroscopically confirmed hot subdwarfs. By directly comparing synthetic SEDs and the observed flux density, we derived stellar parameters (mass, radius, and luminosity) for an unprecedented number of hot subdwarf stars, enabling more conclusive channel discrimination than prior studies.}
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{We developed a deep learning model that combines a convolutional neural network (CNN) with a squeeze-and-excitation (SE) block to calculate synthetic spectral energy distributions (SEDs) for 1,012 spectroscopically confirmed hot subdwarfs. By directly comparing synthetic SEDs and the observed flux density, we derived stellar parameters (mass, radius, and luminosity) for an unprecedented number of hot subdwarf stars, enabling more conclusive channel discrimination than prior studies.}
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% results heading (mandatory)
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{The mass distribution of sdB/sdOB stars confirmed the results from model predictions of binary population synthesis (BPS). A primary and secondary peak (i.e., around 0.56 and 0.4 ${\rm M}_{\odot}$) is obviously presented in the mass distribution of He-rich hot subdwarf stars. By comparing this with the results from the predictions of the recent BPS model, we propose that the merger of two He-WDs could produce most of the observed He-rich hot subdwarf stars, but the mass transfer during the stable Roche lobe overflow phase in binary evolution should be partially conserved.}
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% conclusions heading (optional), leave it empty if necessary
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%________________________________________________________________
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\section{Introduction}
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Hot subdwarf stars are positioned between main-sequence (MS) and white dwarf (WD) regions in the Hertzsprung-Russell diagram (HRD) \citep{1986A&Aheber}. Hot subdwarf stars have very low stellar masses (e.g., 0.5 ${\rm M}_{\odot}$) and thin envelopes ($M_{\text{env}} \le 0.02 M_{\odot}$), but exhibit very high effective temperatures (e.g., $20,000~\mathrm{K} \leq T_{\text{eff}} \leq 70,000~\mathrm{K}$) and large surface gravities (e.g., $5.0 \leq \log g \leq 6.5$). These blue stars have a diversity of atmospheric compositions that could present atmospheres from pure hydrogen (H) to pure helium (He). According to their spectral line features, hot subdwarfs can be classified into sdB, sdO, sdOB, He-sdB, He-sdO, and He-sdOB types \citep{1990_A&AS_moehler,2017_A&A_geier, 2018ApJ...868...70L}. In addition, \citet{2013A&A...551A..31D} designed an MK-like classification scheme by which hot subdwarf stars could be classified in a similar way as normal MS stars (also see \citealt{2021MNRAS.501..623J, 2024PASJ...76.1084Z}). SdB stars are also referred to as extreme horizontal branch (EHB) stars due to their location at the bluest end of the horizontal branch (HB
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). More characteristics of hot subdwarf stars were described in recent excellent reviews of \citet{2009ARA&A..47..211H, 2016PASPHeber}.
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Hot subdwarf stars are positioned between main-sequence (MS) and white dwarf (WD) regions in the Hertzsprung-Russell diagram (HRD) \citep{1986A&Aheber}. Hot subdwarf stars have very low stellar masses (e.g., 0.5 ${\rm M}_{\odot}$) and thin envelopes ($M_{\text{env}} \le 0.02 {\rm M}_{\odot}$), but exhibit very high effective temperatures (e.g., $20,000~\mathrm{K} \leq T_{\text{eff}} \leq 70,000~\mathrm{K}$) and large surface gravities (e.g., $5.0 \leq \log g \leq 6.5$). These blue stars have a diversity of atmospheric compositions that could present atmospheres from pure hydrogen (H) to pure helium (He). According to their spectral line features, hot subdwarfs can be classified into sdB, sdO, sdOB, He-sdB, He-sdO, and He-sdOB types \citep{1990_A&AS_moehler,2017_A&A_geier, 2018ApJ...868...70L}. In addition, \citet{2013A&A...551A..31D} designed an MK-like classification scheme by which hot subdwarf stars could be classified in a similar way as normal MS stars (also see \citealt{2021MNRAS.501..623J, 2024PASJ...76.1084Z}). SdB stars are also referred to as extreme horizontal branch (EHB) stars due to their location at the bluest end of the horizontal branch (HB). More characteristics of hot subdwarf stars were described in recent excellent reviews of \citet{2009ARA&A..47..211H, 2016PASPHeber}.
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Generally, single stars with such low stellar masses as hot subdwarfs cannot evolve into core He burning or even a late stage within Hubble time. Although formation channels connected with single stars were proposed by several authors (\citealt{1993ApJ...407..649C, 2008A&A...491..253M}), \citet{2020A&A...642A.180P} found that binary interactions are always required in the formation of hot subdwarf stars, including those in wide binary systems.
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Furthermore, most of the sdB-type hot subdwarfs were found in close binaries \citep{2001MNRASmaxted, 2004Ap&SSnapiwotzki,2011MNRAScopperwheat, 2025A&A...693A.121H}. These results indicate that binary evolution could provide natural explanations for the formation of hot subdwarfs.
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@@ -112,10 +111,10 @@ Using these SEDs, we calculated the synthetic fluxes at stellar surface and comp
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\label{Fig 1}
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\end{figure*}
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We designed a deep learning model, which integrates a CNN neural network with a SE block (hereafter SENN), to calculate synthetic SEDs for selected hot subdwarf stars. As is shown in \Fig \ref{Fig 1}, SENN accepts normalized stellar spectra with a shape of 2,984 $\times$ 1 as inputs, and processes them through a hierarchical architecture to calculate SEDs. The model comprises three modules. The initial feature embedding module uses a 1D convolution layer (64 filters, 3 kernels, and ReLU activation) to capture local spectral features, and reshape the output into a 64 $\times$ 2982 tensor. The SE feature refinement module is then employed, in which a global average pooling (GAP) layer compresses global spatial information into a channel-wise descriptor. This descriptor is connected by two dense layers to fully capture channel-wise dependencies and compute channel-specific weights. These weights are then applied to the original feature map, producing the final weighted feature map. Finally, the SED regression module is used to flatten the refined features, pass them through a 64-neuron dense layer, and generate SEDs through an output layer.
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We designed a deep learning model, which integrates a CNN with a SE block (hereafter SENN), to calculate synthetic SEDs for selected hot subdwarf stars. As is shown in \Fig \ref{Fig 1}, SENN accepts normalized stellar spectra with a shape of 2,984 $\times$ 1 as inputs, and processes them through a hierarchical architecture to calculate SEDs. The model comprises three modules. The initial feature embedding module uses a 1D convolution layer (64 filters, 3 kernels, and ReLU activation) to capture local spectral features, and reshape the output into a 64 $\times$ 2982 tensor. The SE feature refinement module is then employed, in which a global average pooling (GAP) layer compresses global spatial information into a channel-wise descriptor. This descriptor is connected by two dense layers to fully capture channel-wise dependencies and compute channel-specific weights. These weights are then applied to the original feature map, producing the final weighted feature map. Finally, the SED regression module is used to flatten the refined features, pass them through a 64-neuron dense layer, and generate SEDs through an output layer.
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The SENN model takes observed spectra as input features and their corresponding synthetic SEDs as training labels. Through training processes, SENN
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established a mapping relationship between observed spectra and synthetic SEDs, enabling it to calculated the synthetic SED associated with a given observed spectrum. With these synthetic SED and the observed magnitudes retrieved from the virtual observatory (VO), we could calculate the masses, radii and luminosities of hot subdwarf stars reported in \citet{2022A&ACulpan}, if their atmospheric parameters are known (e.g., $T_{\text{eff}}$ and $\log g$. see Section 2.3).
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established a mapping relationship between observed spectra and synthetic SEDs, enabling it to calculate the synthetic SED associated with a given observed spectrum. With these synthetic SED and the observed magnitudes retrieved from the virtual observatory (VO), we could calculate the masses, radii and luminosities of hot subdwarf stars reported in \citet{2022A&ACulpan}, if their atmospheric parameters are known (e.g., $T_{\text{eff}}$ and $\log g$. see Section 2.3).
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\subsection{Training dataset}
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@@ -131,7 +130,7 @@ and low-quality spectra (e.g., that had a signal-to-noise ratio in the u band of
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Using the SENN model constructed in Section 2.1 and the training dataset selected in Section 2.2, synthetic SEDs for 2047 selected hot subdwarf stars were calculated; these were then used to obtain stellar masses, radii, and luminosities, as is described in the next section. Note that the SENN model is much more efficient at calculating synthetic SEDs than traditional methods. For example, it just needs tens of seconds to obtain synthetic SEDs for 2000 stars, and would be more powerful when confronting with huge numbers of stars.
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In Fig \ref{Fig 2}, we compare the synthetic SED of a hot subdwarf star calculated using the SENN model (dashed blue curve) with that computed directly from the Tlusty model (solid red curve). The near-identical agreement between the two SEDs fully demonstrates that utilizing the deep learning method to calculate theoretical SEDs for hot subdwarfs is both feasible and reliable.
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In Fig \ref{Fig 2}, we compare the synthetic SED of a hot subdwarf star calculated using the SENN model (dashed blue curve) with that computed directly from the Tlusty model (solid red curve). The near-identical agreement between the two SEDs fully demonstrates that utilizing the deep learning method to calculate theoretical SEDs for hot subdwarfs is both feasible and reliable.
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\subsection{Determination of masses, radii, and luminosities for selected hot subdwarf stars}
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@@ -171,9 +170,9 @@ which yielding the intrinsic flux density, $f(\lambda)$. The best-fit $A_{\rm V}
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\label{Fig 2}
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\end{figure}
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Using the method described above, we obtained masses, radii, and luminosities for the selected 2,047 hot subdwarf stars. The stars with mass values lower than 0.1 $M_\odot$ or higher than 1.0 $M_\odot$ are not reported here, since these values could be significantly influenced by large uncertainties of input parameters, and are not reasonable for normal hot subdwarf stars. Furthermore, only stars with reliable parallaxes (e.g., $\sigma_{\varpi}/\varpi\leq$ 0.2) are included in the following analysis. Thus, we finally have 1,012 hot subdwarf stars for which the main parameters are reported in this study (see Table \ref{tab1}), consisting of 606 sdB, 64 sdO, 206 sdOB, 9 He-sdB, 66 He-sdO, and 61 He-sdOB stars, respectively. The obtained parameter values are presented in Table \ref{tab1}.
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Using the method described above, we obtained masses, radii, and luminosities for the selected 2,047 hot subdwarf stars. The stars with mass values lower than 0.1 $M_\odot$ or higher than 1.0 $M_\odot$ are not reported here, since these values could be significantly influenced by large uncertainties of input parameters, and are not reasonable for normal hot subdwarf stars. Furthermore, only stars with reliable parallaxes (e.g., $\sigma_{\varpi}/\varpi\leq$ 0.2) are included in the following analysis. Thus, we finally have 1,012 hot subdwarf stars for which the main parameters are reported in this study (see Table \ref{tab1}), consisting of 606 sdB, 64 sdO, 206 sdOB, 9 He-sdB, 66 He-sdO, and 61 He-sdOB stars, respectively. The obtained parameter values are presented in Table \ref{tab1}.
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Using Monte Carlo methods, we obtained the statistical errors ($\sigma_{sta}$) for mass, radius, and luminosity of the selected stars. Specifically, we calculated the median values for the three parameters, along with their values at the 16th and 84th percentiles. This defines a 68\% confidence interval around the median values and provides the corresponding asymmetric uncertainties.
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Using Monte Carlo methods, we obtained the statistical errors ($\sigma_{sta}$) for mass, radius, and luminosity of the selected stars. Specifically, we calculated the median values for the three parameters, along with their values at the 16th and 84th percentiles. This defines a 68\% confidence interval around the median values and provides the corresponding asymmetric uncertainties.
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On the other hand, we cross-matched the sample from this work with the sample from \citet{2022A&ASchaffenroth}, and identified 24 common sources. By comparing the masses, radii, and luminosities for these 24 sources, we determined the systematic errors ($\sigma_{sys}$), which were calculated using the following formula:
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\begin{equation*}
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@@ -183,7 +182,7 @@ which yielding the intrinsic flux density, $f(\lambda)$. The best-fit $A_{\rm V}
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\begin{equation}
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\sigma=\sqrt{\sigma_{sta}^2+\sigma_{sys}^2}
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.\end{equation}
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Using the method described above, we obtained systematic errors of 0.02 $\rm M_{\odot}$ , 0.002 $\rm R_{\odot}$, and 1.4 $\rm L_{\odot}$ for mass, radius and luminosity, respectively. In Table \ref{tab1}, we presented the final errors for these three parameters, incorporating both statistical errors and systematic errors.
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Using the method described above, we obtained systematic errors of 0.02 $\rm M_{\odot}$ , 0.002 $\rm R_{\odot}$, and 1.4 $\rm L_{\odot}$ for mass, radius and luminosity, respectively. In Table \ref{tab1}, we presented the final errors for these three parameters, incorporating both statistical errors and systematic errors.
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\section{Results}
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\subsection{Main parameters for selected hot subdwarf stars}
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@@ -200,7 +199,7 @@ The masses, radii, luminosities, and other important parameters for the 1,012 se
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The four panels in \Fig \ref{Fig 3} present the relationships between obtained masses and atmospheric parameters; for example, from top left to bottom right, it gives planes of mass versus $T_{\text{eff}}$, ${\rm log} g$, $\log (n_{\text{He}}/n_{\text{H}})$, and $\log L$, respectively. It can be observed that most of the selected hot subdwarfs have radii of between 0.1 and 0.3 $\rm R_{\odot}$, luminosities between 0.5 and 2.5 $\rm L_{\odot}$, and masses between 0.2 and 0.8 ${\rm M}_{\odot}$, respectively. These results are consistent with those of \citet{2023ApJLei}; see also \Fig 3 in their study.
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\subsection{Comparison with previous study}
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In order to evaluate the reliability of the masses, radii, and luminosities obtained in this study, we cross-matched the selected hot subdwarfs with the stars analyzed in \citet{2022A&ASchaffenroth} and \citet{2023ApJLei}, respectively. Comparisons of masses, radii, and luminosities for the common stars are shown in the panels of \Fig \ref{Fig 4}. As can be see in the figure, there is a notable agreement between the results of the present study and previous research, particularly with respect to radius and luminosity. However, the comparison of mass exhibits a slightly larger dispersion than the other two parameters. This is mainly due to the fact that the large uncertainties of surface gravity would directly influence stellar mass determination (see Equation \ref{eq 2}), while it is not used in the determination of radius and luminosity (see Equation \ref{eq 1} and \ref{eq 3}).
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In order to evaluate the reliability of the masses, radii, and luminosities obtained in this study, we cross-matched the selected hot subdwarfs with the stars analyzed in \citet{2022A&ASchaffenroth} and \citet{2023ApJLei}, respectively. Comparisons of masses, radii, and luminosities for the common stars are shown in the panels of \Fig \ref{Fig 4}. As can be seen in the figure, there is a notable agreement between the results of the present study and previous research, particularly with respect to radius and luminosity. However, the comparison of mass exhibits a slightly larger dispersion than the other two parameters. This is mainly due to the fact that the large uncertainties of surface gravity would directly influence stellar mass determination (see Equation \ref{eq 2}), while it is not used in the determination of radius and luminosity (see Equation \ref{eq 1} and \ref{eq 3}).
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\begin{figure*}
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\centering
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\includegraphics[width=0.3\linewidth]{picture/contrast_Schaffenroth_radius.pdf}
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@@ -285,9 +284,9 @@ In the middle panel of \Fig \ref{Fig 9}, we compare the mass distribution of He
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Nevertheless, it leads to a little different conclusion when comparing our results with recent BPS model predictions from \citet{2025PASA...42...12R} (see the right panel in \Fig \ref{Fig 9}). The mass distribution of He-rich stars from the merging channel of \citet{2025PASA...42...12R} (dash-dotted blue curve) presents two distinct mass peaks around 0.55 ${\rm M}_{\odot}$ and 0.41 ${\rm M}_{\odot}$ (see \Fig 14 in their study), which correspond perfectly to the two peaks shown in our study (gray histogram). However, the relative number of He-rich stars around the secondary mass peak (e.g., 0.41 ${\rm M}_{\odot}$) predicted by \citet{2025PASA...42...12R} is less than in this study. As is discussed in Section 3.2.4 of their study, the secondary mass peak heavily depends on mass-transfer accretion efficiency at stable RLOF phase. It would disappear when the accretion efficiency equals 0, and it would merge with the primary peak and form a symmetrical distribution with a peak around 0.47 ${\rm M}_{\odot}$ if the accretion efficiency equals 1.
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Note that the formation of two He-WD binaries\footnote{In \citet{2025PASA...42...12R}, the treatment of the two He-WDs' merging channel was very sample. They did not evolve the two He-WDs binary into merging phase, but instead considered the binary system as hot subdwarfs if they could merge within the age of our Universe (e.g., 14 Gyr).} requires two RLOF phases. The whole envelope of the primary star will be removed through stable mass transfer during the first RLOF phase, while the two components will be surrounded by a CE formed due to unstable mass transfer during the second RLOF phase, and the CE should be ejected before the two He-WDs binary is formed \citep{1984ApJ...277..355W}. The mass-transfer accretion efficiency during the first RLOF phase has significant effects on the loss of angular momentum due to mass loss from the system, which in turn determines the subsequent evolution of the orbital separation. Therefore, a lower accretion efficiency during the first RLOF phase would result in either systems not triggering CE events (too far from each other) or merging (too close), both resulting in a final configuration different from the two He-WD binaries.
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Note that the formation of two He-WD binaries\footnote{In \citet{2025PASA...42...12R}, the treatment of the two He-WDs' merging channel was very sample. They did not evolve the two He-WDs binary into merging phase, but instead considered the binary system as hot subdwarfs if they could merge within the age of our Universe (e.g., 14 Gyr).} requires two RLOF phases. The whole envelope of the primary star will be removed through stable mass transfer during the first RLOF phase, while the two components will be surrounded by a CE formed due to unstable mass transfer during the second RLOF phase, and the CE should be ejected before the two He-WDs binary is formed \citep{1984ApJ...277..355W}. The mass-transfer accretion efficiency during the first RLOF phase has significant effects on the loss of angular momentum due to mass loss from the system, which in turn determines the subsequent evolution of the orbital separation. Therefore, a lower accretion efficiency during the first RLOF phase would result in either systems not triggering CE events (too far from each other) or merging (too close), both resulting in a final configuration different from the two He-WD binaries.
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Based on the discussion mentioned above, if the second mass peak (around 0.4 ${\rm M}_{\odot}$) is a real feature, the two He-WDs merging channel could produce most of the observed He-rich hot subdwarf stars on the condition that mass transfer during the first RLOF phase to produce the two He-WDs' binary should be partially conserved, and the accretion efficiency is not too low.
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Based on the discussion mentioned above, if the second mass peak (around 0.4 ${\rm M}_{\odot}$) is a real feature, the two He-WDs merging channel could produce most of the observed He-rich hot subdwarf stars on the condition that mass transfer during the first RLOF phase to produce the two He-WDs' binary should be partially conserved, and the accretion efficiency is not too low.
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\section{Summary}
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@@ -295,7 +294,7 @@ In this study, a deep learning model SENN was designed to calculate synthetic SE
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The two mass peaks (e.g., 0.47 and 0.37) in the mass distribution of sdB/sdOB stars are consistent with the prediction from BPS models, which corresponds to the production of CE ejection and stable RLOF respectively. There is also a primary peak (around 0.56 ${\rm M}_{\odot}$) and a secondary peak (around 0.4 ${\rm M}_{\odot}$) clearly visible in the mass distribution of He-rich stars. Although the primary mass peak is well predicted by BPS models, the occurrence of the secondary peak in the models depends heavily on the mass-transfer accretion efficiency at stable RLOF stage in binary evolution. These results indicate that the two He-WDs' merging channel could produce most of the observed He-rich hot subdwarf stars, but mass transfer should be partially conserved during the stable RLOF phase. Considering the large uncertainties of the masses obtained in this study, other alternative formation channels for He-rich hot subdwarfs would not be completely excluded. More accurate determinations of the physical parameters of hot subdwarf stars are urgently needed.
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It is important to note that although we could efficiently obtain synthetic SEDs of hot subdwarfs using the SENN model, deriving their masses, radii, and luminosities still requires atmospheric parameters ($T_{\text{eff}}$ and ${\rm log} g$). Accurate atmospheric parameters, however, must still be acquired through the conventional method of synthetic spectral fitting.
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It is important to note that although we could efficiently obtain synthetic SEDs of hot subdwarfs using the SENN model, deriving their masses, radii, and luminosities still requires atmospheric parameters ($T_{\text{eff}}$ and ${\rm log} g$). Accurate atmospheric parameters, however, must still be acquired through the conventional method of synthetic spectral fitting.
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Fortunately, we are actively exploring the use of machine learning methods to predict the atmospheric parameters of hot subdwarfs \citep{2026ApJS..283...16L}. This approach, in the near future, should enable us to directly obtain both the atmospheric parameters and masses of hot subdwarfs using artificial intelligence techniques, without having to compute stellar atmosphere models.
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-------- Forwarding messages --------
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From: "Astronomy and Astrophysics (A&A)" <editorial.office@aanda.org>
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Date: 2026-03-16 19:41:47
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To: leizhenxin2060@163.com
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Subject: aa54562-25: Corrected tex
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Article reference: aa54562-25
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Title: From Synthetic SEDs to Stellar Origins: A Deep Learning Model for Physical Parameter Retrieval in Hot Subdwarf Stars
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Dear Prof. Lei,
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==============
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Additional corrections from the Editorial Office:
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- All the titles (main title, sub/sections, appendices, tables) should be written in the lower case, except the first word and any proper nouns..
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--- 中文翻译 ---
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**发件人**："Astronomy and Astrophysics (A&A)" <editorial.office@aanda.org>
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**日期**：2026-03-16 19:41:47
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**收件人**：leizhenxin2060@163.com
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**主题**：aa54562-25: 修改后的 tex 文件
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**文章参考编号**：aa54562-25
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**标题**：From Synthetic SEDs to Stellar Origins: A Deep Learning Model for Physical Parameter Retrieval in Hot Subdwarf Stars
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**尊敬的雷教授：**
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您的修订版本应在三周内提交。如果修改需要更多时间，请联系编辑部申请延期。
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||||
|
||||
感谢您在本文上花费的时间。
|
||||
|
||||
**您诚挚的，**
|
||||
|
||||
Kit Gilchrist
|
||||
A&A 语言编辑
|
||||
|
||||
==============
|
||||
|
||||
**来自编辑部的补充修改意见：**
|
||||
|
||||
- 所有的标题（主标题、节/小节标题、附录标题、表名）均应使用小写形式，仅首字母和专有名词例外（即句首大写风格）。
|
||||
Reference in New Issue
Block a user