标题Title

New-ANGELS III：M31 内晕视线的软 X 射线发射——XMM-Newton EPIC MOS 测得的共温 0.175 keV 线视总和与一个命名的银河系前景模型的张力

New-ANGELS III: Soft X-Ray Emission toward the Inner Halo of M31 — a Common 0.175 keV Line-of-Sight Sum from XMM-Newton EPIC MOS and a Tension with a Named Milky Way Foreground Model

标题说明：主贡献是「测准线视总和」与「一个命名前景模型留下非负 M31 残差为负」这两件事；检索词含 XMM-Newton、EPIC、MOS、弥漫发射、软质子。运行标题（running head，不超过 44 字符）：Soft X-rays toward the inner halo of M31。

Title note: the contribution is "measure the line-of-sight sum" plus "a named foreground model leaves no non-negative M31 residual"; search terms include XMM-Newton, EPIC, MOS, diffuse emission and soft protons. Running head (at most 44 characters): Soft X-rays toward the inner halo of M31.

作者Authors

<作者名单——由 PI 决定>；单位与通信信息同为占位符。New-ANGELS I 的作者顺序为 Huang, Li, Cui, Bregman, Li, Ponti, Qu, Wang, Zhang，II 为 Huang, Li, Cui, Qu, Bregman, Li, Ponti, Wang，可作为本文顺序的模板。本页不虚构任何作者或单位。

<Author list — PI to decide>; affiliations and correspondence are likewise placeholders. The New-ANGELS I author order is Huang, Li, Cui, Bregman, Li, Ponti, Qu, Wang, Zhang and II is Huang, Li, Cui, Qu, Bregman, Li, Ponti, Wang, which is the natural template for this paper. No author or affiliation is invented here.

摘要Abstract

我们用 XMM-Newton 的 22 个指向（New-ANGELS 遗产巡天，提案 080073）测量 M31 内晕的冷软 X 射线分量，投影半径 10.5–30.8 kpc。14 个经质量筛选的双 MOS 视场给出共温 \(kT=0.175\pm0.004\,\mathrm{keV}\)，异质性统计 \(Q(13)=11.631\)（\(p=0.558\)）。北/西北减南/东南的对比只有 \(0.212\pm0.210\,10^{-15}\,\mathrm{erg\,cm^{-2}\,s^{-1}\,arcmin^{-2}}\)（\(1.01\sigma\)），因此未检测到两侧不对称；两个侧的径向覆盖不同，也限制了这一比较。由于银河系与 M31 的热谱在 CCD 分辨率下近乎简并，我们把这个分量当作完整的视线总和，不把它归给任何一个星系。在吸收 0.5–2.0 keV 比较能带，全场总量为 \(0.867\pm0.044\,10^{-15}\,\mathrm{erg\,cm^{-2}\,s^{-1}\,arcmin^{-2}}\)（统计；两段 −0.055/+0.039），另有 \(+0.007/-0.003\) 的吸收柱重拟合响应与 \(\pm0.027\) 的本地热泡分配项（温度下限 0.08 keV 剖面带的半宽；完整的、依赖温度下限的范围是 −0.061 到至少 +0.035）。总量对 CXB 谱指数与 CGM 丰度的敏感性单独测量（\(0.834\pm0.044\,10^{-15}\,\mathrm{erg\,cm^{-2}\,s^{-1}\,arcmin^{-2}}\)，同口径，−3.9%），作为敏感性报告，不加进误差棒。Locatelli 等人的参考 Combined（\(\beta=0.5\)）银河系模型按固定 O VIII 线归一化换算后预言 \(1.290\,10^{-15}\,\mathrm{erg\,cm^{-2}\,s^{-1}\,arcmin^{-2}}\)，超出实测总量 \(0.423\,10^{-15}\,\mathrm{erg\,cm^{-2}\,s^{-1}\,arcmin^{-2}}\)，留下非负的中心 M31 残差为负——计入该模型自身误差（\(\sigma\approx0.32\)）后这是约 \(1.3\sigma\) 的有条件中心值张力，不是排除。四个独立比较量预言得更低，因此这一冲突特定于该 Locatelli 投影。任何距离分解都需要显式的前景先验。

We measure the cool soft X-ray component toward the inner halo of M31 with 22 XMM-Newton pointings of the New-ANGELS legacy survey (proposal 080073), spanning projected radii of 10.5–30.8 kpc. Fourteen quality-selected dual-MOS fields give a common temperature \(kT=0.175\pm0.004\,\mathrm{keV}\) with a heterogeneity statistic \(Q(13)=11.631\) (\(p=0.558\)). The North/NW minus South/SE contrast is only \(0.212\pm0.210\) in units of \(10^{-15}\,\mathrm{erg\,cm^{-2}\,s^{-1}\,arcmin^{-2}}\) (\(1.01\sigma\)), so no side asymmetry is detected; unequal radial coverage limits the comparison. Because Milky Way and M31 spectra are nearly degenerate at CCD resolution, we treat this component as the full line-of-sight sum, not either galaxy's. In the absorbed 0.5–2.0 keV comparison band the all-field total is \(0.867\pm0.044\) (statistical; two-piece −0.055/+0.039), with a \(+0.007/-0.003\) absorption-column refit response and a \(\pm0.027\) Local-Hot-Bubble allocation term (half-width of the floor-0.08 keV profile band; the full temperature-floor-dependent range is −0.061 to at least +0.035). The total's sensitivity to the CXB photon index and CGM abundance is measured separately (\(0.834\pm0.044\), like-for-like, −3.9 %) and reported as a sensitivity, not in the error bar. The reference Combined (\(\beta=0.5\)) Milky Way model of Locatelli et al., converted at fixed O VIII line normalisation, predicts \(1.290\), exceeding the measured total by \(0.423\) and leaving no non-negative central M31 residual — a conditional central-value tension of about \(1.3\sigma\) with that model's own error (\(\sigma\approx0.32\)), not an exclusion. Four independent comparators predict less, so the conflict is specific to that Locatelli projection. Any distance decomposition requires an explicit foreground prior.

摘要字数（英文）：见 checkpoint 的自检清单。每个数字的来源标记：\(kT\) 与 \(Q\) [s1]；南北对比 [s2]；总量与三项误差 [s3]；模型敏感性 [s4]；Locatelli 预言与残差 [s5]；四个比较量 [s6]。

Abstract word count (English): see the self-check list in the checkpoint. Source markers for each number: \(kT\) and \(Q\) [s1]; the North–South contrast [s2]; the total and its three error terms [s3]; the model sensitivity [s4]; the Locatelli prediction and residual [s5]; the four comparators [s6].

关键词Keywords

关键词（统一天文词表 UAT）：仙女座星系（Andromeda Galaxy）；星系周介质（Circumgalactic medium）；弥漫 X 射线背景（Diffuse x-ray background）；X 射线天文学（X-ray astronomy）；银河系（Milky Way Galaxy）；天文数据还原（Astronomy data reduction）。

Keywords (Unified Astronomy Thesaurus): Andromeda Galaxy; Circumgalactic medium; Diffuse x-ray background; X-ray astronomy; Milky Way Galaxy; Astronomy data reduction.

关键词取自内部修订稿 v2 的 \keywords{} 行（Andromeda Galaxy (39)、Circumgalactic medium (1879)、Diffuse x-ray background (384)、X-ray astronomy (1810)、Milky Way Galaxy (1054)），并按其建议补上「天文数据还原」。这些是词表术语，不是本项目内部标签。

The keywords come from the internal revision v2's \keywords{} line (Andromeda Galaxy (39), Circumgalactic medium (1879), Diffuse x-ray background (384), X-ray astronomy (1810), Milky Way Galaxy (1054)), with "Astronomy data reduction" added as it suggests. These are thesaurus terms, not internal project labels.

1 引言1 Introduction

热星系周气体预期包含大质量旋涡星系相当大一部分重子，但其低密度使直接 X 射线测量变得困难。对单个大质量旋涡星系与叠加样本的深度观测既展示了延展的软 X 射线晕，也表明推断出的剖面依赖于星系质量、未分辨源的扣除与背景处理^[s7]。M31 足够近，其内晕可以用多个 XMM-Newton 视场采样；但它的大角尺度带来另一种限制：M31 晕的发射叠加在银河系、可能还有本星系群的空间结构化软发射之上。本文要测量的正是这个叠加和，而不是任何一个星系的分量。

Hot circumgalactic gas is expected to contain a substantial fraction of the baryons associated with massive spiral galaxies, but its low density makes direct X-ray measurements difficult. Deep observations of individual massive spirals and stacked samples demonstrate extended soft X-ray halos, while also showing that inferred profiles depend on galaxy mass, unresolved-source subtraction and background treatment^[s7]. M31 is close enough that its inner halo can be sampled with multiple XMM-Newton fields, but its large angular extent creates a different limitation: emission from the M31 halo is superposed on spatially structured soft emission from the Milky Way and potentially the Local Group. What this paper measures is that superposed sum, not the component belonging to either galaxy.

本文是 New-ANGELS 系列的第三篇。该 XMM-Newton 遗产巡天覆盖 M31 周围约 7.2 平方度，既研究盘源族也研究延伸到约 30 kpc 的内晕热气体。第一篇给出巡天设计与 4506 个 X 射线源表^[s8]，第二篇推导这些源的亮度函数^[s9]。两篇刻画了本文必须在测量弥漫发射之前排除的致密源族群；这里我们转向弥漫软 X 射线发射本身。

This paper is the third in the New-ANGELS series, an XMM-Newton legacy survey covering approximately 7.2 square degrees around M31 and designed to study both the source populations of the disk and the hot gas of the inner halo out to about 30 kpc. Paper I presented the survey design and a catalogue of 4506 X-ray sources^[s8], and Paper II derived the luminosity function of those sources^[s9]. Both papers characterise the compact-source population that the present analysis must exclude before the diffuse emission can be measured; here we turn to the diffuse soft X-ray emission itself.

用 EPIC 做弥漫发射工作主要受粒子背景与软质子限制。每个视场用同一探测区生成的 ESAS 静态粒子背景（quiescent particle background，QPB）代表探测器粒子本底，它不是空白天空或天体前景谱^[s10]。扣除 QPB 之后残留的谱含天体发射加残余探测器背景与软质子，软质子必须以显式连续谱分量建模；MOS 1.4–2.0 keV 区间因包含很强的 Al K\(\alpha\) 与 Si K\(\alpha\) 仪器线且对残余软质子敏感而被排除^[s11]。EPIC-pn 产品不进入本均匀基线：在所审计的本地 SAS 20.0.0 还原的 PATTERN 不超过 4 的 pn 分支里，22 个视场都有源谱，但只有 21 个有同分支匹配的 QPB 谱，且 22 个源 PHA 里 17 个的干净曝光短于 10 ks；这正是当前 XMM-ESAS 手册指出特定 pn 局限（「角区问题」）的情形——视场外小角区计数统计差、受事件外时间事件影响、且比以往认识到的更易受残余软质子耀斑影响^[s12]。这是产品级背景系统学选择，不是「EPIC-pn 数据一般不可用」的主张。

Diffuse-emission work with EPIC is limited above all by the particle and soft-proton background. Each field uses the ESAS quiescent particle background (QPB) generated in the same detector footprint, which represents the particle background and is not a blank-sky or astrophysical foreground spectrum^[s10]. After QPB subtraction the remaining spectrum contains celestial emission plus residual detector background and soft protons, which are modelled with an explicit continuum component; the MOS 1.4–2.0 keV interval is excluded because it contains the strong Al K\(\alpha\) and Si K\(\alpha\) instrumental features and is sensitive to residual soft protons^[s11]. EPIC-pn products do not enter this homogeneous baseline: in the audited PATTERN 4-or-fewer pn branch of the local SAS 20.0.0 reduction all 22 fields have a source spectrum, but only 21 have a matched QPB spectrum in the same processing branch, and 17 of the 22 source PHA files record a cleaned exposure shorter than 10 ks; this is the regime in which the current XMM-ESAS Cookbook identifies a specific pn limitation known as "the corner problem" — the small out-of-field-of-view corner sample has poor counting statistics, is affected by out-of-time events, and is more sensitive than previously recognised to residual soft-proton flares^[s12]. This is a product-level background-systematics choice, not a claim that EPIC-pn data are generally unusable.

M31 中心几千千秒差距内存在与核球和盘相关的多相弥漫 X 射线发射^[s13]，但这些测量不决定 10–31 kpc 投影半径处较冷气体的幅度。离盘观测给出更近的谱形先例：一次深度 XMM-Newton 观测测到近 0.17–0.18 keV 的分量，并明确把它建模为银河系、M31 与星系际介质的联合发射^[s14]；M31 方向一个可能的「本地热桥」有相近的推断温度^[s15]。银河系巡天也发现 0.15–0.22 keV 附近的特征温度，但空间变化很大^[s16]。

The central few kiloparsecs of M31 contain multiphase diffuse X-ray emission associated with the bulge and disk^[s13], but those measurements do not determine the amplitude of cooler gas at projected radii of 10–31 kpc. Off-disc observations provide a closer spectral precedent: a deep XMM-Newton programme measured a component near 0.17–0.18 keV and explicitly modelled it as the combined emission of the Galaxy, M31 and the intergalactic medium^[s14]; a possible Local Hot Bridge toward M31 has a similar inferred temperature^[s15]. Milky Way surveys also find characteristic temperatures near 0.15–0.22 keV but with substantial spatial variation^[s16].

这些重叠的温度尺度使仅凭 EPIC 谱形做距离归属不可靠。因此本文把分析组织在直接观测到的视线分量周围，

These overlapping temperature scales make distance attribution from an EPIC spectrum alone unreliable. We therefore organise the analysis around the directly observed line-of-sight component,

\[ S_{\rm obs}(E)=S_{\rm MW}(E)+S_{\rm M31}(E), \]

\[ S_{\rm obs}(E)=S_{\rm MW}(E)+S_{\rm M31}(E), \]

在显式标注的条件情景里可加第三项本星系群项。我们提两个少假设的问题：第一，在北/西北与南/东南内晕视场上测到的冷热面亮度是多少？第二，数据对两个被采样侧之间的差约束得多强？M31 与银河系的分解只在这些直接测量之后讨论。

with an optional third Local-Group term in explicitly labelled conditional scenarios. We ask two assumption-light questions. First, what cool thermal surface flux is measured toward the North/NW and South/SE inner-halo fields? Second, how strongly do the data constrain a difference between the two sampled sides? The M31-versus-Milky-Way decomposition is discussed only after these direct measurements.

本节是论文所需的全部背景，后文不再补充。第 2 节说明数据与还原，第 3 节给出结果，第 4 节讨论含义与局限，第 5 节总结。

This section carries all the background the paper needs; none is added later. Section 2 describes the data and reduction, Section 3 gives the results, Section 4 discusses the implications and limitations, and Section 5 summarises.

2 观测与数据还原2 Observations and data reduction

本节给出复现分析所需的全部细节，结果留在第 3 节。

This section gives the detail needed to reproduce the analysis; results are left to Section 3.

2.1 巡天与视场选择2.1 Programme and field selection

我们使用 XMM-Newton 提案 080073「XMM-Newton Legacy Survey of M31 Halo: Searching for the Missing Accreted Hot CGM」（PI J.-T. Li）的观测，由 EPIC 相机获取^[s17]。这些是 New-ANGELS 巡天的晕指向，其源表与亮度函数见第一、二篇^[s18]。所选观测取自 2017 年 6 月 28 日至 2018 年 1 月 17 日；本文使用的 43 个探测器产品全部带 Thin1 滤光片。该分析只用 MOS：21 个视场各有一个 MOS1 与一个 MOS2 谱，0800730101 只贡献 MOS2。

We use observations from XMM-Newton proposal 080073, "XMM-Newton Legacy Survey of M31 Halo: Searching for the Missing Accreted Hot CGM" (PI J.-T. Li), obtained with the EPIC cameras^[s17]. These are the halo pointings of the New-ANGELS programme whose source catalogue and luminosity function are given in Papers I and II^[s18]. The selected observations were taken between 2017 June 28 and 2018 January 17, and all 43 detector products used here carry the Thin1 optical blocking filter. The analysis is MOS-only: 21 fields have one MOS1 and one MOS2 spectrum, while 0800730101 contributes MOS2 only.

22 个视场的母集是提案 080073 中上游项目筛选保留了所需弥漫场产品的子集。0800731701 不在本地还原树中，0800732401 缺少所需的 4.background 产品，0800731201、0800731401、0800731801、0800732501、0800732901 与 0800733001 因极端的 2.0–3.2 keV 观测/QPB 比值被上游排除，0800733101 因极端残余软质子污染与 MOS 覆盖不全被排除。这些排除在第 2.6 节的谱质筛选之前定义母集，它们不是按拟合温度或面亮度挑选的。

The 22-field parent set is the proposal-080073 subset for which the upstream project screening retained the required diffuse-field products. Observation 0800731701 is absent from the local reduction tree, 0800732401 lacks the required 4.background products, 0800731201, 0800731401, 0800731801, 0800732501, 0800732901 and 0800733001 were rejected upstream because of extreme 2.0–3.2 keV observed-to-QPB ratios, and 0800733101 was rejected because of extreme residual soft-proton contamination and incomplete MOS coverage. These exclusions define the parent set before the spectral-quality cuts of Section 2.6; they are not selected on fitted temperature or surface flux.

指向中心取自最终 PHA 文件头。取 M31 中心与距离 785 kpc^[s19]，22 场母集的圆投影半径跨 10.5–30.8 kpc，承载下文每个测量的 14 个视场跨 10.5–28.8 kpc。指向形成两条近似次轴的链（标为北/西北与南/东南），而非完整方位环。在最终主样本中，两侧的中位半径分别为 19.28 与 14.97 kpc，且南/东南侧没有一个主场落在 20–25 kpc。观测清单见附录 A 的表 A1。

Pointing centres are taken from the final PHA headers. For an adopted M31 centre and distance of 785 kpc^[s19], the circular projected radii of the 22-field parent set span 10.5–30.8 kpc, and the 14 fields that carry every measurement reported below span 10.5–28.8 kpc. The pointings form two approximately minor-axis chains, labelled North/NW and South/SE, rather than a complete azimuthal annulus. In the final primary sample the median radii are 19.28 and 14.97 kpc on the two sides, and no South/SE primary field lies at 20–25 kpc. The observation inventory is given in Table A1 of Appendix A.

2.2 SAS 处理溯源2.2 SAS processing provenance

谱来自既有项目还原，使用 XMM-Newton 科学分析系统（SAS）^[s20]。我们审计了每个输入的文件头，而不是指定笼统的「标准 SAS」设置。全部 43 个源 PHA 报告 xmmsas_20211130_0941-20.0.0 与 evselect-3.71.1；其 ARF 报告 arfgen-1.102.1，RMF 报告 rmfgen-2.8.5。每个 PHA 中存储的事件选择要求 PATTERN 不超过 12 且 FLAG==0，因此谱包含有效的 MOS 单–四重事件并拒绝被标记事件。

The spectra were derived from the existing project reduction with the XMM-Newton Science Analysis System (SAS)^[s20]. We audited the headers of every input rather than assigning generic "standard SAS" settings. All 43 source PHA files report xmmsas_20211130_0941-20.0.0 and evselect-3.71.1; their ARFs report arfgen-1.102.1 and their RMFs rmfgen-2.8.5. The event selections stored in every PHA require PATTERN of at most 12 and FLAG==0, so the spectra include valid MOS single–quadruple events and reject flagged events.

最终 PHA 以内嵌 GTI 扩展保存已应用的良时间区间，但本地树不保留上游耀斑光变阈值，也没有能唯一重建全样本这些 GTI 的命令日志；0800732701 只幸存一条部分命令记录，不足以定义均匀的 22 场处方。同样，本地 ccf.cif 文件没有通过记录的标识或哈希与 PHA/ARF/RMF 产品绑定，其文件日期也不能唯一确定每次提取时哪个校准索引是活动的。因此我们报告已验证的 SAS 任务版本与最终干净曝光，但不臆造全样本的耀斑阈值或 CCF 版本。所保留的树足以从 43 个最终谱产品组复现本文分析，不足以做逐比特的 ODF 到 PHA 重建：完整 ODF 材料只为三个挑选的观测在本地保留，多数视场缺少原始 mos-spectra 与 QPB 命令文件。均匀耀斑筛选、校准索引与提取命令溯源的恢复仍是投稿前要求。

The final PHAs contain the applied good-time intervals as embedded GTI extensions, but the local tree does not retain the upstream flare-light-curve thresholds or a command log that uniquely reconstructs those GTIs for the full sample; one partial command record survives for 0800732701 and cannot define a homogeneous 22-field prescription. Likewise the local ccf.cif files are not bound to the PHA/ARF/RMF products by a recorded identifier or hash, and their file dates do not uniquely establish which calibration index was active during each extraction. We therefore report the verified SAS task versions and final cleaned exposures, but do not invent sample-wide flare thresholds or a CCF release. The retained tree is sufficient to reproduce the paper analysis from the 43 final spectral product groups; it is not sufficient for a bitwise ODF-to-PHA rebuild, since complete ODF material is retained locally for only three selected observations and original mos-spectra and QPB command files are absent for most fields. Recovery of the homogeneous flare-screening, calibration-index and extraction-command provenance remains a submission requirement.

2.3 源掩膜与提取区2.3 Source masks and extraction footprint

分析使用 rpc/4.background/bkg_mos[12]_00500-02000_exclude_extent_source_mask 下的产品。提取区是探测器坐标芯片/缝隙掩膜与点/展源排除之后可用的 MOS 视场，不是一个简单的 15 角分圆。权威掩膜几何以内嵌 REGION 扩展与 SLCTEXPRedetect_stack 源位置与展源区域产品。确切的源探测似然阈值与把探测映射到排除椭圆大小的规则无法从当前命令历史恢复，必须在投稿前冻结。

The analysis uses the products under rpc/4.background/bkg_mos[12]_00500-02000_exclude_extent_source_mask. The extraction is the usable MOS field of view after detector-coordinate chip and gap masks and point and extended-source exclusions; it is not a simple 15 arcmin circle. The authoritative mask geometry is embedded in each PHA as REGION extensions and in the SLCTEXPR selection; the embedded regions contain negative detector-coordinate ellipses for excluded sources together with the valid chip and field-of-view geometry. The reduction tree also retains the associated edetect_stack source-position and extended-source region products. The exact source-detection likelihood threshold and the rule that maps detections to exclusion-ellipse size are not recoverable from the current command history and must be frozen before submission.

我们用产品关系 \(\Omega_i=\texttt{BACKSCAL}_i(1/20/60)^2\) 平方角分把 PHA 的 BACKSCAL 换算成立体角，对应 0.05 角秒的 DETX/DETY 采样。得到的探测器专属面积跨 238.3–565.8 平方角分。MOS1 与 MOS2 面积分开保持，因此失效 CCD、芯片缝隙、坏探测器区与源孔都通过各自的面积因子直接进入每个模型。相对于标称 15 角分圆的 706.9 平方角分，单个探测器足迹覆盖 33.7%–80.0%。此前吸收足迹审计所用「每场一个 PHA」约定的两个摘要分别引用，因为它们描述不同样本：在 22 场母集上该约定覆盖 33.7%–52.6%（中位 47.5%），在 14 个主场上覆盖 33.7%–51.1%（中位 45.2%）。15 角分孔径只用于基线 HI4PI 柱密度估计，不用于谱提取。

We convert the PHA BACKSCAL value with the production relation \(\Omega_i=\texttt{BACKSCAL}_i(1/20/60)^2\) square arcminutes, corresponding to the 0.05 arcsec DETX/DETY sampling. The resulting detector-specific areas span 238.3–565.8 square arcminutes. MOS1 and MOS2 areas are kept separate, so failed CCDs, chip gaps, bad detector regions and source holes propagate directly into each model through its own area factor. Relative to the 706.9 square arcminutes of a nominal 15 arcmin circle, the individual detector footprints cover 33.7%–80.0%. Two summaries of the one-PHA-per-field convention used in the earlier absorption-footprint audit are quoted separately, because they describe different samples: over the 22-field parent set that convention covers 33.7%–52.6% (median 47.5%), and over the 14 primary fields it covers 33.7%–51.1% (median 45.2%). The 15 arcmin aperture is used only for the baseline HI4PI column estimate, not for spectral extraction.

2.4 观测谱、QPB 与响应谱2.4 Observed, QPB and response spectra

对每个保留的探测器，我们用四个匹配产品：*-obj.pi（观测弥漫场谱）、*-back.pi（ESAS 静态粒子背景，QPB）^[s21]，以及对应的 *.arf 与 *.rmf。QPB 在与观测谱相同的探测器足迹中生成，代表粒子背景，不是空白天空或天体前景谱。在 Sherpa 中，obj.pi 作为源数据集载入，back.pi 作为其背景连同存储误差载入，QPB 扣除在分组与拟合之前施加。干净探测器曝光跨 2.20–20.57 ks，在 43 个探测器产品上合计 533.571 ks。完整产品路径、任务版本串、曝光、面积、内嵌掩膜检查与质量分类写入机器可读文件 m31_cgmsum_v19_observation_products.csv；其生成器读取冻结的生产清单与实际 FITS 文件头，除非恰好找到 22 个指向、43 个探测器产品、每个 PHA 都是 Thin1 且验证过的 PATTERN/FLAG 选择，否则失败。

For each retained detector we use four matched products: *-obj.pi for the observed diffuse-field spectrum, *-back.pi for the ESAS quiescent particle background (QPB)^[s21], and the corresponding *.arf and *.rmf. The QPB is generated in the same detector footprint as the observed spectrum; it represents the particle background and is not a blank-sky or astrophysical foreground spectrum. In Sherpa, obj.pi is loaded as the source dataset, back.pi is loaded as its background with the stored errors, and QPB subtraction is applied before grouping and fitting. The cleaned detector exposures range from 2.20 to 20.57 ks and sum to 533.571 ks over the 43 detector products. The full product paths, task-version strings, exposures, areas, embedded-mask checks and quality classifications are written to the machine-readable file m31_cgmsum_v19_observation_products.csv; its generator reads the frozen production manifest and the actual FITS headers, and fails unless it finds exactly 22 pointings, 43 detector products, Thin1 in every PHA, and the verified PATTERN and FLAG selections.

2.5 能量筛选与响应感知分组2.5 Energy filtering and response-aware grouping

最终 MOS 拟合域是

The final MOS fitting domain is

\[ 0.4\text{--}1.4~\mathrm{keV}\ \cup\ 2.0\text{--}8.0~\mathrm{keV}. \]

\[ 0.4\text{--}1.4~\mathrm{keV}\ \cup\ 2.0\text{--}8.0~\mathrm{keV}. \]

1.4–2.0 keV 区间被排除，因为它包含很强的 MOS Al K\(\alpha\) 与 Si K\(\alpha\) 仪器特征且对残余软质子敏感。每个拟合阶段的能量选择都先重置宽带再重新施加这个间隙；最终 Sherpa 会话保留两个不相交区间。谱在 QPB 扣除之后分组。从单频道开始，一个 bin 只有在两个条件都满足时才闭合：(1) QPB 扣除后的信噪比

The 1.4–2.0 keV interval is excluded because it contains the strong MOS Al K\(\alpha\) and Si K\(\alpha\) instrumental features and is sensitive to residual soft protons. Every fit-stage energy selection first resets the broad band and then reapplies this gap; the final Sherpa sessions preserve the two disjoint intervals. Spectra are grouped after QPB subtraction. Starting from individual channels, a bin is closed only after both (1) the QPB-subtracted signal-to-noise ratio

\[ {\rm S/N}=\frac{C_{\rm obj}-C_{\rm QPB}}{\sqrt{C_{\rm obj}+C_{\rm QPB}}} \]

\[ {\rm S/N}=\frac{C_{\rm obj}-C_{\rm QPB}}{\sqrt{C_{\rm obj}+C_{\rm QPB}}} \]

达到 6，且 (2) 其频道宽度以不超过 6 的因子采样局部 RMF 的 FWHM。组积累在被忽略频道处重置，组起点强制在 0.4、1.4、2.0 与 8.0 keV。因此没有拟合 bin 跨越被排除的 MOS 区间。

reaches 6, and (2) its channel width samples the local RMF FWHM by no more than a factor of 6. Group accumulation is reset at ignored channels, and group starts are forced at 0.4, 1.4, 2.0 and 8.0 keV. Consequently no fitted bin bridges the excluded MOS interval.

2.6 谱分析与质量选择2.6 Spectral analysis and quality selection

每个指向在 Sherpa 4.18 中独立拟合^[s22]，使用 XSPEC 模型组件^[s23]。在一个指向内，MOS1 与 MOS2 的天体参数相连，而残余仪器线与软质子参数保持探测器专属；不同指向之间不连任何参数。全部 22 个视场在施加质量掩膜前都尝试过。结构验证器要求冻结的输入探测器清单、唯一文件路径、精确的代码/输入/输出/APEC 哈希、最终拟合成功与消息、有限拟合维度、全阶段能量滤除、分组参数、采纳的冻结 \(N_{\rm HI}\) 与预期的冻结 Al/Si 线状态。第二个验证器在 CIAO 中恢复每个保存的 Sherpa 会话，重新检查实际数据集路径、最终拟合结果、滤除、分组起点与间隙、吸收与禁用线参数。因此单凭一个有效的 JSON 边车文件不能把一个视场提升进科学样本。

Each pointing is fitted independently in Sherpa 4.18^[s22] using XSPEC model components^[s23]. Within one pointing the MOS1 and MOS2 celestial parameters are linked, whereas the residual instrumental-line and soft-proton parameters remain detector specific; no parameter is linked between different pointings. All 22 fields were attempted before the quality mask was applied. The structural validator requires the frozen input detector inventory, unique file paths, exact code, input, output and APEC hashes, final fit success and message, finite fit dimensions, all-stage energy filters, grouping parameters, the adopted frozen \(N_{\rm HI}\), and the expected frozen Al/Si line states. A second validator restores each saved Sherpa session in CIAO and rechecks the actual dataset paths, final fit result, filters, grouping starts and gap, absorption and forbidden-line parameters. Thus a valid JSON sidecar alone cannot promote a field into the scientific sample.

20 个视场产生结构有效的 Sherpa 会话，且 20 个都通过独立恢复测试；18 个通过完整技术门。0800731301 与 0800732201 有可恢复会话但最终自由度为非正。对 0800732601 与 0800732701，最终 Sherpa 结果为 succeeded=False 并带「improper input parameters」消息；worker 保留机器可读的失败记录而不发布会话。一个视场进入数值样本的条件是：通过技术验证、拟合质量概率 \(p_{\rm fit}\geq0.01\)、且有有限的 \(\mathrm{CGM}_{\mathrm{sum}}\) 温度与归一化并带正的局部误差。主样本额外要求恰好一个 MOS1 与一个 MOS2 输入。得到的计数为：选定指向 22、可恢复生产会话 20、完整技术验证 18、数值有效 15、双 MOS 主样本 14^[s24]。

Twenty fields produced structurally valid Sherpa sessions, and all 20 passed the independent restore test; eighteen passed the complete technical gate. Fields 0800731301 and 0800732201 have restorable sessions but non-positive final degrees of freedom. For 0800732601 and 0800732701 the final Sherpa result has succeeded=False with an "improper input parameters" message, and the worker retained machine-readable failure records rather than publishing sessions. A field then enters the numerical sample if it passes technical validation, has a fit-quality probability \(p_{\rm fit}\geq0.01\), and has finite \(\mathrm{CGM}_{\mathrm{sum}}\) temperature and normalisation with positive local errors. The primary sample additionally requires exactly one MOS1 and one MOS2 input. The resulting counts are 22 selected pointings, 20 restorable production sessions, 18 complete technical validations, 15 numerically valid fields and 14 dual-MOS primaries^[s24].

2.7 模型拓扑与计数模型2.7 Model topology and count model

贯穿全文，\(\mathrm{CGM}_{\mathrm{sum}}\) 表示视线要求的冷吸收 APEC 分量。它是直接测量的面亮度，不是对任何一个星系的光谱归属，也是下面计数模型中出现的量。若 \(R_i\) 表示探测器 RMF 与其 ARF 的折叠，\(D_i\) 表示同一再分配配单位有效面积，\(\Omega_i\) 是 PHA 立体角，则探测器 \(i\) 的计数模型为

Throughout, \(\mathrm{CGM}_{\mathrm{sum}}\) denotes the cool absorbed APEC component required by the line of sight. It is a directly measured surface brightness, not a spectroscopic assignment to either galaxy, and it is the quantity that appears in the count model below. If \(R_i\) denotes the detector RMF folded with its ARF, \(D_i\) denotes the same redistribution with a unit effective area, and \(\Omega_i\) is the PHA solid angle, the count model for detector \(i\) is

\[ \begin{split} M_i(E)={}&R_i\Big\{\Omega_i\big[G_i(E)+S_{\rm LB}(E)+S_{\rm SWCX}(E)\\ &+A(N_{{\rm HI},i})\{S_{\rm CXB}(E)+S_{\mathrm{CGM}_{\mathrm{sum}}}(E)\\ &\qquad\qquad\quad+S_{\rm hot}(E)\}\big]\Big\}\\ &+D_i\{\Omega_i P_i(E)\}. \end{split} \]

\[ \begin{split} M_i(E)={}&R_i\Big\{\Omega_i\big[G_i(E)+S_{\rm LB}(E)+S_{\rm SWCX}(E)\\ &+A(N_{{\rm HI},i})\{S_{\rm CXB}(E)+S_{\mathrm{CGM}_{\mathrm{sum}}}(E)\\ &\qquad\qquad\quad+S_{\rm hot}(E)\}\big]\Big\}\\ &+D_i\{\Omega_i P_i(E)\}. \end{split} \]

这里 \(G_i\) 是残余探测器线模型，\(P_i\) 是软质子连续谱，其余项是天空面亮度分量。乘以 \(\Omega_i\) 在响应折叠前把每个面亮度归一化转到实际探测器足迹。实现中存在的乘性天空背景尺度固定为 1。拟合代码里称为 MWhalo 的分量就是本文记为 \(\mathrm{CGM}_{\mathrm{sum}}\) 的量；这个历史名称记录该分量起源于一个较早的面向银河系的模型，不携带距离信息。历史的目标专属 SrcApec、SrcPo 与 Srcabs 分量仍留在实现中以保持兼容，但在本独立弥漫场分析中设为零并冻结。因此没有在 \(\mathrm{CGM}_{\mathrm{sum}}\) 之上再拟合一个额外的 M31 专属谱分量。

Here \(G_i\) is the residual detector-line model, \(P_i\) is the soft-proton continuum, and the remaining terms are sky surface-brightness components. Multiplication by \(\Omega_i\) converts every surface-brightness normalisation to the actual detector footprint before response folding. The multiplicative sky-background scale present in the implementation is fixed to unity. The component called MWhalo in the fitting code is the one denoted \(\mathrm{CGM}_{\mathrm{sum}}\) here; the historical name records the component's origin in an earlier Milky-Way-facing model and carries no distance information. The historical target-specific SrcApec, SrcPo and Srcabs components remain in the implementation for compatibility but are set to zero and frozen in this independent diffuse-field analysis. Thus no additional M31-only spectral component is fitted on top of \(\mathrm{CGM}_{\mathrm{sum}}\).

2.8 吸收与原子配置2.8 Absorption and atomic configuration

每个指向的吸收柱固定为 15 角分孔径内 HI4PI 原子 \(N_{\rm HI}\) 图的均匀面积平均^[s25]。在 22 场母集上采纳值跨 \(4.81\times10^{20}\) 到 \(7.64\times10^{20}\,\mathrm{cm^{-2}}\)；上端那个视场 0800731301 被第 2.6 节的质量门排除，所以 14 个主场跨较窄的 \(4.81\times10^{20}\) 到 \(6.92\times10^{20}\,\mathrm{cm^{-2}}\)。该图原生角分辨率 16.2 角分，一个标称孔径因此只含约 2.38 个独立波束。孔径以指向坐标为中心、有完整有效图覆盖，不按 MOS 源掩膜或曝光图加权。

For each pointing the absorption column is fixed to the uniform-area mean of the HI4PI atomic \(N_{\rm HI}\) map within a 15 arcmin aperture^[s25]. Across the 22-field parent set the adopted values span \(4.81\times10^{20}\) to \(7.64\times10^{20}\,\mathrm{cm^{-2}}\); the field at the upper end, 0800731301, is excluded by the quality gates of Section 2.6, so the 14 primary fields span the narrower range \(4.81\times10^{20}\) to \(6.92\times10^{20}\,\mathrm{cm^{-2}}\). The map has a native angular resolution of 16.2 arcmin, so a nominal aperture contains only about 2.38 independent beams. The aperture is centred on the pointing coordinate, has complete valid-map coverage, and is not weighted by the MOS source mask or exposure map.

这些输入是原子 H I 柱，不是总等效 X 射线吸收柱。分子气体、尘埃对气体比、21 厘米光学厚度修正，以及圆形 HI4PI 孔径与不规则 MOS 足迹之间的不匹配都没有计入形式误差，而作为受控的吸收系统学分支保留。XSPEC 配置固定为 angr 太阳丰度表、vern 光电离截面与 APEC/AtomDB 3.0.9^[s26]。确切的 APEC 线与连续谱文件在 CIAO 安装中，其 SHA-256 哈希存在生产清单里。

These inputs are atomic H I columns, not total equivalent X-ray absorbing columns. Molecular gas, the dust-to-gas conversion, 21-cm optical-depth corrections and the mismatch between the circular HI4PI aperture and the irregular MOS footprints are not included in the formal errors; they are retained as controlled absorption-systematics branches. The XSPEC configuration is fixed to the angr solar-abundance table, the vern photoelectric cross sections, and APEC/AtomDB 3.0.9^[s26]. The exact APEC line and continuum files are present in the CIAO installation and their SHA-256 hashes are stored in the production manifest.

2.9 分段拟合过程2.9 Staged fitting procedure

所有拟合用 Gehrels \(\chi^2\) 统计（chi2gehrels）与 Sherpa Levenberg–Marquardt 优化器。分段过程对每个指向相同：(1) 在初始 \(0.2\)–\(1.4\cup2.0\)–\(8.0\) keV 拟合中，把本地热泡设为 \(kT=0.1\) keV、\(Z=1\)，把 \(\mathrm{CGM}_{\mathrm{sum}}\) 设为 \(kT=0.2\) keV、\(Z=0.3\)，热分量固定 \(kT=0.7\) keV、\(Z=1\)；较宽的低能边界只用于这个初始化阶段，最终域在第 3 步施加，且因组起点强制在 0.4 keV，没有低于 0.4 keV 的 bin 进入任何报告的拟合。(2) 在表 1 的边界内解冻本地热泡与 \(\mathrm{CGM}_{\mathrm{sum}}\) 的温度，两个丰度保持固定，重拟合相连的 MOS 谱。(3) 施加最终域并重拟合热、CXB 与残余线参数。(4) 对每个探测器，解冻软质子断幂律的归一化与两个谱指数而保持 3.2 keV 断点固定，联合重拟合所有活动参数。(5) 冻结拟合出的高能软质子指数，以物理次序 \(0\leq\Gamma_{\rm low}\leq\Gamma_{\rm high}\) 重拟合低能指数与归一化；若无约束的中间拟合违反该次序，在最终拟合前以 \(\Gamma_{\rm low}=\Gamma_{\rm high}/2\) 初始化。生产 worker 只在 Sherpa 报告 succeeded=True 时发布会话。每个发布的边车文件记录拟合统计量、方法、bin 数、自由度、全阶段滤除、输入/输出哈希与最终参数状态。

All fits use the Gehrels \(\chi^2\) statistic (chi2gehrels) and the Sherpa Levenberg–Marquardt optimiser. The staged procedure is identical for every pointing: (1) in the initial \(0.2\)–\(1.4\cup2.0\)–\(8.0\) keV fit, set the Local Bubble to \(kT=0.1\) keV and \(Z=1\), set \(\mathrm{CGM}_{\mathrm{sum}}\) to \(kT=0.2\) keV and \(Z=0.3\), and fix the hot component to \(kT=0.7\) keV and \(Z=1\); the wider low-energy bound is used only in this initialisation stage, the final domain is imposed at stage 3, and because group starts are forced at 0.4 keV no bin below 0.4 keV enters any reported fit. (2) Thaw the Local Bubble and \(\mathrm{CGM}_{\mathrm{sum}}\) temperatures within the bounds of Table 1, keep both abundances fixed, and refit the linked MOS spectra. (3) Apply the final domain and refit the thermal, CXB and residual-line parameters. (4) For each detector, thaw the broken-power-law normalisation and both photon indices while keeping the 3.2 keV break fixed, and refit all active parameters jointly. (5) Freeze the fitted high-energy soft-proton index and refit the low-energy index and normalisation with the physical ordering \(0\leq\Gamma_{\rm low}\leq\Gamma_{\rm high}\); if the unconstrained intermediate fit violates the ordering, initialise \(\Gamma_{\rm low}=\Gamma_{\rm high}/2\) before the final fit. The production worker publishes a session only when Sherpa reports succeeded=True. Every published sidecar records the fit statistic, method, number of bins, degrees of freedom, all-stage filters, input and output hashes, and final parameter states.

2.10 派生流量与总体估计量2.10 Derived fluxes and population estimators

恢复每个有效会话后，我们提取拟合的 \(\mathrm{CGM}_{\mathrm{sum}}\) 温度、APEC 归一化，以及保存的 Levenberg–Marquardt 协方差矩阵中它们的块。对能带 \(b\)，一个单位归一化的吸收 phabs*apec 模型配指向专属 \(N_{\rm HI}\) 定义换算 \(C_b(kT)\)。因拟合的 APEC 归一化已是每平方角分，分量面流量为 \(F_b=K_{\mathrm{CGM}_{\mathrm{sum}}}C_b(kT_{\mathrm{CGM}_{\mathrm{sum}}})\)。换算在 0.05 至 10 keV、0.001 keV 间隔的模型能量网格上求值，用与拟合相同的 angr、vern、\(Z=0.3\)、\(z=0\) 与 APEC 3.0.9 配置。我们以一阶 delta 方法传播保存的 \(kT\)–归一化协方差；这些是局部高斯统计近似，不含固定 \(N_{\rm HI}\)、前景、探测器背景、模型拓扑或校准不确定度，也不是剖面似然置信区间。

After restoring each valid session we extract the fitted \(\mathrm{CGM}_{\mathrm{sum}}\) temperature, APEC normalisation, and their block of the saved Levenberg–Marquardt covariance matrix. For a band \(b\), a unit-normalisation absorbed phabs*apec model with the pointing-specific \(N_{\rm HI}\) defines the conversion \(C_b(kT)\). Because the fitted APEC normalisation is already per square arcminute, the component surface flux is \(F_b=K_{\mathrm{CGM}_{\mathrm{sum}}}C_b(kT_{\mathrm{CGM}_{\mathrm{sum}}})\). The conversion is evaluated on a model energy grid with 0.001 keV spacing from 0.05 to 10 keV, using the same angr, vern, \(Z=0.3\), \(z=0\) and APEC 3.0.9 configuration as the fit. We propagate the saved \(kT\)–normalisation covariance with a first-order delta method; these are local Gaussian statistical approximations, they do not include fixed-\(N_{\rm HI}\), foreground, detector-background, model-topology or calibration uncertainty, and they are not profile-likelihood confidence intervals.

下文反复出现两个总体估计量并始终区分。全场逆方差值按 \((\sigma_i^2+\tau^2)^{-1}\) 给全部 14 个主场加权；两侧平衡值是两个侧均值的无权平均，因此给两个被采样侧相等权重。一个外部预言被称为估计量匹配，是指它通过实际视场位置投影后再用与其比较的测量相同的权重组合。这里两个估计量差别很大：因 10 个北/西北视场的剖面半宽小于 4 个南/东南视场，北/西北侧在多元起始基准上携带全场逆方差权重的 70.4%（在 v19 单起始局部协方差权重下为 93.7%）。因此全场值接近北/西北测量，不是无权的足迹平均；凡该区分可能影响结论处，我们都报告两侧平衡的伴随值。

Two population estimators recur below and are distinguished throughout. The all-field inverse-variance value weights all 14 primary fields by \((\sigma_i^2+\tau^2)^{-1}\); the side-balanced value is the unweighted mean of the two side means and therefore gives the two sampled sides equal weight. An external prediction is called estimator-matched when it is projected through the actual field positions and then combined with the same weights as the measurement it is compared against. The two estimators differ substantially here: because the 10 North/NW fields have smaller profile half-widths than the four South/SE fields, the North/NW side carries 70.4% of the all-field inverse-variance weight on the multistart basis (93.7% under the v19 single-start local-covariance weights). The all-field value is consequently close to the North/NW measurement and is not an unweighted footprint average; we report side-balanced companions wherever the distinction could affect a conclusion.

2.11 基线谱分量（表 1）2.11 Baseline spectral components (Table 1)

表 1 来源：内部修订稿 v2 的表 2（Baseline Spectral Components and Parameter Treatment）；Al/Si 行的响应翼上界 12–21% 与方向「偏高、尚未量化、不进误差预算」来自 cognition-os/07_REVISION_LOG.md R040 与 cognition-os/04_DECISION_LOG.md。

Source for Table 1: Table 2 of the internal revision v2 (Baseline Spectral Components and Parameter Treatment); the Al/Si row's response-wing upper bound of 12–21% with direction "upward, not yet quantified, not in the error budget" comes from R040 of cognition-os/07_REVISION_LOG.md and from cognition-os/04_DECISION_LOG.md.

3 结果3 Results

本节按顺序给出四个结果，每个小节回答一个问题、由一个图或表支持、并说明它对下一步的意义。全部数值为多元起始剖面基准，除非另标注为 v19 单起始估计量；统计误差为 1\(\sigma\)。

This section gives four results in order; each subsection answers one question, is supported by a figure or table, and states what it implies for the next step. All values are on the multistart profile basis unless labelled otherwise as a v19 single-start estimator; statistical errors are 1\(\sigma\).

3.1 共温 0.175 keV 分量遍布采样足迹3.1 A common 0.175 keV component spans the sampled footprint

第一个问题是被测分量的温度是否在 14 个主场之间一致。答案是：数据支持一个共同的现象学温度，但不建立空间均匀的等离子体。共同温度为

The first question is whether the measured component's temperature is consistent across the 14 primary fields. The answer is that the data support a common phenomenological temperature but do not establish a spatially uniform plasma. The common temperature is

\[ kT_{\mathrm{CGM}_{\mathrm{sum}}}=0.17531\pm0.00436\,\mathrm{keV}, \]

\[ kT_{\mathrm{CGM}_{\mathrm{sum}}}=0.17531\pm0.00436\,\mathrm{keV}, \]

异质性统计为 \(Q=11.631\)（13 个自由度，\(p=0.558\)），拟合的额外散射为零。分开的侧均值为北/西北 \(0.17469\pm0.00444\,\mathrm{keV}\) 与南/东南 \(0.19314\pm0.02382\,\mathrm{keV}\)，其差为 \(-0.01845\pm0.02423\,\mathrm{keV}\)^[s27]。只有 14 个视场、南/东南侧仅 4 个且误差相对大，这个检验检测适度内散射的功效有限；零最大似然值不是物理均匀性的正面证据。

with a heterogeneity statistic \(Q=11.631\) for 13 degrees of freedom (\(p=0.558\)) and a fitted extra scatter of zero. The separate side means are \(0.17469\pm0.00444\,\mathrm{keV}\) in the North/NW and \(0.19314\pm0.02382\,\mathrm{keV}\) in the South/SE, and their difference is \(-0.01845\pm0.02423\,\mathrm{keV}\)^[s27]. With only 14 fields, four on the South/SE side and comparatively large South/SE errors, this test has limited power to detect modest intrinsic scatter, and the zero maximum-likelihood value is not affirmative evidence for physical uniformity.

3.2 全场总量为 0.867，径向轮廓未检测到梯度3.2 The all-field total is 0.867 and no radial gradient is detected

第二个问题是视线总和多大、随半径如何变化。图 1 给出 14 个主场的多元起始逐场面亮度对投影半径。全场总量为

The second question is how large the line-of-sight sum is and how it varies with radius. Figure 1 shows the multistart per-field surface brightness of the 14 primary fields against projected radius. The all-field total is

\[ S_{\rm obs}=0.867\pm0.044\;(\text{统计}; \text{两段} -0.055/+0.039)\;+0.007/-0.003\;(N_{\rm H}, \text{重拟合})\;\pm0.027\;(\text{本地热泡分配}), \]

\[ S_{\rm obs}=0.867\pm0.044\;(\text{stat}; \text{two-piece} -0.055/+0.039)\;+0.007/-0.003\;(N_{\rm H}, \text{refit})\;\pm0.027\;(\text{LHB allocation}), \]

式中 \(\pm0.027\)（本地热泡分配）是温度下限 0.08 keV 剖面带的半宽；完整的、依赖温度下限的范围是 −0.061 到至少 +0.035。

In this equation the \(\pm0.027\) (LHB allocation) is the half-width of the floor-0.08 keV profile band; the full temperature-floor-dependent range is −0.061 to at least +0.035.

单位为 \(10^{-15}\,\mathrm{erg\,cm^{-2}\,s^{-1}\,arcmin^{-2}}\)，吸收 0.5–2.0 keV，毛总量（包含孔径内未分辨点源）^[s28]。\(\pm0.027\) 只是温度下限 0.08 keV 时那条剖面带的半宽；完整的、依赖下限选择的范围是 −0.061（下限 0.08，−7.0%）到至少 +0.035（下限 0.05，+4.1%，受网格边缘限制，只是下限值）^[s29]。历史值 0.965 是 v19 单起始基准，已被取代，只作为 dated history 保留。

in units of \(10^{-15}\,\mathrm{erg\,cm^{-2}\,s^{-1}\,arcmin^{-2}}\), absorbed 0.5–2.0 keV, gross (unresolved sources inside the apertures are included)^[s28]. The \(\pm0.027\) is only the half-width of the profile band at the 0.08 keV temperature floor; the full, floor-dependent range is −0.061 (floor 0.08, −7.0 %) to at least +0.035 (floor 0.05, +4.1 %, grid-edge-limited, so a lower bound)^[s29]. The historical value 0.965 is the v19 single-start basis, is superseded, and is retained only as dated history.

在 10.5–29 kpc 范围内，轮廓与一个常数一致（常数拟合 \(\chi^2=11.99/13\)，\(p=0.53\)，仅统计的局部协方差误差），点估计 mildly rising；没有检测到约 20–25% 量级的梯度^[s30]。这一平坦性只是对总和成立，不分解距离。对总和的模型敏感性单独测量：同时放开宇宙 X 射线背景谱指数与 CGM 丰度，在同口径权重下给 \(0.834\pm0.044\)（比 0.867 低 0.034，即 3.9%），但该模型未被信息判据选中（\(\Delta\)AIC 约 0 到 +2.1），因此按预登记规则作为敏感性报告，不加进误差棒^[s31]。

Over 10.5–29 kpc the profile is consistent with a constant (constant fit \(\chi^2=11.99/13\), \(p=0.53\), statistical-only local-covariance errors) with a mildly rising point estimate; no gradient is detected at the level of about 20–25%^[s30]. This flatness holds for the sum only and does not decompose distance. The sum's model sensitivity is measured separately: freeing the cosmic X-ray background photon index and the CGM abundance together gives \(0.834\pm0.044\) on like-for-like weights (0.034, or 3.9 %, below 0.867), but that model is not selected by the information criterion (\(\Delta\)AIC of about 0 to +2.1), so under the pre-registered rule it is reported as a sensitivity and not added to the error bar^[s31].

3.3 南北对比是最佳拟合值，不是不对称检测3.3 The North-South contrast is a best-fitting value, not an asymmetry detection

第三个问题是两侧之间检测到多大的差。答案是没有检测到不对称：北/西北的最佳拟合面亮度高于南/东南，但差只有 \(1.01\sigma\)。在吸收 0.4–1.25 keV 主带（完全落在直接拟合的软区间内），北/西北为 \(1.106\pm0.054\)、南/东南为 \(0.894\pm0.203\)，全场逆方差为 \(1.092\pm0.052\)，两侧平衡伴随值为 \(1.000\)，北减南为 \(0.212\pm0.210\)，分数不对称为 \(0.212\pm0.230\)^[s32]。这些 0.4–1.25 keV 数值是 v19 单起始估计量： 只重新定义了 0.5–2.0 keV 总量，因此它们仍需要在多元起始基准上重算，本文把它们标为待重算而不当作现行结果。

The third question is how large a difference is detected between the two sides. The answer is that no asymmetry is detected: the North/NW best-fitting surface brightness exceeds the South/SE value, but the difference is only \(1.01\sigma\). In the absorbed 0.4–1.25 keV primary band, which lies wholly inside the directly fitted soft interval, the North/NW is \(1.106\pm0.054\), the South/SE is \(0.894\pm0.203\), the all-field inverse-variance value is \(1.092\pm0.052\), the side-balanced companion is \(1.000\), the North minus South is \(0.212\pm0.210\), and the fractional asymmetry is \(0.212\pm0.230\)^[s32]. These 0.4–1.25 keV values are v19 single-start estimators: D57 and D65 redefined only the 0.5–2.0 keV total, so they still await recomputation on the multistart basis, and this paper labels them as awaiting recomputation rather than presenting them as current results.

几何不平衡同样重要。主样本含 10 个北/西北但只有 4 个南/东南视场，两侧中位半径相差 4.31 kpc。只按侧求均值会把径向结构与方位结构混在一起。因此我们把这些数值当作描述性经验基线。一个小的观测对比只约束

The geometric imbalance is equally important. The primary sample contains 10 North/NW but only four South/SE fields, and their median radii differ by 4.31 kpc. A side-only mean can mix radial structure with azimuthal structure, so we treat these values as a descriptive empirical baseline. A small observed contrast constrains only

\[ \Delta S_{\rm obs}=\Delta S_{\rm MW}+\Delta S_{\rm M31}, \]

\[ \Delta S_{\rm obs}=\Delta S_{\rm MW}+\Delta S_{\rm M31}, \]

（必要时加类似的本星系群项）。只有在假设银河系贡献在足迹上均匀时，它才约束 M31 不对称；反之只有在假设被采样的 M31 晕对称时，它才约束银河系变化。两个假设都不从当前数据得出。下一步分析必须在同一个似然里拟合一个共同的径向函数与一个侧偏移，两侧用同样的 nuisance 约定。

with an analogous Local-Group term if required. It constrains M31 asymmetry only if the Milky Way contribution is assumed uniform over the footprint, and it constrains Milky Way variation only if the sampled M31 halo is assumed symmetric. Neither assumption follows from the current data. The next analysis must fit a common radial function and a side offset in one likelihood, with the same nuisance conventions on both sides.

3.4 一个命名的银河系参考模型留下非负的中心 M31 残差为负3.4 A named Milky Way reference model leaves no non-negative central M31 residual

第四个问题是一个已发表前景模型与实测总和的比较。为让外部模型能按其自身发表项换算，比较在吸收 0.5–2.0 keV 能带进行；该能带中高于拟合 1.4 keV 边界的部分只贡献不到模型流量的 1%（冻结能带审计：在拟合 \(kT=0.175\) keV、\(Z=0.3\) 与采纳的 \(N_{\rm HI}\) 范围内，整个 1.25–2.0 keV 区间——严格包含被排除的 1.4–2.0 keV 间隙——只占吸收 0.5–2.0 keV 模型流量的 0.56%–0.70%，审计网格上最多 1.4%），因此这些比较不是由外插频道承载的^[s33]。

The fourth question compares a published foreground model with the measured total. The comparison is made in the absorbed 0.5–2.0 keV band so that the external models can be converted on their own published terms; the portion of that band above the fitted 1.4 keV boundary contributes below one percent of the model flux (frozen bandpass audit: at the fitted \(kT=0.175\) keV with \(Z=0.3\) and the adopted \(N_{\rm HI}\) range, the whole 1.25–2.0 keV interval — which strictly contains the excluded 1.4–2.0 keV gap — supplies only 0.56%–0.70% of the absorbed 0.5–2.0 keV model flux, and at most 1.4% anywhere on the audit grid), so these comparisons are not carried by extrapolated channels^[s33].

我们采用 Locatelli 等人的参考 Combined（\(\beta=0.5\)）几何作为垂直银河系预言，而不是他们的 combined-plus-SWCX 系统性检验。该参考模型是球形 \(n_{\rm h}=C r^{-3\beta}\) 晕加指数 \(n_{\rm d}=n_0\exp(-R/R_h)\exp(-|z|/z_h)\) 盘，参数为 \(C=(4.6\pm0.1)\times10^{-2}\)、\(n_0=(3.2\pm0.4)\times10^{-2}\,\mathrm{cm^{-3}}\)、\(R_h=6.2\pm0.4\) kpc、\(z_h=1.1\pm0.1\) kpc、\(kT=0.15\) keV 与发表的参考丰度 \(Z=0.1\,Z_\odot\)。我们把每个主指向从 \((l,b,s)\) 变换到银河系 \((R,z,r)\)，并把分别发射的晕与盘项积分到 350 kpc。绝对换算需要额外检查，因为他们拟合的是 0.614–0.694 keV O VIII 能带图并先用约 80 eV FWHM 核平滑 APEC 谱，而非未平滑的吸收宽带能流。我们在比较窄带发射率前施加同样的平滑并保持拟合的 O VIII 线归一化固定。为与本文分量一致，换算用 \(Z=0.3\,Z_\odot\) 目标 APEC、每个指向的 HI4PI 柱，并积分吸收 0.5–2.0 keV 流量。结果该参考几何在 14 个实际视场位置上预言 \(x=1.158\)–\(1.341\)，其中 \(x_{\rm N}=1.296\)、\(x_{\rm S}=1.213\)、两侧平衡 \(x=1.255\)、全场逆方差 \(x=1.290\)^[s34]。

For the vertical Milky Way prediction we adopt the reference Combined (\(\beta=0.5\)) geometry of Locatelli et al. rather than their combined-plus-SWCX systematic test. The reference model is a spherical \(n_{\rm h}=C r^{-3\beta}\) halo plus an exponential \(n_{\rm d}=n_0\exp(-R/R_h)\exp(-|z|/z_h)\) disk, with \(C=(4.6\pm0.1)\times10^{-2}\), \(n_0=(3.2\pm0.4)\times10^{-2}\,\mathrm{cm^{-3}}\), \(R_h=6.2\pm0.4\) kpc, \(z_h=1.1\pm0.1\) kpc, \(kT=0.15\) keV and a published reference abundance of \(Z=0.1\,Z_\odot\). We transform every primary pointing from \((l,b,s)\) to Galactic \((R,z,r)\) and integrate the separately emitting halo and disk terms to 350 kpc. The absolute conversion requires an extra check because they fit a 0.614–0.694 keV O VIII-band map after smoothing the APEC spectrum with an approximately 80 eV FWHM kernel rather than an unsmoothed absorbed broadband energy flux; we apply the same smoothing before comparing narrow-band emissivities and hold the fitted O VIII line normalisation fixed. For consistency with the component of this paper the conversion uses a \(Z=0.3\,Z_\odot\) target APEC, each pointing's HI4PI column, and integrates the absorbed 0.5–2.0 keV flux. The resulting reference geometry predicts \(x=1.158\)–\(1.341\) across the 14 actual field positions, with \(x_{\rm N}=1.296\), \(x_{\rm S}=1.213\), side-balanced \(x=1.255\) and all-field inverse-variance \(x=1.290\)^[s34].

\(Z=0.1\,Z_\odot\) 线归一化分支给全场值 \(1.291\)，与展示的 \(Z=0.3\) 结果相差不到 0.1%；这个小变化是预期的，因为预言在转到窄带前归一化到 O VIII 线，改变丰度会同时缩放线与连续谱发射率，而不只是缩放固定发射 measure。因此定性结果对该丰度选择稳健：Locatelli 银河系预言单独就超过实测全场总和 \(0.867\pm0.044\)，超出 \(0.423\)，并留下非负的中心 M31 残差为负。计入该模型自身误差（\(\sigma\approx0.32\)）后，这是约 \(1.3\sigma\) 的有条件中心值张力，不是排除^[s35]。结论不依赖用哪个总体估计量。

The \(Z=0.1\,Z_\odot\) line-normalised branch gives an all-field value of \(1.291\), differing by less than 0.1% from the displayed \(Z=0.3\) result; the small change is expected because the prediction is normalised to the O VIII line before being converted to a broad band, so changing abundance rescales both the line and continuum emissivities rather than simply rescaling a fixed emission measure. The qualitative result is therefore robust to this abundance choice: the Locatelli Milky Way prediction alone exceeds the measured all-field sum \(0.867\pm0.044\) by \(0.423\) and leaves no non-negative central M31 residual. With that model's own error (\(\sigma\approx0.32\)) included this is a conditional central-value tension of about \(1.3\sigma\), not an exclusion^[s35]. The conclusion does not depend on which population estimator is used.

4 讨论4 Discussion

本节重述问题与答案，说明结果如何支持答案，与文献比较，逐项量化局限，并给出对他人与后续工作的含义。

This section restates the question and answers it, explains how the results support the answer, compares with the literature, quantifies the limitations one by one, and states the implications for others and for future work.

4.1 被测量的量是视线总和4.1 The measured quantity is a line-of-sight sum

0.175 keV 分量遍布采样足迹且没有检测到过余温度散射，这种一致性不决定它的距离。银河系晕温度分布与当前测量重叠^[s36]，而面向 M31 的目标专属工作也明确识别出一个类似的前景加目标联合分量^[s37]。在 EPIC 分辨率下拟合两个温度几乎相同的自由 APEC 分量会让优化器任意瓜分一个谱形，这样的分解不是物理距离测量。因此第 1 节的方程是中心解释规则。答案因此是：本文测量并约束的是这个总和及其大尺度空间对比，而不是任何一个星系的晕。

The 0.175 keV component is widespread across the sampled footprint and has no detected excess temperature scatter; this consistency does not determine its distance. The Milky Way halo temperature distribution overlaps the current measurement^[s36], and target-specific work toward M31 has explicitly identified a similar combined foreground and target component^[s37]. At EPIC resolution, fitting two freely varying APEC components at nearly the same temperature would allow the optimizer to divide one spectral shape arbitrarily, and such a decomposition would not be a physical distance measurement. The equation of Section 1 is therefore the central interpretation rule. The answer, then, is that this paper measures and constrains the sum and its large-scale spatial contrast, not the halo of either galaxy.

4.2 条件互补与命名先验的阶梯4.2 Conditional complements and the named-prior ladder

图 3 收集全场总和 \(x+y=0.867\) 隐含的中心值记账。它不是置信区间表：文献行的不确定度定义彼此不同，且引用的多元起始值仍带统计与吸收局限，而其模型敏感性单独报告、不加进误差棒。负互补只表示该命名中心外部模型在所采纳换算下与非负二分量分解不相容。

Figure 3 collects the central-value bookkeeping implied by the all-field sum \(x+y=0.867\). It is not a table of confidence intervals: the literature rows have heterogeneous uncertainty definitions and the quoted multistart value still carries statistical and absorption limitations, while its measured model sensitivity is reported separately and is not added to the error bar. A negative complement means only that the named central external model is incompatible with a non-negative two-component decomposition under the adopted conversion.

Ueda Suzaku 指数盘投影到 M31 足迹给 \(x=0.312\)（足迹范围 0.289–0.321），隐含 M31 \(y=0.556\)；HaloSat 盘加绝热晕外推给 \(x=0.565\)（足迹范围 0.526–0.578），隐含 M31 \(y=0.302\)，但这是位于其 73 场 \(b<-30^\circ\) 拟合域之外的补充性方向外推，不是本地测量。Zhang M31 质量叠加在 20 kpc 给 \(y=0.828\)，隐含银河系 \(x=0.039\)；这是一个按恒星质量匹配的总体叠加名义中值（晕质量约为 M31 的 2–4 倍）且未发表协方差，是总体平均、名义中值的比较，不是 M31 专属下界，也绝不是对叠加预期的排除。模拟预言跨更大范围：EAGLE-AGNdT9 \(0.226\)、EAGLE 基准 \(0.450\)、EAGLE-NoAGN \(0.946\)、SIMBA 基准 \(1.635\)、SIMBA-NoAGN \(10.67\)（后者超出坐标范围）^[s38]。

The Ueda Suzaku exponential disk projected to the M31 footprint gives \(x=0.312\) (footprint range 0.289–0.321), implying M31 \(y=0.556\); the HaloSat disk plus adiabatic-halo extrapolation gives \(x=0.565\) (footprint range 0.526–0.578), implying M31 \(y=0.302\), but it is a supplemental directional extrapolation outside its 73-field \(b<-30^\circ\) fit domain and not a local measurement. The Zhang M31-mass stack gives \(y=0.828\) at 20 kpc, implying the Milky Way \(x=0.039\); it is a stellar-mass-matched population-stack nominal median (halo mass 2–4 times M31's) with unpublished covariance, a population-mean nominal-median comparison, not an M31-specific lower bound and never an exclusion of the stacked expectation. The simulation predictions span a much larger range: EAGLE-AGNdT9 \(0.226\), fiducial EAGLE \(0.450\), EAGLE-NoAGN \(0.946\), fiducial SIMBA \(1.635\) and SIMBA-NoAGN \(10.67\) (the last off scale)^[s38].

一个有用的条件阶梯是：(1) 无外部先验：只报告完整视线总和及其空间对比；(2) 均匀银河系先验：把 \(\Delta S_{\rm obs}\) 解释为被稀释的 M31 侧对比；(3) 对称 M31 先验：把 \(\Delta S_{\rm obs}\) 解释为银河系变化；(4) 外部银河系分布：剖面化一个非负 M31 分量并报告带先验标签的上限；(5) 外部星系剖面：拟合一个带先验标签的 M31 径向模板加银河系残差；(6) 本星系群/桥模板：加一个命名的非负 \(S_{\rm LG}\) 项并报告它如何改变条件 M31 与银河系范围。任何条件情形都不应作为直接分解呈现。

A useful conditional hierarchy is: (1) no external prior — report only the full line-of-sight sum and its spatial contrast; (2) a uniform Milky Way prior — interpret \(\Delta S_{\rm obs}\) as a diluted M31 side contrast; (3) a symmetric M31 prior — interpret \(\Delta S_{\rm obs}\) as Milky Way variation; (4) an external Milky Way distribution — profile a non-negative M31 component and report a prior-labelled upper limit; (5) an external galaxy profile — fit a prior-labelled M31 radial template plus a Milky Way residual; (6) a Local-Group or bridge template — add a named non-negative \(S_{\rm LG}\) term and report how it changes the conditional M31 and Milky Way ranges. No conditional case should be presented as a direct decomposition.

4.3 局限，逐项量化4.3 Limitations, quantified one by one

本小节按重要性给出局限。每项给出已量化的大小与其状态。

This subsection gives the limitations in order of weight. Each carries its quantified size and its status.

(a) 本地热泡下限。总量中 \(\pm0.027\) 的本地热泡分配项依赖模型里 0.08 keV 的温度下限：9/14 个场的温度被卡在该下限上。把下限放宽到 0.05 keV 后，中心几乎不变（+0.1%），但剖面带的高侧从 −7.0% 翻向至少 +4.1%（受网格边缘限制，是下限值）。因此完整的、依赖下限选择的范围是 −0.061 到至少 +0.035，而不是一个对称的 \(\pm0.027\)；按轮廓最小值（而非 v19 节点）定义总量时，放宽下限会把中心上移 +2.4%（同样是下限值）。状态：开放；该项保留在引用误差里并按依赖下限描述，固定 \(kT=0.11\) keV 的情形已排队为一个便宜的系统学分支。

(a) The Local Hot Bubble floor. The \(\pm0.027\) Local-Hot-Bubble allocation term in the total depends on the 0.08 keV temperature floor in the model, where 9 of 14 fields had their temperature pinned. Relaxing the floor to 0.05 keV leaves the centre nearly unchanged (+0.1 %) but flips the profile band's high side from −7.0 % to at least +4.1 % (grid-edge-limited, a lower bound). The full, floor-dependent range is therefore −0.061 to at least +0.035, not a symmetric \(\pm0.027\); and when the total is defined at the profile minimum rather than the v19 node, relaxing the floor moves the centre up by +2.4 % (also a lower bound). Status: open; the term stays in the quoted error, is described as floor-dependent, and the fixed-\(kT=0.11\) keV case is queued as a cheap systematic branch.

来源：cognition-os/04_DECISION_LOG.md；cognition-os/07_REVISION_LOG.md R047、R050。

Source: D73 of cognition-os/04_DECISION_LOG.md; R047 and R050 of cognition-os/07_REVISION_LOG.md.

(b) Al/Si 响应翼泄漏。1.4–2.0 keV 整段剔除只占模型流量的 0.37%，因此对流量定义是干净的；但该频段里很强的 Al K\(\alpha\) 与 Si K\(\alpha\) 仪器线被冻结为零，其响应翼会漏进保留的 0.5–1.4 keV。上界相当于 \(\mathrm{CGM}_{\mathrm{sum}}\) 流量水平的 12–21%、方向偏高、尚未量化。状态：开放；不进误差预算，总量数字不变；解冻 Al/Si 归一化的系统学分支已排队。

(b) Al/Si RMF-wing leakage. Excluding the whole 1.4–2.0 keV band moves only 0.37 % of the model flux, so the flux definition is clean; but the strong Al K\(\alpha\) and Si K\(\alpha\) instrumental lines in that band are frozen at zero, and their response wings leak into the kept 0.5–1.4 keV. The upper bound is 12–21 % of the \(\mathrm{CGM}_{\mathrm{sum}}\) flux level, direction upward, not yet quantified. Status: open; it is not in the error budget and the total is unchanged, and the systematic branch that thaws the Al/Si normalisations is queued.

来源：cognition-os/07_REVISION_LOG.md R040；cognition-os/04_DECISION_LOG.md。

Source: R040 of cognition-os/07_REVISION_LOG.md; D72 of cognition-os/04_DECISION_LOG.md.

(c) 模型敏感性。同时放开宇宙 X 射线背景谱指数（1.2–2.2）与 CGM 丰度（0.05–2.0）把同口径总量移到 \(0.834\pm0.044\)（−0.034，−3.9%；去掉四个最大移动场后 −0.050）。该模型未被信息判据选中（\(\Delta\)AIC 约 0 到 +2.1），单个场流量在丰度–归一化山脊上可动 \(\pm66\%\)。状态：已测量；按预登记规则作为敏感性报告，不加进误差棒，引用值 0.867 不变。

(c) Model sensitivity. Freeing the cosmic X-ray background photon index (1.2–2.2) and the CGM abundance (0.05–2.0) together moves the like-for-like total to \(0.834\pm0.044\) (−0.034, −3.9 %; −0.050 with the four largest movers dropped). That model is not selected by the information criterion (\(\Delta\)AIC of about 0 to +2.1), and individual field fluxes can move by \(\pm66\%\) along the abundance–normalisation ridge. Status: measured; under the pre-registered rule it is reported as a sensitivity, not added to the error bar, and the quote 0.867 stands.

来源：cognition-os/04_DECISION_LOG.md；cognition-os/07_REVISION_LOG.md R042；paper_apj_v19_cgmsum_draft/revision_d59_codexnim/measured_total.json 的 model_sensitivity 块。

Source: D68 of cognition-os/04_DECISION_LOG.md; R042 of cognition-os/07_REVISION_LOG.md; the model_sensitivity block of paper_apj_v19_cgmsum_draft/revision_d59_codexnim/measured_total.json.

(d) 年代亏缺未解决。档案外场样本（80–250 kpc）的流量随观测年代分为早期对晚期的台阶（23 个场上台阶比连续趋势拟合更好，\(\Delta\)AIC 约 9.5，最佳切分 2007/2008；改正后的 p = 0.018（13 场）/0.0009（23 场）），原因未解决（太阳风电荷交换或仪器/流程）。因此一切依赖外场年代混合的对比被标为受年代混杂，且在匹配年代的外场重提取完成、决定性年代检验运行之前不作结果引用。状态：开放；决定性检验的判定规则已在任何拟合前预登记，其结果为待定。

(d) The epoch deficit is unresolved. The archival outer sample (80–250 kpc) splits into an early-versus-late epoch step (a step fits better than a continuous trend on 23 fields, \(\Delta\)AIC about 9.5, best cut 2007/2008; corrected p = 0.018 for 13 fields and 0.0009 for 23), with the cause unresolved (solar-wind charge exchange or instrument/pipeline). Every comparison that leans on the epoch mixture of the outer fields is therefore labelled epoch-confounded and is not quoted as a result until matched-epoch outer re-extractions exist and the decisive epoch test has run. Status: open; the decisive test's decision rule is pre-registered before any fit and its result is Pending.

来源：cognition-os/04_DECISION_LOG.md；cognition-os/07_REVISION_LOG.md R043、R023；cognition-os/03_TRUST_TABLE.md 第 86、87、91 行。

Source: D69 of cognition-os/04_DECISION_LOG.md; R043 and R023 of cognition-os/07_REVISION_LOG.md; rows 86, 87 and 91 of cognition-os/03_TRUST_TABLE.md.

(e) 阈值未校准。对集中 M31 \(\beta\) 晕的单侧 95% 上限使用参数在非负边界处的 \(\Delta\mathrm{stat}=2.71\) 规则。该规则形式正确，但尚未用能谱级模拟校准：正在运行的校准（三个真值，每个至少 200 次模拟，14 个场，两个估计量）还没有产生覆盖率数字，且 200 次模拟只能发现严重失准（「已校准」判定在真实覆盖率 0.93 时概率 0.25、0.95 时 0.69）。状态：运行中（待定）；在校准完成前，每个这样的上限都保留「阈值未校准」标签，本文不以结果形式引用任何此类上限。

(e) The threshold is uncalibrated. The one-sided 95% upper limits on a concentrated M31 \(\beta\) halo use the \(\Delta\mathrm{stat}=2.71\) rule for a parameter bounded at zero. The rule is correct in form but is not yet calibrated by spectrum-level simulation: the running calibration (three truths, at least 200 simulations each, 14 fields, two estimators) has produced no coverage number yet, and 200 simulations can only reveal gross miscalibration (a "calibrated" verdict has probability 0.25 at a true coverage of 0.93 and 0.69 at 0.95). Status: running (Pending); until the calibration completes, every such limit keeps the "threshold uncalibrated" label, and this paper quotes none of them as a result.

来源：cognition-os/04_DECISION_LOG.md；cognition-os/07_REVISION_LOG.md R053、R056；.agent/jobs/2026-10-18-e028-stage1/REPORT_CORRECTION_1b_RT53.md。

Source: D72 and D75 of cognition-os/04_DECISION_LOG.md; R053 and R056 of cognition-os/07_REVISION_LOG.md; .agent/jobs/2026-10-18-e028-stage1/REPORT_CORRECTION_1b_RT53.md.

一句话总结本小节：引用总量 \(0.867\pm0.044\) 的统计误差之外，最大的开放项是本地热泡分配（依赖下限，完整范围 −0.061 到至少 +0.035）与尚未量化的 Al/Si 响应翼泄漏（上界 12–21%，方向偏高）；模型敏感性已测量（−3.9%）但不进误差棒；年代亏缺与该阈值两项的解决都在运行中，结果待定。

One sentence summarising this subsection: beyond the statistical error on the quoted total \(0.867\pm0.044\), the largest open items are the Local-Hot-Bubble allocation (floor-dependent, full range −0.061 to at least +0.035) and the not-yet-quantified Al/Si response-wing leakage (upper bound 12–21 %, direction upward); the model sensitivity is measured (−3.9 %) but is not in the error bar; the epoch deficit and the threshold are both being resolved by running work whose results are Pending.

4.4 对他人的含义与后续工作4.4 Implications for others and future work

对做弥漫 X 射线工作的他人，本分析给出几条可操作建议。第一，EPIC 弥漫发射的误差预算必须把粒子背景与软质子当作首要项，而不是残余项：QPB 必须在同一探测器足迹生成，软质子以显式连续谱建模，MOS 1.4–2.0 keV 因强 Al/Si 仪器线与软质子敏感性而排除。第二，若使用 EPIC-pn，必须独立处理其角区 QPB 就绪度（视场外小角区、事件外时间事件、增强的软质子敏感性），本分析因产品级背景系统学不用 pn，这是选择而非普遍否定。第三，任何「仅气体」或「仅 M31」的数字都必须是显式的条件情景，并带上先验名、能带换算与不确定度定义；本论文不给这样的数字。第四，用外部星系叠加剖面作 M31 先验时，应报告其为总体平均名义中值而非 M31 专属下验。第五，比较能带（0.5–2.0 keV）高于拟合边界的部分应给出可量化的上界，本分析给出「不到模型流量 1%」的冻结能带审计。

For others doing diffuse X-ray work this analysis offers several practical recommendations. First, the error budget for EPIC diffuse emission must treat the particle and soft-proton background as the leading term rather than a residual: the QPB must be generated in the same detector footprint, soft protons must be modelled with an explicit continuum, and the MOS 1.4–2.0 keV interval must be excluded for its strong Al/Si instrumental lines and soft-proton sensitivity. Second, if EPIC-pn is used, its corner-QPB readiness (the small out-of-field corner sample, out-of-time events and enhanced soft-proton sensitivity) must be handled independently; this analysis does not use pn for a product-level background-systematics reason, which is a choice and not a general rejection. Third, any "gas-only" or "M31-only" number must be an explicitly labelled conditional scenario carrying the prior's name, band conversion and uncertainty definition; this paper gives no such number. Fourth, when external-galaxy stacking profiles are used as an M31 prior, they should be reported as population-mean nominal medians rather than M31-specific bounds. Fifth, the portion of a comparison band (0.5–2.0 keV) above the fitted boundary should carry a quantified upper bound; this analysis gives a frozen bandpass audit of "below one percent of the model flux".

后续工作按顺序是：完成该阈值的能谱级校准（运行中，结果待定）并用它取代名义阈值；在同一个似然里拟合共同的径向函数加侧偏移，取代按侧均值；运行匹配年代外场的决定性年代检验（判定规则已预登记）；在受控分支网格里量化 Al/Si 响应翼泄漏与固定 \(kT=0.11\) keV 情形；把 0.4–1.25 keV 的半球与两侧平衡估计量在多元起始基准上重算，使全文只用一套一致的估计量。

Future work, in order: complete the spectrum-level calibration of the threshold (running, result Pending) and replace the nominal threshold with it; fit a common radial function plus a side offset in one likelihood instead of side-only means; run the decisive epoch test on matched-epoch outer fields (its decision rule is pre-registered); quantify the Al/Si response-wing leakage and the fixed-\(kT=0.11\) keV case inside the controlled branch grid; and recompute the 0.4–1.25 keV hemisphere and side-balanced estimators on the multistart basis so the paper quotes one consistent estimator set.

来源：cognition-os/04_DECISION_LOG.md 中待 PI 决定的条目；cognition-os/02_CURRENT_QUESTION.md「Concrete execution plan」节。

Source: the items awaiting a PI decision in cognition-os/04_DECISION_LOG.md; the Concrete execution plan section of cognition-os/02_CURRENT_QUESTION.md.

5 总结5 Summary

我们为 22 个穿过 M31 投影内晕（10.5–30.8 kpc）的 New-ANGELS 视线建了一个均匀的 XMM-Newton MOS 基线，其中 14 个经质量筛选的双 MOS 视场（10.5–28.8 kpc）承载下文每个测量。直接结论为：

We have constructed a homogeneous XMM-Newton MOS baseline for 22 New-ANGELS sightlines through the projected inner halo of M31 (10.5–30.8 kpc), of which 14 quality-selected dual-MOS fields (10.5–28.8 kpc) carry every measurement below. The direct conclusions are:

1. 14 个主场显示一个冷分量，共同现象学温度 \(kT=0.17531\pm0.00436\,\mathrm{keV}\)，异质性 \(Q(13)=11.631\)（\(p=0.558\)）（图 1 的温度面板在内部修订稿中）。The 14 primary fields show a cool component with a common phenomenological temperature \(kT=0.17531\pm0.00436\,\mathrm{keV}\) and heterogeneity \(Q(13)=11.631\) (\(p=0.558\)).
2. 吸收 0.5–2.0 keV 全场总量为 \(0.867\pm0.044\)（统计；两段 −0.055/+0.039）\(+0.007/-0.003\)（\(N_{\rm H}\)，重拟合）\(\pm0.027\)（本地热泡分配：温度下限 0.08 keV 剖面带的半宽），毛总量，完整的、依赖温度下限的范围是 −0.061 到至少 +0.035（图 1）。The absorbed 0.5–2.0 keV all-field total is \(0.867\pm0.044\) (stat; two-piece −0.055/+0.039) \(+0.007/-0.003\) (\(N_{\rm H}\), refit) \(\pm0.027\) (LHB allocation: half-width of the floor-0.08 keV profile band), gross, with the full temperature-floor-dependent range −0.061 to at least +0.035 (Figure 1).
3. 轮廓与一个常数一致（\(\chi^2=11.99/13\)），北/西北减南/东南为 \(0.212\pm0.210\)（\(1.01\sigma\)），因此未检测到径向梯度或两侧不对称。The profile is consistent with a constant (\(\chi^2=11.99/13\)) and the North/NW minus South/SE is \(0.212\pm0.210\) (\(1.01\sigma\)), so neither a radial gradient nor a side asymmetry is detected.
4. 该分量是银河系与 M31 发射的未分辨视线总和（可能另加本星系群项）；EPIC 谱不提供唯一的距离分解。The component is the unresolved line-of-sight sum of Milky Way and M31 emission, with a possible additional Local-Group term; EPIC spectra do not provide a unique distance decomposition.
5. 在命名的 Locatelli 参考 Combined 模型与记录的线归一化 \(Z=0.3\) 换算下，预言的银河系流量超过实测总量 \(0.423\)，留下非负的中心 M31 残差为负——计入该模型自身误差（\(\sigma\approx0.32\)）后约 \(1.3\sigma\) 的有条件中心值张力（图 2、图 3）。Under the named Locatelli reference Combined model and the documented line-normalised \(Z=0.3\) conversion, the predicted Milky Way flux exceeds the measured total by \(0.423\) and leaves no non-negative central M31 residual — a conditional central-value tension of about \(1.3\sigma\) with that model's own error (\(\sigma\approx0.32\)) (Figures 2 and 3).
6. 总量对宇宙 X 射线背景谱指数与 CGM 丰度的敏感性已测量为 \(0.834\pm0.044\)（同口径，−3.9%），作为敏感性报告，不加进误差棒。The total's sensitivity to the cosmic X-ray background photon index and the CGM abundance is measured as \(0.834\pm0.044\) (like-for-like, −3.9 %) and reported as a sensitivity, not added to the error bar.
7. 发表级的空间约束需要一个共同的径向加侧似然、边界感知区间与均匀的系统学网格；本稿不以结果形式引用任何此类上限（阈值未校准）或依赖外场年代混合的大核上限（受年代混杂）。Publication-level spatial constraints require a shared radial-plus-side likelihood, boundary-aware intervals and a homogeneous systematic grid; this draft quotes as results neither any such upper limit (the threshold is uncalibrated) nor any large-core limit that leans on the outer fields' epoch mixture (epoch-confounded).

因此稳定的结果不是单独检测到 M31 的热晕，而是对前景简并软分量的可复现测量，以及对其大尺度空间对比的弱约束。

The stable result is therefore not a detection of M31's hot halo by itself, but a reproducible measurement of the foreground-degenerate soft component and a weak constraint on its large-scale spatial contrast.

致谢Acknowledgments

本工作基于 XMM-Newton 获取的观测数据。XMM-Newton 是 ESA 的科学任务，其仪器与贡献直接由 ESA 成员国和 NASA 资助。我们使用了 HI4PI 原子氢巡天。完整致谢、提案信息与资助声明将在作者名单确定后加入。AI 辅助声明：本内部草稿在准备过程中使用了大型语言模型与 AI 代理辅助（按 AAS 政策在此声明）；全部科学内容、数字与判断来自项目记录，且每个数字都对照记录核对过。

This work made use of observations obtained with XMM-Newton, an ESA science mission with instruments and contributions directly funded by ESA Member States and NASA. We used the HI4PI atomic hydrogen survey. Full acknowledgments, proposal information and funding statements will be added after the author list is finalized. AI-assistance statement: large language models and AI agents assisted in preparing this internal draft (declared here per AAS policy); all scientific content, numbers and judgements come from the project records, and every number was checked against them.

设施与软件Facilities and Software

设施：XMM-Newton（EPIC-MOS）。

Facilities: XMM-Newton (EPIC-MOS).

软件：SAS^[s39]、XMM-ESAS^[s40]、Sherpa^[s41]、XSPEC^[s42]、AtomDB/APEC^[s43]、astropy、numpy、scipy、pandas、matplotlib。

Software: SAS^[s39], XMM-ESAS^[s40], Sherpa^[s41], XSPEC^[s42], AtomDB/APEC^[s43], astropy, numpy, scipy, pandas, matplotlib.

数据可用性Data availability

XMM-Newton 观测可从 XMM-Newton Science Archive 获取，观测标识见表 A1。机器可读的测量表、生产清单、拟合代码、验证脚本与图形生成脚本将在投稿前以持久标识归档（占位符，由 PI 决定）。

The XMM-Newton observations are available from the XMM-Newton Science Archive, with the observation identifiers given in Table A1. The machine-readable measurement table, production manifest, fitting code, validation scripts and figure-generation script will be archived with a persistent identifier before submission (placeholder, for the PI to decide).

附录Appendices

附录 A：观测清单（表 A1）Appendix A: observation inventory (Table A1)

14 个双 MOS 主场（10 北/西北、4 南/东南）承载本文每个测量；22 场母集跨 10.5–30.8 kpc，主场跨 10.5–28.8 kpc。曝光是各探测器产品的干净 PHA 曝光，不是独立的航天器时间；43 个 MOS 产品合计 533.571 ks 探测器曝光。完整机器可读清单（指向坐标、开始日期、侧、\(R_{\rm proj}\)、\(t_{\rm M1}\)、\(t_{\rm M2}\)、\(N_{\rm HI}\) 与 v19 用途）见 m31_cgmsum_v19_observation_products.csv 与内部修订稿 v2 的表 1。

The 14 dual-MOS primary fields (10 North/NW, 4 South/SE) carry every measurement here; the 22-field parent set spans 10.5–30.8 kpc and the primaries 10.5–28.8 kpc. Exposures are the cleaned PHA exposures of the individual detector products, not independent spacecraft time; the 43 MOS products sum to 533.571 ks of detector exposure. The full machine-readable inventory (pointing coordinates, start date, side, \(R_{\rm proj}\), \(t_{\rm M1}\), \(t_{\rm M2}\), \(N_{\rm HI}\) and v19 use) is in m31_cgmsum_v19_observation_products.csv and Table 1 of the internal revision v2.

附录 B：样本记账（表 B1）Appendix B: sample accounting (Table B1)

来源：cognition-os/00_AI_BRIEFING.md「Currently trusted」节；内部修订稿 v2 表 4（Sample Accounting）。

Source: the Currently trusted section of cognition-os/00_AI_BRIEFING.md; Table 4 (Sample Accounting) of the internal revision v2.

附录 C：投稿前必须完成的工作Appendix C: work required before submission

本附录列出投稿阻塞项，均来自项目记录，不构成结果：(1) 匹配的空间似然（共同径向加侧偏移，报告联合协方差与侧偏移的似然区间）；(2) 边界感知推断与优化器检查（多元起始、剖面化非负归一化与侧对比、用模拟校准单侧覆盖率，替换每个最终主张用的局部协方差区间）；(3) 受控系统学分支网格（掩膜/曝光加权吸收、全屏 vs 分布银河系吸收、HI/尘埃或总柱处方、软质子模型、CXB 归一化/宇宙方差、SWCX 处理、丰度与 O VIII 到宽带换算、热分量/模型拓扑、拟合能带，并加入 Al/Si 响应翼分支）；(4) 定量的约束产品（侧偏移或分数不对称的校准区间，以及保守的 U0 上包络）；(5) 投稿文档与图形（恢复原始耀斑筛选阈值、把每次提取绑定到校准索引、冻结源探测似然与掩膜半径规则、量化亮内盘/核球、PSF 翼与未分辨致密源向最内保留视场的泄漏、加入 M31 指向足迹图、代表性重分组谱与残差、径向加侧拟合与系统学分支摘要）；(6) 多元起始基准的头条量传播（0.4–1.25 keV 全场、两侧平衡与半球估计量仍在 v19 单起始基准上，需在多元起始基准上重算）；(7) 模型敏感性已完成（/），无需进一步工作。

This appendix lists the submission blockers, all from the project records; none is a result: (1) a matched spatial likelihood (a common radial term plus a side offset, reporting the joint covariance and a likelihood interval for the side offset); (2) boundary-aware inference and optimizer checks (multi-start, profile the non-negative normalisation and side contrast, calibrate one-sided coverage with simulations, replacing every local-covariance interval used for a final claim); (3) a controlled systematic branch grid (mask/exposure-weighted absorption, full-screen versus distributed Milky Way absorption, HI/dust or total-column prescription, soft-proton model, CXB normalisation and cosmic variance, SWCX treatment, abundance and O VIII-to-broadband conversion, hot-component/model topology, fitting band, plus the Al/Si response-wing branch); (4) a quantitative constraint product (a calibrated interval on the side offset or fractional asymmetry and at least the conservative U0 upper envelope); (5) submission documentation and figures (recover the original flare-screening thresholds, bind each extraction to its calibration index, freeze the source-detection likelihood and mask-radius rule, quantify leakage from the bright inner disk/bulge, PSF wings and unresolved compact sources into the innermost retained fields, and add an M31 pointing-footprint figure, representative rebinned spectra and residuals, the radial-plus-side fit and a systematic-branch summary); (6) multistart-basis headline propagation (the 0.4–1.25 keV all-field, side-balanced and hemisphere estimators are still on the v19 single-start basis and must be recomputed on the multistart basis); (7) the model-sensitivity completion is done and needs no further work.

来源：内部修订稿 v2 第 5 节（Analysis Required before Submission）；cognition-os/04_DECISION_LOG.md D70。

Source: Section 5 (Analysis Required before Submission) of the internal revision v2; D70 of cognition-os/04_DECISION_LOG.md.

参考文献References

来源地图（手册专有，不属于投稿论文）Source map (handbook-only, not part of the submitted paper)

下表列出本页每个来源标记：标记、记录来源、所支持的数值。数值从该标记所在段落提取；「定性表述」表示该标记支撑的是定性表述而非数字。摘要中的 [s1]–[s6] 是指向正文标记的简写：[s1]→[s27]，[s2]→[s32]，[s3]→[s28]，[s4]→[s31]，[s5]→[s34]+[s35]，[s6]→[s38]。

The table below lists every source marker on this page: the marker, its record source, and the value(s) it supports. The values are extracted from the paragraph carrying the marker; "qualitative statement" marks a marker that supports a qualitative statement rather than a number. The abstract's [s1]-[s6] are shorthand pointers to the body markers: [s1]->[s27], [s2]->[s32], [s3]->[s28], [s4]->[s31], [s5]->[s34]+[s35], [s6]->[s38].