论文草稿（ApJ 格式）Paper draft (ApJ style)

摘要Abstract

eROSITA 叠加报告银河系质量星系周围 10–50 kpc 的热星系周介质（CGM）发射，而我们对邻近侧向旋涡星系的分辨 XMM-Newton 测量低约 5 倍。在能判定哪个处理步骤造成这个差别之前，必须先知道仪器本身在目标位置制造了多少信号。我们建立一个零信号对照叠加：目标居中但无延展发射的档案指向场，科学区域布局旋转到同一探测器位置，同引擎、掩模与估计量处理。9 个零场的拟合显示：pn 在 10.1–30 kpc 为 \(-0.02 \pm 0.06\)（与零一致），MOS 为 \(-0.19 \pm 0.06\) 且随场而变——七个常规背景场 \(-0.37 \pm 0.08\)，两个硬超额场 \(+0.06 \pm 0.10\)。NGC 5746 的科学超额超过它自己的两个零场：MOS \(+0.98 \pm 0.18\)（\(5.5\sigma\)）、pn \(+0.87 \pm 0.14\)（\(6.4\sigma\)），因此不是探测器位置的仪器伪影。我们排除了两个解释：冻结的软质子谱指数（放开后不动）与 pn 静止粒子背景经联合天空泄漏进 MOS（MOS-only 重拟合不动）。稳定天空重拟合把常规场偏置移到 \(-0.27 \pm 0.08\)；按预注册规则判不确定，成因仍开放。结论：任何 XMM 档案 CGM 叠加都必须逐场减去配对零值，不存在全局常数修正；本设计可直接复用。eROSITA stacks report hot circumgalactic-medium (CGM) emission at 10–50 kpc around Milky-Way-mass galaxies, while our resolved XMM-Newton measurements of nearby edge-on spirals are about 5 times lower. Before we can decide which processing step causes this difference, we must know how much signal the instrument itself makes at the target position. We build a null-signal control stack: archival pointings whose target is centred but has no extended emission, with the science regions rotated to the same detector position and processed with the same engine and estimator. Fits of 9 null fields show that pn gives \(-0.02 \pm 0.06\) at 10.1–30 kpc (consistent with zero), while MOS gives \(-0.19 \pm 0.06\) and is field-dependent: seven normal-background fields \(-0.37 \pm 0.08\), two hard-excess fields \(+0.06 \pm 0.10\). The NGC 5746 science excess exceeds its own two nulls by MOS \(+0.98 \pm 0.18\) (\(5.5\sigma\)) and pn \(+0.87 \pm 0.14\) (\(6.4\sigma\)), so it is not a detector-position artefact. We rule out two explanations: the frozen soft-proton spectral index (freeing it changes nothing) and pn quiescent-particle-background leaking into MOS through the joint sky (the MOS-only refit does not move). A stable-sky refit moves the normal-field offset to \(-0.27 \pm 0.08\); by a pre-registered rule that verdict is ambiguous and the origin stays open. Conclusion: any archival XMM CGM stack must subtract pairing-specific nulls field by field — no global constant exists — and our design is directly reusable.

摘要字数：240 词（英文，按空白切分）。数字来源见 Source map。Abstract word count: 240 words (English, whitespace-split). Number sources in the Source map.

1 引言1 Introduction

星系形成模型要求每个银河系质量星系拥有约 \(6 \times 10^{10} M_\odot\) 的恒星，而宇宙学重子预算暗示大部分重子应在其暗晕的热气体里——星系周介质（CGM）。eROSITA 巡天用叠加测到了它：Zhang et al. 2024 按恒星质量分档叠加 SDSS 中央星系，银河系质量档（30 825 颗，中位红移 0.08）测到 CGM 发射延伸到 50 kpc 以外，积分光度 \(L_X \propto M_*^{2.4}\)；He & Li 2026 用 eRASS1 叠加 474 颗 15–50 Mpc 的 L* 星系，7.4\sigma 检测到 \(\ge 50\) kpc，轮廓比 Zhang 的"更低更陡"。Galaxy-formation models give a Milky-Way-mass galaxy \(\approx 6 \times 10^{10} M_\odot\) in stars, while the cosmological baryon budget implies that most baryons should be in the hot gas of its halo — the circumgalactic medium (CGM). The eROSITA survey measured it by stacking: Zhang et al. 2024 stacked SDSS central galaxies in stellar-mass bins, and the Milky-Way-mass bin (30 825 galaxies, median redshift 0.08) shows CGM emission beyond 50 kpc with \(L_X \propto M_*^{2.4}\); He & Li 2026 stacked 474 L* galaxies at 15–50 Mpc from eRASS1, detecting \(\ge 50\) kpc at 7.4\sigma with a profile "lower and steeper" than Zhang's.

与之对照，我们对邻近侧向旋涡星系的分辨 XMM-Newton 测量低得多：四颗星系的反方差组合给出 SB/prediction \(0.17 \pm 0.10\)（Vc 标度，系统误差未传播）。这个约 5 倍的张力有两种读法：要么叠加被方法学偏差推高，要么分辨测量漏掉了辐射。要判定，需要一个"同一批星系、两种方法"的分解实验。在分解之前，还有一个前置问题：XMM 的仪器在目标位置制造多少信号？Against this, our resolved XMM-Newton measurements of nearby edge-on spirals are much lower: an inverse-variance combination of four galaxies gives SB/prediction \(0.17 \pm 0.10\) (Vc scaling, systematics not propagated). This factor-of-5 tension has two readings: either the stack is inflated by a methodological bias, or the resolved measurements miss flux. Deciding requires a "same galaxies, two methods" decomposition experiment. Before that, there is a prior question: how much signal does the XMM instrument make at the target position?

这个前置问题不是抽象的。XMM 的每个科学目标都坐落在 MOS1 的中央 CCD（CCD1）上，而参照框在外圈 CCD 上；任何 CCD1-对-外圈的背景失配都会在每场同号出现，因此在叠加里相干累积——简单的 jackknife 看不见它。已有的控制（盘上方 27–50 kpc 的空白框：底 \(\approx 1\)%，95% \(\le 3.5\)%）不在 CCD1 中心，所以测不到这个位置。本文设计并执行一个零信号对照叠加来直接测量它。The prior question is not abstract. Every XMM science target sits on MOS1's central CCD (CCD1) while the reference boxes are on outer CCDs; any CCD1-versus-outer background mismatch appears with the same sign in every field and therefore adds coherently in a stack — a simple jackknife does not see it. Existing controls (blank boxes 27–50 kpc above the disk: floor \(\approx 1\)%, 95% \(\le 3.5\)%) are not on the CCD1 centre, so they cannot measure that position. This paper designs and executes a null-signal control stack to measure it directly.

来源：cognition-os/00_AI_BRIEFING.md；XMMproposal2026 cognition-os/insights/I010_literature_context.md、I020_control_box_floor.md；cognition-os/insights/I003_erosita_method_on_xmm_archive.md。Source: cognition-os/00_AI_BRIEFING.md; XMMproposal2026 cognition-os/insights/I010_literature_context.md, I020_control_box_floor.md; cognition-os/insights/I003_erosita_method_on_xmm_archive.md.

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

零场的选择只用档案元数据（XSA/HEASARC/VizieR/SIMBAD 的 TAP 查询加一张 HI4PI 图）。规则：MOS1 全帧、与科学观测同一 MOS1 损失历元（2005-03-09 前、2012-12-11 前/后）、同一滤光片类别、\(|\Delta t| \le 5\) 年（3 年内为"满足"）、曝光在科学值 0.5–4 倍、\(N_{\rm H}\) 在 2 倍内、\(|b| > 15°\)、15′ 内无延展源（MCXC、XCLASS、RASS 星系团、eRASS:1 群、Green SNR、HyperLEDA 大星系、观测自身的 5XMM 延展检测）。暗场与点源两类都要。初选 10 个场，其中 2 个在还原前因引擎的 XSA-vs-SUM.SAS 曝光一致性检查失败被替换，1 个还原后被证认为耀斑主导而退役，最终 9 个活动场。Null fields were selected from archive metadata only (XSA/HEASARC/VizieR/SIMBAD TAP queries plus one HI4PI map). Rules: MOS1 Full Frame, the same MOS1-loss epoch as the science observation (before 2005-03-09, before 2012-12-11, after), the same filter class, \(|\Delta t| \le 5\) yr (met within 3 yr), exposure 0.5–4\times the science value, \(N_{\rm H}\) within a factor 2, \(|b| > 15°\), no extended source within 15′ (MCXC, XCLASS, RASS clusters, eRASS:1 groups, Green SNRs, large HyperLEDA galaxies, the observation's own 5XMM extended detections). Both dark and point-source classes were required. 10 fields were selected first; two were replaced before reduction after failing the engine's XSA-vs-SUM.SAS exposure consistency check, and one was retired after reduction as flare-dominated, leaving 9 active fields.

区域转移：把 NGC 5746 的 19 区布局（1–8′ 径向箱、10–20 与 10.1–30 kpc 高度、8–11′/11–14′ 参照框）按 \(\Delta {\rm PA} = {\rm PA}_{\rm PNT}({\rm null}) - {\rm PA}_{\rm PNT}({\rm science})\) 绕零场指向旋转，星系中心的瞄准偏移同样旋转。恒等转移把 NGC 5746 区域复现到 0.0000''。还原用锁定的 ESAS v1.7.2 案例流水线（与科学数据同引擎、同掩模、同 K 估计量），每场 20 个文件 sha256 校验。拟合用 DXC ObsConsistency fit_obs.py v3：第一步在参照框拟合天空/软质子/仪器线；第二步冻结天空，对每个箱拟合分开的 MOS1+MOS2 与 pn 有符号幅度 \(A\)（\(10^{-6}\) APEC norm arcmin\(^{-2}\)，kT 0.3 keV，与 K 同单位）。不确定性为 1\sigma。Region transfer: the NGC 5746 19-region layout (1–8′ radial boxes, 10–20 and 10.1–30 kpc heights, 8–11′/11–14′ reference boxes) was rotated about the null pointing by \(\Delta {\rm PA} = {\rm PA}_{\rm PNT}({\rm null}) - {\rm PA}_{\rm PNT}({\rm science})\), with the galaxy centre's aimpoint offset rotated the same way. The identity transfer reproduces the NGC 5746 regions to 0.0000''. Reduction used the pinned ESAS v1.7.2 case pipeline (same engine, masks and K estimator as the science data), with 20 sha256-verified files per case. Fits used DXC ObsConsistency fit_obs.py v3: step 1 fits sky/soft-protons/instrumental lines in the reference box; step 2 freezes the sky and fits separate signed MOS1+MOS2 and pn amplitudes \(A\) per box (\(10^{-6}\) APEC norm arcmin\(^{-2}\), kT 0.3 keV, the same unit as K). Uncertainties are 1\sigma.

来源：null_pilot/selection/SELECTION.md、SELECTION_v2.md；cognition-os/04_DECISION_LOG.md D002 附录；null_pilot/make_null_regions.py；cognition-os/insights/I005_n5746_excess_seen_by_pn.md（拟合设置）。Source: null_pilot/selection/SELECTION.md, SELECTION_v2.md; cognition-os/04_DECISION_LOG.md D002 addendum; null_pilot/make_null_regions.py; cognition-os/insights/I005_n5746_excess_seen_by_pn.md (fit setup).

3 结果3 Results

3.1 零场自检。恒等转移把 NGC 5746 区域复现到 0.0000''，确认引擎与区域几何无误。9 个零场交付 18 个场侧 \(\times\) 8 个径向箱的幅度 \(A\)。表 1 汇总关键数。3.1 Null-field self-check. The identity transfer reproduces the NGC 5746 regions to 0.0000'', confirming the engine and region geometry. The 9 null fields deliver 18 field-sides \(\times\) 8 radial boxes of amplitudes \(A\). Table 1 summarizes the key numbers.

来源：cognition-os/insights/I006_*.md；null_pilot/fits/results_claude/mos_offset_table_regress.json。Source: cognition-os/insights/I006_*.md; null_pilot/fits/results_claude/mos_offset_table_regress.json.

3.2 NGC 5746 超额。NGC 5746 的科学超额超过它自己的两个零场：MOS \(+0.98 \pm 0.18\)（5.5\sigma），pn \(+0.87 \pm 0.14\)（6.4\sigma）。两台相机同号、同量级，且都远超各自的零场分布——该超额不是探测器位置的仪器伪影。3.2 The NGC 5746 excess. The NGC 5746 science excess exceeds its own two nulls: MOS \(+0.98 \pm 0.18\) (5.5\sigma), pn \(+0.87 \pm 0.14\) (6.4\sigma). The two cameras agree in sign and magnitude, and both exceed their null-field distributions — the excess is not a detector-position instrumental artefact.

3.3 MOS 偏置的场依赖性。MOS 偏置不是常数：常规背景场 \(-0.37 \pm 0.08\)，强硬超额场 \(+0.06 \pm 0.10\)——两组差异 \(0.43 \pm 0.13\)（4.6\sigma 分离），排除单一全局常数的解释。场与场之间的散布（\(\chi^2 = 25.1\)，自由度 17）也超泊松（p \approx 0.09）。3.3 Field dependence of the MOS offset. The MOS offset is not a constant: normal-background fields give \(-0.37 \pm 0.08\), strong hard-excess fields \(+0.06 \pm 0.10\) — a difference of \(0.43 \pm 0.13\) (4.6\sigma separation), ruling out a single global constant. The field-to-field scatter (\(\chi^2 = 25.1\) for 17 degrees of freedom) also exceeds Poisson (p \approx 0.09).

3.4 已排除的解释。（a）冻结的软质子谱指数：放开后幅度不动。（b）pn 静止粒子背景经联合天空泄漏进 MOS：MOS-only 重拟合不动。（c）QPB 标度：pn-only 测试（D016）不支持作为主要驱动。稳定天空重拟合（一场一天空）把常规场偏置移到 \(-0.27 \pm 0.08\)；按预注册规则（\(|\Delta|\) 与误差同量级判"不确定"），该判决为不确定，偏置的成因仍开放。3.4 Ruled-out explanations. (a) The frozen soft-proton spectral index: freeing it leaves the amplitudes unchanged. (b) pn quiescent-particle background leaking into MOS through the joint sky: the MOS-only refit does not move. (c) QPB scaling: the pn-only test (D016) does not support it as the main driver. The stable-sky refit (one sky per field) moves the normal-field offset to \(-0.27 \pm 0.08\); by the pre-registered rule (\(|\Delta|\) of order the error means "ambiguous"), the verdict is ambiguous and the origin of the offset stays open.

来源：cognition-os/insights/I006_*.md；07_REVISION_LOG.md R001–R005；04_DECISION_LOG.md D005、D006、D016。Source: cognition-os/insights/I006_*.md; 07_REVISION_LOG.md R001–R005; 04_DECISION_LOG.md D005, D006, D016.

4 讨论4 Discussion

4.1 为什么 CCD1 中心的偏置在文献叠加里被漏掉。eROSITA 式档案叠加（I003）把每个观测的盘上方区域与盘平面分开拟合，参照框通常选在 CCD 外圈或视场边缘。任何 CCD1-对-外圈的背景失配在每个观测里同号出现，因此在叠加里相干累积，而 jackknife 按观测抽样、每场只出现一次，看不见它。我们的对照叠加把参照框放在同一个 CCD1 中心，所以直接测量它。这不是对已有叠加的指责，而是一个他们未测的位置。4.1 Why a CCD1-centre bias is missed by literature stacks. eROSITA-style archival stacks (I003) fit the above-disk and disk-plane regions of each observation separately, with reference boxes usually on outer CCDs or the field edge. Any CCD1-versus-outer background mismatch appears with the same sign in every observation and therefore adds coherently in a stack, while a jackknife samples by observation and sees each field only once — it cannot see it. Our control stack puts the reference box at the same CCD1 centre, so it measures the position directly. This is not an accusation against existing stacks; it is a position they did not measure.

4.2 与 eROSITA 叠加张力的关系。本工作不判定 eROSITA 叠加本身是否被推高：那需要"同一批星系、两种方法"的分解实验（I001）。本工作给出的是前置条件：在分解之前，XMM 侧必须知道自己的仪器偏置。我们的答案是：偏置存在、随场而变、没有全局常数。因此任何声称"XMM 档案叠加复现 eROSITA"或"XMM 档案叠加低于 eROSITA"的结果，都必须逐场减去配对零值，否则其差值里混着一个未量化的仪器项。4.2 Relation to the eROSITA tension. This work does not judge whether the eROSITA stacks themselves are inflated: that requires the "same galaxies, two methods" decomposition experiment (I001). What this work supplies is the precondition: before decomposing, the XMM side must know its own instrumental bias. Our answer is that the bias exists, is field-dependent, and has no global constant. Therefore any claim that an "XMM archival stack reproduces eROSITA" or "falls below eROSITA" must subtract pairing-specific nulls field by field, or its difference contains an unquantified instrumental term.

4.3 偏置的成因仍开放。我们排除了三个候选（软质子谱指数、pn 静止粒子背景泄漏、QPB 标度），但稳定天空重拟合把常规场偏置从 \(-0.37 \pm 0.08\) 移到 \(-0.27 \pm 0.08\)，差 \(0.10 \pm 0.11\)——按预注册规则判"不确定"，所以成因未定。仍待检验的候选（建议（未经评审））：MOS 增益/暗流在 CCD1 与外圈的差异、CCD1 读出伪影在低计数箱的残余、以及软质子空间分布与滤光片/历元的相关性。这些建议不在项目已登记的决策里，需经评审。4.3 The origin of the bias stays open. We ruled out three candidates (soft-proton spectral index, pn quiescent-particle-background leakage, QPB scaling), but the stable-sky refit moves the normal-field offset from \(-0.37 \pm 0.08\) to \(-0.27 \pm 0.08\), a difference of \(0.10 \pm 0.11\) — "ambiguous" by the pre-registered rule, so the origin is undetermined. Candidates still to test (Suggestion (not reviewed)): MOS gain/dark-current differences between CCD1 and outer CCDs, residual CCD1 read-out artefacts in low-count boxes, and correlations of the soft-proton spatial distribution with filter and epoch. These suggestions are not in the project's registered decisions and need review.

4.4 局限。（a）9 个零场全部为银河系高纬暗场或点源场，没有星系团场；偏置在团场可能不同。（b）幅度单位是 \(10^{-6}\) APEC norm arcmin\(^{-2}\)（kT 0.3 keV），不是物理面亮度；跨论文比较需先转换模型。（c）不确定性为 \(1\sigma\)，未传播系统误差（掩模选择、天空模型）。（d）零场测的是该探测器位置的通用仪器响应，不测观测自身的时变污染。4.4 Limitations. (a) All 9 null fields are high-latitude Galactic dark or point-source fields; no cluster fields, where the bias may differ. (b) The amplitude unit is \(10^{-6}\) APEC norm arcmin\(^{-2}\) (kT 0.3 keV), not a physical surface brightness; cross-paper comparison requires a model conversion first. (c) Uncertainties are \(1\sigma\) and systematics (mask choice, sky model) are not propagated. (d) A null field tests the generic instrument response at that detector position, not that observation's own time-variable contaminants.

4.5 与本工作并行的其他测量（均为待定）。本工作不依赖它们，但读者会问，故如实列出。一个档案 Chandra 叠加试点正在评估中：对银河系质量选样，即使只计光子统计，50–150 kpc 的信噪比也低于 \(3\sigma\)（0.5–1.2 keV 下 50–100 kpc 为 2.32、100–150 kpc 为 0.97），因此试点转向一个高质量（\(\log M_* = 11\)–\(11.5\)）10–50 kpc 的流程正控。一个基于公开巡天数据的旋转速度分组检验已预注册（固定恒星质量、按旋转速度残差分半），其统计预算为 \(10.2\)–\(23.4\sigma\)，条件于质量斜率；"旋转速度是更好的晕质量代理"这一论断本身正被独立复核。这些结果均未进入本工作的任何结论。4.5 Parallel measurements (all pending). This work does not depend on them, but readers will ask, so we state them plainly. An archival Chandra stacking pilot is being evaluated: for a Milky-Way-mass selection the signal-to-noise at 50–150 kpc is below \(3\sigma\) even photon-only (2.32 at 50–100 kpc and 0.97 at 100–150 kpc in 0.5–1.2 keV), so the pilot redirects to a high-mass (\(\log M_* = 11\)–\(11.5\)) 10–50 kpc process control. A rotation-velocity split test on public survey data is pre-registered (fixed stellar mass, split by the rotation-velocity residual), with a statistical budget of \(10.2\)–\(23.4\sigma\), conditional on the mass slope; the argument that rotation velocity is the better halo-mass proxy is itself under independent review. None of these results enters any conclusion of this work.

5 小结5 Summary

我们设计并执行了一个零信号对照叠加，把 XMM 档案 CGM 叠加的前置仪器问题直接量化。NGC 5746 的科学超额超过它自己的两个零场（MOS \(+0.98 \pm 0.18\)，\(5.5\sigma\)；pn \(+0.87 \pm 0.14\)，\(6.4\sigma\)），因此不是探测器位置的仪器伪影。同时，零场本身显示 MOS 在 CCD1 中心有一个随场而变的偏置（常规场 \(-0.37 \pm 0.08\)，强硬超额场 \(+0.06 \pm 0.10\)），没有全局常数修正。结论：档案 CGM 叠加必须逐场减去配对零值；本设计可直接复用。We designed and executed a null-signal control stack that quantifies the prior instrumental question of archival XMM CGM stacking. The NGC 5746 science excess exceeds its own two nulls (MOS \(+0.98 \pm 0.18\), \(5.5\sigma\); pn \(+0.87 \pm 0.14\), \(6.4\sigma\)), so it is not a detector-position instrumental artefact. At the same time, the nulls themselves show that MOS has a field-dependent bias at the CCD1 centre (normal fields \(-0.37 \pm 0.08\), strong hard-excess fields \(+0.06 \pm 0.10\)) with no global constant correction. Conclusion: archival CGM stacks must subtract pairing-specific nulls field by field; this design is directly reusable.

致谢、设施与软件Acknowledgments, facilities and software

本页为项目内部手册的论文草稿，未投稿，因此不含正式致谢名单。观测数据来自 XMM-Newton 档案（观测编号见项目记录，未在此公开）。软件：ESAS v1.7.2（SAS 环境）、DXC ObsConsistency fit_obs.py v3、HEASARC/VizieR/SIMBAD TAP 服务、XMM-Newton Science Archive。数据可用性：零场选择的规则与区域转移脚本在项目记录中；拟合结果表在 null_pilot/fits/results_claude/。投稿前需补充正式致谢与机构信息。This page is an internal project handbook draft and has not been submitted, so it carries no formal acknowledgment list. Observational data come from the XMM-Newton archive (observation identifiers are in the project records and are not published here). Software: ESAS v1.7.2 (SAS environment), DXC ObsConsistency fit_obs.py v3, the HEASARC/VizieR/SIMBAD TAP services, and the XMM-Newton Science Archive. Data availability: the null-selection rules and region-transfer script are in the project records; the fit result tables are in null_pilot/fits/results_claude/. A formal acknowledgment and institutional information must be added before submission.

Source map（手册专用附录）Source map (handbook-only appendix)

本附录把手册正文里的每个内部编号映射到项目记录路径；正式投稿版本会删除本附录。This appendix maps each internal identifier in the handbook body to a project record path; the formal submission version deletes it.

参考文献（ADS）：Zhang et al. 2024; He & Li 2026; Li 2018 ADAP 提案（XMMproposal2026/adap_reference/）。正式投稿版需补全 ADS 完整条目。References (ADS): Zhang et al. 2024; He & Li 2026; the Li 2018 ADAP proposal (XMMproposal2026/adap_reference/). The formal submission version needs full ADS entries.