0.5–2.0 keV是常见的跨样本文献比较band，因此D42将Figure 3及相连的一致性检验统一到这一convention。它不是v19的直接component-sensitive primary band：其中1.4–2.0 keV跨越了被排除的MOS仪器谱线区间，因此这部分依赖模型外推。直接基线仍是0.4–1.25 keV；对kT=0.175–0.20 keV、Z=0.1–0.3、NH=(4–8)×10²⁰ cm⁻²的APEC grid，该band保留0.4–2.0 absorbed model flux的98.8–99.5%。

0.5–2.0 keV is the common cross-sample literature band, so D42 uses that convention for Figure 3 and its linked consistency diagnostics. It is not the direct component-sensitive primary band of v19: the 1.4–2.0 keV part crosses the excluded MOS instrumental-line interval and therefore depends on model extrapolation. The direct baseline remains 0.4–1.25 keV, which retains 98.8–99.5% of the absorbed 0.4–2.0 model flux across the audited kT=0.175–0.20 keV, Z=0.1–0.3, NH=(4–8)×10²⁰ cm⁻² APEC grid.

外部reference并不共享同一原始observable：Locatelli拟合0.614–0.694 keV O VIII窄带；Zhang使用rest-frame 0.5–2.0 keV；Grayson的emissivity图和比较语境支持intended 0.5–2.0 keV，但profile方法段没有明写event cut。本站先在各自原始band重建，再显式转换到absorbed 0.5–2.0 convention。旧0.4–1.25值仍作为v19 component-sensitive provenance保留，但不再用于Figure 3的一致性比较。

The external references do not share one native observable: Locatelli fits the 0.614–0.694 keV O VIII narrow band; Zhang uses rest-frame 0.5–2.0 keV; and Grayson's emissivity figure and comparison context support an intended 0.5–2.0 keV band, although its profile-method paragraph does not state the event cut explicitly. This site reconstructs each native observable before explicitly converting it to an absorbed 0.5–2.0 convention. The old 0.4–1.25 values remain available as v19 component-sensitive provenance but are no longer used in Figure 3's consistency comparison.

单位均为10⁻¹⁵ erg cm⁻² s⁻¹ arcmin⁻²，固定 N_H=0.056×10²² cm⁻²。90°附近的轻微回升是该 named geometry 的性质，不是观测。

Units are 10⁻¹⁵ erg cm⁻² s⁻¹ arcmin⁻² at fixed N_H=0.056×10²² cm⁻². The mild upturn near 90° is a property of the named geometry, not an observation.

density geometry 对 z 使用 |z|，但真实 Galactic absorption 和其他 foreground 并不保证南北对称。本页连续曲线固定在 M31 所在的 southern branch；若以后接入连续 HI4PI map，必须分别计算正负 b，而不能只靠 |b|。

The density geometry uses |z|, but real Galactic absorption and other foregrounds need not be north–south symmetric. The continuous curve stays on M31's southern branch. A future continuous HI4PI version must compute positive and negative b separately.

采用 r_c=7.39 kpc、β=0.37，并令 absorbed 0.5–2.0 keV S(20 kpc)=0.8285。条件曲线在10/15/20/25/30 kpc约为1.600/1.114/0.828/0.648/0.527。它是 population template，不是本项目从14个 XMM spectra 单独恢复的 M31 profile。

Use r_c=7.39 kpc and β=0.37 with absorbed 0.5–2.0 keV S(20 kpc)=0.8285. The conditional curve is approximately 1.600/1.114/0.828/0.648/0.527 at 10/15/20/25/30 kpc. It is a population template, not an M31 profile recovered independently from the 14 XMM spectra.

五组MW结果都采用完全相同的几何语法：中心值或scenario画成贯穿绘图区的竖线，范围画成竖向span或边界线。它们只固定x=S_MW，并不沿y轴提供额外测量；全高只是让每个study拥有相同视觉权重。真正的y=S_M31条件模板仍是Zhang/Grayson水平线。

All five MW results use the same geometric grammar: central values or scenarios are full-height vertical lines, while ranges are vertical spans or boundary lines. They constrain only x=S_MW and add no measurement along y; full height gives each study equal visual status. The true y=S_M31 conditional templates remain the horizontal Zhang/Grayson lines.

Locatelli 的高值来自一个具体转换链：采用论文指定的 reference Combined β=0.5 geometry，将 n_h²+n_d² 沿14条真实视线从太阳位置积分，得到4.14–4.56 L.U. 的 intrinsic O VIII 0.614–0.694 keV intensity；再用80 eV FWHM Gaussian smoothing 匹配原始 O VIII map 的能量处理。冻结CSV中的 response-matched self-check scale 为0.9498760469603238。最终 Figure 3 不是继续使用 published Z=0.1 broadband，而是固定这条 O VIII line normalization，换成Z=0.3 target APEC，并用每个 pointing 的 HI4PI N_H 做 full foreground screen phabs，得到absorbed 0.5–2.0 keV。

The high Locatelli value follows a specific conversion chain: use the paper-designated reference Combined β=0.5 geometry, integrate n_h²+n_d² from the Solar position through the 14 real sightlines, obtain intrinsic O VIII 0.614–0.694 keV intensities of 4.14–4.56 L.U., and match the original O VIII map treatment with an 80-eV-FWHM Gaussian smoothing. The frozen CSV gives a response-matched self-check scale of 0.9498760469603238. Figure 3 then does not reuse a published Z=0.1 broadband value; it holds that O VIII line normalization fixed, converts to a Z=0.3 target APEC model, and applies each pointing's HI4PI N_H as a full foreground screen phabs to obtain absorbed 0.5–2.0 keV.

重算结果闭合：14场final values为1.158–1.341，North/South inverse-variance means为1.296/1.213，side-balanced辅助summary为1.255，all-field inverse-variance estimator为1.290。图中实心橙线采用1.290，因为它应与观测all-field total 0.965±0.044比较；因此超过all-field观测总量0.326，即约34%。这不是“测得的MW一定这么亮”，而是说明这个 named Locatelli conversion 与我们的 observed CGMsum total 不相容，或者原模型normalization/line-to-broadband/foreground-screen假设在M31低纬视线方向过高。它也不是posterior interval；14-field min–max只是footprint spread。

The recomputation closes: the 14 final field values are 1.158–1.341, the North/South inverse-variance means are 1.296/1.213, the side-balanced auxiliary summary is 1.255, and the all-field inverse-variance estimator is 1.290. The solid orange line uses 1.290 because it is compared with the observed all-field total, 0.965±0.044; it therefore exceeds the all-field observed total by 0.326, or about 34%. This does not mean the MW brightness has been measured to be exactly that high; it means this named Locatelli conversion is inconsistent with our observed CGMsum total, or that its normalization, line-to-broadband conversion, or foreground-screen assumption is too high for this low-latitude M31 direction. It is not a posterior interval; the 14-field min–max is only footprint spread.

有，但要准确命名：Kaaret+20给出的是empirical disk + adiabatic halo，halo是在NFW势中静水平衡的多方气体，不是一个由全天数据拟合的通用spherical β component。原拟合只使用南天 b<−30° 的HaloSat EM；M31十四场约在b=−21.6°，全部在拟合域外。模型几何可以算到M31方向，但结果必须叫extrapolation。

Yes, but it must be named precisely. Kaaret+20 fit an empirical disk plus an adiabatic halo, with the halo a hydrostatic polytrope in an NFW potential, not a generic spherical beta component calibrated by full-sky data. The fit used only southern HaloSat emission measures at b<−30°. All 14 M31 fields are outside the original southern-sky fit domain near b=−21.6°. The geometry can be evaluated toward M31, but the result is an extrapolation.

本页采用论文best fit：n_H,disk=0.0081 Σ(R) exp(−|z|/1.60 kpc)，halo使用Fang+13 adiabatic profile和ρ_V=4.8×10⁻⁵ cm⁻³，积分到260 kpc，并按n_e/n_H=1.2计算EM=∫1.2(n_d+n_h)²ds。由于density fit不提供M31方向温度，band conversion明确补充HaloSat sample median kT=0.225 keV、Z=0.3、Wilms+Verner TBabs和逐场HI4PI。得到all-field 0.678，14场0.632–0.693，patchiness predictor scale为±0.165；条件M31 complement为0.286。若去掉disk–halo cross term，structural check为0.526；它不是confidence bound。

The executable projection uses the published best fit: n_H,disk=0.0081 Σ(R) exp(−|z|/1.60 kpc), the Fang+13 adiabatic profile with ρ_V=4.8×10⁻⁵ cm⁻³, integration to 260 kpc, and n_e/n_H=1.2 in EM=∫1.2(n_d+n_h)²ds. Because the density fit supplies no M31-direction temperature, the band conversion explicitly adds the HaloSat sample median kT=0.225 keV, Z=0.3, Wilms+Verner TBabs, and field-specific HI4PI. The all-field result is 0.678, the 14-field range is 0.632–0.693, the patchiness predictor scale is ±0.165, and the conditional M31 complement is 0.286. A no-cross-term structural check gives 0.526; it is not a confidence bound.

1.255先分别计算North与South的inverse-variance mean，再给两个sides等权，是side-balanced辅助summary。1.290直接对全部14场使用观测inverse-variance weights，并与all-field measured total 0.965配对；新版Figure 3用它作为实心橙色主竖线。它们是不同estimator。

1.255 first computes inverse-variance means within North and South, then weights the two sides equally; it is a side-balanced auxiliary summary. 1.290 applies observational inverse-variance weights to all 14 fields and pairs with the all-field total 0.965; the revised Figure 3 uses it as the solid orange main line. They are different estimators.

不是。它只用published marginal parameter errors做diagonal first-order propagation；Locatelli posterior covariance不可用。因此它只能叫parameter-sensitivity boundaries，不能叫posterior、confidence或credible interval。

No. It uses published marginal parameter errors in a diagonal first-order propagation without the Locatelli posterior covariance. They are parameter-sensitivity boundaries, not a posterior, confidence, or credible interval.

Ueda+22的75°<l<285°、|b|>15°描述130场parent sample；本页采用的n_e0=3.4×10⁻³ cm⁻³来自Table 3的2005–2009、|l|>105°、N=36 disk row。M31的14场仍在这个selected angular domain内，因此可以沿每条真实视线积分并应用逐场HI4PI。得到的0.312是与观测采用相同inverse-variance weights的条件模型值。绿色hatched span是14场nominal spread，绿色点线边界仅展开n₀边际误差；没有参数covariance，不能叫posterior interval。eFEDS和H&S13只提供其他天空方向的测量分布，不能局部化到M31。

Ueda+22 used a 130-field parent sample over 75°<l<285° and |b|>15°. The n_e0=3.4×10⁻³ cm⁻³ normalization used here comes specifically from the Table 3 2005–2009, |l|>105°, N=36 disk row. All 14 M31 fields remain inside that selected angular domain, so the model can be integrated along each actual sightline and converted with field-specific HI4PI. Its 0.312 value uses the same inverse-variance weights as the observed total. The green hatched span is nominal footprint spread and the green dotted boundaries vary only marginal n₀; without parameter covariance this is not a posterior interval. eFEDS and H&S13 instead provide measurements in other sky directions and cannot be localized to M31.

有line catalog，但不能直接变成独立MW broadband prior。X-LEAP I在M31 4.4°内有52条catalog rows，全部被标为M31-contaminated且没有一条属于clean sample；作者还报告约10°–20°的M31-associated enhancement。clean 10°–20°和20°–30° annuli的raw detected O VIII median都约1.41 L.U.，但这是observed line intensity，仍混有方向依赖的SWCX/absorption，也没有MW/M31 component separation。X-LEAP II在M31距Galactic center 118.78°处的经验radial formula给出EM=−0.0011±0.0129 pc cm⁻⁶，本身不提供约束；X-LEAP II也没有发表可用于逐场投影的3D density decomposition。因此它保留为line/temperature validation data set，不画成第六条broadband MW竖线。

X-LEAP provides a line catalog, but not an independent MW broadband prior. X-LEAP I has 52 catalog rows within 4.4° of M31; all are flagged as M31-contaminated and none belongs to the clean sample, and the paper reports an M31-associated enhancement over roughly 10°–20°. The clean 10°–20° and 20°–30° annuli both have a raw detected O VIII median near 1.41 L.U., but these are observed line intensities with direction-dependent SWCX/absorption and no MW/M31 component separation. At M31's 118.78° distance from the Galactic center, the X-LEAP II empirical radial formula gives EM=−0.0011±0.0129 pc cm⁻⁶, which is unconstraining. X-LEAP II does not publish a 3D density decomposition usable for field-by-field projection. It is therefore retained as a line/temperature validation data set rather than plotted as a sixth broadband MW line.

是，但要区分两项结果。Ponti+23在107.5 deg² eFEDS区域发表了可分解的CGM component flux，所以能转换成图中的两条紫色scenario竖线；它离M31至少105°，不是M31同向先验。Yeung+24 Paper I覆盖西半球约2000个spectral bins，但文章主题是Local Hot Bubble，并明确把CGM结果留给Paper II；不能从Paper I虚构一个western-hemisphere broadband CGM分布。

Yes, but two results must be separated. Ponti+23 published a decomposed CGM-component flux for the 107.5 deg² eFEDS field, supporting the two purple vertical scenario lines; it remains at least 105° from M31 and is not M31-matched. Yeung+24 Paper I analyzed roughly 2000 western-hemisphere spectral bins but focused on the Local Hot Bubble and explicitly deferred the CGM results to Paper II. Paper I therefore does not support inventing a western-hemisphere broadband CGM distribution.