MW 纬度切片
MW latitude slice
固定 Galactic longitude,改变南半球 b=−|b|。这是 internal-observer sky slice,不是 MW 三维半径。
Hold Galactic longitude fixed and vary southern b=−|b|. This is an internal-observer sky slice, not a 3D MW radius.
M31 CGMsum · model-to-observable audit
从 Milky Way 三维密度、视线积分和 O VIII emissivity,走到每个 XMM pointing 的 absorbed 0.4–1.25 keV surface brightness;再把它和 M31 周围10–30 kpc的观测视线总和放在同一套可审计坐标中。
Follow the Milky-Way density geometry through line-of-sight integration and O VIII emissivity to the absorbed 0.4–1.25 keV prediction for every XMM pointing, then place it beside the observed line-of-sight sum at 10–30 kpc around M31.
01 · measurement before decomposition
14个 primary fields 给出的是约0.18 keV phenomenological thermal component 的 absorbed surface brightness。当前 fit 中该分量没有独立的 MW/M31 distance tag。
The 14 primary fields measure the absorbed surface brightness of an approximately 0.18 keV phenomenological thermal component. The fit does not attach an independent MW/M31 distance tag.
quality-selected dual-MOS primary sample;不是全部22个 pointings。
Quality-selected dual-MOS primary sample, not all 22 pointings.
这里所有主 surface brightness 都使用 absorbed v19 band convention。
All primary surface brightnesses use the absorbed v19 band convention.
是数据产品名,不是纯 MW,也不是直接测得的 M31 contribution。
A data-product name: neither pure MW nor a directly measured M31 contribution.
不是通用mission-standard band;常见跨样本band是0.5–2.0 keV。这里它是component-sensitive primary observable:完全位于实际拟合的MOS soft interval 0.4–1.4 keV内,避开1.4–2.0 keV禁带。对kT=0.175–0.20 keV、Z=0.1–0.3、NH=(4–8)×1020 cm−2的APEC grid,0.4–1.25保留0.4–2.0 absorbed model flux的98.8–99.5%;扩展上限几乎不增加该冷分量的信号。
It is not a universal mission-standard band; 0.5–2.0 keV is the common cross-sample band. Here it is a component-sensitive primary observable lying wholly inside the fitted MOS soft interval of 0.4–1.4 keV and below the excluded 1.4–2.0 keV interval. Across a kT=0.175–0.20 keV, Z=0.1–0.3, NH=(4–8)×1020 cm−2 APEC grid, 0.4–1.25 retains 98.8–99.5% of the absorbed 0.4–2.0 model flux; raising the upper bound adds almost no signal from this cool component.
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,再显式转换到当前absorbed 0.4–1.25 convention。建议保留0.4–1.25为primary,同时报告0.5–2.0 secondary;不要把它们当成未经转换即可比较的数值。
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 the current absorbed 0.4–1.25 convention. Retain 0.4–1.25 as primary and report 0.5–2.0 as secondary; do not compare the native numbers without conversion.
02 · three different coordinates
把它们混在一起会把 MW latitude dependence、M31-centric radius 和不规则 XMM footprint 误当成同一种“径向变化”。
Mixing them would turn MW latitude dependence, M31-centric radius, and an irregular XMM footprint into one misleading “radial trend.”
固定 Galactic longitude,改变南半球 b=−|b|。这是 internal-observer sky slice,不是 MW 三维半径。
Hold Galactic longitude fixed and vary southern b=−|b|. This is an internal-observer sky slice, not a 3D MW radius.
以 M31 为零点;正值指向 Galactic center,负值背离。R∥=DM31tanθ。
Zero at M31; positive toward the Galactic center, negative away. R∥=DM31tanθ.
用于放置14个观测 CGMsum points 和外部 M31-mass conditional templates;不携带 MW/M31 decomposition。
Places the 14 observed CGMsum points beside external M31-mass conditional templates; it carries no MW/M31 decomposition.
03 · model → observable
橙色 band 不是从论文表格抄来的 broadband prior。它是把一个 O VIII-constrained MW density geometry 投影到14个真实 sightlines,再经过80 eV Gaussian-smoothed emissivity closure、APEC band conversion 和每场 HI4PI absorption 得到的。
The orange band is not a broadband prior copied from a table. It comes from projecting an O VIII-constrained MW density geometry through 14 real sightlines, then applying an 80-eV Gaussian-smoothed emissivity closure, APEC band conversion, and field-specific HI4PI absorption.
使用 Locatelli et al. reference Combined β=0.5,而不是旧 combined+SWCX systematics branch。
Use the Locatelli et al. reference Combined β=0.5 model, not the old combined+SWCX systematics branch.
| β | C | n0 | Rh | zh | kT | Z |
|---|---|---|---|---|---|---|
| 0.5 | 0.046 | 0.032 cm−3 | 6.2 kpc | 1.1 kpc | 0.15 keV | 0.1 Z⊙ |
取 R0=8.2 kpc,s=0.001–350 kpc。实现积分的是 nh²+nd²;没有使用 (nh+nd)²,因此没有人为加入2nhnd cross term。
Use R0=8.2 kpc and s=0.001–350 kpc. The implementation integrates nh²+nd², not (nh+nd)², so it does not insert a 2nhnd cross term.
14个 reference sightlines 的 intrinsic O VIII intensity 约4.14–4.56 L.U.。这里还没有应用 photoelectric absorption,也还不是 broadband energy flux。
The 14 reference sightlines have intrinsic O VIII intensities of about 4.14–4.56 L.U. This is before photoelectric absorption and is not yet a broadband energy flux.
raw target APEC narrow-band emissivity 为1.383×10−16,但 Figure 3 使用 Gaussian-smoothed 1.736×10−16 做 closure。跳过 smoothing 会错误改变 line-to-broadband normalization。这里没有使用真实 MOS RMF/ARF,因此不是 detector response-folded spectrum。
The raw target-APEC narrow-band emissivity is 1.383×10−16, but Figure 3 closes against the Gaussian-smoothed 1.736×10−16. Omitting the smoothing would change the line-to-broadband normalization incorrectly. No real MOS RMF/ARF is used here, so this is not a detector-response-folded spectrum.
其中1 sr=(180×60/π)² arcmin²,最后除以10⁻¹⁵得到网页和 Figure 3 的 primary units。采用 Anders & Grevesse abundance、Verner cross-sections。连续 profile 曲线只使用明确标注的固定 NH;只有14个实测 footprint points 使用各自 HI4PI column。
Here 1 sr=(180×60/π)² arcmin², and division by 10⁻¹⁵ gives the primary units used on this page and in Figure 3. Use Anders & Grevesse abundances and Verner cross-sections. Continuous profile curves use an explicitly labeled fixed NH; only the 14 real footprint points use their individual HI4PI columns.
field min–max、North/South inverse-variance means、side-balanced central 和 all-field inverse-variance central 是四个不同 summaries,不能互换。
Field min–max, North/South inverse-variance means, the side-balanced central, and the all-field inverse-variance central are four different summaries and are not interchangeable.
04 · fixed-longitude latitude slice
固定 l=lM31=121.174329°,沿南半球 b=−|b| 改变视线。这里用固定 NH=0.056×1022 cm−2,目的是单独观察 density geometry,不是假装拥有连续 HI4PI map。
Hold l=lM31=121.174329° and vary the southern sightline b=−|b|. The fixed NH=0.056×1022 cm−2 isolates density geometry; it does not pretend to use a continuous HI4PI map.

| |b| (deg) | MW absorbed 0.4–1.25 keV |
|---|---|
| 10.0000 | 2.400 |
| 20.0000 | 1.661 |
| 21.5733 (M31) | 1.593 |
| 30.0000 | 1.334 |
| 45.0000 | 1.108 |
| 60.0000 | 1.023 |
| 90.0000 | 1.063 |
单位均为10⁻¹⁵ erg cm⁻² s⁻¹ arcmin⁻²,固定 NH=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 NH=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.
05 · signed sky-plane axis
这条轴不是 MW Galactocentric radius。它只是穿过 M31 的天球切线方向,用来检验在 M31 的10–30 kpc角尺度内,MW geometry 是否会制造明显梯度。
This is not a MW Galactocentric radius. It is the tangent-plane direction through M31 used to test whether MW geometry creates a substantial gradient across M31's 10–30 kpc angular scale.

06 · data versus conditional templates
横坐标现在改为 circular M31 projected radius。点是数据;曲线和横带是外部假设。它们可以比较,但不能在图例中混成同一种 measurement。
The horizontal coordinate is now circular M31 projected radius. Points are data; curves and horizontal bands are external assumptions. They can be compared, but not merged into one kind of measurement.

采用 rc=7.39 kpc、β=0.37,并令 S(20 kpc)=0.9418。条件曲线在10/15/20/25/30 kpc约为1.818/1.267/0.942/0.737/0.599。它是 population template,不是本项目从14个 XMM spectra 单独恢复的 M31 profile。
Use rc=7.39 kpc and β=0.37 with S(20 kpc)=0.9418. The conditional curve is approximately 1.818/1.267/0.942/0.737/0.599 at 10/15/20/25/30 kpc. It is a population template, not an M31 profile recovered independently from the 14 XMM spectra.
07 · collapse into the contribution plane
Figure 3 的横轴不是天空位置,而是假定的 MW contribution;纵轴是假定的 M31 contribution。数据本身只给出 x+y=total 的斜带。橙色竖向信息来自前面的14场模型投影。
Figure 3's horizontal axis is not a sky coordinate but an assumed MW contribution; the vertical axis is an assumed M31 contribution. The data provide only diagonal x+y=total bands. The orange vertical information comes from the preceding 14-field model projection.



表中 observed 一列始终是 CGMsum。MW reference 列是 named model projection;二者没有被当成同一种数据。
The observed column remains CGMsum. The MW-reference columns are named model projections; they are not treated as the same kind of data.
| OBSID | 分区Side | Rproj (kpc) | R∥ (kpc) | NH | 观测 CGMsumObserved CGMsum | MW固定NHMW fixed-NH | MW实际HI4PIMW actual HI4PI |
|---|---|---|---|---|---|---|---|
| 800731501 | North/NW | 10.52 | +8.84 | 0.0585 | 1.081 ± 0.147 | 1.611 | 1.580 |
| 800731901 | South/SE | 11.17 | -8.61 | 0.0648 | 0.931 ± 0.729 | 1.572 | 1.468 |
| 800731601 | North/NW | 13.07 | +12.69 | 0.0630 | 0.936 ± 0.110 | 1.602 | 1.518 |
| 800732001 | South/SE | 13.21 | -12.84 | 0.0692 | 0.963 ± 0.289 | 1.585 | 1.431 |
| 800731101 | North/NW | 13.45 | +5.85 | 0.0567 | 1.005 ± 0.761 | 1.631 | 1.622 |
| 800732301 | South/SE | 16.73 | -3.20 | 0.0529 | 0.842 ± 0.671 | 1.545 | 1.582 |
| 800730801 | North/NW | 18.92 | +10.71 | 0.0560 | 0.890 ± 0.519 | 1.643 | 1.643 |
| 800730901 | North/NW | 19.01 | +14.26 | 0.0559 | 1.060 ± 0.142 | 1.633 | 1.634 |
| 800730701 | North/NW | 19.54 | +6.64 | 0.0573 | 0.898 ± 0.205 | 1.652 | 1.636 |
| 800730501 | North/NW | 23.40 | +11.39 | 0.0553 | 1.324 ± 0.170 | 1.659 | 1.668 |
| 800730601 | North/NW | 25.03 | +7.19 | 0.0579 | 1.522 ± 0.215 | 1.671 | 1.646 |
| 800732801 | South/SE | 26.10 | -9.07 | 0.0481 | 0.798 ± 0.350 | 1.523 | 1.619 |
| 800730301 | North/NW | 28.69 | +16.68 | 0.0576 | 1.121 ± 0.147 | 1.669 | 1.649 |
| 800730201 | North/NW | 28.79 | +11.82 | 0.0578 | 1.272 ± 0.163 | 1.679 | 1.656 |
1.560先分别计算 North 与 South 的 inverse-variance mean,再给两个 sides 等权;它用于 Figure 3 的 side-balanced visual center。1.602直接对全部14场使用观测 inverse-variance weights;它与 all-field measured total 1.092 配对,用于 Table 5 conditional complement。它们是不同 estimator。
1.560 first computes inverse-variance means within North and South, then weights the two sides equally; it is the side-balanced visual center in Figure 3. 1.602 applies the observational inverse-variance weights directly to all 14 fields; it pairs with the all-field measured total 1.092 in Table 5. 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 envelope,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. It is a parameter-sensitivity envelope, not a posterior, confidence, or credible interval.
08 · what this page does not claim
09 · reproduce every step
所有页面资产进入 SHA-256 manifest。CSV 保存连续 profiles 和逐场 conversion;JSON 保存参数、单位、estimator 和 build metadata。
Every page asset enters a SHA-256 manifest. CSV files preserve continuous profiles and field-level conversions; JSON preserves parameters, units, estimators, and build metadata.
Build:2026-07-12 16:08 UTC。Canonical URL:m31cgm-mw-m31-profile-explorer.pages.dev。Build: 2026-07-12 16:08 UTC. Canonical URL: m31cgm-mw-m31-profile-explorer.pages.dev.