M31-mass stack
M31-mass stack
按stellar mass bin命名，不是M31本身。
Named by stellar-mass bin, not M31 itself.
Figure 3 · study file
Yi Zhang et al.（2024）论文档案
Yi Zhang et al. (2024) study file
The hot circumgalactic medium in the eROSITA All-Sky Survey. I. X-ray surface brightness profiles
Zhang et al.把大量central galaxies的eROSITA photons按stellar-mass bins堆叠，统计分离hot-CGM、unresolved AGN/XRB/satellites与PSF。Figure 3使用M31-mass bin的population profile作为条件模板，不是M31本身的观测。
Zhang et al. stack eROSITA photons around large samples of central galaxies in stellar-mass bins, statistically separating hot CGM, unresolved AGN/XRB/satellites, and the PSF. Figure 3 uses the M31-mass-bin population profile as a conditional template, not an observation of M31 itself.
DOI 10.1051/0004-6361/202449412
Source snapshot: arXiv:2401.17308v3 · 2026-07-15T10:49:33ZSHA-256 4f96964adc92f9558da6acd9771fc0f612005f3b9eb3712d8e9c6ac89ca39b7c
先看三张讲解图
Start with the three talk figures
先建立视觉主线；讲稿中的Figure 1–3与这里的顺序严格一致。
Establish the visual story first; Figure 1–3 cues in the talk track follow this exact order.
Zhang template与observed total在线性plane中
The Zhang template and observed total in the linear plane
橙色M31 template曲线与observed all-field/side totals同时显示。它是target-side conditional model，不能移到MW foreground x轴。
The orange M31-template curve is shown with observed all-field and side totals. It is a target-side conditional model and cannot be moved onto the Milky-Way foreground x axis.
PDF
20 kpc characteristic value的尺度
Scale of the 20 kpc characteristic value
log view把Zhang 0.828454与五个simulation templates、observed total及MW comparators置于同一正象限，同时保留x/y物理角色。
The log view places Zhang 0.828454 with five simulation templates, the observed total, and MW comparators in one positive quadrant while retaining their x/y physical roles.
PDF
r_c=4 kpc的连续conditional profile
The continuous r_c=4 kpc conditional profile
橙色曲线是published median beta law经共同conversion后的10–30 kpc profile；蓝/红points仍是observed CGMsum，而不是对该template的直接测量。
The orange curve is the published median beta law after the common conversion over 10–30 kpc. Blue/red points remain observed CGMsum, not direct measurements of that template.
PDF5-minute presentation · speaker-ready
一句话结论
One-sentence take-home
Zhang et al.的M31-mass结果是约26,099个external central galaxies的population stack，不是M31 observation。采用published median r_c=4 kpc、β=0.37 profile，在20 kpc得到intrinsic luminosity surface density约1.7253e36 erg s^-1 kpc^-2；经distance-cancel与v19 APEC absorption bridge后，Figure 3冻结ledger值为0.828454。
The Zhang et al. M31-mass result is a population stack of about 26,099 external central galaxies, not an observation of M31. The published median r_c=4 kpc, beta=0.37 profile gives an intrinsic luminosity surface density of approximately 1.7253e36 erg s^-1 kpc^-2 at 20 kpc. After the distance-cancel and v19 APEC absorption bridge, the frozen Figure 3 ledger value is 0.828454.
统一单位：除非另行注明，Figure 3面亮度均为absorbed 0.5–2.0 keV，单位10−15 erg cm−2 s−1 arcmin−2。Common unit: unless noted otherwise, Figure 3 surface brightnesses are absorbed 0.5–2.0 keV in 10−15 erg cm−2 s−1 arcmin−2.
先记住这六个数字
Six numbers to remember
published median core radius
Published median core radius
Table 4的M31-mass value；不是旧的7.39 kpc。
The Table 4 M31-mass value, not the obsolete 7.39 kpc.
projected beta slope
Projected beta slope
与log S_X0=37.1共同定义nominal profile。
Together with log S_X0=37.1, defines the nominal profile.
Figure 3 sampling radius
Figure 3 sampling radius
从连续population profile取characteristic value。
A characteristic value sampled from the continuous population profile.
native luminosity density
Native luminosity density
erg s^-1 kpc^-2；原文有限位数medians与冻结ledger相差4.6 ppm。
erg s^-1 kpc^-2; printed finite-precision medians differ from the frozen ledger by 4.6 ppm.
Figure 3 converted value
Figure 3 converted value
条件M31 template，不是foreground prediction。
A conditional M31 template, not a foreground prediction.
五分钟逐段讲稿
Five-minute talk track
按时间顺序讲；每段先说粗体标题，再用图或数字支撑，不需要另查论文。
Follow the timing in order. State each heading first, then support it with the figure or number; no paper lookup is required.
先纠正M31-mass含义
First correct the meaning of M31-mass
M31-mass是11.0<log(M*/M_sun)<11.25的stellar-mass bin标签。它包含约26,099个z约0.12的external central galaxies，不保证morphology、SFR、halo mass或environment与M31相同。
M31-mass labels the 11.0<log(M*/M_sun)<11.25 stellar-mass bin. It contains about 26,099 external central galaxies near z=0.12 and does not guarantee M31-like morphology, SFR, halo mass, or environment.
native stacked observable
Native stacked observable
eROSITA eRASS:4 photons按central-galaxy bins堆叠，并统计分离hot CGM、unresolved AGN/XRB/satellites与PSF。native profile是intrinsic/rest-frame 0.5–2.0 keV luminosity surface density，不是absorbed angular brightness。
eROSITA eRASS:4 photons are stacked in central-galaxy bins while hot CGM, unresolved AGN/XRB/satellites, and the PSF are separated statistically. The native profile is intrinsic/rest-frame 0.5–2.0 keV luminosity surface density, not absorbed angular brightness.
published beta profile
Published beta profile
projected law为S_X=S_X0[1+(R/r_c)^2]^(−3β+1/2)。M31-mass median使用log S_X0=37.1、r_c=4 kpc、β=0.37；Rvir内hot-CGM residual约3.9σ。Figure 3只用这一个nominal median profile。
The projected law is S_X=S_X0[1+(R/r_c)^2]^(−3beta+1/2). The M31-mass medians are log S_X0=37.1, r_c=4 kpc, and beta=0.37; the hot-CGM residual is about 3.9 sigma within Rvir. Figure 3 uses only this nominal median profile.
20 kpc到angular brightness
From 20 kpc to angular brightness
原文打印至有限位数的medians在20 kpc给约1.72531e36 erg s^-1 kpc^-2；Figure 3冻结ledger采用1.7252986e36，两者只差4.6 ppm。resolved surface brightness的D^-2因子相消后，再用v19 thermal template加入M31 sightline absorption，得到0.828454。
The finite-precision printed medians give about 1.72531e36 erg s^-1 kpc^-2 at 20 kpc; the frozen Figure 3 ledger uses 1.7252986e36, only 4.6 ppm different. After the D^-2 factors cancel for resolved surface brightness, the v19 thermal template adds M31-sightline absorption to give 0.828454.
安全解释
Safe interpretation
0.828454是external-stack population profile移植到M31的条件模板，不是M31 detection，也不是MW foreground。转换采用单一v19 APEC spectrum；published beta-parameter covariance不可用，因此不能把独立marginal ranges随意组合成M31 uncertainty band。
The 0.828454 value is a conditional transplant of an external-stack population profile to M31, not an M31 detection and not a Milky-Way foreground. The transfer uses one v19 APEC spectrum, and the published beta-parameter covariance is unavailable, so independent marginal ranges cannot be combined into an M31 uncertainty band.
从论文到M31 Figure 3
From the paper to M31 Figure 3
population stack
Population stack
选择M31 stellar-mass bin
Select the M31 stellar-mass bin
11.0<log M*<11.25beta profile
Beta profile
采用published median parameters
Adopt published median parameters
r_c=4 kpc, β=0.37radius sample
Radius sample
在20 kpc评价luminosity density
Evaluate luminosity density at 20 kpc
≈1.7253e36distance cancel
Distance cancel
resolved surface brightness conversion
Resolved surface-brightness conversion
D²/D² → 1/(4π)spectral bridge
Spectral bridge
v19 APEC+M31 absorption
v19 APEC plus M31 absorption
0.828454Detailed audit below
以下是逐项provenance与解释边界
Itemized provenance and interpretation boundaries follow
仪器与数据
Instrument and data
eROSITA eRASS:4 stacking，使用rest-frame、absorption-corrected 0.5-2.0 keV luminosity surface-density profiles，并对redshift-dependent PSF和detected sources进行处理。
eROSITA eRASS:4 stacking of rest-frame, absorption-corrected 0.5-2.0 keV luminosity-surface-density profiles, including redshift-dependent PSF treatment and detected-source masking.
观测视线与样本域
Sightlines and sample domain
不是一条MW内部LOS，而是约26099个11.0<log(M*/Msun)<11.25 central galaxies的外部observer projected stacks；median z约0.12、median M*约1.3e11 Msun、median log M200m约12.7。M31-mass只按stellar mass命名，不保证morphology、SFR或halo mass完全等同M31。
This is not an internal-Milky-Way LOS but an external-observer projected stack of about 26,099 central galaxies with 11.0<log(M*/Msun)<11.25, median z about 0.12, median M* about 1.3e11 Msun, and median log M200m about 12.7. The label M31-mass is based on stellar mass alone and does not guarantee matched morphology, SFR, or halo mass.
原文测量量
Native measurement
native profile是erg s-1 kpc-2的intrinsic/rest-frame 0.5-2.0 keV luminosity surface density；hot-CGM residual来自多component statistical decomposition。
The native profile is intrinsic/rest-frame 0.5-2.0 keV luminosity surface density in erg s-1 kpc-2; the hot-CGM residual comes from a multi-component statistical decomposition.
原文模型
Published model
hot-CGM radial profile用projected beta law S_X(R)=S_X0[1+(R/r_c)^2]^(-3 beta+1/2)。M31-mass median参数为log S_X0=37.1、r_c=4 kpc、beta=0.37；Figure 3采用一个nominal median profile，不把S_X0、r_c、beta的独立marginal ranges伪装成M31 prior。
The hot-CGM radial profile uses the projected beta law S_X(R)=S_X0[1+(R/r_c)^2]^(-3 beta+1/2). The M31-mass median parameters are log S_X0=37.1, r_c=4 kpc, and beta=0.37. Figure 3 uses one nominal median profile and does not turn independent marginal ranges of S_X0, r_c, and beta into an M31 prior.
原文结果
Published results
M31-mass bin的hot-CGM residual在Rvir内约3.9 sigma；paper给出shallow beta约0.37并说明population profile。Figure 3选取20 kpc characteristic value。
The M31-mass bin hot-CGM residual is detected at about 3.9 sigma within Rvir. The paper reports a shallow beta near 0.37 and a population profile; Figure 3 samples a characteristic value at 20 kpc.
如何进入M31 Figure 3
Transfer into M31 Figure 3
原文打印至有限位数的median beta参数在20 kpc给约1.72531e36 erg s-1 kpc-2；Figure 3冻结ledger采用1.7252986e36，两者差4.6 ppm。对resolved surface brightness，distance因angular area与flux的D^-2相消。再用v19 thermal template转为M31视线的absorbed angular surface brightness，冻结Figure 3值为0.828454。
The finite-precision printed median beta parameters give approximately 1.72531e36 erg s-1 kpc-2 at 20 kpc; the frozen Figure 3 ledger uses 1.7252986e36, a 4.6 ppm difference. For resolved surface brightness, distance cancels between angular area and flux D^-2. A v19 thermal template then converts to absorbed angular surface brightness along the M31 sightline, with frozen Figure 3 value 0.828454.
假设与解释边界
Assumptions and boundaries
population stack不是M31 measurement；mass label只匹配stellar-mass bin。转换使用单一v19 APEC spectrum而不是stack的完整multiphase distribution；beta参数covariance不可用。
The population stack is not an M31 measurement, and the mass label only matches a stellar-mass bin. The transfer uses one v19 APEC spectrum rather than a full multiphase distribution, and beta-parameter covariance is unavailable.
全天 (l, b) 覆盖图
All-sky (l, b) coverage map
Zhang+24 是约 26,099 个 external central galaxies 的 eROSITA eRASS:4 堆叠（11<log(M*/M_sun)<11.25 bin，median z≈0.12），不是内部 MW sightline。M31（红色五角星）只是 stellar-mass bin 标签，不在单个真实 LOS 上。橙色圆点是十四个 M31 XMM 视场作为位置参考。
Zhang+24 is an eROSITA eRASS:4 stack of about 26,099 external central galaxies in the 11<log(M*/M_sun)<11.25 bin (median z≈0.12), not an internal Milky-Way sightline. M31 (red star) is just a stellar-mass bin label, not a single real LOS. Orange dots mark the fourteen M31 XMM fields as a positional reference.
PDF本论文对应的Figure 3数据点
Figure 3 points from this study
Zhang+24 M31-mass stack at 20 kpc
0.828454 [0.828454, 0.828454]
population template，不是M31本身测量或formal local prior。
A population template, not an M31 measurement or formal local prior.
Primary-source证据地图
Primary-source evidence map
| Location | Claim | Link |
|---|---|---|
| Sample table and selection | M31-mass stellar bin, sample size, redshift, and halo-mass distribution. | primary source |
| Surface-brightness and component-model methods | eRASS:4 stacking, band/frame, PSF, source decomposition, and beta profile. | primary source |
| M31-mass profile figure and fit table | Profile normalization, beta-fit result, and hot-CGM significance. | primary source |