Figure 3最终值

Final Figure 3 value

population template，不是M31本身测量或formal local prior。

A population template, not an M31 measurement or formal local prior.

原文输入量

Native published input

M31-mass external-galaxy stack的20 kpc intrinsic 0.5-2.0 luminosity surface density。

Intrinsic 0.5-2.0 luminosity surface density at 20 kpc from the M31-mass external-galaxy stack.

转换链

Conversion chain

选择M31-mass bin、在20 kpc评价published median beta profile，再做distance-cancel angular conversion和v19 APEC absorption bridge。

Select the M31-mass bin, evaluate the published median beta profile at 20 kpc, then apply the distance-cancel angular conversion and v19 APEC absorption bridge.

1. 不按连续mass relation缩放：直接选择原文11.0<log(M*/Msun)<11.25的M31-mass central-galaxy stack。Do not apply a continuous mass scaling relation: directly select the paper's M31-mass central-galaxy stack at 11.0<log(M*/Msun)<11.25.
2. 采用Table 4打印的M31-mass medians log S_X0=37.1、r_c=4 kpc、beta=0.37，在physical R=20 kpc评价projected beta profile，得到约1.72531e36 erg s^-1 kpc^-2。Figure 3冻结ledger保存1.7252986e36；4.6 ppm差异来自原文参数的有限打印精度，不代表额外科学精度。Use the printed Table 4 M31-mass medians log S_X0=37.1, r_c=4 kpc, and beta=0.37 and evaluate the projected beta profile at physical R=20 kpc, giving approximately 1.72531e36 erg s^-1 kpc^-2. The frozen Figure 3 ledger stores 1.7252986e36; the 4.6 ppm difference reflects finite printed precision, not additional scientific precision.S_X(20)=10^37.1[1+(20/4)^2]^(-3×0.37+1/2)
3. 以冻结ledger的1.7252986e36为数值authority，利用surface-brightness distance cancellation，把luminosity surface density先除以4π kpc_cm²，再除以11,818,102.86004228 arcmin²/sr（等价于乘8.461594994×10^-8 sr/arcmin²），再乘v19 absorbed/intrinsic ratio 0.678988916，得到Figure 3值0.828454。Using the frozen-ledger 1.7252986e36 as the numerical authority, apply surface-brightness distance cancellation: divide luminosity surface density by 4π kpc_cm², then divide by 11,818,102.86004228 arcmin²/sr (equivalently multiply by 8.461594994×10^-8 sr/arcmin²), and apply the v19 absorbed/intrinsic ratio 0.678988916 to obtain the Figure 3 value 0.828454.S_fig=S_L/(4π kpc_cm²)/(11,818,102.86004228 arcmin²/sr)×0.678988916/10^-15

新增假设与边界

Added assumptions and boundaries

• 单一thermal template代替stack的温度/金属丰度分布。One thermal template substitutes for the stack's temperature/metallicity distribution.

Provenance

DOI: 10.1051/0004-6361/202449412

figure3_reference_registry.json · figure3_additional_presentations.json · frozen Figure 3 ledger