M31 elliptical-annulus profile overview
A single place to browse the completed radial inspection, pure-data band-flux, saved-session soft-band fit-quality, and no-background terminal fit-parameter profiles. The statistical meaning of each section differs, and the sections cannot substitute for one another.
1. XSherpa inspect / data profiles
This is a pure-inspection coaxial spectral-shape comparison: one annulus per color graded from inner to outer, with all ObsID×MOS1/MOS2 kept independent — no coadd, stack, model, or fit. The y-axis is ARF-unfolded sb_flux (counts s−1 keV−1 cm−2 arcmin−2). This section is not a radial-point profile, so no radial x/y error bars are defined; the energy axis and spectral shapes are for inspection only.
Coaxial inspect: 16′ annuli only

Coaxial inspect: preferential 8′ inner annuli

2. Direct-data band-flux profiles
Pure data, no physical model. Each faint point is one independent ObsID×MOS spectrum; the dark points and solid line are the inverse-variance average over the same region. Horizontal error bars are the exact annulus half-widths; vertical error bars are the propagated statistical errors multiplied by the max(1, sqrt(χ²/dof)) Birge factor to record the extra inter-spectrum dispersion. Units are counts s−1 cm−2 arcmin−2; the left/right panels of each figure show the non-overlapping 16′ bins and the preferential 8′ inner bins, respectively.
Direct-data band flux: 0.5–0.6 keV

Direct-data band flux: 0.6–0.7 keV

Direct-data band flux: 0.7–1.0 keV

3. 0.4–1.4 keV fit-quality (saved terminal sessions)
This is a quality metric, not a new band-only fit: all saved MOS datasets belonging to each joint fit are included, accumulating χ²=Σ(Δχ²) (χ² Gehrels) only over saved grouped bins that fall entirely within 0.4–1.4 keV. χ²/Nbin is the exact ratio over the selected bins; the approximate reduced χ² in the last column subtracts the full 0.4–7.2 keV free-parameter count and is for comparison only — it must not be read as the reduced χ² of a band-only refit. This table carries no x/y error bars.
| region | strategy | MOS spectra | Nbin | χ² | χ²/Nbin | reduced χ² (approx.) |
|---|---|---|---|---|---|---|
a032_040 | M31CGM BKG-anchor | 43 | 600 | 918.65 | 1.5311 | 2.7099 |
a032_040 | no independent BKG region | 43 | 600 | 627.12 | 1.0452 | 1.8664 |
a032_048 | M31CGM BKG-anchor | 51 | 1205 | 2.0806e+03 | 1.7267 | 2.3221 |
a032_048 | no independent BKG region | 51 | 1205 | 1.3738e+03 | 1.1401 | 1.5384 |
a040_048 | M31CGM BKG-anchor | 51 | 869 | 1.1359e+03 | 1.3071 | 2.0284 |
a040_048 | no independent BKG region | 51 | 869 | 812.54 | 0.93503 | 1.4588 |
a048_056 | M31CGM BKG-anchor | 58 | 890 | 1.0698e+03 | 1.2021 | 1.9848 |
a048_056 | no independent BKG region | 58 | 890 | 995 | 1.118 | 1.8563 |
a048_064 | M31CGM BKG-anchor | 63 | 1384 | 1.8901e+03 | 1.3657 | 1.8844 |
a048_064 | no independent BKG region | 63 | 1384 | 1.7660e+03 | 1.276 | 1.766 |
a056_064 | M31CGM BKG-anchor | 62 | 707 | 836.35 | 1.183 | 2.5191 |
a056_064 | no independent BKG region | 62 | 707 | 799 | 1.1301 | 2.4286 |
a064_080 | M31CGM BKG-anchor | 59 | 989 | 1.1398e+03 | 1.1525 | 1.8035 |
a064_080 | no independent BKG region | 59 | 989 | 1.0997e+03 | 1.1119 | 1.7483 |
a080_096 | M31CGM BKG-anchor | 43 | 572 | 549.57 | 0.96078 | 1.7671 |
a080_096 | no independent BKG region | 43 | 572 | 546.74 | 0.95584 | 1.7751 |
4. Current complete 8′ no-background fit-parameter profile
This is the current authoritative complete 8′ elliptical-annulus no-background profile, superseding the previous 7-point parameter figure on this page. The 9 radial points are a016_024, a024_032, a032_040, a040_048, a048_056, a064_072, a072_080, a080_088, a088_096。
Δχ²=1 interval with the saved nuisance parameters frozen. It is not a profile-likelihood or multi-parameter confidence interval. Generated UTC:2026-09-09T04:16:04.785110Z; input fit-index SHA-256:0af1de490a30a23739f8e52587b05f5e0b5b5b9bcfbdc1fe0e0e57c3c773e1ca.a056_064 is excluded by an explicit quality decision. Ring_v7 is a non-radial spatial region, handled only as a separate non-radial fit, so it is not included in this elliptical semi-major-axis profile.
Complete 8′ profile (2-column)

Complete 8′ profile (1-column)

| region | a interval | MOS spectra | MWhalo kT [keV] | MWhalo norm | SrcApec kT [keV] | SrcApec norm |
|---|---|---|---|---|---|---|
a016_024 | 16–24′ | 28 | 0.21818 [−0.0018396, +0.0022476] | 3.9883e-06 [−7.1890e-08, +7.7630e-08] | 0.9005 [−0.011275, +0.021276] | 3.1883e-07 [−9.1714e-09, +1.0159e-08] |
a024_032 | 24–32′ | 34 | 0.20892 [−0.0015634, +0.0016665] | 3.5994e-06 [−5.8829e-08, +6.0617e-08] | 0.88304 [−0.012173, +0.018835] | 2.1778e-07 [−6.7863e-09, +7.2677e-09] |
a032_040 | 32–40′ | 43 | 0.19057 [−0.0016105, +0.0016054] | 3.6785e-06 [−6.0475e-08, +7.9774e-08] | 0.76438 [−0.0036193, +0.077246] | 2.0721e-07 [−5.7466e-09, +7.6931e-09] |
a040_048 | 40–48′ | 51 | 0.19767 [−0.001232, +0.001473] | 3.3134e-06 [−4.1763e-08, +6.0682e-08] | 0.75128 [−0.0034808, +0.04709] | 1.9936e-07 [−4.1289e-09, +6.2756e-09] |
a048_056 | 48–56′ | 58 | 0.19147 [−0.0012613, +0.0016152] | 2.8745e-06 [−4.1410e-08, +5.5102e-08] | 0.78208 [−0.0072044, +0.023868] | 1.7641e-07 [−3.4829e-09, +6.2541e-09] |
a064_072 | 64–72′ | 55 | 0.19729 [−0.0015459, +0.0019825] | 2.6332e-06 [−4.5784e-08, +5.8894e-08] | 0.76968 [−0.012893, +0.0461] | 1.2402e-07 [−4.2253e-09, +6.3659e-09] |
a072_080 | 72–80′ | 52 | 0.19119 [−0.0017594, +0.0024474] | 2.3321e-06 [−4.3549e-08, +7.6989e-08] | 0.72036 [−0.0079269, +0.10584] | 1.0933e-07 [−3.7304e-09, +7.7203e-09] |
a080_088 | 80–88′ | 42 | 0.20804 [−0.0027735, +0.0031449] | 1.9491e-06 [−4.3571e-08, +8.0513e-08] | 0.72734 [−0.012222, +0.15704] | 8.4451e-08 [−4.7652e-09, +8.3552e-09] |
a088_096 | 88–96′ | 40 | 0.20762 [−0.0035386, +0.0038194] | 2.0629e-06 [−6.7646e-08, +8.6947e-08] | 0.74785 [−0.01928, +0.18895] | 8.7493e-08 [−7.1239e-09, +9.6003e-09] |
Public data summary:sanitized complete-8arcmin profile manifest. It contains no raw spectra, responses, saved-session files, session hashes, or local paths.
Selection and exclusion boundaries
a056_064is excluded by an explicit quality decision and therefore does not enter the complete 8′ parameter profile in section 4; it is still retained in the existing inspection, band-flux, and the section-3 quality table.Ring_v7was only fit as a non-radial point, so it is not used as an elliptical-annulus radial profile point.a096_112anda112_128both have outer radii larger than 100′ and do not enter the post-fit profiles in sections 3/4;a080_096is retained (outer edge=96′).a128_144has no accepted fit and is therefore not listed in the post-fit tables. All existing terminal results remain individually viewable in the complete annulus fit catalog.
Public data summary:sanitized profile manifest. It contains no absolute paths, raw/response data, saved-session files, or session hashes.