M104 R4–7 Disk-Combination Temperature Discrepancy Audit
Finding
The apparent paradox was caused primarily by a 90-degree physical-label rotation, not by the extracted sector boundaries themselves.
The historical region basenames contain DS9 pie angles. DS9 angles are measured from the image x-axis, whereas celestial position angle is measured North through East. For this WCS:
sky PA = (DS9 angle - 90 deg) mod 360.
This correction was independently verified from the WCS centroids of the actual ESAS 700–1000 eV source images.
Correct physical mapping
| Historical region basename | Actual sky direction | Physical component | v22 FAST kT (keV) |
|---|---|---|---|
regionR4-7_Angle315-45 |
West; sky PA 225–315° | Disk W | 0.706 |
regionR4-7_Angle45-135 |
North; sky PA 315–45° | Wind N | 0.780 |
regionR4-7_Angle135-225 |
East; sky PA 45–135° | Disk E | 0.677 |
regionR4-7_Angle225-315 |
South; sky PA 135–225° | Wind S | 0.760 |
Therefore, the two values previously called “Disk E/W” (0.780 and 0.760 keV) are actually the north and south wind sectors. The true independent disk-sector values are 0.706 and 0.677 keV, with arithmetic mean 0.692 keV. This is qualitatively consistent with the user’s approximately 0.7 keV combined-disk value.
The legacy regionR4-7_Angle1 combined-disk FAST result is 0.634 keV, not 0.78 keV. The remaining 0.058 keV difference from the independent-sector mean is not a geometry contradiction.
Geometry verification
After applying the DS9-to-sky angle conversion:
- Disk W + Disk E reconstruct legacy
regionR4-7_Angle1. - Wind N + Wind S reconstruct legacy
regionR4-7_Angle2. - Four-sector union fraction: 1.000000000.
- Four-sector gap and overlap fractions: 0.
- Disk union versus legacy Angle1 mismatch: 0.000619.
- Wind union versus legacy Angle2 mismatch: 0.000226.
The residual mismatch is below 0.1% of the annulus and comes from the legacy box/circle implementation, not a sector swap or missing quadrant.
Why 0.692 and 0.634 are not expected to match exactly
The legacy combined-disk PHA is not the literal sum of the current production sector PHAs.
For MOS2:
| Quantity | Legacy combined disk Angle1 | Current Disk W + Disk E | Legacy / current sum |
|---|---|---|---|
| Exposure | 65,232 s | 80,001 / 80,014 s | — |
| 0.4–3.2 keV source counts | 4,573 | 8,005 | 0.571 |
| Full PHA counts | 9,299 | 15,222 | 0.611 |
| BACKSCAL | 60,236,784 | 70,493,260 | 0.855 |
| 700–1000 eV source-image counts | 726 | 1,414 | 0.513 |
OBS_ID header |
missing | 0900170101 |
— |
Additional non-equivalences:
- The legacy combined fit uses MOS1+MOS2, while current Disk W is MOS2-only and Disk E is MOS1+MOS2.
- The legacy products predate the final production extraction/OBS_ID repair and have a shorter exposure.
- The v22 branch freezes the same SoftProton surface-normalization parameter,
6.24577e-05, but the executed model isrsp_flat(skyarea * SoftProton), withskyareaderived from PHABACKSCAL. The integrated SP contribution therefore does scale with extraction area; there is no evidence for a missing SP area-scaling bug. - APEC temperature, free CXB normalization, detector responses, masks, and QPB are fitted nonlinearly; a combined best fit is not an arithmetic average even for otherwise identical inputs. The final CXB norms also differ substantially between the legacy and sector fits, indicating partition-dependent CXB/APEC degeneracy.
Quality caveat
The corrected Disk E fit (regionR4-7_Angle135-225) has reduced statistic 1.60 and q-value 0.017, with instrument-dependent low-energy residuals. Its 0.677 keV temperature is provisional.
Evidence products
- Corrected geometry manifest:
r47_four_sector_ds9_region_manifest.csv - Geometry verification:
r47_four_sector_geometry_verification.txt - Physical-label regression test:
/u/Lang3/program/XARTATOMS/tests/test_r47_four_sector_physical_labels.py - Actual ESAS source-image figures:
/u/Lang3/program/XARTATOMS/figure/r47_r46_actual_esas_source_images/