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:

  1. The legacy combined fit uses MOS1+MOS2, while current Disk W is MOS2-only and Disk E is MOS1+MOS2.
  2. The legacy products predate the final production extraction/OBS_ID repair and have a shorter exposure.
  3. The v22 branch freezes the same SoftProton surface-normalization parameter, 6.24577e-05, but the executed model is rsp_flat(skyarea * SoftProton), with skyarea derived from PHA BACKSCAL. The integrated SP contribution therefore does scale with extraction area; there is no evidence for a missing SP area-scaling bug.
  4. 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/