01 · INPUT
Raw EVENTS
Historical 2.1.filter MOS1 ori event; SHA-256 has been checked. Extract the raw 1-s broad rate.
← Return to the original M31 2.1 selection overview
Scope boundary. This page reproduces the current 2.1 core on the same historical MOS1 raw event file:
2.1qdp51 time estimator: the 1-s rate enters selection after centered 51-s smoothing. It is not a replacement for the historical 2.1.filter ; no 3B/4.background spectra or response were extracted, and no SP physical judgment was made.
full spectrum Al line（first scan）0.2063 ± 0.0038count/s; about 55σ, not weak
first-scan fit-eligible points18 / 100the quartic ultimately uses 14 points
second-scan fit-eligible points81 / 100the quartic ultimately uses 66 points
maximum adjacent-trial replacement1,8201-s decision bins (first scan)
Conclusion first
Counting statistics of the Al line are not the dominant problem. The first-scan full spectrum has 21,313 counts in 1–2 keV, with fit χ2/dof=152.7/141=1.08; the low/high sub-spectra near the crossing still have 3,993/17,320 counts, with 1.37 and 1.00, respectively.The second-scan full/low/high spectra likewise have 8,862/4,022/4,840 counts, respectively.
The steps come from sample construction. Each trial centre rate shifts a finite-width rate window to the right. The low subset is not a nested expansion of the previous subset: one set of times is added while another is removed. Thus every fit uses different time intervals, exposure, and grouping; the premise that “line area changes continuously with rate” does not hold.
What does the current workflow actually do?
Below is the actually executed QDP51 branch. Apart from the time estimator, it retains the current 2.1 broad-detector PI=0.2–10 keV definition, two scan rounds, the Poisson σ formula, zero-rate-neighbor rejection, and the BTI guard.
02 · DECISION RATE
51-s centered smoothing
The decision rate at each 1-s time comes from a local 51-s window; adjacent samples share 50/51 seconds and cannot be treated as independent measurements.
03 · TRIAL GTIs
100 centre rates
For each m, construct m ± 0.8√(m/51) low/high GTIs. Scan the full interval first, then use subsets within the first-pass GTI for the second round.
04 · LINE FITS
Two sub-spectra
Each trial low/high sub-spectrum is grouped independently with ≥100 counts and ≥6 PI channels, then fitted with continuum + Al + Si; the line centroid/width for that round is fixed from the full spectrum.
05 · CROSSING
Selection, quartic, roots
After removing NaN/MAD outliers, fit 4th-degree polynomials to the low/high Al areas separately; select the root within the scan range and closest to the histogram peak.
At which step do the discontinuities appear?
The top row shows the Al area and error bar obtained for each trial; pale points are the raw scan, and solid points are those entering the quartic after outlier filtering. The bottom row is not a fit result: it shows how each trial reconstructs the subset. Blue/red indicate low/high exposure, and brown indicates 1-s decision bins whose membership changed relative to the previous trial.
first scan: sparsity is not line failure
- Each trial requires
high exposure / low exposure ≤ 6; the actual ratio spans 2.20–99.19. - Thus 82 of 100 points are skipped by the guard before fitting; 4 of the remaining 18 points are removed by MAD filtering of uncertainty/area.
- The low mask can change up to 1,820 1-s bins between adjacent trials; low-subset exposure is not monotonically cumulative, but first increases and then decreases.
second scan: more points, but still not a continuous curve
- Of 100 points, 19 are skipped by the same time-ratio guard, and another 15 do not enter the quartic after MAD filtering.
- Adjacent trials can still reassign up to 911 1-s bins; every Al area corresponds to a different set of times.
- The closest actual second-round point to “equality” is at 1.817 count/s, low−high = −0.00040 ± 0.00787 count/s, only 0.05σ; the crossing is an interpolation product, not a directly measured sharp physical transition.
Sub-spectra and residuals: did the line fit itself fail?
There is no evidence of “complete fit failure”. Columns are full, low, and high; each upper panel shows data, the total model, continuum, Al, and Si components, while the lower panel retains normalized residuals and vertical error bars. Note: this is a detector-space screening model internal to the filter, not a response-folded astrophysical spectral fit.
| stage / subset | 1–2 keV counts | grouped bins | χ²/dof | Al area (count/s) |
|---|---|---|---|---|
| first / full | 21,313 | 149 | 152.7 / 141 = 1.08 | 0.2063 ± 0.0038 |
| first / low | 3,993 | 39 | 48.0 / 35 = 1.37 | 0.2012 ± 0.0059 |
| first / high | 17,320 | 135 | 131.1 / 131 = 1.00 | 0.2079 ± 0.0043 |
| second / full | 8,862 | 71 | 81.2 / 63 = 1.29 | 0.2001 ± 0.0041 |
| second / low | 4,022 | 39 | 53.2 / 35 = 1.52 | 0.2026 ± 0.0058 |
| second / high | 4,840 | 46 | 47.5 / 42 = 1.13 | 0.1982 ± 0.0053 |
Three kinds of “discontinuity” to distinguish
| Source | Evidence in this case | Meaning for the crossing |
|---|---|---|
| Selection-set jumps | The sliding finite window makes the low/high GTIs non-nested; each step replaces up to 1,820 decision bins, and the GTI is split into hundreds of segments. | Al area is a statistic of a different time mixture and should not be assumed to be a continuous function. |
| Regrouping and joint fitting at every trial | Low/high are grouped independently for every trial, while the continuum and both line areas are free simultaneously; the area of a given line correlates with the continuum slope and the Si line. | The error bars describe a single fit to a fixed subset and do not include systematic uncertainty from subset selection or the crossing. |
| Post-processing interpolation | Only 14 first-scan points and 66 second-scan points enter the degree-4 polynomial; the root is obtained from the difference between the two fitted curves. | Reporting a numerical crossing is not equivalent to measuring a physical transition with an uncertainty. |
A numerical issue requiring a separate fix
The current code sets np.polyfit before w = 1 / area_err**2. However, np.polyfit of w multiplies the unsquared residual directly; for Gaussian errors, the documented convention is w = 1 / sigma. Therefore, points with smaller errors are currently weighted in the objective as 1/σ⁴ rather than 1/σ² , making the quartic crossing more sensitive to a few points.NumPy documentation
This is not a strategy silently modified by this page. This page only exposes it. The next step should separate this weighting correction from “fixed grouping / bootstrap crossing / nested cumulative split” as independent control experiments, rather than changing them together with the GTI policy.
Reviewable raw diagnostic products
All numbers on the page come from the same diagnostic rerun: event SHA-256 b3851726…e3bfc9, ESPFILT SHA-256 3aad44d2…97ddd. No new GTI, clean event, or background spectrum was written.