01 · Question
In one sentence
In the EPIC field of view of NGC 3221, for discrete sources detected in both 2004 and 2023 with the strictest filtering, the ratio of 0.3–10 keV fluxes r_j = F_j(2023)/F_j(2004) what is its distribution? What fraction of these sources have log r_j confidence intervals that exclude zero?
This is not a yes/no question about "variable or not". It measures a continuous quantity: the variable fraction f_var and its confidence interval, and |log r_j| the distribution. Instrumental background (effective-area calibration across epochs, pn Full Frame vs Extended Full Frame mode differences, MOS MEDIUM→THIN1 filter changes, and background per epoch) is stated upfront, not fitted a posteriori.
02 · Sky geometry and archive coverage
Five nuclear pointings, 19 years apart
NGC 3221 (RA=10h22m20s, Dec=+21°34′10″, D=51.76 Mpc) has five public XMM EPIC scientific observations: 0202730101 in 2004 and the series 0922170101–0401 in 2023 May. All are nuclear pointings, and the EPIC 15′ radius field of view fully covers the D25 ellipse (3.3′×0.8′).
XMM RGB uses the positive-intensity p0.5–p99.5 percentile clip shared by all channels and asinh stretch; blue-gray indicates zero coverage, not low surface brightness. Display stretch does not participate in exposure correction, scientific flux, or any variability measurement; overlay lines use the original WCS.
03 · Why it matters
A long-held assumption never measured
X-ray binary population studies (XLF–SFR/M⋆ scaling) stack single-epoch source lists as "this galaxy's sources". This practice implicitly assumes:the brightest discrete source is stable on a decade timescale. This assumption has never been tested at 51.76 Mpc, because few galaxies have the same instrument, same filter, and multi-epoch data spaced far enough apart.
NGC 3221 happens to have: 37 ks and 438 ks of EPIC-pn THIN1 in 2004 and 2023. Das+2026 used these data to analyze ISM/extraplanar biphasic hot gas and to report day-timescale variability of six ULX in 2023—but did not measure the frozen-threshold flux ratio, nor did they give f_var, nor did they state the instrumental background.
If the brightest source varied significantly over the 19-year baseline, then: (i) the scatter floor of the XLF stacking would need to be raised; (ii) on this target, the CGM source masks of I106/I117—using the 2023 source list to mask the 2004 data—would leak. If the brightest source is stable, then mask reuse and epoch combination yield a physically grounded upper limit.
04 · What to measure
Depth asymmetry sets the sample size
The 2004 epoch had 26.6 ks of clean pn exposure, the 2023 epoch 297.5 ks—an 11.2× depth ratio. At 51.76 Mpc, the 5σ flux limit for the 2004 epoch is ≈2.1×10³⁹ erg/s, and for the 2023 epoch ≈6.2×10³⁸ erg/s. The jointly detected sample is limited by the shallower 2004 epoch.
Preregistered observables: for each source in the jointly detected sample, measure r_j = F_j(2023)/F_j(2004) and its confidence interval; for the sample as a whole, report f_var（log r_j the fraction of sources with confidence intervals excluding zero, and its Clopper-Pearson confidence interval, and |log r_j| the distribution.
05 · If the answer is the opposite
Four outcomes, all informative
- NON-STATIONARY POPULATION：
f_varSignificantly above the instrumental background. The brightest source truly varied over 19 years—the single-epoch source list is not a stable description. The XLF stacking scatter floor would need to be raised, and source-mask reuse across epochs would need re-pricing. - STATIONARY WITHIN THE FLOOR：
f_varConsistent with the background, report an upper limit. The brightest source is stable within attainable precision. This directly licenses CGM source-mask reuse and epoch combination for I106/I117 etc., removing an unpriced systematic error term. - PARTIALLY RESOLVED POPULATION：The jointly detected sample is smaller than the preregistered minimum (which is physically the most likely outcome), but the 19-year flux ratio of the nuclear AGN can still be measured with high precision (S/N=24.8 vs 82.9). This in itself is a result for this galaxy's AGN.
- INCONCLUSIVE：If the detection threshold, depth matching, or background recovery prerequisites are not met, then no physical conclusion is drawn. An honest INCONCLUSIVE is more valuable than a dressed-up null.
On the meaning of null:If the 2004 epoch has no detection at a source position, thisdoes notmean "the source did not exist in 2004". It means: at this aperture, in this band, at this sensitivity, the surface brightness is below S. The source could be fainter, hotter, colder, or outside the extraction region.
06 · Cost
Pure archive, zero new observations
This idea requests no new telescope time. All data are already in the public archive. The PI must authorize a bounded R6 HEAVY calculation: clean event selection on the five ObsIDs (I179-E4), depth-matched common-source recovery (I179-E1), and cross-epoch response/background processing (I179-E3).
The main risk is sample size: at S/N>5 the jointly detected sample may have only 4 sources,f_var the Clopper-Pearson interval is very wide at n=4. This is an intrinsic constraint at 51.76 Mpc, not a methodological limitation.
07 · Observation log
The data underlying this page
| ObsID | Epoch | Off-nucleus offset (′) | Planned exposure (ks) | Clean pn (ks) | Clean fraction |
|---|---|---|---|---|---|
| 0202730101 | 2004-05-30 | 0.693 | 37.0 | 26.6 | 71.9% |
| 0922170101 | 2023-05-02 | 0.001 | 108.6 | 72.2 | 66.5% |
| 0922170201 | 2023-05-04 | 0.001 | 109.9 | 78.0 | 71.0% |
| 0922170301 | 2023-05-10 | 0.001 | 109.6 | 79.6 | 72.6% |
| 0922170401 | 2023-05-12 | 0.001 | 109.7 | 67.7 | 61.7% |
| Total | — | 474.8 | 324.1 | — | |
Clean pn exposure comes from Das+2026 Table 1. The 2004 epoch was pn THIN1 Full Frame + MOS MEDIUM Full Frame; the 2023 epoch was pn THIN1 Extended Full Frame + MOS THIN1 Full Frame. RGS is present in all five ObsIDs.
Chandra context (not entering the decision rules): two ACIS non-lightcurve observations totaling 29.630 ks (2001 + 2008). Suzaku: one ObsID 121.246 ks. Neither is sensitive enough at 51.76 Mpc to detect discrete sources.
08 · Sources and boundaries
Every number is traceable
All numbers on this page come from the following sources, each independently verifiable:
- NGC 3221 coordinates, D25, PA, distance: SIMBAD/NED, recorded at
shared/survey/per-target/NGC3221.md - XMM observation metadata: XSA TAP v_exposure, SHA-256
1b033d9b… - Clean pn exposure: Das+2026 Table 1 (2026ApJ...997..177D)
- ULX luminosity and S/N calculation: R3 evidence bundle
cycles/cycle-obs9/evidence/idea-I179.md§3.2 - Non-preemptive verification: ADS bounded query q3=0, q4=0 (T11274), Das+2026 supplementary materials check (no flux ratio table)
D25 parameters source: UGC (1973UGC...C...0000N), PA=167° (B1950). Note: directory-equivalent-light PA fitting is done on the outer rim of light, and does not necessarily trace the visible disk in warped or interacting systems. NGC 3221 is a high-inclination (b/a=0.24) SB-type barred spiral, and the D25 ellipse is used only for indicating field-of-view coverage, not for placing extraction apertures.
This page does not request HEAVY authorization, does not close any gate, does not change any idea's lifecycle, score, or Elo. It is merely a demonstration: this problem is worth a bounded R6 calculation to answer.