I422 | The leverage is at the ends, not the middle: pushing the B–v_esc relation below 200 km/s with XMM snapshots

01 · Question

In one sentence: in dwarf galaxies, is the hot-phase gas's "stay or go" set by the potential well's depth, or not carried by X-rays at all?

Star formation heats gas to millions of degrees and drives it out of the disk. This hot-phase wind has two possible fates: breaking free of gravity into the intergalactic medium (escape), or falling back onto the disk to be recycled. The entire mass-loading literature writes "can it escape" as a property of the wind—launch speed, mass loading, driving mechanism—with the potential well appearing only as a threshold to be compared against. The P005 question card (marked INTERESTING by the PI on 2026-09-06) put this question on stage, and I399 has already established the archival end of the B–v_esc slope on four nearby edge-on galaxies.

I422 is the new-observation half of the same estimator. It asks: in dwarf starbursts with v_esc = 100–180 km/s, does B still fall on the same relation? If yes, hot-phase escape is predicted by the same rotation curve across a factor of nine in binding energy; if not—especially if the hot-phase mass fraction tends to zero—then the X-ray wind-escape literature does not hold at the mass scale where feedback is calibrated.

02 · Why it matters

Two named physical endpoints, and whose published conclusions would move

This is not "measure a few more galaxies". Each endpoint of the B–v_esc slope α is a named physical hypothesis, and whose conclusions would move can be written down:

α = −2 (potential well decides): kT_mw is the same in every wind—a universal launch/thermalization temperature. B then scales as 1/v_esc² only. This means given a rotation curve, any galaxy's hot-phase fate can be predicted without taking an X-ray image. What needs revision is the low-mass-end recycling models: at the mass scale where Oppenheimer+2010, Mitchell+2020, and Muratov+2015 do most of their work, they must carry a hot escape channel they currently lack.
α = 0 (universal bound state): kT_mw ∝ μ m_p v_esc²/5, the hot phase is virialized with its host, and B is universal. This means Boettcher & Hodges-Kluck 2024 and XRISM 2026 (escape side) and the recycling side do not actually contradict each other on the hot phase—they report the same universal boundary state in galaxies of different depths. But I422's low-mass end adds an X-ray-specific constraint to this endpoint: at v_esc = 197 km/s, α = 0 requires kT_mw = 0.041 keV, below EPIC's ~0.1 keV hot-gas detection floor. So in these dwarfs, the real measurement is the hot-phase mass fraction, not the temperature itself.
Hot-phase mass fraction ≈ 0: If the dwarfs' hot-phase mass fraction is measured to tend to zero, then the low-mass-end escape question is not a hot-phase question at all, and the X-ray wind-escape literature—including the repeatedly cited M82 result—cannot be extrapolated to the mass scale where feedback is calibrated. This is the result that would most change how low-mass CGM budgets are written.

No overclaiming: this is 3–4 galaxies, one CCD, one thermal (not kinematic) estimator. It does not "validate" any cosmological prescription; it constrains α or the hot-phase mass fraction on these galaxies, at this projected scale, at this precision. Its value: this is the first time this ratio is measured with a single method, at the low-mass end, with independently constrained potential wells.

03 · Design arithmetic: why the leverage is at the ends, not the middle

Six middle points buy 7% precision; three low points buy 37%

This card originally intended to fill the middle gap at v_esc = 250–450 km/s—the hole the archive leaves between NGC 55/NGC 4449 and NGC 891/NGC 4594. The arithmetic below says that is nearly worthless, so the design changed:

Design plot: σ(α) versus the number of added pointings M. The three curves correspond to filling the middle (250–450 km/s), extending the low end (100–180 km/s), and a compact low-end cluster (120–160 km/s). The low-end extension reaches σ(α)=0.098 at M=3 with endpoint separation 20.3σ; filling the middle reaches only 0.144 at M=6. — **Design decision plot.** Vertical axis σ(α) (20% B precision per target), horizontal axis the number of added snapshot pointings M. The green curve is the low-end extension (100–180 km/s), red is filling the middle (250–450 km/s), blue is the compact low-end cluster (120–160 km/s).Key reading: Filling the middle only lowers σ(α) from 0.155 to 0.144 at M=6 (7% improvement); extending the low end reaches 0.098 already at M=3 (37% improvement), raising endpoint separation from 12.9σ to 20.3σ. Numbers come from the actually-run `r2_growth_arithmetic.py` (see sources at the end).

The reason is recorded in the card: filling the middle increases the point count N but shrinks the horizontal-axis spread sd(log v_esc), and the two nearly cancel. Extending the low end increases both N and the spread. This arithmetic is a design decision, not decoration.

M = 3 or 4, not 6. The payoff flattens after M=3: 3→4 buys 0.005, 4→6 buys 0.007. Requesting six pointings to obtain the precision three already deliver is an over-ask a TAC would reject, and the card caps itself here.

04 · The archive cannot answer this question

Existing XMM depth for the five candidate galaxies, and why it is not enough

I422's estimator is a spectrally resolved kT_mw measured in minor-axis annuli matched at r/r_25. The existing XMM archive for the five candidates is as follows:

Archive coverage. Blue bars are planned XMM PN exposure (ks, logarithmic axis), red bars total Chandra ACIS-S exposure. NGC 7090 has the deepest XMM archive (150.98 ks, including a 106 ks pointing from 2020), but the R1 archive check records: this is still not a spectrally resolved temperature profile on minor-axis annuli matched at r/r_25. NGC 1569 has only one 15 ks public EPIC science ObsID (0112290801). Chandra's role is point-source masking—its 0.5″ resolution does not help for 30″–100″ annuli, and the post-2010 soft-band contamination sits exactly on the band the temperature comes from. Numbers come from the R1 archive check (2026-09-16) and the per-target pages.

NGC 1569's date-gating risk. The same XSA query lists six 2025–2026 science records (0961590101–0601), proprietary until 2027-03-23. If that is a deep dwarf-halo program, NGC 1569's new-observation case expires on that date and the target moves to the archival half. This does not affect the other four candidates, but must be checked before writing the proposal. Gate I422-G2, DATE-GATED(2027-03-23).

NGC 7090's depth flag. The 150.98 ks planned PN exposure is the deepest of the five candidates, more than three times the sum of the other four. If the "existing XMM depth insufficient" filter has any quantitative threshold, NGC 7090 is the first candidate it bites. R1 records this number but does not filter—that is the job of gate I422-G1d.

05 · If the answer is the opposite, or unmeasurable

Unmeasurable does not mean absent: upper limits are also named P005 results

If the dwarfs' hot-phase mass fraction is measured to tend to zero, that is not a boring null. It says: the low-mass-end escape question is not a hot-phase question at all, and the X-ray wind-escape literature does not hold at the mass scale where feedback is calibrated. This is the result that would most change how low-mass CGM budgets are written.

If a target's diffuse emission is undetected, the deliverable is an upper limit on the hot-phase emission measure, and hence on the hot-phase mass fraction—one of P005's two named results, not a failed pointing. A program that returns a point whether the outcome is a detection or a limit is not the kind of proposal D002 warns about (only 3 of 21 Virgo edge-on late-type galaxies show significant off-disk diffuse X-ray emission, a ~14% detection rate).

Unmeasurable does not mean absent. If a target's B interval is wide enough to cover both endpoints, that target yields a "below S"-style constraint at its aperture, band, and achieved sensitivity—not "this galaxy has no hot halo". If sensitivity was never qualified, the honest write-up is INCONCLUSIVE—an honest INCONCLUSIVE beats a dressed-up null. Background covariance (the 0.3–0.7 keV Galactic foreground) is a systematics already named by N8, gate I422-G4; unresolved compact-source contamination is gate I422-G5 (measured by sibling card I421).

06 · Cost, and what is still unknown

This page's single request: decide whether this new-observation design is worth entering target-list qualification

Known cost: 3–4 single-pointing XMM EPIC snapshots, THIN1 or MEDIUM, Full Frame. Each galaxy's D25 and required annuli fit in one EPIC field at 3–7 Mpc. No mosaic, no monitoring. Chandra archival masks used where available. Per-target exposure is not asserted in this card—that is gate I422-G3 (R6).

Still unknown, and must be done before the target list closes:

I422-G1 (blocking): The target list. Which of the five candidates pass (a) H I rotation curve undisturbed by mergers—the same filter I399 used to reject M82, NGC 4631, NGC 3628, which may also kill I420; (b) inclination permitting minor-axis annuli; (c) v_esc within 100–180 km/s; (d) existing XMM depth insufficient. And whether I159 has already claimed NGC 1569's new-observation case.
I422-G2: NGC 1569's six 2025–26 proprietary records (expiring 2027-03-23).
I422-G3: Per-target exposure and achievable kT_mw precision (R6).
I422-G4: 0.3–0.7 keV background covariance (N8).
I422-G5: Unresolved compact-source contamination (I421).
I422-G6: The v_esc derivation must be homogeneous with the six archival targets, otherwise the slope inherits a systematics that does not cancel (an I399-G3 inheritance).

The real gamble: If all targets are non-detections, the paper is a set of hot-phase mass-fraction upper limits—publishable, informative, but clearly not as good as a slope. A fundable gamble with a stated worst case is the shape D047 requires.

This is a "one page for one hour" decision: this page is the one product the pipeline currently asks a human to read. If the target list is destined not to close, the honest answer is to say so now and save the qualification computations.

Sources and reproducibility

The evidence boundary of this page

All σ(α), lever-arm, and endpoint-prediction numbers: python3 cycles/cycle-obs3/materials/R2_P005_sample_growth_20260907/r2_growth_arithmetic.py (actually re-run this shift, reproducing the card §E table byte for byte).
Archive exposures: R1 archive check cycles/cycle-obs3/r1_i422_archive_check_20260916.md (2026-09-16, run 1789584545), and the shared/survey/per-target/ pages (NGC 1569 ^T9332, NGC 625 ^T9337, NGC 7090 ^T6721, NGC 5253 ^T3757, NGC 4214 ^T2328).
Literature (original language preserved): Boettcher & Hodges-Kluck 2024 (2024ApJ...975..128B)、XRISM 2026 (2026arXiv260324674X)、Oppenheimer+2010 (2010MNRAS.406.2325O)、Mitchell+2020 (2020MNRAS.497.4495M)、Muratov+2015 (2015MNRAS.454.2691M)、Summers+2004 (2004MNRAS.351....1S)、Hartwell+2004 (2004MNRAS.348..406H)、Ott+2005 (2005MNRAS.358.1423O/1453O)、Martin+2002 (2002ApJ...574..663M)。
This page has no single-sky WCS figure; both figures are scalar plots generated by the deterministic script make_figures.py, with geometry/numbers recorded in fig/figure_geometry.json.