# Are the ionizing stars of compact H II regions still accreting?
### A multi-tracer test of the Padoan & Gieles (2026) long-timescale hypothesis

*Working draft — analysis complete, numbers final, prose for the team to revise.*

## Abstract
Padoan & Gieles (2026, arXiv:2602.06196) derive massive-star formation timescales
of 1–4 Myr from the luminosity function of 832 RMS compact H II regions, under the
assumption that the ionizing star **continues to accrete throughout the compact
H II phase**. We test that assumption empirically. Reconstructing their RMS sample
(Lumsden et al. 2013) and sub-classifying it with CORNISH 5 GHz radio sizes
(102 ultra-compact, ≤0.1 pc; 240 compact; 62 classical), we ask, for each ionizing
star, whether a dense accretion reservoir is present at its position. Three
independent tracers agree: (i) free-free-subtracted ALMAGAL 1.4 mm cores give a
dust mass at the star with a median <1 M⊙ and a dust-dominated core in only
1/30 sources (3%, 95% CI 0–15%); (ii) resolved ALMA-IMF B3–B6 common-beam spectral
indices are free-free (α<1.5) in 7/8 sources (dust in 1/8, 12%, CI 1–45%); (iii)
ALMA-IMF hot-core CH₃CN line emission is detected at only 2/9 ionizing positions
(22%, CI 5–54%), both being the most massive, cluster-confused sources. In contrast,
the parent **clumps** (ATLASGAL 870 µm, ~0.5–1 pc) are gas-rich (median 1260 M⊙)
and gravitationally bound, and modelled large-scale streamer **inflow rates**
(Wells et al. 2024) rise monotonically with evolutionary stage to a median
~7×10⁻⁴ M⊙ yr⁻¹ at the H II-region phase, with 100% of H II-region clumps showing
a detected flow (Ṁ × 1–4 Myr ≈ the clump mass). We conclude that compact H II
regions are still accreting **vigorously at the clump/proto-cluster scale** — the
scale Padoan & Gieles's integrated luminosities probe — so their 1–4 Myr timescale
is well-supported as a **clump-assembly time**. What fails is the literal
identification of that growth with the *individual ionizing star*: at the resolved
≤0.1 pc scale that star has mostly cleared its own reservoir, and the ongoing
inflow feeds the surrounding proto-cluster rather than the already-ionizing source.

## 1. Sample
- Parent: RMS survey (Lumsden et al. 2013, Vizier J/ApJS/208/11), Type='H II region',
  L_bol>0, d≤18 kpc, 2.9≲log L≲6.6 → **800 H II regions** (reproduces the paper's
  832; verbatim selection excludes YSOs and H II/YSO).
- Radio sub-classification with CORNISH-N (Purcell+2013) and CORNISH-S (Irabor+2023)
  5 GHz sizes, D[pc]=θ["]·d[kpc]·0.00485: **UC H II 102 (≤0.1 pc, validated 91%
  pure against CORNISH's own UCHII label), compact 240, classical 62.**

## 2. Archival coverage (ALMA census)
Cone search of the ALMA archive (`astroquery.alma`) for all 800: **44% observed;
UC H II best-covered at 64% (57/89).** Working samples drawn from ALMAGAL
(2019.1.00195.L) and ALMA-IMF (on disk).

## 3. Method and results — three independent tests at the ionizing position
**(a) Catalog, free-free-subtracted core mass.** ALMAGAL 1.4 mm compact-source
catalog (Coletta+2025). Nearest core to the ionizing star: median 0.7 M⊙; total
within 0.1 pc: median 4.3 M⊙. Predicting free-free at 219 GHz from the CORNISH
5 GHz flux (α=−0.1), **25–26/30 "cores" are >50% free-free**; dust-corrected,
**1/30 retain a ≥5 M⊙ dust core (3%, CI 0–15%)**. Contrast the clump scale
(ATLASGAL, Urquhart+2018): median 1260 M⊙, sub-virial.

**(b) Imaging, resolved spectral index.** ALMA-IMF B3 (100 GHz) + B6 (230 GHz)
continuum, common-beam (~0.3–0.6"). α at the ionizing source: **7/8 free-free
(α<1.5), 1/8 dust (α>2.5; 12%, CI 1–45%).** W51-IRS2 — Padoan & Gieles–relevant
and the canonical "clustered, ambiguous" case — is **unambiguously free-free
(α≈0)**: no dust accretion core at its ionizing source.

**(c) Imaging, hot-core chemistry.** ALMA-IMF CH₃CN / CH₃CN v₈=1 moment-0 maps,
S/N within 2.5". **2/9 ionizing positions show a hot core (22%, CI 5–54%)** —
W51-IRS2 main (CH₃CN 64σ, SiO outflow 152σ) and G010.62 main — both the brightest,
most massive, and cluster-confused. **7/9 show no hot core**, consistent with (a)
and (b).

## 4. Discussion
All three tracers converge: a **minority (point estimates 3–22%, all 95% upper
bounds <~54%, best constraint ≤15%)** of (U)C H II ionizing stars carry an
accretion signature at their position. The exceptions are the most massive,
clustered sources, where the signal cannot be cleanly assigned to the ionizing
star versus a neighboring protostar — the W51-IRS2 ambiguity. Meanwhile the parent
clumps remain gas-rich and bound. The natural reconciliation: gas is still being
processed at the **clump/proto-cluster scale**, but the individual ionizing star
has largely cleared or exhausted its immediate (≤0.1 pc) reservoir. Since the
Padoan & Gieles luminosity function uses clump-integrated L_bol, their 1–4 Myr is
consistent as a clump-assembly time; the literal per-star "still accreting"
premise holds only for a minority.

## 5. Caveats / limits (archival coverage, not physics)
- Imaging arms have small N (8–9) → wide CIs; the catalog arm (N=30) is the tightest.
- Interferometers resolve out smooth envelopes → ALMAGAL core masses are
  compact-structure lower bounds.
- Free-free subtraction (a) assumes co-location of CORNISH flux with the core and
  optically-thin α; optically-thick cm would raise mm free-free (strengthens the
  conclusion).
- The resolved imaging set is compact H II + W51-IRS2, **not** a strict ≤0.1 pc
  UC H II (G337.92 falls off the B6 mosaic edge; ALMA staging inaccessible from the
  analysis host). The strict-UC-H II conclusion rests on the catalog arm.
- Hot-core S/N in a 2.5" box (0.02–0.1 pc) can include close neighbors; W51-IRS2's
  hot core is real but is the protocluster.

## Data & reproducibility
All catalogs, scripts, and figures in `/orange/adamginsburg/galactic_plane_surveys/
uchii_2026/` (see `RESULTS.md`). Key tables: `UCHII_master_deliverable.fits`,
`almaimf_alpha_commonbeam.fits`, `phase6_line_signatures.fits`, `uchii_cores.fits`.
Figures: `fig_summary`, `fig_accreting_funnel`, `fig_alpha`, `fig_convergence`.