# RMO85 — Published interpretation and the additional RMO check

**Result in one sentence:** Ma et al. report a shock interpretation; an independent RMO confirmation using the EUV delays requires a consistent density convention and a matched emission calculation.

Event: **13 June 2010**. This is a bounded follow-up to the RMO76 source audit, using published scalar inputs. The checked MHD reconstruction remains a conditional model. Its successful conservation and speed checks do not automatically validate the emission model or identify the observed front.

## Published interpretation

[Ma et al. (2011)](https://doi.org/10.1088/0004-637X/738/2/160) interpret the coronal dome as a CME-associated shock and support a fast-mode component in the associated EUV wave. Their analysis combines morphology, motion, radio and EUV emission. They also discuss limitations of the intensity-ratio timing approximation, including foreground/background, density structure and expansion cooling ([accessible arXiv version, Sections 3.3 and 4](https://arxiv.org/html/1106.6056v1)). These are the authors' conclusions and caveats, not new RMO findings.

## What RMO adds, and what confirmation requires

RMO84 tested a restricted scalar approximation rather than reproducing the full observational analysis. In that test, no common density matches both EUV delays and the radio bound at the five tabulated temperatures. The exact arithmetic and its conditional assumptions are retained below. The mismatch identifies an unresolved requirement for **our independent replication**; it does not overturn the published interpretation or establish an error in the final journal article.

Before using this emission comparison as independent confirmation, RMO needs:

1. The final source version and a consistent density convention in the timing calculation.
2. Evidence that the radio and EUV constraints refer to the same plasma and relevant time interval.
3. Defined measurement errors and their shared dependencies, without treating quoted uncertainties automatically as hard bounds.
4. An emission calculation that accounts for the relevant thermal/density history, initial ionization state, channel response and background, with its assumptions tested.

These are requirements for the proposed RMO verification, not a claim that the original authors ignored them. If a discrepancy survives those checks, it should be reported with its precise scope and evidence. Neither agreement nor disagreement is assumed in advance.

## Source and input provenance

[Ma et al. (2011), arXiv:1106.6056v1](https://arxiv.org/pdf/1106.6056v1), page 10, Eqs. 8–9 and Table 2: five temperatures (2.4–3.2 MK), four ionization coefficients at each temperature, tabulated times, density 9.4 × 10⁷ cm⁻³, and observed rises 100 ± 12 s and 275 ± 12 s. Section 3.2 gives harmonic frequencies 132 ± 5 and 165 ± 15 MHz. The coefficients and text agree in the HTML and extracted PDF text. The publisher PDF was inaccessible; the arithmetic finding here is explicitly about arXiv v1. No original observations were downloaded.

The last coefficient in Eq. 9 is interpreted as Fe XV, following the table and accompanying prose; the displayed equation has Fe V. We retain this explicit indexing assumption. Numerical source transcriptions and locators are in `solar_joint_check/sources.json`.

## 1. Check the density used in the time calculation

Let C₂₁₁ = 1/q₁₂ + 1/q₁₃ and C₃₃₅ = C₂₁₁ + 1/q₁₄ + 1/q₁₅. The tested approximation is tλ = Cλ(T)/nₑ: one constant temperature and one common density for both channels.

Our direct calculation at 2.8 MK gives:

| Density used, cm⁻³ | Calculated t₂₁₁, s | Calculated t₃₃₅, s |
|---|---:|---:|
| 6.00 × 10⁷ | 82.704 | 277.356 |
| 9.36 × 10⁷ (= 6.00 × 10⁷ × 1.56) | 53.015 | 177.793 |
| 9.40 × 10⁷ | 52.790 | 177.036 |

The printed table entries, 83 and 277 s, are close to the first row. Across all five temperatures, both table columns are reproduced to within one second using 6.00 × 10⁷ cm⁻³; they are not reproduced using the stated 9.40 × 10⁷ cm⁻³. Exact rational arithmetic and a separate 75-digit Decimal calculation agree. Replacing 9.40 by the unrounded product 9.36 does not resolve the difference.

This is a reproducibility discrepancy in the tested approximation and source version. It is not evidence that the observed feature is not a shock. The final published calculation or a more detailed model may use additional information not represented by this table.

## 2. Require both EUV channels to describe the same plasma

Treat the quoted time errors as simultaneous bounds **for this conditional test**:

- t₂₁₁ ∈ [88, 112] s;
- t₃₃₅ ∈ [263, 287] s.

These are not newly established confidence intervals. With fixed T and coefficients, each channel gives nₑ ∈ [Cλ/tλ,max, Cλ/tλ,min]. The two intervals must intersect. Equivalently, density cancels from the ratio:

\[
\frac{t_{335}}{t_{211}}=\frac{C_{335}(T)}{C_{211}(T)},\qquad
\frac{t_{335}}{t_{211}}\in[263/112,\,287/88]=[2.3482,\,3.2614].
\]

| Tabulated T, MK | Predicted time ratio | One density fits both time bounds? |
|---|---:|---|
| 2.4 | 3.5278 | No |
| 2.6 | 3.4330 | No |
| 2.8 | 3.3536 | No |
| 3.0 | 3.2865 | No |
| 3.2 | 3.2290 | Yes, nₑ ∈ [4.5021, 4.5472] × 10⁷ cm⁻³ |

Only one of the **five tested rows** admits a common density. This is not a measured temperature, a fitted confidence region, or an exclusion of temperatures between or outside the rows. No rate interpolation was performed. The relatively narrow intersection at 3.2 MK inherits the fixed-rate, constant-plasma and hard-bound assumptions.

## 3. Keep the radio-derived parameters linked

For harmonic emission with the stated upstream/downstream lane assignment, let \(K = 8980\ \mathrm{Hz}\,\mathrm{cm}^{3/2}\). Then

\[
n_1=\left(\frac{f_L}{2K}\right)^2,\quad
X=\left(\frac{f_U}{f_L}\right)^2,\quad
n_2=n_1X=\left(\frac{f_U}{2K}\right)^2.
\]

The lower frequency cancels. Varying the derived n₁ and X independently would discard their shared dependence on fL. The audit preserves this identity exactly. With fU ∈ [150, 180] MHz, the conditional downstream-density range is

\[
n_2\in[6.9754,\,10.0446]\times10^7\ \mathrm{cm}^{-3}.
\]

It does not intersect the common EUV density at the tested 3.2 MK row. None of the other four rows fits both EUV delays even before adding radio. Thus no common density satisfies all three constraints at these five temperatures under this approximation.

The conclusion assumes the radio and EUV signals sample the same relevant plasma, the harmonic/lane assignment is correct, and the quoted frequency errors are simultaneous bounds. The calculation does not establish those assumptions. EUV is ultraviolet emission; radio supplies a separate auxiliary constraint.

## What the observer can say

**The event has a published shock interpretation. RMO reproduces a conditional MHD model; its independent check against the EUV emission still needs a consistent, matched forward calculation.**

Matching two channels separately with different densities would not be a successful joint test. Likewise, using a downstream temperature already obtained from a shock model as an independent measurement would test the same assumption twice.

The next useful question is whether the observed rise times genuinely trace the assumed ionization sequence in the same plasma. Changing density along its history, initial ion fractions, temperature evolution, emitting volume, foreground/background and channel response can affect the mapping from plasma evolution to an intensity-ratio rise. The present calculation includes none of those effects; it cannot decide which is responsible for the mismatch. A failure of this approximation is not a failure of ideal MHD or proof of a non-wave explanation.

## Verification and next dependency

The saved audit uses exact fractions for all printed decimal inputs and a separate high-precision summation. It checks the shared radio identity, density cancellation in the EUV ratio, agreement between the ratio and interval-intersection criteria, all five table rows, a feasible two-channel witness, the unrounded density product, and the joint radio comparison. These are arithmetic controls on one event, not independent observations.

Reproduce without a network:

```bash
python3 solar_joint_check/audit.py
python3 solar_joint_check/plot.py
```

Outputs: `RMO_solar_joint_check.json`, `verification.json`, vector PDF/SVG, and this report. RMO76 source audit, the validated diagnosis modules and all earlier numerical results remain unchanged. The QuickLook addition is a saved, explicitly conditional solar check with downloadable evidence.

Before an observational claim: reconcile the source-version arithmetic, establish error semantics and same-parcel/time correspondence, and specify a forward emission model with independently constrained inputs.  No new solar discovery, full emission calculation, global Riemann uniqueness, statistical significance or native-browser acceptance is claimed here.

RMO85 is an attribution and explanation update. The RMO84 arithmetic, numerical output, vector figures and validation records are unchanged.