# RMO88 — Does the magnetic comparison survive speed errors?

**Result in one sentence:** under the adopted normal-speed, sound-speed and radio bounds, a gas-only shock compresses too much if the upstream plasma is at rest; permitting an unmeasured outward plasma flow can change that conclusion.

Event: **13 June 2010, comparison at 05:40 UT**. This is a bounded extension of the RMO76 scalar comparison. It does not replace the RMO84/85 emission audit or classify a new solar front.

## Published result and RMO's added check

[Ma et al. (2011), Section III.3](https://arxiv.org/html/1106.6056v1) already compared gas-dynamic compression with the radio estimate and argued that magnetic effects matter. We retain that attribution. Our addition is to test this comparison across explicit bounds on the existing speed and sound-speed inputs, and to calculate how an unknown plasma velocity affects it. This is not claimed as a new solar discovery.

The kinematic coefficients are from [Kozarev et al. (2011), Table 1 and Section II.1, accessible arXiv v1](https://arxiv.org/html/1406.2372v1). They describe front edges under a spherical/radial deprojection. They are neither local plasma velocities nor independently measured shock normals. The two papers discuss association between EUV and radio features; exact spatial correspondence of every quantity is not established by this calculation.

## 1. Compare speeds at the radio time

We evaluate each published fit at 05:40 UT, 180 s after its 05:37 origin:

\[
D=D_0+a\Delta t.
\]

For this conditional test only, each quoted plus/minus is treated as a simultaneous hard bound. The resulting outer half-width is

\[
\delta D=\delta D_0+\Delta t\,\delta a.
\]

| Published profile | Central speed at 05:40 (km/s) | Conditional bounds (km/s) |
|---|---:|---:|
| 193/I | 599.69 | 548.39–650.99 |
| 193/II | 607.86 | 576.13–639.59 |
| 211/I | 584.89 | 516.39–653.39 |
| 211/II | 579.71 | 528.33–631.09 |
| 193/AVG | 603.77 | 543.62–663.92 |
| 211/AVG | 581.40 | 495.77–667.03 |

The union envelope is **495.77–667.03 km/s**. The profiles and their published averages are not six independent data sets. We do not average them again or combine their errors as independent evidence. All remain alternative source summaries within one conservative outer envelope.

This is not an observational confidence interval. If the published errors are marginal standard deviations instead, the variance is

\[
\sigma_D^2=\sigma_{D_0}^2+\Delta t^2\sigma_a^2+
2\Delta t\,\operatorname{Cov}(D_0,a).
\]

Without the covariance, the possible standard deviation spans
\(|\sigma_{D_0}-\Delta t\sigma_a|\) to \(\sigma_{D_0}+\Delta t\sigma_a\).
Our rectangle does not set covariance to zero: it encloses any joint set contained in the assumed marginal bounds. Some corners may be unreachable under the actual unrecovered fit covariance. Source error definitions are still needed before making a statistical claim.

## 2. Test gas-only compression with those bounds

We retain the supplied sound-speed range **126–186 km/s** and \(\gamma=5/3\). This does not rederive total gas pressure from electron thermometry. Composition, electron/ion temperatures and thermal closure remain assumptions.

In a frame where the front moves outward at normal speed \(D_n\), let the upstream plasma's outward normal velocity be \(v_n\). For the branch considered here,

\[
U_1=D_n-v_n>c_1,\qquad
X_g=\frac{4U_1^2}{U_1^2+3c_1^2}.
\]

The stationary-upstream comparison takes \(v_n=0\) and identifies the source front speed with \(D_n\). These are explicit physical assumptions, not additional measurements.

At rest, monotonicity gives **Xg = 2.8124–3.6132** over the full chosen speed/sound box. The radio-lane assignment gives

\[
X_r=(f_U/f_L)^2\in[(150/137)^2,(180/127)^2]
=[1.1988,2.0088].
\]

There is no overlap. The smallest gas compression exceeds the largest radio ratio by **0.8036**. We use the two original lane frequencies jointly; the derived density ratio is not varied independently of them. Electron and mass-density ratios are equated only for fixed composition.

**Physical interpretation:** with these assignments and assumptions, a gas-only adiabatic shock cannot explain the compression. Magnetic stresses remain a viable way to reduce it, consistent with the published argument. This test neither measures a field nor establishes its orientation or a fast/slow family. It also does not exclude non-wave explanations, other thermal closures, other feature associations or all parallel MHD structures.

## 3. A missing plasma velocity changes the inference

The greatest upstream speed relative to the front allowed by the gas model and the adopted radio/sound bounds is

\[
U_{1,\max}=c_{1,\max}\sqrt{\frac{3X_{r,\max}}{4-X_{r,\max}}}
=323.5827\ \mathrm{km\,s^{-1}}.
\]

Therefore the first possible contact between the scalar ranges, anywhere in the outer speed envelope, occurs at

\[
v_{n,\min}=D_{n,\min}-U_{1,\max}
=172.1873\ \mathrm{km\,s^{-1}}.
\]

This is a **threshold in the assumed model**, not a measured coronal flow. An outward flow below that threshold preserves the exclusion over this box; a flow at or above it is a necessary opening for overlap, not a guarantee that all observations can be fitted. Different normal geometry, sound-speed conventions or radio-lane assignments change the threshold.

As a falsification control, we construct one gas-shock endpoint with Dn = 495.77 km/s, c1 = 186 km/s, the radio upper ratio and the corresponding outward flow. Its states satisfy direct inertial-frame mass, momentum and energy balance and have positive entropy change. It demonstrates why gas-only exclusion is not unconditional when plasma velocity is unconstrained. It is not an observed state, a best fit, or a witness within an unknown narrower observational covariance region. No radio-emission or EUV image model is fitted by this control.

The plot's right panel varies the assumed upstream flow from 0 to 300 km/s, with the same linked gas relation throughout. This is a sensitivity curve, not a time history or measured flow distribution.

## What should be measured next?

**Constrain the upstream plasma velocity along the local front normal**, and verify the front, thermal region and radio source refer to the same relevant plasma and time. A Doppler component alone still needs its projection relative to that normal. Stereoscopy constrains geometry but does not itself supply plasma velocity.

The earlier reconstructed perpendicular fast-shock model remains a conditional example. The present scalar contrast cannot upgrade it to an independently identified solar shock. The separate EUV-emission comparison remains open with its original source and density-history limitations.

## Reproduction and checks

Run from the project root:

```sh
python3 solar_speed_check/audit.py
python3 solar_speed_check/plot.py
```

The audit uses exact fractions for the printed source decimals and monotonic endpoint bounds. A separate 75-digit Decimal calculation uses the general-gamma gas relation. Direct lab-frame Rankine–Hugoniot evaluation checks the constructed moving-plasma counterexample. **29 focused checks pass**, including endpoint construction, the inverse threshold, entropy, original nominal compression and retained/lost exclusion controls at 150 and 180 km/s. Arithmetic precision does not increase observational precision.

Files: `RMO_solar_speed_check.json`, `verification.json`, vector PDF/SVG, and this report. The PDF was rendered and visually inspected. All previous scientific scripts, results and images remain unchanged.