# RMO76: EUV front, radio constraints and a conditional shock reconstruction

**Result in one sentence:** For the adopted 13 June 2010 numbers, a perpendicular fast-shock model satisfies conservation and characteristic-speed checks; this is a conditional physical reconstruction, while independent identification of the observed front remains open.

EUV means extreme ultraviolet. It is not radio emission. This example combines an EUV front with additional radio observations. Radio data are useful here, but are not a mandatory input for the RMO framework.

## Source information and its role

| Source | Quantity used | Role in this audit |
|---|---|---|
| [Ma et al. (2011), Sections III.1-III.3](https://arxiv.org/html/1106.6056v1) | EUV pattern speed about 600-550 km/s | Motion of a bright feature; not directly a plasma velocity |
| Same work, Eq. 3 / Fig. 7, 05:40 UT | Harmonic lanes 132 ± 5 and 165 ± 15 MHz; reported density ratio 1.56 ± 0.1 | Density ratio assumes upstream/downstream lane assignment; covariance and meaning of ± need clarification |
| Same work, Eqs. 5-7 | Adopted sound speed 156 ± 30 km/s and perpendicular geometry; calculated downstream temperature 2.8 ± 0.6 MK | Model inputs and output; downstream temperature must not be reused as an independent measurement |
| Same work, Fig. 8 | EUV rise times 100 ± 12 and 275 ± 12 s | Additional observables for a future emission-model comparison |
| [Kozarev et al. (2011), Table 1 / Section III.2](https://arxiv.org/html/1406.2372v1) | Front-edge kinematic fits; region-averaged DEM | Time and feature matching control; Ma uses a slightly different temperature region |

The source quantities and locators are transcribed in `solar_diagnosis_audit/sources.json`. No raw images, spectra or new observational archives were acquired. DOI identifiers: Ma, 10.1088/0004-637X/738/2/160; Kozarev, 10.1088/2041-8205/733/2/L25.

## 1. Radio uncertainty must be carried through the density ratio

Our arithmetic uses

\[
X=(f_U/f_L)^2=1.5625.
\]

Two explicit readings of the quoted frequency errors give different objects. Neither is silently selected as the actual observational uncertainty model.

**If the ± values are simultaneous hard bounds**, monotonicity gives exact endpoint fractions

\[
X\in\left[\frac{150^2}{137^2},\frac{180^2}{127^2}\right]
\simeq[1.1988,\,2.0088].
\]

**If they are marginal standard deviations**, first-order propagation gives

\[
\sigma_X=2X\sqrt{a^2+b^2-2r_fab},\qquad
a=\frac{15}{165},\quad b=\frac5{132},
\]

where \(r_f\) is the correlation between the two fitted frequencies. For independent lanes, \(\sigma_X=0.3078\). Its smallest first-order value over \(-1\le r_f\le1\) is 0.1657. A standard deviation of 0.1 would require \(r_f=1.2596\), outside this domain.

This does **not** establish an error in the original analysis. The quoted errors may have a different definition or come from a different fitting procedure. It establishes an RMO input requirement: retain the joint fitting/error provenance before treating the narrower ±0.1 as a justified independent uncertainty. The hard-bound range is not a confidence interval; first-order propagation is not a nonlinear uncertainty proof.

## 2. A concrete physical comparison survives the broader bounds

For an unmagnetized ideal gas with \(\gamma=5/3\), normal upstream flow \(u_1\), and sound speed \(c_1\),

\[
X_{\rm gas}=\frac{(\gamma+1)M_1^2}{(\gamma-1)M_1^2+2},\qquad M_1=u_1/c_1.
\]

At the adopted \(u_1=600\) and \(c_1=156\) km/s, this gives **3.3256**. If \(c_1\in[126,186]\) km/s is treated as a hard bound while \(u_1=600\) is held fixed, the compression is **3.1049-3.5326**. It does not overlap the broader radio-derived interval above.

**Physical meaning:** under this particular speed, sound-speed and radio-lane interpretation, an unmagnetized gas shock cannot explain the inferred compression. A magnetic-pressure contribution is a viable way to reduce that compression. This comparison does not exclude all nonshock explanations or establish the MHD family by itself. Pattern speed, front-normal speed and upstream plasma speed still need to be distinguished. The quoted time-dependent EUV speed range has not been converted into an error bar at 05:40 UT.

## 3. Reconstructing an explicit perpendicular model

For a stationary planar front, choose \(\rho_1=u_1=\mu_0=1\), \(B_n=0\), and zero tangential velocities. Set \(r=1.56\), \(b=p_1=(156/600)^2/(5/3)\), and \(A=B_{t1}^2\). The nontrivial compressed solution of mass, induction, momentum and energy balance gives

\[
A=\frac{2(4-r)-10br}{r(r+5)},\quad
u_2=1/r,\quad B_{t2}=r\sqrt{A},\quad
p_2=b+1-1/r+\tfrac12 A(1-r^2).
\]

This is our algebraic reconstruction under prescribed geometry, checked against direct flux evaluation and the separate compression equation. It does not estimate an observed magnetic angle or provide a measured downstream state.

| Derived quantity | Value |
|---|---:|
| Upstream Alfvén Mach number | 1.5522 |
| Upstream plasma beta | 0.1955 |
| Upstream normal flow / fast speed | 600.0 / 416.8 km/s |
| Downstream normal flow / fast speed | 384.6 / 521.9 km/s |
| Entropy increase, \(\Delta s/c_v\) | 0.1814 |
| Thermodynamic temperature ratio | 1.6127 |

The flow crosses from super-fast to sub-fast with compression and positive entropy production. Independent direct balance of mass, momentum, induction and energy has an absolute residual below \(10^{-50}\) in 60-digit arithmetic; the independent compression equation recovers 1.56 to the same tolerance. Arithmetic precision does not imply observational precision.

If the adopted upstream temperature is identified with the one-fluid thermodynamic temperature, the model gives about **2.90 MK** downstream. This is a prediction, not independent thermometry. Reproducing a model-derived temperature cannot validate that model a second time. The sound-speed convention is taken as supplied for replication; converting electron temperature into total gas pressure for real inputs requires composition and electron/ion assumptions.

**Production limitation found:** the unchanged local classifier returns `DEGENERATE_NOT_CLASSIFIED` for this exact \(B_n=0\) request, even though its conservation check passes. The perpendicular limit deliberately lies outside its current ordinary oblique classifier. No artificial small normal field was inserted. The saved request is explicitly an `exact_synthetic` conditional model; it is not a solar observation file or a browser literature draft.

The conditional physical result is therefore not being presented as a newly successful production-classifier result. It establishes a reproducible target for a separately checked perpendicular-limit extension. It establishes neither a full Riemann fan nor completeness, dynamical stability or uniqueness of solar interpretation.

## 4. Compare the same time before comparing speeds

The coefficients in [Kozarev et al., Table 1](https://arxiv.org/html/1406.2372v1) refer to the 05:37 UT start. Our evaluation of \(v=v_0+a\Delta t\) at \(\Delta t=180\) s gives:

| Profile | Calculated speed at 05:40 UT, km/s |
|---|---:|
| 193/I | 599.69 |
| 193/II | 607.86 |
| 211/I | 584.89 |
| 211/II | 579.71 |
| 193 average | 603.77 |
| 211 average | 581.40 |

The initial 730-740 km/s averages should not be directly compared with a later 600 km/s model input. Time alignment removes much of that apparent difference. These are evaluations of published central fit coefficients, not new measured points or proof of matching patches. We do not invent propagated uncertainties: \(\mathrm{Var}[v(t)]=\mathrm{Var}[v_0]+\Delta t^2\mathrm{Var}[a]+2\Delta t\,\mathrm{Cov}(v_0,a)\), and that covariance is not supplied here. Brightest-crest and leading-edge tracking also need separate matching.

## What the observer can say now

“A magnetic shock model can account for the adopted motion and radio-inferred compression. The reconstructed perpendicular case has the fast-shock speed ordering. Its geometry and downstream state remain model-dependent; a complete observational classification has not yet been obtained.”

This is an EUV-front example with auxiliary radio constraints. The ionization-delay observables can be held out for a later forward-model comparison, accounting for emitting volume, foreground/background, density history and electron/ion temperatures. They are not automatically independent of each other, nor are they direct gas-state inputs.

## Next concrete scientific step

Validate the perpendicular-limit treatment against the present exact reconstruction, an independent reference and nonshock/degenerate controls before expanding the production classifier. For the solar inference, keep the radio error definition and EUV/radio patch association unresolved until supported. Then compare predicted EUV evolution with retained emission observables, using the same region and time and explicit alternatives. A successful conditional reconstruction must remain distinguishable from observational identification.

The 13 February 2009 stereoscopy example retains its geometry-control role. Its date, authors, existing plots and limitations are unchanged. This audit does not replace that demo or alter the agreed main QuickLook text.

## Reproduce and inspect

From the project root, run:

```bash
python solar_diagnosis_audit/audit.py
python solar_diagnosis_audit/plot.py
```

The audit uses Python's standard library and the unchanged local classifier. Plotting uses Matplotlib. Seven focused checks pass: central arithmetic, the first-order correlation bound, direct RH balance, the separate compression equation, the unmagnetized limit, entropy/fast-speed ordering, and the production classifier's explicit perpendicular-limit response. These are numerical and model checks, not seven independent solar observations.

Full numeric output: `RMO_solar_diagnostic_audit.json`. Standalone conditional request: `RMO_Ma2010_conditional_model_request.json`. Vector figure: `RMO_EUV_radio_source_audit.pdf` and `.svg`. All are included in the R0-R76 archive. Main QuickLook, prior scientific code and historical results are preserved.