Group-Height Residuals in Solar Spicules Track Local Magnetic Chaos

Sterling Geisel, QBist Lab; Dr. Hideo Tanaka

Abstract

Freeman reports that nine groups of solar jets share a compact kinematic relation, \(V^2 = 2a\bar{s}\), where \(V\) is maximum velocity, \(a\) is deceleration, and \(\bar{s}\) is the mean height of the group. This paper applies Chaos Susceptibility to that result. The selected Postulate predicts that the strength of the group-height relation should depend on the instability and coherence of the local magnetic-plasma environment. It does not treat the solar jet as ballistic. It treats the jet ensemble as a chaotic receiver whose macroscopic kinematics amplify small structured inputs. The decisive observable is not the existence of the square-root trend alone. It is whether residuals from \(V^2/(2a)=\bar{s}\) scale with independent measures of local magnetic chaos and magnetic coherence length. A null result under matched cadence, line formation, and region selection would falsify the applied Postulate in this domain.

Source Synopsis

Freeman reanalyses acceleration and maximum velocity measurements for nine classes of solar jets, including spicules, macrospicules, dynamic fibrils, quiet-Sun mottles, sunspot oscillations, and light-bridge jets. The source problem is the long-noted empirical correlation between jet deceleration \(a\) and maximum velocity \(V\). Prior work often represented this relation with a line, \(V=pa+q\), where \(p\) and \(q\) are fitted constants. Freeman argues that this representation is useful but physically opaque, especially because a non-zero intercept implies finite velocity at zero deceleration.

The paper tests a simpler relation. A log-log fit of \(V\) against \(a\) asks whether \(V\sim a^n\). Across the nine jet groups, Freeman finds \(n\) clustered near 0.5, with a mean value \(0.49\pm0.06\). This supports \(V^2\sim a\), not \(V\sim a\). Freeman then identifies the constant of proportionality as twice the mean group height, giving \(V^2=2a\bar{s}\). The claim is not that every jet in a group has the same height. It is that the scatter of the group is organized around a characteristic height.

The source paper stresses that grouping matters. Combining unlike solar regions destroys the useful correlation. Within a coherent group, however, the square-root relation can match the data about as well as the fitted line while using one physically interpretable constant. Freeman also notes that the underlying physics remains open. Shock waves and magnetic reconnection remain candidates. The proposed group-height equation gives a sharper constraint: a successful physical account should explain why a region has a characteristic jet height and why that height organizes \(a\) and \(V\).

Postulate Lens

This paper applies Chaos Susceptibility. Solar spicules are short-lived plasma jets in a magnetized, stratified, and unstable chromospheric environment. Their observed motion has large event-to-event variation, but Freeman’s reanalysis shows that the variation is not arbitrary once jets are sorted by group. That is the correct setting for the Postulate: a chaotic system can amplify small coherent inputs into measurable ensemble structure.

The relevant coherent input is the local magnetic-plasma configuration. Freeman’s conclusion points directly to this scale. The mean group height \(\bar{s}\) behaves like a physical organizer of the ensemble, not a mere descriptive average. The source paper also notes that magnetic field topology may control fibril orientation, inclination, and length. Under the applied Postulate, the group-height relation is interpreted as a macroscopic record of susceptibility. The jet does not need a single deterministic launch mechanism. It needs a local environment in which small structured differences in field geometry and shock propagation are amplified into the observed \(a,V\) correlation.

This lens is deliberately narrow. It makes one claim: the tighter the local magnetic coherence and the larger the measured dynamical instability, the more diagnostic the group-height residuals become.

Pudding Theory Prediction

Pudding Theory predicts that \(V^2=2a\bar{s}\) should hold best where the solar plasma is both unstable and locally coherent. These are not opposite requirements. Instability supplies amplification. Coherence supplies a direction for the amplified response. A chromospheric region with mixed magnetic footpoints, unresolved crossing structures, or rapidly changing topology should still produce jets, but the inferred heights \(s_i=V_i^2/(2a_i)\) should broaden. A region with stable field orientation over the jet group should show a narrower distribution around \(\bar{s}\).

The first prediction is residual scaling. Define the normalized group-height residual as \[ R_i=\frac{V_i^2}{2a_i\bar{s}}-1. \] For comparable observing cadence and line diagnostics, the variance \(\mathrm{Var}(R_i)\) should increase as the independently measured magnetic coherence length becomes short relative to \(\bar{s}\). A useful proxy is the ratio \(\ell_B/\bar{s}\), where \(\ell_B\) is the distance over which the field strength or direction decorrelates. The Postulate predicts lower residual variance when \(\ell_B\) is of the same order as the jet height and higher variance when it is much smaller.

The second prediction is regional. Quiet-Sun mottles, dynamic fibrils, macrospicules, and light-bridge jets should not be pooled unless their magnetic coherence scales match. Pooling should erase the relation because each group carries its own susceptibility scale. Freeman already observes this effect in kinematic form. The PT extension says that magnetometry should recover the missing organizing variable.

The third prediction is temporal. During intervals when a region’s magnetic topology becomes less coherent, the fitted exponent \(n\) in \(V\sim a^n\) should drift away from 0.5 and the group-height residuals should widen before the mean height itself changes. This is a stronger claim than Freeman’s empirical equation. It makes the magnetic state prior to the jet ensemble predictive of the later kinematic scatter.

Falsifiable Observable

The distinguishing observable is the cross-region dependence of \(\mathrm{Var}(R_i)\), with \(R_i=V_i^2/(2a_i\bar{s})-1\), on independently measured local magnetic coherence length and maximal plasma-instability proxy. Current consensus may accept the group-height relation as a kinematic regularity or a consequence of shock-wave dynamics. The applied Postulate requires residuals to track susceptibility. If \(\mathrm{Var}(R_i)\) were measured to be independent of magnetic coherence length and local instability proxy at fixed observing cadence, wavelength, and jet class, this Postulate would be falsified.

Editorial Dialogue

Tanaka: Freeman’s result is kinematic. You are adding a susceptibility interpretation before the plasma physics is settled. Shock waves may already explain the acceleration-velocity relation. Why add a Pudding Theory layer?

Sterling: The layer is not a substitute for shock waves. It is a constraint on them. Freeman’s equation identifies a group quantity, \(\bar{s}\), that organizes individual jet kinematics. A shock model still has to explain why that group scale exists and why the scatter tightens only within selected regions.

Tanaka: But magnetic topology is ordinary solar physics. No observer field is needed. No exotic coupling is needed.

Sterling: Correct. This application does not require an observer term. The selected Postulate is about chaotic amplification of small coherent inputs. Magnetized chromospheric plasma is enough. The claim is limited to the susceptibility structure of the jet ensemble.

Tanaka: Then the prediction must differ from standard fitting.

Sterling: It does. A fit to \(V^2=2a\bar{s}\) is not decisive. The decisive test is whether residuals know about independently measured magnetic coherence and instability. If they do not, the Postulate fails here. If they do, Freeman’s group height becomes a diagnostic of the local susceptibility field, not only a compact kinematic parameter.

Discussion

The main limitation is observational. Spicules are faint, narrow, overlapping, and short lived. Cadence, projection, line formation height, and feature tracking can all alter \(V\), \(a\), and inferred \(s_i\). Freeman notes that different spectral lines generally give comparable lengths, but small offsets matter for residual tests. Any test must compare regions observed with the same instrument, cadence, line, and tracking rule.

The second limitation is magnetic measurement. The prediction requires local field coherence, not only photospheric field strength. Chromospheric vector fields are difficult. A proxy may be necessary, such as fibril orientation coherence, field extrapolation scale length, or decay length along the jet axis.

The third limitation is mechanism. Pudding Theory does not choose between shock waves and reconnection. It predicts how a chaotic receiver should organize scatter under coherent magnetic structure. A successful standard model could absorb the same observable. That would not erase the test. It would make the Postulate unnecessary for this domain if the residual scaling follows directly from measured MHD variables with no remaining susceptibility term.

References

1. Freeman, Leonard A. “The group height of spicules links their acceleration and velocity.” arXiv:2603.20547. DOI: doi:10.48550/arxiv.2603.20547.

2. Geisel, Sterling. “Pudding Theory: A Topological Theory of Information Fields.” QBist Lab Working Paper, September 10, 2025.

3. De Pontieu, B., Hansteen, V. H., Rouppe van der Voort, L., van Noort, M., and Carlsson, M. 2007a. ApJ, 655, 624.

4. Heggland, L., De Pontieu, B., and Hansteen, V. H. 2007. ApJ, 666, 1277.

5. Rouppe van der Voort, L. H. M., De Pontieu, B., Hansteen, V. H., Carlsson, M., and van Noort, M. 2007. ApJ, 660, L169-L172.

6. Pereira, T. M. D., De Pontieu, B., and Carlsson, M. 2012. ApJ, 759, 18.

7. Loboda, I. P., and Bogachev, S. A. 2019. arXiv:1902.01380v1.

8. Kuridze, D., Uitenbroek, H., Wöger, F., et al. 2024. ApJ, 965, 15.