Discovering Dual-Origin Slow Wind from Solar Orbiter with Self-Supervised Contrastive Learning

Henry Han; Jorge Yero Salazar

astro-ph.SRAug 22, 2026

Discovering Dual-Origin Slow Wind from Solar Orbiter with Self-Supervised Contrastive Learning

Authors: Henry Han, Jorge Yero Salazar

Organizations: Department of Computer Science, Baylor University, One Bear Place, Waco, TX 76798, USA

Abstract

Whether the slow solar wind originates from one coronal source or two distinct channels remains a central open question in heliophysics. Resolving this requires unsupervised separation of two populations that arrive at nearly the same bulk speed and differ mainly in heavy-ion composition. We present Solar-CDC, a self-supervised contrastive deep clustering (CDC) framework that maps plasma observables to a latent space via a Transformer encoder, optimizes a triplet margin loss, and updates pseudo-labels via $k$ -means. Theoretically, we prove that neighborhood-preserving embeddings such as t-SNE and UMAP are fundamentally constrained. Preserving the neighbor graph leaves the cross-cluster cut fraction unchanged, and preserving all but a fraction $\varepsilon$ of its links moves that fraction by at most $\varepsilon$ . Neither bound depends on the target dimension. A margin objective rewrites the graph and drives the cut fraction to zero. Empirically, on 30,602 Solar Orbiter observations, thirty combinations of dimensionality reduction and clustering peak at a silhouette of $0.454$ , whereas Solar-CDC reaches $0.869$ . Escaping the geometric bound alone does not guarantee physical validity: TriMap also optimizes triplets and reaches $0.824$ , yet its clusters score below chance against the published composition taxonomy. Solar-CDC instead recovers clusters with mean charge-state ratios of $0.080$ , $0.160$ , and $0.400$ , placing the intermediate population inside the window associated with coronal-hole boundaries. Even when the defining charge-state ratio is withheld from the inputs entirely, the model still recovers the taxonomy defined on it. Solar-CDC thus connects self-supervised representation learning to coronal source diagnostics. Importantly, a learning loss recovers physical populations only when driven by dynamically updated physically-aware clusters rather than distances.

Figures & tables

Figure 1: Why a threshold on one variable is not enough. (a) The $\mathrm{O}^{7+}/\mathrm{O}^{6+}$ distribution over the 30,602 Solar Orbiter observations, with the coronal-hole ( $0.145$ ) and streamer-belt ( $0.20$ ) reference values marked. (b) Bulk speed against composition: the two slow-wind channels are stacked in composition at essentially the same speed, so a velocity cut cannot separate them.

Figure 2: Solar-CDC. Triplets drawn from the current pseudo-labels pass through the shared encoder; the classification head is trained on those pseudo-labels while the triplet term acts on the latent codes, and both gradients reach the encoder. The lower half of the diagram is the part that makes the method self-supervised: the pseudo-labels are not given, they are produced by $k$ -means, on the observables at epoch 0 and on the latent codes every $p$ epochs thereafter, and they decide in turn which observations are drawn as positives and negatives.

Panel of Figure 3 — Figure 3: The two alternating phases of training. The regular step refines the encoder given fixed pseudo-labels; the reassignment step updates the pseudo-labels given the improved encoder.

Figure 4: Warmup: pseudo-labels are initialized by $k$ -means on the standardized observables, bypassing the randomly initialized encoder.

neighborhood preserving
Space	$\beta_{10}$ , recovered partition	$\beta_{10}$ , threshold partition
Input, seven observables	0.064	0.131
t-SNE [ 12 ] ( $q=2$ )	0.071	0.158
UMAP [ 14 ] ( $q=2$ )	0.084	0.197
PHATE [ 16 ] ( $q=2$ )	0.148	0.228
PCA [ 15 ] ( $q=2$ )	0.174	0.215

Table 1: Cut fraction

\beta_{10}

(

\kappa=10

8{,}000

-point subsample). As Props. 1 – 2 require, neighborhood-preserving methods stay within

\varepsilon

of the input metric, and none improves on it; Solar-CDC reduces it to near zero.

	Latent dimension $m$
Heads	2	4	8	16	32
1	0.869	0.828	0.820	0.755	0.725
2	0.829	0.806	0.773	0.748	0.764
4	0.866	0.814	0.792	0.752	0.728
8	0.840	0.821	0.809	0.756	0.772
16	0.832	0.834	0.779	0.775	0.740

Table 2: Silhouette over the Solar-CDC hyperparameter grid (30,602 observations, seven observables,

k=3

, 200 epochs, pseudo-label period

p=4

, Euclidean triplet distance). All 30 runs converged to three non-empty clusters.

neighborhood preserving
Reduction	K-Means	GMM	Agglomerative
PCA [ 15 ] (2-D)	0.400	0.360	0.414
t-SNE [ 12 ] ( $p{=}30$ )	0.428	0.427	0.388
t-SNE ( $p{=}100$ )	0.438	0.424	0.422
t-SNE ( $p{=}200$ )	0.450	0.440	0.372
UMAP [ 14 ] (15 nn)	0.443	0.452	0.420

Table 3: Silhouette of each dimensionality-reduction baseline inside its own two-dimensional embedding (8,000-point subsample; every method here is superlinear in

N

), against Solar-CDC in its learned representation. The grouping is the one Sec. 5 predicts: the methods that aim to preserve neighborhoods sit together, and the one that optimizes triplet order does not.

$k$	Silhouette	vs. $k=3$
2	$0.856\pm 0.033$	$p=0.42$
3	$0.843\pm 0.035$	—
4	$0.765\pm 0.044$	$p=3.9\times 10^{-4}$
5	$0.688\pm 0.089$	$p=2.6\times 10^{-4}$

Table 4: Cluster-count sweep, ten seeds per

k

(mean

\pm

s.d.), with the silhouette computed exactly on all

30{,}602

observations. Both

k=2

and

k=3

are significantly better than

k=4

and

k=5

; they are not distinguishable from each other.

Method	Inputs	NMI	ARI	Matched acc.
Random labeling	—	0.000	0.000	0.337
Largest class only	—	0.000	0.000	0.501
TriMap [ 1 ] + Agglom.	seven	0.036	$-0.021$	0.465
$k$ -means	seven	0.348	0.284	0.628
Solar-CDC	seven	$\mathbf{0.422\pm 0.079}$	$0.385\pm 0.088$	$\mathbf{0.706\pm 0.046}$
$k$ -means, control	six	0.311	0.259	0.613

Table 5: Agreement with the external

\mathrm{O}^{7+}/\mathrm{O}^{6+}

taxonomy of [ 21 , 5 , 9 ] , defined by published thresholds rather than by archived class labels, and unseen during training. Solar-CDC values are means over five seeds (16 heads,

m=2

). The 6-observable control is trained without

\mathrm{O}^{7+}/\mathrm{O}^{6+}

and scored against the same reference.

Figure 5: The three recovered clusters in learned and physical spaces (colors consistent throughout; $6{,}000$ random observations sampled for legibility). (a) The 2-D latent codes. (b) Bulk speed vs. $\mathrm{O}^{7+}/\mathrm{O}^{6+}$ , with dashed lines marking the published coronal-hole ( $0.145$ ) and streamer-belt ( $0.20$ ) thresholds. The two slow-wind populations share an identical speed range but divide sharply at the compositional boundary. (c) Correlated charge-state ratios. The separation spans the broader composition space rather than relying on a single variable. (d) Bulk speed vs. density. The two slow clusters perfectly interleave. Together, panels (b) and (d) visualize the core premise of our method: the distinct origins of the slow wind are clearly separable by composition, yet completely invisible to classical kinematic properties.

Cluster	$n$	$\bar{v}_{p}$	$\bar{N}_{p}$	$\overline{\mathrm{O}^{7+}\!/\mathrm{O}^{6+}}$	$\overline{\mathrm{C}^{6+}\!/\mathrm{C}^{4+}}$	$\overline{\mathrm{Fe/O}}$	$\overline{Q_{O}}$
0 coronal hole	10,415	526	14.2	0.080	2.14	0.146	6.07
1 boundary type	12,581	374	28.1	0.160	4.37	0.154	6.15
2 streamer belt	0 7,606	379	32.3	0.400	11.00	0.220	6.39

Table 6: Mean plasma properties per cluster, ordered by charge state (16 heads,

m=2

). Cluster 0 isolates the fast wind, while Clusters 1 and 2 partition the slow wind. This compositional profile represents the 11 of 24 runs that successfully resolve the boundary population. For physical context, established

\mathrm{O}^{7+}/\mathrm{O}^{6+}

thresholds are:

<0.145

(coronal-hole interior),

0.145

–

0.20

(boundary), and

>0.20

(streamer belt) [ 9 , 21 , 5 ] . Note: Silhouette scores here are computed across the full dataset rather than the held-out split, precluding direct comparison with Table 2 .

Figure 6: Distribution of each observable per cluster (boxes: quartiles; whiskers:

1.5\times

IQR; outliers omitted). Separation is monotone and largest in the charge-state variables, and smallest in bulk speed, where clusters 1 and 2 overlap almost completely.

Appendix figures & tables1 asset

Supplementary material from the paper’s appendix.

Appendix

	seven observables					with time and label columns
Heads	2	4	8	16	32	2	4	8	16	32
1	0.869	0.828	0.820	0.755	0.725	0.857	0.803	0.811	0.746	0.687
2	0.829	0.806	0.773	0.748	0.764	0.842	0.783	0.804	0.753	0.730
4	0.866	0.814	0.792	0.752	0.728	0.853	0.786	0.790	0.721	0.714
8	0.840	0.821	0.809	0.756	0.772	0.850	0.762	0.796	0.750	0.689
16	0.832	0.834	0.779	0.775	0.740	0.846	0.818	0.799	0.746	0.703

Appendix

Table 7: Silhouette over the full grid, with the seven observables and with the two extra columns of Sec. 6.1 appended to the input (30,602 observations,

k=3

, 200 epochs,

p=4

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