Expansion of magnetic clouds in the outer heliosphere

A large amount of magnetized plasma is frequently ejected from the Sun as coronal mass ejections (CMEs). Some of these ejections are detected in the solar wind as magnetic clouds (MCs) that have flux rope signatures. Magnetic clouds are structures that typically expand in the inner heliosphere. We derive the expansion properties of MCs in the outer heliosphere from one to five astronomical units to compare them with those in the inner heliosphere. We analyze MCs observed by the Ulysses spacecraft using insitu magnetic field and plasma measurements. The MC boundaries are defined in the MC frame after defining the MC axis with a minimum variance method applied only to the flux rope structure. As in the inner heliosphere, a large fraction of the velocity profile within MCs is close to a linear function of time. This is indicative of} a self-similar expansion and a MC size that locally follows a power-law of the solar distance with an exponent called zeta. We derive the value of zeta from the insitu velocity data. We analyze separately the non-perturbed MCs (cases showing a linear velocity profile almost for the full event), and perturbed MCs (cases showing a strongly distorted velocity profile). We find that non-perturbed MCs expand with a similar non-dimensional expansion rate (zeta=1.05+-0.34), i.e. slightly faster than at the solar distance and in the inner heliosphere (zeta=0.91+-0.23). The subset of perturbed MCs expands, as in the inner heliosphere, at a significantly lower rate and with a larger dispersion (zeta=0.28+-0.52) as expected from the temporal evolution found in numerical simulations. This local measure of the expansion also agrees with the distribution with distance of MC size,mean magnetic field, and plasma parameters. The MCs interacting with a strong field region, e.g. another MC, have the most variable expansion rate (ranging from compression to over-expansion).

💡 Research Summary

The paper investigates how magnetic clouds (MCs)—the interplanetary manifestations of coronal mass ejections (CMEs) that exhibit clear flux‑rope signatures—expand as they travel through the outer heliosphere, from 1 to 5 astronomical units (AU). While numerous studies have characterized MC expansion near Earth (≈1 AU), the behavior at larger heliocentric distances remained poorly constrained. Using the Ulysses spacecraft, which traversed a wide range of latitudes and distances, the authors analyze in‑situ magnetic field and plasma data for a statistically significant sample of MCs.

First, the MC boundaries are identified in the spacecraft frame, and the cloud axis is determined by a minimum variance analysis (MVA) applied exclusively to the flux‑rope portion of the data, thereby minimizing contamination from surrounding solar‑wind structures. Within each MC, the bulk plasma velocity is examined as a function of time. A striking majority of events display a nearly linear decrease of velocity across the cloud, a hallmark of self‑similar expansion. In a self‑similar scenario the radial size R of the cloud follows a power‑law with heliocentric distance, R ∝ r^ζ, where ζ is a dimensionless expansion index. The authors compute ζ directly from the slope of the velocity profile (α) using the relation ζ = α r / V₀, where V₀ is the leading‑edge speed and r the spacecraft distance from the Sun.

The MCs are then divided into two categories. “Non‑perturbed” clouds retain a linear velocity profile for essentially the entire interval, indicating that they evolve largely undisturbed by external forces. For this group the authors find an average ζ = 1.05 ± 0.34, slightly higher than the inner‑heliosphere value (ζ ≈ 0.91 ± 0.23). This suggests that, beyond 1 AU, the ambient solar‑wind dynamic pressure drops faster than the internal magnetic pressure, allowing the cloud to expand a bit more rapidly. The corresponding scaling of physical parameters—cloud diameter D ∝ r^ζ, mean magnetic field B ∝ r⁻²ζ, and plasma density n ∝ r⁻²ζ—matches the measured trends, confirming the internal consistency of the method.

In contrast, “perturbed” MCs exhibit strongly distorted velocity profiles, often due to interactions with high‑speed streams, preceding or trailing CMEs, or other large‑scale structures. Their expansion index is markedly lower, ζ = 0.28 ± 0.52, indicating that expansion is largely suppressed, and in some cases the cloud may even be compressed. This behavior aligns with numerical MHD simulations that predict a temporal evolution where external pressure fluctuations can halt or reverse the self‑similar expansion of a flux rope.

A particularly interesting subset consists of MCs that encounter a strong magnetic field region, such as another MC. For these interacting events ζ spans a broad range from negative values (compression) to values exceeding 1.5 (over‑expansion). This wide dispersion underscores the sensitivity of MC dynamics to the surrounding solar‑wind environment and highlights that MCs are not isolated entities but can be significantly reshaped by neighboring structures.

The authors also compare the locally derived ζ with the global distance dependence of MC size, magnetic field strength, and plasma parameters. For non‑perturbed clouds, the observed power‑law exponents (size ∝ r¹·⁰⁵, B ∝ r⁻²·¹) are in excellent agreement with the ζ‑based expectations, reinforcing the notion of a quasi‑self‑similar expansion throughout the outer heliosphere. Perturbed clouds show larger scatter, reflecting the variable external forces they experience.

In summary, the study demonstrates that magnetic clouds continue to expand in a self‑similar fashion well beyond 1 AU, but the expansion rate is not universal. Unperturbed clouds expand slightly faster than their inner‑heliosphere counterparts, while clouds that are dynamically disturbed expand more slowly or may even contract. The expansion index ζ, derived directly from in‑situ velocity profiles, provides a robust, local diagnostic that correlates with global scaling laws and with the outcomes of numerical simulations. These findings have practical implications for space‑weather forecasting and for planning deep‑space missions, as they improve our ability to predict the size, magnetic field strength, and plasma conditions of CMEs at planetary distances far from the Sun.