Dust maps offer a new way to estimate cosmic-ray scattering in a star-forming cloud

Why look at dust to study cosmic rays?

Cosmic rays are energetic charged particles that help set the ionisation and chemistry of molecular clouds, the cold gas and dust where stars form. Their paths are influenced by magnetic fields. When a particle encounters magnetic fluctuations at the right scale, it can be scattered, changing its direction. Scattering affects the distance it travels before its path is substantially redirected; that distance is called the mean free path.

Scientists often describe cosmic-ray transport with a diffusion coefficient. But values inferred from observations averaged across large areas can blur differences between local environments. Szu-Ting Chen and colleagues set out to estimate scattering in individual parts of NGC 1333, a nearby star-forming cloud complex, and compare the wider cloud with IRAS 4A, a much smaller protostellar core within it.

From polarisation patterns to scattering estimates

The team analysed James Clerk Maxwell Telescope POL-2 observations of nine regions in NGC 1333, and higher-resolution ALMA observations of two regions in IRAS 4A. Polarised emission from aligned dust grains traces the orientation of the magnetic field projected on the sky. The researchers measured how those orientations varied with separation, using a statistical tool called a structure function to estimate the scale-by-scale power in magnetic fluctuations.

They also estimated magnetic-field strengths using the Davis–Chandrasekhar–Fermi method, which combines field-angle dispersion with gas density and velocity measurements. Finally, they applied quasi-linear gyro-resonant theory: a model that connects magnetic fluctuation power at a particle’s resonant scale to its rate of scattering and an effective diffusion coefficient. In plain language, the method estimates how strongly fluctuations at the relevant scale can redirect a cosmic ray.

These are model-based estimates, not direct tracking of cosmic-ray trajectories. The observations constrain the calculation only over a limited range of spatial scales, corresponding to proton energies of about 0.24–5.3 peta-electronvolts (PeV) in the NGC 1333 regions and 10–57 tera-electronvolts (TeV) in IRAS 4A. Several of the nine cloud regions did not provide enough usable spectral information for a diffusion estimate.

What the study found

Within the energy ranges constrained by the measured fluctuations, the estimated coefficients span roughly 3 × 10²⁸ to 10³¹ square centimetres per second. Estimates differ substantially from region to region. The authors find stronger scattering where the magnetic-field orientations have greater angular dispersion, although that dispersion reflects both small-scale fluctuations and larger-scale field curvature.

A comparison between IRAS 4A and the larger NGC 1333 region that contains it suggests that scattering in the core may be stronger by one to two orders of magnitude. This is not a direct, like-for-like measurement at the same observed energies: the comparison requires extending the larger region’s result beyond its measured energy interval. The authors therefore describe the core estimates as indicative and say a larger sample is needed to confirm the difference.

The key scale-related result is that the inferred scattering mean free paths exceed the sizes of the individual regions analysed. That means the reported coefficients should not be read as evidence that cosmic rays diffuse within each small region. Rather, they characterise local scattering conditions. A cloud-wide diffusive description would require particles to encounter multiple regions, potentially with different scattering rates.

Where the uncertainty lies

The estimates depend on assumptions as well as measurements. Dust polarisation shows only the plane-of-sky field orientation, averaged through the emitting material; it does not reveal the full three-dimensional field. The magnetic-field strength calculation also relies on assumptions about the gas and field, and the authors note that density, linewidth and polarisation may not trace exactly the same material. Their model assumes a simplified magnetic geometry and uses quasi-linear theory, which may be less reliable when fluctuations are strong or coherent.

The energy limits matter too. Values quoted at 1 GeV are extrapolations, not direct constraints from these polarisation data. For NGC 1333, changing the assumed spectrum of unresolved fluctuations changes the extrapolated estimates by about a factor of 30. The paper also notes that limited resolution can hide small-scale fluctuations, affecting the inferred scattering.

The manuscript is available as an arXiv preprint. Its title page identifies it as an Astronomy & Astrophysics manuscript, but the received and accepted dates are left unspecified in the supplied text. As with any preprint, these results should be treated as research in progress rather than as a settled measurement. The study offers a method for linking observed magnetic structure to local cosmic-ray scattering; establishing how those local conditions combine into transport across an entire cloud remains an open question.