Time-dependent cosmic-ray escape from wind bubbles: hard spectra formation
Abstract
Overview: Wind-driven bubbles are dynamic systems that can accelerate cosmic rays, depending on their physical properties, up to very high energies. We investigate how a time-dependent description of the particle transport may impact the escaping cosmic-ray flux. Model: The wind bubble system is modeled as spherically symmetric. Cosmic rays are continuously injected at the position of the termination shock and propagate through advection and diffusion until the escape at the time-dependent position of the forward shock, which is treated as a free escape boundary. Methods: The one-dimensional spherical time-dependent transport equation is solved by transforming it into the corresponding set of stochastic differential equations, and integrated with a modified version of the open source cosmic-ray propagation framework CRPropa. Results: We find that, during the wind driven phase, the downstream escaping spectra from wind bubbles can be harder than ∼ E−2, the conventional expectation from diffusive shock acceleration. Depending on the turbulence model the initial energy spectrum can be significantly suppressed at lowest energies, which could be an observable feature to distinguish between different turbulence realizations. This effect could lead to an efficient confinement of low energy particles, potentially leading to observable implication in terms of multi-messenger radiation and cosmic-ray accumulated grammage within the bubble.
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BibTeX
@misc{merten2026timedependent,
title = {{Time-dependent cosmic-ray escape from wind bubbles: hard spectra formation}},
author = {Lukas Merten and Sophie Aerdker and Enrico Peretti},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.12390},
eprint = {2606.12390},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.12390},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Time-dependent cosmic-ray escape from wind bubbles: hard spectra formation
AU - Lukas Merten
AU - Sophie Aerdker
AU - Enrico Peretti
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2606.12390
UR - https://arxiv.org/abs/2606.12390
AB - Overview: Wind-driven bubbles are dynamic systems that can accelerate cosmic rays, depending on their physical properties, up to very high energies. We investigate how a time-dependent description of the particle transport may impact the escaping cosmic-ray flux. Model: The wind bubble system is modeled as spherically symmetric. Cosmic rays are continuously injected at the position of the termination shock and propagate through advection and diffusion until the escape at the time-dependent position of the forward shock, which is treated as a free escape boundary. Methods: The one-dimensional spherical time-dependent transport equation is solved by transforming it into the corresponding set of stochastic differential equations, and integrated with a modified version of the open source cosmic-ray propagation framework CRPropa. Results: We find that, during the wind driven phase, the downstream escaping spectra from wind bubbles can be harder than ∼ E^−2, the conventional expectation from diffusive shock acceleration. Depending on the turbulence model the initial energy spectrum can be significantly suppressed at lowest energies, which could be an observable feature to distinguish between different turbulence realizations. This effect could lead to an efficient confinement of low energy particles, potentially leading to observable implication in terms of multi-messenger radiation and cosmic-ray accumulated grammage within the bubble.
ER -