[Paper Review] What sources are the dominant Galactic cosmic-ray accelerators?

Jacco Vink|arXiv (Cornell University)|Dec 20, 2022

Astrophysics and Cosmic Phenomena4 citations

TL;DR

This paper argues that while supernova remnants (SNRs) are the dominant sources of Galactic cosmic rays up to ~10 TeV, a second component—potentially from star-forming regions or pulsars—must account for cosmic rays up to the 'knee' at ~3×10¹⁵ eV. Using H.E.S.S. observations of Westerlund 1, it shows that a low diffusion coefficient (~10²⁶ cm² s⁻¹) and high Alfvén speed (>100 km s⁻¹) enable second-order Fermi acceleration to PeV energies, suggesting star-forming regions can act as collective PeVatrons.

ABSTRACT

Supernova remnants (SNRs) have long been considered to be the dominant source of Galactic cosmic rays, which implied that they provided most of the energy to power cosmic rays as well as being PeVatrons. The lack of evidence for PeV cosmic rays in SNRs, as well as theoretical considerations, has made this scenario untenable. At the same time the latest LHAASO and other gamma-ray results suggest that PeVatrons lurk inside starforming regions. Here I will discuss why SNRs should still be considered the main sources of Galactic cosmic rays at least up to 10 TeV, but that the cosmic-ray data allow for a second component of cosmic rays with energies up to several PeV. This second component could be a subset of supernovae/SNRs, reacceleration inside starforming regions, or pulsars. As a special case I show that the recent observations of Westerlund 1 by H.E.S.S. suggest a low value of the diffusion coefficient inside this region, which is, together with an Alfvén speed > 100 km/s, a prerequisite for making a starforming region collectively a PeVatron due to second order Fermi acceleration.

Motivation & Objective

• To resolve the long-standing PeVatron problem: why SNRs fail to explain the cosmic-ray 'knee' at ~3×10¹⁵ eV despite being the dominant source of Galactic cosmic rays.
• To evaluate whether star-forming regions, particularly superbubbles like Westerlund 1, can act as collective PeVatrons through second-order Fermi acceleration.
• To reconcile observational gamma-ray data from LHAASO and H.E.S.S. with theoretical models of cosmic-ray acceleration and diffusion in dense, magnetized environments.
• To assess the energetic and physical conditions required for a star-forming region to sustain PeV cosmic-ray acceleration, including diffusion coefficient, magnetic field strength, and Alfvén speed.

Proposed method

• Uses the diffusion-reaction equation to model cosmic-ray transport and acceleration in a spherical shell, with the diffusion coefficient D derived from the gamma-ray morphology and timescale.
• Applies the second-order Fermi acceleration timescale τ_acc ≈ 8D₁/V_s² to estimate acceleration efficiency, assuming Alfvén speed V_A ≥ 100 km s⁻¹.
• Estimates the diffusion coefficient D from the shell radius R_shell and escape timescale τ using R_shell = √(6Dτ), yielding D ≈ 3×10²⁶ cm² s⁻¹ at 100 TeV.
• Uses the Alfvén speed formula V_A = B/√(4π·1.4·n_H·m_p) to infer required magnetic field and density conditions for high V_A and low D.
• Compares the observed gamma-ray spectrum of Westerlund 1 (cutoff at ~40 TeV) with theoretical expectations to infer that cosmic rays are accelerated to >100 TeV before escape.
• Evaluates the energetic budget by comparing the required D and τ to the observed cosmic-ray energy density and supernova rate, ensuring consistency with U_cr ≈ 1 eV cm⁻³ and ˙E_sn ≈ 10⁴¹ erg s⁻¹.

Experimental results

Research questions

• RQ1 Can supernova remnants alone explain the cosmic-ray 'knee' at ~3×10¹⁵ eV, given their observed gamma-ray spectral cutoffs below 100 TeV?
• RQ2 What physical conditions in star-forming regions like Westerlund 1 enable second-order Fermi acceleration to reach PeV energies?
• RQ3 Is the observed gamma-ray morphology and spectrum of Westerlund 1 consistent with a low diffusion coefficient and high Alfvén speed?
• RQ4 Can the collective energy input from multiple supernovae and stellar winds in a superbubble sustain PeV cosmic-ray acceleration?
• RQ5 What constraints do the observed cosmic-ray spectrum hardening at ~10 TeV and PeV gamma-ray sources from LHAASO place on the existence of a second, high-energy cosmic-ray component?

Key findings

• The observed gamma-ray spectrum of Westerlund 1 shows a cutoff at ~40 TeV, implying that cosmic-ray protons are accelerated to energies above 100 TeV before escape, consistent with PeVatron activity.
• The inferred diffusion coefficient at 10 TeV is D ≈ 10²⁶ cm² s⁻¹, which is close to the Bohm diffusion limit (η ≈ 3), indicating strong magnetic turbulence.
• A high Alfvén speed of V_A ≥ 100 km s⁻¹ is required, which implies a low internal hydrogen density n_H ≤ 0.2 cm⁻³ and a magnetic field B ≈ 10 μG, consistent with conditions in evolved superbubbles.
• The combination of low diffusion and high Alfvén speed enables second-order Fermi acceleration to reach PeV energies within ~200,000 years, matching the age of Westerlund 1.
• The energy budget is consistent with the observed cosmic-ray energy density and supernova rate, supporting the idea that star-forming regions can be collective PeVatrons.
• The paper concludes that while SNRs are the dominant source of Galactic cosmic rays below ~10 TeV, a second component—potentially from star-forming regions or a subset of SNRs—must account for cosmic rays up to the 'knee'.