The Cosmic-ray Knee as a Local Signature of Nearby PeVatrons

TL;DR

This work examines whether the cosmic-ray knee at $\sim 4\ \mathrm{PeV}$ is a Galaxy-wide feature or a local signature from nearby PeVatrons. Using CR propagation in an anisotropic Galactic magnetic field and interstellar medium, it shows that the knee's origin hinges on the birth rate of PeVatrons and the presence of nearby powerful sources, favoring a local-knee scenario for low birth rates. The study identifies a nearby, middle-aged source at $\sim 1$ kpc (ages $\sim 0.1$–1 Myr) as the most plausible contributor to the knee, with the Cygnus Cocoon highlighted as a strong candidate; gamma-ray observations and anisotropy constraints are used to test this scenario. Limitations include neglecting heavier nuclei, Southern sky sources, and spatially dependent diffusion; future work with full-sky data and more elaborate transport models could further constrain the local-knee hypothesis and its association with observed UHE gamma-ray structures.

Abstract

A "knee" in the cosmic-ray spectrum, characterized by a sudden steepening of the spectral shape at $\sim 4$ PeV, may be interpreted either as a global feature of Galactic cosmic rays or as a local signature. In the former scenario, cosmic-ray spectra throughout the Galaxy would be similar to that observed in the solar neighborhood, and the knee would be a common feature of the cosmic-ray sea. In the latter scenario, the PeV cosmic-ray flux varies across the Galactic disk, and the knee is dominantly contributed by a small number of nearby sources. By simulating cosmic-ray propagation in the Galactic magnetic field and interstellar medium, we show that the two scenarios correspond to different regimes of the birth rate of PeV proton accelerators and depend on the presence of powerful nearby sources. By comparison with both cosmic-ray and gamma-ray observations, we find that a local knee would be best explained by sources located at distances of order $\sim1$ kpc and with ages in the range 0.1-1 Myr, with the Cygnus Cocoon being a particularly promising candidate.

Figures (6)

• Figure 1: Counts of 1 PeV cosmic rays normalized to the maximum pixel (top row) and the maximum fraction originating from a single source (bottom row) for locations across the disk with $|z|<0.17$ kpc, sampled in spacial bins of 0.4 kpc in the x and y directions. Sources are assumed to follow a pulsar distribution in space and uniform distribution in time, and steadily emit cosmic rays during a lifetime of 100 kyr. The left, middle, and right panels correspond to source birth rates of 10%, 1%, and 0.1% of a baseline, supernova-like rate of $0.01\,\rm yr^{-1}$, respectively. The black star marks the position of the Sun.
• Figure 2: Proton spectrum at the sun's position from a fiducial source at 1 kpc away in the direction of the Galactic center, with an age of 10 kyr (red), 100 kyr (orange), 1 Myr (green), and 10 Myr (blue). The cosmic rays are injected following an $dN/dE\propto E^{-2}\exp(-E/3\,{\rm PeV})$ spectrum with a total energy of $10^{51}$ erg from the proton rest mass to 100 PeV. The black data points show the measurement of the proton spectrum by LHAASO LHAASOKnee.
• Figure 3: Gamma-ray emission at 100 TeV produced by cosmic rays diffusing from test sources aged 10 kyr to 10 Myr, through interactions with neutral hydrogen. The proton spectrum is assumed to follow $dN/dE_p\propto E_p^{-2}\exp(-E/3\,{\rm PeV})$ as in Figure \ref{['fig:spectrum_source']} and is normalized to the LHAASO data point at 3 PeV. The total cosmic-ray injection energy above the proton rest mass in the four cases are $10.5$, $0.7$, $3.9$ and $29.5$$\times 10^{51}$ erg, respectively.
• Figure 4: Cosmic-ray spectrum (left) and longitudinal distribution of the diffuse gamma-ray emission from their interaction with neutral (HI) and molecular hydrogen (H$_2$) (right) from a model where a large population of cosmic-ray sources following the pulsar distribution dominantly contribute to cosmic rays below 100 TeV and a single source, the Cygnus Cocoon, dominantly contributes to the knee.
• Figure 5: Same as Figure \ref{['fig:1PeV']}, but with the source birth rate fixed at $f_{\rm SN}=1\%$ and the source lifetime varied as $\Delta t =$ 1 Myr, 100 kyr, and 10 kyr.