Galactic and Extragalactic Cosmic Rays

• Galactic and extragalactic cosmic rays are highly energetic particles originating from within the Milky Way and beyond, exhibiting unique energy spectra and chemical compositions.
• The transition between these components is marked by spectral features like the knee, second knee, and ankle, with models (ankle, dip, mixed composition) explaining the observed shifts.
• Propagation through interstellar and intergalactic magnetic fields, along with diffusion effects, requires multi-messenger approaches to accurately identify sources and understand anisotropies.

Galactic and extragalactic cosmic rays (CRs) are highly energetic particles—mainly nuclei and electrons—that pervade interstellar, intergalactic, and circumgalactic environments. Their paper encompasses origin, composition, energy spectrum, acceleration processes, propagation through magnetized plasma, and interactions with background fields. The distinction between galactic (primarily originating from within the Milky Way) and extragalactic (originating beyond the Galaxy) components is foundational to understanding the observed all-particle spectrum from MeV up to ZeV energies. The interplay between source astrophysics, cosmic-ray transport, and magnetic field structure across different regimes is central to current research.

1. Models and Energy Scales of the Galactic–Extragalactic Transition

The transition from galactic to extragalactic cosmic rays is observed in the energy range between ≈0.1–10 × 10¹⁸ eV. Competing models for this transition are categorized as “ankle,” “dip,” and “mixed composition” scenarios (Aloisio et al., 2012, Berezinsky, 2013, Aloisio et al., 2017, Cristofari, 26 Nov 2024):

• Ankle Model: The ankle is a spectral hardening feature at ~4–10 × 10¹⁸ eV. In this model, the steeply declining galactic CR spectrum (dominated by high-energy heavy nuclei) intersects a flatter extragalactic component (protons or mixed nuclei). This model requires the galactic component to extend to significantly higher energies than predicted by standard diffusive-shock-acceleration in isolated supernova remnants (SNRs) (Parizot, 2014, Aloisio et al., 2012, Aloisio et al., 2017, Cristofari, 26 Nov 2024).
• Dip Model: This scenario interprets the ankle as a spectral dip produced by energy losses of extragalactic protons propagating through the cosmic microwave background (CMB) via electron-positron pair production: $p + \gamma_{\rm CMB} \to p + e^+ + e^-$ (Berezinsky, 2013, Aloisio et al., 2017). The transition from galactic to extragalactic composition occurs at lower energy, near the second knee (≈(4–7)×10¹⁷ eV), with extragalactic protons dominating above ≈1 EeV.
• Mixed Composition Model: Here, the extragalactic component consists of a distribution of nuclei, typically reflecting the abundances in the interstellar medium. Both the galactic and extragalactic CRs contribute in the transition region, leading to a smooth variation from heavy to light-dominated spectra (Aloisio et al., 2012, Mollerach et al., 2020, Kachelriess, 2022, Cristofari, 26 Nov 2024).

All models are predicated on the intersection of a steeply falling galactic spectrum (with maximal iron energy $$E^{\rm max}_{\rm Fe} \sim 1\times10^{17}\,\text{eV}$$ in the Standard Model) and a flatter or harder extragalactic spectrum, with experimental signatures including spectral changes and composition evolution (Aloisio et al., 2012, Cristofari, 26 Nov 2024).

2. Properties of the Galactic Component at High Energies

Maximum Energy: For shock acceleration in standard SNRs, the Hillas criterion in one formulation is $$E_{\rm max} \approx \xi \,(R_{\rm sh}/\mathrm{pc})\,(u_{\rm sh}/1000\,\mathrm{km\,s}^{-1})\,(B/\mu{\rm G})\,{\rm TeV}$$, with efficiency parameter ξ ranging from 0.1 to 3 depending on environmental amplification (Cristofari, 26 Nov 2024). Only rare, high-energy core-collapse SNe, potentially with amplified fields (by factors of 10–1000), are plausible PeVatrons. Non-resonant streaming instabilities (Bell mechanism) can drive these amplifications transiently.

Composition and Spectral Shape: The position of the knee shifts with nuclear charge Z, implying a rigidity-dependent cutoff—protons at ~few PeV, heavier nuclei proportionally higher (Sveshnikova et al., 2013, Aloisio et al., 2012). After propagation and escape (e.g., with D ∝ E^{0.7}), the observed spectrum steepens above the knee (E^–3.05 or steeper), matching the all-particle energy distribution (Istomin, 2014). The chemical composition transitions from proton-rich at lower energies to heavier elements (iron and intermediate-mass nuclei) at the highest energies achieved by Galactic CRs (Cristofari, 26 Nov 2024).

Source Classes: The main sources considered are SNRs, massive star clusters, and superbubbles. While the standard SNR-GCR connection struggles to attain UHE energies, collective effects in superbubbles or rare, magnetically favorable SNRs may achieve the required E_{\rm max} (Parizot, 2014, Aloisio et al., 2017, Cristofari, 26 Nov 2024).

Propagation: Propagation in the interstellar medium is dominated by diffusion and escape. After the Galactic jet episode (for scenarios invoking energetic past activity), the “knee” is a consequence of energy-dependent escape (D ∝ E^{0.7}) and the subsequent decrease in residence time with energy (Istomin, 2014). Additionally, the composition measured above the knee is shaped by the energy-dependent loss of lighter elements (Sveshnikova et al., 2013).

3. Extragalactic Cosmic Rays and Their Source Populations

Energy Spectrum and Composition: Extragalactic CRs above ≈10¹⁷–10¹⁸ eV are increasingly well described by models involving one or more source populations, each with rigidity-dependent injection and propagation cutoffs (Mollerach et al., 2020, Kachelriess, 2022). The two-population model posits:

• A low-energy extragalactic population (source density ≳10^{-3} Mpc^{-3}, γ ≈ 3.5) dominates from ≈10¹⁷ to a few ×10¹⁸ eV.
• A high-energy population (density ≲10^{-4} Mpc^{-3}, γ ≈ 2–2.4) dominates beyond the ankle, with individual nuclear species cut off at E ≈ Z E_{\rm cut}.

Rigidity dependence $$\Phi_i(E) \propto E^{-\gamma} /\cosh(E/(Z_iE_{\rm cut}))$$ is used for each element, with the magnetic horizon and suppression by intergalactic magnetic fields shaping the observed flux, particularly at lower energies due to finite source density and diffusive propagation (Mollerach et al., 2020).

Candidate Sources: The most promising source classes, constrained by Hillas and Blandford criteria and by the required UHECR emissivity, are luminous and numerous radio galaxies (FR-I, Seyfert), hypernovae, and possibly starburst galaxies if they host a high rate of extreme events (Kachelriess, 2022, Cristofari, 26 Nov 2024). Only these satisfy $E_{\rm max} \sim \Gamma Z e B R_s$ for the highest observed energies. For instance, even with relativistic boosting, UHECR acceleration requires AGN jets or hypernova/GRB shock environments (Kachelriess, 2022).

Anisotropy and Source Distributions: The Pierre Auger Observatory observes statistically significant correlations between the arrival directions of the highest energy CRs (E > 56 EeV) and nearby AGNs (within ~75 Mpc and 3° angular separation) (0711.2256). This correlation rejects isotropy at >99% C.L. and matches the expectation of limited GZK propagation distance (the so-called GZK horizon, ~200 Mpc for 60 EeV protons). However, unambiguous source identification remains challenged by the incomplete AGN catalog and the possible contribution of sources with a similar spatial distribution.

4. Magnetic Fields and Propagation Effects

Galactic and Extragalactic Magnetic Fields: CR trajectories are deflected by both GMF and IGMF, leading to complex arrival direction patterns and energy-dependent anisotropies (Harari et al., 2010, Mollerach et al., 2022). The GMF introduces remapping from halo-incidence to Earth-arrival directions, especially at low rigidities:

• Deflection angle $$\delta\mathbf{u} \approx (q/E) \int \mathrm{d}\mathbf{l} \times \mathbf{B}$$
• Electric field effects from galactic rotation add a small, direction-dependent momentum change:

$$p_f = p_i + (q/c^2) \int \mathrm{d}l \cdot [(V - V_\odot) \times B]$$

• The combined impact modifies both amplitude and phase of the observed dipole anisotropy, producing the observed right-ascension phase transition at EeV energies (Mollerach et al., 2022, Harari et al., 2010).

Compton-Getting and Higher-Order Anisotropies: At high energies, the Compton-Getting dipole (from the motion of the observer with respect to the frame where CRs are isotropic) is modulated and can be suppressed by magnetic deflections and electric field effects; higher-order harmonics emerge as rigidity decreases (Harari et al., 2010, Mollerach et al., 2022).

Magnetic Horizon Effect: The finite coherence length and amplitude of extragalactic magnetic fields, combined with sparse source density, generate an energy-dependent spectral suppression—the magnetic horizon—below which particles cannot reach Earth within a Hubble time. This is especially significant for the “high-energy” extragalactic component (Mollerach et al., 2020).

5. Observational Signatures: Spectrum, Composition, and Anisotropy

All-Particle Spectrum: The spectrum exhibits the “knee,” “second knee,” “ankle,” and GZK cutoff (or “instep,” per recent notation) (Kachelriess, 2022):

• The knee (few PeV): Steepening of the galactic CR spectrum; interpreted as maximum energy for standard SNRs or as a leakage feature.
• The second knee (~(4–7)×10¹⁷ eV): Marks the fading of the galactic heavy component and onset of extragalactic CR dominance in most models (Berezinsky, 2013, Aloisio et al., 2012, Parizot, 2014, Kachelriess, 2022).
• The ankle (~3–10×10¹⁸ eV): Hardening usually marking the full dominance of the extragalactic component, or a propagation-induced feature (proton dip).
• The GZK cutoff (~5×10¹⁹ eV): Suppression due to energy losses from photopion production on the CMB for UHE protons.

Composition Evolution: The composition changes from predominantly protons below the knee to heavier nuclei near and above the knee; at higher energies, scenarios diverge—Auger data indicate a trend toward heavier composition above the ankle, while HiRes/TA data support a light (proton-dominated) UHE composition (Berezinsky, 2013, Parizot, 2014, Buitink et al., 2016, Kachelriess, 2022). High-precision Xmax measurements (e.g., with LOFAR, Pierre Auger Observatory) show the extragalactic component between 10¹⁷–10¹⁸ eV is mixed but light-dominated, with ~80% light (He-dominated) nuclei in the LOFAR analysis (Buitink et al., 2016).

Anisotropy: The expected dipole anisotropy amplitude and right-ascension phase both evolve with energy, reflecting the transition from galactic-dominated to extragalactic-dominated regimes and the compounding impact of GMF deflections and velocity-dependent effects (Mollerach et al., 2022, Giacinti et al., 2011). Observed anisotropies and their limits constrain both the composition and the allowed maximum energy of galactic sources.

6. Theoretical and Experimental Challenges

Limitations in Source Models: The ankle model demands unexpectedly strong Galactic accelerators (to EeV energies), while the dip and mixed composition models face tension with observed composition—specifically, the need to explain a heavy composition in the Auger data above several EeV (Aloisio et al., 2012, Berezinsky, 2013, Cristofari, 26 Nov 2024).

Propagation and Interpretation Ambiguities: Modeling the observed spectrum and composition requires integrating source injection spectra, rigidity-dependent cutoffs, energy-dependent escape, propagation losses (pair production, photopion production, photodisintegration), magnetic field structure, and the spatial/temporal source distribution (Mollerach et al., 2020, Giacinti et al., 2015, Aloisio et al., 2017). Numerical frameworks such as CRPropa enable detailed, multi-scale simulations incorporating these effects (Batista et al., 2013).

Multi-messenger Context: Observations in gamma rays, X-rays, and neutrinos—combined with CR data—form a multi-messenger approach essential for source identification, constraining emission models, and clarifying the role of dark matter annihilation (whose gamma and neutrino signals must be separated from CR-generated backgrounds) (Picozza et al., 2012, Allahverdi et al., 2011).

7. Implications and Future Prospects

The detailed picture emerging from recent research indicates:

• The transition between galactic and extragalactic cosmic rays is neither abrupt nor universal in energy, but model-dependent and composition-sensitive, occurring most plausibly at or below the “ankle,” and potentially as low as the “second knee” (Berezinsky, 2013, Aloisio et al., 2017, Cristofari, 26 Nov 2024).
• Accurately characterizing the high–energy end of the galactic spectrum—its composition, maximum energy, and spectral shape—remains essential for robust discriminations among models (Cristofari, 26 Nov 2024).
• Next-generation gamma-ray observatories (CTA, LHAASO, SWGO) and low-threshold extensions to existing CR experiments (AugerPrime, TAx4, etc.) are instrumental for probing the Pevatron candidate population and the galactic-extragalactic transition region.
• Ongoing multi-messenger efforts (including neutrino and gamma-ray correlation studies) help to distinguish among source classes (AGN, starburst, hypernovae) and will further resolve inconsistencies in the energy spectrum, mass composition, and anisotropy data (Kachelriess, 2022).
• Understanding the impact of intervening magnetic fields, both Galactic and extragalactic, is a prerequisite for source identification and for interpreting the observed large-scale anisotropies and arrival directions at the highest energies (Mollerach et al., 2022, Harari et al., 2010).

In conclusion, the paper of galactic and extragalactic cosmic rays involves an interplay of astrophysical source modeling, propagation in turbulent and large-scale magnetic fields, energy-dependent composition evolution, and anisotropy analysis—a multifaceted framework connecting cosmic-ray physics with high-energy astrophysics and particle astrophysics. The accumulated experimental and theoretical insights have narrowed scenarios for the galactic-extragalactic transition but definitive resolution requires further progress in high-precision composition measurements, identification of individual sources, and in situ characterization of cosmic magnetic fields across all intermediate and ultra-high energy regimes.