34-EFT.WP.Astro.Acceleration v1.0 | Chapter 9 Cosmic Rays: Source Classes & Observables

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Chapter 9 Cosmic Rays: Source Classes & Observables

I. Abstract & Scope
This chapter stratifies cosmic-ray source classes, establishes priors, standardizes the observable bundle, and defines the mapping from acceleration channels to source injection Q_src(E,Z), then to observables {N(E), Phi(E)} via workflows M60-*. Channel attribution and multi-messenger consistency criteria and benchmarks are provided.

II. Dependencies & References

• Unified symbols & do-not-confuse: Chapter 2 Tab. 2-1 and P12-*.
• Kinematics & channels: Chapter 3 S20-; reconnection & shear: Chapter 4 S30-, Chapter 5 S40-; comparators: Chapter 6 S45-.
• Spectrum formation & transport: Chapter 7 S50-, Chapter 8 S52-.
• Data & reproducibility: Data.DatasetCards v1.0, Methods.Repro v1.0, Methods.Inference v1.0.

III. Normative Anchors (added in this chapter, M60-*)

• M60-1 (Source Stratification & Priors): Define classes C = {SNR, PWN, AGN_Jet, GRB, Starburst, GC, Cluster, Magnetar, …}; register geometric scales, B_vec, medium fields, and EM–HE proxies for each; establish priors π_c(θ_c).
• M60-2 (Observable Bundle): Standardize O = { dN/dE, Phi(E), alpha_spec(E), X_Z(E), delta_aniso(E), Phi_gamma(E), Phi_nu(E), Pi(E), timing } with units and uncertainty reporting.
• M60-3 (Injection Mapping): From {A_rec(E), A_shear(E)} and {tau_esc(E), tau_loss(E)} build
  Q_src(E,Z; θ) = Q0_Z * ( E / E0 )^{-alpha_inj(Z)} * f_cut(E; E_max(Z)),
  rigidity R = p c_ref / ( Z * e_charge ); rigidity break R_br gives E_br(Z) = Z * e_charge * R_br * c_ref.
• M60-4 (Propagation & Synthesis): Per class, call Chapter 8 closure {D(E), A_loss(E), tau_esc(E)} to obtain N(E) and Phi(E); apply line-of-sight and response corrections where needed.
• M60-5 (Multi-Messenger Consistency): From Q_src and medium fields synthesize secondary Phi_gamma(E) and Phi_nu(E) and joint them with the CR observables in the likelihood.
• M60-6 (Joint Likelihood & Evidence): L = L_spec + L_comp + L_aniso + L_gamma + L_nu + L_polar + L_timing; output {posterior, evidence}.
• M60-7 (Channel Attribution & Dominant Bands): Estimate {w_rec(E), w_shear(E)} and dominance eta_dom(E) (Chapter 6); emit energy-band masks for spectrum and transport workflows.
• M60-8 (Benchmarks & Regression): Define minimal benchmarks and stratified CV per class; maintain versioned baselines.

IV. Body Structure

I. Source Classes & Physical Priors

• SNR: shell/contact instabilities shape the S tensor; local sheet reconnection coexists; L ~ 1–10 pc.
• PWN: strong magnetization; shear–reconnection coupling significant; B_vec controls HE losses and E_max(Z).
• AGN_Jet (incl. blazar/lobe): large-scale shear and sheet reconnection alternate in dominance; multi-zone transport prominent.
• GRB: prompt/afterglow stages; sheet geometry evolves rapidly; R_rec and sigma_shear time-variable.
• Starburst / GC / Cluster: multi-zone diffusion and advection dominate; strong constraints from secondaries and anisotropy.
• Magnetar: high tension fields and fast reconnection; ToA/polarization sensitive to sheet activity.

II. Observables & Mappings

• Spectrum & flux: dN/dE, Phi(E); local index alpha_spec(E) = - d ln N / d ln E.
• Composition: X_Z(E) with Σ_Z X_Z(E) = 1; rigidity breaks unified by R_br.
• Anisotropy: diagnostic delta_aniso(E) ≈ ( 3 * D(E) / c_ref ) * | ∇ n | / n (used diagnostically, not a new minimal equation).
• Polarization & timing: Pi(E); light curves/delays. Any ToA quantity must record both forms with explicit path and measure:
  T_arr = ( 1 / c_ref ) * ( ∫_{gamma(ell)} n_eff d ell ) and T_arr = ( ∫_{gamma(ell)} ( n_eff / c_ref ) d ell ), with delta_form.
• Multi-messenger: Phi_gamma(E), Phi_nu(E) jointly constrain injection and propagation with the medium/density fields.

III. Injection–Transport–Observation Harmonization

• Injection: via M60-3 from {A_acc, tau_*} to Q_src; infer alpha_inj and E_max(Z) from Chapter 7 {alpha_loc, E_max} and harmonize with Chapter 8 {D, A_loss}.
• Transport: via M60-4 solve n(E,r) and Phi_obs(E); use algebraic one-zone closure or multi-zone series/parallel equivalents.
• Observation: assemble O with unit/dimension audits; fold EM/neutrino channels into the joint likelihood M60-6.

IV. Methods & Flows (M-series)

• M60-1 (Register Class Priors): For each c ∈ C, create parameter cards {L, B_vec, u_adv, ρ(r), θ_c} and priors π_c(θ_c).
• M60-2 (Observable Packaging): Build dataset cards with units, conventions, systematics, and covariance.
• M60-3 (Injection Generation): From {A_rec, A_shear} and {tau_esc, tau_loss} generate Q_src(E,Z); convert R_br to E_br(Z).
• M60-4 (Propagation Solve): Call Chapter 8 to obtain {N(E), Phi(E)} and spatial distributions; apply line-of-sight and instrument response as required.
• M60-5 (Multi-Messenger Synthesis): From Q_src and medium fields compute {Phi_gamma, Phi_nu}; fit jointly with CR observables.
• M60-6 (Joint Inference): Minimize L and output {posterior, evidence} and channel weights {w_rec, w_shear}.
• M60-7 (Benchmarks & Regression): For each class, set benchmark subsets and regression tests; track versions and compatibility.

V. Cross-References within/beyond this Volume

• Channels & kinematics: Chapters 3–5 (A_acc = A_rec + A_shear); comparator dominance eta_dom(E): Chapter 6.
• Spectrum & breaks: Chapter 7 (alpha_loc, E_br, E_max).
• Transport & losses: Chapter 8 (D(E), A_loss(E), tau_esc(E)).
• Data & reproducibility: dataset/model/pipeline cards and Methods.Repro v1.0.

VI. Validation, Criteria & Counterexamples

1. Positive criteria:
   • An energy band with tau_acc(E) < min{ tau_loss(E), tau_esc(E) } and hardening in alpha_spec(E) consistent with class priors.
   • Rigidity scaling: E_br(Z) ∝ Z.
   • {Phi_gamma, Phi_nu} and Phi(E) jointly explained by the same Q_src and {D, A_loss} in a common window.
2. Negative criteria:
   • Setting w_rec or w_shear to zero does not reduce evidence → corresponding channel nonessential.
   • Failure of rigidity scaling (E_br(Z) not linear in Z), or delta_aniso(E) inconsistent with the energy scaling of D(E).
3. Contrasts:
   • Under fixed transport, compare {reconnection only, shear only, reconnection+shear} injections and their impacts on {alpha_spec, X_Z, delta_aniso}.
   • Fit ToA with both forms in parallel and record delta_form to test timing/delay–path consistency.

V. Figures & Tables (this chapter)

4. Tab. 9-1 Source-class stratification & priors (fields: Class / Geometry / B_vec / Medium / Key Scales / Priors).
5. Tab. 9-2 Observable bundle & units (dN/dE, Phi(E), X_Z(E), delta_aniso(E), Pi(E), Phi_gamma, Phi_nu).
6. Tab. 9-3 Injection parameters & default priors (alpha_inj, E_max(Z), R_br, Q0_Z, f_cut).
7. Tab. 9-4 Dataset-card template (fields: Instrument / Band / Unit / Calibration / Systematics / Covariance / See).
8. Tab. 9-5 Criteria & comparator checklist (rigidity scaling, channel dominance, anisotropy scaling, ToA dual-form consistency).