Role of particle interactions in high-energy astrophysics

1. Role of particle interactions in high-energy astrophysics Uncorrelated fluxes Hadronic interactions Air showers Thomas K. Gaisser

2. Particle interactions for cosmic rays • Atmosphere • Nuclear targets • Nuclear projectiles • Forward region • High energy • “Minimum bias” • Limited guidance from accelerator data • Astrophysics • Astrophysical uncertainties are more severe Thomas K. Gaisser

3. Particle production: two scenarios • Inject beam of particles • follow secondary cascades in target • Earth or stellar atmosphere • Inject particles from cosmic accelerators • diffuse in low-density gas • occasional interactions Thomas K. Gaisser

4. Equation for change in particle i in delta distance Primary particles from all directions per unit sphere Basic formulation Thomas K. Gaisser

5. Example: production of diffuse g in ISM Thomas K. Gaisser

6. p0 2 g in diffuse ISM Thomas K. Gaisser

7. Diffuse galactic g spectrum High-energy spectrum flatter than 2.7. Possible contribution from interactions with source spectrum? Thomas K. Gaisser

8. Cascades in the atmosphere

9. Unstable hadrons: interaction or decay? • Decay length, p+/- : gctp (cm) • in (g/cm2)  dp = rgctp = rEptpc / mpc2 • lp = dp defines rcritical = 0.018 (lp / 100 g/cm2) / Ep • Earth’s atmosphere at X = 100 g/cm2 : r ~ 10-4 • this density exceeds rcritical when Ep > ep, • where ep ~ 115 GeV: Ep > ep, interaction > decay • Around astrophysical acceleration sites • r < rcritical even for very high Ep Thomas K. Gaisser

10. Boundary conditions & scaling • Air shower, primary of mass A, energy E0 : • N(X=0) = A d (E- E0 /A) for nucleons • N(X=0) = 0 for all other particles • Uncorrelated flux from power-law spectrum: • N(X=0) = fp(E) = K E-(g+1) • ~ 1.7 E-2.7 ( cm-2 s-1 sr-1 GeV-1 ), top of atmosphere • Fji( Ei,Ej) has no explicit dimension, F  F(x) • x = Ei/Ej &∫…F(Ei,Ej) dEj / Ei  ∫…F(x) dx / x2 • Expect scaling violations from mi, LQCD ~ GeV Thomas K. Gaisser

11. Example: flux of nucleons l ~ constant, leading nucleon only Separate X- and E-dependence; try factorized solution, N(E,X) = f(E) g(X): Separation constant LN describes attenuation of nucleons in atmosphere Uncorrelated fluxes in atmosphere

12. Evaluate LN: Flux of nucleons: K fixed by primary spectrum at X = 0 Nucleon fluxes in atmosphere Thomas K. Gaisser

13. Account for p  n CAPRICE98 (E. Mocchiutti, thesis) Comparison to proton fluxes

14. Primary spectrum of nucleons • Plot shows • 5 groups of nuclei • plotted as nucleons • Heavy line is E-2.7 fit to protons Thomas K. Gaisser

15. Production spectrum of p± at high energy: Decay probability per g/cm2 m production spectrum: Note extra power of 1/E for E >> ep = 115 GeV p±  m± in the atmosphere Thomas K. Gaisser

16. Comparison to measured m flux • High-energy analysis • o.k. for Em > TeV • Low-energy: • dashed line neglects m decay and energy loss • solid line includes an analytic approximation of deday and energy loss by muons Thomas K. Gaisser

17. Uncertainties for uncorrelated spectra • p  K+L gives dominant contribution to atmospheric neutrino flux for En > 100 GeV • p  charm gives dominant contribution to neutrino flux for En > 10 or 100 or ? TeV • Important as background for diffuse astrophysical neutrino flux because of harder spectrum Thomas K. Gaisser

18. Calculations of air showers • Cascade programs • Corsika: full air-shower simulation is the standard • Hybrid calculations: • CASC (R. Engel, T. Stanev et al.) uses libraries of presimulated showers at lower energy to construct a higher-energy event • SENECA (H-J. Drescher et al.) solves CR transport Eq. numerically in intermediate region • Event generators plugged into cascade codes: • DPMjet, QGSjet, SIBYLL, VENUS, Nexus Thomas K. Gaisser

19. 1 x1 x2 s12 = x1x2s = 2mx1x2Elab > few GeV resolves quarks/gluons in target; Gluon structure function: g(x) ~ (1/x2)p, p ~ 0.2 …. 0.4 E1 E3 E2 Hadronic interactions at UHE • Scaling assumption for fast secondaries is equivalent to assuming distribution of final state radiation from leading di-quark is independent of beam energy • At higher energy more complex interactions may be important Thomas K. Gaisser

20. {…} is probability of at least one interaction at impact parameter b s is nucleon-nucleon cross section T(b) is number of target nucleons at impact parameter b sN is partial cross section for N wounded nucleons Geometrical model of p-A interactions Thomas K. Gaisser

21. Wounded nucleons & inelasticity Mean number of wounded nucleons: spA ~ A⅔ , so <Nw> ~ A⅓ ZNN(air) = P1∫ x1.7 dx + P2 ∫ x1.7 log(1/x) dx + ½ P3 ∫ x1.7 [log(1/x)]2 dx ≈ 0.3 Thomas K. Gaisser

22. x1 x2 s12 = x1x2s = 2mx1x2Elab > few GeV resolves quarks/gluons in target; Gluon structure function: g(x2) ~ (1/x2)p, p ~ 0.2 …. 0.4 E1 E3 E2 Analogy of pp and p-nucleus physics • If Atarget = Atarget(E) then • NW would increase with E • Inelasticity ≡ 1 - <x(E)> would also increase ~ A⅓ • Something like this happens with pp collisions (M. Strikman, R. Engel) • Amount of scaling violation is uncertain Thomas K. Gaisser

23. HiRes new composition result: transition occurs before ankle G. Archbold, P. Sokolsky, et al., Proc. 28th ICRC, Tsukuba, 2003 Model-dependence of Xmax Sybil 2.1 (some screening of gluons at small x) QGSjet (strong increase of gluon multiplicity at small x) • Xmax ~ l log(E0 / A) with scaling • With increase of inelasticity, • Primary energy is further subdivided: • Xmax ~ l log{ E0 / (A * (1 - <x(E)>) ) }

24. 1 Inelasticity 0 17 15 16 18 19 Example of increasing inelasticity Effect is limited because energy not carried by leading nucleon is divided among pions, which divide the remaining energy, as in scaling. Such a large change would have a significant effect on interpretation -in terms of composition -of energy in a ground array