Neutrino Flavor Ratios as a Probe of Cosmic Ray Accelerators( 予定 ) Norita Kawanaka (UTokyo) Kunihito Ioka (KEK, Sokendai)

Neutrino Flavor Ratios as a Probe of Cosmic Ray Accelerators( 予定 ) Norita Kawanaka (UTokyo) Kunihito Ioka (KEK, Sokendai)

Introduction High Energy Neutrinos are produced in Cosmic Ray Accelerators (GRBs, AGNs, hypernovae, etc.) via hadronic interactions Cosmic ray protons + ambient matter p + p π + µ + +ν µ e + +ν µ +ν e +ν µ or π µ +ν µ e +ν µ +ν e +ν µ Cosmic ray protons + photon Lield Φ 0 0 νe : Φ νµ =1: 2 : 0 0 : Φ ντ p +γ π + µ + +ν µ e + +ν µ +ν e +ν µ

Neutrino Flavor Composition!cε ν / Δm 2 c 4 propagation effect (distance >> ) observed Φ νe mixing matrix 0 0 0 : Φ νµ : Φ ντ =1: 2 : 0 Φ νe : Φ νµ : Φ ντ 1:1:1 à For initial Llux ratio, the observed ratio is expected to be Additional effects can modify the Llavor ratio at the source. multi- pion production (Murase & Nagataki 06; Baerwald et al. 11 etc.) π/µ cooling before their decay (Kashti & Waxman 05 etc.) helicity dependence of µ decay (Hummer et al. 10; Lipari et al. 07 etc.) re- acceleration of π/µ (Murase et al. 12; Klein et al. 13 etc.) new physics? The measurement of Llavor ratios can be a good probe of CR accelerators and neutrino properties.

Reacceleration Process primary particle acceleration à hadronic interactions during the acceleration à secondary particle acceleration primary 2ndary shock à The spectrum of secondary particles becomes harder than primaries. # Stochastic acceleration is also possible (Murase et al. 2012). downstream upstream The spectral index of accelerated protons would be γ 4 where γ=3r/(r-1) (r: compression ratio)

Case of Cosmic Ray Positrons Positron excess reported by PAMELA/AMS- 02 Positrons may be produced inside the SNRs and reaccelerated to have a harder spectrum (Blasi 2009; see also NK 2012). The excesses of anti- proton and secondary nuclei (B, Ti etc.) are also predicted (Blasi & Serpico 2009; Mertsch & Sarkar 2009, 2014 etc.) Aguilar et al. 2013 Mertsch & Sarkar 2014

Transport equation of secondary particles (positrons, anti- protons, etc.) Q ± (x,p) is proportional to the distribution function of primary protons downstream where ~p -γ+α for D(p) p α hard e + injection! Blasi (2009)

Reacceleration of π transport equation of the pion distribution function f π (x,p) (stationary) background Lluid velocity decay source term p ξ p p : relation between the momentum of a secondary π and that of a primary proton Hereafter we assume Bohm- like diffusion (D(p) p)

upstream Solutions (π) downstream at the shock front: A π, B π : p- independent factors ~ D(p) u 1 2 Q π,0 p ( )

Reacceleration of µ transport equation of the muon distribution function f µ (x,p) (stationary) source term decay ξ µ : fraction of energy transferred from a pion to a muon

upstream & downstream Solutions (µ) at the shock front: q ± i,a, q ± i,b ~ Q µ

Application to the GRB internal shock (1) shock rest frame à mildly- or non- relativistic shock dissipation radius t dyn = r cγ 0.3s Γ 2.5 Δt ms

Application to the GRB internal shock (2) L b =3 10 51 erg/s, Γ=10 2.5, r=10 14 cm t acc < τ π when t acc < τ µ when τ π < t π,syn when ε π < 5.1 10 15 ev Γ 3 2.5Δt ms 1/2 τ L µ < t µ,syn when ε µ < 2.4 10 14 ev Γ 2.5 γ,51 3 Δt ms 1/2 L γ,51

Pion/Muon Spectra at the Source disappointing results: reaccelerated pions/muons are subdominant component compared to those advected downstream Maybe the reason is: Both D(p) and τ π,µ p 1 Q π,0 p ( ) p 4 ε 2 ( ) What if D(p) p q with q>1? What if we choose different parameters? (e.g. shorter dynamical timescale r/cγ)

Summary(?) Flavor compositions of high energy neutrinos may be a good probe of cosmic- ray accelerators in the future. We estimate the effect of π/µ reacceleration before their decay on the resulting neutrino spectrum. So far, the reacceleration seems not so eflicient. Because of Bohm- like diffusion? What if r/cγ< τ π,µ?