1. Testing the origin of the UHECRs with neutrinos Walter Winter DESY, Zeuthen, Germany Kavli Institute for Theoretical Physics (KITP), Santa Barbara, CA, USA UHECR 2014,Springdale, UT, USA Oct. 12-15, 2014 TexPoint fonts used in EMF: AAA

2. Walter Winter | UHECR 2014 | Oct. 13-15, 2014 | Page 2 Contents > Introduction > Can the observed neutrinos come from the same sources as the UHECRs? > GRBs as test case for the UHECR-neutrino connection > Summary

3. Walter Winter | UHECR 2014 | Oct. 13-15, 2014 | Page 3 3 Cosmic messengers Physics of astrophysical neutrino sources = physics of cosmic ray sources

4. Walter Winter | UHECR 2014 | Oct. 13-15, 2014 | Page 4 2014: 37 neutrinos in the TeV-PeV range Science 342 (2013) 1242856; update by Gary Hill @ Neutrino 2014 Where do these come from? Prompt atmospherics? Directional information: Clustering? Isotropic/from Galactic plane/Galactic center? Why no events > few PeV? Can these come from the sources of the ultra-high energy cosmic rays? Which source class? More than one? Flavor composition?  Requires more statistics

5. Walter Winter | UHECR 2014 | Oct. 13-15, 2014 | Page 5 Connection with primary nuclei? > In pp and p  interactions, the secondary pions take about 20% of the proton energy, the neutrinos about 5% (per flavor) > PeV neutrinos must come from 20-500 PeV nuclei (depending on comp.) > Observed cosmic ray composition non-trivial function of energy (at Earth!) > Simple example: Neutrinos from cosmic ray interactions with hydrogen in the Milky Way [O(0.1-1) event] > Connection with UHECR sources requires extrapolation over several orders of magnitude both in spectrum and composition Gaisser, Stanev, Tilav, 2013 UHECRs prima- ries Joshi, Winter, Gupta, MNRAS, 2014

6. Walter Winter | UHECR 2014 | Oct. 13-15, 2014 | Page 6 Fitting the observed neutrino spectrum > Simplest possible model: Ap (or AA) interactions in sources; SFR evolution > Possible fits to data: WW, arXiv:1407.7536 (PRD, accepted) Protons  =2 B ~ 10 4 G (magnetic field effects on sec. pions, muons, kaons) Nuclei  =2, E max =10 10.1 GeV Composition at source with  =0.4 Protons  =2 E max =10 7.5 GeV Protons,  =2.5 [Problem: Fermi diffuse  -ray bound Murase, Ahlers, Lacki, PRD 2013 ]

7. Walter Winter | UHECR 2014 | Oct. 13-15, 2014 | Page 7 Connection to UHECRs? WW, arXiv:1407.7536 (PRD, accepted) Protons  =2 B ~ 10 4 G Nuclei  =2, E max =10 10.1 GeV Composition at source with  =0.4 Protons  =2 E max =10 7.5 GeV Protons,  =2.5 [Problem: Fermi diffuse  -ray bound Murase, Ahlers, Lacki, PRD 2013 ] Yes, but: Energy input per decade very different in neutrino-relevant and UHECR energy ranges (Energetics seem to favor  ~2, see e.g. B. Katz, E. Waxman, T. Thompson, and A. Loeb (2013), 1311.0287 )  will come up again later! Yes, but: Synchrotron losses limit maximal proton energies as well. Need large Doppler factors (e. g. GRBs) Yes, but: Need energy- dependent escape timescale leading to break/cutoff within source (diff. from ejection!) see e.g. Liu et al, PRD, 2004; arXiv:1310.1263 Yes, but: A(E) change somewhat too shallow to match observation; difference source-observation from propagation?

8. Walter Winter | UHECR 2014 | Oct. 13-15, 2014 | Page 8 > Idea: Use timing and directional information to suppress atm. BGs > Stacking limit exceeds observed neutrino flux (~10 -8 ) by one order of magnitude; interesting to test specific models Nature 484 (2012) 351 > Prediction (One zone model. based on fixed collision radius models) almost reached (some recent corrections!) GRBs as a test case (Source: NASA) GRB gamma-ray observations (e.g. Fermi, Swift, etc) (Source: IceCube) Neutrino observations (e.g. IceCube, …) Coincidence! (Hümmer, Baerwald, Winter, PRL 108 (2012) 231101; method based on Guetta et al, 2004; Waxman, Bahcall 1997)

9. Walter Winter | UHECR 2014 | Oct. 13-15, 2014 | Page 9 GRB - Internal shock model (Source: SWIFT) Prompt phase Collision of shells  Shocks  Particle acc. “Isotropic equivalent energy“  (Simulation by M. Bustamante) Observable: Light curves Engine (intermittent)

10. Walter Winter | UHECR 2014 | Oct. 13-15, 2014 | Page 10 UHECR-neutrino connection: escape mechanisms? Baerwald, Bustamante, Winter, Astrophys. J. 768 (2013) 186 Optically thin (to neutron escape) Optically thick (to neutron escape) Direct proton escape (UHECR leakage) n p p n n n n n p p ‘ ~ c t‘ p  ‘ ~ R‘ L n p p p p p  One neutrino per cosmic ray  Protons magnetically confined  Neutron escape limited to edge of shells  Neutrino prod. relatively enhanced  p  interaction rate relatively low  Protons leaking from edges dominate

11. Walter Winter | UHECR 2014 | Oct. 13-15, 2014 | Page 11 An example (before propagation)  For high enough acceleration efficiencies: R‘ L can reach shell thickness at highest energies (if E‘ p,max determined by t‘ dyn )  Hard spectrum, aka “high pass filter“ (Globus et al, 2014)  Relative importance depends on optical thickness to p  interactions (from: Baerwald, Bustamante, Winter, Astrophys. J. 768 (2013) 186) Neutron spectrum harder than E -2 proton spectrum (only adiabatic energy losses)

12. Walter Winter | UHECR 2014 | Oct. 13-15, 2014 | Page 12 Combined source-propagation model: Ankle transition (  p =2, fit range 10 10... 10 12 GeV) > Neutron-dominated cases can be constrained by neutrino emission > Baryonic loading f e -1 (energy protons to photons) typically somewhat larger than IceCube assume, to fit UHECR data (here L iso =10 52 erg s -1, E iso =3 10 52 erg) (Baerwald, Bustamante, Winter, Astropart. Phys. 62 (2015) 66; figures with TA data)  =300  =800

13. Walter Winter | UHECR 2014 | Oct. 13-15, 2014 | Page 13 Combined source-propagation model: Dip transition (  p =2.5 with SFR evolution, fit range 10 9... 10 12 GeV) > Neutron-dominated cases even more extreme > Required baryonic loading f e -1 extremely large; implication of unequal energy output per decade (bolometric correction) (Baerwald, Bustamante, Winter, Astropart. Phys. 62 (2015) 66; figures with TA data)  =300  =600 10 50.5 erg/s

14. Walter Winter | UHECR 2014 | Oct. 13-15, 2014 | Page 14 Parameter space constraints (ankle model, fit to TA data) Example: Moderate acc. efficiency, escape by Bohm-like diffusion, SFR evolution of sources, ankle transition (Baerwald, Bustamante, Winter, Astropart. Phys. 62 (2015) 66; figures with TA data) Best-fit (shaded contours: TA UHECR fit) Current IceCube limit IceCube expectation (15yr) log 10 f e -1 (baryonic loading) obtained from fit Optically thick p  Direct escape … but - maybe - assigning one parameter set to all shells is too simple?

15. Walter Winter | UHECR 2014 | Oct. 13-15, 2014 | Page 15 The future: more dynamical collision models > Set out a number of shells with a Lorentz factor distribution > Shells collide, merge and cool by radiation of energy > Light curve predictable (see below) > Efficient energy dissipation (e. g. into gamma-rays) requires broad Lorentz factor distribution (Bustamante, Baerwald, Murase, Winter, 2014; based on collision model Kobayashi, Piran, Sari, 1997; see Globus et al, 2014 for a similar approach)

16. Walter Winter | UHECR 2014 | Oct. 13-15, 2014 | Page 16 Consequences for different messengers > Collision radii reach from below photosphere to circumburst medium > UHECR escape as neutrons (red) and directly (blue) at intermediate radii > Energy output ~ no of collsions x energy per collision (counting important!) > The burst looks different in different messengers! (Bustamante, Baerwald, Murase, Winter, 2014)

17. Walter Winter | UHECR 2014 | Oct. 13-15, 2014 | Page 17 Consequences for neutrino production > Neutrino flux comes from a few collisions at photosphere > Photospheric radius and photohadronic interactions both depend on particle densities (scale at same way) > Super-photospheric (minimal?) prediction hardly depends on baryonic loading,  (different from earlier works!) > Testable in high-energy extension of IceCube? > Sub-photospheric contribution could be much larger. However: photons from below photosphere not observable (Bustamante, Baerwald, Murase, Winter, 2014) E iso =10 53 erg per GRB

18. Walter Winter | UHECR 2014 | Oct. 13-15, 2014 | Page 18 Summary > Neutrino observations open new window to cosmic ray source identification; data (discovery and constraints) become meaningful > UHECR connection somewhat more challenging, as several orders of magnitude in energy between UHECRs and primaries leading to observed neutrino flux > GRBs are an interesting test case, as  The constraints are strongest on GRBs because of timing cuts  Well-motivated models for gamma-ray emission exist  IceCube data already test the parameter space > Different messengers are produced in different regions of a GRB. Multi-messenger connections are more model-dependent than previously anticipated > Heavy nuclei are anticipated to escape from larger radii than protons, as disintegration is to be avoided – but they can survive

19. Walter Winter | UHECR 2014 | Oct. 13-15, 2014 | Page 19 BACKUP

20. Walter Winter | UHECR 2014 | Oct. 13-15, 2014 | Page 20 Optically thin to neutrons Neutrino production from: Baerwald, Hümmer, Winter, Astropart. Phys. 35 (2012) 508 Dashed arrows: kinetic equations include cooling and escape Q(E) [GeV -1 cm -3 s -1 ] per time frame N(E) [GeV -1 cm -3 ] steady spectrum Input  Object-dependent:B‘

21. Walter Winter | UHECR 2014 | Oct. 13-15, 2014 | Page 21 > Energy losses in continuous limit: b(E)=-E t -1 loss Q(E,t) [GeV -1 cm -3 s -1 ] injection per time frame (from sep. acc. zone) N(E,t) [GeV -1 cm -3 ] particle spectrum including spectral effects NB: Need N(E) to compute particle interactions > Simple case: No energy losses b=0: > Special cases:  t esc ~ R/c (leaky box)  t esc ~ E - . Consequence: N(E) ~ Q inj (E) E -   Escape: Q esc (E) = N(E)/t esc ~ Q inj (Neutrino spectrum from N(E) can have a break which is not present in escaping primaries Q esc (E)) Kinetic equations (steady state, one zone) InjectionEscapeEnergy losses

22. Walter Winter | UHECR 2014 | Oct. 13-15, 2014 | Page 22 22 Peculiarity for neutrinos: Secondary cooling Baerwald, Hümmer, Winter, Astropart. Phys. 35 (2012) 508; also: Kashti, Waxman, 2005; Lipari et al, 2007 Decay/cooling: charged , , K > Secondary spectra ( , , K) loss- steepend above critical energy  E‘ c depends on particle physics only (m,  0 ), and B‘  Leads to characteristic flavor composition and shape  Decouples maximal neutrino and proton energies E‘ c Pile-up effect  Flavor ratio! Spectral split Example: GRB Adiabatic 

23. Walter Winter | UHECR 2014 | Oct. 13-15, 2014 | Page 23 From the source to the detector: UHECR transport > Kinetic equation for co-moving number density: > Energy losses  UHECR must from from our local environment (~ 1 Gpc at 10 10 GeV, ~ 50 Mpc at 10 11 GeV) Photohadronics Hümmer, Rüger, Spanier, Winter, 2010 Pair production Blumenthal, 1970 Expansion of Universe CR inj. z-dep! (M. Bustamante) [here b=-dE/dt=E t -1 loss ] GZK cutoff

24. Walter Winter | UHECR 2014 | Oct. 13-15, 2014 | Page 24 Cosmogenic neutrinos > Prediction depends on maximal proton energy, spectral index , source evolution, composition > Can test UHECR beyond the local environment > Can test UHECR injection independent of CR production model  constraints on UHECR escape (courtesy M. Bustamante; see also Kotera, Allard, Olinto, JCAP 1010 (2010) 013) Cosmogenic neutrinos EeV Protons

25. Walter Winter | UHECR 2014 | Oct. 13-15, 2014 | Page 25 UHECR transition models > Transition between Galactic (?) and extragalactic cosmic rays at different energies: > Ankle model:  Injection index  ~ 2 possible (  Fermi shock acc.)  Transition at > 4 EeV > Dip model:  Injection index  ~ 2.5-2.7 (how?)  Transition at ~ 1 EeV  Characteristic shape by pair production dip Figure courtesy M. Bustamante; for a recent review, see Berezinsky, arXiv:1307.4043 Extra- galactic

26. Walter Winter | UHECR 2014 | Oct. 13-15, 2014 | Page 26 26 More details: Gamma-ray observables? > Redshift distribution > Can be integrated over. Total number of bursts in the observable universe  Can be directly determined (counted)!  Order 1000 yr -1 (Kistler et al, Astrophys.J. 705 (2009) L104) ~ (1+z)  Threshold correction SFR

27. Walter Winter | UHECR 2014 | Oct. 13-15, 2014 | Page 27 Consequence: Local GRB rate > The local GRB rate can be written as where f z is a cosmological correction factor: (for 1000 observable GRBs per year and 30% of all bursts seen) (Baerwald, Bustamante, Winter, arXiv:1401.1820)

28. Walter Winter | UHECR 2014 | Oct. 13-15, 2014 | Page 28 Required baryonic loading (analytical) > Required energy ejected in UHECR per burst: > In terms of  -ray energy: > Baryonic loading f e -1 ~50-100 for E -2 inj. spectrum (f bol ~ 0.2), E ,iso ~ 10 53 erg, neutron model (f CR ~ 0.4) [IceCube standard assumption: f e -1 ~10] ~1.5 to fit UHECR observations ~5-25 Energy in protons vs. electrons (IceCube def.) How much energy in UHECR? Fraction of energy in CR production?