Ultra High Energy Extragalactic Cosmic Rays: Propagation

Todor StanevBartol Research InstituteDept Physics and AstronomyUniversity of Delaware

Energy loss processes protons nuclei gamma rays spectrum evolution in propagation

Magnetic fields extragalactic galactic

Secondary particles generated in propagation neutrinos gamma rays

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The main energy loss process of the ultra high energyprotons in the Universe is photoproduction interactionsin the microwave background. The photoprocustioncross section is very well measured in accelerator experiments.

Photoproduc-tion cross section in themirror system,i.e. photonsinteractingon targetprotons.

The UHE protons energy is so high that they can interact on photons from the microwave background and produce secondary pions. The threshold is when the center of mass energy exceeds the proton mass + the pion mass: Eε(1−cosθ) > (mp+mπ)2

For the average microwave background photon the threshold is at 1020 eV. Averaged over the photon spectrum and direction the threshold is a factor of 2 lower.

The inelasticity of the proton in these interactions is impor-tant energy dependent parameter.At threshold protons lose lessthan 20% of their energy. Atvery high energy the loss canreach 50%.

The energy loss length ofprotons in the microwavebackground is about 14 Mpcabove 4x1020 eV, about afactor of 4 above the proton interaction length.The arow in the left upperside of the graph shows theenergy loss length in the BHelectron-positron pair produ-ction. The proton energy lossis the ratio of electron toproton mass. The crosssection is high.

The mark at 4,000 Mpc shows the energy loss to theexpansion of the Universefor H0=75 km/Mpc/s.

Neutron decay length is alsoshown with dashed line.

Secondary gamma rays and neut-rinos (cosmogenic neutrinos) areproduced in propagation.

    

The process has the characteristic feature that while the crosssection increases with the photon energy in the proton framep) the inelasticity decreases. As a result the energy losslength for protons has a minimum at about 2.1019 eV and increases at higher proton energy. Another feature is the small dependence of Ee on the proton energy.

Example: the spectrumof positrons generatedby interactions of pro-tons in the microwave background radiation. Electron spectrum does not change linearly with proton energy.

Bethe-Heitler pairproduction

    

Interactions in the MBRdominate the protonenergy loss above 30 EeV. Below thatenergy protons interact in the IRB.At higher redshift MBR dominates atlower energy becauseof its faster cosmolo-gical evolution.R

atioRatio of the total mean free path to that in the IRB

Other photon fields: infrared radiation

    

From: Bertone et al

Heavy nuclei lose energyin photodisintegration on all photon fields. A beam of heavy nuclei injected at large distancefrom us changes its composition in propaga-tion. At distances larger than the energy lossdistance it is a purelyproton beam after the secondary neutrons decay.

Energy loss time for He, C, Si, and Fe nuclei. (1 Mpc = 1014 s)

Photodisintegration

Calculations done by two groups that afterward joined:Chicago + Paris: ParisChicago

The whole disintegrationchain is followed in thecalculations.

From: Khan et al, 2003

    

Energy loss length vsenergy for differentnuclei (Allard et al, 2005)

    

Energy loss lengths of protons in the microwave background and of gammarays in MBR and radio background.

The figure gives an idea for the ratio of the electromagneticand hadronic cross sections in astrophysics. Electrons (likethe gamma rays) always interact faster, but the rates depend on the specific seed photon field.

    

The energy spectra of UHECR (extragallactic) at Earth depend on:

- Acceleration spectra at the sources.

- Spatial distribution of the sources (nearby ones).

- Cosmological evolution of the sources (may eliminate some of the models).

- Chemical composition of UHECRs at their sources (see Allard et al, = 2.2-2.4 ).

- Average extragalactic magnetic field (high fields may create cut-offs – we can see only a small fraction of the Universe, low fields would enhance source recognition.

How do we deal with these parameters is the key for determination of the transition region starting from thehughest energies.

Evolution of the cosmic ray spectrum in propaga-tion on different distances.

The solid line shows the injec-tion spectrum.

The top panel is without cosmological evolution of thecosmic ray sources and thelower one is with (1+z)3evolution up to z = 1.7.

There is a pile-up of protonsjust below 1020 eV. Integra-tion over source distance will produce the expected energy distribution forhomogeneous isotropic source distribution.

    

Because of the strong proton energy loss high redshifts z do not contribute much to the highest energy cosmic rays. Here is an example with the W&B parameters.

Contribution of cosmic ray sourcesat different redshiftto the observed flux.The solid black lineis the flux in case ofisotropic distributionof the cosmic raysources and a flatinjection spectrumfor cosmologicalevolution (1+z)3.

    

One possibility is that extragalactic cosmic rays arenot protons only – they have mixed composition and loseenergy on propagation mostlyon spallation in photon fields.This changes the story quite a bit: the dip at 1019 eV becomesshallower being filled with spallation nucleons. The injec-tion spectrum for no cosmolo-gical evolution becomes flatter.

The spectra generated with mixed composition bend almostat the same position as protonsspectra do. Can one alter that?

From: Allard, Parizot & Olinto, 2005

Chemical composition at the sources

The spectral shape after propagation of the mixedcomposition models depends not only on the injection spectrum but also on the initial cosmic ray composition. It could easily be made to fit observations. (Bertone et al, 2002)

The cosmic ray spectrum measured by the Auger groupcan also be fitted with at least three different models asshown below (Yamamoto for Auger): either a steep (=2.55)without evolution or a flat (=2.3) with a strong cosmologicalevolution ( (1+z)5 ) if the UHECR were protons.

If they were nucleithe accelerationspectrum is stillflat - = 2.2. Wecannot distinguishbetween these models from theshape of the measured spectrum.

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While the proton spectraintegrated over redshiftalways maintain power law shape, the photon spectra after propagation have very complicated shape. There is a minimumdue to the interactions inthe microwave background.

Top-down models can berestricted with the amountof GeV gamma rays, as done here for X-particlemass of 1016 GeV and 1 nG magnetic field.

From: Protheroe&Stanev (1996)

    

Fraction of gamma raysin HE cosmic rays(Auger Coll. 2007)Current limits are strict – 2 % at 1019 eV and 5% at 2x1019 eV.

The fraction of gamma rays has been limited by severalair shower experiments using the shower profile, the muon content and the angular distribution of the detected air showers to several % of the total flux. The statistics is, however, too low to do that at the highest energies. So .... for the origin of UHECR top/down models are still possible.

Galactic and extragalactic magnetic fields

Magnetic fields are important for charged particle propagation for two main reasons: -- scattering in the magnetic fields can hide the cosmic ray sources -- it could restrict the distance cosmic rays can propagate.

Heavy nuclei expirience more scattering since theyhave lower rigidity (momentum/charge)

Our believe is that extragalactic magnetic fields followthe distribution of the matter density and only a tiny fraction of the Universe has significant fields. The average field strength may reach 1 nG with an average coherencelength of 1 Mpc (average distance btw galaxies).

Although not very well known, we have approximatemodels for the regular magnetic field and some knowledgeof the random fields. The angular distance of the AugerUHECR with the correlating AGN is the same order ofmagnitude as in some of these models.

    

The propagation of UHECR is influenced very strongly by magneticfields, both galactic and extragalactic.

- galactic magnetic fields deflect UHECR protons only a few degrees away from the direction of their sources. In case of heavy nuclei the deflection could be stronger, as 1018 V particles gyrate along the magnetic field lines.

- random extragalactic fields, if they have strengths of nG on Mpc scale, can impose a relatively small `horizon'. Protons of energy below 1020 eV scatter and loose energy so much that they can not reach us in Hubble time. This may restrict the region from which this particles can reach us.

Points are results of Monte Carlo propagation. The heavy grey line shows propagation time (analytic estimate, Achterberg) exceeding Hubble time.

The worst case for cosmic ray astronomy would beif they were organized large scale (> 1 Mpc) extragalactic magnetic fields, even in the nGaussrange. The example above shows how particle scattering gets organized in they presence – 10 nGfield in this case. Auger results do not show the existence of such fields.

    

Cosmogentic neutrinos are neutrinos from the propagation of extragalactic cosmic rays in the Universe. These neutrinos were first proposed and their flux was calculated in 1969 by Berezinsky & Zatsepin. An independent calculation was done by Stecker in 1973. In 1983 Hill & Schramm did another calculation and used the non-detection by Fly's Eye of neutrino induced air showers to set limits on the cosmological evolution of the cosmic rays sources.

The main difference with the processes in AGN and GRB is that the main photon target is the microwave background (2.75oK) of much lower temperature than the photon emission of these sources. This raises the proton photoproduction threshold to very high energy: Actually the proton photoproduction threshold in the MBR is about 3.1019 eV. There is also productionin the isotropic infrared/optical background.

The photoproduction energy loss of the extragalactic cosmic rayscause the GZK effect – the end of the cosmic ray spectrum.

Secondary particles generated in propagation

    

Cosmogenic neutri-nos are very sensi-tive to the cosmolo-gical evolution of the cosmic ray sources because ofthe lack of energy loss. This could be useful for establishing a model for the extra-galactic cosmic rays.

Note the logarithmic scale in redshift. Cosmological parametersare as in the cosmic ray example. The contribution increases until the source luminosity is significant (z = 2.7 in the W&B model). At higher redshift the production is still high because of the (1+z)3 increase of the MBR density and the lower energy threshold for photoproduction.

The figure shows the fluxes of electron and muonneutrinos and antineutrinos generated by proton propagation on (bottom to top) 10, 20, 50, 100 & 200 Mpc in MBR. The top of the blue band shows the proton injection spectrum(E-2 in this example).

Muon neutrinos and antineutrinos are generated with a spectrum similar to the one of electron neutrinos at twice that rate. As far as neutrinos are concerned the cascade development is full after propagation on 200 Mpc. Even the highest energy protons have lost enough energy to be below threshold. Slightly more of the proton energy loss goes to cosmogenic gammarays generated in photoproduction and in the BH pair creation.

From: Engel, Seckel & Stanev, 2001

    

The electromagnetic particles also have a double peakeddistribution, higher energy gamma rays from neutral mesondecay and electrons from neutron decay. The furtherdevelopment of electromagnetic cascades depends on thestrength of magnetic fields – electrons easily lose energy on synchrotron radiation even in 1 nG fields.

Comparison of neutrinoand electromagnetic fluxes generated byprotons in propagationon 200 Mpc in MBR.

    

Muon neutrinos and antineutrinos generated in propagationfrom isotropically and homogeneously distributed sourcesto us from two of UHECR proton models. Cosmological evolution of the sources (1+z)3 is taken into account for the W&B model. In case of mixed composition only the protoncomponent generates high energy neutrinos.

    

The same for electron neutrinos and antineutrinos

    

The interaction rate for cosmogenic neutrinos from the W&B model is higher by about a factor of 10. This is notdue as much to the neutrino flux, which at maximum is only a factor of 2 different, but on the lower neutrino energy in the Berezinsky et al model. Neutrino interaction cross section still increases with energy even above 1016 eV.

    

In the mixed composition model only the electron antineutrino flux (from neutron decay, yellow symbols) is higher than that in the proton models. The muon neutrino and antineutrino fluxes (also tau neutrinos atEarth because of oscillations) are lower. Electron anti-neutrino flux peaks below the Glashow resonance.

    

The cosmogenic neutrino flux above 1018 is the sameas the UHECR flux. The difference in the hadron andneutrino cross sections makes it so much difficult todetect. The theoretical neutrino rate (no efficiency) isabout 0.3 events per km3.yr. Bigger detectors neededfor detection.

    

Ultrahigh energy cosmic ray spectrum is shaped by thepropagation from the sources to us as a function of thecosmic ray acceleration spectrum and their chemicalcomposition at the sources

The chemical composition of UHECR is currently not obvious.Contrary to expectations the Auger results suggest a mixednuclear composition. Data is not fully consistent – thewith AGN may point at protons as the highest energy cosmic rays.

The possible detection of cosmogenic neutrinos (IceCube,Auger, ANITA, RICE, Moon Observations) will be very important for understanding of the origin and propagationof these exceptional particles.

Summary