Cosmic Rays and Cosmology

T.Wibig(a) and A W Wolfendale(b) (a) Physics Department, University of Lodz, Lodz, Poland

(b) Physics Department, University of Durham, Durham, UK.

An analysis is given of several aspects of the relationship between Cosmic Rays and Cosmology. These include the possibility of foreground effects on the CMB due to CR interactions in various locations. The form

of the fractional energy loss rate of protons and iron nuclei propagating through the various radiation fields is

examined and the importance of the infra-red radiation field in certain cosmic ray production scenarios is

stressed.

All the available measurements of the energy spectrum of the highest energy particles are taken and a best-

estimate is derived. Comparison is made with predictions for alternative assumptions about the origin and nature

of the primary particles. It is concluded that there is no need to involve exotic mechanisms for the particles

beyond the ‘GZK cut-off’; indeed, it is claimed that with a sufficiently hard production spectrum a ‘cut-off’- is

not expected. In fact, it is maintained that the term ‘cut-off’ is a misnomer. This is not to say that there is no

interest in the particles of the very highest energies; there is – the mechanisms whereby these particles attain

their energies is a great mystery.

1. ENERGY DENSITIES

It is well know that there is near equality of the

energy densities in cosmic rays, the local Galactic magnetic field, gas motions and

starlight. The equality of cosmic ray energy

density and magnetic field is often considered

to be significant and have relevance to the trapping of particles in the Galaxy.

The situation for extragalactic particles is

shown in Figure 1, where a variety of other energy densities are also shown. Some attempt

to find significance can be made here too.

Evidently there is no connection between the (likely) energy density of EG CR (the value of

10-6 eVcm

-3 comes from an extrapolation back

to low energies of an E-2 spectrum – see later)

and that of EG starlight. Concerning the energy density of the EG magnetic field, there is only

fragmentary information, we, ourselves, equate

the EGCR energy density to B2/4π, thereby

finding B ~ a few nG.

‘PE of gal’ refers to the potential energy

released when galaxies form; it has been

pointed out by one of us (Wolfendale, 1983)

that this is a useful yardstick to give an upper limit to the energy available for EG cosmic

rays; we see that the CR energy density

corresponds to about 1% of the PE energy released – a not unreasonable value.

Of greater significance for the cosmological

aspect is the energy density of the CMB (0.24

eVcm-3) and that in the fluctuations of the

CMB. Interestingly, the energy in fluctuations

is of the same order as that in the EG CR in

general. We have searched for an effect due to the interaction of UHE CR with the CMB

photons on the CMB itself but found nothing

significant, despite the cascading down of the energy lost in the CR – CMB collisions.

However, in view of the fact that galaxy –

galaxy and cluster-collisions occurred rather

frequently at red-shifts of a few it is just conceivable that some effects may manifest

themselves there.

Nuclear Physics B (Proc. Suppl.) 136 (2004) 179–184

0920-5632/$ – see front matter © 2004 Elsevier B.V. All rights reserved.

www.elsevierphysics.com

doi:10.1016/j.nuclphysbps.2004.10.005

Fig. 1 Energy densities in extragalactic space

2. GALACTIC FOREGROUND AND CMB FLUCTUATIONS

Sometime ago, Banday et al, (1991) made a

detailed analysis of the likely contribution to

the CMB fluctuations from CR electron-

synchrotron radiation and dust in the Galactic Halo. They found that in the tens of GHz

region approaching 10% of the fluctuation

signal on large angular scales (≈7o) could be

due to the sum of synchrotron and dust.

Interestingly, there is a region where the sum

has roughly the correct frequency dependence (3K black-body).

Further work has been done by us.

Remarkably, there is some evidence for a

correlation of the large scale low temperature regions of the WMAP (Tegmark et al, 2003)

CMB fluctuations and the regions of the Halo

where we (Fathoohi et al, 1995; Chi et al, 1995) previously found steep cosmic ray proton and

electron spectra. The CR spectra came from an

analysis of gamma ray data (from EGRET) at

various energies. Figure 2 shows the situation. The CR spectra seem to correlate with the

presence of the ‘Galactic chimneys’, where the

HI column density is low. A possibility is that it is in these regions that the CMB intensities

are more accurate, elsewhere there is a finite

contribution to the ‘2.7K map’. It should be

remarked that it is just on these large scales that there is the well known deficit of ‘power’ in the

CMB fluctuations. As Tegmark et al. (2003)

have reported, the power falls below expectation for ℓ-values below about 10

(angular scale above 18o). This aspect deserves

further study, not least because, if true, the power deficit indicates a radical rethink of

contemporary cosmology (eg Efsthatiou, 2003).

Very recently we have searched for the effect in

EGRET data for gamma rays of energy 30 GeV (Hunter et al, 1997) and found a positive

correlation between intensity and CMB

temperature.

3. COSMIC RAY CASCADING

THROUGH THE UNIVERSE

It is well known that the energy released in

UHECR – CMB interactions cascades through

the Universe, leading to a characteristic form for the cosmic gamma ray spectrum. Figure 3

shows the situation. It is important to realize

the connection between the very highest and the

very lowest energies. Thus, there is a restriction on models for the highest energy

particles, particularly by way of an assumed

cosmological increase in source output.

T. Wibig, A.W. Wolfendale / Nuclear Physics B (Proc. Suppl.) 136 (2004) 179–184180

Fig. 2 Galactic map showing the large scale minima

in the CMB radiation (from Tegmark et al, 2003), the regions of high steepness in the cosmic ray

electron and proton spectra (from Fathoohi et al,

1995 and Chi et al, 1995) and the positions of the

‘Galactic chimneys’. There may be a correlation

which indicates a residual cosmic ray foreground

contribution to the CMB on large scales. In turn,

this may relate to the apparent deficit in CMB power

at small ℓ-values

The work reported in Figure 3 leads to a

restriction on the maximum red shift (zm) of ~5

and the maximum cosmological source strength increase parameter β (in (1+z)

β) of βmax ≈ 3.7.

A case in point concerns quasars. Insofar as

there are few close enough to allow, say, 1020

eV protons to survive the CMB, and since low

energy particles (<1018

eV) may never arrive,

because of slow diffusion in the nG fields in the

IGM, it leaves only a narrow window of energy where arrival could occur. Now if, as we

discuss later, there are strong IR fields near the

sources even these particles will be diminished in number. The good side of this argument is

that neutrinos would arrive; previous

calculations of the flux of ultra-high energy neutrinos may have given under-estimates.

Fig. 3 Overview of the cosmic ray spectrum

showing the Galactic and Extragalactic components

and the gamma ray spectrum resulting from

cascading of the products of p-CMB interactions

(after Wdowczyk et al, 1972; Wdowczyk and

Wolfendale, 1990).

4. THE ENERGY SPECTRUM OF

UHECR

In previous work (Szabelski et al., 2002) we combined the data to produce a ‘best-estimate’.

Here, we go a step further and produce two!

The principle is straight forward – to identify the ankle in each published spectrum (all of

them show one) and to normalize the energy

scales so that they coincide. The intensities are then also normalized to the same value. We can

find no fault with this procedure for deriving

the spectral shape. The problem concerns the

absolute energy scale to adopt; this scale is important because the so-called ‘GZK cut-off’

is at a specific absolute energy (our objection to

the ‘cut-off’ terminology will be given later).

As is well known, there are direct

experiments which give particles having very high energies (eg AGASA, Haverah

Park) and indirect ones which give lower energies (eg HiRes). In Figure 4 we give

the dispersion of the points – each with its

T. Wibig, A.W. Wolfendale / Nuclear Physics B (Proc. Suppl.) 136 (2004) 179–184 181

quoted error- for 10 bins; the lower energy calibration has been adopted but there is no

difference in the relative spreads for the other calibration .

Fig. 4 Primary energy spectrum of UHECR.

Distribution of the intensity, energy points for the

arrays listed. It will be noted that only in the final

two energy bins is the dispersion unreasonably large.

Units as in Fig.5.

It will be noted that it is only for the final two bins that there is a dispersion very much bigger

than the quoted errors (although it is true that

for all energies the spread is outside some of the

errors; it is a well known fact that ‘errors are underestimated’).

Of particular importance is the reasonable

dispersion extending to energies somewhat above the ankle, viz we are confident in the

shape near the ankle. Figure 5 gives the

resultant spectra.

Fig. 5(a) Primary energy spectrum of ultra-high

energy cosmic rays. The points represent the

summary of the world’s data after normalization to

the same ‘ankle’ position and using the scale for the

Hi-Res experiment. The sharp minimum (‘ankle’) at

log (E) ~ 18.7 is regarded by us as strong evidence

for a transition from Galactic (G) to Extragalactic

(EG) particles; primary protons are assumed in the

comparison of expectation with the points but the results for primary iron nuclei would be similar, in

view of the normalization of the expectations to the

EG line at 1019

eV.

The lines represent expectations for a universal

distribution of sources beyond 6 Mpc (sources closer

than this would have been recognized already). The

numbers in brackets are the exponents of the

injection spectra adopted in the calculations

T. Wibig, A.W. Wolfendale / Nuclear Physics B (Proc. Suppl.) 136 (2004) 179–184182

5. INTERPRETATION OF THE SPECTRA

Limited space allows us only to give a brief discussion here. We limit attention to two

questions: “is there a GZK cut-off predicted or can a conventional universal origin

model explain the data”. The answer is that with an injection spectrum sufficiently flat

there is no cut-off; Figure 5 shows that, for a differential exponent of 1.8 (AKENO) or

2.0 (HiRes), there is a reasonable fit to the data. Protons have been assumed but there

is an equally good fit with iron nuclei. Figure 5(b) shows the widely reported

prediction by Takeda et al (1998) – denoted ‘T’.

We consider this prediction to be inappropriate for an injection spectrum that has an energy-

independent exponent.

Some discussion of the flat spectrum needed, ie

gamma : 1.8-2.0 is required. Although the standard Fermi –acceleration mechanism gives

2.0 (in the absence of losses), relativistic shocks

in plasmas with low beta values can give values as low as 1.0 (Schlickeiser, 2001). Thus, there

is no fundamental problem.

The actual mechanism of acceleration is unknown, as is the site of such acceleration.

Some indication of the site may come from the

eventual knowledge of the precise shape of the

spectrum, although the accurate mass composition will also need to be known. The

reason for this statement relates to the signature

of losses on the infra-red background, (IRB) as will be discussed in the final section.

6. THE ROLE OF INFRA-RED

RADIATION

Many calculations have included the low level of the IRB for propagation in the IGM

in general. The fact that the ambient level there corresponds to only ~1% of that in the

CMB (Stecker and Salamon, 1999) means

that the attenuation of protons is very small. However, if the IRB level is high enough

there will clearly be an effect (Wdowczyk and Wolfendale, 1975). We have recently

realized that under certain circumstances the level near the particle sources can be

high and the loss serious. The effect on the spectral shape can be correspondingly

significant.

Fig. 5(b) As Figure 5(a) but for the normalization

of the experimental data to the intensity and energy

determined in the AGASA experiment. ‘T’ denotes a prediction commonly quoted but one

which we regard as inappropriate; certainly,

uniform UHECR injection with an energy –

independent exponent would not give such a

catastrophic fall. It is evident that a GZK – ‘cut-off-

is neither observed nor predicted

The appropriate scenarios would be, for

example,

i) quasars, or other very powerful AGN; ii) sources within galaxy clusters.

In both cases there will be associated magnetic

fields which will slow down the escape of the

particles from the source region and allow interactions with the abundant IR photons

present there. Very recently we (Wibig &

Wolfendale, 2004) have made specific

T. Wibig, A.W. Wolfendale / Nuclear Physics B (Proc. Suppl.) 136 (2004) 179–184 183

calculations; the situation for galaxy clusters, where typical magnetic fields of 5µG exist

(Clarke et al, 2001), are particularly interesting.

7. CONCLUSION

CONCLUSIONS We conclude that :

• Low energy CR may give significant

foreground contamination of the CMB;

• There is strong evidence for a transition

from Galactic to Extragalactic particles

at a little below 1019

eV;

• The term ‘GZK cut-off’ is a misnomer;

• The infra-red radiation near the source

of UHECR may cause significant loss.

ACKNOWLEDGEMENTS One of us (AWW) thanks the organizers of the

meeting for support and for arranging such a

splendid program.

REFERENCES

Banday, A J et al, Astrophys. J. 375, 432

(1991)

Chi, X et al, J.Phys.G 21, 1547 (1995) Clarke, T E et al, Astrophys.J.547, L111 (2001)

Efstathiou, G, astro-ph/0303127 (2003)

Fathoohi, L J et al, J.Phys.G 21, 679 (1995) Hunter, S D et al, Astrophys.J. 481, 205 (1997)

Schlickeiser, R, Cosmic Ray Astrophysics,

Springer (2001) Stecker, F W and Salamon, M H, Astrophys. J.

512, 521 (1999)

Szabelski, J et al, Astropart.Phys.17, 125 (2002) Takeda, M M et al, Phys.Rev.Lett. 81 1163

(1998)

Tegmark, M et al, astro-ph/0302496 (2003) Wolfendale A W , Q.JL.R.Stro.Soc. 24, 122

(1983)

Wdowczyk, J. and Wolfendale, A W, Nature, 258, 217 (1975) & Astrophys.J. 349, 35 (1990)

Wdowczyk, J et al, J.Phys.A. 5, 1419 (1972)

Wibig, T and Wolfendale, A W (2004, in

preparation)

T. Wibig, A.W. Wolfendale / Nuclear Physics B (Proc. Suppl.) 136 (2004) 179–184184