High energy cosmic ray mass spectroscopy. II. Masses in the range 1014–1017 eV

Astroparticle Physics ELSEVIER

Astroparticle

Physics 7 (1997) 203-211

High energy cosmic ray mass spectroscopy. II. Masses in the range 1014-1017 eV A.D. Erlykin ‘, A.W. Wolfendale

*

Department of Physics, University of Durham, Durham. DHl 3L.E, UK Received 21 February

1997; revised 27 March 1997; accepted

8 April 1997

Abstract In earlier papers we made the case for there being two peaks in the extensive air shower (EAS)size spectra in the size range 5 105-IO’ particles which we identified, somewhat tentatively, with, respectively, the CNO group of nuclei and Fe nuclei. Here, the problem of the mass composition is looked at in more detail. From an analysis of the sharpness of the first peak and its separation from the second we conclude that the ‘CNO’ group in the ‘single source’ spectrum comprises mainly oxygen nuclei, a conclusion that is consistent with a single local, recent supernova having provided the acceleration via shocks in the hot interstellar medium. 0 1997 Elsevier Science B.V.

1. Introduction The so-called ‘knee’ in the size spectrum of extensive air showers (EAS) produced by primary cosmic rays at = lo6 particles for showers recorded near sea level - and at somewhat larger sizes at mountain altitudes - has excited interest for many years. It is too sharp to be ascribed to diffusive properties of the interstellar medium (ISM) or, in our view, to an assembly of supernova remnants (SNR). Rather, we have, in [l], drawn attention to a structure in the knee region which is indicative of acceleration of the particles by a single recent nearby SN; the argument [l] against many SN being that different SN will invariably give rise to particle spectra having maximum energies of different values and the knee will be smoothed out. We find that the ‘knee’

* Corresponding author. ’ Permanent address: P.N. Lebedev Physical Institute, Leninsky Prospekt 53, 117924 Moscow,

Russia).

0927-6505/97/$15.00 Copyright PII SO927-6505(97)00020-O

is best explained by a smoothly changing size spectrum on which is superimposed a sharp peak, due to a differential energy spectrum of the form E-* for the primary particles before a peak in the E3 I(E) spectrum, at the knee, and a rapid fall above. In [l] and, in more detail, in [2], we drew attention to another peak at about 0.6 higher in the log N, scale, where N, is the total number of particles inferred for the shower at the detection level. Admittedly, the statistical significance of the second peak is not as strong as that of the first but it is certainly strong enough to merit mention - with a view to later work having a specific ‘target’ to aim at (this ‘target’ aspect is surely important, whether our detailed analysis is correct or not there is presumably structure in the size spectrum at some level). Fig. 1 gives a summary of the size spectra used in our series of analyses; the claimed CNO (denoted ‘oxygen’) and Fe peaks are indicated. In the earlier work we used an SNR acceleration model due to Berezhko et al. [3] to make a quite

0 1997 Elsevier Science B.V. All rights reserved.

204

A.D. Erlykin.

DIFFERENTIAL d

,,,,,I,,,

A. W. Wolfendale / Astroparticle

EAS SIZE SPECTRUM Oxygen Iron ,,I,,,,,,

Physics 7 (I 997) 203-21

some tens of percent, coincident with our peak energies. Despite the yet-to-be-confirmed nature of our arguments, we go on to examine the region encompassing the ‘CNO’ and ‘Fe’ peaks in more detail. In an attempt to derive results of higher accuracy than hitherto we analyze using smaller log N, intervals; this is the reason for differences in appearance of the slope and sharpness plots here and in [I] and [2]. 2. The sharpness

Fig. 1. Summary of results on the differential size spectra. Table 1 indicates the sources of the basic data which we have analysed using our method. The spectra are displaced horizontally so that the knee positions coincide (the vertical line through the knee is marked ‘Oxygen’). The legitimacy of this procedure is defined in our earlier publications [ 1.21;briefly, the average displacement of ‘our’ knee position from expectation is only = 0.1 in log(N, /NF”). The spectra are displaced upwards for reasons of clarity; Table 1 gives the key.

strong claim that the first peak is due to the CNO group of nuclei and the second to Fe. This ‘identification’ arose because the model [3] predicts, for a SNR exploding in the hot ISM - and where the nuclei are fully ionized - maximum CR energies at - 3 X lOI eV and 1.2 X 1016 eV for CNO and Fe respectively (Em, a Z). These energies are, within Table I EAS arrays and our estimates

of the knee positions

EAS array

Reference

Chacahaya Tibet Tien Shan EAS TOP- 1 EAS TOP-2 EAS TOP-3 Akeno Moscow State Univ. Kascade

[41 [51 [61 [71

[81 [91

HOI

I

of the CNO peak

In [ 1,2], and as mentioned above, we stressed the need for the energy spectrum of the incident particles responsible for the peak to be sharp, (i.e. for there to be a sharp cut-off of I(E) and thus a sharp peak in E3 I(E)). A lack of sharpness, coupled with the inevitable EAS propagation fluctuations and the ‘reception’ fluctuations, would not give a sufficiently sharp peak in the ground level size spectrum. Our earlier analyses [1,2] focused on the so-called sharpness index, defined as x = d2(log I( N,))/(d(log NC>)*, the characteristic dependence of this index on N, in each and every set of experimental data examined being the basis of our analysis. Table 1 gives details of the sources of data used in the analysis. The need for a sharp peak in the initiating particle spectrum has made us focus attention on the likely relative individual C, N and 0 components. If, for example, disregarding nitrogen, there were equal fluxes of C and 0 nuclei, the resulting primary energy spectrum - and consequent size spectrum would not be sharp. Specifically, since C and 0 give, with the model, maximum energies of 6 X and 8 X

and their differences Depth (g cm-*)

Log Np

K(I) for Fig.

5.50

6.46

+ 1.0

606

6.40

0.0

690 829 88.5 980 920 1020 1020

6.15 6.10 6.07 6.20 6.08 5.65 5.66

+ 0.75 + 0.25 0.0 -0.25 - 0.75 - 1.0 - 1.75

1

205

A. D. Erlykin. A. W. Wolfendale / Astroparticle Physics 7 (1997) 203-211

(4. 1Ol4 eV>, respectively, the ‘sharp spike’ would

extend over a factor 1.33 in energy and, roughly, 0.11 in log N,. Such a spread might be hard to accommodate, as will now be demonstrated. Before analyzing the experimental (EAS) situation we consider the ratio of oxygen to carbon, denoted O/C - in terms of number of nuclei - in various astronomical situations, the argument being that the very high energy CR represent these nuclei accelerated in some way (by a SNR shock in our preferred model [3]). Although, as will be pointed out shortly, the solar system abundance has O/C = 2.4 [l 11, observations on the ambient low energy cosmic rays suggest O/C close to unity [12,13] at fixed energy per nucleon. The equivalent examination of the abundance at fixed energy per nucleus increases the value somewhat, to O/C - 1.5 at 10 GeV, i.e. still a considerable carbon fraction. The situations will be considered in turn. 3. The abundances

of C, N and 0 nuclei

3. I. General remarks The best known abundances of the elements are probably those for the solar system [ 111. In terms of Table 2 Carbon and Oxygen abundances: oxygen/carbon

one silicon atom the relative numbers of C, N and 0 atoms are: 10.1, 3.1 and 23.8. We start by considering nitrogen. This element is certainly low in abundance in the solar system in comparison with C and 0 [l 11; thus N/C - 0.3 and N/O - 0.1. For low energy cosmic rays [ 121, the N/O ratio is found to be even lower than that for solar system material. At higher energies (- 100 GeV/nucleon) [13] the N/O and N/C ratios are also low. (However, see later for the C/O ratio at these energies). Neglect of nitrogen is a procedure that is aided by the fact that the peak of the nitrogen spectrum will be below that of the certainly stronger oxygen component ( EmX a Z> and will only affect the Ew2 side of the spectrum - and this, only to a small degree. Thus, in what follows we neglect nitrogen. 3.2. Carbon and oxygen The important datum here is the ratio of Oxygen to Carbon and in Table 2 we give a summary of the ratios for a variety of situations and by a variety of workers. Although it is true that for each situation there is a spread of values, a number of general features appear, as follows:

ratio

Ratio Solar system [ 111 Solar photosphere [ 111 ISM in galaxy [ 14,301

2.36 2.34 2.3

ISM in ICI61 3, NGC: 682,300/2 and 300/5 [15]

3.6-5.0

Orion nebula [ 161 Cyguus loop [ 161 Path to 5 oph (171 Solar wind [ 1l] Solar corona [ 111 Solar energetic particles [l 11 Crab nebula [l&19]

1.26 1.58 3.1 2.34 2.51 2.40 0.9-2.5

Ratio Ambient cosmic rays [12,13] E: 2.10’ eV/nucleon 10’0 10”

0.80 1.0 1.1

E: IO” eV/nucleus 10”

1.5 1.7

SNR

M peg. 15 Mo DO1 25 MO [20] ‘massive’ I211

3.4 9.1 7.1

M peg, signifies the mass of the progenitor star which gives rise to the SNR.

A.D. Erlykin, A. W. Wolfendale/Astroparticle

206

the ‘solar system’ value is - 2.4; local nebulae have - 1.4; energetic solar phenomena have - 2.4; SNR ejecta from SN of ‘high’ mass have > 3; ambient cosmic rays have values which start at - 0.8 at 2.108 eV/nucleon and increase somewhat with increasing energy. 3.3. Interpretation of the shape of the ‘CNO peak’ An analysis has been made of the transition: energy spectrum + size spectrum (to correspond to a mean atmospheric depth of 834 gcme2 - this value being the average for all the arrays used) + slope + sharpness for the constituent spectra: carbon (C), oxygen (01, ‘Heavy nuclei’, viz. Ne-S(H) and iron (Fe). In Fig. 2 two situations are indicated: with C

x

DlffERENTlAL

Physics 7 (1997) 203-21 I

present and 0 absent (A, = 1) and C absent (A, = 0). A, means the fraction of C in the CNO group sufficiently far from their peaks, i.e. E 5 IO6 GeV, where the differential production spectrum is of the form Ee2. The C/O ratio is thus CCfor A, = 1 and 0 for A, = 0. The relative contributions of CNO, H and Fe in our ‘single source’ model have been ‘tuned’ in order to provide a fit to the measured size spectrum. The shape in the region of the peak is not predicted with any accuracy by the model [3]; the shape chosen is considered by us to be ‘reasonable’; a further relinement will be considered later. Examining Fig. 2 (sharpness) we note that AC = 0 provides a good lit whereas A, = 1 does not. Concentrating on the region up to log N, = 6.6, i.e. the region where the two cases (A, = 0, 11 give different

SINGLE SOURCE MODEL OF THE KNEE AT PRIMARY ENERGY SPECTRUM

l“““““““““‘1

E full

line:

AC =

0

dashed line: Q

= 1

doshed lina: 4

4

N

5

6 MN.

7

tl

DlffERENTtAL EAS SIZE SPECTRUM

....,....,,,l’,~... full line: 4

= 1

total

-

doshed line: &

0 = 1

Fig. 2. The constituent energy spectra, size spectrum, differential slopes of size spectra and sharpness (= differential of slope with respect to log NJ. Two situations are indicated: 6) all oxygen, A, = 0. (ii) all carbon, A, = 1. The sharpness is seen to tit the experimental data in case (i) (full line) but not in case (ii>.

A.D. Erlykin, A. W. Wolfendale/Astroparticte

for A,=O, 51.0for A,=1 and results, x *=14.1 25.4 for A, = 0.5 (the last-mentioned case is not shown in the figure to avoid confusion). The corresponding chance probabilities are 17%, < 10e6 and 0.53%. It is clear that A, = 1 can be ruled out and a 50-50 mixture of C and 0 is very unlikely; d, = 0 is allowed, however. It is interesting to examine the width of the first peak. In units of log N, the full widths at half height are 0.40 for A, = 0, 0.35 for A, = 1, 0.45 for A, = 0.5. The observed value is 0.30 f 0.1; thus, there is a better fit to a ‘pure’ composition than to a mixed one (although, obviously, studying the width alone does not allow a distinction between pure 0 and pure 0. This conclusion is strengthened by a consideration of the peak sharpness; with A, = 0.5 the peak sharpness would be 1.4 to be compared with the observed value of 2.0 * 0.2. In view of the likely presence of other ‘errors’, not allowed for in the analysis, it is unwise to press the x2-analysis too far; rather, we conclude that ‘oxygen predominates’. Very approximately it is likely that O/C > 2.5. The inferred value, O/C 2 2.5 is clearly inconsistent with that for low energy cosmic rays (say E < 10” eV) and is significantly higher than most of the values relating to the Galactic ISM and to solar wind particles, as given in Table 2. However, SN ejecta, as exemplified by SNR values for high mass SN progenitors ( Mprog > 15 MO - see Table 2), satisfy the requirements. The excess of oxygen over carbon for such SN occurs because nuclear burning taking place before the explosion converts carbon into oxygen. Although it is premature to conclude that an SNR from a high mass SN was definitely responsible for the high energy CR for a variety of reasons, including dilution of the SNR ratio by the ambient ISM and the ever-present possibility that a strongly Z-dependent shock acceleration process could yield a situation in which conventional ISM nuclei are accelerated, nevertheless, it is apparent that a high mass SN is a strong possibility. The fact that the required value of O/C ( 2 2.5) is greater than O/C for energies from the lowest to at least 10” eV/nucleon (Table 2) is interesting in its own right. It is likely that these comparatively low energy particles (E < 10” eV/nucleon) are acceler-

Physics 7 (1997) 203-211

207

ated by weak shocks in the more general ISM - with its lower O/C ratio; this aspect will be considered in some detail in a later paper. 3.4. The separation sity peaks

of the ‘CNO’ and ‘iron’ inten-

It is appreciated that the method of analysis adopted so far, by way of the sharpness index, is one of some complexity and indirectness. A more direct approach is to search for the first order effect, viz the signature in the total intensity. The model on which our analysis is based [3] and on which the interpretation of the results largely depends - predicts that the maximum CR energy is given by Em, = 4. Z. 1014 eV for a particular, but very reasonable, combination of SN and ISM properties. The result is that if we persist with our argument that the second intensity peak is due to iron, then measuring back from this peak we should be able to tell what the charge is of the predominant particles in the CNO peak. In terms of energy the ratio of iron peak/‘CNO’ peak will be (26/Z) = 4.3 for carbon and 3.25 for oxygen. The relationship between the mean size of a shower, N,, and its primary energy, E, at mountain altitude, is universally written as log N, = a + b log E where E is the primary particle energy (in GeV) and N, is the shower size at the detection level. In principle, a and b depend on primary mass, interaction model and depth of observation but this dependence is very weak. We have studied the dependence from various calculations reported in the literature, for the quantity b (‘a’ is not as important since we are examining the difference in the peak intensities). For protons and showers in the vertical direction near sea level, we find: b = 1.13 [23], 1.12 [24], 1.13 [25], 1.18 [26], 1.14 1271 for what we think is a representative set of calculations. All the calculations show, as expected, a small increase in going to heavier nuclei, typically Ab = 0.06 in going from protons to iron. Transferring from sea level (1034 gem-*) to the average atmospheric depth adopted here (834 gem-2) reduces b by typically 0.03. Averaging the values and transforming to iron and 834 gem-* yields b = 1.17. In the present work we use the results of a recent comprehensive set of calculations [28]. Here, for 834 gem-*, a = - 1.36 and - 1.74, b = 1.16 and 1.20

A.D. Erlykin. A. W. Wolfendale/Astroparticle

208

for CNO and Fe respectively. ‘b’ is seen to close to the average of the previous set and the uncertainty in this quantity is probably no more than f0.02. The displacement of the peaks then follows;

A log N, = 0.54 for oxygen;

m

6

= 0.68 for carbon.

Physics 7 (I 997) 203-211

Allowance for curvature in the single particle spectrum near maximum, the different amplitudes of C and 0 and the effect of fluctuations changes the values (see Fig. 2) to A log N, = 0.57 for oxygen; = 0.70 for carbon. These are the values shown in Fig. 3.

MEAN DISPLACEMENT OF INTENSITY POINTS FROM THE KNEE I ” I a ” 8 y $ymw

f

A(W’,)

Fig. 3. a. Displacement of A (log N. 3 . I( N,)) from the running mean over A log N, = f 0.25 versw log N,. The N, values are displaced, in each experiment, so that the ‘knee’ is in the same place, as in Fig. 1. The dashed line is drawn through the weighted averages with weights inversely proportional to squared errors. The dash-dotted line is the same, but weights being inverse errors. b. Mean displacement of intensity points from the knee. The ‘0’ and ‘Fe’ peaks arc strongly visible. The displacements expected from pure 0 and C peaks are. indicated by arrows. The full line is our best-fit from the model; it is clearly not a perfect tit although the peaks are in the correct positions.

209

A. D. Erlykin, A. W. Wolfendale/ Astroparticle Physics 7 f 1997) 203-21 I

Here, then, is another discriminant for the oxygen, carbon problem. In determining the actual value of A log N, we used the following method. Each size spectrum was analysed by adopting a running mean over A log N, = f0.25 and by determining the difference of each intensity point from the running mean. By ‘intensity point’ we mean log( N,’ . I( N,)>. This method has the advantage of providing an accurate estimate of the mean positions of the centers of the peaks although the relative magnitudes are not represented; this is because the widths of the peaks are not the same (nor should they be). The actual profiles of the peaks will be considered later in a separate analysis. The results for the measured displacement of the peaks are given in Fig. 3 where the expected displacements for 0 (0.57) and C (0.70) are also shown. The peak intensity is seen to be close to ‘Fe-O’, implying that, again oxygen predominates. Allowance for statistical errors and the effect of uncertainty in b referred to above results in a conservative estimate: O/C 2 1.5. Fig. 3 is also of value in giving further contirrnation to the validity of the ‘iron peak’ as being an actual excess. It will be noted that two sets of points are given. They differ in that one takes the individual weights to be proportional to the inverse of the square of the statistical errors, the other uses simply the inverse of the error. In view of the undoubted presence of errors other than statistical - which degrade the weight of ‘very precise’ measurements more so than those of lower precision, which already have low weight - the simple inverse is probably the safer one to use.

Table 3 Iron and oxygen abundances:

iron/oxygen

3.5. Relative amplitudes

of the 0 and Fe peaks

Clearly, there is information of relevance in the relative amplitudes of the oxygen and iron peaks, and in the magnitude of the intensity of the heavy component. As remarked already (Section 3.3) the relative magnitudes of 0, H and Fe are tuned to the observed shower size spectral shape. Fig. 2 gives the constituent energy spectra with the constituent shower size spectra from each component being indicated; it will be noted that the ratio of iron to oxygen is 10-O.’ = 0.20 for energy per nucleus. The corresponding ratio in terms of energy per nucleon is 5.7%. Inspection of Table 3, which gives Fe/O ratios for a variety of situations shows a wide range of values. As with the situation for Table 2 we can consider some average values, thus: ‘solar system ISM’ - 4%; SN ejecta = 1.5%; energetic solar phenomena = 20%; cosmic rays, low energy (N 300 MeV/nucleon) = 2.4%, high energy (10’2-10’4 eV/ nucleon) 3 10%. Before making our comparison we note that, unlike the situation for C and 0, 0 and Fe are well separated in the Periodic Table. Thus, the acceleration efficiency as a function of Z will be important, as well as the nature of the input nuclei from the ISM (assuming, as we do, that SNR shocks accelerate particles from the ‘thermal pool’). In a later publication we will examine the ‘acceleration efficiency’ aspect in some detail, suffice it to say that we interpret the well-known correlation of the low energy CR intensity divided by solar system abundance with the first ionization potential rather as

ratio (and Fe/CNO) Ratio

Solar system [l 1) Solar photosphere ‘Local galactic KM’ [ 141 SNR: 10 MO progenitor [20] Solar wind [l l] Solar energetic particles [ 111 Solar corona [ 111

‘Corrected

for loss by fragmentation

3.8% 3.5% 4% = 1.5% 19% 22% 22%

during propagation

Ambient CR f Fe / 0) Low energy

- 200 MeV/nucleotP

[ 121, 4%

Ambient CR (Fe / CNO) Low energy - 200 MeV/nucleon” [12], 2.4% High energy [ 13,221 10” eV/nucleus 64%/nucleon 10% lOI eV/nucleus 58%/nucleon 9% High energy [our analysis] Single source: per nucleus: 20%. per nucleon: 5.7% from the sources, viz. ‘source’

spectra.

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A.D. Erlykin, A. W. Wolfendale/Astroparticle

a correlation with Z itself. If this is a general law, and we have as yet no proof, then we would expect for accelerated SN ejecta (our contention) a Fe/O ratio of 1.5% X (Z,,/Z,) viz. 4.9%. On the other hand, with solar system material (for which the ratio is _ 4%) the corresponding Fe/O ratio would be 4% X (26/8) = 13%. ‘Our’ 5.7% is clearly nearer the SN ejecta value. 4. Conclusions A number of analyses add weight to our earlier contention [1,2] that a single SNR is accelerating particles from a medium which is rich in SN ejecta (and material ejected before the SN). These analyses are: (i) The demonstration that the narrowness of the ‘CNO-peak’ in the shower size spectrum and its sharpness in the knee shows that one of the components, must dominate. Our calculations yield a dependence of sharpness on shower size (Fig. 2) which indicates that the preferred component is oxygen. (ii) The separation of the CNO and Fe intensity peaks indicates also that oxygen and not carbon predominates (iii) The relative height of the Fe and 0 singlesource spectra, invoked by us, is close to what would be expected from SN-ejecta being accelerated by a mechanism similar to that invoked to explain the relative intensities of low energy particles. The low energy particles have an intensity which is in accord with solar system material accelerated with an efliciency proportional to Z, the operative ‘energy’ being energy per nucleon, and this efficiency ‘law’ seems to hold for the single source particles, too. The conclusion that SN-ejecta are preferentially accelerated receives strong support from the fact that there is no evidence for hydrogen and helium nuclei coming from the single source. Considering hydrogen, the lack of a peak in the size spectrum at < 2, log N, - 5 in Fig. 2 implies hydrogen/oxygen a value much smaller than that seen in low energy cosmic rays (220 for the same energy per nucleon, viz. an expected value of N 25 for the same energy/nucleus and a differential energy spectrum of the form E-‘>. Later work will deal with the acceleration mechanism and the case will be put forward for the cosmic

Physics 7 (I 997) 203-21

I

ray spectra having their mass spectrum as measured because of the Z-dependent acceleration mechanism rather than the commonly held view that many individual sources inject mass components dependent on their first ionization potentials. In fact, it has been pointed out [29] that the first ionization potential is well correlated with the condensation temperatures of the elements; thus, condensation from gas to dust phase may play an important part in defining the chemical composition of the cosmic rays. Clearly, we have at least three possibilities for the observed cosmic ray composition (models based on: first ionization potential, condensation from gas to dust, and now a Z-dependent acceleration). It should be made clear, however, that our conclusions about the CNO peak being mainly oxygen and the second peak being due to iron are not dependent on the subtleties of the acceleration process.

Acknowledgements The authors are grateful to Professor G.B. Khristiansen, M. Nagano, G. Navarra and N.M. Nesterova for providing numerical data on EAS size spectra and for useful discussions. They also thank Professors E. Berezhko, L. Drury, N. Hotta, V. Prosin, G. Schatz and A.A. Watson for helpful comments. Dr. S. Machavariani is also thanked for her help in processing the data. The Royal Society, Trevelyan College, Durham and the UK’s Particle Physics and Astronomy Research Council all contributed financial support. ADE thanks particularly the Senior Common Room of Trevelyan College for convivial company and friendship.

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