Actually, the Yakutsk array has two kind of triggers to select the showers from the background: produced by the scintillators and by Cherenkov light detectors.
The first one is operating when the coincident signal (particle density > 0.5 m^{-2}) in two scintillators of each station within 2 microseconds occurs - the signal passes then on to the central controller. Trigger-500 is then produced in the case of coincident signal (in 40μs) from three or more stations at ~500 m spacing. Similarly, trigger-1000 is produced by ~1 kilometer spacing stations.
The second case is photomultiplier tube (PMT) detectors subset which has independent Cherenkov light trigger formed by three or more PMTs having detected light intensities above given threshold within 10 microseconds. The signal integration time of the individual PMT is 0.5 microseconds.
The main distinctive feature of the Yakutsk array is the air Cherenkov light measurement. The total flux of the light emitted in atmosphere, Q_{tot}, is used as the main estimator of the primary particle energy. In order to derive the relation between Q_{tot} and ionization loss of the shower electrons in atmosphere we have to use the classic formula by Tamm and Frank for the Cherenkov photons emitted when relativistic electron moves in air faster than light (phase velocity c/n). Resulting formula gives a relation between Q_{tot} and ionization loss of the shower in atmosphere with parameters determined by detector sensitivity and atmospheric transparency factors characteristic for the Yakutsk array. Estimated values of ionization loss Eem are shown in Figure together with model calculation results in the case of primary proton (P) and iron nucleus (Fe).
Other portions of the energy carried out by electromagnetic and muonic components beyond the surface is evaluated using the total number of electrons and muons measured on the ground. Residuary energy fractions transferred to neutrinos, hadrons, etc. (illustrated in Figure), unmeasurable with this array, are estimated by model calculations. In this procedure only about 10% of the primary energy is evaluated using model assumptions. That is why we consider the energy estimation algorithm in use in the Yakutsk group to be model-independent in the first approximation.
To derive the array acceptance equal to the product of array area, observation periods duration and solid angle, we have used the real duration of the array duty time periods; and have calculated the shower triggering area as a function of energy and zenith angle; solid angle = p . The array configuration has been changed several times since 1974; the actual perimeter was used for each particular time period. For the highest-energy showers the extended perimeter was applied. In this case the array area is increased 1.4 times while the shower parameters reconstruction is still possible with acceptable error.
In addition to the charged particle detection on the ground, we have another technique at the Yakutsk array - the air Cherenkov light measurement, which can be used to draw out the CR spectrum in independent way. The Cherenkov detector sub-array is covering only about 3 square km area, while scintillator stations can measure the spectrum at highest energies.
The resulting differential all-particle spectrum of cosmic rays is given in Figure in comparison with the Yakutsk array spectrum derived from the charged particle measurements under trigger-500 and trigger-1000 within array area, and within extended array area for the events of the highest energies selected with trigger-1000. Two spectra of the Yakutsk array are compatible within errors above 1 EeV but diverge at lower energies. Possible reason of a discrepancy is systematic error in primary energy estimation near the scintillator threshold of the trigger-500.
We confirm with both datasets analysis the existence of an 'ankle' feature in the shape of spectrum below 10 EeV, i.e. the flattening in the spectral index revealed earlier by all the groups working in this energy range. At the highest energy end of the spectrum we still have a deficit in agreement with the expected GZK cutoff due to interactions of CRs with relic microwave background. The Cherenkov light detector data is compatible with a well-known 'knee' feature of spectrum at ~3 PeV.
Two irregularities of the measured spectrum - the 'knee' and the 'dip' can be explained in the model of anomalous diffusion of galactic cosmic rays in fractal interstellar medium as was shown by Lagutin et al. Resulting spectra of the primary nuclei groups are shown by curves in Fig. 3, together with the total spectrum marked 'All'.
Comparison of our results (triangles – scintillator data, squares – Cherenkov light data) with other spectra measured with AGASA (circles), Auger (crosses) and HiRes (rhombuses) arrays is shown in Fig. 2. In the energy range below 1 EeV intensities are highest of the Yakutsk array data. Most likely it is due to different energy estimation technique used in three cases - resultant energies diverge. In AGASA case the model dependent relation between S_{600} and E is used; HiRes team measures the fluorescence light flux which is connected to ionization loss of electrons in atmosphere; both methods are used by Pierre Auger Observatory. Our estimation for vertical showers gives energy higher than model calculations by (30-40)% at E~0.5 EeV and by (15-20)% at E~50 EeV.
The spectrum tail above 10 EeV measured with scintillators is consistent with the GZK cutoff contrary to AGASA result, although the statistical significance of this conclusion is insufficient due to a few showers detected in the highest energy domain.
]]>The optimal primary mass composition (supposed consisting of 5 nuclei groups) which minimize chi-square deviation of the model distribution from observed one is given in table in three energy intervals.
Primary energy, EeV | P, % | α, % | Medium, % | Heavy, % | Superheavy, % |
0.5 | 39±11 | 31±13 | 18±10 | 7±6 | 5±4 |
1 | 41±8 | 32±11 | 16±9 | 6±4 | 5±3 |
5 | 60±14 | 21±13 | 10±8 | 5±4 | 3±3 |
In the framework of QGSjet model one can conclude that the average mass composition of cosmic rays changes with primary energy. At E~1 EV the PCR flux consists of ~70% protons and helium nuclei, while it reaches ~80% above 5 EeV.
Another possibility to infer the mass composition of PCR is to use the muon component measurements in EAS. In this case we have selected showers with E≥1 EeV and zenith angles θ<60^{0}. The shower axes are within the array area and not less than three muon detectors have nonzero responses in a particular shower event.
The muon density at distance 1000 m from the shower core is analysed as a function of primary energy (Fig. 2).
In Fig. 2 the experimental data are given in the energy intervals 1-10 EeV (squares), 10-100 EeV (circles) and 100-1000 EeV (triangles). The QGSjet model calculation results are shown by dotted line (primary proton, ±1σ) and by dashed line (iron nuclei). Solid lines (red and black) show the upper and lower limits in the case of photon origin EAS. The conclusion can be drawn, confirming one given above, that air showers at E≥3 EeV are formed mainly by light nuclei with the pronounced fraction of protons and helium.
]]>It should be noted that in this energy region the observed distribution is affected by the inhomogeneity of the sky survey during the diurnal cycle and seasonal variations of atmospheric conditions. That is why the special correction method was used in the first two lowest energy intervals.
Table lists the results of harmonic analysis. There is no anisotropy in the energy intervals except 10-30 EeV where we found a significant (~ 3s ) first harmonic amplitude in the right ascension: A_{1}=26.4± 8%, j _{1}=2.3± 1.2^{h}. Reducing log_{10}E interval twice or to quarter doesn’t eliminate the anisotropy. It remains if we divide an observation period into two equal parts as well.
Energy bins, lgE, eV |
Event number |
A_{1}, % |
d A_{1}, % |
j _{1}, hrs |
d j _{1} _{ }hrs |
p(>A_{1}) |
Observation period |
17.0-17.5 |
147314 |
0.5 |
0.5 |
21.1 |
3.8 |
0.399 |
May1982-May2000 |
17.5-18.0 |
88208 |
1.1 |
0.7 |
23.6 |
2.4 |
0.069 |
May1982-May2000 |
18.0-18.5 |
27301 |
0.7 |
0.9 |
22.7 |
4.6 |
0.712 |
Jan1974-May2000 |
18.5-19.0 |
3250 |
3.6 |
2.5 |
2.9 |
2.7 |
0.355 |
Jan1974-May2000 |
19.0-19.5 |
312 |
26.4 |
8.0 |
2.3 |
1.2 |
0.004 |
Jan1974-May2000 |
> 19.5 |
37 |
6.8 |
23.2 |
6.3 |
13.1 |
0.959 |
Jan1974-May2000 |
In order to reveal the area on the sky where an excess flux is located we have used the wavelet analysis which has been already demonstrated to be going on well in many applications in various scientific fields. The continuous isotropic wavelet transform of the observed distribution in equatorial coordinates is convenient to search for large-scale anisotropy in arrival direction distribution. The wavelet analysis is a logical evolution of the harmonic analysis which is effective for determination of the local features of aperiodic functions. The method, as well as the harmonic analysis, is based on the expansion of an original function in an orthonormal basis, but wavelets, in contrast to harmonic functions, are localized in both physical and Fourier transform spaces.
The deviation of the observed-to-expected amplitude ratio of the wavelet coefficient from 1 can be used as a measure of deviation from the isotropic expectation. The most appropriate in this case is the Marr wavelet (‘Mexican hat’); 2-dimensional version is illustrated in Fig. 1.
An expected declination spread of isotropic arrival directions is sufficiently non-uniform due to array acceptance. So we have calculated the wavelet transform as a sum of delta functions in both cases: for observed and expected isotropic distribution of N equatorial angles in each energy bin. Expected one is averaged over a sample of 1000 trials. To estimate the dispersion of the transform, (wv_{max}-wv_{min})/(wv_{max}+wv_{min}), the first harmonic amplitude in right ascension was used. Resulting observed/expected ratio is given in Fig. 2. There is an energy bin, 10-20 EeV, where the observed amplitude is significantly greater than isotropic one: wv_{observed}/wv_{isotropic}=2.83± 0.51; the maximum coordinates are α=(2.3± 1.3) h; δ=52.5^{0±}7.5^{0}; scale parameter 10^{0}<20^{0}. When R<10^{0 }there is no statistically significant deviation from the isotropic expectation in all energy/angular bins.
As it was shown above, the first harmonic amplitude of the Yakutsk array data distribution in right ascension sufficiently deviates from the expected-for-isotropy value in the vicinity of E=10 EeV. Presumably, the transition region from Galactic to extra-galactic CRs is somewhere below this energy.
As was shown earlier, cosmic rays originating in the Galactic disk have two distinctive features in their arrival directions - galactic plane enhancement and north-south asymmetry - which can be used to detect the Galactic CR contribution to the primary flux in the transition area. An analysis of the UHECR Galactic latitude distribution observed with the Yakutsk EAS array was used to estimate the probable fraction of Galactic protons and nuclei in the primary beam. Indeed, the results show a southern excess in the region 5-20 EeV where the deviation of the North-South asymmety parameter from the value expected in the isotropic case is 3.5s , while the galactic plane enhancement parameter indicates no significant deviation from the situation for no asymmetry.
Our finding with wavelet analysis confirms these hints, and is further strengthening the evidence of the anisotropy in arrival directions of UHECRs detected with the Yakutsk array in the interval 10<20 EeV.
Due to space localization of the Marr wavelet we can point out a sky area where an excess UHECR flux is detected in our data in the particular energy range. The corresponding scale parameter of the wavelet is limited within 10^{0}<20^{0}. It should be noted that an upper limit is due to applicability restriction of the wavelet on equatorial sphere, rather than the data distribution feature.
The anisotropy in arrival directions revealed in the Yakutsk array data by three different methods of data handling can be attributed to non-zero galactic nuclei fraction. These nuclei of average charge ~10 can amount up to 10% of the primary isotropic flux at energy E~10 EeV. In this case the hypothesis is congruent to other indications given by giant arrays of the excess flux of nucleons from galactic plane/center at E~1 EeV.
]]>We used the deviation of the observed number of events N from the expected-for-isotropy number N_{0} in units of the r.m.s.: (N-N_{0})/Ö N_{0}, where N and N_{0} are numbers of EAS in the solid angles with opening angles 8^{0} and 45^{0}, respectively. The values of deviations were found when a 1^{0}*1^{0} area was sequentially displaced over the entire sphere.
Figure shows the relative deviations of UHECR flux (E>8 EeV) in Galactic coordinates. Numerous local regions of positive and negative, high and low, excess around expected-for-isotropy values are seen over the entire sphere. This suggests that the UHECR anisotropy, if exists, is multipolar in pattern.
No excess flux is observed from the Galactic Disk, except the spot at l_{G}=137.4^{0} where Galactic and Supergalactic planes intersect. There is no slightest hint at an excess flux even from the Galactic Center, where the most active and powerful matter conversion processes take place. There is no excess flux at the exit of the Local Galactic Arm either. These facts probably indicate the minor role the Galaxy plays in generation of particles in the energy region above 8 EeV.
A completely different picture opens up in the Supergalaxy. A correlation between UHECR arrival directions and the Supergalctic Plane (shown by solid curve) is seen in the Northern hemisphere. A pronounced excess in the sector l_{SGÎ }(0^{0}-210^{0}), with its maximum at l_{SG}=120^{0} is also seen. However, there is no such clear correlation in the Southern Hemisphere, except the local region of the sky with equatorial coordinates α=0^{0} and δ=-85^{0}. Curiously, it lies near the Supergalactic plane in a direction that is almost opposite to that of the Northern hemispere. A whole picture indicates a dominant role the Supergalaxy (Local Supercluster of galaxies) plays in forming the excess cosmic ray flux at energies above 8 EeV.
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An example of very inclined EAS detected in Yakutsk |
The geomagnetic field effect on charged particles in inclined extensive showers is interesting both for complete use of observational data in analysis – it would enhance the utilized aperture of air shower array, and to derive the enhanced information on EAS development in atmosphere, concerning the high energy muonic component, mainly.
These showers should differ from vertical one by the reduced electron-to-muon ratio because their electromagnetic component is strongly absorbed by the greatly enhanced atmospheric slant depth, and by the pronounced asymmetry in lateral distribution of muons due to divergence of charged particles in the Earth’s magnetic field.
The analysis of inclined showers produced by the primary protons, nuclei, photons or neutrinos requires a radically different approach.The data provided by these events are difficult to analyse because the conventional methods used for interpretation of low zenith angle showers are usually based on the approximate circular symmetry of the density distribution. An example of the very inclined shower detected with the Yakutsk array is given. Upper part shows the particle density as a function of distance to x and y axes in the chosen bands. In the part below the particle number densities in a plane perpendicular to shower axis are given. Oval lines are equidensity level curves. Vector above x axis is a projection of the Lorentz force vector.
Ovality of lateral density distribution of muons |
The ovality of muon density patterns arises because of the different muon paths from the production point to ground level. The cumulative effects of all muon interactions (such as magnetic deflections and continuous energy loss) and decays depend mainly on the Lorentz force. It can be parameterized by a ‘geomagnetic factor’ in a particular event, g=sinξsec^{2q}, where ξ is angle between shower axis and field vector.Muon density distribution ovality can be measured as the ratio <a/b> at equal density, where a and b are projections of the shower core distance on axes along and perpendicular to ξ.The ovality measured in 12 very inclined EAS (from q =67^{0} to 78^{0}) with energies above 10 EeV, i.e. a/b ratio as a function of the geomagnetic factor of showers reveals the pronounced effect beyond the bounds of statistical errors and in agreement with model prediction (dashed curve).
Azimuthal distribution of the event rate of showers |
Another effect can be detected in showers with fixed zenith angle andr _{600 }- the particle density at r=600 m from the core: one can measure the azimuthal modulation of EAS event rate due to the muon density lateral distribution asymmetry depending onc . Indeed, the observational data of the Yakutsk array have revealed the geomagnetic effect on the reliable statistical basis. Figure shows the distribution of the relative number of EAS events above 0.05 EeV measured with the Yakutsk array in the period 1974-1995, zenith angles in the bins 20^{o}-30^{o}, 40^{o}-50^{o}, 60^{o}-70^{o}. The function 1+A_{1 ´ }cos(a -a _{1}) is shown by dashed lines.
Zenith angle dependence of harmonics |
In Figure on the right the amplitude (upper panel) and phase (lower panel, 1^{st} harmonic) of the first three harmonics of the distribution versus zenith angle are shown The second and third harmonics amplitudes come up to the expected value for the uniform distribution of azimuths shown by a dashed line for the measured number of showers in each interval. Dotted lines show the r.m.s. deviations from the expected amplitudes. The first harmonics amplitude (triangles) essentially differs from zero at zenith angles larger than 20^{0}. In this region one can discard the uniform distribution with the chance probability below 10^{-14} basing on the probability for the uniform distribution to have the first harmonic amplitude A_{1}: P(>A_{1})= exp(-n´ A_{1}^{2}/4). The approximation 0.2´ sin^{2q}is shown by the dash-and-dot line. The first harmonic phase coincides with the magnetic meridian in Yakutsk.
For showers arriving from the north observed particle densities in detectors are higher than in “southern” showers of the equal r_{600} with equal zenith angle. When we select showers with the same observed densities r _{600}, the real primary energy of showers arriving from the north is less. It results in a decrease in corresponding event rate, because the number of showers at the array diminishes as the energy decreases in the region 0.01<E<0.1 EeV. The amplitude of the first harmonic is defined by a relative value of density changemeasured for the southern and northern showers.
The inclined showers ought to be analyzed taking into account a geomagnetic effect on the lateral distribution of charged particles. A common algorithm based on the axially symmetric function, for instance, results in the primary energy overestimated up to 28%.
Geomagnetic distortion of EAS arrival directions |
Observed distribution of arrival directions in a horizontal system is distorted due to azimuthal event rate modulation in the geomagnetic field. The right ascension distribution isn’t affected because of diurnal spreading. On the other hand, the declination distribution should be corrected.
We have used two distributions in azimuth: the uniform one and the observed spread of the Yakutsk array data in order to simulate the ratio of distorted to isotropic arrival directions. From the experimental dataset zenith and azimuth angles were extracted of showers in the energy ranges above 0.1 and 2 EeV; then the uniform sidereal time distribution was added to convert arrival directions to equatorial and galactic co-ordinates. In the case of isotropic spread a uniform distribution in azimuth was used instead of experimental one. The resultant ratios of observed to isotropic shower numbers as a function of declination and galactic co-ordinates are found. There exists an obvious systematic disfiguration of the initial isotropic distribution of a magnitude up to 10%.
We have demonstrated the azimuthal effect on EAS event rate caused by the geomagnetic field using a bulk of the Yakutsk array data above 0.1 EeV. The value of the effect is approximately the same in the whole energy range. The primary energy and arrival directions of showers appear to be modified due to geomagnetic distortion of the EAS particle density with a magnitude up to 10-20%, relative to the case when a field is switched off.
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