Cosmic rays

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The cosmic radiation (obsolete also cosmic rays ) is a high-energy particle radiation which comes from the sun, the Milky Way and distant galaxies. It consists mainly of protons , as well as electrons and completely ionized atoms. About 1000 particles per square meter per second hit the Earth's outer atmosphere . Interaction with the gas molecules creates a shower of particles with a large number of secondary particles, of which only a small part reaches the earth's surface.

The secondary cosmic radiation changed by interactions with the atmosphere (with up to 10 11 particles per primary particle) can be detected on the ground or by balloon probes . The air showers are a few square kilometers horizontally, but only a few meters vertically. They give clues to the type and energy of the cosmic primary particles. The course of its front suggests the direction of incidence.

In 1912 Victor Franz Hess postulated a so-called cosmic radiation in order to explain the higher electrical conductivity of the atmosphere measured during a balloon flight and the increase in gamma radiation at higher altitudes. This is secondary cosmic radiation.

The cosmic gamma radiation is generally not expected to cosmic rays. Nevertheless, the term cosmic "radiation" has held up.

Classification and designations according to origin

Spatial distribution of the sources of cosmic gamma rays with energies above 100 MeV. Their distribution also gives clues to the origin of the particle radiation. The bright band is the Milky Way, with its center in the middle.

Depending on the origin, cosmic radiation is divided into solar radiation ( English Solar cosmic ray , SCR ), galactic (English galactic cosmic ray , GCR ) and extragalactic radiation.

Solar wind
Particle flux densities around 10 7 cm −2 s −1 , low energies, mainly protons and alpha particles. Particle density around 5 cm −3 . Cause of the northern lights .
Sun flares , CME
Characteristics: temporal increase in particle flux density within a few hours and days to 10 8 to 10 10 cm −2 s −1 , energies around 10 MeV, particle density up to 50 cm −3 .
Van Allen belt
is sometimes counted as cosmic rays.
Galactic Cosmic Rays (GCR)
low particle flux densities, very high energies (1 GeV and higher), proportion of heavy ions up to iron. With increasing energy, the deflection by magnetic fields decreases and the anisotropy of the radiation increases.
(Engl. Anomalous cosmic rays anomalous cosmic rays , ACR )
probably arises from the interaction of the solar wind with the local interstellar matter (LISM) in the area of ​​the termination shock near the heliopause . Characteristics: lower energy than GCR , fewer hydrogen and carbon ions than hydrogen and carbon in the LISM.
Extragalactic Cosmic Rays
Highest energies up to a few 10 20  eV. The flux densities are below 10 −20 particles per second and square meter. Like galactic cosmic rays, extragalactic rays also consist of protons and heavier ions.
Shock front acceleration (theoretical): the incident proton is mirrored back and forth between two shock fronts and absorbs energy in the process.

Possible sources of galactic and extragalactic cosmic rays could only be identified in the last few years. Candidates for this include shock fronts from supernova explosions, cosmic jets from black holes or from pulsars . For particle energies below 10 18  eV (= 1 EeV) an origin within the Milky Way is assumed, sources in other galaxies are more likely for higher energies . Cosmic magnetic fields deflect the particles. They therefore seem to fall almost isotropically on the earth. However, since many sources emit gamma radiation in addition to particles,  several sources have already been identified for the energy range below 10 15 eV.

It is also assumed that at least some of the sources of cosmic rays also emit neutrinos . In July 2018, a source of extragalactic radiation, a black hole in the galaxy almost four billion light-years away with the catalog number TXS 0506 + 056 in the constellation Orion, was discovered in this way.

composition

Energy spectrum of cosmic rays

The galactic cosmic radiation consists of approximately 87% protons (hydrogen nuclei), 12% alpha particles (helium nuclei) and 1% heavier atomic nuclei. The frequency distribution of the atomic nuclei corresponds roughly to the solar element abundance . Exceptions are mainly lithium (Li), beryllium (Be) and boron (B), which are up to 500,000 times more common in cosmic radiation than in solar matter as a result of spallation reactions when passing through interstellar matter. When interacting with the atmosphere, one does not observe the original radiation on earth, but rather the reaction products from the interaction with the atmosphere, in particular with nitrogen and oxygen as well as carbon . The proportion of elements heavier than iron and nickel is not yet exactly known, traces of bismuth have been detected.

The distribution of the particles per time, N (E), as a function of the energy E follows a power law:

N (E) ~ E −γ

With:

γ = 2.7 for E <4 · 10 15  eV
γ = 3 for 4 x 10 15  eV <E <5 x 10 18  eV
γ <3 for E> 10 18  eV
γ ≫ 3 for E> 10 20  eV (energies greater than 10 20  eV are not observed)

Measurements carried out in 2008 seem to confirm the GZK cutoff above 5 · 10 19 electron volts . According to this, interactions with the cosmic background radiation limit the particle energy to 10 20 to 10 21  eV if the free path of 160 million light years is exceeded.

Only small traces of antimatter can be found in cosmic rays , and this presumably originates entirely from interactions between charged particle radiation and interstellar gas. This is seen as an indication that antimatter is not permanent in our universe.

History of exploration

Ionization measurements by Hess (1912) and Kolhörster (1913 and 1914)

In 1912 Victor Franz Hess discovered (secondary) cosmic rays with the help of balloon flights in the earth's atmosphere and published this in the Physikalische Zeitschrift . Since the origin of the radiation was unclear, it was called cosmic radiation for a long time . After cosmic rays had proven to be extremely important for the discovery and research of new elementary particles through the work of other researchers, Hess received the 1936 Nobel Prize in Physics .

In 1929, Walther Bothe and Werner Kolhörster tried to prove that cosmic rays were high-energy gamma rays . For their experiments they used a measuring arrangement that essentially consisted of two Geiger-Müller counter tubes , between which absorbers of different thicknesses in the form of iron or lead plates could be placed. They assumed that a gamma quantum can only be detected with a Geiger-Müller counter tube if it first knocks an electron out of an atom. This electron would then be detected by the counter tube. In fact, they very soon discovered coincidences , i.e. events that occurred in both counting tubes at the same time. In these cases an electron released by a gamma quantum must have crossed both counting tubes.

They determined the energy of these supposed electrons by placing thicker and thicker absorbers (metal plates) between the two counting tubes until there were no more coincidences. To their astonishment, Bothe and Kolhörster found that 75% of the coincidences could not even be prevented by a four centimeter thick gold bar. In fact, the particles that triggered the Geiger-Müller counter tubes were as penetrating as the cosmic radiation itself. Accordingly, contrary to popular belief, the radiation could not be gamma radiation, but had to consist at least partly of charged particles with very high penetrating power. They were able to show that the secondary radiation, which is generated by the primary cosmic radiation in interaction with our atmosphere, consists of electrically charged particles.

Marcel Schein in Chicago was able to prove in the early 1940s that the particles of primary cosmic radiation are protons . From 1938 to 1941 he carried out a series of experiments with balloon probes to investigate cosmic rays in the highest altitudes of the earth's atmosphere and was able to show that these particles could not be electrons or positrons , since their properties did not correspond to the behavior of high-energy electrons that was already known; it had to be protons .

Scott E. Forbush demonstrated in 1946 that solar flares emit particles up into the GeV range.

In order to explain the high energies of the primary particles, Enrico Fermi postulated a possible acceleration mechanism in 1949 as a statistical acceleration in magnetized plasma (“magnetic clouds”) with flat shock fronts . A shock front can be given, for example, by a gas that propagates very quickly compared to the surroundings. Shock fronts occur mainly after supernova explosions in the repelled shell of the supernova . With this statistical acceleration, the energy of the gas is transferred to the particle over a long period of time by means of "impacts". This creates a power spectrum, but with a spectral index γ that differs from the measurement data.

Significance in the history of research

Before the development of particle accelerators for the GeV energy range, cosmic radiation was the only source of high-energy particles for experiments in particle physics . Many particles, e.g. B. positron , muon , pion , kaon , were first detected in cosmic rays. For this purpose, measurements were made on mountain peaks or with photosensitive plates carried by free balloons .

Interaction with matter

Cosmic radiation triggers spallation reactions when it penetrates matter . By measuring the frequency of the spallation products in meteorites , for example, their length of stay in space can be determined ( irradiation age ). It was also possible to establish that the mean intensity of galactic cosmic rays has changed by a factor of two at most for at least 100 million years.

Interaction with the earth's atmosphere

Particle shower

Cosmic particle shower, triggered by a high-energy particle in the atmosphere at an altitude of 20 km

When entering the earth's atmosphere at an altitude of 20 km above the surface, the cosmic rays generate particle showers .  More than a million secondary particles are created from a proton with an energy of 10 15 eV. Only a small part of them reach the surface of the earth.

By spallation originate from nitrogen and oxygen atoms neutrons, protons, charged (π + , π - ) and neutral (π 0 ) pions . The neutral pions annihilate, the charged ones decay into muons :

The muons are also unstable and decay into electrons and neutrinos :

A chill possesses

  • a soft electromagnetic component, among other things by the decay of π 0 and the annihilation of positron-electron pairs
  • a hard muonic as well
  • a hadronic component that contains mostly protons and neutrons.

The components can be registered independently of each other on earth and serve to detect cosmic rays.

Cosmogenic nuclides

Cosmic rays contribute to the formation of a number of cosmogenic nuclides in the earth's atmosphere and crust, which are often radionuclides . On the one hand, heavy atoms are split into lighter atoms by cosmic rays through a spallation reaction . This is how so-called meteoric beryllium is produced from the oxygen in the earth's atmosphere:

On the other hand, atoms can capture secondary neutrons or protons, i.e. those that are released during spallation reactions like the one above, from cosmic rays. This is the main mechanism of production for the carbon isotope C-14:

The resulting C-14 is technically of interest for radiocarbon dating : It is bound in living plants during the metabolism, but decays with a half-life of 5730 years, so that after the end of the metabolism, its content decreases and its share on the age of organic substances can be closed.

Often the production by cosmic rays is the greatest natural source of these radionuclides, which brings a number of uses for isotope research . Due to the radioactivity of the cosmogenic nuclides, their amount remains constant over time. In addition to the 10 Be and 14 C already mentioned, these cosmogenic radionuclides also include 3 H , 26 Al and 36 Cl .

Possible climate impact

Cosmic radiation (red) and global temperature (black) assumed from geochemical findings for the past 500 million years
Galactic cosmic rays and measured global temperature from 1951 to 2006. The temperature (red) shows a clearly positive trend, while this is not the case with the galactic cosmic rays. No trend can be seen here.
The solar activity shields the influence of galactic radiation from the earth according to its changing strength; here the course of solar activity since 1975.

A connection between the formation of clouds and galactic cosmic rays (Galactic cosmic rays, GCR) has been postulated in the USA since the 1970s. Since the 1990s, the Danish physicist and climate researcher Henrik Svensmark contributed in particular to spreading this thesis. An overview study by several international research institutions from 2006 considered the influence of a dynamic heliosphere on the earth's climate as likely when considering very long periods of time. There are various hypotheses about the causal relationship with cloud formation. Research projects on the mechanism of a connection between cosmic radiation and cloud formation are currently underway at CERN (project CLOUD Cosmics Leaving OUtdoor Droplets), the first climate chamber on a particle accelerator.

Nir Shaviv interprets the paradox of the weak young sun and the overall course of the earth's climate history over millions of years as part of an overall model. In addition to an effect of greenhouse gases on the climate, an interplay of solar wind , star formation rate and cosmic radiation are postulated. While in the first three billion years of the earth's history a strong solar wind largely shielded the cooling effect of cosmic radiation, the regularly occurring global cold periods then coincided with equally regular spiral arm passages of the heliosphere, which indicates a significant influence of global cosmic radiation. A study published in The Astrophysical Journal Letters in 2009 tested the hypothesis using a more accurate CO data-based approach and found no evidence of the approach proposed by Shaviv et al. postulated connection. In 2010 it was claimed to have completely refuted Svensmark's theses on the influence of cosmic rays on global warming. A research team led by Frank Arnold from the Max Planck Institute for Nuclear Physics found no correlation between cloud cover and ion concentration when investigating six striking Forbush events .

Another study looked at the relationship between solar activity and cosmic rays in terms of short periods of time. According to this, the recent rise in the air temperature near the ground cannot be ascribed to solar effects. The correlation between temperature and GCR assumed by Svensmark was criticized as being “only indicative” and “misleading”. There is no measurable effect on cloud formation or on the temperature profile. In the years 1951–2006 (see illustration) the air temperatures show a continuous trend, which is missing in the case of cosmic radiation. According to Kasting, the thesis would therefore also be “ (…) highly speculative and, furthermore, the mechanism is unlikely to work as well as the proposer thinks it will ” (Kasting (2005), p. 120, German: “(…) Höchst speculative and the mechanism will hardly be as strong as the lecturer assumes ”).

Shaviv explains the absence of current global warming with the heat storage capacity of the oceans and considers cosmic radiation to be much better suited to explain this in combination than greenhouse gases alone.

The thesis sparked controversy after Shaviv's joint publication with Leibniz Prize winner Jan Veizer in GSA Today. In a comment published in Eos , Stefan Rahmstorf and others assumed that Shaviv and Veizer had serious methodological and content-related weaknesses. Rahmstorf's argument that a recognized physical mechanism was lacking was adopted in the IPCC reports. Veizer and Shaviv rejected Rahmstorf's allegations as politically motivated character assassination.

In a study published by the Royal Astronomical Society in 2012, Svensmark postulated a clear connection between biodiversity, plate tectonics, in particular their influence on the extent of coastal areas and the number of supernovae in the vicinity of the earth over the last 500 million years. Basically, the biodiversity in the sea is dependent on the sea level and the cosmic radiation rate GCR derived from the occurrence of supernovaerates. The primary bioproductivity of the sea, the net growth of the photosynthetically active bacteria there, can only be explained by the GCR. In addition, an inverse relationship can be found between increased supernovae phenomena and the carbon dioxide content of the atmosphere, which Svensmark attributes to increased bioproductivity in colder ocean areas.

Intensity and evidence

Various methods are used to detect cosmic rays. The particle flux (number of incident particles per unit area and unit time) at low energies is large enough to be detected directly with balloon and satellite detectors. At higher energies, the air showers triggered by the radiation are observed from the ground; Large-scale arrangements of many detectors with high time resolution make it possible to reconstruct the energy and direction of incidence of the original particle. Are proven thereby

With fluorescence telescopes (the Fly's-Eye in Utah , USA) the highest particle energy measured to date of 3.2 · 10 20  eV was observed in 1991 , which led to the name “ Oh-My-God-Particle ”. Assuming that the particle was a proton, the center of gravity energy in collisions with particles in the earth's atmosphere was around 10 15  eV (for comparison: the LHC at CERN should have a center of gravity energy of 13 · 10 12 for proton-proton collisions  eV, i.e. about a hundredth of this energy).

A current experiment for the observation of high-energy cosmic rays is the Pierre Auger Observatory , which extends over an area of ​​3000 km². This experiment uses Cherenkov detectors and fluorescence telescopes at the same time.

Apart from the long-term constancy, there are short-term periodic and non-periodic fluctuations in the intensity of cosmic rays. The intensity fluctuates depending on the eleven-year sunspot cycle ; the more sunspots there are, the lower the intensity of the galactic cosmic rays. There is also a 27-day fluctuation that is linked to the rotation of the sun . Faint full-day and half-day fluctuations are also observed by earth-based detectors. Solar flares or other solar activities can also cause sudden, temporary drops in intensity, which, after their discoverer Scott E. Forbush, are called Forbush events . A sudden increase in intensity is also observed less frequently.

Secondary cosmic rays

Of the secondary particles generated in interactions with the atmosphere, mainly positive and negative muons with a flux density of approx. 100 m −2 s −1 can be observed at sea level . The ratio of positive to negative muons is about 1.27. Due to their high energies, these muons can hardly be shielded by ordinary means and are therefore noticeable as a disruptive "background" in particle detectors . For measurements of the particle flux density of cosmic neutrinos, for example, or for gamma spectroscopy of very weak samples, one therefore has to go to laboratories deep underground in old mines or tunnels, e.g. B. the Laboratori Nazionali del Gran Sasso .

The spark chamber is an impressive method of observing the occurrence and direction of flight . However, it is only used for demonstration purposes today.

Cosmic radiation and air traffic

High-energy radiation from space is much more apparent at high altitudes than at sea level. Therefore, the radiation exposure for air travelers is increased. As early as 1990, the International Commission on Radiation Protection (ICRP) determined from estimates that flight personnel are exposed to doses from natural cosmic radiation that are comparable or even higher than those of people who deal with artificial radiation in medicine and technology. The ICRP therefore presented recommendations on dose limit values , which were incorporated into European law in 1996 and the German Radiation Protection Ordinance in 2001. The radiation exposure is particularly high when flying in the polar regions or over the polar route .

The introduction of dose limits requires that the current radiation doses can also be determined. Therefore, as a result of the ICRP recommendations, a number of European institutes set up research programs, the aim of which was the theoretical and experimental recording of natural radiation exposure in airplanes. The EPCARD program was developed at the University of Siegen and at the GSF - Research Center for Environment and Health . With its help it is possible to calculate the dose from all components of the natural penetrating cosmic radiation on any flight route and flight profile.

With a simplified EPCARD version, dose calculations can be carried out on the Internet. This gives airlines the opportunity to determine how high their staff is and whether their pilots even reach the limit of 1 mSv per year set out in the Radiation Protection Ordinance, from which a dose report must be sent regularly to the Federal Aviation Office.

See also

literature

  • A. Unsöld, B. Baschek: The new cosmos . Springer-Verlag, ISBN 3-540-42177-7
  • C. Grupen: Astroparticle Physics . Springer-Verlag, ISBN 3-540-41542-4
  • Gerhard Börner, Matthias Bartelmann: Astronomers decipher the book of creation . In: Physics in our time 33 (3), 2002, pp. 114–120, ISSN  0031-9252
  • Werner Hofmann: The most energetic radiation in the universe . In: Physics in our time 33 (2), 2002, pp. 60-67, ISSN  0031-9252
  • Karl Mannheim ÷ At the source of cosmic rays - observations reveal shock waves from supernova remnants as efficient particle accelerators , Physik Journal 12 (4), 18–19 (2013)

Videos

Web links

Commons : Cosmic Rays  - collection of images, videos and audio files

Individual evidence

  1. Johannes Blümer: Particles in the Pampas. Physik Journal Vol. 9, June 2010, pp. 31-36
  2. n-tv.de: Researchers find neutrino source, riddle about cosmic rays solved , July 12, 2018.
  3. ^ First Observation of the Greisen-Zatsepin-Kuzmin Suppression , abstract from Phys. Rev. Lett. 100, 101101 (2008).
  4. Hess, On the observation of penetrating radiation during seven free balloon flights , Phys. Z., Volume 13, 1912, pp. 1084-1091.
  5. Bruno Rossi : Prof. Marcel Schein . Obituary. In: Nature . Vol. 186, No. 4722, April 30, 1960, pp. 355–356 , doi : 10.1038 / 186355a0 (English, obituary).
  6. Marcel Schein, William P. Jesse, EO Wollan: The Nature of the Primary Cosmic Radiation and the Origin of the Mesotron . In: Physical Review . Vol. 59, April 1, 1941, pp. 615 , doi : 10.1103 / PhysRev.59.615 .
  7. Andreas Börner et al .: First results of surface exposure dating on large glacial debris through in-situ formed cosmogenic beryllium-10 in Mecklenburg-Western Pomerania (northeast Germany) . In: Journal of Geological Sciences . tape 41 , no. 4 , 2013, p. 123-143 .
  8. ^ Robert E. Dickinson : Solar variability and the lower atmosphere . In: Bulletin of the American Meteorological Society PDF 815 kB , 12/1975, Vol. 56, Issue 12, pp. 1240-1248, doi : 10.1175 / 1520-0477 (1975) 056 <1240: SVATLA> 2.0.CO; 2
  9. K. Scherer, H. Fichtner, T. Borrmann, J. Beer, L. Desorgher, E. Flükiger, H. Fahr, SE Ferreira, UW Langner, MS Potgieter: Interstellar-Terrestrial Relations: Variable Cosmic Environments, The Dynamic Heliosphere , and Their Imprints on Terrestrial Archives and Climate . In: Space Science Reviews 127 (1-4), 2006, p. 327.
  10. a b ipcc.ch
  11. CLOUD Project Documents . Retrieved November 25, 2008.
  12. Cloud in the particle accelerator . New project examines the influence of cosmic radiation at CERN . In: SCINEXX , August 27, 2008.
  13. NJ Shaviv: Toward a solution to the early faint Sun paradox: A lower cosmic ray flux from a stronger solar wind , J. Geophys. Res., 108 (A12), 2003, p. 1437, doi: 10.1029 / 2003JA009997 .
  14. ^ Andrew C. Overholt, Adrian L. Melott, Martin Pohl: Testing the Link between Terrestrial Climate Change and Galactic Spiral Arm Transit . In: The Astrophysical Journal Letters . 705, No. 2, October 2009. doi : 10.1088 / 0004-637X / 705/2 / L101 .
  15. Jump up J. Calogovic, C. Albert, F. Arnold, J. Beer, L. Desorgher, EO Flueckiger: Sudden cosmic ray decreases: No change of global cloud cover . In: Geophysical Research Letters , 37, 2010, L03802, doi: 10.1029 / 2009GL041327 , abstract . See also: Cloud cover unaffected by cosmic rays . In: Informationsdienst Wissenschaft , March 9, 2010 and Cosmic rays don't make clouds . In: Spektrumdirekt , March 10, 2010.
  16. klimafakten.de/Urs Neu (2011): "Cosmic radiation causes climate change" ( Memento from January 16, 2012 in the Internet Archive )
  17. M. Lockwood, C. Fröhlich (2007): Recent oppositely directed trends in solar climate forcings and the global mean surface air temperature . In: Proceedings of the Royal Society A, p. 1382, PDF .
  18. IG Usoskin, GA Kovaltsov: Cosmic rays and climate of the Earth: Possible connection. In: CR Geoscience , 340, 2008, pp. 441-450. doi: 10.1016 / j.crte.2007.11.001
  19. Peter Laut: Solar activity and terrestrial climate: an analysis of some purported correlations. In: Journal of Atmospheric and Solar-Terrestrial Physics , Vol. 65, 2003, pp. 801-812, doi: 10.1016 / S1364-6826 (03) 00041-5 , PDF .
  20. ^ Amato T. Evan, Andrew K. Heidinger, Daniel J. Vimont: Arguments against a physical long-term trend in global ISCCP cloud amounts. In: Geophysical Research Letters , Vol. 34, 2007, L04701, doi: 10.1029 / 2006GL028083 .
  21. T. Sloan, AW Wolfendale: Testing the Proposed causal link between cosmic rays and cloud cover . In: Environ. Res. Lett. , Vol. 3, 2008, 024001, doi: 10.1088 / 1748-9326 / 3/2/024001 , PDF, preprint . Proponents such as Svensmark and Shaviv accuse the opponents of making rookie mistakes and systematically ignoring the effects. Counter-argumentation among other things in Is the causal link between cosmic rays and cloud cover really dead ?? April 11, 2008.
  22. ^ IG Richardson, EW Cliver, HV Cane: Long-term trends in interplanetary magnetic field strength and solar wind structure during the twentieth century. In: J. Geophys. Res. , 107 (A10), 2002, p. 1304, doi: 10.1029 / 2001JA000507
  23. ^ JF Kasting: Methane and climate during the Precambrian era . In: Precambrian Research , 137, 2005, pp. 119-129.
  24. ^ J. Shaviv: On climate response to changes in the cosmic ray flux and radiative budget . In: Journal of Geophysical Research , Vol. 110, Edition A8, pp. A08105.1 – A08105.15, 2005, doi: 10.1029 / 2004JA010866 , accessed 08/2009.
  25. Nir J. Shaviv, Ján Veizer: Celestial driver of Phanerozoic climate? In: Geological Society of America . Volume 13, No. 7, July 2003, pp. 4-10
  26. Stefan Rahmstorf et al. (2004): Cosmic Rays, Carbon Dioxide, and Climate . In: Eos , Vol. 85, No. 4, January 27, 2004. Answer: Nir J. Shaviv, Jan Veizer : Detailed Response to “Cosmic Rays, Carbon Dioxide and Climate” by Rahmstorf et al. April 4, 2004.
  27. a b c d e Henrik Svensmark: Evidence of nearby supernovae affecting life on Earth. In: Monthly Notices of the Royal Astronomical Society. 423, 2012, p. 1234, doi : 10.1111 / j.1365-2966.2012.20953.x .
  28. ^ C. Grupen: Astroparticle Physics , Springer 2005, ISBN 3-540-25312-2 , page 149.
  29. radiation exposure of the flight crew. (No longer available online.) In: springermedizin.at. September 29, 2011, archived from the original on August 26, 2017 ; accessed on August 26, 2017 (English).
  30. Online version