Overview
We outline the role of the location of the shower maximum in the atmosphere for the interpretation of the primary particle parameters, its dependence on primary energy and mass, and illuminate the different possibilities that air shower observables offer to estimate the depth of the shower maximum. These are explained on the basis of measurements of ground level observables such as atmospheric Cherenkov or fluorescence photons, shower particles, and on combined data from hybrid experiments. The essentials of the associated theoretical work are discussed and results from simulations that are needed for the interpretation of the measurements are summarized. The discussion is kept on a more general level, details are to be found in the chapters that deal with the specific observables (Chaps. 10, 16 and 17). Subsequently, the influence of different atmospheric effects such as seasonally changing density profiles, or the use of different atmospheric models on the height of the shower maximum and the consequences for the interpretation of the data with respect to primary mass are analyzed. The concept of the elongation rate is introduced and its interpretation discussed. Numerous experimental and theoretical data are presented.
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Notes
- 1.
Note that some authors refer to the depth of shower maximum as the elongation, not to be confused with the elongation rate.
- 2.
Molecular effects that influence the radiation length in air are discussed in Sect. 4.2.2, 6.2, and in Chap. 21.
- 3.
For a more complete list of references concerning the Cherenkov technique and measurements, see Chap. 16.
- 4.
For showers of much lower primary energy a smaller core distance is more suitable. This is discussed in greater detail in Chap. 16.
- 5.
Further details concerning the primary energy dependence of the lateral density distribution of Cherenkov photons are given in Chap. 16.
- 6.
A different expression is given by these authors in an earlier paper (Hammond et al., 1977a).
- 7.
The authors frequently give 865 g cm−2 for the atmospheric depth for average zenith angles.
- 8.
- 9.
Due to the finite size of the 34Â m2 detectors an additional uncertainty of about 10Â ns must be added.
- 10.
In the early papers that deal with this topic, D [g cm−2] is interpreted as the depth (or height h 0 [m]) of the first interaction in the atmosphere. However, it was soon realized that the depth (or height h max [m]) of maximum development, X max [g cm−2], as defined earlier manifests a stronger correlation with the rise time of the shower front than h 0 (see Fig. 7.19) and is therefore a more reliable signature of the degree of longitudinal development of a shower.
- 11.
Note that for fluorescence measurements the air Cherenkov component of the showers can present a disturbing background contribution that must be accounted for.
- 12.
These detectors do not have omnidirectional sensitivity, i.e., they do not have a true Fly’s Eye geometry, but cover only a limited solid angle, adequate to overlook the air space above the surface array.
- 13.
Some authors use slightly different values for χ 0; see Sects. 4.2.2, 6.2.2, Table B.2, and Tsai (1974).
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Grieder, P.K. (2010). Depth of Shower Maximum and Elongation Rate. In: Extensive Air Showers. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-76941-5_7
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