#####################################################################################
##  (c) Copyright by Pierre Auger Collaboration 2019                               ##
##                                                                                 ##
##  Publications using or referring to these data should cite the following        ## 
##  reference:                                                                     ##
##                                                                                 ##
##    Alexey Yushkov for the Pierre Auger Collaboration,                           ##
##    "Mass composition of cosmic rays with energies above 10^17.2 eV from         ##
##    the hybrid data of the Pierre Auger Observatory",                            ##
##    Proceedings of the 36th International Cosmic Ray Conference, Madison, U.S.A  ##
##    PoS (2019) 482                                                               ## 
##                                                                                 ##
##  and                                                                            ##
##                                                                                 ##
##    P. Abreu et al (Pierre Auger Collaboration), JCAP 02 (2013) 026              ##
##                                                                                 ##
##                                                                                 ##
##  Data are provided as is and might be subject to future changes.                ##
##                                                                                 ##
##                                                                                 ##
##                                                                                 ##
##  These data are released under the Creative Commons Attribution-ShareAlike 4.0  ##
##  International License (CC BY-SA 4.0). For more details see                     ##
##  http://creativecommons.org/licenses/by-sa/4.0/                                 ##
##                                                                                 ##
#####################################################################################
#
# mean and variance of lnA distribution as function of energy (ICRC 2019)
#
#  (1) meanLgE:        <lg(E/eV)>
#  (2) mean_lnA:       <lnA>
#  (3) mean_Stat:      statistical uncertainty of lnA
#  (4) mean_SystLow:   lower systematic uncertainty of lnA
#  (5) mean_SystUp:    upper systematic uncertainty of lnA
#  (6) Var_lnA:        lnA variance V(lnA)
#  (7) Var_StatLow:    lower statistical uncertainty of V(lnA)
#  (8) Var_StatUp:     upper statistical uncertainty of V(lnA)
#  (9) Var_SystLow:    lower systematic uncertainty of V(lnA)
#  (10) Var_SystUp:    upper systematic uncertainty of V(lnA)
#
#
# hadronic model: Sibyll2.3c
#---------+----------+-----------+--------------+-------------+---------+-------------+------------+-------------+------------
# meanlgE | mean_lnA | mean_Stat | mean_SystLow | mean_SystUp | Var_lnA | Var_StatLow | Var_StatUp | Var_SystLow | Var_SystUp
#---------+----------+-----------+--------------+-------------+---------+-------------+------------+-------------+------------
   17.26       2.01     0.1          0.36	     0.42         1.85      0.6            0.63        0.76	     0.8      	 
   17.35       1.68   	0.08         0.34   	     0.41 	  2.04      0.5     	   0.52        0.8   	     0.87    
   17.45       1.82   	0.06         0.33   	     0.41 	  1.43      0.38   	   0.39        0.72  	     0.78    
   17.55       1.78   	0.06         0.32   	     0.4   	  1.55      0.39   	   0.4         0.69  	     0.78    
   17.65       1.78   	0.05         0.32   	     0.4   	  1.23      0.3     	   0.3         0.66  	     0.74    
   17.75       1.61   	0.06         0.31   	     0.4   	  1.62      0.42   	   0.44        0.67  	     0.78    
   17.85       1.56   	0.04         0.29   	     0.39 	  1.32      0.22   	   0.22        0.63  	     0.75    
   17.95       1.48   	0.04         0.29   	     0.39 	  1.35      0.25   	   0.25        0.64  	     0.77    
   18.05       1.38   	0.05         0.28   	     0.39 	  1.35      0.3     	   0.31        0.66  	     0.8     
   18.15       1.31   	0.05         0.28   	     0.39 	  1.26      0.28   	   0.28        0.66  	     0.81    
   18.25       1.28   	0.05         0.28   	     0.38 	  1.12      0.29   	   0.3         0.66  	     0.8     
   18.35       1.31   	0.06         0.28   	     0.37 	  1.04      0.35   	   0.36        0.65  	     0.77    
   18.45       1.34   	0.06         0.28   	     0.36 	  0.79      0.34   	   0.35        0.62  	     0.72    
   18.55       1.47   	0.07         0.28   	     0.35 	  0.66      0.35   	   0.36        0.59  	     0.66    
   18.65       1.49   	0.08         0.29   	     0.34 	  1.13      0.45   	   0.46        0.59  	     0.64    
   18.75       1.86   	0.07         0.29   	     0.33 	  0.32      0.33   	   0.34        0.49  	     0.51    
   18.85       1.85   	0.08         0.3     	     0.32 	  0.19      0.32   	   0.33        0.49  	     0.47    
   18.95       1.97   	0.09         0.31   	     0.31 	  0.02      0.36   	   0.37        0.46  	     0.42    
   19.05       2.04   	0.1          0.31   	     0.3   	  0.17      0.39   	   0.41        0.45  	     0.39    
   19.15       2.25   	0.1          0.32   	     0.29 	 -0.02      0.37   	   0.39        0.41  	     0.34    
   19.25       2.23   	0.14         0.33   	     0.28 	  0.59      0.62   	   0.68        0.45  	     0.35    
   19.35       2.49   	0.13         0.34   	     0.28 	  0.14      0.42   	   0.46        0.4   	     0.3     
   19.44       2.74   	0.18         0.35   	     0.28 	  0.61      0.57   	   0.62        0.39  	     0.28    
   19.55       2.67   	0.17   	     0.37   	     0.28 	 -0.25      0.43   	   0.48        0.38  	     0.27    
   19.73       3.4    	0.19   	     0.39   	     0.29 	  0.06      0.33   	   0.36        0.3   	     0.22    
#
#
#
# hadronic model: EPOS-LHC
#---------+----------+-----------+--------------+-------------+---------+-------------+------------+-------------+------------
# meanlgE | mean_lnA | mean_Stat | mean_SystLow | mean_SystUp | Var_lnA | Var_StatLow | Var_StatUp | Var_SystLow | Var_SystUp
#---------+----------+-----------+--------------+-------------+---------+-------------+------------+-------------+------------
   17.26      1.54  	0.1	     0.37	    0.43          2.03	     0.64	  0.67		 0.84	    0.88 
   17.35      1.2	0.08   	     0.36   	    0.42      	  2.2        0.53         0.55           0.89       0.96
   17.45      1.35 	0.06   	     0.34   	    0.42      	  1.6        0.41    	  0.42   	 0.79       0.87
   17.55      1.32 	0.06   	     0.34  	    0.42      	  1.72       0.42   	  0.43   	 0.77       0.86
   17.65      1.32 	0.05   	     0.33  	    0.41      	  1.4        0.32    	  0.32   	 0.73       0.83
   17.75      1.15 	0.06   	     0.32  	    0.41      	  1.79       0.45   	  0.47   	 0.75       0.87
   17.85      1.1  	0.04   	     0.3   	    0.4       	  1.47       0.23   	  0.24   	 0.71       0.85
   17.95      1.01 	0.04   	     0.3   	    0.41      	  1.49       0.27   	  0.28   	 0.72       0.87
   18.05      0.91 	0.05   	     0.29  	    0.41      	  1.47       0.33   	  0.33   	 0.75       0.91
   18.15      0.85 	0.05   	     0.29  	    0.4       	  1.36       0.3     	  0.3            0.76       0.92
   18.25      0.81 	0.05   	     0.29  	    0.4       	  1.2        0.32    	  0.32   	 0.76       0.92
   18.35      0.84 	0.06   	     0.29  	    0.39      	  1.11       0.38   	  0.39   	 0.74       0.88
   18.45      0.88 	0.06   	     0.3   	    0.38      	  0.84       0.38   	  0.38   	 0.72       0.84
   18.55      1.01 	0.07   	     0.3   	    0.37      	  0.71       0.38   	  0.39   	 0.68       0.77
   18.65      1.02 	0.08   	     0.3   	    0.36      	  1.2        0.49    	  0.51   	 0.69       0.75
   18.75      1.41 	0.08   	     0.31  	    0.35      	  0.39       0.37   	  0.38   	 0.59       0.6 
   18.85      1.4  	0.08   	     0.32  	    0.34      	  0.24       0.36   	  0.37   	 0.59       0.57
   18.95      1.52 	0.1   	     0.32  	    0.33      	  0.06       0.4     	  0.42   	 0.56       0.51
   19.05      1.59 	0.11   	     0.33  	    0.32      	  0.22       0.44   	  0.46   	 0.56       0.48
   19.15      1.8  	0.11   	     0.34  	    0.31      	  0.04       0.41   	  0.44   	 0.52       0.42
   19.25      1.78 	0.15   	     0.35  	    0.3       	  0.67       0.7     	  0.76   	 0.56       0.43
   19.35      2.05 	0.13   	     0.37  	    0.3       	  0.23       0.48   	  0.52   	 0.5        0.37
   19.44      2.31 	0.19   	     0.38  	    0.29      	  0.76       0.65   	  0.7            0.49       0.35
   19.55      2.23 	0.18   	     0.39  	    0.29      	 -0.19       0.5    	  0.55   	 0.49       0.34
   19.73      3.0  	0.21   	     0.42  	    0.31      	  0.25       0.38   	  0.41   	 0.38       0.27
#
#
#
# hadronic model: QGSJetII-04
#---------+----------+-----------+--------------+-------------+---------+-------------+------------+-------------+------------
# meanlgE | mean_lnA | mean_Stat | mean_SystLow | mean_SystUp | Var_lnA | Var_StatLow | Var_StatUp | Var_SystLow | Var_SystUp
#---------+----------+-----------+--------------+-------------+---------+-------------+------------+-------------+------------
   17.26     1.09       0.1           0.38	    0.44	   0.86      0.72	     0.75        1.02         1.1 
   17.35     0.73   	0.08  	      0.37   	    0.44	   0.91      0.6   	     0.62        1.07  	      1.17
   17.45     0.86   	0.06  	      0.35   	    0.43	   0.29      0.46 	     0.47        0.96  	      1.08
   17.55     0.81   	0.06  	      0.34   	    0.43	   0.39      0.47 	     0.48        0.94  	      1.07
   17.65     0.78   	0.05  	      0.33   	    0.42	   0.02      0.36 	     0.36        0.89  	      1.03
   17.75     0.59   	0.07  	      0.32   	    0.42	   0.36      0.51  	     0.52        0.9   	      1.07
   17.85     0.52   	0.04  	      0.31   	    0.41	  -0.01      0.26 	     0.26        0.86  	      1.04
   17.95     0.42   	0.04  	      0.3     	    0.41	  -0.04      0.3  	     0.31        0.86  	      1.06
   18.05     0.29   	0.05  	      0.3     	    0.41	  -0.09      0.36 	     0.37        0.88  	      1.1 
   18.15     0.21   	0.05  	      0.3     	    0.41	  -0.25      0.33 	     0.34        0.89  	      1.11
   18.25     0.16   	0.05  	      0.3     	    0.4 	  -0.44      0.35 	     0.36        0.88  	      1.09
   18.35     0.17   	0.06  	      0.3     	    0.4 	  -0.54      0.42 	     0.43        0.87  	      1.06
   18.45     0.19   	0.07  	      0.3     	    0.39	  -0.82      0.42 	     0.43        0.85  	      1.0 
   18.55     0.31   	0.07  	      0.3     	    0.38	  -0.92      0.43 	     0.44        0.81  	      0.92
   18.65     0.31   	0.08  	      0.31   	    0.36	  -0.41      0.55 	     0.56        0.82  	      0.9 
   18.75     0.68   	0.08  	      0.31   	    0.35	  -1.15      0.41 	     0.43        0.71  	      0.74
   18.85     0.66   	0.08  	      0.32   	    0.34	  -1.33      0.4  	     0.41        0.71  	      0.7 
   18.95     0.77   	0.1    	      0.33   	    0.33	  -1.48      0.45 	     0.47        0.68  	      0.64
   19.05     0.82   	0.11  	      0.33   	    0.32	  -1.3       0.5   	     0.52        0.68  	      0.61
   19.15     1.02   	0.11  	      0.34   	    0.31	  -1.43      0.47 	     0.5         0.65  	      0.54
   19.25     0.98   	0.15  	      0.35   	    0.3 	  -0.78      0.78 	     0.84        0.69  	      0.55
   19.35     1.25   	0.13  	      0.37   	    0.3 	  -1.16      0.55 	     0.59        0.64  	      0.49
   19.44     1.49   	0.19  	      0.38   	    0.29	  -0.52      0.75 	     0.81        0.64  	      0.48
   19.55     1.4    	0.18  	      0.39   	    0.29	  -1.55      0.58 	     0.64        0.64  	      0.47
   19.73     2.14   	0.2   	      0.42   	    0.3 	  -0.81      0.48 	     0.51        0.57  	      0.42
