K09=[...  %points from Khatmi & Kasen 2019, figure  8, xs=0.9, note that ts=10 days.
    %   tpeak[days]                 Lpeak/Q_0
    6.482758620689655, 0.5343859743202031
    12.482758620689658, 0.24513136019864165
    14.482758620689655, 0.17784209564522407
    16.482758620689655, 0.14432353598487588
    18.48275862068966, 0.10961804184383245
    21.51724137931035, 0.08241431535909768
    22.48275862068965, 0.07145999193275465
    22.48275862068965, 0.06388458261759926
    24.48275862068966, 0.0553931891394047
    26.48275862068966, 0.04541331726010195
    ];
tpeak_over_ts_xs09_Khatmi=K09(:,1)/10; Lpeak_over_Q0_xs09_Khatmi=K09(:,2); 

xs0=[...  % results using Eqs 8-9 this work for xs=0
%    tpeak/ts           Lpeak/Q_0
2.30041e+01  2.07480e-03 
1.83416e+01  3.28593e-03 
1.46624e+01  5.19756e-03 
1.17630e+01  8.19426e-03 
9.48770e+00  1.28299e-02 
7.69361e+00  1.98534e-02 
6.27393e+00  3.01940e-02 
5.14494e+00  4.49008e-02 
4.23819e+00  6.50353e-02 
3.49817e+00  9.15126e-02 
2.89626e+00  1.24941e-01 
2.40233e+00  1.65487e-01 
1.99434e+00  2.12792e-01 
1.65621e+00  2.65971e-01 
1.37503e+00  3.23693e-01 
1.14075e+00  3.84326e-01 
9.45572e-01  4.46109e-01 
7.82622e-01  5.07333e-01 
6.46730e-01  5.66481e-01 
5.33649e-01  6.22331e-01 
4.39545e-01  6.73997e-01 
3.61447e-01  7.20930e-01 
2.96712e-01  7.62885e-01 
2.43165e-01  7.99867e-01 
1.98984e-01  8.32069e-01 
1.62593e-01  8.59810e-01 
1.32671e-01  8.83490e-01 
1.08117e-01  9.03544e-01 
8.79973e-02  9.20410e-01
]; tpeak_over_ts_xs0=xs0(:,1); Lpeak_over_Q0_xs0=xs0(:,2);

xs09=[...  % results using Eqs 8-9 this work for xs=0.9
%    tpeak/ts           Lpeak/Q_0
2.03897e+01  3.68629e-04 
1.61961e+01  5.84090e-04 
1.30041e+01  9.25021e-04 
1.05470e+01  1.46236e-03 
8.63044e+00  2.30137e-03 
7.11419e+00  3.59316e-03 
5.99379e+00  5.54332e-03 
5.08976e+00  8.42243e-03 
4.36688e+00  1.25728e-02 
3.78470e+00  1.84135e-02 
3.30692e+00  2.64401e-02 
2.91491e+00  3.72178e-02 
2.57999e+00  5.13674e-02 
2.29001e+00  6.95390e-02 
2.03812e+00  9.23717e-02 
1.81626e+00  1.20452e-01 
1.62137e+00  1.54187e-01 
1.44085e+00  1.93782e-01 
1.27582e+00  2.39106e-01 
1.12272e+00  2.89628e-01 
9.80162e-01  3.44389e-01 
8.48659e-01  4.02057e-01 
7.28990e-01  4.61068e-01 
6.21417e-01  5.19810e-01 
5.26196e-01  5.76800e-01 
4.43059e-01  6.30810e-01 
3.71099e-01  6.80933e-01 
3.09540e-01  7.26586e-01 
2.57203e-01  7.67493e-01 
2.13022e-01  8.03622e-01 
1.75913e-01  8.35136e-01 
1.44882e-01  8.62326e-01 
1.19049e-01  8.85568e-01 
9.76231e-02  9.05274e-01 
7.98921e-02  9.21866e-01 
]; tpeak_over_ts_xs09=xs09(:,1); Lpeak_over_Q0_xs09=xs09(:,2);

loglog(tpeak_over_ts_xs09_Khatmi,Lpeak_over_Q0_xs09_Khatmi,'ro'); hold on;
loglog(tpeak_over_ts_xs09,Lpeak_over_Q0_xs09,'kx'); 
loglog(tpeak_over_ts_xs0,Lpeak_over_Q0_xs0,'kx'); 

LpQ0_of_tp_ts_beta=@(tp_ts,beta)2/beta^2*tp_ts.^(-2).*(1-(1+beta*tp_ts).*exp(-beta*tp_ts));
tp_ts=10.^(-1.4:0.1:1.4);
plot(tp_ts,LpQ0_of_tp_ts_beta(tp_ts,2.3),'r-')
plot(tp_ts,LpQ0_of_tp_ts_beta(tp_ts,3.65),'k-')
plot(tp_ts,LpQ0_of_tp_ts_beta(tp_ts,1.36),'k-')