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Table B.1.

Frequencies of twin kHz QPOs and the best parameters in 4U 1636–53.

Input parameters The first fitted parameters The second fitted parameter Characteristic values

fl (Hz) fu (Hz) τ L (km) kTe (keV) kTb (keV) 𝒳2/d.o.f. L2 (km) 𝒳2/d.o.f. η Δ H ˙ 1 $ \Delta {\dot{H}_1} $ Δ H ˙ 2 $ \Delta {\dot{H}_2} $
558.15 ± 6.92 879 . 25 5.61 + 5.49 $ 879.25_{-5.61}^{+5.49} $ 8.4 ± 0.5 9.1 ± 2.2 3.6 ± 0.3 0.1966 ± 0.0002 36 / 44 9.08 ± 0.01 47 / 47 1.0 9.69 16.20
574.42 ± 5.43 884 . 05 4.40 + 4.52 $ 884.05_{-4.40}^{+4.52} $ 9.4 ± 0.1 3.7 ± 0.1 3.16 ± 0.01 0.2062 ± 0.0001 38 / 44 3.670 ± 0.002 47 / 47 0.0 4.05 13.70
575.87 ± 2.74 909.49 ± 3.83 8.9 ± 0.2 12.0 ± 0.4 3.33 ± 0.07 0.19971 ± 0.00004 25 / 44 11.880 ± 0.009 47 / 47 1.0 12.86 27.65
590.01 ± 6.37 867.78 ± 3.78 8.2 ± 0.2 9.8 ± 1.8 3.63 ± 0.07 0.1966 ± 0.0001 20 / 44 9.722 ± 0.007 49 / 47 1.0 14.73 25.04
612.14 ± 5.04 906.11 ± 4.47 8.3 ± 0.4 5.7 ± 0.3 3.46 ± 0.2 0.1997 ± 0.0001 24 / 45 5.63 ± 0.00 49 / 48 1.0 12.77 15.01
637.41 ± 4.86 930 . 24 12.55 + 12.70 $ 930.24_{-12.55}^{+12.70} $ 10.1 ± 0.1 4.0 ± 0.9 2.89 ± 0.07 0.1988 ± 0.0001 14 / 44 3.953 ± 0.002 48 / 47 0.5 11.94 13.62
640.23 ± 2.72 964.57 ± 5.50 10.0 ± 0.4 6.0 ± 0.1 2.9 ± 0.1 0.20089 ± 0.00004 77 / 44 5.914 ± 0.005 47 / 47 0.5 12.96 14.91
649.55 ± 4.28 936.25 ± 10.28 8.3 ± 0.6 2.6 ± 0.3 3.5 ± 0.3 0.1978 ± 0.0004 36 / 44 2.5603 ± 0.0001 56 / 47 0.4 13.08 13.62
650.68 ± 4.23 991 . 97 11.29 + 8.71 $ 991.97_{-11.29}^{+8.71} $ 8.6 ± 0.5 6.9 ± 0.5 3.3 ± 0.2 0.2078 ± 0.0003 32 / 44 6.841 ± 0.007 46 / 47 0.1 10.14 12.14
653 . 58 3.82 + 3.66 $ 653.58_{-3.82}^{+3.66} $ 984.64 ± 5.69 8.4 ± 0.7 7.9 ± 0.1 3.5 ± 0.4 0.2013 ± 0.0002 30 / 45 7.694 ± 0.018 49 / 48 0.0 16.19 22.56
659.10 ± 2.12 975.20 ± 4.12 9.6 ± 0.8 5.4 ± 0.4 2.9 ± 0.3 0.1989 ± 0.0002 26 / 44 5.385 ± 0.001 48 / 47 0.6 17.03 13.25
675.51 ± 1.42 970.16 ± 4.83 9.2 ± 0.8 6.4 ± 0.9 3.1 ± 0.3 0.2094 ± 0.0001 6 / 45 6.392 ± 0.003 49 / 48 0.0 10.88 12.45
689.14 ± 42.36 1022.49 ± 42.36 9.2 ± 0.9 2.8 ± 0.6 3.1 ± 0.3 0.2000 ± 0.0001 23 / 44 2.751 ± 0.003 50 / 47 0.1 14.60 11.47
696.99 ± 1.01 1007.83 ± 9.49 8.6 ± 0.3 4.8 ± 0.8 3.3 ± 0.1 0.1998 ± 0.0001 30 / 44 4.7770 ± 0.0003 48 / 47 0.5 19.93 12.71
700.10 ± 2.72 1005.88 ± 7.68 9.5 ± 0.7 8.4 ± 0.7 3.0 ± 0.3 0.2003 ± 0.0002 15 / 44 8.332 ± 0.006 47 / 47 1.0 24.10 14.50
718 . 56 1.78 + 1.81 $ 718.56 _{-1.78}^{+1.81} $ 988.76 ± 12.25 9.5 ± 0.2 5.3 ± 0.6 2.99 ± 0.07 0.19973 ± 0.00006 13 / 44 5.256 ± 0.003 49 / 47 0.4 20.84 14.45
770.02 ± 42.55 1092.21 ± 42.55 9.7 ± 0.4 5.0 ± 0.9 2.9 ± 0.1 0.2039 ± 0.0003 24 / 44 4.9465 ± 0.0003 48 / 47 0.2 18.86 10.09
772.80 ± 1.33 1070.88 ± 7.04 9.9 ± 0.4 8.2 ± 0.3 2.9 ± 0.1 0.2052 ± 0.0001 36 / 44 8.115 ± 0.005 46 / 47 0.1 21.47 13.77
877.07 ± 29.23 1126.12 ± 29.23 10.0 ± 0.2 7.5 ± 0.1 2.75 ± 0.06 0.2137 ± 0.0002 51 / 48 7.473 ± 0.004 52 / 51 0.0 12.04 7.86
883.19 ± 3.67 1187.03 ± 6.72 9.2 ± 0.3 3.9 ± 0.2 3.0 ± 0.1 0.2106 ± 0.0001 59 / 48 3.871 ± 0.001 51 / 51 0.0 9.53 4.88
883.44 ± 1.10 1132.73 ± 6.47 10.2 ± 0.6 6.4 ± 0.4 2.7 ± 0.1 0.2130 ± 0.0005 21 / 44 6.351 ± 0.003 48 / 47 0.0 10.79 7.05
913.75 ± 40.91 1161.56 ± 40.91 9.2 ± 0.1 8.7 ± 0.6 2.94 ± 0.07 0.2133 ± 0.0003 36 / 48 8.644 ± 0.005 50 / 51 0.0 12.12 7.97
913.98 ± 2.97 1223.44 ± 6.32 9.4 ± 0.1 4.8 ± 1.5 2.98 ± 0.03 0.20961 ± 0.00003 43 / 48 4.713 ± 0.001 51 / 51 0.0 9.07 4.40
922 . 59 2.13 + 1.62 $ 922.59_{-2.13}^{+1.62} $ 1164.83 ± 5.82 8.9 ± 0.4 5.3 ± 0.8 3.0 ± 0.1 0.2119 ± 0.0001 44 / 44 5.2900 ± 0.0004 48 / 47 0.0 8.93 6.17
923.31 ± 3.91 1193 . 66 4.91 + 4.78 $ 1193.66_{-4.91}^{+4.78} $ 10.3 ± 0.3 6.9 ± 0.4 2.64 ± 0.05 0.2154 ± 0.0002 48 / 48 6.869 ± 0.003 52 / 51 0.0 8.46 4.90
925 . 03 4.43 + 4.44 $ 925.03_{-4.43}^{+4.44} $ 1191.40 ± 2.57 9.6 ± 0.3 6.3 ± 0.6 2.82 ± 0.09 0.2122 ± 0.0002 14 / 48 6.219 ± 0.002 52 / 51 0.0 9.20 5.57
932 . 44 5.14 + 5.28 $ 932.44_{-5.14}^{+5.28} $ 1191.81 ± 5.26 9.96 ± 0.06 7.1 ± 0.1 2.73 ± 0.01 0.21029 ± 0.00006 32 / 44 7.0306 ± 0.0001 48 / 47 0.0 10.77 6.88
948 . 89 14.11 + 11.18 $ 948.89_{-14.11}^{+11.18} $ 1197 . 21 3.77 + 3.68 $ 1197.21_{-3.77}^{+3.68} $ 9.1 ± 0.2 9.9 ± 0.7 2.91 ± 0.07 0.2091 ± 0.0002 20 / 44 9.8445 ± 0.0001 48 / 47 0.1 15.10 10.11

Notes. This table lists the frequencies of 28 twin kHz QPOs and the best parameters in 4U 1636–53 for every group of twin QPOs. The first two parameters (fl and fu) in the first column are from the observation and the values of other parameters are obtained from this model.

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