X-ray Study of Low-mass Young Stellar Objects in the ρ Ophiuchi ...

8.2. CORRELATION BETWEEN THE FLARE X-RAY PARAMETERS 1098.2 Correlation between the Flare X-ray ParametersFigures 8.1 and 8.2 show the correlations between the derived parameters of flares; τ r vs τ d and< kT > vs τ r . In these figures, we exclude those flares that could not determine errors mainly dueto the limited statistics. Possible positive and negative log-linear correlations can be seen in τ r vsτ d and < kT > vs τ r , respectively. We hence check the significances of these correlations usingthe Cox’s proportional hazard model (Isobe et al., 1986) in ASURV. This gives the significances of∼99 % (τ r vs τ d ) and ∼94 % (< kT > vs τ r ). We further estimate the best-fit log-linear modelswith ASURV to be( τ ds ) = 102.5±0.4 ( τ rs )0.4±0.1 , (8.2)( τ rs ) = 103.8±0.1 ( < kT >keV )−0.4±0.3 . (8.3)These models are shown by the solid lines in Figures 8.1 and 8.2.Fig. 8.1.— Relation between the rise and decay timescales of flares (τ r and τ d ). Symbols arethe same as Figure 7.6. The solid line represents the best-fit log-linear correlations derived withASURV (Eq.8.2). The dashed line is the best-fit model of Eq.(C.12).