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

8.3. MAGNETIC RECONNECTION MODEL 1118.3.1 τ r vs τ d – Implication of the pre-flare densityFrom Eq.(C.12), the reconnection model predicts the positive correlation between τ r and τ d asτ d = Aτr1/2 . The slope of 1/2 shows good agreement with the observed value of 0.4±0.1 (Eq.8.2),hence supports our assumption that the decay phase is dominant by radiative cooling. FromEq.(C.12), we re-estimate log(A) with the fixed slope of 1/2 to be 2.06±0.04 (the dashed line inFigure 8.1). We also calculate log(A) separately for each class, then obtain 2.1±0.1, 2.0±0.1, and2.0±0.1 for class I, II, and III+III c , respectively. We see no significant difference between theclasses, hence A is assumed to be the same for all sources. Since A is a function of n c (Eq.C.13),we can determine n c to ben c = 10 10.48±0.09 ( M A0.01 ) [cm−3 ]. (8.4)Considering the possible range of M A (0.001–0.1), this favors higher pre-flare density for YSOs(10 9 –10 12 cm −3 ) than that for the sun (∼10 9 cm −3 ). In fact, Kastner et al. (2002) derived theplasma density of a CTTS (TW Hydrae) using the ratio of Ne IX and O VII triplets and foundextremely high density of ∼10 13 cm −3 even in their quiescent phase. Hence larger n c value forYSOs than that for the sun would be common feature.8.3.2 < kT > vs τ r – Loop length and magnetic field strengthThe predicted correlations between < kT > and τ r are shown in Eqs. (C.14) and (C.15). Positive(τ r ∝< kT > 7/2 ) and negative (τ r ∝< kT > −7/6 ) correlations are expected for the constant Band L values, respectively. The dash-dotted and dashed lines in Figure 8.2 show the constant Band L lines, in which we uniformly assume n c = 10 10.48 cm −3 (Eq.8.4). Our observed negativecorrelation therefore predicts that flares with higher temperature is mainly due to larger magneticfield. However, the observed slope of −0.4±0.3 is significantly flatter than −7/6 (Eq. C.15), hencethe effect of L would not be negligible. We estimate the mean B and L for each class (Table 8.2)using the mean values of < kT > and τ r (Figures 7.4b and 7.5a), which is summarized in Table8.2. Younger sources tend to show larger B values; the mean values of B are ∼500, 300, and 200 Gfor class I, II, and III+III c sources, respectively. This is consistent with the observed result ofhigher plasma temperature for younger sources. Also, the estimated values of L (10 10 –10 11 cm)suggest that L is nearly the same among these classes, comparable to the typical radius of YSOs.These results indicate that the flare loops for all classes are localized at the stellar surface, whichis in sharp contrast with the idea of the flares for class I sources triggered by the larger flare loopsconnecting the star and the disk (Montmerle et al., 2000).It is conceivable that the class III flares with unusually long timescales (A-2, A-63, and BF-96)mainly affect the systematically lower B for class III sources. Since it is possible that two or more