tokens: range 4.7 M ⊙ –7.8 M ⊙ . In Fig. 1 (a)– (c), variations of TCAF model fitted shock location (in r s ), normalization and mass values with time (day in MJD) are shown, when all model parameters were assumed to be free. Fig. 1 (d) shows the variation of model fitted masses when the normalization was frozen at an average value of 139.07. Figure 1. Variations of TCAF model fitted parameters: (a) shock location (in r s ), (b) normalization ( N ) and (c) mass of the black hole ( M BH in M ⊙ ) over the entire period of the 2010 outburst of MAXI J1659−152, when all model parameters are kept as free. In (d), TCAF fitted M BH is shown when the model normalization was kept frozen at 139.07, which we obtained from taking an average of the normalization values of panel (a). Table 1. TCAF model fitted mass and normalization values. Here, X=95358-01, Y=95108-01, and Z=95118-01 are the initial parts of the observation IDs. In columns 4 and 5, the TCAF fitted model normalization and BH mass values are shown when all TCAF-related parameters are free while fitting the spectra and in column 6, model fitted mass values are shown when normalization is frozen at 139.07. 1σ errors for N and masses are shown in superscripts. We can also cross-check the range of the predicted mass by the above method when we vary M BH versus the reduced χ 2 of the best-fitted spectra. The best fit using the current version (v0.3) of the TCAF model was obtained based on the model fitted reduced χ 2 values when found nearly equal to unity. In Paper I and in Table 1 , model parameters are given when best fits are obtained. After achieving satisfactory model fits, we kept all model parameters, such as sub-Keplerian rate , Keplerian rate , location of the shock X s , compression ratio R and normalization N , frozen, except the mass of the black hole, and found how the reduced χ 2 changed with the mass of the black hole. In Fig. 3 (a)–(c), the variation of reduced χ 2 with mass of the BH is shown for three different spectra (obs. IDs: 95118-01-06-01, 95118-01-16-01, 95118-01-21-00) selected from three different spectral states (SIMS, HIMS and HS, respectively). As in the earlier cases, if we consider to be the upper limit for acceptable fits, we obtain a mass in the range 4.4 M ⊙ –7.3 M ⊙ . 3.2 QPO frequency(ν<sub>QPO</sub>) – time (day) evolution: fitted with POS model Low-frequency QPOs are very commonly seen in PDSs of X-ray intensity variations (light curves) emitted from discs surrounding stellar massive black holes. Sometimes the dominating frequencies of these QPOs (generally type ‘C’) are found to evolve with time, mostly in HS and HIMS from both rising and declining phases of an outburst. The monotonic evolution of these QPO frequencies could be fitted very well by a propagating oscillatory shock (POS) model (see Chakrabarti et al. 2005 , 2008 ; Chakrabarti, Dutta Pal 2009 ; Debnath et al. 2010 , 2013 ; Nandi et al. 2012 ). According to the POS model, the frequency is inversely
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