Results of the spectral fits to the RXTE/PCA observations (filled circles) performed during the outbursts of RX J0440.9 + 4431 occurred in 2010 and 2011 (Table 2). The best fit spectral parameters obtained from the XMM-Newton observation (2011 March 18) are also included and represented with a star (uncertainties are at 68% c.l. and lower limits at 90% c.l.).The bmc model was used for all fits, but during the two observations performed when the source reached the highest flux, an exponential cut-off at high energy was needed to properly fit the data (see Sect. 3.4). The black body radius r_BB is obtained from Eq. (2) setting C = 1. The red solid lines in the right panels represents the best fit relations of Eq. (3), (4) obtained from the PCA data only.