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Long-term Optical Studies of the Be/X-ray Binary RX J0440.9+4431/LS V+44 17

We present the spectroscopic and photometric observations on the Be/X-ray binary RX~J0440.9+4431 from 2001 to 2014. The short-term and long-term variability of the H$α$ line profile indicates that one-armed global oscillations existed in the circumstellar disk. Several positive and negative correlations between the $V$-band brightness and the H$α$ intensity \textbf{were} found from the long-term photometric and spectroscopic observations. We suggest that the monotonic increase of the $V$-band brightness and the H$α$ brightness between our 2005-2007 observations might be the result of a continuous mass ejection from the central Be star, while the negative correlation in 2007-2010 should be caused by the cessation of mass loss from the Be star just before the decline in $V$-band brightness began (around our 2007 observations). With the extension of the ejection material, the largest circumstellar disk during the last two decades has been observed in our 2010 observations with an equivalent width of $\sim$$-12.88$ Å, which corresponds to a circumstellar disk with a size of 12.9 times the radius of the central Be star. Three consecutive X-ray outbursts peaking around MJD 55293, 55444, and 55591 might be connected with the largest circumstellar disk around the Be star. We also use the orbital motion of the neutron star as a probe to constrain the structure of the circumstellar disk and estimate the eccentricity of the binary system to be $\ge$ 0.4. After three years of the H$α$ intensity decline after the X-ray outbursts, a new circumstellar disk was being formed around the Be star after our 2013 observations.