Only a few binary systems with compact objects display TeV emission . The physical properties of the companion stars represent basic input to understand the physical mechanisms behind the particle acceleration , emission , and absorption processes in these so-called gamma-ray binaries . Here we present high-resolution and high signal-to-noise optical spectra of ( catalog LS~2883 ) , the Be star forming a gamma-ray binary with the young non-accreting pulsar ( catalog PSR~B1259 $ - $ 63 ) , showing it to rotate faster and be significantly earlier and more luminous than previously thought . Analysis of the interstellar lines suggest that the system is located at the same distance as ( and thus is likely a member of ) ( catalog Cen~OB1 ) . Taking the distance to the association , d = 2.3 kpc , and a color excess of E ( B - V ) = 0.85 for ( catalog LS~2883 ) , results in M _ { V } \approx - 4.4 . Because of fast rotation , LS 2883 is oblate ( R _ { { eq } } \simeq 9.7 \ > R _ { \sun } and R _ { { pole } } \simeq 8.1 \ > R _ { \sun } ) and presents a temperature gradient ( T _ { { eq } } \approx 27 500 K , \log g _ { { eq } } = 3.7 ; T _ { { pole } } \approx 34 000 K , \log g _ { { pole } } = 4.1 ) . If the star did not rotate , it would have parameters corresponding to a late O-type star . We estimate its luminosity at \log ( L _ { * } / L _ { \sun } ) \simeq 4.79 , and its mass at M _ { * } \approx 30 \ > M _ { \sun } . The mass function then implies an inclination of the binary system i _ { { orb } } \approx 23 \arcdeg , slightly smaller than previous estimates . We discuss the implications of these new astrophysical parameters of ( catalog LS~2883 ) for the production of high energy and very high energy gamma rays in the ( catalog PSR~B1259 $ - $ 63 ) / ( catalog LS~2883 ) gamma-ray binary system . In particular , the stellar properties are very important for prediction of the line-like bulk Comptonization component from the unshocked ultra-relativistic pulsar wind .