  We measure the bivariate luminosity function (BLF) of galaxy pairs and use it
to probe and characterize the galaxy-galaxy interaction between pair members.
The galaxy pair sample is selected from the main galaxy sample of Sloan Digital
Sky Survey and supplied with a significant number of redshifts from the LAMOST
spectral and GAMA surveys. We find the BLFs depend on the projected distance
$d_{\text{p}}$ between pair members. At large separation $d_{\text{p}} > 150
h^{-1}\ \text{kpc}$, the BLF degenerates into a luminosity function (LF) of
single galaxies, indicating few interactions between pair members. At $100
h^{-1}\ \text{kpc} \leq d_{\text{p}} \leq 150 h^{-1}\ \text{kpc}$, the BLF
starts to show the correlation between pair members, in the sense that the
shape of the conditional luminosity function (CLF) of one member galaxy starts
to depend on the luminosity of the other member galaxy. Specifically, the CLF
with a brighter companion has a steeper faint-end slope, which becomes even
more significant at $50 h^{-1}\ \text{kpc} \leq d_{\text{p}} \leq 100 h^{-1}\
\text{kpc}$. This behavior is consistent with the scenario, \textit{and also is
the observational evidence}, that dynamic friction drives massive major merger
pairs to merge more quickly. At close distance $d_{\text{p}} \leq 50 h^{-1}\
\text{kpc}$, besides the merging time-scale effect, the BLF also shows an
overall brightening of $\Delta M_r \geq 0.04$ mag, which reveals the enhanced
star formation of the close-pair phase. By combining another statistical
conclusion that the star formation rate of late-type galaxies in close pairs is
enhanced at a level of about 40\%, we further conclude that the average
starburst time-scale of close pairs is as long as 0.4 Gyr.
