Bivariate Luminosity Function of Galaxy Pairs

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.