Numerical simulation of sky localization for LISA-TAIJI joint observation

LISA is considered to be launched alongside the Athena to probe the energetic astrophysical processes. LISA can determine the direction of sources for Athena's follow-up observation. As another space gravitational wave mission, TAIJI is expected to be launched in the 2030s. The LISA-TAIJI network would provide abundant merits for sources understanding. In this work, we simulate the joint LISA-TAIJI observations for gravitational waves from coalescing supermassive black hole binaries and monochromatic sources. By using the numerical mission orbits, we evaluate the performances of sky localization for various time-delay interferometry channels. For 30 days observation until coalescence, the LISA-TAIJI network in optimal operation can localize all simulated binary sources, $({10}^{7},3.3\ifmmode\times\else\texttimes\fi{}{10}^{6}){M}_{\ensuremath{\bigodot}}$, $({10}^{6},3.3\ifmmode\times\else\texttimes\fi{}{10}^{5}){M}_{\ensuremath{\bigodot}}$, and $({10}^{5},3.3\ifmmode\times\else\texttimes\fi{}{10}^{4}){M}_{\ensuremath{\bigodot}}$ at redshift $z=2$, in $0.4\text{ }\text{ }{\mathrm{deg}}^{2}$ (field of view of Wide Field Imager on Athena). The angular resolution can be improved by more than ten times comparing to LISA or TAIJI single detector at a given percentage of population. The improvements for monochromatic sources at 3 and 10 mHz are relatively moderate in one year observation. The precision of sky localization could be improved by a factor of 2 to 4 comparing to single LISA at a given percentage of sources. For a simulated 90 days observation for monochromatic waves, the LISA-TAIJI network still represents a considerable localization advantage which could be more than ten times better.