Parameter estimation of coalescing supermassive black hole binaries with LISA

Laser Interferometer Space Antenna (LISA) will routinely observe coalescences of supermassive black hole (BH) binaries up to very high redshifts. LISA can measure mass parameters of such coalescences to a relative accuracy of 10(-4)-10(-6), for sources at a distance of 3 Gpc. The problem of parameter estimation of massive nonspinning binary black holes using post-Newtonian (PN) phasing formula is studied in the context of LISA. Specifically, the performance of the 3.5PN templates is contrasted against its 2PN counterpart using a waveform which is averaged over the LISA pattern functions. The improvement due to the higher order corrections to the phasing formula is examined by calculating the errors in the estimation of mass parameters at each order. The estimation of the mass parameters M and eta is significantly enhanced by using the 3.5PN waveform instead of the 2PN one. For an equal mass binary of 2x10(6)M at a luminosity distance of 3 Gpc, the improvement in chirp mass is similar to 11% and that of eta is similar to 39%. Estimation of coalescence time t(c) worsens by 43%. The improvement is larger for the unequal mass binary mergers. These results are compared to the ones obtained using a nonpattern averaged waveform. The errors depend very much on the location and orientation of the source and general conclusions cannot be drawn without performing Monte Carlo simulations. Finally the effect of the choice of the lower frequency cutoff for LISA on the parameter estimation is studied.