Effect of higher harmonic corrections on the detection of massive black hole binaries with LISA

Massive black hole binaries are key targets for the space based gravitational wave Laser Interferometer Space Antenna (LISA). Several studies have investigated how LISA observations could be used to constrain the parameters of these systems. Until recently, most of these studies have ignored the higher harmonic corrections to the waveforms. Here we analyze the effects of the higher harmonics in more detail by performing extensive Monte Carlo simulations. We pay particular attention to how the higher harmonics impact parameter correlations, and show that the additional harmonics help mitigate the impact of having two laser links fail, by allowing for an instantaneous measurement of the gravitational wave polarization with a single interferometer channel. By looking at parameter correlations we are able to explain why certain mass ratios provide dramatic improvements in certain parameter estimations, and illustrate how the improved polarization measurement improves the prospects for single interferometer operation.

Figure 1

A comparison of parameter extraction for equal mass binaries using restricted (dark solid line) and higher harmonic corrected (light solid line) waveforms, as a function of redshifted chirp mass and at a distance of 10 Gpc. The values quoted are median values from a $2\times {10}^4$ point Monte Carlo simulation. Also plotted are the median results for an almost equal mass case (dashed lines) where $m_1/m_2=1.22$.

Figure 2

A comparison of parameter extraction for binaries with a mass ratio of 10 using restricted (dark solid line) and higher harmonic corrected (dashed line) waveforms, as a function of redshifted chirp mass and at a distance of 10 Gpc. The values quoted are median values from a $2\times {10}^4$ point Monte Carlo simulation. Note in this case that a system with $M_c={10}^8{M}_{\odot }$ is not visible.

Figure 3

Main correlation breaking for equal mass binaries with a chirp mass of ${10}^7{M}_{\odot }$ due to the inclusion of higher harmonic corrections. The restricted waveform correlations are given by the dark line and the HHC correlations are given by the lighter line.

Figure 4

Main correlation breaking for unequal mass binaries with a chirp mass of ${10}^7{M}_{\odot }$ due to the inclusion of higher harmonic corrections. The restricted waveform correlations are given by the dark line and the HHC correlations are given by the lighter line.

Figure 5

A comparison of parameter extraction for equal mass binaries using restricted one-channel (dotted line), restricted two-channel (solid line) and higher harmonic corrected one-channel (dash-dotted line) and two-channel (dashed line) waveforms, as a function of redshifted chirp mass and at a distance of 10 Gpc. The values quoted are median values from a $2\times {10}^4$ point Monte Carlo simulation.

Figure 6

A comparison of parameter extraction for binaries with a mass ratio of 10 using restricted one-channel (dotted line), restricted two-channel (solid line) and higher harmonic corrected one-channel (dash-dotted line) and two-channel (dashed line) waveforms, as a function of redshifted chirp mass and at a distance of 10 Gpc. The values quoted are median values from a $2\times {10}^4$ point Monte Carlo simulation.

Figure 7

Histograms for the error in the polarization angle $\psi$ for restricted (dark) and corrected (light) waveforms using a single LISA detector, for systems with a redshifted chirp mass of ${10}^7{M}_{\odot }$, a mass ratio of 10, at a distance of 10 Gpc.

Figure 8

An examination of parameter correlations for the case of a single LISA detector for systems with a redshifted chirp mass of ${10}^7{M}_{\odot }$, a mass ratio of 10, at a distance of 10 Gpc. The dark line denotes the restricted waveforms, while the light line signifies the corrected waveforms.