1. The Effect of Higher Harmonic Corrections on Non-Spinning Massive BH Binaries for LISA. Ed Porter (AEI) & Neil Cornish (MSU)

2. 2 Two Main Questions: GWDAW 12, December 2007, Boston, USA 1)1 detector vs. 2: Can we still do GW astronomy? Will the higher harmonics play a role? 2)HCPN vs. RPN: What are the effects on distance and sky resolution? What correlations are broken/enhanced by the extra harmonics?

3. 3 HCPN Waveforms. GWDAW 12, December 2007, Boston, Germany The strain of the GW at LISA is where and the dimensionless velocity is defined in terms of the orbital frequency by and the phase evolution is kept at 2-PN order. The importance of the HHCs are the H’s ~ (m1 – m2) / (m1 + m2) at odd orders.

4. 4 Monte Carlo. Short run, 1000 points Short run, 1000 points Different red-shifted chirp masses Different red-shifted chirp masses Mass ratios of 1 and 0.1 Mass ratios of 1 and 0.1 Distance of 10 Gpc Distance of 10 Gpc Time of observation of 1 year Time of observation of 1 year Time of coalescence of 0.999 yrs Time of coalescence of 0.999 yrs Maximum allowed frequency of 5 mHz. Maximum allowed frequency of 5 mHz. All other parameters randomized. All other parameters randomized. LISA cutoff frequency of 0.01 mHz with red noise. LISA cutoff frequency of 0.01 mHz with red noise. One detector ( X ) and two detector cases ( AE ) One detector ( X ) and two detector cases ( AE ) Low frequency approximation Low frequency approximation GWDAW 12, December 2007, Boston, USA

5. 5 Monte Carlo. GWDAW 12, December 2007, Boston, USA The SMBH is defined by the parameter set : Use a Fisher Matrix and a correlation matrix Fisher is calculated using numerical differencing

6. 6 Effect of HHCs on SNR GWDAW 12, December 2007, Boston, USA Some Effects known: Enhances SNR for high masses Overestimates SNR for low masses. NOT A GOOD WAY TO JUDGE THE EFFECT OF HHCs!

7. 7 Effect of HHCs on Distance Estimation We can not see the high unequal mass binaries. While the very high equal mass systems can be seen, we can not determine the distance. 1 vs. 2 detector LISA dependent on mass ratio GWDAW 12, December 2007, Boston, USA

8. 8 Effect of HHCs on Sky Resolution At very high equal mass, the HHCs resolve the source as long as all links are working GWDAW 12, December 2007, Boston, USA

9. 9 What Happens When We Use HHCs We need to understand exactly what changes when we include HHCs Investigate the correlation coefficients matrix Look at the ratio of AE0 / AE2 coefficients Look at 10 7 solar mass case where HHCs are expected to play a major role

10. 10 GWDAW 12, December 2007, Boston, USA What Happens When We Use HHCs The unequal mass case

11. 11 GWDAW 12, December 2007, Boston, USA What Happens When We Use HHCs The equal mass case : major correlation breaking

12. 12 GWDAW 12, December 2007, Boston, USA What Happens When We Use HHCs The equal mass case : intermediate correlation breaking

13. 13 GWDAW 12, December 2007, Boston, USA What Happens When We Use HHCs The equal mass case : correlation tightening

14. 14Conclusion SNR is not the best way to compare the effect of HHCs SNR is not the best way to compare the effect of HHCs In some cases, with HHCs 1 detector is as good as 2 without HHCs In some cases, with HHCs 1 detector is as good as 2 without HHCs HHCs can improve sky resolution by 2~5 HHCs can improve sky resolution by 2~5 At very high mass, HHCs enhance detection and sky resolution At very high mass, HHCs enhance detection and sky resolution HHCs can improve distance estimation by 2~10 HHCs can improve distance estimation by 2~10 Similar results for mass estimation Similar results for mass estimation Need to run longer Monte Carlo Need to run longer Monte Carlo Confident of our results : same codes used for MLDCs Confident of our results : same codes used for MLDCs and have previously compared Fisher results against MCMC chains. and have previously compared Fisher results against MCMC chains. HHCs can even give visible improvement for low mass systems. HHCs can even give visible improvement for low mass systems. GWDAW 12, December 2007, Boston, USA