Mergers of Eccentric Binaries and LIGO: Detection and Estimation Biases Birjoo Vaishnav1, Deirdre Shoemaker2, Matt Benacquista1, Ian Hinder3 1CGWA,
University of Texas Brownsville, 2CRA, GeorgiaTech, 3AEI, Potsdam How efficient are circular templates in capturing eccentric merger signal?
LIGO Event rates for Eccentric Stellar Mass Binaries Dynamical friction leads to self segragation of black holes in the core of galactic nuclei, leading to encounters of black hole binaries. O’Leary, Kocsis and Loeb [1] found that such binaries can be highly eccentric and the expected event rate of such events can be quite high for Advanced LIGO. The table and figure in this section are from O’Leary et al[1].
Parameter Estimation Biases due to non-eccentric templates If a detection using non-eccentric templates is not subjected to additional filtering with eccentric waveforms, there can be biases in the parameters of the binary additional to the statistical error given by the Fisher matrix. Such a systematic bias due an inaccurate model of the signal-which neglects eccentricity, can be up to an order of magnitude higher than the statistical error. Such errors are similar to those discussed by Cutler and Vallisneri [3], and motivate inclusion of eccentricity in parameter estimation efforts for LIGO. In the figure below, the legend indicates the eccentricity and the percent mass bias upon using non-eccentric templates to filter eccentric signals is plotted. The effect is significant for eccentricities greater than 0.1 and masses less than 150 solar mass. Athe bias goes down for eccentricity 0.3 compared to eccentricity 0.25 as the fitting factors in the mass range of interest are significantly low, and varying the mass does not help increase it because the waveform is much different from the noneccentric ones. These results look different from the recent paper by Cokelaer and Pathak[4].
For the case of moderate to small eccentricity signal, if an eccentric binary black hole merger template bank is not used for stellar/intermediate mass binaries, the event loss can be significant for the mass range [40-100] Msun. For lower masses, the circular templates may be enough for detection. Plotted below are the fitting factors for an eccentric, equal mass binary signal with non-eccentric, equal mass templates. The legend indicates eccentricity near merger, the numerical relativity waveforms used are from [2].
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The matched filtering signal to noise squared per logarithmic eccentricity bin for advanced LIGO is shown below. The binaies are assumed at a distance of 1 Gpc. Figure courtesy [1]. Eccentric binaries can contribute significantly to the signal for this case. These signals may be burst like or inspiral-like depending on the eccentricity and the initial periapsis.
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References
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Eccentricity Reach vs mass æ
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The range of eccentricity that would be detectable by a non-eccentric template bank depends on the mass and the fitting factor threshold, higher the threshold, more restricted is the range of eccentricities detectable by circular templates. The legend indicates threshold fitting factor/minimal match values.
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1. R.O’Leary, B. Kocsis, A. Loeb, 2008 arXiv:0807:2368v2[astro-ph]
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2. I.Hinder, B. Vaishnav, F. Herrmann, D.Shoemaker, P.Laguna, Phys.Rev.D 77:081502,2008 3. C.Cutler and M. Vallisneri, Phys.Rev.D 76: 104018,2007
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4. T. Cokelaer and D. Pathak Class.Quant.Grav.26:045013,2009
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Acknowledgements BV thanks the Center for Gravitational Wave Astronomy, University of Texas Brownsville for research and travel funding. MB and BV acknowledge NS CREST award #0734800
