Interpreting the results of searches for gravitational waves from coalescing binaries

We describe a method to obtain an astrophysical result from the output of a search for gravitational waves from coalescing binaries. Specifically, we introduce a method based on the loudest event statistic to calculate an upper limit or interval on the astrophysical rate of binary coalescence. The calculation depends upon the sensitivity and noise background of the detectors, and a model for the astrophysical distribution of coalescing binaries. There are significant uncertainties in the calculation of the rate due to both astrophysical and instrumental uncertainties as well as errors introduced by using the post-Newtonian waveform to approximate the full signal. We catalog these uncertainties in detail and describe a method for marginalizing over them. Throughout, we provide an example based on the initial LIGO detectors.

[1]  Gabriela Gonzalez,et al.  The LIGO Scientific Collaboration , 2015 .

[2]  A. Rodriguez.  Reducing False Alarms in Searches for Gravitational Waves from Coalescing Binary Systems , 2008, 0802.1376.

[3]  Vicky Kalogera,et al.  Host Galaxies Catalog Used in LIGO Searches for Compact Binary Coalescence Events , 2007, 0706.1283.

[4]  et al,et al.  Search for gravitational waves from binary inspirals in S3 and S4 LIGO data , 2007, 0704.3368.

[5]  M. Loupias,et al.  The Virgo status , 2006 .

[6]  C. Broeck,et al.  Phenomenology of amplitude-corrected post-Newtonian gravitational waveforms for compact binary inspiral: I. Signal-to-noise ratios , 2006, gr-qc/0607092.

[7]  B. S. Sathyaprakash,et al.  A template bank to search for gravitational waves from inspiralling compact binaries: I. Physical models , 2006, gr-qc/0604037.

[8]  C. Broeck.  Binary black hole detection rates in inspiral gravitational wave searches , 2006, gr-qc/0604032.

[9]  T. Regimbau,et al.  Expected Coalescence Rates of Ns-Ns Binaries for Laser Beam Interferometers , 2005, astro-ph/0510727.

[10]  M. M. Casey,et al.  Upper limits on gravitational wave bursts in LIGO's second science run , 2005 .

[11]  et al,et al.  Search for gravitational waves from galactic and extra-galactic binary neutron stars , 2005, gr-qc/0505041.

[12]  Bruce Allen.  χ2 time-frequency discriminator for gravitational wave detection , 2005 .

[13]  M. Landry,et al.  Calibration of the LIGO detectors for S3 , 2005 .

[14]  Duncan A. Brown.  SEARCHING FOR GRAVITATIONAL RADIATION FROM BINARY BLACK HOLE MACHOS IN THE GALACTIC HALO , 2004, 0705.1514.

[15]  Martin M. Fejer,et al.  Analysis of LIGO data for gravitational waves from binary neutron stars , 2004 .

[16]  T. Damour,et al.  Gravitational radiation from inspiralling compact binaries completed at the third post-Newtonian order. , 2004, Physical review letters.

[17]  P. Brady,et al.  Upper limits on gravitational-wave signals based on loudest events , 2004, gr-qc/0405044.

[18]  V. Kalogera,et al.  Gravitational Waves from Extragalactic Inspiraling Binaries: Selection Effects and Expected Detection Rates , 2004, astro-ph/0402091.

[19]  A. Karimi,et al.  Master‟s thesis , 2011 .

[20]  M. Ramer,et al.  THE COSMIC COALESCENCE RATES FOR DOUBLE NEUTRON STAR BINARIES , 2004 .

[21]  B. C. Joshi,et al.  The Cosmic Coalescence Rates for Double Neutron Star Binaries , 2003, astro-ph/0312101.

[22]  Tomasz Bulik,et al.  A Comprehensive Study of Binary Compact Objects as Gravitational Wave Sources: Evolutionary Channels, Rates, and Physical Properties , 2001, astro-ph/0111452.

[23]  B. Iyer,et al.  Gravitational-Wave Inspiral of Compact Binary Systems to 7/2 Post-Newtonian Order , 2001, gr-qc/0105099.

[24]  P. Canitrot.  Systematic errors for matched filtering of gravitational waves from inspiraling compact binaries , 2001 .

[25]  T. Damour,et al.  A Comparison of search templates for gravitational waves from binary inspiral , 2000, gr-qc/0010009.

[26]  W. Anderson,et al.  Excess power statistic for detection of burst sources of gravitational radiation , 2000, gr-qc/0008066.

[27]  T. Damour,et al.  Transition from inspiral to plunge in binary black hole coalescences , 2000, gr-qc/0001013.

[28]  B. Owen,et al.  Gravitational waves from inspiraling compact binaries: Validity of the stationary-phase approximation to the Fourier transform , 1999, gr-qc/9901076.

[29]  T. Damour,et al.  Effective one-body approach to general relativistic two-body dynamics , 1998, gr-qc/9811091.

[30]  D. Chakrabarty,et al.  Neutron Star Mass Measurements. I. Radio Pulsars , 1998, astro-ph/9803260.

[31]  T. Damour,et al.  Improved filters for gravitational waves from inspiraling compact binaries , 1997, gr-qc/9708034.

[32]  S. Droz,et al.  Gravitational waves from inspiraling compact binaries: Second post-Newtonian waveforms as search templates. II , 1997, gr-qc/9705034.

[33]  Luc Blanchet,et al.  Gravitational waveforms from inspiralling compact binaries to second-post-Newtonian order , 1996, gr-qc/9602024.

[34]  Blanchet,et al.  Erratum: Gravitational waves from inspiralling compact binaries: Energy loss and waveform to second-post-Newtonian order , 1995, Physical review. D, Particles and fields.

[35]  T. Apostolatos,et al.  Search templates for gravitational waves from precessing, inspiraling binaries. , 1995, Physical review. D, Particles and fields.

[36]  Blanchet,et al.  Gravitational-radiation damping of compact binary systems to second post-Newtonian order. , 1995, Physical review letters.

[37]  Thorne,et al.  Spin-induced orbital precession and its modulation of the gravitational waveforms from merging binaries. , 1994, Physical review. D, Particles and fields.

[38]  Flanagan,et al.  The last three minutes: Issues in gravitational-wave measurements of coalescing compact binaries. , 1992, Physical review letters.

[39]  E. Phinney.  The Rate of Neutron Star Binary Mergers in the Universe: Minimal Predictions for Gravity Wave Detectors , 1991 .

[40]  Albert A. Mullin,et al.  Extraction of signals from noise , 1970 .

[41]  W. Bonnor,et al.  Gravitational Radiation , 1958, Nature.