Chirp mass

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The chirp mass of a compact binary star system with component masses and is given by .[1][2] In general relativity, the chirp mass determines the leading-order amplitude and frequency evolution of the gravitational-wave signal emitted by the binary during its inspiral. To lowest order in a post-Newtonian expansion, the evolution of the waveform’s phase depends only on the chirp mass:

 

 

 

 

(1)

where , , and are the speed of light, Newton's gravitational constant, the observed gravitational wave frequency (twice the orbital frequency) and the first time derivative of , respectively.[3][4] Accordingly, in gravitational-wave astronomy, the chirp mass can be accurately measured by detectors from frequency and gravitational strain of the gravitational wave.[5]

Rewrite equation (1) to obtain the frequency evolution of gravitational waves from a coalescing binary:[6]

 

 

 

 

(2)

Integrating equation (2) with respect to time gives:[6]

 

 

 

 

(3)

where C is the constant of integration. Furthermore, on identifying and , the chirp mass can be calculated from the slope of the line fitted through the data points (x, y).

References[edit]

  1. ^ L. Blanchet; T. Damour; B. R. Iyer; C. M. Will; A. G. Wiseman (1995). "Gravitational-Radiation Damping of Compact Binary Systems to Second Post-Newtonian order". Phys. Rev. Lett. 74 (3515): 3515–3518. arXiv:gr-qc/9501027Freely accessible. Bibcode:1995PhRvL..74.3515B. doi:10.1103/PhysRevLett.74.3515. 
  2. ^ L. Blanchet; B. R. Iyer; C. M. Will; A. G. Wiseman (1996). "Gravitational waveforms from inspiralling compact binaries to second-post-Newtonian order". Classical Quantum Gravity. 13 (575): 575–584. arXiv:gr-qc/9602024Freely accessible. Bibcode:1996CQGra..13..575B. doi:10.1088/0264-9381/13/4/002. 
  3. ^ B. P. Abbott (LIGO Scientific Collaboration and Virgo Collaboration) et al. (2016). "Observation of Gravitational Waves from a Binary Black Hole Merger". Physical Review Letters. 116 (6): 061102. arXiv:1602.03837Freely accessible. Bibcode:2016PhRvL.116f1102A. doi:10.1103/PhysRevLett.116.061102. PMID 26918975. 
  4. ^ Curt Cutler and Éanna E. Flanagan (1994). "Gravitational waves from merging compact binaries: How accurately can one extract the binary's parameters from the inspiral waveform?". Physical Review D. 49 (6): 2658–2697. arXiv:gr-qc/9402014Freely accessible. Bibcode:1994PhRvD..49.2658C. doi:10.1103/PhysRevD.49.2658. 
  5. ^ Jim Wheeler (2013), Lecture Notes: Gravitational waves (PDF), Department of Physics - Utah State University, retrieved 14 February 2016 
  6. ^ a b V Tiwari, S Klimenko, V Necula and G Mitselmakher (2016). "Reconstruction of chirp mass in searches for gravitational wave transients". Classical and Quantum Gravity. 33 (1). Bibcode:2016CQGra..33aLT01T. doi:10.1088/0264-9381/33/1/01LT01.