Mathematics – Logic
Scientific paper
Nov 1993
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993phrvd..48.4738m&link_type=abstract
Physical Review D (Particles, Fields, Gravitation, and Cosmology), Volume 48, Issue 10, 15 November 1993, pp.4738-4756
Mathematics
Logic
75
Binary And Multiple Stars, Observational Cosmology
Scientific paper
We explore the feasibility of using LIGO and/or VIRGO gravitational-wave measurements of coalescing, neutron-star-neutron-star (NS-NS) binaries and black-hole-neutron-star (BH-NS) binaries at cosmological distances to determine the cosmological parameters of our Universe. From the observed gravitational waveforms one can infer, as direct observables, the luminosity distance D of the source and the binary's two ``redshifted masses,'' M'1≡M1(1+z) and M'2≡M2(1+z), where Mi are the actual masses and z≡Δλ/λ is the binary's cosmological redshift. Assuming that the NS mass spectrum is sharply peaked about 1.4Msolar, as binary pulsar and x-ray source observations suggest, the redshift can be estimated as z=M'NS/1.4Msolar-1. The actual distance-redshift relation D(z) for our Universe is strongly dependent on its cosmological parameters [the Hubble constant H0, or h0≡H0/100 km s-1Mpc-1, the mean mass density ρm, or density parameter Ω0≡(8π/3H20)ρm, and the cosmological constant, Λ, or λ0≡Λ/(3H20)], so by a statistical study of (necessarily noisy) measurements of D and z for a large number of binaries, one can deduce the cosmological parameters. The various noise sources that will plague such a cosmological study are discussed and estimated, and the accuracies of the inferred parameters are determined as functions of the detectors' noise characteristics, the number of binaries observed, and the neutron-star mass spectrum. The dominant source of error is the detectors' intrinsic noise, though stochastic gravitational lensing of the waves by intervening matter might significantly influence the inferred cosmological constant λ0, when the detectors reach ``advanced'' stages of development. The estimated errors of parameters inferred from BH-NS measurements can be described by the following rough analytic fits: Δh0/h0~=0.02(N/h0)(τR)-1/2 (for N/h0<~2), where N is the detector's noise level (strain/Hz) in units of the ``advanced LIGO'' noise level, R is the event rate in units of the best-estimate value, 100 yr-1 Gpc-3, and τ is the observation time in years. In a ``high density'' universe (Ω0=1, λ0=0) ΔΩ0~=0.3(N/h0)2(τR)-1/2, Δλ0~=0.4(N/h0)1.5(τR)-1/2, for N/h0<~1. In a ``low density'' universe (Ω0=0.2, λ0=0), ΔΩ0~=0.5(N/h0)3(τR)-1/2, Δλ0~=0.7(N/h0)2.5(τR)-1/2, also for N/h0<~1. These formulas indicate that, if event rates are those currently estimated (~3 per year out to 200 Mpc), then when the planned LIGO and/or VIRGO detectors get to be about as sensitive as the so-called ``advanced detector level'' (presumably in the early 2000s), interesting cosmological measurements can begin.
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