Moving gravitational wave sources at cosmological distances: Impact on the measurement of the Hubble constant

Abstract

Standard sirens - GW sources with an EM counterpart - can be used to measure H_0 directly which should help to ease the existing Hubble tension. However, if the source has a relative velocity to the expanding universe on top of its motion due to the Hubble flow, a relativistic redshift affects the redshift of the EM counterpart and the apparent distance of the GW source, and thus it needs to be corrected to obtain accurate measurements. We study the effect of such a relative velocity on GWs for a source in an expanding universe showing that the total redshift of the wave is equal to the product of the relativistic redshift and the cosmological redshift. We, further, find that a relative velocity of the source changes its apparent distance by a factor (1+z_rel)^2 in contrast to a linear factor for the cosmological redshift. We discuss that the additional factor for the relativistic redshift is a consequence of a velocity-dependent amplitude for GWs. We consider the effect of the relative velocity on the chirp mass and the apparent distance of the source an observer would infer when ignoring this velocity. We find that for different astrophysical scenarios the error can range between 0.1 % and 7 % for the chirp mass while the error in the apparent distance can be between 0.25 % and 15 %. Furthermore, we consider the error introduced in the measurement of H_0 using standard sirens for two cases: (i) when the effect of velocity on the redshift of the EM counterpart is considered but not on the apparent distance obtained from GWs and (ii) when the effect of the relative velocity is ignored completely. We find that in the first case the error can reach 1 % for a source moving due to the peculiar velocity of its host galaxy and that in the second case the error can be more than 5 % for a source at the distance of GW150914 with the same velocity.

14 pages, 5 figures

References in corpus (35)

• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology
• Multi-messenger Observations of a Binary Neutron Star Merger
• Gravitational Waves and Gamma-rays from a Binary Neutron Star Merger: GW170817 and GRB 170817A
• Advanced LIGO
• GWTC-2: Compact Binary Coalescences Observed by LIGO and Virgo During the First Half of the Third Observing Run
• In the Realm of the Hubble tension $-$ a Review of Solutions
• A gravitational-wave standard siren measurement of the Hubble constant
• A kilonova as the electromagnetic counterpart to a gravitational-wave source
• Optical emission from a kilonova following a gravitational-wave-detected neutron-star merger
• The Combined Ultraviolet, Optical, and Near-Infrared Light Curves of the Kilonova Associated with the Binary Neutron Star Merger GW170817: Unified Data Set, Analytic Models, and Physical Implications
• Measurements of the Hubble Constant: Tensions in Perspective
• Cosmology Intertwined II: The Hubble Constant Tension
• Large Merger Recoils and Spin Flips From Generic Black-Hole Binaries
• Candidate Electromagnetic Counterpart to the Binary Black Hole Merger Gravitational Wave Event S190521g
• On the Hubble constant tension in the SNe Ia Pantheon sample
• On the evolution of the Hubble constant with the SNe Ia Pantheon Sample and Baryon Acoustic Oscillations: a feasibility study for GRB-cosmology in 2030
• Why reducing the cosmic sound horizon alone can not fully resolve the Hubble tension
• Consistency tests of $\Lambda$CDM from the early integrated Sachs-Wolfe effect: Implications for early-time new physics and the Hubble tension
• Does Hubble Tension Signal a Breakdown in FLRW Cosmology?
• Descope of the ALIA mission
• Binary Black Holes: Spin Dynamics and Gravitational Recoil
• Implications for the Hubble tension from the ages of the oldest astrophysical objects
• Wet Extreme Mass Ratio Inspirals May Be More Common For Spaceborne Gravitational Wave Detection
• Hubble tension or a transition of the Cepheid SnIa calibrator parameters?
• Superkicks in Hyperbolic Encounters of Binary Black Holes
• The effect of matter structure on the gravitational waveform
• Electromagnetic Signatures of Relativistic Explosions in AGN Disks
• The Hubble Tension Revisited: Additional Local Distance Ladder Uncertainties
• The last migration trap of compact objects in AGN accretion disc
• Black hole kicks as new gravitational wave observables
• Direct determination of supermassive black hole properties with gravitational-wave radiation from surrounding stellar-mass black hole binaries
• Excitation of gravitational wave modes by a center-of-mass velocity of the source
• Exciting modes due to the aberration of gravitational waves: Measurability for extreme-mass-ratio inspirals
• Hunting intermediate-mass black holes with LISA binary radial velocity measurements

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• Multimessenger hierarchical triple merger gravitational-wave event pair GW190514-GW190521 inside AGN J124942.3 + 344929
• The Use of Binary Black Holes Merging in AGN Disks for Hubble Constant Measurements
• Influence of cosmic expansion on gravitational waveforms