Fig. 2: Detectability contours of the modulating SMBHB amplitude \({{{{\mathcal{A}}}}}_{{{{\rm{mod}}}}}\) experienced by a stellar-mass compact binary.
From: Imprints of massive black-hole binaries on neighbouring decihertz gravitational-wave sources
The binaries are located in a fiducial host galaxy at redshift z = 0.84. The modulated GW signal from the compact binary is observed with DECIGO over T = 10 years. Left: to compute this sensitivity we vary the modulating amplitude \({{{{\mathcal{A}}}}}_{{{{\rm{mod}}}}}\) and frequency \({f}_{{{{\rm{mod}}}}}\) of the SMBHB and indicate the relative uncertainty \(\Delta {{{{\mathcal{A}}}}}_{{{{\rm{mod}}}}}/{{{{\mathcal{A}}}}}_{{{{\rm{mod}}}}}=1{0}^{0}\) and 10−1, respectively, by which a given amplitude could be recovered with dashed contour lines, using parameter estimation with the Fisher matrix. Black contour lines assume that a GW150914 (ref. 100)-like BBH with a chirp mass of \({{{\mathcal{M}}}}=28.0\,{{{{\rm{M}}}}}_{\odot }\) is observed. Blue contour lines assume a GW170817 (ref. 68)-like BNS (\({{{\mathcal{M}}}}=1.188\,{{{{\rm{M}}}}}_{\odot }\)). We also show for the BNS the sensitivity curve from a full Bayesian analysis with an MCMC (solid blue line) that corresponds to the Fisher matrix uncertainty \(\Delta {{{{\mathcal{A}}}}}_{{{{\rm{mod}}}}}/{{{{\mathcal{A}}}}}_{{{{\rm{mod}}}}} \approx 1{0}^{-1/2}\) (Methods and Supplementary Fig. 2). Right: we show the sensitivity in terms of the minimum detectable chirp mass \({{{{\mathcal{M}}}}}_{{{{\rm{mod}}}}}={({{{{\mathcal{A}}}}}_{{{{\rm{mod}}}}}d)}^{3/5}/{(\uppi {f}_{{{{\rm{mod}}}}})}^{2/5}\) of the SMBHB for a fiducial distance d = 1 pc to the BBH/BNS. The red line indicates the frequency above which our assumption of a monochromatic SMBHB breaks down. Note that the number of SMBHBs near this limit is anyways highly suppressed (Methods).
