Estimating spinning binary parameters and testing alternative theories of gravity with LISA

Abstract

We investigate the effect of spin-orbit and spin-spin couplings on the estimation of parameters for inspiralling compact binaries of massive black holes, and for neutron stars inspiralling into intermediate-mass black holes, using hypothetical data from the proposed Laser Interferometer Space Antenna (LISA). We work both in Einstein's theory and in alternative theories of gravity of the scalar-tensor and massive-graviton types. We restrict the analysis to non-precessing spinning binaries, i.e. to cases where the spins are aligned normal to the orbital plane. We find that the accuracy with which intrinsic binary parameters such as chirp mass and reduced mass can be estimated within general relativity is degraded by between one and two orders of magnitude. We find that the bound on the coupling parameter omega_BD of scalar-tensor gravity is significantly reduced by the presence of spin couplings, while the reduction in the graviton-mass bound is milder. Using fast Monte-Carlo simulations of 10^4 binaries, we show that inclusion of spin terms in massive black-hole binaries has little effect on the angular resolution or on distance determination accuracy. For stellar mass inspirals into intermediate-mass black holes, the angular resolution and the distance are determined only poorly, in all cases considered. We also show that, if LISA's low-frequency noise sensitivity can be extrapolated from 10^-4 Hz to as low as 10^-5 Hz, the accuracy of determining both extrinsic parameters (distance, sky location) and intrinsic parameters (chirp mass, reduced mass) of massive binaries may be greatly improved.

Figures (9)

• Figure 1: Analytic approximation to the LISA root noise spectral density curve used in this paper and in Ref. BC (dashed line) and the curve produced using the LISA Sensitivity Curve Generator SCG (solid line). The SCG curve has been multiplied by a factor of $\sqrt{3/20}$ to obtain an effective non-sky averaged noise spectral density (see Sec. \ref{['noisecurves']}). The SCG noise curve does not include the extragalactic white dwarf confusion noise while the analytical approximation curve does.
• Figure 2: Left: luminosity distances $D_L$ of NS-BH binaries observed with SNR=10 as a function of the black hole mass. We assume that the NS mass $M_{\rm NS}=1.4 M_\odot$. Right: SNR for equal mass BH-BH binaries at $D_L=3$ Gpc as a function of the total mass. Solid lines refer to the LISA noise curve (\ref{['Shtot']}) used in this paper; dashed lines refer to the same noise curve without including the white-dwarf confusion noise. The "bump" in the noise curve due to white-dwarf confusion noise is responsible for the dip in the SNR for MBH binaries of masses $\sim 10^6 M_\odot$.
• Figure 3: Monte Carlo simulation of $10^4$ binaries with observed total mass $(1.4+10^3)M_\odot$ in general relativity, with single-detector SNR=10, $\Omega_\Lambda=0.7$, $\Omega_M=0.3$. Top: probability distributions of the angular resolution $\Delta \Omega_S$ in steradians for one detector (left) and two detectors (right). In each figure, from left to right, the histograms refer to no spins, SO included, and SO and SS included. Bottom: probability distributions of $\Delta D_L/D_L$ for one detector (solid) and two detectors (dashed); $\Delta D_L/D_L$ is essentially unaffected by the inclusion of spins, so we only show histograms without the spin terms.
• Figure 4: Monte Carlo simulation of $10^4$ binaries with observed total mass $(1.4+10^3)M_\odot$ in general relativity, with single-detector SNR=10, $\Omega_\Lambda=0.7$, $\Omega_M=0.3$. Top four panels: probability distribution of the errors on the chirp mass $\Delta {\cal M}/{\cal M}$, the reduced mass $\Delta \mu/\mu$, the SO parameter $\Delta \beta$ and the SS parameter $\Delta \sigma$. Bottom panel: bound on $\omega_{\rm BD}$ when a Brans-Dicke term is included. Solid (dashed) lines refer to one (two) detector(s).
• Figure 5: Monte Carlo simulation of $10^4$ binaries with total mass $(10^6+10^6)M_\odot$ in general relativity, with $D_L=3$ Gpc, $\Omega_\Lambda=0.7$, $\Omega_M=0.3$, with no spins. Panels show probability distributions of the SNR, the distance determination error $\Delta D_L/D_L$, the redshift errors $\Delta {z}/{z}$ and $(\Delta {z}/{z})_{\rm best}$ and the angular resolution $\Delta \Omega_S$ in steradians. Solid (dashed) lines refer to one (two) detector(s).