Eccentricity evolution of compact binaries and applications to gravitational-wave physics

Searches for gravitational waves from compact binaries focus mostly on quasicircular motion with the rationale that wave emission circularizes the orbit. Here, we study the generality of this result, when astrophysical environments (e.g., accretion disks) or other fundamental interactions are taken into account. We are motivated by possible electromagnetic counterparts to binary black hole coalescences and orbits, but also by the possible use of eccentricity as a smoking gun for new physics. We find that (i) backreaction from radiative mechanisms, including scalars, vectors and gravitational waves, circularize the orbital motion. (ii) By contrast, environmental effects such as accretion and dynamical friction increase the eccentricity of binaries. Thus, it is the competition between radiative mechanisms and environmental effects that dictates the eccentricity evolution. We study this competition within an adiabatic approach, including gravitational radiation and dynamical friction forces. We show that there is a critical semimajor axis below which gravitational radiation dominates the motion and the eccentricity of the system decreases. However, the eccentricity inherited from the environment-dominated stage can be substantial, and in particular can affect LISA sources. We provide examples for GW190521-like sources.

Figure 1

Eccentricity evolution of a binary system, with an initial semiaxis $a/M={10}^7$. Bottom axis shows the semimajor axis as function of eccentricity, top axis shows the GW frequency. We run the binary up to a distance of $a=100M$. Blue bands indicate LISA’s frequency range [43]. Left panel: we consider a system with an initial eccentricity of $e={10}^{-3}$ and different values of the environment density. Dashed line in inset shows threshold values for which periastron is $100M$. Right panel: we fix the density to be $\rho M^2={10}^{-29}$, changing the initial eccentricity of the system. The vertical line indicates the critical distance, given by Eq. (52).

Figure 2

Eccentricity evolution for different initial mass ratios ($q=1.0$, 1.5 and 2.0), when accretion is included. The dashed line is an analytical fit that enable us to predict at which distance the system will reach highly eccentric motion.

Figure 3

Comparison between the numerical integration of Eq. (37) and the result from the adiabatic approach. We plot the deviation normalized by the adiabatic result.