Synthetic model of the gravitational wave background from evolving binary compact objects

Modeling the stochastic gravitational wave background from various astrophysical sources is a key objective in view of upcoming observations with ground- and space-based gravitational wave observatories such as Advanced LIGO, VIRGO, eLISA, and the pulsar timing array. We develop a synthetic model framework that follows the evolution of single and binary compact objects in an astrophysical context. We describe the formation and merger rates of binaries, the evolution of their orbital parameters with time, and the spectrum of emitted gravitational waves at different stages of binary evolution. Our approach is modular and allows us to test and constrain different ingredients of the model, including stellar evolution, black hole formation scenarios, and the properties of binary systems. We use this framework in the context of a particularly well-motivated astrophysical setup to calculate the gravitational wave background from several types of sources, including inspiraling stellar-mass binary black holes that have not merged during a Hubble time. We find that this signal, albeit weak, has a characteristic shape that can help constrain the properties of binary black holes in a way complementary to observations of the background from merger events. We discuss possible applications of our framework in the context of other gravitational wave sources, such as supermassive black holes.

Figure 1

Evolution of eccentricity for a $30M_{\odot }-30M_{\odot }$ binary with different initial eccentricities and separations. These different initial conditions induce the difference in merging time scales of several orders of magnitude.

Figure 2

The region in parameter space (eccentricity and semimajor axis) corresponding to rapid mergers (i.e. within the age of the Universe) to the left of the solid lines and slow mergers (i.e. taking longer than the age of the Universe) to the right of the solid lines. Each line corresponds to a different mass of the BBH components, as indicated in the legend.

Figure 3

A schematic representation of our model framework. Stars form from interstellar gas with metallicity $Z$ as described in an underlying model of galactic evolution. Massive stars end their lives as BHs or NSs, according to their initial mass and metallicity. We assume that part of these objects forms binary systems: $BH-BH$, $NS-NS$, and $BH-NS$. Gravitational waves are produced during the inspiral phase and merger of binary systems prior to their collapse into a BH (marked by red arrows) and during the core collapse of massive stars. The latter also affect the metallicity of the interstellar gas.

Figure 4

The source density $\mathrm{d}{n}_i/\mathrm{d}t(M,z)$ for our chosen astrophysical model as a function of BH (source frame) mass at three different redshifts. The population builds over time with the number density of BBH with masses around $\sim 20–25M_{\odot }$ growing considerably faster than that of other masses due to the transition of stars above $\sim 30M_{\odot }$ from direct collapse, which occurs at low metallicities, to SN explosion (and associated lower remnant masses) at higher metallicities.

Figure 5

GW background from inspiraling and merging binary black holes with $a_{\min }=0.2\mathrm{AU}$ (red line), the range $a_{\min }=0.15–0.3\mathrm{AU}$ (red shaded area), and the GW background from merging BBH from Ref. [34] where the merger rate was normalized to the observed value (black lines). Also shown are the expected sensitivities of Advanced LIGO during observing run O5 [5] (solid magenta line), eLISA [10] (solid blue line), DECIGO [54] (dashed blue line), and the Cosmic Explorer [55] (dashed magenta line). The last two curves were estimated from the expected strain sensitivities.

Figure 6

Gravitational wave background from inspiraling binary neutron stars that did not merge during the Hubble time.