Stochastic Gravitational-Wave Background due to Primordial Binary Black Hole Mergers

TL;DR

The stochastic background arising from the incoherent superposition of such primordial binary black hole systems in the Universe is computed and it is concluded that constraining the dark matter component in the form of black holes using stochastically gravitational-wave background measurements will be very challenging.

Abstract

Recent Advanced LIGO detections of binary black hole mergers have prompted multiple studies investigating the possibility that the heavy GW150914 binary system was of primordial origin, and hence could be evidence for dark matter in the form of black holes. We compute the stochastic background arising from the incoherent superposition of such primordial binary black hole systems in the universe and compare it to the similar background spectrum due to binary black hole systems of stellar origin. We investigate the possibility of detecting this background with future gravitational wave detectors, and discuss the possibility of using the stochastic gravitational-wave background measurement to constrain the dark matter component in the form of black holes.

Figures (5)

• Figure 1: Primordial BBH merger rate per halo as a function of the halo virial mass for the Prada et al. prada and Ludlow et al. ludlow concentration models, assuming $\lambda = 1$, and for several values of redshift. The local $z=0$ curves are to be compared to the Figure 1 of bird.
• Figure 2: Primordial BBH merger rate per comoving volume as a function of redshift, using the Prada et al. prada and Ludlow et al. ludlow concentration models, assuming $\lambda = 1$, and for several halo mass function models watsonPStinker. Note that the fiducial stellar BBH model is computed using black hole binaries which trace the cosmic star formation rate, and thus peaks around $z\sim 1-2$GW150914stoch. The Poisson band around the fiducial stellar model represents the statistical uncertainty in the local rate of BBH mergers GW150914stoch. The primordial BBH merger rate in all considered models is weakly dependent on redshift and slightly increases with redshift.
• Figure 3: Gravitational-wave energy density as a function of frequency for the same models of the halo mass function and concentration as considered in Figure \ref{['rmerger_vs_z']} and assuming $\lambda = 1$. While different primordial models agree with each other within a factor of $\sim 2$, the fiducial stellar model is significantly louder. We note that the amplitude of the stellar fiducial model is currently uncertain due to the large errors on the local rate of BBH mergers, as denoted by the Poisson band GW150914stoch. Also shown is the projected final sensitivity of advanced detectors, denoted O5 GW150914stoch.
• Figure 4: Gravitational-wave energy density for the primordial BBH model is shown as a function of frequency for several values of the black hole mass, assuming the Ludlow et al. concentration model ludlow and the Watson et al. model of the halo mass function watson. Also shown is the projected final sensitivity of advanced detectors, denoted O5, as well as the fiducial stellar model and its Poisson error band GW150914stoch.
• Figure 5: Gravitational-wave energy density for the primordial BBH model is shown as a function of redshift for three selected frequencies: 10 Hz, 60 Hz, and 160 Hz. For all curves we assume the Ludlow et al. concentration model ludlow and the Watson et al. model of the halo mass function watson. The majority of the signal is generated at redshifts below $\sim 3$, implying that the uncertainties in the concentration and halo mass function models at high redshifts have a small impact on the gravitational wave energy density spectrum.