Popcorn in the sky: Identifying primordial black holes in the gravitational-wave background

Abstract

Primordial black holes (PBHs) are possible sources of a gravitational-wave background (GWB), detectable with the next observing runs of LIGO--Virgo--KAGRA. In case of a detection, it will be crucial to distinguish the possible sources of this GWB. One under-explored possibility is to exploit the duty cycle that quantifies the number of sources present in the time domain signal, which can be very different depending on the nature and population of the sources. We compute the duty cycle for a realistic population of PBH binaries, isolating the shot-noise, popcorn and continuous contributions to the GWB. We identify the dependence of the duty cycle on the signal frequency, duration and amplitude as a crucial metric for distinguishing PBHs from other sources in the GWB and constraining PBH models. Our work motivates the development of specific analysis tools to extract these observables, in order to unlock new cosmological insights with upcoming GW data.

Figures (5)

• Figure 1: Normalized strain time series and power spectral densities in the shot-noise (red), popcorn (blue), and continuous (green) regimes for three toy models of compact-binary populations. Despite having near-identical frequency spectra, the three models are drastically different in the time domain, illustrating the additional information accessible via statistics such as the duty cycle.
• Figure 2: The duty cycle as a function of the maximum redshift for three pairs of component masses $m_1$ and $m_2$ of early PBH binaries, in one e-fold of frequency around 40 Hz. The popcorn region is enclosed by the two dashed lines indicating $\Delta(z) = 0.1$ and $1$.
• Figure 3: Top panel: Assumed PBH mass distribution, from Bagui:2021dqi, showing features from the sound speed reduction at the electroweak and QCD epochs. Bottom panel: The duty cycle distribution as a function of the masses $m_1$ and $m_2$ for early PBH binaries with the considered mass distribution, a maximum redshift $z_{\rm max} = 100$, at a frequency of 40 Hz. The white dashed lines enclose the popcorn region between $\Delta = 0.1$ and $1$.
• Figure 4: Expected distributions of the duty cycle with GW signal strain $h$ and duration $\Delta T$ at $f=40$ Hz, for our benchmark PBH model (two top and panels) and for astrophysical black holes (third panel) and neutron stars (bottom panel). The white contours indicate the popcorn regions, defined as $0.1<\Delta < 1$.
• Figure 5: Comparison between the GWB from early PBH binaries with the mass distribution shown in Fig. \ref{['fig:Delta_of_m']} (blue lines) and the one from ABHs (red and pink lines) and NS (green lines). The solid, dashed, dot-dashed and dotted lines show respectively the total background and the shot-noise, popcorn and continuous distributions, obtained when sources are ranked with respected to the strain $h(f)$. For PBHs, the popcorn background is dominant between 10 and 100 Hz in the sensitivity band of LVK, whereas for ABH and NS, the shot-noise GWB dominates.