The so-called ‘Cosmic Dawn’, i.e. the age during which the very first sources of light (stars, black holes, galaxies) kindled in the Universe, and the subsequent epoch of reionization (EoR) during which most of the hydrogen of the intergalactic medium (IGM) returned to its ionized state, are the two of the most fascinating and poorly understood phases of the evolution of the Universe.
Referring to the redshift-dependent Binary black holes (BBH’s) merger rate, a larger number of BBHs would merge at earlier epochs and thus most of the individually unresolved merger populations produce a GW background (GWB). The detection of a GWB will be used to probe the formation epoch and efficiency of coalescing BBHs, constrain the mass function for massive star/BH populations initiated in the early universe, and even provide information on the history of cosmic reionization.
More specifically, the existence of high-redshift (high-z from now on) , massive BBH populations (e.g., the remnant BHs of Population III stars; hereafter PopIII stars), would produce a GWB detectable by LIGO/Virgo with a unique spectral shape that flattens significantly at ∼ 30 Hz, which is distinguishable from the spectral index of ∼ 2/3 generically produced by lower redshift and less-massive BBHs. A recent population synthesis study also claimed a deviation of the spectral index from the canonical value if the PopIII contribution is included.
Massive stellar progenitors of merging BBHs formed at the cosmic dawn are also efficient producers of ionizing radiation in the early universe and are expected to dominate the reionization process. Recently, Planck has reported an updated estimate of the optical depth of the universe to electron scattering inferred from the cosmic microwave background (CMB) anisotropies;
τe ≃ 0.052 ± 0.008. This low value would give a stringent constraint on the star formation history and the total stellar mass budget available for BBH formation at higher redshifts. Therefore, this constrains the amplitude of a GWB owing to BBH mergers originating from high-z populations.
Now, Inayoshi and colleagues studied the upper bound of the GWB produced by BBH mergers taking into account the constraint on the cumulative stellar mass from cosmic reionization.
“We find that even with the upper bound, the GWB signal is still detectable at the Advanced LIGO–Virgo design sensitivity, while the merger rate at z ≃ 0 is consistent or lower than the observed GW event rate.“— told Inayoshi, first author of the study
Under this constraint from the reionization history, the merger rate for the high-redshift BBH population becomes as high as R_BBH ≃ 5−30 Gpc¯3 yr¯1 at z ≃ 0 for a wide range of the parameters of the delay-time a (DTD) for BBH coalescences.
Since a vast majority of the BBHs merge in the early universe, the merger rate increases to R_BBH ≃ 103–4 Gpc¯3 yr¯1 at z ≃ 6 − 10 for the DTD index of 1.0 ≲ n ≲ 1.5. As a result of their frequent mergers, researchers concluded that the amplitude of the GWB produced by the high-redshift (high-z) BBH population can be as high as Ωgw ≃ 1.48 × 10¯9 at f = 25 Hz, where the Advanced LIGO–Virgo detectors are the most sensitive (in detecting this GWB signal), while the merger rate at z ≃ 0 is consistent or lower than the observed GW event rate. The detection of this level of GWB would also indicate a major contribution of the high-z BBH population to the local GW events.
Using the updated BBH properties from the LIGO–Virgo O3a observing run and the new value of τe, they also inferred a GWB spectral shape, with a characteristic flattening at f ≳ 20 − 30 Hz from the value of 2/3, which is even more skewed toward lower frequencies if the mass function is more top-heavy than in the local universe.
“This would allow us to extract information on the mass function of merging BBHs at high redshifts“— told Inayoshi, first author of the study
Reference: Kohei Inayoshi, Kazumi Kashiyama, Eli Visbal, Zoltan Haiman, “Gravitational wave backgrounds from coalescing black hole binaries at cosmic dawn: an upper bound”, ArXiv, pp. 1-15, 2021. https://arxiv.org/abs/2103.12755
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