- The ultimate signature that can potentially distinguish between different formation scenarios of black holes is through evolution of the merger rate with redshift.
- Mukherjee and Silk suggested that, as primordial black holes are going to be present before the formation of the stars, and the merger rate of these sources at high redshift is going to be large compared to astrophysical black holes,we can be able to distinguish them by using the stochastic GW background.
- According to them, we should be able to distinguish between the different populations of black holes with the forthcoming O5 and A+ detector sensitivities.
- The accurate measurement of the power-law index, and constraints on the astrophysical time-delay parameter, characteristic mass scale of PBHs, and the fraction of PBH/ABH should be feasible at O5 and A+ sensitivities.
How are black holes forming in the Universe? There are two formation scenarios of black holes, the first is astrophysical scenario, in which black holes are formed from the deaths of stars and second is, from primordial fluctuations, which takes place in the early universe. One of the primary challenges is to distinguish between astrophysical black holes (ABH) forming from stellar deaths and primordial black holes (PBHs) arising from an early universe origin. Now, Mukherjee and silk in their recent paper showed how we can distinguish between ABHs and PBHs using the stochastic gravitational wave background (SGWB).
The ultimate signature that can potentially distinguish between different formation channels of black holes is through evolution of the merger rate with redshift. Gravitational Waves (GW) sources produced from the deaths of stars form after the formation of the first stars, whereas primordial black holes exist in large numbers at very high redshift before any stars formed. This is one of the key differences that can be used to distinguish between a population of ABHs and PBHs.
For the ABHs, even though one would expect the merger rate of black holes to be related to the star formation rate of the Universe, one of the major sources of uncertainty in the merger rate is due to the time delay between the formation and merger of GW sources. For GW sources with small time delays ( < 100 Myr), the peak of the mergers of GW sources is around the peak of the star formation rate (z ≈ 2), whereas for the scenarios with larger time delays, the peak of the merger of the ABHs can be shifted towards lower redshifts. However for primordial black holes, the merger rate is always an increasing function of redshift. Thus, different populations of GW sources present at early epochs can be distinguished by using the stochastic GW background to explore the high redshift Universe.
“In future a joint multi-messenger study of the stochastic GW background and different probes of star formation rate using electromagnetic signal will further improve the capability to distinguish between the population of ABHs and PBHs.”
Now, Mukherjee and Silk construct a hybrid merger rate model of ABHs and PBHs, by taking into account the time delay between formation and mergers of the astrophysical sources and incorporating a general redshift dependence of the PBH merger rate. Their hybrid model is driven by use of the Madau-Dickinson star formation rate history (SFR) to derive the astrophysical black hole merger rate and a power-law model for the primordial black hole merger rate. The free parameters of this model are the time delay parameter, the local merger rate, the index of the power-law model of PBH merger rate, the characteristic mass-scale of PBHs, and the fraction of PBHs over ABHs. This five-parameter model makes it possible to perform a relatively fast MCMC search of GW sources to jointly probe the parameter space of ABHs and PBHs.
They showed that, current data can only rule out very large values of the power law index of the merger rate for PBHs and cannot constrain the time-delay parameter. However, in the near future from O5 and A+ sensitivities, the stochastic GW background should be a powerful probe that is capable of distinguishing between different populations of the GW sources.
“The accurate measurement of the power-law index, and constraints on the astrophysical time-delay parameter, characteristic mass scale of PBHs, and the fraction of PBH/ABH should be feasible at O5 and A+ sensitivities.”
In future work, they will explore the measurability of the stochastic GW signal from space-based GW detectors such as Laser Interferometer Space Antenna (LISA) and the next generation ground-based detectors such as the Einstein Telescope, and the Cosmic Explorer.
Reference: Suvodip Mukherjee, Joseph Silk, “Can we distinguish astrophysical from primordial black holes via the stochastic gravitational wave background?”, Arxiv, pp. 1-9, 2021. https://arxiv.org/abs/2105.11139
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