Abstract Gravitational-wave detectors are starting to reveal the redshift evolution of the binary black hole (BBH) merger rate,RBBH(z). We make predictions forRBBH(z) as a function of black hole mass for systems originating from isolated binaries. To this end, we investigate correlations between the delay time and black hole mass by means of the suite of binary population synthesis simulations,COMPAS. We distinguish two channels: the common envelope (CE), and the stable Roche-lobe overflow (RLOF) channel, characterized by whether the system has experienced a common envelope or not. We find that the CE channel preferentially produces BHs with masses below about 30M⊙and short delay times (tdelay≲ 1 Gyr), while the stable RLOF channel primarily forms systems with BH masses above 30M⊙and long delay times (tdelay≳ 1 Gyr). We provide a new fit for the metallicity-dependent specific star formation rate density based on the Illustris TNG simulations, and use this to convert the delay time distributions into a prediction ofRBBH(z). This leads to a distinct redshift evolution ofRBBH(z) for high and low primary BH masses. We furthermore find that, at high redshift,RBBH(z) is dominated by the CE channel, while at low redshift, it contains a large contribution (∼40%) from the stable RLOF channel. Our results predict that, for increasing redshifts, BBHs with component masses above 30M⊙will become increasingly scarce relative to less massive BBH systems. Evidence of this distinct evolution ofRBBH(z) for different BH masses can be tested with future detectors.
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SCALING PROPERTIES OF QUEUES WITH TIME-VARYING LOAD PROCESSES: EXTENSIONS AND APPLICATIONS
New computing and communications paradigms will result in traffic loads in information server systems that fluctuate over much broader ranges of time scales than current systems. In addition, these fluctuation time scales may only be indirectly known or even be unknown. However, we should still be able to accurately design and manage such systems. This paper addresses this issue: we consider an M / M /1 queueing system operating in a random environment (denoted M / M /1( R )) that alternates between HIGH and LOW phases, where the load in the HIGH phase is higher than in the LOW phase. Previous work on the performance characteristics of M / M /1( R ) systems established fundamental properties of the shape of performance curves. In this paper, we extend monotonicity results to include convexity and concavity properties, provide a partial answer to an open problem on stochastic ordering, develop new computational techniques, and include boundary cases and various degenerate M / M /1( R ) systems. The basis of our results are novel representations for the mean number in system and the probability of the system being empty. We then apply these results to analyze practical aspects of system operation and design; in particular, we derive the optimal service rate to minimize mean system cost and provide a bias analysis of the use of customer-level sampling to estimate time-stationary quantities.
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- PAR ID:
- 10251971
- Date Published:
- Journal Name:
- Probability in the Engineering and Informational Sciences
- ISSN:
- 0269-9648
- Page Range / eLocation ID:
- 1 to 42
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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