[Paper Review] The coalescence rates of double black holes

Krzysztof Belczyński, T. Bulik+2 more|arXiv (Cornell University)|Jun 2, 2011

Pulsars and Gravitational Waves Research3 citations

TL;DR

This paper investigates the coalescence rates of double black hole (BH-BH) binaries using population synthesis models and empirical observations, finding that BH-BH systems are the most promising gravitational wave sources. It predicts merger rates of 42.9 Myr⁻¹ in a mixed-metallicity local universe and detection rates of ~5 per year for LIGO/Virgo, with empirical data from IC10 X-1 and NGC300 X-1 supporting a merger rate of 0.36⁺⁰.⁵⁰₋₀.²⁶ Mpc⁻³ Myr⁻¹.

ABSTRACT

We present the summary of the recent investigations of double black hole binaries in context of their formation and merger rates. In particular we discuss the spectrum of black hole masses, the formation scenarios in the local Universe and the estimates of detection rates for gravitational radiation detectors like LIGO and VIRGO. Our study is based on observed properties of known Galactic and extra-galactic stellar mass black holes and evolutionary predictions. We argue that the binary black holes are the most promising source of gravitational radiation.

Motivation & Objective

• To estimate the merger rates of double black hole binaries in the local universe using updated stellar evolution models.
• To assess the impact of metallicity and common envelope evolution on BH-BH formation and coalescence rates.
• To compare theoretical predictions with empirical observations from X-ray binaries IC10 X-1 and NGC300 X-1.
• To evaluate the detectability of BH-BH mergers by LIGO/Virgo under different sensitivity assumptions.
• To reconcile theoretical merger rates with observational constraints from extra-galactic black hole binaries.

Proposed method

• Employed the StarTrack population synthesis code to simulate 2 million massive binary stars across varying metallicities.
• Incorporated updated stellar physics, including supernova simulations, compact object formation, and mass loss rates producing 30–80 M☉ black holes.
• Modeled common envelope evolution with two extreme assumptions: optimistic (A, no suppression) and pessimistic (B, suppression via Hertzsprung gap stars).
• Calculated Galactic merger rates assuming 100% solar or 10% solar metallicity, and a 50–50 mixture based on Sloan Digital Sky Survey data.
• Estimated empirical merger rates from observed X-ray binaries IC10 X-1 and NGC300 X-1 using observable volume and X-ray active lifetime.
• Converted merger rate densities to LIGO/Virgo detection rates using sensitivity distances (e.g., 18 Mpc for initial LIGO).

Experimental results

Research questions

• RQ1 What is the expected merger rate of double black hole binaries in a Milky Way-like galaxy with mixed metallicity environments?
• RQ2 How do common envelope evolution models (optimistic vs. pessimistic) affect the predicted formation rates of BH-BH systems?
• RQ3 How does decreasing metallicity influence the survival and merger rates of double black hole binaries?
• RQ4 What is the empirical merger rate of BH-BH binaries inferred from observed X-ray binaries like IC10 X-1 and NGC300 X-1?
• RQ5 How do theoretical predictions compare with expected detection rates in LIGO/Virgo, given their sensitivity limits?

Key findings

• In a mixed-metallicity local universe (50% solar, 50% 10% solar metallicity), the predicted Galactic merger rate for BH-BH binaries is 42.9 Myr⁻¹.
• The optimistic common envelope model (A) yields a BH-BH merger rate of 84.2 Myr⁻¹ at 0.1 Z☉, while the pessimistic model (B) reduces it to 6.1 Myr⁻¹.
• For LIGO/Virgo with a sensitivity distance of 18 Mpc, the detection rate for BH-BH binaries is 4.9 yr⁻¹ under the realistic 50–50 metallicity mixture.
• Empirical analysis of IC10 X-1 and NGC300 X-1 yields a merger rate density of 0.36⁺⁰.⁵⁰₋₀.²⁶ Mpc⁻³ Myr⁻¹, corresponding to approximately one detection per year at a 100 Mpc horizon.
• Theoretical and empirical estimates are in strong agreement, both indicating BH-BH binaries are the dominant gravitational wave source among double compact objects.
• The optimistic model (A) cannot yet be excluded by LIGO/Virgo data due to low average sensitivity (d₀,nsns ≈ 9 Mpc), which reduces expected detection rates by a factor of 8.