[Paper Review] Metallicity dependence of black hole main sequence binaries detectable with Gaia

Tomoya Kinugawa, Masaki Yamaguchi|arXiv (Cornell University)|Oct 23, 2018

Pulsars and Gravitational Waves Research1 references4 citations

TL;DR

This paper uses binary population synthesis to model black hole-main sequence (BH-MS) binaries in the Milky Way, showing that Gaia can detect 200–400 such systems at solar metallicity (Z⊙) and 70–400 at 0.1Z⊙. The metallicity of the main-sequence companion enables spectroscopic follow-up to probe the metallicity dependence of black hole formation, offering a direct observational test for progenitor populations including metal-poor stars.

ABSTRACT

LIGO has detected gravitational waves from massive binary black hole mergers. In order to explain the origin of such massive stellar-mass black holes, extreme metal poor stars including first stars have been invoked. However, black holes do not carry information of the metallicity. In order to check the metallicity dependence of the black hole formation, we focus on galactic black hole-main sequence binaries (BH-MSs). Using a binary population synthesis method, we find that $\gaia$ can detect $\sim200-400$ BH-MSs whose metallicity is $\zsun$ and $\sim70-400$ BH-MSs whose metallicity is $0.1\zsun$. With the spectroscopic observation on 4-m class telescopes, we can check the metallicity of BH-MSs. The metallicity dependence of the black hole formation might be checked by the astrometry and spectroscopic observations.

Motivation & Objective

• To investigate the detectability of black hole-main sequence (BH-MS) binaries by Gaia across different metallicities.
• To assess whether Gaia's astrometric measurements combined with spectroscopic follow-up can reveal the metallicity dependence of black hole formation.
• To model the population of BH-MS binaries using binary evolution prescriptions sensitive to metallicity, particularly focusing on mass loss and common envelope phases.
• To quantify the number of detectable BH-MS systems at solar and sub-solar metallicities (Z⊙ and 0.1Z⊙) under realistic Gaia detection limits.

Proposed method

• Binary population synthesis using a modified BSE code with updated wind mass loss rates dependent on luminosity and metallicity: Ẇ_WR ∝ L^1.5 Z^0.86 and Ẇ_LBV = 1.5×10⁻⁴ M⊙ yr⁻¹.
• Incorporation of common envelope evolution with αλ = 1, where energy from orbital decay unbinds the envelope, and post-CE separation determines binary survival.
• Use of initial mass function f(M₁) ∝ M₁⁻².³⁵ (5–100 M⊙), uniform mass ratio q ∈ (0.1, 1), and inverse separation distribution f(a) ∝ 1/a for 10⁵ simulated binaries.
• Application of Gaia detection criteria: parallax signal-to-noise >10, limiting magnitude G ≈ 20 mag, and period range 50 days < P < 5 yr to match Gaia's cadence.
• Two star formation models: a constant SFR over 10 Gyr with equal Z⊙ and 0.1Z⊙ fractions (Mix model), and a chemically evolving model (ChemiEvo) with time-dependent metallicity.
• Comparison of BH-MS populations in the full galaxy versus those detectable by Gaia to assess selection effects and metallicity-dependent detection biases.

Experimental results

Research questions

• RQ1 How many black hole-main sequence binaries are detectable by Gaia at solar and sub-solar metallicities (Z⊙ and 0.1Z⊙)?
• RQ2 How does the metallicity of the main-sequence companion in BH-MS systems affect their detectability by Gaia?
• RQ3 Can spectroscopic follow-up with 4-meter telescopes reliably measure the metallicity of the main-sequence companion in Gaia-detected BH-MS systems?
• RQ4 What is the metallicity dependence of the black hole mass function in BH-MS binaries, and how does it differ between Z⊙ and 0.1Z⊙ populations?
• RQ5 How do differences in mass loss and common envelope evolution at varying metallicities affect the final population of observable BH-MS systems?

Key findings

• Gaia can detect approximately 200–400 black hole-main sequence binaries at solar metallicity (Z⊙), and 70–400 at 0.1Z⊙, depending on the star formation model.
• In the Mix model, the number of detectable BH-MS systems is higher at 0.1Z⊙ than at Z⊙ due to reduced mass loss and lower common envelope merger probability in low-metallicity binaries.
• In the ChemiEvo model, the number of detectable BH-MS systems is six times lower at 0.1Z⊙ than at Z⊙, due to shorter lifetimes of massive stars and earlier evolution of high-mass binaries.
• The mass distribution of black holes in Gaia-detected BH-MS systems shows a clear dependence on metallicity: systems with black holes above ∼18 M⊙ are likely of Pop II origin.
• Main-sequence companions in Gaia-detected systems are biased toward higher masses, as low-mass companions are too faint to be detected, even if they exist in the full population.
• Spectroscopic follow-up with 4-meter telescopes can measure the metallicity of the main-sequence companion, enabling direct inference of the progenitor metallicity of the black hole.