Potential Kick Velocity distribution of black hole X-ray binaries and implications for natal kicks (1908.07199v2)

Abstract: We use Very Long Baseline Interferometry to measure the proper motions of three black hole X-ray binaries (BHXBs). Using these results together with data from the literature and Gaia-DR2 to collate the best available constraints on proper motion, parallax, distance and systemic radial velocity of 16 BHXBs, we determined their three dimensional Galactocentric orbits. We extended this analysis to estimate the probability distribution for the potential kick velocity (PKV) a BHXB system could have received on formation. Constraining the kicks imparted to BHXBs provides insight into the birth mechanism of black holes (BHs). Kicks also have a significant effect on BH-BH merger rates, merger sites, and binary evolution, and can be responsible for spin-orbit misalignment in BH binary systems. $75\%$ of our systems have potential kicks $>70\,\rm{km~s^{-1}}$. This suggests that strong kicks and hence spin-orbit misalignment might be common among BHXBs, in agreement with the observed quasi-periodic X-ray variability in their power density spectra. We used a Bayesian hierarchical methodology to analyse the PKV distribution of the BHXB population, and suggest that a unimodal Gaussian model with a mean of $107\pm16\,\rm{km~s^{-1}}$ is a statistically favourable fit. Such relatively high PKVs would also reduce the number of BHs likely to be retained in globular clusters. We found no significant correlation between the BH mass and PKV, suggesting a lack of correlation between BH mass and the BH birth mechanism. Our Python code allows the estimation of the PKV for any system with sufficient observational constraints.

Kick Velocity Distribution of Black Hole X-ray Binaries: Insights into Natal Kicks

The paper by P. Atri et al. presents an analysis of the potential kick velocity (PKV) distribution of black hole X-ray binaries (BHXBs), using their peculiar velocities when crossing the Galactic plane as a proxy for natal kicks. The authors integrate observations from Very Long Baseline Interferometry (VLBI) and Gaia DR2 data to derive the three-dimensional motions of a sample of 16 BHXBs. By focusing on the potential velocity imparted at the time of BH formation, the paper offers insights into the birth mechanisms of black holes, potentially distinguishing between direct collapse and supernova (SN) formations.

Methodology

The paper combines measurements of proper motions with systemic radial velocities and distances to determine the Galactic orbits of BHXBs. The authors present a Bayesian hierarchical model to analyze PKV distributions. The methodology involves the integration of orbits over 10 Gyr to account for possible plane crossings and the use of a Monte Carlo simulation to propagate measurement uncertainties. This approach enables the estimation of PKV distributions even without precise measurements for some parameters.

Numerical Findings

1. PKV Distribution: The unimodal Gaussian distribution with a mean PKV of 107 ± 16 km/s provides a statistically favorable fit, although a bimodal distribution cannot be entirely ruled out.
2. High-Velocity Kicks: About 75% of the systems have PKVs exceeding 70 km/s, suggesting significant kicks and potentially common spin-orbit misalignments.
3. Correlation Assessments: No significant correlation is found between BH mass and PKV, nor does the current height above the Galactic plane serve as a reliable proxy for PKV.

Implications

Theoretical

The results challenge the assumption of a direct correlation between BH mass and natal kicks, aligning with theoretical predictions that do not suggest a clear mass threshold for direct collapse BH formation. The multiple peaks in the PKV distribution hint at various possible formation pathways that require further exploration.

Practical

The research provides important constraints on the population synthesis models used for BH formation, especially in dense environments like globular clusters. The lack of systems at very high velocities suggests a lower BH retention rate in such clusters if analogous conditions apply broadly across BH populations.

Future Directions

The paper lays groundwork for refining gravitational wave source models by highlighting the significance of natal kicks and their implications on BH binary evolution, particularly spin-orbit alignment considerations. Further, this paper encourages the necessity for more precise measurements of system parameters to refine the PKV distribution and understand natal kicks better.

In conclusion, P. Atri et al. provide critical empirical constraints on the natal kick velocities of BHXBs, contributing valuable insights into stellar collapse mechanisms. The paper emphasizes the importance of understanding the dynamics of BH birth, which has far-reaching implications for the modeling of both isolated and binary BH systems in astrophysics. Future observational campaigns and theoretical developments will be crucial to fully elucidate the complexities revealed by this analysis.