Kinematics show consistency between stellar mass and supermassive black hole parent population jet speeds

TL;DR

The study investigates whether BHXRB jet speeds share the same intrinsic Lorentz-factor distribution as AGN jets, challenging the view that BHXRBs are intrinsically slower. It models the BHXRB parent population with a power-law Lorentz-factor distribution, $N(\Gamma) \propto \Gamma^b$, and uses an isotropic inclination distribution to simulate observed $\beta_{\rm app}$, accounting for distance uncertainties. Through Anderson-Darling tests and hierarchical Bayesian nested sampling, it finds a consistent power-law shape with $b = -2.64_{-0.55}^{+0.46}$, and shows that $\Gamma_{\max}$ remains largely unconstrained by kinematics, while selection biases largely explain the slower apparent speeds in BHXRBs. Comparisons to AGN populations (MOJAVE, BASS, FermiLAT) reveal overlap in the allowed $b$-space, supporting a common underlying jet physics across BH mass scales, though differences in sample selection can shift the inferred exponents. The work highlights the need for larger BHXRB samples to tighten constraints and suggests that jet acceleration processes may be broadly universal across stellar and supermassive black holes.

Abstract

Jets from stellar-mass and supermassive black holes provide the unique opportunity to study similar processes in two very different mass regimes. Historically, the apparent speeds of black hole x-ray binary (BHXRBs) jets have been observed to be lower than jet speeds from active galactic nuclei (AGN) and specifically blazars. In this work, we show that selection effects could be the primary cause of the observed population differences. For the first time, it is possible to perform a statistical analysis of the underlying BHXRB jet Lorentz factor distribution. We use both the Anderson-Darling test and apply nested sampling to this problem. With Bayes factors, we confirm that the Lorentz factor distribution of BHXRBs is best described with a power law, the same model that has been applied to AGN jets. For a Lorentz factor distribution following $\rm N(Γ) \propto Γ^b$ we find a value for the exponent of $b=-2.64_{-0.55}^{+0.46}$. This exponent is consistent with values found in AGN population studies, within $1σ$ for \textit{Swift}-BAT and \textit{Fermi}-LAT selected AGN. The best-fit exponent for the radio selected MOJAVE sample is just above our $2 σ$ limit. This is a remarkable agreement given the different scales at which the jets are observed. The observed slower apparent speeds in BHXRBs are largely due to the much larger inclinations in this sample. Furthermore, nested sampling confirms that $Γ_{\rm max}$ is completely unconstrained using this method. Therefore, based on kinematics alone, BHXRB jets are broadly consistent with being just as relativistic as those from supermassive black holes.

Figures (6)

• Figure 1: Comparison of the inclination angle and apparent speed distributions of XRB and AGN jets. X-ray binary sample of apparent speed and inclinations used in this work as presented in fender_speeds_2025 shown as orange data points. The marker symbol indicates the class of object. The blue data points show the MOJAVE 1.5 Jy Quarter Century sample lister_mojave_2009homan_mojave_2021. The dotted black curve shows the maximum observable apparent speed due to inclination effects at an infinitely high Lorentz factor and at $\Gamma=5$. The histograms are marginalized over each axis and show the sample fraction of each of the populations. The populations occupy very different regions of parameter space.
• Figure 2: The change in observed apparent speed with changing intrinsic Lorentz factors at different inclination angles. This figure shows the asymptotic flattening of the apparent speed at high inclinations. This effect affects the XRB sample strongly.
• Figure 3: Comparison between Nested Sampling approach as well as Anderson-Darling test statistic rejection fraction for the exponent of the Lorentz factor power law describing the distribution in BHXRBs. The green histogram is the nested sampling posterior, with the posterior density shown on the left y-axis. The corresponding quantiles are shown with the gray lines. The right y-axis shows the rejection fraction, where the blue line is the rejection fraction at $p<0.05$, which corresponds to a confidence interval of $95\%$. And the orange line at $p<0.01$ which corresponds to a confidence interval of $99\%$ when using the Anderson-Darling test.
• Figure 4: The results of the Nested Sampling analysis of the BHXRB sample. The plots on the diagonal show the marginalised 1D histograms for each parameter, while the other plots show 2D marginalised distributions. The quoted uncertainties are $1\sigma$ limits.
• Figure 5: The comparison of AGN power law exponents with the BHXRB results in this work. The solid error bars come from $\chi^2$ model fitting, while the dotted error bars indicate that this error comes from Monte Carlo simulations and describe the bin width between different models. The dashed error bars for the BHXRB AD test case are described in Section \ref{['sec:modelsel']}.