Characterizing the velocity of a wandering black hole and properties of the surrounding medium using convolutional neural networks

Abstract

We present a method for estimating the velocity of a wandering black hole and the equation of state for the gas around, based on a catalog of numerical simulations. The method uses machine learning methods based on convolutional neural networks applied to the classification of images resulting from numerical simulations. Specifically we focus on the supersonic velocity regime and choose the direction of the black hole to be parallel to its spin. We build a catalog of 900 simulations by numerically solving Euler's equations onto the fixed space-time background of a black hole, for two parameters: the adiabatic index Γ with values in the range [1.1, 5/3], and the asymptotic relative velocity of the black hole with respect to the surroundings v∞, with values within [0.2, 0.8]c. For each simulation we produce a 2D image of the gas density once the process of accretion has approached a stationary regime. The results obtained show that the implemented Convolutional Neural Networks are capable to classify correctly the adiabatic index 87.78% of the time within an uncertainty of ±0.0284 while the prediction of the velocity is correct 96.67% of the times within an uncertainty of ±0.03c. We expect that this combination of a massive number of numerical simulations and machine learning methods will help analyze more complicated scenarios related to future high resolution observations of black holes, like those from the Event Horizon Telescope.Observations of horizon size scale images of supermassive black holes are expected to be possible soon with the Event Horizon Telescope, in particular observations of Sgr A * [1] and M87 [2]. Recent observations have also shown potential black holes wandering across different scenarios in the interstellar medium, which are based on line emission offsets of sources with respect to the center of their host galaxies. A recent example is the radio-loud QSO 3C 186, which is potentially a candidate of a black hole recoil [3]. Other candidates for wandering black holes are NGC 3718 [4], the quasar SDSS 0956+5128 [5] and SDSS 1133 [6]. At a different mass scale there is also the case of the so called Bullet, a potential high velocity feature detected in the W44 supernova remnant [7]. We foresee that the resolution of wandering black holes will also increase within the next few years.Combining these observations, we see that the study of traveling black holes is important in two landscapes. The first one is related to the progenitor of the moving black hole as the result of the merger of two original smaller black holes, as already shown for the candidate QSO 3C 186 in [8]. The second landscape relates to the effects produced by the black hole on the gas around. In this article we study the second problem by analyzing idealized but feasible scenarios of the effects produced by a fast black hole on the gas around it. We set the problem as the accretion of wind and present a method based on deep learning, to study two properties of the system -the velocity of the black hole and the equation of sta...

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