Quantifying Roche Lobe Overflow in the Formation of Merging Black Hole Binaries

TL;DR

This paper introduces a new high-resolution modeling method for Roche lobe overflow in binary systems, applied to M33 X-7, revealing insights into stable and unstable mass transfer processes relevant to black hole binary formation.

Contribution

It presents a novel modeling approach for RLO systems that captures detailed dynamics without symmetry assumptions, applied to M33 X-7, and explores the stability and evolution of mass transfer across overfilling factors.

Findings

Extreme overflow causes conservative unstable mass transfer.

Non-conservative stable mass transfer occurs at lower overfilling factors.

New relations for binary parameters as functions of overfilling factor.

Abstract

We demonstrate a new methodology to model Roche lobe overflow (RLO) systems to unprecedented resolution simultaneously across the envelope, donor wind, tidal stream, and accretion disk regimes without reliance upon previously-universal symmetry, mass flux, and angular momentum flux assumptions. We have applied this method to the semidetached high-mass X-ray binary (HMXB) M33 X-7 in order to provide a direct comparison to recent observations of an RLO candidate system at two overflow states of overfilling factors f = 1.01 and f = 1.1. We found extreme overflow ( f = 1.1) to exhibit entirely conservative unstable mass transfer (MT), with tidal stream density and deflected angle comparable to predictions. The f = 1.01 case differed in stream geometry, accretion disk size, and efficiency, demonstrating non-conservative stable MT through a ballistic uniform-width stream. The non-conservative and stable nature of the f = 1.01 case MT also suggests that existing assumptions of semi-detached binaries undergoing RLO may mischaracterize the parameter space of stability for the L1 flow. We also conducted a piecewise evolution of M33 X-7 across nearly the entirety of RLO phase from onset to runaway unstable MT. We present the first model of the efficiency of MT and its associated angular momentum across overfilling factor parameter space. We also present novel relations for binary separation, mass ratio, L1 mass transfer rate, and Roche timescale as they vary with respect to the overfilling factor. These provide constraints on the threshold for the onset of unstable MT which ultimately led in our system to exponentially faster MT evolution. Collectively these parameter constraints, relations, and explorations probe RLO dynamics in HMXBs and their role and distribution as progenitors of binary black holes and common envelopes.