Understanding the evolution of black hole spin in X-ray binary systems: Case study of XTE~J1550-564

TL;DR

This study models the full binary evolution of XTE J1550-564 to test whether the observed BH spin $a^*\approx0.49$ can arise from accretion onto an initially non-rotating BH. Using a grid of 480 models with varying donor mass, BH mass, orbital period, mass-loss efficiency $\beta$, and magnetic braking laws (MB0, MB3, CARB), the authors identify six progenitors that reproduce all key observables within their errors. They find mass-transfer rates are sub-Eddington and that stronger MB prescriptions either drive exchange too quickly (MB3) or yield extended, sub-Eddington transfer with only marginal spin-up (CARB), leaving the observed spin difficult to achieve without assuming a nonzero initial BH spin or additional physics such as irradiation-induced episodes. The results reinforce the view that BH spin evolution in X-ray binaries remains an open problem, with accretion alone under standard physics insufficient to explain moderate to high spins in systems like XTE J1550-564.

Abstract

We present a comprehensive study of the X-ray binary system XTE~J1550-564, with the primary objective of analyzing the evolution of the black hole's spin parameter. To achieve this objective, we embarked on the necessary step of identifying a plausible progenitor for the system. Using a set of models covering various parameter combinations, we were able to replicate the system's observed characteristics within acceptable error margins, including fundamental parameters such as component masses, orbital period, donor luminosity, and effective temperature. The model results indicate the possibility of diverse evolutionary pathways for the system, highlighting the significant role played by the initial mass of the donor star and the efficiency of mass transfer episodes. While some models are well-aligned with estimates of the mass transfer rate, they all fall short of explaining the black hole's observed moderate spin ($a^* = 0.49$). We also explored alternative magnetic braking prescriptions, finding that only an extreme and fully conservative scenario, based on the convection and rotation boosted prescription, can reproduce the observed spin and only in a marginal way. Our study attempts to shed light on the complex dynamics of black hole X-ray binaries and the challenges of explaining their observed properties with theoretical models.

Figures (6)

• Figure 1: Evolution of fundamental quantities as a function of time for the models listed in Table \ref{['tab:models']}. Observed values are indicated by horizontal black lines, with their respective errors represented by the shaded gray area. Each point on the graph corresponds to when the model reaches the ${t_\mathrm{obs}}$ value.
• Figure 2:
• Figure 3: Absolute value of the mass loss rate (full line) and mass accretion rate (dashed line) as a function of the donor's mass for the best models. Horizontal black lines represent the estimations for the mass loss rate derived from the works of Coriat2012, Orosz2011 and the estimation we obtained with Webbink83. The donor's mass ($M_\mathrm{d} = 0.3$ M$_\odot$) is indicated by a vertical black line, with a shaded area representing the observational error. The dots depict the donor's mass and mass loss rate (or mass accretion rate) at $t_{\mathrm{obs}}$ for each model.
• Figure 4: Evolution of the dimensionless BH spin parameter $a^*$ as a function of the donor mass. The observational data obtained by Steiner2011 of $a^* = 0.49^{+0.13}_{-0.20}$ is depicted as a black horizontal line, with the shaded gray area representing the error margin.
• Figure 5: Evolution of the models computed using the MB3 prescription. Top-left: Donor's mass vs. orbital period. Top-right: Hertzprung-Russel diagram. Bottom left: Donor's mass vs. mass transfer rate. Bottom right: Donor's mass vs. BH spin parameter. Black lines indicate the observed values of the donor mass, luminosity, effective temperature, orbital period, mass transfer rate, and BH spin parameter; shaded grey areas represent their associated uncertainties. The color gradient traces the system’s age during the mass transfer episode.