Formation of Binary Millisecond Pulsars with Helium White Dwarfs in a New Magnetic Braking Prescription

TL;DR

This paper explores how a new magnetic braking law affects the formation of binary millisecond pulsars with helium white dwarfs, broadening the initial conditions for their evolution and potential observability.

Contribution

It introduces a convection and rotation boosted magnetic braking law that expands the initial parameter space for forming binary MSPs with He WDs compared to the standard model.

Findings

CARB magnetic braking enables formation of compact MSP-WD systems over wider initial conditions.

The study provides a new relation between orbital period and white dwarf mass.

Potential detection of these systems as low-frequency gravitational wave sources.

Abstract

Magnetic braking (MB) mechanism plays a vital role throughout the evolution of low-mass X-ray binaries (LMXBs). Considering the standard MB prescription, the initial orbital periods of LMXBs that can evolve into binary millisecond pulsar (MSP) with He white dwarfs (WDs) and short orbital periods ($2-9~\rm hours$) are within an extremely narrow interval, which was named the fine-tuning problem. Employing the detailed binary evolution model, we investigate the evolution of LMXBs in both the standard and convection and rotation boosted (CARB) MB laws. In the standard MB case, it is difficult for donor stars to form a He core and exhaust H envelope through mass transfer at short orbital periods, making them semidetached systems. The CARB MB mechanism can drive LMXBs evolve toward compact detached MSP-WD systems in wide initial orbital periods, over which binary MSPs with long orbital periods will be produced. We obtain the initial parameter space of binary MSPs with He WDs in the initial orbital period and donor-star mass plane, which can be applied to future statistics study by population synthesis simulations. We also discuss a new relation between orbital period and WD mass, formation of persistent ultra-compact X-ray binaries with relatively long orbital periods, and detectability of compact MSP-WD systems as low-frequency gravitational wave sources.