Binary Pulsars in Magnetic Field versus Spin Period Diagram

TL;DR

This study analyzes 186 binary pulsars in the magnetic field versus spin period diagram, revealing their distribution relative to the spin-up line and proposing a minimum accretion rate for millisecond pulsar formation.

Contribution

It provides a detailed analysis of binary pulsar distribution in the B-P diagram and introduces a minimum accretion rate necessary for MSP formation based on observational data.

Findings

Most BPSRs are near the spin-up line with $ ext{~}10^{16} g/s$ accretion rate.

All MSPs are above the spin-up line with $ ext{~}10^{15} g/s$ accretion rate.

Seven BPSRs above the limit line are discussed with possible causes.

Abstract

We analyzed 186 binary pulsars (BPSRs) in the magnetic field versus spin period (B-P) diagram, where their relations to the millisecond pulsars (MSPs) can be clearly shown. Generally, both BPSRs and MSPs are believed to be recycled and spun-up in binary accreting phases, and evolved below the spin-up line setting by the Eddington accretion rate ($\dot{M}{\bf \simeq}10^{18} g/s$). It is noticed that most BPSRs are distributed around the spin-up line with mass accretion rate $\dot{M}=10^{16} g/s$ and almost all MSP samples lie above the spin-up line with $\dot{M}\sim10^{15} g/s$. Thus, we calculate that a minimum accretion rate ($\dot{M}\sim 10^{15} g/s$) is required for the MSP formation, and physical reasons for this are proposed. In the B-P diagram, the positions of BPSRs and their relations to the binary parameters, such as the companion mass, orbital period and eccentricity, are illustrated and discussed. In addition, for the seven BPSRs located above the limit spin-up line, possible causes are suggested.