Spin period evolution of a recycled pulsar in an accreting binary

Abstract

We investigate the spin period evolutions of recycled pulsars in binary accreting systems. Taking both the accretion induced field decay and spin-up into consideration, we calculate their spin period evolutions influenced by the initial magnetic field strengths, initial spin periods, and accretion rates. The results indicate that the minimum spin period (or maximum spin frequency) of a millisecond pulsar (MSP) is independent of the initial conditions and accretion rate when the neutron star (NS) accretes the mass of ∼0.2 M . The accretion torque with the fastness parameter and gravitational wave (GW) radiation torque may be responsible for the formation of the minimum spin period (maximum spin frequency). The fastest spin frequency (716 Hz) of MSP can be inferred to associate with a critical fastness parameter of about ω c = 0.55. Furthermore, comparisons with the observational data are presented in the field period (B − P) diagram.

Testing the accretion-induced field-decay and spin-up model for recycled pulsars

“…These bimodal distributions in magnetic fields and spin periods are shown, e.g., in Fig. 1 in Wang et al (2011) and also Fig. 1 of this paper, which, with data taken from ATNF pulsar catalogue, shows a large population of normal pulsars and a smaller population of MSPs.…”

“…We have tested the accretion-induced field-decay and spin-up model for recycled MSPs (Zhang & Kojima 2006;Wang et al 2011). In our computation, we have considered lognormal distributions of initial B and P in the range of B 0 = 10 10.5 −10 14 G and P 0 = 0.1−30 s, a Gaussian neutron star mass distribution in the range of M = 0.9−2.2 M , a uniform neutron-star radius distribution of R = 10−20 km, a lognormal distribution of the accretion rate ofṀ = 10 16 −10 18 g/s, and an accretion time of Δt = 10 7 −10 9 yr. We found that the computed B and P distributions of recycled MSPs are insensitive to mild variations in the width of the initial distributions.…”

“…According to the data taken from ATNF catalogue, the log B and log P distributions of normal pulsars can be well-described by a Gaussian function (see Wang et al 2011). We therefore take lognormal distributions as the inputs to the initial magnetic fields and spin periods.…”

“…We take μ = log B(G) = 12 and σ = 0.5 for the B distribution (see e.g. Hartman et al 1997;Hobbs et al 2011;Kaspi 2010;Wang et al 2011) and μ = log P(s) = 0 and σ = 0.4 for the P distribution (see e.g. Lorimer 2011, and references therein).…”

On the progenitors of millisecond pulsars by the recycling evolutionary channel

“…The spin period of a dead pulsar should satisfy P 2 s > B /1.7 × 10 11 (Bhattacharya et al 1992) and the upper limit of the spin period for normal radio pulsars is 11 s (Manchester 2004). Wang et al (2011) proposed that the minimum spin period of the NS is insensitive to its initial spin period and magnetic field. Therefore, we adopt an initial spin period of P s, i = 10 s and initial magnetic field of B = 10 12 G for the accreting NS.…”