The inner disc radius in the propeller phase and accretion-propeller transition of neutron stars

Abstract

We have investigated the critical conditions required for a steady propeller effect for magnetized neutron stars with optically thick, geometrically thin accretion disks. We have shown through simple analytical calculations that a steady-state propeller mechanism cannot be sustained at an inner disk radius where the viscous and magnetic stresses are balanced. The radius calculated by equating these stresses is usually found to be close to the conventional Alfvén radius for spherical accretion, r A . Our results show that: (1) a steady propeller phase can be established with a maximum inner disk radius that is at least ∼ 15 times smaller than r A depending on the mass-flow rate of the disk, rotational period and strength of the magnetic dipole field of the star, (2) the critical accretion rate corresponding to the accretion-propeller transition is orders of magnitude lower than the rate estimated by equating r A to the co-rotation radius. Our results are consistent with the properties of the transitional millisecond pulsars which show transitions between the accretion powered X-ray pulsar and the rotational powered radio pulsar states.

Accretion and propeller torque in the spin-down phase of neutron stars: The case of transitional millisecond pulsar PSR J1023+0038

“…As shown recently (Ertan 2017) the maximum r in at which the propeller mechanism can work is much smaller than r A , but not much larger than r co . The critical accretion rate, M crit for the transition to accretion with spin-down (weak propeller) is orders of magnitude smaller than the rate corresponding to r A r co .…”

“…We pursue these results obtained by Ertan (2017) to model the spin-down torques and the luminosities of the tMSPs. Our model is described in Section 2.…”

NuSTAR and Parkes observations of the transitional millisecond pulsar binary XSS J12270–4859 in the rotation-powered state

“…Instead, the modulation increases by a factor ∼2.2 in 2014 and has a well defined double-peaked maximum, with peak separation ∆Φ orb ∼ 0.36 and a dip reaching ∆I ∼ 13% with respect to the maximum. If the shocked pulsar wind retains a moderately relativistic bulk motion, the synchrotron emission is expected to be Doppler boosted at inferior conjunction and de-boosted at superior conjunction of the NS, thus producing an Xray orbital modulation (Arons & Tavani 1993;Dubus et al 2010Dubus et al , 2015. The bulk Lorentz factor ΓL = (1 − β 2 ) −1/2 and bulk velocity β = v/c, drive the Doppler boosting as δ boost = [ΓL(1 − β cos θv)] −1 where θv is the viewing angle of the observer (Dubus et al 2010).…”

“…The bulk Lorentz factor ΓL = (1 − β 2 ) −1/2 and bulk velocity β = v/c, drive the Doppler boosting as δ boost = [ΓL(1 − β cos θv)] −1 where θv is the viewing angle of the observer (Dubus et al 2010). The synchroton flux is expected to be enhanced by a factor δ 2+(p−1)/2 boost , along the orbit (Dubus et al 2015) with a maximum to minimum flux ratio simplified as ∼ [(1 + β sin i)/(1 − β sin i)] 2+(p−1)/2 (Dubus et al 2010). The observed modulation amplitudes in 2013 and 2015, assuming (p − 1)/2 = Γx = 1.2 and binary inclination in the range 46 o − 55 o , would then give β ∼ 0.2 and ΓL ∼ 1.02 while in 2014 β ∼ 0.3 and ΓL ∼ 1.05, indicating moderately relativistic bulk flow.…”

Long-term evolution of RRAT J1819–1458

“…In the longterm evolution, rout decreases with decreasing X-ray irradiation flux that can be written as Firr 1.2CLx/(πr 2 ) (Fukue 1992), where r is radial distance from the star, Lx is the Xray luminosity of the star, and C is the irradiation parameter which depends on the disc geometry and the albedo of the disc surfaces. Individual source properties of AXP/SGRs, XDINs, HBRPs, and CCOs could be reproduced self consistently with TP ∼ 50 − 150 K (Benli & Ertan 2016, 2017, 2018b and C ∼ (1 − 7) × 10 −4 (Ertan &Çalışkan 2006; Ertan et al 2007). The TP values estimated in our model are in agreement with results indicating that the disc is likely to be active at temperatures ∼ 300 K (Inutsuka & Sano 2005), while our C range is similar to that estimated for the lowmass X-ray binaries (see e.g.…”