Mechanism and thresholds of rapid switching between accretion-powered and rotation-powered states in transitional millisecond pulsars

The 2013 discovery that the neutron star IGR J18245-2452/PSR J1824-2452I in the globular cluster M28 swung, within days, from a month-long accretion-powered X-ray pulsar outburst back to a rotation-powered radio pulsar established an unstable intermediate phase in the evolution of low-mass X-ray binaries (LMXBs) — the transitional millisecond pulsars (tMSPs) — but left the physics of the switching unexplained. The problem asks for a quantitative, observationally validated account of these state transitions: the critical mass-transfer rates and the time-dependent behaviour of the magnetospheric radius relative to the co-rotation and light-cylinder radii at which the system moves between accretion, propeller, and radio-pulsar regimes; the efficiency with which the pulsar wind ejects inflowing matter and the associated energetics (neutron-star magnetic field, conversion of rotational power into X-rays); the disc build-up and dispersal dynamics on transition timescales; and whether rotation-powered radio pulsations routinely switch on during the X-ray quiescence of ordinary accreting millisecond X-ray pulsars, i.e., how common the transitional phase is among LMXBs. A decade of multiwavelength work has mapped the phenomenology (three confirmed tMSPs, bistable high/low X-ray modes with anti-correlated radio and gamma-ray emission, propeller and wind-heating models, microjansky-level non-detections of radio pulsations in quiescent AMXPs) but has not settled the switching mechanism, its thresholds, or its population statistics; the problem remains open.

Background

In the recycling scenario, a weakly magnetized neutron star in a low-mass X-ray binary (LMXB) accretes gas and angular momentum from a companion star through an accretion disc and is spun up to millisecond periods; when the mass-transfer rate declines, the system ends its life as a rotation-powered radio millisecond pulsar (MSP), whose radio and gamma-ray emission is powered by the star's rotating magnetic dipole rather than by accretion. Accreting millisecond X-ray pulsars (AMXPs) are LMXBs in which coherent X-ray pulsations at the neutron-star spin period show that matter is channeled onto the magnetic poles while the disc is bright. The physical gate between the two regimes is set by the interplay of the accretion flow and the magnetosphere. The magnetospheric (Alfvén) radius $R_{\mathrm{m}}$ is where the magnetic pressure of the neutron-star dipole stops the infalling plasma; the co-rotation radius $R_{\mathrm{co}}$ is the distance at which field lines corotating with the star rotate at the local Keplerian speed; the light-cylinder radius $R_{\mathrm{LC}}=c/2\pi\nu_{\mathrm{s}}$ (with $c$ the speed of light, $\nu_{\mathrm{s}}$ the spin frequency) is where they would rotate at the speed of light, so that field lines beyond it open and launch the relativistic pulsar wind. Classical theory distinguishes: direct accretion onto the surface when $R_{\mathrm{m}}<R_{\mathrm{co}}$; a propeller regime when $R_{\mathrm{co}}<R_{\mathrm{m}}<R_{\mathrm{LC}}$, in which the centrifugally accelerated magnetosphere expels inflowing gas; and a radio-pulsar regime when $R_{\mathrm{m}}>R_{\mathrm{LC}}$, in which the pulsar wind itself ejects the matter transferred by the companion (radio ejection). For the weak fields invoked here, of order $10^{8}$–$10^{9}\ \mathrm{G}$, the boundaries between these regimes correspond to critical values of the mass-inflow rate that had never been measured in a single system. IGR J18245-2452 in the globular cluster M28 is a $3.93\ \mathrm{ms}$ pulsar in an $11\ \mathrm{h}$ orbit previously known as the radio pulsar PSR J1824-2452I. In 2013 it was caught as an accretion-powered X-ray pulsar during a month-long outburst (with a disc apparently truncated at an inner radius of order $50\ \mathrm{km}$) and returned to its rotation-powered radio state within days, proving that transitions occur in both directions on unexpectedly short timescales. Two analogous systems are now known — PSR J1023+0038, discovered as a radio pulsar in a binary that had accreted in 2000–2001, and XSS J12270-4859/PSR J1227-4853 — defining the class of transitional MSPs (tMSPs). Between outbursts these systems spend long stretches in a sub-luminous disc state, fainter than any other LMXB, in which the X-ray output stochastically alternates on timescales of order $10\ \mathrm{s}$ between a high mode ($L_X\approx3\times10^{33}\ \mathrm{erg\,s^{-1}}$, showing coherent X-ray, ultraviolet and optical pulsations at the spin period, i.e., residual channeled accretion), a low mode ($\approx5\times10^{32}\ \mathrm{erg\,s^{-1}}$), and flares; radio and X-ray modes are anti-correlated, and the gamma-ray flux is enhanced several-fold relative to the radio-pulsar state. Despite detailed modeling (propeller outflows, pulsar-wind heating of the inner disc, general-relativistic magnetohydrodynamic and particle-in-cell simulations), no accepted physical account of the switching itself — which regime boundary is crossed, at what inflow rate, and what triggers the stochastic mode changes — exists, and the prevalence of this behaviour across the AMXP population is unknown.

Problem Statement

Establish a quantitative, observationally validated physical account of the switching between accretion-powered and rotation-powered states in binary millisecond pulsars — the phenomenon discovered in IGR J18245-2452/PSR J1824-2452I — and determine how generic it is. The common objective subsumes the following linked questions arising from the source discovery and the subsequent observations: (1) identify the physical mechanism and the critical mass-transfer (mass-inflow) rates at which the system moves between the accretion regime ($R_{\mathrm{m}}<R_{\mathrm{co}}$), the propeller regime ($R_{\mathrm{co}}<R_{\mathrm{m}}<R_{\mathrm{LC}}$), and the rotation-powered regime ($R_{\mathrm{m}}>R_{\mathrm{LC}}$), including the time-dependent behaviour of the magnetospheric radius during transitions; (2) determine the efficiency with which the pulsar wind ejects the matter transferred by the companion, together with the associated energetics — the neutron-star magnetic field strength (order $10^{8}$–$10^{9}\ \mathrm{G}$ is invoked but not measured) and the conversion efficiency between spin-down power and the quiescent X-ray luminosity; (3) disentangle partial obscuration/eclipsing of radio pulses by intra-binary plasma from genuine suppression of the radio emission mechanism during accretion; (4) model the build-up and dispersal of the truncated inner accretion disc (radii of order tens of km) on the short timescales that accompany the state transitions; and (5) establish whether rotation-powered radio pulsations routinely switch on during the X-ray quiescent states of ordinary accreting millisecond X-ray pulsars, and how common this unstable intermediate (transitional) evolutionary phase is among low-mass X-ray binaries. A complete answer comprises a model whose predicted transition thresholds and broadband energetics match the available time-resolved multiwavelength (radio, X-ray, optical/infrared, gamma-ray) observations of transitional systems, the diagnostic that disentangles partial obscuration/eclipsing of radio pulses by intra-binary plasma from genuine suppression of the radio emission mechanism during accretion, the model of the build-up and dispersal of the truncated inner accretion disc on the short timescales that accompany the state transitions, and a population-level determination (detections or well-quantified limits) of the prevalence of the transitional phase; the deliverables in items (1)–(5) jointly support this single objective, the physics of the accretion–rotation transition at the end of the recycling process.

References

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