Asymmetrical mass ejection from proto-white dwarfs and the formation of eccentric millisecond pulsar binaries

Binary millisecond pulsars (MSPs) are believed to have descended from low-mass X-ray binaries (LMXBs), which have experienced substantial mass transfer and tidal circularization. Therefore, they should have very circular orbits. However, the discovery of several eccentric binary MSPs (with eccentricity $e\sim 0.01-0.1$) challenges this standard picture. Three models have been proposed thus far based on accretion-induced collapse of massive white dwarfs (WDs), neutron star-strange star transition, and formation of circumbinary disks. All of them are subject to various uncertainties, and are not entirely consistent with observations. Here we propose an alternative model taking into account the influence of thermonuclear flashes on proto-WDs. We assume that the flashes lead to asymmetrical mass ejection, which imparts a mild kick on the proto-WDs. By simulating orbital changes of binary MSPs with multiple shell flashes, we show that it is possible to reproduce the observed eccentricities, provided that the kick velocities are around a few kms$^{-1}$.