Can eccentric binary millisecond pulsars form by accretion-induced collapse of white dwarfs?

Wen-Cong Chen 0 1 2 Xi-Wei Liu 0 4 Ren-Xin Xu 2 Xiang-Dong Li 0 3 0 Key Laboratory of Modern Astronomy and Astrophysics (Nanjing University), Ministry of Education , Nanjing 210093 , China 1 Department of Physics, Shangqiu Normal University , Shangqiu 476000 , China 2 School of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking University , Beijing 100871 , China 3 Department of Astronomy, Nanjing University , Nanjing 210093 , China 4 College of Science, Huazhong Agricultural University , Wuhan 430070 , China A B S T R A C T Binary radio pulsars are generally believed to have been spun up to millisecond periods (i.e. recycling) via mass accretion from their donor stars, and they are the descendants of neutron star low-mass X-ray binaries. However, some studies indicate that the formation of pulsars from the accretion-induced collapse (AIC) of accreting white dwarfs (WDs) cannot be excluded. In this work, we use a population-synthesis code to examine if the AIC channel can produce eccentric binary millisecond pulsars (BMSPs) in the Galaxy. Our simulated results indicate that only when the natal MSPs receive a relatively strong kick ( 100 km s1), can the AIC channel produce 10-180 eccentric (e > 0.1) BMSPs in the Galaxy, most of which are accompanied by a helium star. Such a kick seems to be highly unlikely in the conventional AIC process, hence the probability of forming eccentric BMSPs via the AIC channel can be ruled out. Even if a high kick is allowed, the AIC channel cannot produce eccentric BMSPs with an orbital period of 20 d. Therefore, we propose that the peculiar BMSP PSR J1903 +0327 cannot be formed by the AIC channel. However, the AIC evolutionary channel may produce some fraction of isolated MSPs, and even submillisecond pulsars if they really exist. 1 I N T R O D U C T I O N Millisecond pulsars (MSPs) are characterized by short pulse periods (P 20 ms), low spin-down rates (P 1019 to 1021 s s1), old characteristic ages [ = P /(2P ) 1091010 yr] and weak surface magnetic fields (B 108109 G) (Manchester 2004). About 80 per cent of the MSPs are in binaries, but only 1 per cent of the total pulsars (Bhattacharya & van den Heuvel 1991; Lorimer 2008). Standard models proposed that MSPs are formed in neutron star (NS) low-mass X-ray binaries (LMXBs), in which the NS has accreted the mass and angular momentum from its companion, and been spun up to a short spin period (Alpar et al. 1982; Tauris & van den Heuvel 2006). Meanwhile, mass accretion on to the NS induces its initial magnetic field (B0 10121013 G) to decline to B 108109 G.1 When the mass transfer ceases, a binary millisecond pulsar (BMSP) is formed. E-mail: (W-CC); (X-DL) 1 As an alternative mechanism of accretion-induced field decay, the magnetic field of the NS may be screened or buried by the accreted material (Taam & van den Heuvel 1986; Cumming, Zweibel & Bildsten 2001). However, the origin of the MSPs still presents some controversial puzzles. First, can the known NS LMXBs evolve into the observed MSPs in the Galactic disc (Kulkarni & Narayan 1988)? Statistical analyses show that the birth rate of LMXBs is 12 orders of magnitude lower than that of MSPs (Cote & Pylyser 1989; Lorimer 1995). Secondly, it is hard to understand how the isolated MSPs in the Galactic disc were formed via the standard recycling scenario. Although evaporation of the donor stars by the high-energy radiation of the MSPs might account for the origin of the isolated MSPs, the observed time-scales for evaporating a companion star seem too long. Thirdly, in standard model the strong tidal effects operating in the binary during the mass transfer serve to circularize the orbit. However, the discovery of the eccentric (e = 0.44) BMSP PSR J1903+0327 in the Galactic plane has challenged the standard scenario (Champion et al. 2008). As an alternative evolutionary channel, BMSP may originate from the accretion-induced collapse (AIC) of an accreting white dwarf (WD; Michel 1987). Ivanova & Taam (2004) suggested that AIC may occur by thermal time-scale mass transfer in such binaries with orbital periods of a few days. Once the accreting ONe WD grows to the Chandrasekhar limit, the electron-capture process may induce gravitational collapse rather than Type Ia supernova. As a result of angular momentum and magnetic flux conservations, an MSP with rapid spin and low magnetic field may be produced. To account for its observed characteristics, the bursting pulsar GRO J174428 was suggested to be originated from the AIC of a massive ONe WD (van Paradijs et al. 1997; Xu & Li 2009). Recently, the estimated birth rate of MSPs by population-synthesis calculations shows that the often-neglected AIC channel cannot be ignored (Hurley et al. 2010). In the AIC channel the puzzles in the standard recycling model mentioned above might disappear. First, the AIC of accreting WDs has been raised to interpret the birth-rate discrepancy (Bailyn & Grindlay 1990), and the AIC process may be associated with the rprocess nucleosynthesis of heavy (baryon number A > 130) nuclei (Qian & Wasserburg 2003). Secondly, a kick velocity caused by asymmetric collapse may be produced during AIC of WDs. An appropriate kick can disrupt the binary system and result in the birth of isolated MSPs. Otherwise, the binary survives and an eccentric BMSP is formed. Ferrario & Wickramasinghe (2007) argued that the AIC channel could form BMSPs of all of the observed types. Champion et al. (2008) proposed that the AIC of a massive and rapidly rotating WD could produce the observed orbital parameters of PSR J1903+0327. In this work, employing the binary population-synthesis approach we attempt to investigate if the AIC evolutionary channel can produce a population of eccentric BMSPs, as well as isolated MSPs. In Section 2, we describe the population-synthesis approach and the evolution model of MSPs. The simulated results by population synthesis are given in Section 3. Finally, we present a brief discussion and summary in Section 4. 2 I N P U T P H Y S I C S 2.1 Population synthesis Using an evolutionary population synthesis based on the rapid binary star evolution (BSE) code (e.g. Hurley, Pols & Tout 2000; Hurley, Tout & Pols 2002), we attempt to study the statistical properties (such as the birth rate, total number, the distributions of orbital period and eccentricity) of MSPs formed via the AIC process of a massive ONe WD in the Galaxy. In calculation, we consider the evolution of single stars with binary star interactions, which includes the mass transfer and accretion via stellar winds and Roche lobe overflow, common envelope (CE) evolution, supernovae and AIC kick, tidal friction and orbital angular momentum loss containing gravitational wave radiation and magnetic braking. All stars are assumed to be born in binary systems, and start with zero eccentricities and a solar metallicity (Z = 0.02). We adopt the following input parameters for the s (...truncated)