Under One Sky: The IAU Centenary Symposium Proceedings IAU Symposium No. , C. Sterken, J. Hearnshaw & D. Valls-Gabaud, eds. doi:10.1017/xxxxx Accretion Induced Collapse of White Dwarfs as an Alternative Symbiotic Channel to Millisecond Pulsars Ali Taani Physics Department, Faculty of Science, Al-Balqa Applied University, 19117 Salt, Jordan Abstract. Recently, it has given extra motivation to the unresolved population of millisecond pulsars (MSPs) produced from the recycling process. This implies the apparent role of the accretion induced col- lapse (AIC) in white dwarfs (WDs) in this issue. We ﬁnd that the distribution of Nobs,orb closely follows an exponential distribution. We determine the best-ﬁt value of the mean Nobs,orb, by ﬁtting our data with an exponential distribution for MSP populations. As a result, reaching the Chandrasekhar limit may cause the massive WD to explode as a Type Ia supernova (in the case of a CO WD) or to ignite the AIC process (in the case of an ONeMg WD; and possibly also in some CO WDs merging) producing peculiar MSP systems. Keywords. pulsars: general, stars: neutron stars, white dwarfs, evolution: kinematics and dynamics. 1. Introduction Millisecond pulsars (MSPs) are remarkable objects born via type II supernovae (SNe) explo- sions and characterized by short spin periods (Pspin ≤20 ms), weak magnetic ﬁelds (B ≤109 G) extremely old ∼109 yr based on the recycling process. ATNF census of Galactic 446 MSPs in both the Galactic plane and in globular clusters (Manchester et al. 2005). They are often found in binaries (about 65%) with white dwarfs (WDs) in circular orbits having companions of masses ∼0.15M⊙−0.45M⊙(see e.g., Alpar et al. 1982; Bhattacharya & van den Heuvel 1991; Taani et al. 2012a,b; Taani & Vallejo 2017). It was suggested that MSPs were formed in low-mass X-ray binary systems (LMXBs). This argument called for a recycling process in which the slowly rotating, old Neutron Star (NS) may be spun-up into an MSP via accretion from a binary companion (Alpar et al. 1982; Bhattacharya & van den Heuvel 1991; Taani et al. 2012a,b; Taani 2016). More recently, the discovery of many pulsars like PSR J1023+0038 (Archibald et al. 2009), where radio emission is likely to have only recently switched on after the LMXB phase, has recently supported this link. Another alternative formation, is the accretion induced collapse (AIC) of an ONeMg white dwarf (WD) (see i.e, Nomoto 1987; Hurley et al. 2010; Taani et al. 2012a; Taani & Khasawneh 2017; Tauris et al. 2017; Ablimit et al. 2021). In this scenario, mass transfer can increase the mass of a WD towards the Chandrasekhar mass. Close to this mass limit, degeneracy pressure can no longer support the star, where the supporting electron pressure is robbed by inverse β decays (Kitsikis et al. 2005), consequently, losing enough energy in neutrinos. This causes it to collapse and violently release its gravitational energy, which might be observable by gravitational wave observatories such as LIGO, VIRGO and GEO (Metzger et al. 2009; Darbha et al. 2010). The purpose of this paper is to estimate the contribution of the AIC process, which could inﬂuence the observed population of MSPs. c ⃝International Astronomical Union, 2021