Formation of low-mass helium white dwarfs orbiting binary millisecond pulsars

Abstract

Millisecond pulsars (MSPs) belong to a class of radio pulsars characterized by high rotational spin rates and low magnetic fields. These neutron stars are believed to be the end-product of binary evolution, in which an old neutron star accretes matter and angular momentum from a close stellar companion for an extended period of time, while being observable as an X-ray binary. During this evolutionary phase, they acquire millisecond spin periods and, after the accretion episode ceases, they are reactivated as radio emitting pulsars. The majority of MSP companions are low-mass helium-core white dwarfs (He WDs). However, MSP systems harbouring carbon-oxygen white dwarfs (CO WD), neutron stars, or ultra light companions have also been found, suggesting a diversity in the nature of their progenitors. A handful of MSPs are observed in very compact orbits, P_orb ≃ 2 - 9 hr, orbiting around low-mass He WDs with masses below 0.25 M_⊙ and surface gravities 5 < log g < 7, the so-called extremely low-mass helium white dwarfs (ELM WDs). <br /> Today we know of the existence of more than 80 ELM WDs. The increasing number of discovered ELM WDs reveals that they are formed in different environments, from the Galactic disk to open and globular clusters. ELM WDs are most likely the result of binary evolution as they cannot be formed from single stars within a Hubble time. Indeed, over 80% of the observed ELM WDs are found in binary systems, most commonly around a more massive CO WD. The new wealth of data raises questions regarding the puzzling presence of metals in the atmospheres of young bloated ELM proto-WDs and the newly discovered pulsations in three ELM proto-WDs. In this context, improved stellar evolutionary models in which binary evolution is fully accounted for are needed in order to explain the formation and the observed properties of these objects. <br /> In this thesis, we investigate the formation of MSPs found in compact orbits with ELM WD companions through numerical calculations using state-of-the-art stellar evolutionary codes. In particular, we examine if the observed systems can be reproduced by theoretical modelling using standard prescriptions of angular momentum loss with contributions from gravitational wave radiation, magnetic braking and mass loss. We find that a severe fine-tuning in the initial orbital period is necessary to reproduce the observed number of MSPs with ELM WD companions suggesting that something needs to be modified or is missing in the standard input physics of their modelling. <br /> Moreover, we explore the formation and cooling of ELM WDs through a large grid of computed models suited for environments with different metallicities, with emphasis on the proto-WD phase. Specifically, we analyse in detail the evolutionary times of these objects which are of great importance in providing an accurate independent age estimate for MSP systems. For the first time, we study the combined effects of element diffusion, i.e. gravitational settling, thermal and chemical diffusion, and rotational mixing on the evolution of these WDs. Our results show that rotational mixing plays a key role in determining the chemical composition of the surface layers of ELM proto-WDs, but it does not affect their internal structure. This finding has important implications for the asteroseismology studies of ELM proto-WDs which are currently pursued. Furthermore, we suggest that the spin frequencies of the resulting WDs are well above the orbital frequencies, a result which needs to be confirmed by further dedicated observations.