Models of low-mass helium white dwarfs including gravitational settling, thermal and chemical diffusion, and rotational mixing

Abstract

A large number of extremely low-mass helium white dwarfs (ELM WDs) have been discovered in recent years. The majority of them are found in close binary systems suggesting they are formed either through a common-envelope phase or via stable mass transfer in a low-mass X-ray binary (LMXB) or a cataclysmic variable (CV) system. Here, we investigate the formation of these objects through the LMXB channel with emphasis on the proto-WD evolution in environments with different metallicities. We study for the first time the combined effects of rotational mixing and element diffusion (e.g. gravitational settling, thermal and chemical diffusion) on the evolution of proto-WDs and on the cooling properties of the resulting WDs. We present state-of-the-art binary stellar evolution models computed with MESA for metallicities of Z = 0.02, 0.01, 0.001 and 0.0002, producing WDs with masses between ∼0.16−0.45 M . Our results confirm that element diffusion plays a significant role in the evolution of proto-WDs that experience hydrogen shell flashes. The occurrence of these flashes produces a clear dichotomy in the cooling timescales of ELM WDs, which has important consequences e.g. for the age determination of binary millisecond pulsars. In addition, we confirm that the threshold mass at which this dichotomy occurs depends on metallicity. Rotational mixing is found to counteract the effect of gravitational settling in the surface layers of young, bloated ELM proto-WDs and therefore plays a key role in determining their surface chemical abundances, i.e. the observed presence of metals in their atmospheres. We predict that these proto-WDs have helium-rich envelopes through a significant part of their lifetime. This is of great importance as helium is a crucial ingredient in the driving of the κ-mechanism suggested for the newly observed ELM proto-WD pulsators. However, we find that the number of hydrogen shell flashes and, as a result, the hydrogen envelope mass at the beginning of the cooling track, are not influenced significantly by rotational mixing. In addition to being dependent on proto-WD mass and metallicity, the hydrogen envelope mass of the newly formed proto-WDs depends on whether or not the donor star experiences a temporary contraction when the H-burning shell crosses the hydrogen discontinuity left behind by the convective envelope. The hydrogen envelope at detachment, although small compared to the total mass of the WD, contains enough angular momentum such that the spin frequency of the resulting WD on the cooling track is well above the orbital frequency.

The Green Bank North Celestial Cap Pulsar Survey. III. 45 New Pulsar Timing Solutions

“…The low eccentricity and few-day orbital period of PSR J0740+6620 are consistent with expectations for an He WD companion. A well-defined relationship is observed between P b and M c in such systems (Tauris & Savonije 1999;Istrate et al 2016) and, in the case of PSR J0740+6620, predicts a companion mass M 0.2  . We can also calculate the minimum companion mass by assuming i=90°and M M 1.4 p =  and find M M 0.2 c,min =  .…”

“…These values were converted to extinctions in each PS1 band using Table 6 from Schlafly & Finkbeiner (2011). The resulting magnitude limits were translated to upper limits on WD effective temperatures (T eff ) using models for WD mass, radius, and temperature from Istrate et al (2016). The best WD T eff constraints are listed for each pulsar's minimum/median companion mass in Table 8, along with the PS1 bands providing those constraints, and modeled WD cooling ages (Istrate et al 2016).…”

Pulsating white dwarfs

“…Using their measured radial velocities, and proper motions if available, [14] estimated their U, V, W velocities and show there would be a large number of hypervelocity A stars, not detected up to date. If these stars are in fact low mass counterparts of interacting binary evolution, similar to the models of [13,15], they are mainly concentrated in the Galactic disk. Considering we do not know their metallicities, and that low ionization potential metals contribute significantly to the electron pressure, we estimated their surface gravities with two sets of models, a pure hydrogen model and a solar composition model.…”

“…We calculated the single star evolutionary models shown in the figure with the MESA ( [12]) evolutionary code, including diffusion. In Figure 2 the evolutionary models are those with rotation and diffusion of [13].…”

“…[17] found an RR Lyrae with 0.26 M , and [16] found a 0.23 M pulsating subdwarf (sdBV). Interacting binary with mass exchange models by [13] show that during a hydrogen shell burning pulse, an extremely low mass white dwarf can cross the main sequence, horizontal branch and even giant instability strip. [18] estimate that up to 5% of stars that cross the RR Lyrae and Cepheid instability strip are binaries.…”