White dwarf magnetospheres: Shielding volatile content of icy objects and implications for volatile pollution scarcity
Authors: Zhou Wen-Han 
Published: July 2024

. IntroductionBetween 25% and 50% of discovered white dwarfs have been found to contain heavy elements in their atmospheres (Koester et al, 2014). The sinking timescale of these heavy elements is relatively short, ranging from several days (for hydrogen-dominated white dwarfs) to millions of years (for helium-dominated white dwarfs). Therefore, these heavy elements are believed to originate from external sources other than the white dwarf core, due to the rapid sedimentation of heavy elements in white dwarfs. It is widely believed that the pollution results from the accretion of planetary material, with supportive evidence from observed dusty disks and transiting planets around white dwarfs. Therefore, the composition of pollutants in white dwarfs' atmospheres provides valuable information about the history of exoplanetary systems.Interestingly, the dominant elements found in accreted material on white dwarfs are rock-forming elements such as Mg, Ca, and Fe, with only a few white dwarfs being polluted by icy materials. This is inconsistent with the abundance of icy objects in exo-Kuiper belt or exo-Oort Cloud objects. Several mechanisms have been proposed to account for the scarcity of volatiles, including the primordially dry nature of the pollutants and observational bias due to asynchronous accretion. However, recent research shows that volatile vapor is necessary to the accretion disk to offer a drag to the debris, thereby facilitating the high accretion rates deduced from observation (Okuya et al, 2023). This implies that volatiles could exist with refractory elements in the disk, but be prevented from accretion onto the white dwarf by some unknown physical process.White dwarfs have been observed to have atmospheres polluted by heavy elements, which are thought to be accreted from planetary objects. Refractory pollution, such as silicate and iron elements, is more commonly observed than volatile pollution, which includes carbon, nitrogen, oxygen, and sulfur. It is currently unclear whether this scarcity of volatile pollution is due to the prevalence of dry pollutants, such as asteroids and rocky planets, or some unknown mechanism that shields the volatiles. In this work, We propose a mechanism to explain the lack of volatile pollution, which involves the shielding of volatiles by the magnetic field in the scenario of comet accretion.&#160;2. Results&#160;We find that the volatile content in the tidal fragments of comets can effectively sublimate during the process of orbital circularization. Following sublimation, the resulting volatile vapor may be shielded by the magnetosphere of white dwarfs, provided that the magnetosphere radius is greater than the corotation radius. The effectiveness of this volatile-shielded mechanism is determined by the extent of sublimation occurring outside the corotation radius. The main processes in this scenario are the following:(1) Tidal fragmentation and orbital circularization of comets. Comets are tidally disrupted within the tidal disruption radius. The generated fragments with a maximum size of ~ 200m migrate inward due to the Alfv&#233;n wing drag and/or dust drag. In this work, we incorporate the Alfv&#233;n wing drag to model the behavior of exo-Oort Cloud objects.(2) Volatile sublimation. After crossing the ice line, the interior of fragments gets heated up to the sublimation temperature of volatile materials, resulting in gas release from the surface. We adopt the physical properties of Solar System comets to study the thermal evolution and vapor evolution.&#160;(3) Given that the corotation radius is smaller than the magnetosphere radius, the photoionized vapor is shielded from the corotation radius.Our findings reveal that objects with a size smaller than 500 m can experience complete volatile loss within 1 Myr. The effectiveness of the volatile-shielded mechanism hinges on whether the orbital circularization timescale is shorter or longer than the dry-out timescale. If it is longer, all the volatile content can be shielded from the corotation radius of the white dwarf. However, for a shorter circularization timescale, smaller icy objects can be completely dried out while larger objects retain some volatile content, leading to partial dryness and the presence of volatile material within the corotation radius. Consequently, the volatile-shielded mechanism cannot provide effective protection in such cases. A surface magnetic field weaker than 100~T could allow a sufficiently long circularization timescale for the volatile-shielded mechanism to work. As we mentioned, the prerequisite of this mechanism is that the magnetosphere radius is larger than the corotation radius. For example, for a white dwarf with a rotational period of two days, the magnetic field must be larger than 1~T.&#160;&#160;By introducing the magnetic shielding of volatile, we extrapolated a correlation between a white dwarf's magnetic field, spin period,&#160; and the composition of the pollutants. We applied our model to nine white dwarfs with known magnetic fields, rotational periods, and atmosphere compositions, and observed that the polluted white dwarf G29-38 (WD2326+049) is volatile shielded in our model, potentially explaining the excess of volatile elements such as C and S in the disk relative to the white dwarf atmosphere. The other eight white dwarfs under investigation {{exhibit receptivity to volatiles.}} This is consistent with the presence of hydrogen in the four investigated DBA white dwarfs.&#160;However, the lack of hydrogen in the four examined DB white dwarfs cannot be explained by our shielding mechanism and may be attributed to the absence of planetary systems or other unknown mechanisms. We suggest that future observations of white dwarfs with different magnetic fields and rotational periods will provide more insights into the efficiency of the volatile-shielded mechanism. Additionally, our model is highly sensitive to the orbital evolution and material properties of exocomets, and a comparison between observations and our model may lead to valuable constraints on the properties and origins of pollutants.ReferencesKoester, D., G&#228;nsicke, B. T., &amp; Farihi, J. (2014). The frequency of planetary debris around young white dwarfs.&#160;Astronomy &amp; Astrophysics,&#160;566, A34.Okuya, A., Ida, S., Hyodo, R., &amp; Okuzumi, S. (2023). Modelling the evolution of silicate/volatile accretion discs around white dwarfs.&#160;Monthly Notices of the Royal Astronomical Society,&#160;519(2), 1657-1676.