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Tidal Disruption of Planetary Bodies by White Dwarfs I: a Hybrid SPH-Analytical Approach

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Tidal Disruption of Planetary Bodies by White Dwarfs I: a Hybrid SPH-Analytical Approach MNRAS 492, 5561–5581 (2020) doi:10.1093/mnras/staa142 Advance Access publication 2020 January 16 Tidal disruption of planetary bodies by white dwarfs I: a hybrid SPH-analytical approach Uri Malamud 1,2‹ and Hagai B. Perets 1,3 Downloaded from https://academic.oup.com/mnras/article-abstract/492/4/5561/5707426 by California Institute of Technology user on 26 March 2020 1Department of Physics, Technion – Israel Institute of Technology, Technion City, 3200003 Haifa, Israel 2School of the Environment and Earth Sciences, Tel Aviv University, Ramat Aviv, 6997801 Tel Aviv, Israel 3TAPIR, California Institute of Technology, Pasadena, CA 91125, USA Accepted 2020 January 12. Received 2020 January 9; in original form 2019 November 21 ABSTRACT We introduce a new hybrid method to perform high-resolution tidal disruption simulations, at arbitrary orbits. An SPH code is used to simulate tidal disruptions only in the immediate spatial domain of the star, namely, where the tidal forces dominate over gravity, and then during the fragmentation phase in which the emerging tidal stream may collapse under its own gravity to form fragments. Following each hydrodynamical simulation, an analytical treatment is then applied to instantaneously transfer each fragment back to the tidal sphere for its subsequent disruption, in an iterative process. We validate the hybrid model by comparing it to both an analytical impulse approximation model of single tidal disruptions, as well as full-scale SPH simulations spanning the entire disc formation. The hybrid simulations are essentially indistinguishable from the full-scale SPH simulations, while computationally outperforming their counterparts by orders of magnitude. Thereby our new hybrid approach uniquely enables us to follow the long-term formation and continuous tidal disruption of the planet/planetesimal debris, without the resolution and orbital configuration limitation of previous studies. In addition, we describe a variety of future directions and applications for our hybrid model, which is in principle applicable to any star, not merely white dwarfs. Key words: hydrodynamics – white dwarfs – transients: tidal disruption events. et al. 2006, 2008; Dennihy et al. 2016, 2018;Cauleyetal.2018). The 1 INTRODUCTION origin of material at such close proximity to the WD is clearly not Given the short sinking time-scale of elements heavier than helium primordial (Graham et al. 1990), since the WD disruption radius in the atmospheres of white dwarfs (WD, Koester 2009), the large is of the order of the progenitor star’s main-sequence physical fraction of WDs that are polluted with heavy elements (Zuckerman radius (Bear & Soker 2013). It is instead thought to originate et al. 2003, 2010;Koester,Gansicke¨ & Farihi 2014) is readily from planetary bodies which are perturbed by some mechanism explained by accretion of planetary material (Debes & Sigurdsson (Debes & Sigurdsson 2002; Bonsor, Mustill & Wyatt 2011;Debes, 2002;Jura2003; Kilic et al. 2006;Jura2008). The current view, Walsh & Stark 2012; Kratter & Perets 2012; Perets & Kratter 2012; based on the inferred composition of both WD atmospheres (Wolff, Shappee & Thompson 2013; Michaely & Perets 2014;Veras& Koester & Liebert 2002; Dufour et al. 2007; Desharnais et al. Gansicke¨ 2015; Stone, Metzger & Loeb 2015; Hamers & Portegies 2008; Klein et al. 2010;Gansicke¨ et al. 2012; Jura & Young 2014; Zwart 2016; Veras 2016; Payne et al. 2016; Caiazzo & Heyl 2017; Harrison, Bonsor & Madhusudhan 2018; Hollands, Gansicke¨ & Payne et al. 2017; Petrovich & Munoz˜ 2017; Stephan, Naoz & Koester 2018; Doyle et al. 2019;Swanetal.2019)andtheirdiscs Zuckerman 2017; Smallwood et al. 2018) to highly eccentric orbits (Reach et al. 2005;Juraetal.2007;Reachetal.2009; Jura, Farihi & with proximity to the WD, and are subsequently tidally disrupted Zuckerman 2009; Bergfors et al. 2014; Farihi 2016;Manseretal. to form a circumstellar disc of planetary debris. 2016; Dennihy et al. 2018) suggests that the polluting material is To date, there exist very few detailed simulations of disc forma- terrestrial-like and typically dry. tion by tidal disruptions. The study of Veras et al. (2014) constitutes Orbiting dust is deduced from measurements of infrared excess, the most detailed and relevant work thus far, which investigates the while gas is inferred from metal emission lines. The spatial initial formation of WD debris discs, caused by the tidal disruption distribution of the gas is typically within the WD tidal disruption of kilometre-sized asteroids (∼1014 kg). It follows a similar study radius, and it often orbits the star with some eccentricity (Gansicke¨ by Debes et al. (2012) which only considered the first initial tidal disruption of an extremely eccentric asteroid instead of the entire debris disc formation, while both studies used the same modified N-body code (PKDGRAV). Under the conditions discussed in the Veras E-mail: [email protected] C 2020 The Author(s) Published by Oxford University Press on behalf of the Royal Astronomical Society 5562 U. Malamud and H. B. Perets et al. (2014) paper, the disrupted asteroid debris fill out a highly approach is to omit unnecessary calculations far from the vicinity eccentric ring of debris, along the original asteroid trajectory. The of the star, by fully following the disruption and coagulation of material in this disc does not immediately accrete on to the WD at particles into fragments with SPH, only when they are within the this early stage, and instead the disc is required to evolve further, star’s immediate environment. For the reminder of their orbits, frag- perhaps through various radiation processes (Veras et al. 2015), into ment trajectories are calculated and tracked analytically assuming a more compact state. Keplerian orbits. I.e. we make the assumption (for simplicity) that Being conceptually similar, the study of Weissman et al. (2012, the disc of debris is largely collisionless, as well as dynamically Downloaded from https://academic.oup.com/mnras/article-abstract/492/4/5561/5707426 by California Institute of Technology user on 26 March 2020 basedontheN-body code developed by Movshovitz, Asphaug & unaffected by radiation or other processes, and then instantaneously Korycansky 2012) investigates the tidal disruption of the Sun- transfer the fragments back to the tidal sphere for their next flyby, in grazing, Kreutz-family progenitor. Their results show that the dis- an iterative process. Our assumptions are discussed and quantified. ruption around the Sun breaks the object into multiple clumps, de- With each disruption, the semimajor-axis dispersion of newly pending on the exact density and perihelion distance assumed. They formed fragments depends on the exact size and orbit of their suggest that the observed size distribution of the Kreutz group can progenitor. The hybrid code handles the synchronization, and timing perhaps be produced, however multiple returns are needed by the and dissemination of SPH jobs. The disc formation completes only parent object and its initial ensuing fragments in order to provide the when reaching one of two outcomes: either all fragments have observed temporal separation of major fragments. The Weissman ceased disrupting given their exact size, composition and orbit; et al. (2012) and Debes et al. (2012) studies underline the difficulties or fragment disruption is inhibited when reaching the numerical of modelling such tidal disruptions – since these objects are often minimum size – that of a single SPH particle. highly eccentric (with e approaching 1), time-step limitations make The hybrid approach enables studying tidal disruptions for any tracking of the entire orbit for multiple returns computationally progenitor orbit (even objects originating from tens or hundreds implausible. One can substantially reduce either the resolution or of au) with the same efficiency. The code easily handles partial the eccentricity (or both) in order to circumnavigate this problem, disruptions (i.e. those resulting in little mass shedding when the which was precisely the solution adopted by Veras et al. (2014)in pericentre distance is sufficiently large), since now the number of order to enable multiple returns (orbits) in their simulations. iterations is not limited by a large semimajor axis. At the opposite end of the planetary size distribution, some studies The layout of the paper is structured as follows: in Section 2, we consider the tidal disruption of gas giants, demonstrating the exact first outline an analytical model of tidal disruptions. This model same problem. Faber, Rasio & Willems (2005), Liu et al. (2013)use provides invaluable insights about the outcome of single tidal an SPH code in order to simulate a close gas giant flyby around a star disruptions. While discussing its limitations, we develop a deeper (i.e. a single tidal encounter), whereas Guillochon, Ramirez-Ruiz & understanding of what may be expected in performing full numerical Lin (2011) use a grid-based code and considered both single as well tidal disruption simulations involving terrestrial- or dwarf-sized as multiple passage encounters. As in the Veras et al. (2014) study, planets; In Section 3, we then perform full-scale tidal disruption multiple returns were accomplished only by considerably lowering simulations using SPH. We discuss the code details and setup, show the assumed eccentricity of the planets. the various disruption outcomes which depend on our choice of Using a very simple analytical model, we demonstrate in
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