MNRAS 445, 2794–2799 (2014) doi:10.1093/mnras/stu1926

Post-main-sequence debris from rotation-induced YORP break-up of small bodies

Dimitri Veras,1‹ Seth A. Jacobson2,3 and Boris T. Gansicke¨ 1 1Department of Physics, University of Warwick, Coventry CV4 7AL, UK 2Laboratoire Lagrange, Observatoire de la Coteˆ d’Azur, Boulevard de l’Observatoire, F-06304 Nice Cedex 4, France 3Bayerisches Geoinstitut, Universtat¨ Bayreuth, D-95440 Bayreuth, Germany

Accepted 2014 September 14. Received 2014 September 8; in original form 2014 July 24

ABSTRACT Downloaded from Although discs of dust and gas have been observed orbiting white dwarfs, the origin of this circumstellar matter is uncertain. We hypothesize that the in situ break-up of small bodies such as spun to fission during the giant branch phases of stellar evolution provides an important contribution to this debris. The YORP (Yarkovsky–O’Keefe–Radviesvki–Paddock) effect, which arises from radiation pressure, accelerates the spin rate of asymmetric asteroids, http://mnras.oxfordjournals.org/ which can eventually shear themselves apart. This pressure is maintained and enhanced around dying stars because the outward push of an due to stellar mass loss is insignificant compared to the resulting stellar luminosity increase. Consequently, giant star radiation will destroy nearly all bodies with radii in the range 100 m–10 km that survive their parent star’s main-sequence lifetime within a distance of about 7 au; smaller bodies are spun apart to their strongest, competent components. This estimate is conservative and would increase for highly asymmetric shapes or incorporation of the inward drag due to giant star stellar

wind. The resulting debris field, which could extend to thousands of au, may be perturbed at University of Colorado on October 21, 2014 by remnant planetary systems to reproduce the observed dusty and gaseous discs which accompany polluted white dwarfs. Key words: : general – minor planets, asteroids: general – planets and satellites: dynamical evolution and stability – stars: AGB and post-AGB – stars: evolution – white dwarfs.

by yielding a lower limit of the order of a micron, but no upper 1 INTRODUCTION limit (Reach et al. 2009). Because the discs are extremely com- Observations unambiguously demonstrate that single white dwarfs pact in radial extent (∼1R), planets have difficulty reaching such (WDs) harbour dusty and gaseous circumstellar discs. The mounting close separations. A single planet’s orbit will be pushed outwards discoveries, particularly within the last decade, result in a current by mass-loss during the giant branch phases of stellar evolution, tally of about 30 dusty discs (Zuckerman & Becklin 1987; Becklin and can reverse direction only by giant star/planet tides (Mustill & et al. 2005; Kilic et al. 2005; Reach et al. 2005; Farihi, Jura & Villaver 2012; Adams & Bloch 2013; Nordhaus & Spiegel 2013; Zuckerman 2009) and 7 gaseous discs (Gansicke¨ et al. 2006, 2008; Villaver et al. 2014), severe anisotropy in the mass-loss distribution Gansicke,¨ Marsh & Southworth 2007;Gansicke¨ 2011;Farihietal. (Veras, Hadjidemetriou & Tout 2013b), or through stellar flybys 2012; Melis et al. 2012); some systems include both dusty and (Veras et al. 2014b). All these scenarios are unlikely, as tidal pre- gaseous discs (Brinkworth et al. 2009; Melis et al. 2010; Brinkworth scriptions would have to be finely tuned to prevent engulfment into et al. 2012). Every one of these discs is accompanied by detections the star, mass-loss can be considered isotropic within a few hundred of metals in WD atmospheres, indicating accretion from the disc. au and the probability of a flyby causing a near-collisional orbital Although we know that the disc matter arises from remnant plan- perturbation is too low. etary systems, we do not know from what part of those systems. Systems with multiple planets present different difficulties. Be- Whether the progenitors, which remain undetected, are planets, as- cause mass-loss changes the stability boundary in multiplanet sys- teroids or , they are assumed to be tidally or sublimationally tems (Debes & Sigurdsson 2002; Voyatzis et al. 2013), giant branch disrupted into discs (Graham et al. 1990;Jura2003; Bear & Soker evolution can trigger gravitational scattering instabilities amongst 2013; Stone, Metzger & Loeb 2014; Veras et al. 2014a). Dust mod- the planets. Detailed simulations of two-planet (Veras et al. 2013b) elling provides partial constrains on the particle sizes in these discs and three-planet (Mustill, Veras & Villaver 2014) systems across all phases of evolution, including the main-sequence and WD phases, indicate that the frequency of planets scattered to near-collisional E-mail: [email protected] orbits with the WD is too small to explain the observations.

C 2014 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society Post-MS rotational fission of asteroids 2795

Smaller bodies transported inwards from an external reservoir 2008; Rossi, Marzari & Scheeres 2009). Acceleration is also re- represent more likely progenitors. Both compositionally and dy- sponsible for driving small bodies to rotational fission – the process namically, comets cannot be the primary precursor of the discs whereby objects with little or no tensile strength can fall apart and (Zuckerman et al. 2007; Veras, Shannon & Gansicke¨ 2014c), al- their elements enter a mutual orbit due to centrifugal accelerations though comets can contribute to some discs, particularly around the matching or exceeding gravitational accelerations (Scheeres 2007b; youngest WDs (Stone et al. 2014). Walsh, Richardson & Michel 2008; Jacobson & Scheeres 2011). Asteroids1 originating from an external belt are the more likely YORP-induced rotational fission leads to the creation of asteroid choice. By interacting with one planet, a fraction of a belt of debris pairs (Walsh et al. 2008;Pravecetal.2010) and binary asteroids can scatter close to or directly into the WD. Bonsor, Mustill & Wyatt (Jacobson & Scheeres 2011) which match the characteristics of (2011) showed how a planet plus a Kuiper belt analogue can scatter those observed in the Solar system. This fission also significantly some of the belt into inner regions of a WD system. Debes, Walsh affects the size–frequency distribution of the asteroids in the main & Stark (2012) demonstrated that a planet can trap exo- belt (Jacobson et al. 2014). members in an interior resonance before eventually Consider a solid body in orbit around a star. The evolution of the scattering them to the Roche radius of the WD. Frewen & Hansen spin (s) of this object may be expressed as (Scheeres 2007a) (2014) extended these studies and found that when the planet is of   ds Y f a lower mass and eccentric, then more asteroids encounter the WD = √ , (1) 2 2 2 dt 2πρR a − e Downloaded from radius. 1 In summary, although explorations of the potential sources of disc where R is the mean radius of the body, ρ is its density, a and e are progenitors in WD systems are at an early stage, asteroids are likely the semimajor axis and eccentricity of its orbit, f is a force and Y to be the dominant source. This paper proposes that many asteroids ∈ [0, 1) is a constant determined by the physical properties of the will not survive the giant branch stages of stellar evolution intact due body. The value of Y may be thought of as the extent of asymmetry = = / to radiation-induced rotational fission. Consequently, the reservoir of the asteroid. For a perfectly symmetric body, Y 0 ds dt, http://mnras.oxfordjournals.org/ of material available to form discs around WDs is composed of which means that the asteroid’s initial spin angular momentum smaller fragments than what was previously assumed. We describe is conserved and the asteroid maintains its original spin. Some this type of disruption in Section 2 and conclude in Section 3. Solar system-based examples include the asteroids , with Y = 0.022 (Kaasalainen et al. 2007) and 54509 YORP, with Y = 0.005 (Taylor et al. 2007). Observational limitations currently 2 SPIN EVOLUTION prevent us from measuring Y for small bodies residing outside of the Solar system. In this section, we first describe the primary driver of spin (Sec- The force f is given by equations 23– 26 of Scheeres (2007a), and tion 2.1) and the critical spin at which disruption occurs (Section 2.2) is a function of the incident stellar light pressure, the body’s albedo,

before characterizing the spin evolution along the main sequence at University of Colorado on October 21, 2014 the fraction of radiation pressure due to specular reflection and the (Section 2.3), giant branches (Section 2.4) and WD (Section 2.5) Lambertian scattering coefficient. For the Solar system, this force phases of stellar evolution. We conclude with numerical simulations (f = f) is linearly proportional to the Solar radiation constant, and (Section 2.6). is approximately equal to 1017 kg m s−2. Therefore, we assume here for general planetary systems f = kf,wherek = L/L, such that 2.1 The YORP effect L denotes luminosity. The YORP (Yarkovsky–O’Keefe–Radviesvki–Paddock) effect is the rotational acceleration of a body due to the anisotropic absorp- 2.2 The critical disruption spin tion and radiation of light. The effect was first proposed in the Observations of Solar system asteroids exhibit a sharp and unmis- context of absorbing stellar UV and visible light and the emittance takable cutoff on a rotation period/radius diagram (originally fig. 1 of thermal radiation due to the local heating of the body (Rubincam of Harris 1994 and recently fig. 1 of Jacobson et al. 2014), sug- 2000), although the role of conducted heat is now considered as gesting that asteroids with radii greater than about 250 m break up possibly as important (Golubov & Krugly 2012). when their rotational period becomes shorter than 2.33 h. The crit- Observationally measured rotational acceleration of a number of ical spin at which disruption occurs (≡ scrit) can take one of several asteroids has matched predictions from the YORP theory. Exam- analytical forms (e.g. equations 34– 38 of Davidsson 1999). Given ples include 54509 YORP (2000 PH5) (Lowry et al. 2007; Taylor our lack of knowledge of extrasolar asteroids, we assume they are et al. 2007) and 1862 Apollo (Kaasalainen et al. 2007). The YORP strengthless rubble piles similar to what is observed in the Solar effect also torques the spin pole of small bodies, aligning prograde system (Richardson et al. 2002), and hence orbiters and anti-aligning retrograde orbiters with the angular mo-   π ρ 1/2 mentum vector of their heliocentric orbits (Vokrouhlicky&´ Capekˇ 2 −4 −1 scrit ≡ √ = 7.48 × 10 rad s . (2) 2002) and leaving entire asteroid families aligned (Vokrouhlicky,´ 3π/Gρ 2gcm−3 Nesvorny´ & Bottke 2003), thereby affecting the drift of smaller In the Solar system, the 2.33 h critical limit corresponds to a density members due to the Yarkovsky effect (Bottke et al. 2002). As the of about 2 g cm−3. spin axis is re-oriented, the body is spun down or up, helping to explain both the excess of slow rotators in the asteroid population and the pile-up of rapid rotators at the spin barrier (Pravec et al. 2.3 Main-sequence evolution The Solar system is roughly 4.5 Gyr old, and contains an −4 ∼5 × 10 M⊕ asteroid belt that has been continually ground down 1 Here and throughout the text, asteroid is used synonymously for a small from an ∼M⊕ primordial belt (Bottke et al. 2005) through dynami- body and does not necessarily imply a rocky composition. cal processes such as collisional evolution (O’Brien & Sykes 2011).

MNRAS 445, 2794–2799 (2014) 2796 D. Veras, S. A. Jacobson and B. T. Gansicke¨

The most asymmetric asteroids with orbits close to the Sun will for 1–5 M. We use their values for terrestrial planets as a proxy have already been destroyed by rotational overspinning. In fact, the to guide our choices for our initial pericentre [ ≡ a(1 − e)] such YORP spin time-scale is shorter than the spin time-scale induced by that our asteroids will survive engulfment along the giant branch collisions for asteroids in the main belt with sizes 10 km (Marzari, phases. Rossi & Scheeres 2011 and equations 2– 3 of Jacobson et al. 2014). Some asteroids have changed their shape due to collisions, even- tually becoming asymmetric and hence destroyed. Despite these 2.4.2 Wind drag possibilities, some asteroids will likely survive for the remaining Even if a small body survives engulfment and withstands impact main-sequence lifetime of the Sun. Extrasolar systems may exhibit from the strong stellar wind, its outward motion due to stellar mass the same characteristics, perhaps typically featuring asteroid belts loss might be counterbalanced by drag forces within the wind itself two to three orders of magnitude greater in mass than the Solar (Bonsor & Wyatt 2010; Dong et al. 2010). These authors show that system’s (Debes et al. 2012). Our focus here is on the population inward drift due to drag requires knowledge of the wind speed, of asteroids which survive until the beginning of their star’s giant is strongly dependent on the body size and predominantly occurs branch phases. when mass-loss is strong. However, they do not consider how asym- metry affects the inward motion. Nevertheless, any type of inward

2.4 Giant branch stellar evolution drift of asymmetric asteroids will shorten the rotational disruption Downloaded from time-scale. We do not model wind drag, and in effect then place As the star evolves off the main sequence, asteroid orbits that are a conservative upper limit on this time-scale by considering only within a few hundred au will evolve adiabatically (Veraset al. 2011), outward motion due to mass-loss. meaning that the semimajor axis will expand but the eccentricity will remain constant. Mass emanating from the star during the gi- ant branch phases will impact orbiting asteroids (see equations 2– 2.4.3 The Yarkovsky effect http://mnras.oxfordjournals.org/ 3 of Duncan & Lissauer 1998) and perhaps change their shape. However, without a detailed model of impact, the character of this Different from YORP, the Yarkovsky effect is the orbital recoil change is unknown, and hence we fix Y as a constant.2 Mass clumps experienced by a body – even if symmetric – due to thermal ra- accompanying superwinds on the asymptotic giant branch may de- diation, and acts primarily on bodies with sizes between 1 and stroy particularly small asteroids outright. In this vein, the effect of 100 m for the relevant time periods and distances in our Solar sys- anisotropic stellar mass loss may be more important for destruction tem (e.g. Farinella, Vokrouhlicky´ & Hartmann 1998). Like YORP, of small bodies than for their orbital variations from adiabaticity the Yarkovsky effect has been empirically verified (e.g. Rubincam (Veras et al. 2013b). The smallest bodies, with radii below about 1987), and is a detailed function of parameters such as the temper- 1 cm, will be entrained by the stellar wind (Dong et al. 2010). ature, albedo, shape and size of the body. The resulting drift in the at University of Colorado on October 21, 2014 In order to estimate the time-scale for asteroidal break-up due to body can be towards or away from the star. Solar system asteroids overspinning, we must consider the form of L(t). The evolution of with radii under 100 m experience a typical maximum drift of about −3 −1 the luminosity of a star is a complex function of its physical proper- 10 au Myr (Farinella et al. 1998). ties from the zero-age main-sequence (ZAMS) , and hence are Here we consider only larger objects, and hence avoid the detailed not amenable to simple functional forms. Therefore, we compute modelling which would be necessary to understand the influence L(t) along the giant branch phases by using the SSE stellar evolution of the Yarkovsky effect. Nevertheless, we point out that the orbital code (Hurley, Pols & Tout 2000) with a standard Reimers mass-loss evolution of these smaller asteroids may be dramatically affected coefficient of 0.5 on the red giant branch and the semi-empirical by re-radiation. For Solar system asteroids, the insolation due to mass-loss rate of Vassiliadis & Wood (1993) along the asymptotic Yarkovsky is proportional to the orbital acceleration and hence the giant branch phases. All simulations assume Solar metallicity at the time evolution of orbital parameters such as the semimajor axis ZAMS. (section 3.1 and equation 42 of Bottke, Rubincam & Burns 2000) and eccentricity. Consequently, for extrasolar systems, the contribu- tion to the asteroid’s motion includes a multiplier k = L/L in the 2.4.1 Stellar tides equations for da/dt and de/dt, just as for equation (1). By using SSE, we find that for main-sequence stellar masses of {1M,2M, Small bodies which lie too close to an evolving star will be engulfed 3M,4M,5M,6M,7M,8M}, the maximum fac- by the expanding envelope. The envelope expands to a distance in tor increase in luminosity (kmax)is≈{4070, 9200, 18 700, 31 800, au roughly equal to the initial number of Solar masses contained 46 300, 61 800, 70 000, 92 000}. Consequently, the maximum pos- within the star (fig. 2 of Veras et al. 2013a). However, stellar tides sible drift due to Yarkovsky is about 10−6 au yr−1 for the lowest extend beyond the reach of the star, as will be true with likely mass stars and 10−4 au yr−1 for the highest mass stars. These values fatal consequences for the (Schroder¨ & Connon Smith 2008). are comparable to the orbital expansion rates due to mass-loss at Mustill & Villaver (2012) quantified this extended reach along the the tip of the asymptotic giant branch. giant branch phases by modelling how the stellar surface pulses. Their fig. 7 plots the orbital distance of the initially most distant planet engulfed by the bloated star as a function of stellar mass 2.5 WD stellar evolution When the star becomes a WD, its luminosity profile changes, 2 In reality, variations in asteroid shape could occur on shorter time-scales quickly becoming sub-solar. The time since becoming a WD is than the YORP time-scale, and the interplay between the two can signifi- known as the cooling age. The cooling ages at which WD lumi- cantly influence whether fission occurs (Cotto-Figueroa et al. 2013). Addi- nosities become sub-solar are a few Myr in all cases. After another tionally, exo- impacts on asteroids could enhance or mitigate the 10 Myr, the luminosity decreases by an order of magnitude. For YORP effect (Wiegert 2014). cooling ages of 100 Myr, k ∼ 0.01. Consequently, any asymmetric

MNRAS 445, 2794–2799 (2014) Post-MS rotational fission of asteroids 2797

Spin evolution during giant branch phases Spin evolution during giant branch phases 3 3 a0 3.0 au, e 0.00, Y 0.01, R 1km, 2gcm a0 3.0 au, e 0.00, Y 0.01, R 10 km, 2gcm

0.1 MZAMS 1.0M 0.001 MZAMS 2.0M M 1.0M Breakup ZAMS Spin MZAMS 3.0M s s MZAMS 2.0M 0.01 4 MZAMS 4.0M 10 MZAMS 3.0M rad rad MZAMS 5.0M MZAMS 4.0M MZAMS 5.0M Spin Spin 0.001 10 5 Breakup Spin 10 4 10 6

0.001 0.01 0.1 1 10 100 1000 0.001 0.01 0.1 1 10 100 1000 Time since star turns off of main sequence Myr Time since star turns off of main sequence Myr Downloaded from 3 3 a0 7.0 au, e 0.00, Y 0.01, R 1km, 2gcm a0 7.0 au, e 0.00, Y 0.01, R 10 km, 2gcm 0.1 0.001 Breakup MZAMS 1.0M MZAMS 1.0M Spin MZAMS 2.0M 4 0.01 10 MZAMS 2.0M

MZAMS 3.0M http://mnras.oxfordjournals.org/ M 4.0M MZAMS 3.0M s ZAMS s MZAMS 4.0M MZAMS 5.0M 5 rad 0.001 rad 10 M 5.0M Breakup ZAMS Spin Spin Spin 10 4 10 6

10 5 10 7 0.001 0.01 0.1 1 10 100 1000 0.001 0.01 0.1 1 10 100 1000 at University of Colorado on October 21, 2014 Time since star turns off of main sequence Myr Time since star turns off of main sequence Myr

Figure 1. Exo-asteroid belts will be destroyed during giant branch evolution. The left- and right-hand panels, respectively, feature the spin-up of objects with radii of R = 1, 10 km, and the top and bottom panels, respectively, place these bodies on initial a0 = 3.0, 7.0 au circular orbits (e = 0). The objects have typical asteroid densities of ρ = 2gcm−3 and a degree of asymmetry corresponding to Y = 0.01. The horizontal black lines represent the critical spin value at which an asteroid will tear itself apart (equation 2). All objects are assumed to begin life on the giant branch with no spin, and the curves are drawn fromthe beginning of the red giant branch phases. Dots indicate when the stars become WDs. The stars are all assumed to initially harbour Solar metallicity.

asteroids which have survived to this stage are likely to remain intact main sequence will likely reach the disruption limit. The higher the for several Gyr of WD evolution unless they are already spinning stellar mass, the faster the disruption occurs. Asteroids which fail to near the critical rate. disrupt before the WD is formed are likely to remain intact orbiting the WD (in the absence of other influences), as extending the plots to include WD luminosity causes the curves to nearly flatline. Consequently, we predict that WD systems can be split into three 2.6 Simulations regions with regard to populations of objects with radii of about Here, we perform simulations that showcase the extent of rota- 100 m–10 km: (1) an inner region, which is devoid of such aster- tional disruption when the parent star leaves the main sequence. oids, (2) an intermediate region, which is strewn with debris from We assume, conservatively, that all asteroids begin evolving during rotational break-up, and (3) an outer region, which contains predom- giant branch evolution without any spin and that the asteroid shape inantly fully intact asteroids. The boundaries between the regions (Y = 0.01) does not change. The eccentricity of the asteroid remains are strongly dependent on the ZAMS stellar mass; the boundary be- constant, as adiabatic mass-loss predicts. Both the luminosity of the tween the second and third regions is shown in Fig. 2 , which plots star and the semimajor axis of the asteroid are varied; the latter is the maximum possible distance at which asteroids can be broken varied adiabatically and so is independent of initial orbital orienta- apart by YORP. This figure illustrates that this destruction boundary tion. We model the evolution of stars with main-sequence progenitor ranges from a few tens of au to a few thousands of au depending masses of 1–5 M, as these likely represent the range of progenitor on asteroid radius. Broken-up asteroids could then provide a widely masses which have yielded the vast majority of currently observed extended debris reservoir of pollutants with a particular size distri- WDs. bution (Wyatt et al. 2014) to be delivered to the WD via dynamical We present results in Fig. 1, which highlights the great extent interactions with planets. These results could also have implications of radiation-induced destruction for any exo-asteroid belts. Even for debris discs which are observed around subgiant and giant stars slightly asymmetric asteroids as large as 10 km at 7 au on the (Bonsor et al. 2013, 2014).

MNRAS 445, 2794–2799 (2014) 2798 D. Veras, S. A. Jacobson and B. T. Gansicke¨

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