1. Theoretical difficulties with standard models Mark Wyatt Institute of Astronomy, University of Cambridge

2. Models for origin of hot extrasolar dust Models classified by origin of the dust mass and evolution: In situ origin: Steady state: Asteroid belt / ongoing planet formation Stochastic: Recent impact External origin: Steady state: Comets scattered, or dust dragged, in from outer belt Stochastic: Recent dynamical instability Stellar origin:

3. What is a standard model? My interpretation: dust produced from a belt of planetesimals orbiting the star r Diameter, D n(D) D min D max Collisions grind planetesimals into smaller and smaller fragments resulting in collisional cascade with a size distribution of approximately: n(D)  D -3.5 Mass Cross-sectional area x x x x x x x x x x x x x x x x x x Removed by radiation pressure

4. Radiation pressure halo Large particles confined to belt, but a population of small bound and unbound grains extends to large radii (Wyatt 1999, Krivov et al. 2000, Thebault & Augereau 2001, Strubbe & Chiang 2006) AU Mic Explains structure of most known extrasolar debris disks, noting different wavelengths probe different grain sizes Distance from star Surface density  = F rad /F grav  (0.4/D)(L * /M * )

5. Steady state evolution model Size distribution evolves by steady state collisions (Dominik & Decin 2003; Wyatt et al. 2007) : dM disk /dt = -M disk /t col  -M disk 2 M disk = M 0 [1+t/t col ] -1 Disk mass and fractional luminosity fall off once largest objects are depleted in collisions on a timescale t col, a timescale which depends on initial disk mass and radius Diameter, D n(D) D min D max Evolution of size distribution

6. Explains 24 and 70  m stats 24 and 70 μ m statistics explained using a population model (Wyatt et al. 2007; Lohne et al. 2008) : All stars have one planetesimal belt that evolves in steady state from t=0 Distribution of initial mass is that of protoplanetary disks, and of radii is n(r)  r -0.8

7. Old asteroid belts must be faint Close-in disks quickly drop below detection threshold due to collisional erosion (Wyatt et al. 2007) Known 1au dust (e.g., η Corvi) is >1000 times too bright for its age, a problem two orders of magnitude worse for dust at 0.1au Luminosity evolution of 1au asteroid belt Predicted luminosities increase with more realistic strength laws (e.g., Lohne et al. 2008; Heng & Tremaine 2010), but can’t overcome this conclusion As M tot = M tot0 / ( 1 + t/t c0 ) and t c0 ~ 1 / M tot0, at late times M tot is independent of M tot0, and planetesimal belts have a maximum fractional luminosity at a given age (Wyatt et al. 2007) : f max ~ 0.16x10 -3 r 7/3 t -1

8. Extreme eccentricity Planetesimals on extreme eccentricity orbits (pericentres coincident with hot dust, apocentres far out) have long collision lifetimes (Wyatt et al. 2010) Implications for hot dust: Significant mass at late times for in situ model, but origin of comet-like population (mini-Oort clouds; Raymond & Armitage 2013 )? All collisions occur at pericentre Planetesimals spend most time at apocentre e.g., application to β Leo (Churcher et al. 2010)

9. Stranded mass Giant planets’ irregular satellites have collisionally evolved size distribution (Bottke et al. 2010) In standard model, largest objects become stranded, so significant mass remains in situ at late times (Heng 2011; Kennedy & Wyatt 2011) Implications for hot dust: possible in situ source of mass in planetesimals (or planets), continuously ablated or released stochastically in collisions? 1 10 100 Size (km)

10. Dust dragged in from outer belt Solar debris: P-R drag dominated For low density disks P-R drag makes dust migrate in before it is destroyed in collisions The Solar System’s debris is such an example Stellar wind drag acts in a similar way, and can be more important than P-R drag for low mass stars (Plavchan et al. 2005; Reidemeister et al. 2011) Distance from star Surface density

11. Simple model for dragged in dust Planetesimal belt produces dust of one size (β) which then spirals toward star getting destroyed in mutual collisions on the way (Wyatt 2005) ; resulting distribution depends only on  0 =t pr /t col =10 4 τ eff (r/M * ) 0.5 Tenuous disks Dense disks More complex models include a size distribution for the dust (Wyatt et al. 2011) and take into account dust production in collisions (Reidemeister et al. 2011; van Lieshout et al. 2014; Shannon et al. in prep) Planetesimal belt Surface density Distance from star

12. Insignificance of PR drag? For detectable disks, PR drag is necessarily insignificant, since these must be dense enough for  0 >1 (Wyatt 2005; Wyatt et al. 2007) However, some dust always makes it in at some level, and the model quantifies what that is and allows us to predict emission levels  0 =1 Note that for dense disks, the amount of hot dust is independent of the outer belt density: τ max = 2.5x10 -5 (M * /r) 1/2, although this may be overestimated (van Lieshout et al. 2014)

13. Predicted emission from dragged in dust Model predicts 0.1-1% mid-IR excesses, agreeing with KIN 8.5μm detections for 5/20 stars with outer Kuiper belts (Mennesson et al. 2014) However, note that such hot emission is inevitable, unless dust migration prevented by intervening planets (Moro-Martin & Malhotra 2005; Kennedy & Piette 2015), so perhaps model just needs tweaking? Model predictions can be improved (van Lieshout et al. 2014), but KIN is empirical calibration; extrapolation to near-IR predicts lower excesses

14. Trapping of dust by a planet? As zodiacal dust spirals past Earth it encounters Earth’s resonances and some gets trapped causing a clump of dust that follows the Earth (Dermott et al. 1994) Semi-analytic model of this process (Shannon et al. 2015), shows this is a minor perturbation, as trapping time is of order PR drag time… but perhaps there are other trapping mechanisms (sublimation/gas/magnetic fields)

15. Conclusions In situ origin: Steady state: Asteroid belt Ongoing planet formation Stochastic: Recent impact External origin: Steady state: Comets scattered in Dust dragged in from outer belt Stochastic: Recent dynamical instability Stellar origin: Only if young, or extreme eccentricities, but significant mass can remain in big objects Level expected lower than observed, but can be enhanced by trapping; outer belt required, but not strongly correlated

16. Hot dust around White Dwarfs Several white dwarfs have near-IR emission from hot dust close to the ~1R sun tidal destruction radius (von Hippel et al. 2007; Farihi et al. 2009), some also have CaII emission from circumstellar gas at same location (Gaensicke et al. 2009), while more have metal polluted atmospheres from accretion of rocky material (Girven et al. 2012) Wavelength ( μm) Flux (mJy)