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Transcript
Theoretical difficulties with
standard models
Mark Wyatt
Institute of Astronomy, University of Cambridge
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:
What is a standard model?
My interpretation: dust
produced from a belt of
planetesimals orbiting
the star
Collisions grind planetesimals into
smaller and smaller fragments
resulting in collisional cascade with a
size distribution of approximately:
n(D)  D-3.5
Removed by
radiation pressure
r
n(D)
Dmin
x
x
xx
xx
x
x
x
Cross-sectional
area
Dmax
Mass
Diameter, D
Radiation pressure halo
Large particles
confined to belt, but
a population of
small bound and
unbound grains
extends to large
radii (Wyatt 1999, Krivov
 = Frad/Fgrav  (0.4/D)(L*/M*)
Surface density
et al. 2000, Thebault &
Augereau 2001, Strubbe &
Chiang 2006)
Explains structure of
most known
extrasolar debris
disks, noting
different
wavelengths probe
different grain sizes
AU Mic
Distance from star
Steady state evolution model
Size distribution evolves by steady
state collisions (Dominik & Decin 2003;
Wyatt et al. 2007):
dMdisk/dt = -Mdisk/tcol  -Mdisk2
Mdisk = M0 [1+t/tcol]-1
Evolution of size distribution
Dmin
n(D)
Dmax
Diameter, D
Disk mass and fractional luminosity
fall off once largest objects are
depleted in collisions on a timescale
tcol, a timescale which depends on
initial disk mass and radius
Explains 24 and 70m stats
24 and 70μm 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
Old asteroid belts must be faint
As Mtot = Mtot0 / ( 1 + t/tc0 ) and tc0 ~ 1 / Mtot0 , at late times Mtot is
independent of Mtot0 , and planetesimal belts have a maximum fractional
luminosity at a given age (Wyatt et al. 2007): fmax ~ 0.16x10-3 r7/3 t-1
Close-in
disks quickly
drop below
detection
threshold
due to
collisional
erosion
(Wyatt et al.
2007)
Luminosity
evolution of 1au
asteroid belt
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
Predicted luminosities increase with more realistic strength laws (e.g.,
Lohne et al. 2008; Heng & Tremaine 2010), but can’t overcome this conclusion
Extreme eccentricity
Planetesimals on extreme eccentricity orbits (pericentres coincident with
hot dust, apocentres far out) have long collision lifetimes (Wyatt et al. 2010)
e.g., application to β Leo (Churcher et al. 2010)
All collisions
occur at
pericentre
Planetesimals
spend most
time at
apocentre
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)?
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)
1
10
Size (km)
100
Implications for hot dust: possible in situ source of mass in planetesimals
(or planets), continuously ablated or released stochastically in collisions?
Dust dragged in from outer belt
Surface density
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
Distance from star
Solar debris:
P-R drag dominated
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)
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=tpr/tcol=104τeff(r/M*)0.5
No Collisions
"cycles.1e5.n" using 1:2:3
2
1
Tenuous
disks
1e-06
0.5
0
Dense disks
Planetesimal belt
Surface density
1.5
-0.5
1e-07
-1
-1.5
-2
1e-08
-2-1.5-1-0.5 0 0.5 1 1.5 2
No Dust Produced
"cycles.1e5.n" using 1:2:31
2
1.5
1
1e-06
0.5
0
-0.5
1e-07
-1
Distance from star
-1.5
-2
1e-08
-2-1.5-1-0.5 0 0.5 1 1.5 2
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)
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: τmax = 2.5x10-5 (M*/r)1/2,
although this may be overestimated (van Lieshout et al. 2014)
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)
Model predictions can be improved
(van Lieshout et al. 2014), but KIN is
empirical calibration; extrapolation
to near-IR predicts lower excesses
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?
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)
Conclusions
In situ origin:
• Steady state:
• Asteroid belt
• Ongoing planet formation
• Stochastic:
• Recent impact
Only if young, or extreme
eccentricities, but
significant mass can
remain in big objects
External origin:
• Steady state:
• Comets scattered in
• Dust dragged in from outer belt
• Stochastic:
• Recent dynamical instability
Stellar origin:
Level expected lower
than observed, but can
be enhanced by
trapping; outer belt
required, but not
strongly correlated
Hot dust around White Dwarfs
Flux (mJy)
Several white dwarfs have near-IR emission from hot dust close to the
~1Rsun 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)