Download Beta Pictoris

Lecture L11
ASTC25
1. Discovery and study of dusty disks in Vega-type systems
2. Evidence of planetesimals and planets in the Beta Pictoris system
3. Replenished dust disks: collisions and nature of dust
Discovery and study of dusty disks:
Scattered light tells us how the scattering area is distributed around
the star and how reflective particles are
Thermal radiation measurements and images (at wavelengths of
10 microns and larger) tell us how the
absorbing and emitting area of particles is distributed around
the star and how hot particles are.
Neither the optical nor the mid-infrared images/data alone
allow us to separate the contributions of the area and the emissivity
(scattering/emission coefficient).
Albedo (percentage of light scattered) can only be found by
comparing observations done in the visible and mid-infrared (or
far-IR) spectral domains.
Infrared excess stars (Vega phenomenon)
Beta Pictoris
thermal radiation imaging (10 um)
Lagage & Pantin (1993)
1984
1993
Beta Pictoris, visible scattered starlight
comparison with IR data yields a high albedo, A~0.4-0.5
(like Saturn’s rings but very much unlike the black particles of
cometary crust or Uranus’ rings).
This is how disks
look when just
discovered
A new edgeon disk!
NICMOS/
HST
(Schneider
et al 2005)
near-IR band
(scattered
light)
This is how disks look a decade later - much better quality data, fewer
artifacts, disks appear smoother.
Disk of
Alpha Pisces
Austrini
(a PsA)
= Fomalhaut
a bright
southern star
type A
HD 141569A is a Herbig emission star
>2 x solar mass, >10 x solar luminosity,
hydrogen emission lines H  are double,
because they come from a rotating inner
gas disk.
CO gas has also been found at r = 90 AU.
Observations by Hubble Space Telescope
(NICMOS near-IR camera).
Age ~ 5 Myr,
a transitional disk
Gap-opening PLANET ?
So far out??
R_gap ~350AU
dR ~ 0.1 R_gap
HD 14169A disk gap confirmed by new observations
(HST/ACS)
Evidence of planetesimals and planets
in the vicinity of beta Pictoris:
1. Lack of dust near the star (r<30AU)
2. Spectroscopy => Falling Evaporating Bodies
3. Something large (a planet) needed to perturb FEBs so
they approach the star gradually.
4. The disk is warped somewhat, like a rim of cowboy hat, and that
requires the gravitational pull of a planet on an orbit inclined
by a few degrees to the plane of the disk.
5. Large reservoir of parent (unseen) bodies of dust needed,
of order 100 Earth masses of rock/ice. Otherwise the dust would
disappear quickly, on collisional time scale
B Pic b(?) sky?
Beta Pictoris
Evidence of large bodies (planetesimals, comets?)
11 micron image analysis
converting observed flux
to dust area
(Lagage & Pantin 1994)
FEB = Falling Evaporating Bodies hypothesis in Beta Pictoris
FEB
star
H & K calcium absorption lines
are located in the center of
a stellar rotation-broadened line
absorption line(s) that
move on the time scale
of days as the FEBs
cross the line of sight
1. Temperature of solid particles around a star
2. Finding out the dust distribution
(optical thickness)
3. Radiation pressure
- size distribution of particles
- elliptic orbits of stable particles
4. Collisional lifetime ~ orbital period / optical thickness
5. Composition and crystallinity of particles
Calculating the temperature of
dust & larger bodies
The physics of dust and
radiation is very simple
In the past the amount of
dust hidden by coronograph mask
had to be reconstructed using
MEM= maximum entropy method
or other models. Today scattered
light data often suffice.
tau = optical thickness perpendicular
to the disk (vertical optical thicknass)
Equilibrium temperature of solid particles (from dust to
atmosphereless planets)
A = Qsca = albedo (percentage of light scattered)
Qabs = absorption coefficient, percentage of light absorbed
Qabs + Qsca = 1 (this assumes the size of the body >> wavelength
of starlight, otherwise the sum, called extinction coefficient
Qext, might be different)
total absorbing area = A, total emitting area = 4 A (spherical particle)
Absorbed energy/unit time = Emitted energy /unit time
A Qabs(vis) L/(4 pi r^2) = 4A Qabs(IR) sigma T^4
L = stellar luminosity, r = distance to star, L/4pi r^2 = flux of energy,
T = equilibrium temperature of the whole particle, e.g., dust grain,
sigma = Stefan-Boltzmann constant (see physical constanys table)
sigma T^4 = energy emitted from unit area of a black body in unit time
Qabs(vis) - in the visible/UV range where starlight is emitted/absorbed
Qabs(IR) - emissivity=absorptivity (Kirchhoffs law!) in the infared,
where thermal radiation is emitted
Equilibrium temperature of solid bodies falls with the square-root of r
T^4 = [Qabs(vis)/ Qabs(IR)] L/(16 pi r^2 sigma)
which can be re-written using Qabs(vis) = 1-A as
T = 280 K [(1-A)/Qabs(IR) (L/Lsun)]^(1/4) (r/AU)^(-1/2)
Table of theoretical surface temperature T of planets if Qabs(IR)=1, and the actual
surface temperature Tp. Differences between the two mostly due to greenhouse effect
Body
Albedo A
T(K)
Tp(K)
comments
_________________________________________________________
Mercury
0.15
433
433
Venus
0.72
240
540
huge greenhouse
Earth
0.45
235
280
greenhouse
Moon
0.15
270
270
Mars
0.25
210
220
weak greenhouse
asteroid (typical) 0.15
160
160
Ganimede
0.3
112
112
Titan
0.2
86
90(?)
Pluto
0.5
38
38
Optical thickness:
  (r ) 
 eq ( r ) 
perpendicular to the disk
in the equatorial plane
(percentage of starlight scattered and absorbed, as
seen by the outside observer looking at the disk
edge-on, aproximately like we look through the
beta Pictoris disk)
What is the optical thickness
  (r ) ?
It is the fraction of the disk surface covered by dust:
here I this example it’s about 2e-1 (20%) - the disk is optically
thin ( = transparent, since it blocks only 20% of light)
picture of a small portion of
the disk seen from above
Examples: beta Pic disk at r=100 AU opt.thickness~3e-3
disk around Vega
opt.thickness~1e-4
zodiacal light disk (IDPs) solar system ~1e-7
STIS/Hubble imaging
(Heap et al 2000)
Modeling
(Artymowicz,unpubl.):
parametric, axisymmetric disk
cometary dust phase function
Vertical optical
thickness 
Radius r [AU]
Vertical
profile of
dust density
Height z [AU]
Dust processing: collisions
1. Collisional time formula
2. The analogy with the early solar system
(in the region of today’s TNOs =
trans-Neptunian objects, or in other words,
Kuiper belt objects, KBOs; these are asteroid-sized
bodies up to several hundred km radius)
t coll  Time between collisions (collisional lifetime) of a typical
alpha meteoroid. Obviously, inversely proportional to
the optical thickness (doubling the optical depth results in
2-times shorter particle lifetime, because the rate of collision
doubles).
t coll  P /(8  )
P = orbital period, depends on radius as in Kepler’s III law.
This formula is written with a numerical coefficient of 1/8, to
reflect the fact that a disk made of equal-sized particles needs to
have the optical thickness of about 1/4 to make every particle
traversing it vertically collide with some disk particle, on average.
The vertical piercing of the disk is done every one-half period, because
particles are on inclined orbits and do indeed cross the disk nearly
vertically, if on circular orbits. If the orbits are elliptic, a better
approximate formula has a coefficient of 12 replacing 8 in the above
equation.
How does the Vega-phenomenon relate to our Solar System
(Kuiper belt, or TNOs - transneptunian objects)
Chemistry/mineralogy/crystallinity of dust
all we see so far is silicate particles similar to
the IDPs (interplanetary dust particles from
our system)
ice particles are not seen, at least not in the dust size range
(that is also true of the IDPs)
Microstructure of circumstellar
disks: identical with IDPs
(interplanetary dust particles)
mostly Fe+Mg silicates
(Mg,Fe)SiO3
(Mg,Fe)2SiO4
Small dust is observed due to its large total area
Parent bodies like these (asteroids, comets) are the ultimate sources of
the dust, but remain invisible in images due to their small combined
area
Comet
A rock
is a rock
is a rock…
which one is
from the Earth?
Mars?
Beta Pic?
It’s hard to tell from just spectroscopy or even looking at it!
EQUILIBRIUM COOLING SEQUENCE
Chemical unity
of nature… and it’s
thanks to
stellar nucleosynthesis!
T(K)
What minerals will
precipitate from a
solar-composition,
cooling gas? Mainly
Mg/Fe-rich silicates and
water ice. Planets are
made of precisely these
things.
Silicates
silicates
ices
The disk particles
are made of the
Earth-type minerals!
(olivine, pyroxene,
FeO, PAH= Polycyclic
Aromatic Hydrocarbons)
Crystallinity of minerals
Recently, for the first time observations showed the difference
in the degree of crystallinity of minerals in the inner vs. the outer disk
parts. This was done by comparing IR spectra obtained with single dish
telescopes with those obtained while combining several such telescopes
into an interferometric array (this technique, long practiced by radio
astronomers, allows us to achieve very good, low-angular resolution,
observations).
In the following 2 slides, you will see some “inner” and
“outer” disk spectra - notice the differences, telling us about the different
structure of materials:
amorphous silicates = typical dust grains precipitating from gas,
for instance in the interstellar medium, no regular crystal structure
crystalline grains= same chemical composition, but forming a regular
crystal structure, thought to be derived from amorphous grains by
some heating (annealing) effect at temperatures up to ~1000 K.
~90% amorphous
compare
~60% amorphous
~45% amorphous
Beta Pic,
~95% crystalline