Lecture L11 ASTC25

1. Discovery and study of dusty disks in Vega-type systems2. Evidence of planetesimals and planets in the Beta Pictoris system3. Replenished dust disks: collisions and nature of dust

Discovery and study of dusty disks:

Scattered light tells us how the scattering area is distributed aroundthe 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 aroundthe star and how hot particles are.

Neither the optical nor the mid-infrared images/data aloneallow 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 (orfar-IR) spectral domains.

Infrared excess stars (Vega phenomenon)

Beta Pictoris thermal radiation imaging (10 um)Lagage & Pantin (1993)

1984

1993Beta Pictoris, visible scattered starlightcomparison with IR data yields a high albedo, A~0.4-0.5(like Saturn’s rings but very much unlike the black particles ofcometary crust or Uranus’ rings).

A new edge-on disk!

NICMOS/HST

(Schneideret al 2005)

near-IR band(scattered light)

This is how disks look when justdiscovered

This is how disks look a decade later - much better quality data, fewerartifacts, disks appear smoother.

Disk of Alpha PiscesAustrini(a PsA)= Fomalhaut

a bright southern startype 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 planetsin the vicinity of beta Pictoris:

1. Lack of dust near the star (r<30AU)2. Spectroscopy => Falling Evaporating Bodies3. 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

Beta Pictoris

11 micron image analysis converting observed fluxto dust area (Lagage & Pantin 1994)

B Pic b(?) sky?

Evidence of large bodies (planetesimals, comets?)

FEB = Falling Evaporating Bodies hypothesis in Beta Pictoris

absorption line(s) thatmove on the time scale of days as the FEBs cross the line of sight

H & K calcium absorption linesare located in the center of a stellar rotation-broadened line

FEB

star

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 maskhad to be reconstructed usingMEM= maximum entropy methodor other models. Today scattered light data often suffice.

tau = optical thickness perpendicularto 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 absorbedQabs + Qsca = 1 (this assumes the size of the body >> wavelength

of starlight, otherwise the sum, called extinction coefficientQext, might be different)

total absorbing area = A, total emitting area = 4 A (spherical particle)

Absorbed energy/unit time = Emitted energy /unit timeA Qabs(vis) L/(4 pi r^2) = 4A Qabs(IR) sigma T^4L = 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 timeQabs(vis) - in the visible/UV range where starlight is emitted/absorbedQabs(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 433Venus 0.72 240 540 huge greenhouse Earth 0.45 235 280 greenhouse Moon 0.15 270 270Mars 0.25 210 220 weak greenhouseasteroid (typical) 0.15 160 160Ganimede 0.3 112 112Titan 0.2 86 90(?)Pluto 0.5 38 38

Optical thickness:

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)

)(

)(

r

r

eq

What is the optical thickness ?

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

)(r

Vertical optical thickness

Vertical profile ofdust density

Radius r [AU] Height z [AU]

STIS/Hubble imaging (Heap et al 2000)

Modeling (Artymowicz,unpubl.):parametric, axisymmetric diskcometary dust phase function

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-sizedbodies up to several hundred km radius)

collt 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 collisiondoubles).

)/( 8Ptcoll

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 tohave 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 aboveequation.

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 circumstellardisks: 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 ofthe dust, but remain invisible in images due to their small combinedarea

Comet

A rock is a rock is a rock…

which one isfrom the Earth?

Mars?

Beta Pic?

It’s hard to tell from just spectroscopy or even looking at it!

What minerals will precipitate from asolar-composition,cooling gas? Mainly Mg/Fe-rich silicates and water ice. Planets are made of precisely these things.

Silicatessilicates

ices

T(K)

Chemical unityof nature… and it’sthanks to stellar nucleosynthesis!

EQUILIBRIUM COOLING SEQUENCE

The disk particlesare made of the Earth-type minerals!

(olivine, pyroxene, FeO, PAH= PolycyclicAromatic Hydrocarbons)

Crystallinity of minerals

Recently, for the first time observations showed the differencein the degree of crystallinity of minerals in the inner vs. the outer diskparts. This was done by comparing IR spectra obtained with single dishtelescopes with those obtained while combining several such telescopesinto an interferometric array (this technique, long practiced by radioastronomers, 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 differentstructure 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 bysome heating (annealing) effect at temperatures up to ~1000 K.

~90% amorphous

~95% crystalline

~45% amorphous

com

pare

~60% amorphous

Beta Pic,