Download Protoplanetary Discs

Protoplanetary Discs
Star formation Lecture Series
12 December 2012
Andrea Stolte
Protoplanetary Discs
Outline of lectures
Oct. 10th : Practical details & Introduction
Oct. 17th : Physical processes in the ISM (I): gas + dust radiative processes, solving radiative transfer
Oct. 24th : Physical processes in the ISM (II): thermal balance of the ISM, heating/cooling mechanisms
Oct. 31st : Interstellar chemistry
Nov. 7th : ISM, molecular clouds
Nov. 14th : Equilibrium configuration and collapse
Nov. 21th : Protostars
Nov. 28th : Pre-main sequence evolution
Dec. 5th : Dies Academicus
Dec. 12th : Discs
Dec. 19st : Planet formation
Jan. 9th : Formation of high-mass stars
Jan. 16th : IMF and star formation on the galactic scale
Jan. 23th : Extragalactic star formation
Jan. 30th : Visit of Effelsberg (?)
Organisational: Effelsberg & Exam date
Wednesday, Jan 30 excursion?
Wednesday, Feb 13 exam?
Andrea Stolte
Outline of today’s lecture
Literature:
Accretion Processes in Star Formation
Lee Hartmann 2000, (Cambridge Univ Press)
Chapters 5 & 6
Star Formation
Palla & Stahler 2004, Wiley-VCH (Weinheim)
Chapter 11.3, 17.3
An Introduction to Star Formation
Ward-Thompson & Whitworth 2011
Cambridge University Press (Cambridge)
Chapter 8.1,8.2
(for a brief overview)
Andrea Stolte
Outline of today’s lecture
Circumstellar discs
Historical note
Discovery of T Tauri stars
Indirect evidence for circumstellar discs
Direct disc observations
Disc radiation
Energy sources
Accretion luminosity
Irradiation of central star light
Angular momentum transport
Spectral energy distributions
A brief introduction to SEDs
Disc classification scheme
Disc models
The optically thick accretion disc
Measuring disc masses
Disc evolution & depletion mechanims
Andrea Stolte
Circumstellar discs around young stars
Motivation:
• most, if not all, young stars form through disc
accretion.
• These discs are the places of planet formation.
Andrea Stolte
Young, circumstellar discs
A brief history:
• The “Solar nebular hypothesis”
1734:
Emanuel Swedenborg: Nebular Hypothesis "Urnebel"
1755:
Immanuel Kant: Rotating Cloud "Urwolke"
“Allgemeine Naturgeschichte und Theorie des Himmels”
1796:
Pierre-Simon Laplace: Rotating Gasball w/ Gravitation
But: Planets have 99% of angular momentum in solar system
⇒ Angular momentum problem!
time passes...
1972:
Victor Safronov: Solar Nebula-Disc-Model
⇒ First full explanation of the formation of the Sun & Planets
The solution: Disc solves the angular momentum problem!
1974:
Lynden-Bell & Pringle: Calculation of full disc model
Andrea Stolte
Indirect evidence for circumstellar gas + dust discs
T Tauri 100 year lightcurve
T Tauri 3 year lightcurve
T Tauri stars were discovered as a new class of variable sources.
Early on, it was suggested that they might be young stars harbouring
circumstellar discs, from which planets might form.
Discovery & definition: Joy 1945, Herbig 1962
Identification as PMS stars: Ambartsumian 1947, 1952
Andrea Stolte
Indirect evidence for circumstellar gas + dust discs
“If this interpretation of T Tauri stars is correct, it will provide new
and important evidence on the conditions under which the planets in
the solar system were formed.”
Lynden-Bell & Pringle 1974
(as quoted in Hartmann 2000)
Definitions:
T Tauri star (TTS): young star ≲ 10-20 Myr with 0.5 < M < 2 Msun
Classical TTS: T Tauri star with strong infrared excess
Weak-line TTS: T Tauri star without infrared excess (or very little)
Herbig Ae/Be star: young star ≲ 10 Myr
with M ≳ 2 Msun
“e” = strong emission lines (Hα, Brγ) are seen in spectra
Andrea Stolte
NASA/ESA, L. Ricci / ESO
Indirect evidence for circumstellar gas + dust discs
Despite historical predictions...
Discs are a relatively young field of astronomy
What caused discs to be - finally - detected?
1. The invention of infrared detectors
⇒ Infrared measurements revealed circumstellar matter
in “spectral enegery distributions” (SEDs)
⇒ Differences between “extinction” and “excess” allowed
the conclusion that matter is distributed not in a shell,
but in a disc
2. The sensitivity of optical & infrared telescopes
⇒ Disc material is cold, and central stars are extincted, hence faint
3. The enhancement of spatial resolution
⇒ direct detections of discs became possible
Andrea Stolte
NASA/ESA, L. Ricci / ESO
Indirect evidence for circumstellar gas + dust discs
• Spectral energy distributions (coarse spectra)
• Infrared “excess” emission
Andrea Stolte
NASA/ESA, L. Ricci / ESO
Young stars with discs vs pre-main sequence stars
The strong infrared emission shows up as “infrared excess”
* Class I (disc/envelope)
•
Class II (disc)
o Class III (remnant disc)
normal
reddening path
objects with IR
excess
Hillenbrand 1992
Andrea Stolte
NASA/ESA, L. Ricci / ESO
Young stars with discs vs pre-main sequence stars
The location of stars with discs is comparable to that of PMS stars
Herbig Ae & Be stars
Pre-Main Sequence stars
Herbig Be
star with disc
Hillenbrand 1992
Bochum 6
age: 10 Myr
Mathew et al. 2010
Andrea Stolte
NASA/ESA, L. Ricci / ESO
Where we are today: Catalogue of 160 resolved discs
http://circumstellardisks.org
160 directly imaged/resolved discs
* 128 Pre-main sequence discs = young discs, possibly accreting
* 32 debris discs = residual discs possibly with planets
Andrea Stolte
NASA/ESA, L. Ricci / ESO
Direct detection of young, circumstellar discs
Chris O’Dell / Rice Univ. NASA
Andrea Stolte
Direct detection of young, circumstellar discs
in shadowed light...
“silhouette discs”
slide NASA/ESA,
courtesy Sebastian
Wolf/
L. Ricci
ESO
Direct detection of young, circumstellar discs
NASA/ESA, L. Ricci / ESO
Direct detection of young, circumstellar discs
NASA/ESA, L. Ricci / ESO
Direct detection of young, circumstellar discs
Disc radiation can be observed directly with long-wavelength imaging.
Outline of today’s lecture
Circumstellar discs
Historical note
Discovery of T Tauri stars
Indirect evidence for circumstellar discs
Direct disc observations
Disc radiation
Energy sources
Accretion luminosity
Irradiation of central star light
Angular momentum transport
Spectral energy distributions
A brief introduction to SEDs
Disc classification scheme
Disc models
The optically thick accretion disc
Measuring disc masses
Disc evolution & depletion mechanims
Andrea Stolte
Approximate treatment of discs
Circumstellar discs are heated by two mechanism:
• accretion = inspiral of material to the central star
• light from the central star
Here, we make the following simplifying assumptions:
• Keplerian velocity vcirc >> inward motion by drag/viscosity
→ gas/dust to first order on circular Keplerian orbits
→ drag forces by viscosity can -- to first order! - be neglected
• self-gravity of disc is neglected, Mdisc << Mstar
→ total kin + pot energy of particle with mass m in the disc:
E = - GM* m / 2r
is determined by stellar potential.
• Ṁ = mass accretion rate is constant with time
• “steady-state disc” = the disc is constant over considered timescales
Andrea Stolte
Accretion as the energy source
If accretion is the dominant source of luminosity, all light emitted from
the disc has to be balanced by the accretion luminosity.
Plausibility argument:
- a particle of mass Δm accreted from infinity initially has E grav = 0
- at the surface of the star, the virial theorem demands that the same particle
has
Egrav = 2 Ekin, Kepler = Δm v2 = G M* Δm / R*
The total energy available from accreting particles from large radii onto the stellar
surface is then given by:
ΔEacc = [ 0 ‒ G M* Ṁ / R* ] = ‒ G M* Ṁ / R*
energy at infinity
energy at stellar surface
Again following the virial theorem, 1/2 of this energy will heat the star,
1/2 will be radiated away as accretion luminosity.
Andrea Stolte
NASA/ESA, L. Ricci / ESO
Accretion as the energy source
If accretion is the dominant source of luminosity, all light emitted from
the disc has to be balanced by the accretion luminosity.
As material spirals in, the potential engery has to be radiated away by the disc.
Imagine a small disc particle at radius R is accreted through an annulus ΔR:
Lacc = GM* Ṁ ΔR
2R
Ṁ : accretion rate
R
M* : mass of the star
ΔR
R
is radiated away through the disc surface:
GM* Ṁ ΔR
2R
‗ 2 x 2πRΔR σTd4
R
area of escaping radiation
Solving for Td gives the variation of the disc temperature with radius
Td,acc =
(
GM* Ṁ
8πσ R3
)
1/4
=
(
GM* Ṁ
8πσ
)
1/4
Andrea Stolte
-3/4
R
Accretion as the energy source
In a real optically thick accretion disc, heating will influence the inner parts
of the disc nearest to the star (R ~ few R*). Here, viscosity cannot be ignored.
When viscosity and dissipation is taken into account, the full solution becomes:
Td,acc =
(
3GM* Ṁ
8πσ R3
)
1/4
⎡
1‒
⎣
R*
(R )
1/2
⎤
⎦
with a temperature maximum at Rmax = 1.36 R*
Tmax = 0.488
(
3GM* Ṁ
8πσ R*
3
1/4
)
For accretion as the major energy source of the disc luminosity, T ~ R -3/4 for the
outer disc where R > R*, with an extra viscosity term when progressing towards
the stellar surface.
Andrea Stolte
NASA/ESA, L. Ricci / ESO
Disc heating as the energy source
If disc heating from the central star is the dominant source of
luminosity, (almost) all light emitted from the disc has to be balanced
by the “irradiation” luminosity.
Disc irradiation:
L* <cos φ> = 4π R2 σSB Td4
at every R in the disc.
φ
R*
R
where <cos φ> ~ R*/R is the average angle of incidence.
Td,heat =
(
L * R*
4πσ
1/4
)
-3/4
R
In both cases, the disc temperatures varies as R-3/4 .
If accretion and irradiation both contribute significantly to the light:
Td = Td,heat + Td,acc ~ R-3/4
Andrea Stolte
NASA/ESA, L. Ricci / ESO
Accretion vs. disc heating
Which process dominates?
Typical T Tauri star accretion rates: Ṁ ~ 10-8 Msun/yr
⇒ L* >> GM* Ṁ / R*
In many T Tauri stars, irradiation dominates, and disc heating defines T d .
In more massive stars, during eposides of burst-like accretion,
accretion rates can achieve Ṁ ~ 10-4 Msun/yr
⇒ L* ≲ GM* Ṁ / R*
During accretion bursts, the accretion luminosity dominates.
There is no unique answer to the question which process dominates.
A high or low accretion rate is a good indicator, especially in low-mass stars.
In high-mass stars, such as Herbig Be stars, the stellar luminosity may always win.
Andrea Stolte
NASA/ESA, L. Ricci / ESO
Outline of today’s lecture
Circumstellar discs
Historical note
Discovery of T Tauri stars
Indirect evidence for circumstellar discs
Direct disc observations
Disc radiation
Energy sources
Accretion luminosity
Irradiation of central star light
Angular momentum transport
Spectral energy distributions
A brief introduction to SEDs
Disc classification scheme
Disc models
The optically thick accretion disc
Measuring disc masses
Disc evolution & depletion mechanims
Andrea Stolte
Angular momentum transport
The idea that young stars accumulate material via disc accretion
was brought forth to solve the angular momentum problem.
Why is angular momentum transported outwards?
Energy balance for 2 particles in the disc:
E
‗ ‒ GMm1 ‒ GMm2 ‗ _ GM
2r1
2r2
2
( mr
1
1
+ m2
r2
)
Angular momentum of the 2 particles in the disc:
J = (GM)1/2 (m1 r11/2 + m2 r21/2)
Angular momentum has to be conserved.
The energy in the system is not conserved: Energy is radiated away as accretion
luminosity as material spirals in. Hence the total system energy is decreased.
Andrea Stolte
NASA/ESA, L. Ricci / ESO
Angular momentum transport
Why is angular momentum transported outwards?
Angular momentum of the 2 particles in the disc:
J = (GM)1/2 (m1 r11/2 + m2 r21/2)
To conserve angular momentum, we move the particles in opposite directions
in the disc:
ΔJ = (GM)1/2 (m1 r11/2 (1+Δr1/r1 )1/2 + m2 r21/2 (1+Δr2 /r2)1/2)
Δr1
r1
Angular momentum conservation ( --> excercise 1):
m1 r1-1/2 Δr1 = ‒ m2 r2-1/2 Δr2
which allows us to eliminate either Δr1 or Δr2 when we derive ΔE.
Andrea Stolte
Δr2
r2
Angular momentum transport
Energy difference in the system after moving both particles (in terms of particle 1):
‗ ‒ GMm1Δ r1
ΔE
2r12
r13/2 _
( r23/2 1
)
ΔJ1 = (GM)1/2 m1 r1-1/2 Δr1
Case: particle 1 is initially further out than particle 2
r1 / r2 > 1: ΔE < 0 if Δ r1 > 0
→
m1 is moved further outwards
at the same time, m2 is moved inwards, and m1 carries out angular momentum.
Case: particle 1 is initially further in than particle 2
r1 / r2 < 1: ΔE < 0 if Δ r1 < 0
→
m1 is moved further inwards
at the same time, m2 is moved outwards, and m2 carries out angular momentum.
The accretion process tends to move particles inwards to decrease the energy of
the disc-star system.
Angular momentum is conserved by moving particles with higher J outwards,
particles with lower J inwards.
Andrea Stolte
NASA/ESA, L. Ricci / ESO
Angular momentum transport II
The outwards transport of angular momentum is related to the fact that the disc
has viscosity, but the process can be understood qualitatively.
In a Keplerian disc:
v2 = GM* / R
implies:
Ω = v / R ~ R-3/2
⇒ particles at smaller R move faster than particles at larger R.
Friction:
inner particle angular velocity is slightly decreased
⇒ particle looses J as it moves further in
outer particle angular velocity is slightly increased
⇒ particle gains J as it moves further out
If there is viscosity, particles at smaller R will drag particles at larger R,
trying to increase those particles angular velocity.
At the same time, particles at larger R will try to slow down particles at smaller R.
The net effect is carrying out angular momentum to large radii in the disc,
while carrying inwards a substantial fraction of the disc mass (but not all mass).
NASA/ESA, L. Ricci / ESO
Outline of today’s lecture
Circumstellar discs
Historical note
Discovery of T Tauri stars
Indirect evidence for circumstellar discs
Direct disc observations
Disc radiation
Energy sources
Accretion luminosity
Irradiation of central star light
Angular momentum transport
Spectral energy distributions
A brief introduction to SEDs
Disc classification scheme
Disc models
The optically thick accretion disc
Measuring disc masses
Disc evolution & depletion mechanims
Andrea Stolte
A brief introduction to SEDs
Discs were originally detected, suspected, and classified from
spectral energy distributions
In essence, a spectral energy distribution is a very coarse spectrum.
Andrea Stolte
NASA/ESA, L. Ricci / ESO
A brief introduction to SEDs
Discs were originally detected, suspected, and classified from
spectral energy distributions
In essence, a spectral energy distribution is a very coarse spectrum.
B
V
R
I
z
••
•
•
•
Andrea Stolte
NASA/ESA, L. Ricci / ESO
Wavelength regime of discs
Discs are detected by their dust emission.
The predominant wavelength regime covers all infrared wavebands.
UV Vis NIR MIR
FIR
mm
radio
UV: 20 - 400 nm
Visible: 400 - 800 nm
Near IR: 0.8 - (2.5-5) μm
Mid IR: (2.5-5) - (25-40) μm
Far IR: (25-40) - 300 μm
sub-mm: 300 - 1000 μm
mm: 1 mm - 1 cm
radio: > 1 cm
Andrea Stolte
NASA/ESA, L. Ricci / ESO
Wavelength regime of discs
Discs are detected by their dust emission.
The predominant wavelength regime covers all infrared wavebands.
→
→
→
→
Credit: IPAC/Caltech
Andrea Stolte
NASA/ESA, L. Ricci / ESO
Disc evolution & classification
Different groups of star-disc systems were identified based on their
infrared SED shapes.
Class I - the youngest systems
Stellar photosphere dominates visible λ
Disc emission can have gaps
Class I:
λFλ ~ λs ≥ 0
λ ≥ 2 μm
-- optically thin envelope in equ. with star
L* = 16π r2 σ T4(r) → T(r) ~ r-1/2 → λFλ ~ λ0
Lower-mass stars are more frequent in Class I
Far-IR emission can be much
stronger than stellar
photosphere
=> infalling envelope
Hillenbrand et al. 1992
Andrea Stolte
Disc evolution & classification
Different groups of star-disc systems were identified based on their
infrared SED shapes.
Class II - young stars with discs
Stellar photosphere dominates visible λ
Disc emission dominates infrared λ
Class II:
λFλ ~ λ-4/3
λ ≥ 2 μm
-- flat, optically thick accretion discs
-- characteristic “gap” at 1-2 μm
• optically thin region within few R*
→ absence of warm dust = “holes”
T Tauri stars & Herbig Ae (Be) stars alike
Disc luminosity can dominate
over stellar luminosity
Hillenbrand et al. 1992
Andrea Stolte
Disc evolution & classification
Different groups of star-disc systems were identified based on their
infrared SED shapes.
Class III - young stars without dusty discs
Disc emission can be very weak
Class III:
λFλ ~ λ-3
-- stellar photosphere in Rayleigh-Jeans limit
-- emission, if any, from residual disc
→ warm dust is already processed into
planetesimals
Many Herbig Be stars → more massive stars
loose discs more rapidly than lower-mass stars
at the same age!
Hillenbrand et al. 1992
Andrea Stolte
NASA/ESA, L. Ricci / ESO
Disc evolution & classification
What does the shape of the SED tell us about disc physics?
Class I:
λFλ ~ λs ≥ 0
λ ≥ 2 μm
gap
-- optically thin envelope in equ. with star
L* = 16π r2 σ T4(r) → T(r) ~ r-1/2 → λFλ ~ λ0
Lower-mass stars are more frequent in Class I
λFλ ~ λ-4/3
λ ≥ 2 μm
-- flat, optically thick accretion discs
-- characteristic “gap” at 1-2 μm
• optically thin region within few R*
→ absence of warm dust = “holes”
gap
Time
Class II:
T Tauri stars & Herbig Ae (Be) stars alike
Class III:
λFλ ~ λ-3
-- stellar photosphere in Rayleigh-Jeans limit
-- emission, if any, from residual disc
→ warm dust is already processed into planetesimals
Many Herbig Be stars → more massive stars loose discs
more rapidly than lower-mass stars at the same age!
Hillenbrand et al. 1992
Outline of today’s lecture
Circumstellar discs
Historical note
Discovery of T Tauri stars
Indirect evidence for circumstellar discs
Direct disc observations
Disc radiation
Energy sources
Accretion luminosity
Irradiation of central star light
Angular momentum transport
Spectral energy distributions
A brief introduction to SEDs
Disc classification scheme
Disc models
The optically thick accretion disc
Measuring disc masses
Disc evolution & depletion mechanims
Andrea Stolte
Disc evolution & classification
What does the shape of the SED tell us about disc physics?
Andrea Stolte
NASA/ESA, L. Ricci / ESO
Disc models - the steady-state optically thick disc
Optically thick discs can be modelled as accretion (or irradiation) discs
We have seen before that the temperature follows an R-3/4 dependence:
Td,acc =
(
GM* Ṁ
8πσ
1/4
)
Td,acc = T0 R -3/4
( R0)
-3/4
R
=
where
GM* Ṁ 1/4 R -3/4
( 8πσ R*3 ) ( R*)
T0 =
(
GM* Ṁ 1/4
)
8πσ R*3
is a characteristic temperature
(approx twice Tmax)
If the disc radiates as a black body at every radius R, the disc luminosity at each
wavelength or frequency can be approximated using the Planck function:
Lν =
∫ πB
ν
Td(R) 2π R dR
insert Bν
&
set x = hν/kT(R)
Inserting the Planck function and the above approximation, we can show that:
Lν =
16π2hR02
3c
2
( )
kT0
8/3
h
⇒ Lν ~ ν1/3 or λLλ ~ λ-4/3
ν1/3
∫
x5/3 dx
x
(e - 1)
where the last term is ~ constant.
compare to Black Body: λBλ ~ λ-4
At R > R*, the disc luminosity falls off much less steeply than
a blackbody with the hottest T in the disc.
Disc models - accretion rates
Optically thick accretion discs without inner holes:
λ-4/3
Hillenbrand et al. 1992
Andrea Stolte
NASA/ESA, L. Ricci / ESO
Disc models - inner holes
Optically thick discs with inner holes:
Hillenbrand et al. 1992
Andrea Stolte
NASA/ESA, L. Ricci / ESO
Schematic view of a young stellar disc
The complete picture is, naturally, a bit more complicated...
Hartmann 2000
Andrea Stolte
NASA/ESA, L. Ricci / ESO
Measuring disc masses from observations
At long wavelengths, discs are optically thin.
The light permeating the disc traces the amount of material
along the line of sight, and the disc mass can be measured.
Andrea Stolte
Measuring disc masses from observations
Assumptions: i) geometrically thin disc
ii) vertically isothermal => T = T(R)
iii) emission is black body of local T(R)
The locally emitted flux can then be integrated to yield the apparent luminosity:
Rd
νLν = 4πd2 νFν = 4π cos(i)
∫R νB
ν
[1‒ exp(‒τν/cos(i))] 2πR dR
i
where:
τν = optical depth at radius R
(assumed constant in z)
Fν = flux measured on Earth
Optically thick disc case:
⇒ νLν = 4π cos(i)
∫ νB
Optically thin disc case:
⇒ νLν = 4π cos(i)
τν >> 1
ν
2πR dR
τν << 1
∫ νB
ν
=>
d = distance to the source
i = disc inclination angle
Ri = inner disc radius
Rd = outer disc radius
1‒ exp(‒τν/cos(i)) → 1
independent of τν → Σmass
=>
1‒ exp(‒τν/cos(i)) → τν
kν Σmass 2πR dR
Andrea Stolte
with τν = kν Σmass → disc mass!
Measuring disc masses from observations
The integral can be solved using:
T(R) = T0 (R/R0)-q
specifically at disc edge: T(R d) = T0 (Rd/R0)-q
Σ(R) = Σ0 (R/R0)-p
Rd
Md = 2π Σ RdR
Ri
Discs are optically thin in the long-wavelength regime:
∫
Rayleigh-Jeans:
hν << kT
→ Bν = 2ν2 kT / c2
⇒ νLν = 8πk ν3 κν / c2 Md T(Rd) (2-p)/(2-p-q)
The temperature-radius relation is known from the optically thick wavelength
regime, where we estimated:
T(R) ~ R-3/4
hence q = 0.75
from disc models it is also known that
Σ(R) ~ R-3/4 to R-1 hence p ~ 0.75 can be assumed
Measuring νLν and making assumptions about κν, the disc mass can be derived.
Andrea Stolte
Disc mass vs stellar mass
Williams & Cieza 2011
Andrea Stolte
NASA/ESA, L. Ricci / ESO
Outline of today’s lecture
Circumstellar discs
Historical note
Discovery of T Tauri stars
Indirect evidence for circumstellar discs
Direct disc observations
Disc radiation
Energy sources
Accretion luminosity
Irradiation of central star light
Angular momentum transport
Spectral energy distributions
A brief introduction to SEDs
Disc classification scheme
Disc models
The optically thick accretion disc
Measuring disc masses
Disc evolution & depletion mechanims
Andrea Stolte
Disc destruction & depletion mechanisms
The fraction of discs in young star clusters decreases with age:
After 5 Myr, there are
essentially no discs left.
5 Myr
If discs are left, they
mostly survive around
low-mass (T Tauri) stars.
Hillenbrand 2005
Andrea Stolte
NASA/ESA, L. Ricci / ESO
Disc destruction & depletion mechanisms
What destroys young circumstellar discs?
T Tauri stars: 40 % “weak-line” WTTS
60 % “classical” CTTS = thick discs
Herbig Be stars: only few % discs after 2-3 Myr
I. UV radiation destroys dust grains
→ as dust is the main opacity source, discs become
optically thin and hence do not reprocess starlight
and irradiate in thermal wavelengths anymore
High-mass stars have substantially more UV radiation
→ discs around high-mass stars are rapidly depleted
II. Binary companions tidally truncate discs
→ the tidal forces between binary stars can disrupt
the outer regions of discs in tight binary systems
→ most stars are born in binaries!
GG Tau
30% of T Tauri stars have companions with R ≲ 30 AU
Mathieu et al. 1999
→ discs around stars born in multiple systems are depleted
Andrea Stolte
Disc destruction & depletion mechanisms
What destroys young circumstellar discs?
III. Disc depletion by grain growth
→ as dust particles stick together and increase in size,
they reprocess light at increasingly longer λ
→ the inner rim of the disc gets depleted early,
the disc beomces invisible in the near-infrared
Formalhaut’s Disc (~100-300 Myr)
Formation of planetesimals explains transition discs (10 Myr),
but the timescales for planet formation are not yet well known.
Andrea Stolte
Summary
I. T Tauri stars and Herbig Ae/Be stars are pre-main sequence stars with discs.
The disc emission is evidenced by excess flux in infrared to mm wavelengths.
=> Stars with discs are characterised by their infrared to mm SEDs.
II. The existence of discs around young stars solves the angular momentum problem.
In the disc, angular momentum is carried outwards with low-mass particles,
while the majority of the mass is transported inwards, and accreted onto the star.
III. The luminosity of young stars’ discs is generated by accretion or irradiation luminosity
of the central star light. In both cases, the most simple, basic disc model suggests
a temperature profile:
T ~ R-3/4
-4/3
This can be used to show that λLλ ~ λ
. The SED of the disc falls off much less
rapidly than the Rayleigh-Jeans tail of the star, hence the infrared excess emission.
IV. Discs are optically thin in the far-infrared to mm regime. Here, the measured flux
traces the amount of material in the disc, and the disc mass can be derived.
Disc masses are typically small fractions of a few % of the stellar mass.
There is a weak tendency for higher-mass stars to harbour higher-mass discs
(and possibly form higher-mass planets).
Andrea Stolte
Next lecture... 19 December!
Formation of planets and planetary systems
Next time, we will study the evolution of the disc into a planetary system.
Andrea Stolte