(continued)
Accretion Processes in Star Formation
Lee Hartmann
Cambridge Astrophysics Series, 32
Cambridge University Press
(also from Nuria Calvet talks (2004)
Energetic Problem in TTS
•CTTS, Lbol > L* ( > 10% on
average).
•An additional source of
energy is required.
•This source must also be
responsible for the other
peculiarities:
• Broad emission lines
• “Veiling”
• NIR excess
• Forbidden emission lines
LJ , good measure of L*, because the stellar
luminosity peaks in J band
from Hartmann 1998
The origin of the energy excess
• FUV spectra ~ solar
cromosphere and active
stars (stronger lines,
however)
•In’70s, amplified
cromosphere?
•NO, a more extended
region is required to
account for the observed
Ha flux
Calvet et al 2004
Observed Ha line profiles of CTTS
Peak ~ v0
Broad wings
Absorption blueshifted
component.
Edwards et al 1994
Line formation: P Cygni profile
Line is formed in
an expanding
shell as,eg, in a
wind~spheric
structure
BUT the CTTS
profiles are NOT
single P Cygni
profiles, but much
more complex!
Redshifted absorption in CTTS line profiles
Infall signature – Inverse
P Cygni profile
Edwards et al 1994
“infall” and “outflow” signatures in the same line profile
Hartmann 1982
“infall”and “outflow”
•Accretion energy is the most likely source for the extra
emission of CTTS, and it is naturally expected to be released in
the process of star formation.
•TTS emission line profiles cannot be interpreted in the frame
of a spheric wind or collapse.
•Observations indicate that the “cores” are slowly rotating:
Core-collapse under conservation of energy (E) and angular
momentum (J) results in the formation of a disk (“accretion
disk”).
•Accretion disks play important role
•Disk associated with YSO have been observed:
Silhouettes
Dark shadow in
contrast with the
bright background in
the Orion nebula
Proplyds
Photoevaporated disks
Scattered light from the YSO
Stapelfeldt et al
Stellar light is scattered by the surface of the disk.
Disk are not plane, but flared.
Gravitational collapse conserving E and J  formation of a disk
Material with highest J at largest r  most of the mass of core lands on disk.
Accretion mass to form the star, in two stages:
cloud  disk = infall
disk  star = accretion
Relevant luminosities to be considered: potential energy released in:
Linf (star): radial infall to the star
Linf (disk): infall to the disk
Linf ~ G (dMinf /dt) M*/R (R: radius where material lands; dMinf /dt:infall
mass accretion rate; M*: stellar mass )
Lacc : accretion from disk onto the star
L* : stellar luminosity
Lobs: Observed luminosity
All of them have to be estimated and compared to identify the accretion
processes.
The mass infall rate can be estimated from the density of the infalling envelope
model that produced the observed SED:
Assuming spherical infall at large distances, by mass conservation:
dM /dt = 4pr2rv,
inf
with v = vff = (GM*
/r)1/2
Model for ClasI in Taurus MC  dMinf /dt
Linf >> L obs ~ 1 Lsol
~2- 4 x 10-6 Msol/yr  Linf ~ 15-30 Lsol
“ENERGETIC PROBLEM”
Actually, is not a problem  If infall occurs onto the disk, as expected
from angular momentum conservation, for typical disk radii 
Linf ~ 0.002-0.03 Lsol
Accretion Disk
•Disk formation during the collapse phase is followed by a
longer phase of disk accretion:
•Most of the disk mass will be accreted onto the star.
•To conserve J, this phase requires to move a small fraction of
disk particles at larger radial distances.
The subsequent evolution of the star-disk system will be
controlled by the rate at which J is transported in the disk
(mechanisms not well known).
The “idea” of the accretion
(from Lynden-Bell and Pringle (1974)
Let be two particles of masses m1 and m2 orbiting around a central mass M:
The energy, E and angular momentum, J are given by:
By a perturbation of orbits, with conservation of momentum:
The energy is minimized and the momentum conserved by moving closer to M the
closest particle and far, the fartest particlebasic action of accretion disk: energy is
released as material both accretes and spreads to a larger distances.
The procces requires some way of connecting different particles in the disk:
Differential rotation: Energy is lost due to frictional dissipation: Net Eg of
the system decreases:
net motion of the disk mass, inward=>ACCRETION
Conservation of J requires internal torques to transport material outwards:
the gas has turbulent, random motions which cause mixing in radial direction
of material with different specific angular momentum :
MOMENTUM TRANSFER in terms of kinematic viscosity (Frank et al. 1992)
Material at R position, with an angular velocity W(R) moves at R+DR
Material at R+DR, with W(R+DR) < W(R) moves at R.
Torque, dJ/dt ~ 2 p S n R3 dW/dR
S: surface density; n : viscosity n ~ wl (characteristic velocity and scale length of
turbulent motion)
Use:
n = a cs H (cs:
(Shakura y Sunnyaev 1973).
sound speed; H scale height of disk)
Diffusion of a ring of material
1 mass: initially at R=R1
t >> R12/n:
Most of the mass,
at centre
t=0
Most of J, far away
DISK LUMINOSITY
• Energy loses due to viscosity (/surface):
D(R)=dE/dt=1/2 n S (R dW/dR)2
For steady accretion, dM/dt = cte:
Total luminosity accreting from infinity : L = G M* (dM/dt)/R*
At R*, with a orbital velocity= (GM*/R*)1/2 , E = 1/2 G M* (dM/dt)/R*
Total luminosity emitted by the disk : Ldisk = ½ G M* (dM/dt)/R*
The energy is released in the boundary layer, where material stop
Boundary layer
Schematic diagram of the angular
velocity in the region where the
disk reaches the stellar surface.
The point where dW/dR =0 is
assumed to be a small distance
dR << R* . The narrow region
where the disk material loses
most of its rotational kinetic
energy is the boundary layer
Temperature distribution of the disk
For steady accretion (dM/dt =cte), dE/dt = D (R) is independent of n
(viscosity).
For a optically thick disk, its effective temperature Tvis(R) can be
found assuming blackbody radiation of the disk
D(R) = s Tvis4
Luminosity of the disk
The luminosity as a function of n emitted by the disk
Rdisk
Ln = 2
p Bn (Tvis) 2 p R dR
R*
For optically-thick disk:
High n : SED of blackbody at T of the hot inner edge of the disk.
Low n : asymptotic behaviour n Ln a n4/3 a l-4/3
SED OF THE OPTICALLY-THICK STEADY DISK
Hartmann 1998
Emission from standard steady disk
Could account for CTTS luminosity excess?:
Ldisk = ½ G M* (dM/dt)/R*
Luminonsity radiated by the boundary layer : Lbl= ½ G M* (dM/dt)/R*.
Assuming Lbl = 4 p R*2 f s Tbl4,
with f (fractioon of area) ~ 1% (~Rbl/R ) and Tbl ~ 8000K, for typical CTTS
parameters:
Could account for energy excess as:
IR and UV excess
“veiling”
Could not account:
Observed line-profiles
LINE PROFILES ARE NOT EXPLAINED
•Volume of the boundary layer is not enough to account for the Ha fluxes
observed
•Radial velocities derived for the steady flux are appreciably lower than
radial velocities measured from the redshifted absorption line feature.
MAGNETOSPHERIC ACCRETION
Strength of stellar magnetic field, from Zeeman effect:
Measure the broadening of magnetic
sensitive lines
Dlz ~l2 g B
(g: Lande factor)
B=0
Also, from spectropolarimetry
B ~ few kG
Johns-Krull et al. (1999)
MAGNETOSPHERIC ACCRETION IN TTS
The effects of stellar magnetic field cannot be neglected in understanding accretion onto
TTS.
For spherical (free-fall) accretion, assuming balance between magnetic pressure and ram
pressure of accretion, when B2/8 p > ½ r v2 , the ionized accreting gas cannot fall freely, but
halted by magnetic forces.
~
~
-3,
Assuming with vinfall
vff ; dipolar field, B
r
Accretion is halted by magnetic field at a ”truncation radius”
rt = 7 R* B4/7 (dM/dt) -2/7 M*-1/7 R*5/7
(B in 1 kG units, dM/dt in 10-8 Msol/yr, M* in 0.5 Msol and R* en 2 Rsol )
For star+disk, the ”truncation radius” Rt ~ g rt, (g <1, ~ 1/3 – 2/3)
B (of star) truncates the disk at a few R*
Matter falls onto the star along the field lines, essentially with free-fall velocity
See Hartmann 1998, secs 8.11,8.12)
Scheme of line formation in the magnetospheric accretion flow
•Most flux at line center comes
from regions where matter is lifted
from the disk (larger volume,v~0) .
•The wings come from material
approaching to the stellar surface
(line width~free-fall velocity at the
stellar surface)
• An acccretion shock is formed,
emitting at much higher T than the
stellar photosphere, when the
material reaches the photosphere
•Blueshifted emission comes from
flow at the back of the star, falling
in
•Redshifted emission is formed if
the line-of-sight crosses the
infalling material in front of the hot
accretion shock
Observed H and NaD line profiles in CTTS & magnetospheric accretion
model
observation
model
Muzerolle et al. 2001, ApJ, 550, 944
Muzerolle et al. 2001, ApJ, 550, 944
dM/dt 
However, Ha line profiles
of CTTS with the highest
dM/dt are not well fitted.
They are formed in a wind,
in agreement with the
characteristic P-Cygni
profiles.
Accretion shock luminosity
The accretion shock
Calvet & Gullbring 1998, ApJ, 509,802
material in
fre-fall –
pre-shock
X
shock
X
Post-shock
Hot photosphere
Material falling along magnetic field lines will
reach the stellar surface at free-fall
velocities. It has to slow down through a
shock just above the stellar surface.
Soft X rays from the shock heat the photosphere
below, and the pre-shock region above
along the accretion column.
(Roughly, 0.5 Lsh is emitted in each direction)
The heated material re-emitts the energy
Lsh = z Lacc, with z = (1-R*/Rt)
Falling material at vff = (2GM*/R*)(1-R*/Rt)1/2
Lsh = GM*(dM/dt)/R* (1-R*/Rt)1/2 ~ 0.8 Lacc , Rt ~3-5 R*
Accretion shock models based in these simple models can explain very well the optical
and UV excess in CTTS. Thus, measure of Lacc from these excess and estimate of dM/dt
Accretion shock emission
•Emission from shock can
account for the UV flux
excess.
•By measuring the luminosity
from the flux
•~ 0.8 G M* dM/dt / R*
•From M* y R* using the
position in the HR diagram
=> dM/dt !
Gullbring et al. 2000, ApJ, 544, 927
Accretion shock models vs observations
Accretion shock models fit the
observed flux excess:
F ~ 1010 – 1011 erg s-1 cm-2
Thp ~ 7000-9000 K
f ~ 0.1-1%
model
Calvet & Gullbring 1998, ApJ, 509,802
Accretion rates in CTTS
<dM/dt> ~ 10-8 Msol/yr
In agrement with values used to
estimate Rt
Hartmann et al. 1998