Accretion Processes in Star Formation

Lee Hartmann

Cambridge Astrophysics Series, 32

Cambridge University Press

(also from Nuria Calvet talks (2004)

(continued)

Energetic Problem in TTSEnergetic Problem in TTS

from Hartmann 1998

•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

The origin of the energy excessThe 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 Hflux

Calvet et al 2004

Observed HObserved Hline profiles of CTTSline profiles of CTTS

Peak ~ v0

Broad wings

Absorption blueshifted component.

Edwards et al 1994

Line formation: P Cygni profileLine 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 profilesRedshifted absorption in CTTS line profiles

Edwards et al 1994

Infall signature – Inverse P Cygni profile

“infall” and “outflow” signatures in the same line profile

Hartmann 1982

““infall”and “outflow”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:

SilhouettesSilhouettes

Dark shadow in contrast with the bright background in the Orion nebula

ProplydsProplyds

Photoevaporated disks

Scattered light from the YSOScattered light from the YSO

Stellar light is scattered by the surface of the disk.Disk are not plane, but flared.

Stapelfeldt et al

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 starL* : 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 envelopemodel that produced the observed SED:

Assuming spherical infall at large distances, by mass conservation:

dMinf /dt = 4r2v,

with v = vff = (GM*/r)1/2

Model for ClasI in Taurus MC dMinf /dt ~2- 4 x 10-6 Msol/yr Linf ~ 15-30 Lsol

Linf >> L obs ~ 1 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).

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 “idea” of the accretionThe “idea” of the accretion(from Lynden-Bell and Pringle (1974)(from Lynden-Bell and Pringle (1974)

The energy is minimized and the momentum conserved by moving closer to M the closest particle and far, the fartest particlebasic 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 directionof 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 (R) moves at R+RMaterial at R+R, with (R+R) < (R) moves at R.

Torque, dJ/dt ~ 2 R3 d/dRsurface density; : viscosity ~ wl (characteristic velocity and scale length of turbulent motion)

Use: = = c css H H (cs: sound speed; H scale height of disk)(Shakura y Sunnyaev 1973).

Diffusion of a ring of material

t=0

Most of the mass, at centre

Most of J, far awayt >> R12/

1 mass: initially at R=R1

DISK LUMINOSITYDISK LUMINOSITY

• Energy loses due to viscosity (/surface): D(R)=dE/dt=1/2 (R d/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 : LLdiskdisk = ½ G M = ½ G M** (dM/dt)/R (dM/dt)/R**

The energy is released in the boundary layerboundary layer, where material stop

Boundary layerBoundary layer

Schematic diagram of the angular velocity in the region where the disk reaches the stellar surface. The point where d/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 diskTemperature distribution of the disk

For steady accretion (dM/dt =cte), dE/dt = D (R) is independent of (viscosity).

For a optically thick disk, its effective temperature Tvis(R) can be found assuming blackbody radiation of the disk D(R) = Tvis

4

Luminosity of the diskLuminosity of the disk

The luminosity as a function of emitted by the disk

L = 2 B (Tvis) 2 R dRR*

Rdisk

For optically-thick disk:High : SED of blackbody at T of the hot inner edge of the disk.

Low asymptotic behaviour L 4/3 -4/3

SED OF THE OPTICALLY-THICK STEADY DISKSED OF THE OPTICALLY-THICK STEADY DISK

Hartmann 1998

Emission from standard steady diskEmission 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 R*2 f Tbl

4,

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 EXPLAINEDLINE PROFILES ARE NOT EXPLAINED

•Volume of the boundary layer is not enough to account for the Hfluxes observed•Radial velocities derived for the steady flux are appreciably lower than radial velocities measured from the redshifted absorption line feature.

MAGNETOSPHERIC ACCRETIONMAGNETOSPHERIC ACCRETION

Strength of stellar magnetic field, from Zeeman effect:

B=0

Johns-Krull et al. (1999)

B ~ few kG

Measure the broadening of magnetic sensitive lines

z ~2 g B (g: Lande factor)

Also, from spectropolarimetry

MAGNETOSPHERIC ACCRETION IN TTSMAGNETOSPHERIC 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 > ½ v2 , the ionized accreting gas cannot fall freely, but halted by magnetic forces.

Assuming with vinfall ~ vff ; dipolar field, B ~ r-3,

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 ~ rt, ( <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 velocitySee Hartmann 1998, secs 8.11,8.12)

Scheme of line formation in the magnetospheric accretion flowScheme 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 Observed H and NaD line profiles in CTTS & magnetospheric accretion model model

Muzerolle et al. 2001, ApJ, 550, 944

model

observation

dM/d

t

However, Hline profilesof CTTS with the highest dM/dt are not well fitted. They are formed in a wind, in agreement with the characteristic P-Cygni profiles.

Muzerolle et al. 2001, ApJ, 550, 944

Accretion shock luminosityAccretion shock luminosity

The accretion shockThe accretion shock

X

X

material in fre-fall – pre-shock

shock

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 = GM*(dM/dt)/R* (1-R*/Rt)1/2 ~ 0.8 Lacc , Rt ~3-5 R*

Calvet & Gullbring 1998, ApJ, 509,802

Lsh = Lacc, with = (1-R*/Rt)Falling material at vff = (2GM*/R*)(1-R*/Rt)1/2

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 emissionAccretion shock emission

Gullbring et al. 2000, ApJ, 544, 927

•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 !

Accretion shock models vs observationsAccretion shock models vs observations

Calvet & Gullbring 1998, ApJ, 509,802

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

Accretion rates in CTTSAccretion rates in CTTS

Hartmann et al. 1998

<dM/dt> ~ 10-8 Msol/yr

In agrement with values used to

estimate Rt