Accretion Processes in Star Formation Lee Hartmann Cambridge Astrophysics Series, 32 Cambridge University Press (also from Nuria Calvet talks (2004) (continued)

Energetic Problem in TTS from Hartmann 1998 CTTS, L bol > 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 L J, good measure of L *, because the stellar luminosity peaks in J band

The origin of the energy excess FUV spectra ~ solar cromosphere and active stars (stronger lines, however) In70s, amplified cromosphere? NO, a more extended region is required to account for the observed H flux Calvet et al 2004

Observed H line profiles of CTTS Peak ~ v 0 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 Edwards et al 1994 Infall signature – Inverse P Cygni profile

infall and outflow signatures in the same line profile Hartmann 1982

infalland 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 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: L inf (star): radial infall to the star L inf (disk): infall to the disk L inf ~ G (dM inf /dt) M * /R (R: radius where material lands; dM inf /dt:infall mass accretion rate; M * : stellar mass ) L acc : accretion from disk onto the star L * : stellar luminosity L obs: 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 inf /dt = 4 r 2 v, with v = v ff = (GM * /r) 1/2 Model for ClasI in Taurus MC dM inf /dt ~2- 4 x M sol /yr L inf ~ L sol L inf >> L obs ~ 1 L sol ENERGETIC PROBLEM Actually, is not a problem If infall occurs onto the disk, as expected from angular momentum conservation, for typical disk radii L inf ~ L sol

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 m 1 and m 2 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 accretion (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 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 (R) moves at R+ R Material at R+ R, with (R+ R) < (R) moves at R. Torque, dJ/dt ~ 2 R 3 d /dR surface density; : viscosity ~ wl (characteristic velocity and scale length of turbulent motion) = c s H Use: = c s H (c s : 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 away t >> R 1 2 / 1 mass: initially at R=R 1

DISK 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 * L disk = ½ G M * (dM/dt)/R * Total luminosity emitted by the disk : L disk = ½ G M * (dM/dt)/R * boundary layer 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 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 disk For steady accretion (dM/dt =cte), dE/dt = D (R) is independent of (viscosity). For a optically thick disk, its effective temperature T vis (R) can be found assuming blackbody radiation of the disk D(R) = T vis 4

Luminosity of the disk The luminosity as a function of emitted by the disk L = 2 B (T vis ) 2 R dR R*R* R disk 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 DISK Hartmann 1998

Emission from standard steady disk Could account for CTTS luminosity excess?: L disk = ½ G M * (dM/dt)/R * Luminonsity radiated by the boundary layer : L bl = ½ G M * (dM/dt)/R *. Assuming L bl = 4 R * 2 f T bl 4, with f (fractioon of area) ~ 1% (~R bl /R ) and T bl ~ 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 H 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: 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 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 B 2 /8 > ½ v 2, the ionized accreting gas cannot fall freely, but halted by magnetic forces. Assuming with v infall ~ v ff ; dipolar field, B ~ r -3, Accretion is halted by magnetic field at a truncation radius r t = 7 R * B 4/7 (dM/dt) -2/7 M * -1/7 R * 5/7 (B in 1 kG units, dM/dt in M sol /yr, M * in 0.5 M sol and R * en 2 R sol ) For star+disk, the truncation radius R t ~ r t, ( <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 Muzerolle et al. 2001, ApJ, 550, 944 model observation

dM/dt However, H 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. Muzerolle et al. 2001, ApJ, 550, 944

Accretion shock luminosity

The 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 L sh is emitted in each direction) The heated material re-emitts the energy L sh = GM * (dM/dt)/R * (1-R * /R t ) 1/2 ~ 0.8 L acc, R t ~3-5 R * Calvet & Gullbring 1998, ApJ, 509,802 L sh = L acc, with = (1-R * /R t ) Falling material at v ff = (2GM * /R * )(1-R * /R t ) 1/2 Accretion shock models based in these simple models can explain very well the optical and UV excess in CTTS. Thus, measure of L acc from these excess and estimate of dM/dt

Accretion 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 observations Calvet & Gullbring 1998, ApJ, 509,802 Accretion shock models fit the observed flux excess: F ~ – erg s -1 cm -2 T hp ~ K f ~ 0.1-1% model

Accretion rates in CTTS Hartmann et al ~ M sol /yr In agrement with values used to estimate R t