- Slides: 21
Why do T Tauri disks accrete? Lee Hartmann University of Michigan
Why do T Tauri disks accrete? • Ionized disk; Balbus-Hawley (magnetorotational) instability or MRI - yields “alpha” disk viscous behavior, accretion. • Problem: T Tauri disks have extremely low thermal ionization levels farther out than about 0. 1 AU. • Gammie (1996) suggested that cosmic rays (later, stellar X-rays) could provide sufficient ionization - at least in upper disk layers - for the MRI to operate implies possible presence of “dead zone” with potential consequences for planet formation.
FU Ori outbursts - evidence for dead zone? Book Gammie & Hartmann in prep- outbursts due to thermal instability (also Armitage, Livio, & Pringle) Need to deliver 0. 01 M in 100 yr - large amount of mass at relatively small radii (< 1 AU); dead zone? ?
Modelling of FU Ori SED with Spitzer/IRS Green et al. - IRS - high d. M/dt out to ~ 1 AU. . . Zhu et al. in preparation - study disk to large wavelengths large disk radii mass, surface density reqired at ~ 1 AU. . .
Problem: Disk accretion rates depend on M* d. M/dt M*2 Calvet et al. 2004, Muzerolle et al. 2003, 2005, White & Ghez 2001, White & Basri 2003, Natta et al 2004 NO dependence on M* predicted by simple dead zone model
Why do T Tauri stars accrete? • Padoan et al. (2005) suggested: Bondi-Hoyle accretion! • Padoan et al. use N ~ 103 cm-3, v ~ 1 km/s, get accretion rate ~ 10 -8 M yr-1, as typical of (~ 1 M ) CTTS • Unfortunately, Sicilia-Aguilar et al. (2005) studied Tr 37, a 4 Myr-old cluster in an H II region (IC 1396), which has accretion rates similar to Taurus. But N ~ 3 -15 cm-3, and cs ~ 10 km/s; Bondi-Hoyle thus predicts • d. M/dt (Tr 37) ~ 10 -5 d. M/dt (Taurus). • Also; doesn’t deal with angular momentum/disks.
Tr 37: O 6 star + globule in H II region O star Optical (H II region, ionized gas) IRAC 3. 6 m (hot dust, PAHs) MIPS 24 m (hot dust, PAHs) Sicilia-Aguilar, Muzerolle et al. 2004
Formation in H II region does not require atypical disk accretion (and evolution) Sicilia-Aguilar et al. 2004
Dead zone model with irradiation? Gammie model: d. M/dt determined by radius at which T ~ 1000 K; then thermal ionization large enough for MRI. Original model; only viscous heating. If heating by stellar radiation dominates, then d. M/dt a M* (inner edge) or a M*1/2 (flat disk) Does a depend upon M*? X-ray ionization - X-rays are weaker in lower-luminosity stars; but models predict a is only logarithmically dependent upon X-ray flux (large optical depths; Glassgold et al. 1997). In addition, LX L* ; thus same flux at radius at which T=Tc Also: pure irradiation limit not quite right, according to D’Alessio disk models - accretion heating significant - intermediate case from pure viscous heating (Gammie 1996 model); weaker dependence upon M*
Viscous accretion disk? Suppose no dead zone; fully viscous ; then low d. M/dt low disk mass (and low , so easier to fully ionize with X rays) 2 ways to get this: start off with low Md ; but if Md M* (gravitational instability) then get d. M/dt M* alternatively; small mass small initial cloud small initial disk radius faster viscous evolution at the same age, lower mass stars have less disk mass, d. M/dt depends more steeply on M*
Viscous accretion disks? Pure (evolved) viscous model; the accretion rate and the disk mass scale as M*5/2 ; thus very low d. M/dt very low disk mass. • advantage; full MRI gives very low d. M/dt for BDs (low ) • disadvantage; Klein et al. , Scholz et al. detect mm emission from a few young brown dwarf disks - suggest M(disk) is not so small (find little trend with M*). . . but opacity • model requires extensive viscous evolution. If the initial disk radius is very large - 100 AU or more - then this limit of the viscous scaling is not correct, at least early on. • Perhaps the brown dwarf disks can be mostly ionized. But it is more difficult to fully ionize the more massive disks, given the larger inner disk surface densities different behavior at high/low M* ? • Dust settling should yield higher d. M/dt - no evidence from IRS (Furlan et al. 2006) • Do Herbig Ae stars have X-ray emission? If not, why do they accrete?
Disk masses and dust emission T Tauri disk masses are supposed to be (mostly) too low for gravitational instability (M(disk) < 0. 1 M* ). Andrews & Williams 2005 However, this assumes a specific dust opacity which is not that of the ISM dust evolution
Disk masses and dust opacities D’Alessio et al. (1999) considered power-law dust size distributions, with fixed small size and maximum size a(max). The STANDARD dust opacity used for computing disk masses corresponds to a relatively narrow range of a(max). Smaller and larger values yield smaller opacities and thus larger masses. For large a(max), the spectral index, , depends only upon the power law index, NOT upon a(max). So < 2 only indicates some grain growth, not a(max) ~ 1 mm.
Disk masses? Andrews & Williams (2005) found that F , 2. This means EITHER 0 if optically thin (unlikely) or optical depth important - which means both spectral index AND mass are very uncertain.
Disk masses? If the standard opacity requires grain growth to 1 mm at ~100 AU - why shouldn’t there have been much more growth (thus lower opacity) at smaller radii (where the dead zone would be)? Difficult to avoid the inference that disk masses have been systematically underestimated.
Gravitational instability? Are T Tauri disk masses larger than conventionally estimated? From accretion rate estimates and timescales in Taurus: d. M/dt ~ 10 -8 M yr-1, t ~ 1 -2 Myr M(disk, accreted) ~ 0. 01 - 0. 02 M BUT; this is a LOWER limit to what was originally there, as some disk mass remains. White & Hillenbrand (2005) argue that d. M/dt has been underestimated by neglecting the red excess emission, by a factor of two or so: M(disk, accreted) ~ 0. 02 - 0. 04 M ~ 0. 025 - 0. 05 M* , not far below the ~ 0. 1 M* level. N. B. the IM-mass CTTS have M(disk, accreted) much closer to 0. 1 M* Finally; minimum-mass solar nebula of 0. 01 M is just enough to make Jupiter, essentially. Many extrasolar planets have several times Jupiter’s mass; implies M(disk) >> 0. 01 M .
Accreted mass significant for solar-mass stars d. M/dt x 106 yr = 0. 1 M* - grav. instability? Calvet et al. 2004, Muzerolle et al. 2003, 2005, White & Ghez 2001, White & Basri 2003, Natta et al 2004
Why not gravitational fragmentation? should happen early, not later - why then do disks disappear over a few to 10 Myr? Disks lasting for several Myr - not all photoevaporated - in fact, mostly not photoevaporated Tr 37 cluster - O 7 central star; yet disk frequency not much different than in Taurus Tr 37 7160 • debris (1. 5 -2. 5 M )
Why do T Tauri disks accrete? • probably MRI in inner and outer disks. . . • dead zones preferentially in higher-mass objects (? ) • gravitational instability not ruled out for angular momentum transport, at least in some objects/parts of the disk
Dead zone model with irradiation? Tc ~ 1000 K is temp for thermal activation of MRI not as strong a dependence on M* as desired - and less if flat disk, or if combination of irradiation and viscous heating.
Viscous accretion disk? steep dependence on M*, but. . .