Disk fragmentation,the Brown Dwarf Desert,

and the Stellar Upper Mass Limit

Chris Matzner

University of Toronto

Yuri Levin, U. Leiden Kaitlin Kratter, U. Toronto

Disk fragmentation in the main accretion phase

Patel et al 04

Which protostellar disks accrete stably, and which undergo gravitational fragmentation?

Fragmentation is sensitive to the thermal evolution of the disk…*

*see posters by Kai, Stamatellos

amax c 0.3Most useful for: - Self-luminous disks with negligible irradiation - Setting lower limits on the radius of fragmentation and Mfrag

Rafikov; Whitworth & Stamatellos

tcool K Period/2and Qmin c 1

Disk fragments when…

Gammie 2001

oM > Q3amax

Gcs3

c Gcs3

This form is most useful for: - Disks heated by irradiation as well as viscosity - Disks with imposed mass accretion

Gammie 2001

Disk fragments when…

oM > Q3amax

Gcs3

c Gcs3

Fed by collapsing mol. core c Gcs(core) 3

Implication: A disk fragments if it is cooler than its core

Irradiation by reprocessed starlight can stabilize it out to thousands of years!

Low-mass star formation

Outflow cavityInfall

Innermost streamline Reprocessed

starlight

Tcore= 10K

CDM & Y.Levin 2005

Disk fragments when

Tdisk K 15K

Accretion heating alone stabilizes the disk for periods less than a few centuries.

see poster by Stamatellos

see poster by Kai

Grether & Lineweaver 2006

Stabilized by viscous heating

Stabilized by irradiation

Stabilizing effect More luminous central star

Which wins?

More rapid accretion: fragment when

Massive star formation

T K170 oM- 42/3K

Destabilizing effect

Kratter & CDM 2006

Kratter & CDM 2006

Kratter & CDM 2006Observer’s-eye view

disks

toroids

Kratter & CDM 2006

Fragmentation acceleratesas mass increases

Theorists-eye view

Sharp drop in dustopacity at high accn rates

McKee & Tan 2003 (fiducial model)

Stellar upper mass limit

If not radiation pressure, then disk fragmentation?

Few other mechanisms get worse above a threshold oM

Conclusions & Challenges

For Numericists: Isothermal codes should make too many BDs by disk fragmentation Radiation-diffusion: stabilize out to century periods Irradiation, outflow cavity: stabilize even further

For Observers: Find 0.1-1 (or more) companions 150 AU (or less) from young O stars Find gravitational spirals in the gas

M9

For Theorists Brown Dwarf Desert and upper mass limit are both made in disks? Must account for magnetic fields! Must model global modes for massive disks. (w/ M. Krumholz & K. Kratter)