Chapter 2: Protostellar collapse and star

formation

One of 3 branches of proton-proton chain

CNO cycle:C, N O atoms act as catalysts

T-dependence of pp chain and CNO cycle

Hydrostatic equilibrium: negative feedback loop

If core T drops, •fusion rate drops, •core contracts•heats up

If core heats up,•fusion rate rises•core expands •cools down

Mass element dmConstant density Inward force = outward force

Main sequence stars are modeled as concentric spherical shells in hydrostatic equilibrium

The Main Sequence

L = A sT4

Demographics of Stars

• Observations of star clusters show that star formation makes many more low-mass stars than high-mass stars

Giant molecular clouds are the sites of star formation

GMC: Length scale ~ 10-100 pcT = 10 – 20 KMass ~ 105 – 106 Msun

Clumps:Length scale ~ 2-5 pcT = 10 – 20 KMass ~ 103 – 104 Msun

Cores:Length scale ~ 0.1 pcT = 10 KMass ~ 1 Msun

Clouds exhibit a clumpy structure

Star forming regions in Orion

What supports Cloud Cores from collapsing under their own gravity?

• Thermal Energy (gas pressure)

• Magnetic Fields

• Rotation (angular momentum)

• Turbulence

Gravity vs. gas pressure

• Gravity can create stars only if it can overcome the forces supporting a cloud

• Molecules in a cloud emit photons: – cause emission spectra– carry energy away– cloud cools– prevents pressure buildup

Virial theorem: 2K + U = 0

What happens when a cloud core collapses?

If 2K > |U|, then

• Force due to gas pressure dominates over gravity• Cloud is supported against collapse

Assume a spherical cloud with constant density

Gravitational potential energy

Kinetic energy

where

In order for the cloud to collapse under its own gravity,

where

Using the equality and solving for M gives a special mass, MJ, called the Jeans Mass, after Sir James Jeans.

Jeans Criterion

When the mass of the cloud contained within radius Rc exceeds the Jeans mass, the cloud will spontaneously collapse:

You can also define a Jeans length, RJ

Figure from Jeff Hester & Steve Desch, ASU

Figure from Jeff Hester & Steve Desch, ASU

“protoplanetary disks”

HH Objects

Collapse slows before fusion begins: Protostar

• Contraction --> higher density • --> even IR and radio photons can’t escape • --> Photons (=energy=heat) get trapped • --> core heats up (P ~ nT)• --> pressure increases• Protostars are still big --> luminous!• Gravitational potential energy --> light!

What supports Cloud Cores from collapsing under their own gravity?

• Thermal Energy (gas pressure)

• Magnetic Fields

• Rotation (angular momentum)

• Turbulence

Angular momentum problem

• A protostellar core has to rid itself of 1000x Jsolar system

• Core collapse produces a disk whose j increases with r

• To redistribute (and/or lose) J takes >> orbital timescale

• The disk is stable over ~106 years

Homework for Wednesday Sept. 14

• Problem 2-5 from book• One paragraph on a possible topic for your semester

project (for topics, check out the author’s blog or astrobites; then find a peer-reviewed paper on the subject from NASA ADS)

• Estimate how the angular momentum is currently distributed in the solar system (sun & planets). Compare to the angular momentum of a uniform spherical gas cloud with ‘typical’ properties for a collapsing molecular cloud core.

Protostellar evolution onto the main sequence

Protostellar evolution for Different Masses

• Sun took ~ 30 million years from protostar to main sequence

• Higher-mass stars evolve faster

• Lower-mass stars evolve more slowly

4000 K

Hayashi Track

Physical cause: at low T (< 4000 K), no mechanisms to transport energy out

Such objects cannot maintain hydrostatic equilibrium

They will rapidly contract and heat until closer to being in hydro. eq.

Mass accretes onto the star via an accretion disk (Krumholtz et al 2009)

Necessary to build stars > 8 Msun

Phases of star formation

Spectral energy distribution

http://feps.as.arizona.edu/outreach/sed.html

dust sublimes at ~2000 K

p depends on grain properties,0<p<2Smaller grains = flatter T(R) =smaller p

Comparing disk observations to models:

Modeling SED’s with some simplifying assumptions:

1. Dust grains are perfect blackbody emitters/absorbers2. Disk is optically thick3. Disk is geometrically thin

Reality:

1. Radiation absorption and emission depends on size, composition, shape, orientation (!) of grains (more so for optically thin disk)

2. Optically thick = disk grains absorb only on the outside of disk, we only see emission from these grains

3. Geometrically thick = disk self-gravity, etc

continuous disk that extends out from the surface of the star to 100 AU

same disk with an inner hole of 0.3 AU

A gap = cleared by a planet?

Class II: “Classical T Tauri star”SED = star + disk, disk lifetime~ 106 yrClass III:PMS star w/ debris disk

http://ssc.spitzer.caltech.edu/documents/compendium/galsci/

Class 0 Protostar:Earliest stage of collapse, no star visible, no disk visibleClass I: bipolar outflow, jets ~100 km/s, still embedded in infalling material heated by star + disk

T Tauri : the prototype protostar

http://ssc.spitzer.caltech.edu/documents/compendium/galsci/

http://vinkovic.org/Projects/Protoplanetary/

http://vinkovic.org/Projects/Protoplanetary/

Anatomy of a flared accretion disk (Kenyon & Hartmann 1987)

Star surface

Kenyon & Hartmann 1987: disks w/ “reprocessed” radiation

MSH=0

H=0.1R9/8

H=0.1R5/4

Addt’l energy from accr

H=0.1R9/8

H=0.1R5/4

H=0

Effect of the ‘photospheric’ scale height

Effect of observing angle

SED’s for accretion disks with H=0.1R9/8

M=10-8 Msun/year

M=0

Chiang and Goldreich 1997

Dust is hotter than gas

“interior”

IPS = iron poor silicatesIRS = iron rich silicates

Debris disks are found around 50% of sunlike stars up to 1 Byr old