chapter 2: protostellar collapse and star formation
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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. - PowerPoint PPT PresentationTRANSCRIPT
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Chapter 2: Protostellar collapse and star
formation
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One of 3 branches of proton-proton chain
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CNO cycle:C, N O atoms act as catalysts
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T-dependence of pp chain and CNO cycle
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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
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Mass element dmConstant density Inward force = outward force
Main sequence stars are modeled as concentric spherical shells in hydrostatic equilibrium
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The Main Sequence
L = A sT4
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Demographics of Stars
• Observations of star clusters show that star formation makes many more low-mass stars than high-mass stars
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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
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Clouds exhibit a clumpy structure
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Star forming regions in Orion
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What supports Cloud Cores from collapsing under their own gravity?
• Thermal Energy (gas pressure)
• Magnetic Fields
• Rotation (angular momentum)
• Turbulence
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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
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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
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Assume a spherical cloud with constant density
Gravitational potential energy
Kinetic energy
where
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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.
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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
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Figure from Jeff Hester & Steve Desch, ASU
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Figure from Jeff Hester & Steve Desch, ASU
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“protoplanetary disks”
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HH Objects
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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!
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What supports Cloud Cores from collapsing under their own gravity?
• Thermal Energy (gas pressure)
• Magnetic Fields
• Rotation (angular momentum)
• Turbulence
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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
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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.
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Protostellar evolution onto the main sequence
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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
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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.
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Mass accretes onto the star via an accretion disk (Krumholtz et al 2009)
Necessary to build stars > 8 Msun
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Phases of star formation
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Spectral energy distribution
http://feps.as.arizona.edu/outreach/sed.html
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dust sublimes at ~2000 K
p depends on grain properties,0<p<2Smaller grains = flatter T(R) =smaller p
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Comparing disk observations to models:
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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
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continuous disk that extends out from the surface of the star to 100 AU
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same disk with an inner hole of 0.3 AU
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A gap = cleared by a planet?
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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
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T Tauri : the prototype protostar
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http://ssc.spitzer.caltech.edu/documents/compendium/galsci/
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http://vinkovic.org/Projects/Protoplanetary/
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http://vinkovic.org/Projects/Protoplanetary/
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Anatomy of a flared accretion disk (Kenyon & Hartmann 1987)
Star surface
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Kenyon & Hartmann 1987: disks w/ “reprocessed” radiation
MSH=0
H=0.1R9/8
H=0.1R5/4
Addt’l energy from accr
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H=0.1R9/8
H=0.1R5/4
H=0
Effect of the ‘photospheric’ scale height
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Effect of observing angle
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SED’s for accretion disks with H=0.1R9/8
M=10-8 Msun/year
M=0
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Chiang and Goldreich 1997
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Dust is hotter than gas
“interior”
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IPS = iron poor silicatesIRS = iron rich silicates
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Debris disks are found around 50% of sunlike stars up to 1 Byr old