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 Main sequence stars are modeled as concentric spherical shells in hydrostatic equilibrium Mass element dm Constant density Inward force = outward force 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 pc T = 10 – 20 K Mass ~ 105 – 106 Msun Clumps: Length scale ~ 2-5 pc T = 10 – 20 K Mass ~ 103 – 104 Msun Cores: Length scale ~ 0.1 pc T = 10 K Mass ~ 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 What happens when a cloud core collapses? Virial theorem: 2K + U = 0 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 r0 3 GM U » 5 Rc 3 K = NkT 2 Mc N= mm H 2 c In order for the cloud to collapse under its own gravity, 3M c kT 3GM < mm H 5Rc 2 c æ 3M c ö Rc = ç ÷ è 4 pr 0 ø 1/3 where Using the equality and solving for M gives a special mass, MJ, called the Jeans Mass, after Sir James Jeans. æ 5kT ö æ ö 3 MJ » ç ÷ ç ÷ è Gmm H ø è 4pGmm H r0 ø 3/2 1/2 Jeans Criterion When the mass of the cloud contained within radius Rc exceeds the Jeans mass, the cloud will spontaneously collapse: Mc > MJ You can also define a Jeans length, RJ æ 15kT ö RJ » ç ÷ è 4 pGmm H r 0 ø 1/2 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 peerreviewed 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 Hayashi Track Physical cause: at low T (< 4000 K), no mechanisms to transport energy out Such objects cannot maintain hydrostatic equilibrium 4000 K 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 æ R ö- p T(R) = 2000Kç ÷ è R* ø dust sublimes at ~2000 K p depends on grain properties, 0<p<2 Smaller 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/absorbers 2. Disk is optically thick 3. 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 0 Protostar: Earliest stage of collapse, no star visible, no disk visible Class I: bipolar outflow, jets ~100 km/s, still embedded in infalling material heated by star + disk Class II: “Classical T Tauri star” SED = star + disk, disk lifetime~ 106 yr Class III: PMS star w/ debris disk http://ssc.spitzer.caltech.edu/documents/compendium/galsci/ 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 H=0.1R5/4 H=0.1R9/8 Addt’l energy from accr H=0 MS Effect of the ‘photospheric’ scale height H=0.1R5/4 H=0.1R9/8 H=0 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 “interior” Dust is hotter than gas IPS = iron poor silicates IRS = iron rich silicates Debris disks are found around 50% of sunlike stars up to 1 Byr old