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Protostellar evolution ● ● ● ● ● ● ● Timescales Collapse Evolution Deuterium burning Rotation Disks Observations of disks and protostars Peter Schilke Inside out collapse Peter Schilke Inside out collapse 3 s m0 v Inside-out collapse: the central mass M ∗ t = t G 2G M ∗ t u r , t =− ( free-fall velocity) r and the accretion rate 3 3/ 2 m0 v s T 2 −6 Ṁ =4 r u= ≈2×10 M ⊙ G 10 K 5 so it takes about 5×10 years for 1 M ⊙ Peter Schilke Protostellar development timescale KelvinHelmholtz timescale: (timescale for which a star can create its luminosity out of gravitational energy): KH = m E g =G r dE g dt 2 Eg dE g /dt M R with m= , r = 2 2 2 =L GM KH = 2RL Peter Schilke MassLuminosity Relation: L ∝ M3.2 MassRadius relation: R ∝ M0.6 Peter Schilke KH Timescale: KH ∝ M1.8 detailed models Peter Schilke Palla & Stahler (1990) tKH=tacc dM/dt=10-5 MO/yr r Ze oe ag m n ai ce en qu se Sun Timescales Peter Schilke Models of star formation Example: ● ● ● ● collapse of cylindrical, magnetized cloud gradual collapse and accretion through ambipolar diffusion initially rapid collapse after cloud becomes magnetically supercritical Peter Schilke Models of star formation Peter Schilke Density Peter Schilke Evolution As the clump collapses, the dust becomes optically thick ● it's not longer isothermal any more heats up until hydrostatic core (first core) is formed which is thermally supported ● ● ● ● Mass about 0.05 M⊙ Size about 5 AU 3 ℜT internal energy U = M 2 GM equal to gravitational energy W =− R −1 M R GM T= =850 [K] 3ℜ R 0.05 M ⊙ 5 AU Peter Schilke Central temperature Peter Schilke Breakdown of first core thermal energy per molecule at 2000 K is about 0.74 eV dissociation energy of H2 is 4.48 eV ● ● ● for quite some time the gravitational energy goes into dissociation of H2 and NOT into raising the temperature while the density rises Discussion of Bonnor-Ebert spheres: ● ● at some critial density the core is unstable to collapse and cannot be supported thermally any longer Peter Schilke Accretion luminosity At some point the temperature is high enough to ionize hydrogen (13.6 eV ● ● ● ● ● dynamically stable protostar Radius of several R⊙ Mass 0.1 M⊙ T > 105 K Accretion on this object still going on ● ● all energy is converted into Luminosity G M ∗ Ṁ M∗ R∗ Ṁ Lacc = ≈60 L⊙ −5 −1 R∗ 1 M ⊙ 5 R⊙ 10 M ⊙ yr −1 Peter Schilke Protostar definition ● ● ● ● Mass gaining star whose luminosity stems mainly from external accretion. Dust around the protostar is destroyed (vaporization of grains at 1500 K) The (optical) radiation is absorbed by the outer dust shell and re-radiated in the IR Protostars are invisible in the optical Peter Schilke Protostellar structure Peter Schilke Temperature structure: inner ● Accretion velocity ● −1/ 2 2G M ∗ M∗ −1 v ff = =280 [km s ] R∗ 1M⊙ ● 1/ 2 R∗ 5 R⊙ which lead to postshock temperatures in excess of 106 K UV and X-ray photons absorbed in (opaque, ionized) radiative precursor Peter Schilke Temperature structure: inner ● ...which radiates like a blackbody with a temperature given by the Stefan-Boltzmann law 2 4 4 R∗ B T eff ≈ L acc T eff ≈ G M ∗ Ṁ 4 B R Ṁ T eff ≈7300 [K] −5 −1 10 M ⊙ yr 3 ∗ 1/ 4 1/ 4 −3/ 4 1/ 4 M∗ 1M⊙ R∗ 5 R⊙ Peter Schilke Temperature structure: outer ● ● ● This radiation (of a stellar-like photosphere) is transmitted through the opacity gap, absorbed by the dust and re-radiated at the dust photosphere like a black body with an approximate temperature of 300 K and radius 14 AU Peter Schilke Results of calculations Peter Schilke Isotemperature maps Peter Schilke Protostellar evolution Calculated with stellar structure equations Temperature in interior rises Nuclear fusion starts: Deuterium burning ● ● ● ● ● ● ● H + 1H →3He + when the temperature reaches 106 K when this happens, the temperature in the interior rises so high that it cannot be transported by radiation in the (opaque) medium convection starts in the center 2 Peter Schilke Mass-radius relation Peter Schilke Deuterium burning phase ● ● There isn't much deuterium ([D/H] = 2.5 10-5) and it is rapidly exhausted in the interior supply from outside through convection total luminosity 12 L⊙ Peter Schilke Rotation Rotation cannot be ignored Magnetic braking is fairly efficient in the outer parts of a collapsing cloud ● ● ● magnetic braking: transport of angular momentum by torsional Alfvén waves Peter Schilke Inner part ● ● ● ● ● Through decoupling of ions and neutrals in the inner part, magnetic braking is not efficinent in the interior If the angular momentum is large enough, it will miss the protostar entirely and hit a disk range of angular momenta is present in infalling matter at any time maximum impact distance in the equatorial plane is known as centrifugal radius cen that sets the scale for a protostellar disk Peter Schilke Orbits 2 3 0 1/ 2 vs t T cen ≈ =0.3 AU 16 10 K 0 −14 −1 10 s 2 t 5 10 yrs 3 Peter Schilke Birth of a disk ● ● t 0= a disk is born when infalling gas misses the protostar critical time determined using cen = R* 16 R∗ 1/3 2 0 R∗ =3×10 [ yr ] 3⊙ 4 1/ 3 −2/ 3 0 −14 −1 vs −1 vs 10 s 0.3 km s the mass of the protostar is M = Ṁ t 0 leading to −1/3 ¿ M 0= 16 R∗ v 3 G 2 0 8 1/ 3 s =0.2 M ⊙ 1/3 R∗ 3⊙ 0 −14 −1 10 s −2/3 vs 0.3 km s −1 8 /3 Peter Schilke Disks ● ● ● If there is no disk, infalling mass coming from above and below the midplane will collide there and create a disk The accretion shock now is on the surface of the disk as well as on the protostar there is a radial infall in the disk Peter Schilke Streamlines in disks Peter Schilke Inner and Outer disks Peter Schilke Disk evolution ● ● ● Spiral patterns expands with t3 At time t1 = 1.43 t0, the streamlines start missing the protostar (at a radius of 0.34 cen) boundary between (tenuous) outer disk and (dense) inner disk with almost circular orbits Peter Schilke Mass transport rate Peter Schilke Peter Schilke Star formation Peter Schilke Disk model Peter Schilke Observations of disks Direct ● Optical (silhouette) ● ● Not deeply embedded objects Millimeter/Submillimeter ● ● ● Dust Molecular lines Indirect ● ● SEDs Results: ● ● Sizes ~ 100 AU Peter Schilke Disks MBM12 3C Jayawardhana et al. 2002 β Pic HH 30 Peter Schilke HH 30 Peter Schilke SEDs Star Disk Peter Schilke GG Tau – the ring world Peter Schilke Disk evaporation: proplyds Peter Schilke Physical Structure of PPDs Irradiation Dust heating Gas heating UV photons radiation Star dust IR Star . electron dust Irradiation from the central star heats gas & dust in disks Peter Schilke Radiation processes Peter Schilke Chemical Structure of PPDs UV surface intermediate midplane Surface layer : n~104-5cm-3, T>50K Photochemistry Intermediate : n~106-7cm-3, T>40K Dense cloud chemistry Midplane : n>107cm-3, T<20K Freeze-out Peter Schilke Disk chemical structure Peter Schilke Excursion: Comets and solar system Markwick & Charnley 2004 Peter Schilke Solar disk Peter Schilke Structure of solar system Peter Schilke Exoplanets Peter Schilke Planet formation Peter Schilke Planet formation Peter Schilke Debris disks Disks around evolved (but young) stars Not remnants of protostellar disks ● ● ● ● Dust is blown away Have to be replenished from destructive collisions of planetesimals (asteroid-like objects) Peter Schilke rogues gallery τ Ceti ε Eridani Vega (α Lyr) Fomalhaut (α PsA) β Pic Peter Schilke Peter Schilke Peter Schilke Peter Schilke