Stellar structure and evolution Pierre Hily-Blant 2017-18 April - PowerPoint PPT Presentation

Stellar structure and evolution Pierre Hily-Blant 2017-18 April 29, 2018 IPAG pierre.hily-blant@univ-grenoble-alpes.fr, OSUG-D/306

9 Star formation 9.1. Introduction 9 – Star formation Introduction Collapse of spherical gaseous configurations Stability of isothermal self-gravitating spheres Numerical simulations Formation of the protostar Current view of star formation Initial mass function Open questions

9 Star formation 9.1. Introduction 3 On-going star formation: evidences • Star formation is an on-going process in the MW • Various evidences • We see star forming: young stellar objects (YSOs) ∼ 1 Myr • Open clusters and associations remain visible despite differential rotation which would bring them apart by ∼ 10 kpc in 10 Gyr); • We see massive stars on the main sequence: lifetime on the MS is τ MS ∼ 10 10 M / L yr, and L ∝ M α with α = 3 − 4 . 5. For M = 10 M ⊙ , τ MS = 3Myr ≪ age of the Galaxy;

9 Star formation 9.1. Introduction 4 Star formation All stars form in molecular clouds (here: Taurus molecular cloud)

9 Star formation 9.1. Introduction 5 Molecular gas in the Milky Way +30° Beam +30° +20° +20° +10° +10° Galactic Latitude 0° 0° −1 0° −1 0° − 20° − 20° −3 0° −3 0° 180° 170° 160° 150° 140° 130° 120° 110° 100° 90° 80° 70° 60° 50° 40° 30° 20° 10° 0° 350° 340° 330° 320° 310° 300° 290° 280° 270° 260° 250° 240° 230° 220° 210° 200° 190° 180° Galactic Longitude Ursa Major Polaris Flare Ophiuchus +20° Cam Cepheus Maddalena’s Galactic Latitude Flare Cloud CTA-1 Hercules Aquila Lupus F IG . 2.–Velocity-integrated CO map of the Milky Way. The angular resolution is 9´ over most S147 S212 G r i f t Rift Coal Mon Gem S147 of the map, including the entire Galactic plane, but is lower (15´ or 30´) in some regions out S235 e a t R Sack Vela OB1 CMa OB1 OB1 of the plane (see Fig. 1 & Table 1). The sensitivity varies somewhat from region to region, 0° W3 NGC7538 Cas A OB7 Cyg X Cyg W51 W44 Galactic G317 − 4 Carina Rosette λ O r since each component survey was integrated individually using moment masking or clipping Center Nebula Gum Mon R2 i 0.0 0.5 1.0 1.5 2.0 in order to display all statistically significant emission but little noise (see §2.2). A dotted line Lacerta Nebula S. Ori ∫ marks the sampling boundaries, given in more detail in Fig. 1. − 20° Per OB2 Aquila R CrA Chamaeleon Filament R i g n log T mb d v (K km s −1 ) Tau-Per-Aur South Ori A & B Complex Pegasus Orion Complex 180° 120° 60° 0° 300° 240° 180° Galactic Longitude Dame et al. (2001)

9 Star formation 9.1. Introduction 6 Molecular clouds distribution Koda+09 M51 at 160 pc resolution; Molecular clouds are distributed along

9 Star formation 9.1. Introduction 7 Milky Way: Overview • Mass of galactic disk + bulge: 6 × 10 10 M ⊙ • Mass is dominated by dark matter (90%) • Baryonic mass is essentially in the form of gas • Dust is 1% in mass • 10 11 stars in the MW

9 Star formation 9.1. Introduction 8 Molecular gas in the Milky Way Stars form in molecular clouds

9 Star formation 9.1. Introduction 9 Star formation • Overall: good understanding • Outstanding issues remain: Star formation is one of the main open question in astrophysics • What determines the rate of star formation ? • How are the kinetic energy and angular momentum removed from the collapsing cloud ? • What determines the initial mass function ? • How did the first stars formed in the Universe ?

9 Star formation 9.1. Introduction 10 Observations of star formation

9 Star formation 9.1. Introduction 11 Prestellar core Pre-stellar cores (here Barnard 68)

9 Star formation 9.1. Introduction 12 Protostar • Class 0 protostar: L1527 • Located in the Taurus cloud (140 pc) • Very early stage of collapse • Age ∼ 0.3 Myr • Mass of the protostar: 0.19 ± 0.04 M ⊙ • Protostar/envelope mass ratio ∼ 0.2 • Luminosity: accretion (6.6 × 10 − 7 M ⊙ /yr)

9 Star formation 9.1. Introduction 13 Protostar

9 Star formation 9.1. Introduction 14 Protostar

9 Star formation 9.1. Introduction 15 Protostar

9 Star formation 9.1. Introduction 16 Outflows and Herbig-Haros objects HH212: molecular hydrogen

9 Star formation 9.1. Introduction 17 Outflows and Herbig-Haros objects HH212

9 Star formation 9.1. Introduction 18 TTauri stars and circumstellar disks HL Tau protoplanetary disk with ALMA

9 Star formation 9.1. Introduction 19 Primitive solar system Comet McNaught

9 Star formation 9.1. Introduction 20 Primitive solar system Comet 67P/C-P with ESA/Rosetta

9 Star formation 9.1. Introduction 21 Exoplanetary systems The Trappist-1 system with NASA/Spitzer

9 Star formation 9.1. Introduction 22 Exoplanetary systems

9 Star formation 9.1. Introduction 23 From clouds to stars to planets • All stars form in molecular clouds • Molecular clouds: n ∼ 10 3 cm − 3 , T ∼ 30 K, ∼ 1-10 Myr ? • Prestellar cores: n ∼ 10 4 cm − 3 , T ∼ 10 K, ∼ 1 Myr ? • Protostars: n > 10 5 cm − 3 , short phase, ∼ few 0.1 Myr ? • Protoplanetary disks: ∼ 10 Myr before gas dissipation • Planet formation: rapid (less than few 100 Myr) • Life: less than 1 Gyr ? (oldest microfossils: at least 3.7 Gyr old)

9.2. Collapse of spherical gaseous 9 Star formation configurations 9 – Star formation Introduction Collapse of spherical gaseous configurations Stability of isothermal self-gravitating spheres Numerical simulations Formation of the protostar Current view of star formation Initial mass function Open questions

9.2. Collapse of spherical gaseous 9 Star formation configurations 25 Jeans analysis From molecular clouds to protostars • Uniform density • Jeans criterium: a cloud of mass M > M J is unstable � 3 / 2 � � 1 / 2 � 3 kT 3 M J = α G µ m a 4 πρ 0 • Jeans Length � 1 / 2 � 9 kT R J = 4 πα G µ m a ρ 0 • Jeans density � 3 3 � 3 kT ρ J = 4 π M 2 αµ m a G • Note: α = 3 / 5 for a spherical distribution

9.2. Collapse of spherical gaseous 9 Star formation configurations 26 Jeans analysis M † R † n H T M R J J cm − 3 K M ⊙ pc msol pc 1.3 10 7 Diffuse WNM 1 8000 – – 400 > 10 4 GMC ( H 2 ) 50 30 30 400 3 3 × 10 3 Molecular clouds 500 25 10 100 0.9 10 4 Prestellar cores 10 few 0.1 5.5 0.1 • Values for spherical geometry and molecular gas • Note: observationally, prestellar cores have a typical size ∼ 0 . 1pc

9.2. Collapse of spherical gaseous 9 Star formation configurations 27 Fragmentation • Note: Jeans analysis does not include gas dynamics, no mag. pressure, no rotation, etc. • How do we form stars with mass much lower than that of the original cloud ? No definitive answer: fragmentation, competitive accretion. Fragmentation • Collapse if M > M J ; during collapse, ρ increases; regions of the cloud become Jeans-unstable; they collapse, separate (motions); etc...

9.2. Collapse of spherical gaseous 9 Star formation configurations General equations 28 Special case: Isothermal sphere • Prestellar cores: isothermal evolution towards protostar formation (efficient cooling by molecular line emission) • Pressure: P = nkT + aT 4 / 3; cold prestellar cores, radiative pressure is negligible • EOS: P = c 2 s ρ

9.2. Collapse of spherical gaseous 9 Star formation configurations General equations 29 Special case: Isothermal sphere • Self-gravitating sphere of an isothermal, perfect, gas • Start with dP / dr = − Gm ( r ) ρ ( r ) / r 2 and dm / dr = 4 π r 2 ρ ( r ) plus the EOS • Usual change of variable: • ρ = ρ c e − ψ • r = a ξ , a = ( kT / 4 π G µ m H ρ c ) 1 / 2 = c s / (4 π G ρ c ) 1 / 2 • Particular instance of the Lane-Emden equation for isothermal case: 1 d � ξ 2 d ψ � = e − ψ ξ 2 d ξ d ξ s / ( G 3 / 2 ρ 1 / 2 • Mass: (show that) M ( ξ ) = M 0 m ( ξ ) with M 0 = c 3 ) c √ and m ( ξ ) = ξ 2 ψ ′ ( ξ ) / 4 π

9.2. Collapse of spherical gaseous 9 Star formation configurations General equations 30 Singular isothermal sphere • Particular solution of the Lane-Emden equation: infinite central density c 2 s ρ ( r ) = 2 π Gr 2 • Equilibrium solutions: infinite extent, infinite mass !

9.2. Collapse of spherical gaseous 9 Star formation configurations General equations 31 Non-singular solutions • Boundary conditions: ψ = ψ ′ = 0 at ξ = 0 • Numerical integration (using RK4 scheme) • Two 1st order ODE: u = ψ , v = ξ 2 ψ ′

9.2. Collapse of spherical gaseous 9 Star formation configurations General equations 32 Non-singular solutions • Family of solutions (central density, n c , in cm − 3 ) • µ = 2 . 33 (fully molecular); T = 10 K

9.3. Stability of isothermal self-gravitating 9 Star formation spheres 9 – Star formation Introduction Collapse of spherical gaseous configurations Stability of isothermal self-gravitating spheres Numerical simulations Formation of the protostar Current view of star formation Initial mass function Open questions