Formation of Brown Dwarfs. PHY 688, Lecture 30 Apr 15, 2009

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1 Formation of Brown Dwarfs PHY 688, Lecture 30 Apr 15, 2009

2 Course administration final presentations reminder Outline see me for paper recommendations 2 3 weeks before talk: Apr 27 May 1 talks class re-scheduling reminder no class Apr 17, Fri (ASNY mtg) attend Apr 15 (Wed) talk by Eric Jensen, 1pm ESS 450 no class Apr 24, Fri (Astro2010 Town Hall mtg) two 1.5-hour classes on Apr 27, 29 (Mon, Wed): 10:40 12:00pm Review of previous lecture substellar populations: planets, brown dwarfs Formation of brown dwarfs empirical evidence theoretical scenarios Apr 15, 2009 PHY 688, Lecture 30 2

3 Previously in PHY 688 Apr 15, 2009 PHY 688, Lecture 30 3

4 Planet Mass and Period Distribution dn = CM α P β dlnm dlnp α = 0.31 ± 0.2 β = 0.26 ± 0.1 N(M,P) cumulative number of planets with masses up to M and periods up to P i.e., dn/dm M α 1 ; dn/dp P β 1 (Cummings et al. 2008) Apr 15, 2009 PHY 688, Lecture 30 4

5 Planet Mass and Period Distribution dn = CM α P β dlnm dlnp α = 0.31 ± 0.2 β = 0.26 ± 0.1 N(M,P) cumulative number of planets with masses up to M and periods up to P i.e., dn/dm M α 1 ; dn/dp P β 1 deficit of gas giant planets in day periods (Cummings et al. 2008) Apr 15, 2009 PHY 688, Lecture 30 5

6 Exoplanet Frequency statistics and extrapolations are for Sun-like (spectral type FGK; ~1 M Sun ) stars M dwarfs (<0.5 M Sun ) are 5 10 times less likely to have M sin i = M Jup planets in P < 2000 days Apr 15, 2009 PHY 688, Lecture 30 6 (Cummings et al. 2008)

7 Precision Radial Velocity Planets general trends: minimum mass distribution semi-major axis distribution eccentricity vs. semimajor axis Apr 15, 2009 PHY 688, Lecture 30 7 (Marcy et al. 2008)

8 Precision Radial Velocity Planets general trends: minimum mass distribution semi-major axis distribution eccentricity vs. semimajor axis host mass distribution Apr 15, 2009 PHY 688, Lecture 30 8 (Marcy et al. 2008)

9 Precision Radial Velocity Planets general trends: minimum mass distribution semi-major axis distribution eccentricity vs. semimajor axis host mass distribution host metallicity dependence (Santos et al. 2004; Valenti & Fischer 2008) Apr 15, 2009 PHY 688, Lecture 30 9

10 Low-mass Star Formation e.g., Taurus molecular cloud nearest star-forming region 1 Myr age 140 pc away 50 pc across brow dwarfs: SpT > M6 red crosses stars: SpT M6 blue circles formation of isolated brown dwarfs and stars is co-spatial (Luhman et al. 2007) Apr 15, 2009 PHY 688, Lecture 30 10

11 The (Sub)stellar Initial Mass Function (~1 Myr) (~2 Myr) (~1 Myr) (~1 Myr) The IMF is approximately consistent among various star-forming regions (Luhman et al. 2007) Apr 15, 2009 PHY 688, Lecture 30 11

12 The Universal Mass Function (traced by solid points in figure to the right) ξ(m) = dn/dm m α α = 0.3 ± m/m Sun < 0.08 α = 1.3 ± m/m Sun < 0.50 α = 2.3 ± m/m Sun BD: brown dwarfs MD/KD: M/K dwarfs IMS: intermediate-mass stars, etc (Kroupa 2002; Kroupa & Bouvier 2003) Apr 15, 2009 PHY 688, Lecture 30 12

13 Binaries: Separation Increases with Total Mass (Burgasser et al. 2007) Apr 15, 2009 PHY 688, Lecture 30 13

14 Binaries: Period Distribution of FGK Stars log-normal % # log P # log P f (logp) "exp' 2 & ' 2$ log P ( ) 2 ( * ) * AU logp = $ log P = 2.3 (P in days) (Duquennoy & Mayor 1991) Apr 15, 2009 PHY 688, Lecture 30 14

15 (Sub)stellar Companions: Mass Function and the R.V. Brown Dwarf Desert P < 8 yr (a < 4 AU) planets 10 15% 15% brown dwarfs <0.5% stars ~22% (Mazeh et al. 2003) Apr 15, 2009 PHY 688, Lecture 30 15

16 Binaries: Period Distribution log-normal AU r.v. brown dwarf desert partly due to radial velocity ~0.5% BDs direct imaging ~3% BDs fewer binaries with short periods fewer low-mass ratio (q<0.1) systems (Duquennoy & Mayor 1991) Apr 15, 2009 PHY 688, Lecture 30 16

17 Course administration final presentations reminder Outline see me for paper recommendations 2 3 weeks before talk: Apr 27 May 1 talks class re-scheduling reminder no class Apr 17, Fri (ASNY mtg) attend Apr 15 (Wed) talk by Eric Jensen, 1pm ESS 450 no class Apr 24, Fri (Astro2010 Town Hall mtg) two 1.5-hour classes on Apr 27, 29 (Mon, Wed): 10:40 12:00pm Review of previous lecture substellar populations: planets, brown dwarfs Formation of brown dwarfs empirical evidence theoretical scenarios Apr 15, 2009 PHY 688, Lecture 30 17

18 Brown Dwarfs Form Like H-Burning Low-Mass Stars statistical properties of brown dwarfs form a continuum with those of low-mass stars homogeneously mixed in star-forming regions Apr 15, 2009 PHY 688, Lecture 30 18

19 Stars and Brown Dwarfs Are Homogeneously Mixed e.g., Taurus molecular cloud nearest star-forming region 1 Myr age 140 pc away 50 pc across brow dwarfs: SpT > M6 red crosses stars: SpT M6 blue circles formation of isolated brown dwarfs and stars is co-spatial star and brown dwarf spatial kinematics are indistinguishable RV = 15.7 ± 0.9 km/s for BDs in Chamaeleon I (~2 Myr old) RV = 14.7 ± 1.3 km/s for stars (Luhman et al. 2007) Apr 15, 2009 PHY 688, Lecture 30 19

20 Brown Dwarfs Form Like H-Burning Low-Mass Stars statistical properties of brown dwarfs form a continuum with those of low-mass stars homogeneously mixed in star-forming regions initial mass function (IMF) continuity Apr 15, 2009 PHY 688, Lecture 30 20

21 IMF Is Continuous across Substellar Boundary (~1 Myr) (~2 Myr) (~1 Myr) (~1 Myr) (Luhman et al. 2007) Apr 15, 2009 PHY 688, Lecture 30 21

22 Brown Dwarfs Form Like H-Burning Low-Mass Stars statistical properties of brown dwarfs form a continuum with those of low-mass stars homogeneously mixed in star-forming regions initial mass function (IMF) continuity continuity in binary properties Apr 15, 2009 PHY 688, Lecture 30 22

23 Binaries Separations Vary Gradually across Substellar Boundary (Burgasser et al. 2007) Apr 15, 2009 PHY 688, Lecture 30 23

24 (Sub)stellar Companions: Mass Function and the R.V. Brown Dwarf Desert P < 8 yr (a < 4 AU) planets 10 15% 15% brown dwarfs <0.5% stars ~22% (Mazeh et al. 2003) Apr 15, 2009 PHY 688, Lecture 30 24

25 Companion Mass Function Is Continuous across Substellar Boundary 100-star Palomar AO survey (~1 M primaries) CMF: a = AU field MF (Chabrier 2003) dn / dm M 0.4 brown dwarfs ~3% (Kouwenhoven et al. 2005; Metchev & Hillenbrand 2009) Apr 15, 2009 PHY 688, Lecture 30 25

26 Brown Dwarfs Form Like H-Burning Low-Mass Stars statistical properties of brown dwarfs form a continuum with those of low-mass stars homogeneously mixed in star-forming regions initial mass function (IMF) continuity continuity in binary properties disks, accretion, and outflows Apr 15, 2009 PHY 688, Lecture 30 26

27 Disk Accretion Rates Are Continuous across Substellar Boundary (Muzerolle et al. 2005) Apr 15, 2009 PHY 688, Lecture 30 27

28 Brown Dwarfs Form Like H-Burning Low-Mass Stars statistical properties of brown dwarfs form a continuum with those of low-mass stars homogeneously mixed in star-forming regions initial mass function (IMF) continuity continuity in binary properties disks, accretion, and outflows rotation and x-rays Apr 15, 2009 PHY 688, Lecture 30 28

29 X-ray Activity Is Continuous across substellar boundary (Preibisch et al. 2005) Apr 15, 2009 PHY 688, Lecture 30 29

30 Brown Dwarfs Form Like H-Burning Low-Mass Stars statistical properties of brown dwarfs form a continuum with those of low-mass stars homogeneously mixed in star-forming regions initial mass function (IMF) continuity continuity in binary properties disks, accretion, and outflows rotation and x-rays A single formation mechanism is likely responsible for ~ M Sun stars upper limit set by radiation pressure lower limit set by gas opacity possible overlap with planetary mass range (<0.015 M Sun ) Apr 15, 2009 PHY 688, Lecture 30 30

31 ! From Lecture 6: Star Formation Occurs in Molecular Clouds Jeans mass minimum mass / density for gravitational collapse collapse occurs on free-fall (dynamical) time-scale Apr 15, 2009 PHY 688, Lecture 30 31! $ M J = " 5 6 c s ' & % 36G 3 ) #( 1 2 $ c * (2M Sun ) s ' & ) % 0.2kms +1 ( or # J, " 5 c s 6 36G 3 M J 2 t ff " # R 2 GM 3 sound speed $ n ' & ) % 10 3 cm +3 ( ( ) 3 2 ( ) " 35min & $ 1 2 ( ' ) + g cm %3 * +1 2 %1 2

32 Theories of Gravitational Collapse and Fragmentation 3-D collapse and hierarchical fragmentation isothermal collapse of optically thin cloud ρ J increases parts of the cloud start collapsing independently (fragmentation) fragmentation continues until heat from collapsing fragments can no longer be radiated away because of high rate of collapse or high (>1) optical depth: the opacity limit of fragmentation 2-D one-shot fragmentation of shock-compressed layers star formation occurs where turbulent flows collide produce a shockcompressed layer or filament filaments fragment directly into pre-stellar cores with masses down to opacity limit fragmentation of a circumstellar disk gravitationally unstable (massive) disk fragments fragments rapidly cool and loose angular momentum, thus forming pre-stellar cores Apr 15, 2009 PHY 688, Lecture 30 32

33 Thermodynamics of Collapse and Fragmentation collapse occurs if M > M J or ρ > ρ J for fragment to continue collapsing, it must radiate away PdV heat efficiently medium must be optically thin luminosity > heat maximum critical density ρ crit beyond which medium becomes optically thick i.e., need ρ J < ρ < ρ crit minimum collapsing mass M min has ρ J ~ ρ crit at the opacity limit M min ~ M Sun ~ 3M Jup Apr 15, 2009 PHY 688, Lecture 30 33

34 Problems with 3-D Fragmentation no conclusive evidence that it operates in nature not seen in numerical simulations proto-fragments collapse more slowly than larger structure because of being less Jeans unstable likely to merge with other fragments before condensation becomes nonlinear proto-fragments increase their mass by a large factor through accretion can not form low-mass stars individual fragments will be back-warmed by ambient radiation field from other cooling fragments increases Jeans mass, so again can not form low-mass stars Apr 15, 2009 PHY 688, Lecture 30 34

35 2-D One-Shot Fragmentation of Shock-Compressed Layers 2-D fragment assembly motions are within plane of compressed layer one-shot not hierarchical fastest-growing fragments become Jeans unstable no larger structure that is even less stable against Jeans collapse hence, unlike in 3-D hierarchical fragmentation, fragments do not merge condensation in a layer is very fast limited accretion no back-warming from ambient fragments, since none exist outside of 2-D layer low-mass star formation pathways are preserved avoids all problems of 3-D fragmentation Apr 15, 2009 PHY 688, Lecture 30 35

36 Fragmentation of a Circumstellar Disk fragmentation occurs in disks with sufficiently large surface density (Toomre instability) fragmentation must occur on dynamical time scale, or spiral arms are formed that dissolve the over-density two critical conditions then need to be met to condense fragment into a pre-stellar core: fragment needs to quickly radiate away thermal energy from compression also on dynamical time scale (~ days years) angular momentum needs to be efficiently removed by gravitational torques in the disk potentially a viable mechanism for forming low-mass stars and brown dwarfs in disks around massive stars Apr 15, 2009 PHY 688, Lecture 30 36

37 Numerical Simulations of Star Formation Apr 15, 2009 PHY 688, Lecture 30 37

38 Star Formation: Low vs. High Initial Density Apr 15, 2009 PHY 688, Lecture 30 38

39 Star Formation: without vs. with Radiative Feedback Apr 15, 2009 PHY 688, Lecture 30 39

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