The Role of Turbulence and Magnetic Fields for Star Formation Christoph Federrath Cosmic Dust and Magnetism – Daejeon – 01 November 2018 Optical M51: The Whirlpool Galaxy Infrared Infrared: NASA, ESA, M. Regan & B. Whitmore (STScI), & R. Chandar (U. Toledo);Optical: NASA, ESA, S. Beckwith (STScI), & the Hubble Heritage Team (STScI/AURA)
Star Formation is inefficient Federrath – Korea 2018
Star Formation is Inefficient (Federrath 2015 MNRAS; 2018 Physics Today) Movies available: http://www.mso.anu.edu.au/~chfeder/pubs/ineff_sf/ineff_sf.html Gravity Turbulence only Turb+ Turb+ Mag+ Magnetic Jet/Outflow Fields Feedback Federrath – Korea 2018
Turbulence Stars Feedback (Federrath & Klessen 2012; Federrath et al. 2017) Magnetic Fields Turbulence driven by Dynamics - Shear Solenoidal - Jets / Outflows (shear) - Cloud-cloud collisions - Winds / Ionization fronts - Spiral-arm compression Elmegreen & Scalo (2004) - Supernova explosions Compressive Mac Low & Klessen (2004) - Gravity / Accretion McKee & Ostriker (2007) Padoan et al. (2014) Carina Nebula, NASA, ESA, N. Smith (University of California, Berkeley), and The Hubble Heritage Team (STScI/AURA), and NOAO/AURA/NSF Federrath – Korea 2018
Turbulence driving – solenoidal versus compressive Ornstein-Uhlenbeck process (stochastic process with autocorrelation time) → forcing varies smoothly in space and time, following a well-defined random process Solenoidal forcing Compressive forcing Ñ× f = 0 Ñ x f = 0 Federrath – Korea 2018
Turbulence driving – solenoidal versus compressive Movies available: http://www.mso.anu.edu.au/~chfeder/pubs/supersonic/supersonic.html Column Density solenoidal forcing compressive forcing D f ~ 2.6 D f ~ 2.3 (see Federrath et al. 2009; Roman-Duval et al. 2010; Donovan-Meyer et al. 2013) Compressive forcing produces stronger density enhancements (Federrath 2013, MNRAS 436, 1245: Supersonic turbulence @ 4096 3 grid cells) Federrath – Korea 2018
The density PDF → Star Formation Density PDF log-normal: (Federrath et al. 2010) sol comp Vazquez-Semadeni (1994); Padoan et al. (1997); Ostriker et al. (2001); Hopkins (2013) b = 1/3 (sol) b = 1 (comp) Federrath et al. (2008, 2010); Price et al. (2011); Konstandin et al. (2012); Molina et al. (2012); Federrath & Banerjee (2015); Nolan et al. (2015) Federrath – Korea 2018
The density PDF → Star Formation No star formation Active star formation Gas density n [par=cles/cm 3 ] Gas density n [par=cles/cm 3 ] A B A B Ac*ve star No star forma*on forma*on log PDF(s) log PDF(s) Large Small dense-gas dense - gas frac=on frac=on medium low medium low density density density density Log. density contrast s=ln(n/<n>) Log. density contrast s=ln(n/<n>) Kainulainen, Federrath, Henning (2014, Science ) 2D → 3D conversion (Brunt, Federrath, Price 2010a,b) Federrath – Korea 2018
The Star Formation Rate Statistical Theory for the Star Formation Rate: freefall mass SFR ~ Mass/time time fraction s crit Hennebelle & Chabrier (2011) : “multi-freefall model” Federrath & Klessen (2012) Federrath – Korea 2018
The Star Formation Rate Statistical Theory for the Star Formation Rate: freefall mass SFR ~ Mass/time time fraction Hennebelle & Chabrier (2011) : “multi-freefall model” Federrath & Klessen (2012) Federrath – Korea 2018
The Star Formation Rate Statistical Theory for the Star Formation Rate: freefall mass SFR ~ Mass/time time fraction From sonic and Jeans scales: Hennebelle & Chabrier (2011) : “multi-freefall model” (Krumholz & McKee 2005, Padoan & Nordlund 2011) (e.g., Federrath et al. 2008) 2 E kin /E grav forcing Mach number Federrath & Klessen (2012) Federrath – Korea 2018
Density PDF → Star Formation Rate 2 E kin /E grav forcing Mach number (solenoidal forcing) Federrath & Klessen (2012) Federrath – Korea 2018
Density PDF → Star Formation Rate 2 E kin /E grav forcing Mach number (compressive forcing) Federrath & Klessen (2012) Federrath – Korea 2018
Density PDF → Star Formation Rate Numerical experiment for Mach 10 and α vir ~ 1 Movies available: http://www.mso.anu.edu.au/~chfeder/pubs/sfr/sfr.html Solenoidal Driving (b=1/3) Compressive Driving (b=1) SFR ff (simulation) = 0.14 x 20 SFR ff (simulation) = 2.8 SFR ff (theory) = 0.15 x 15 SFR ff (theory) = 2.3 Theory and Simulation agree well. Federrath & Klessen (2012) Federrath – Korea 2018
The Star Formation Rate – Magnetic fields Statistical Theory for the Star Formation Rate: freefall mass SFR ~ Mass/time time fraction MAGNETIC FIELD: (Padoan & Nordlund 2011; Molina et al. 2012) 2 E kin /E grav forcing Mach number plasma β=P th /P mag Federrath & Klessen (2012) Federrath – Korea 2018
The Star Formation Rate – Magnetic fields Numerical experiment for Mach 10 and α vir ~ 1 Movies available: http://www.mso.anu.edu.au/~chfeder/pubs/sfr/sfr.html B =0 ( M A =∞, β = ∞) B =3μG ( M A =2.7, β = 0.2) SFR ff (simulation) = 0.46 x 0.63 SFR ff (simulation) = 0.29 SFR ff (theory) = 0.45 x 0.40 SFR ff (theory) = 0.18 Magnetic field reduces SFR and fragmentation (by factor 2) → IMF Federrath & Klessen (2012) Federrath – Korea 2018
The Star Formation Rate – Magnetic fields Numerical experiment for Mach 10 and α vir ~ 1 Movies available: http://www.mso.anu.edu.au/~chfeder/pubs/sfr/sfr.html B =0 ( M A =∞, β = ∞) B =3μG ( M A =2.7, β = 0.2) SFR ff (simulation) = 0.46 x 0.63 SFR ff (simulation) = 0.29 SFR ff (theory) = 0.45 x 0.40 SFR ff (theory) = 0.18 Magnetic field reduces SFR and fragmentation (by factor 2) → IMF Federrath & Klessen (2012) Federrath – Korea 2018
The role of magnetic field structure Serpens SMM1 Hull et al. (2017) Federrath – Korea 2018
The role of magnetic field structure ALMA cores and dust polarization in Perseus Cox et al. (2018) Federrath – Korea 2018
Jet/Outflow Feedback SO shows outflow in HH211-mms core in Perseus Lee et al. (2018) → ALMA to zoom in on details of accretion disk and outflow launching See also Zhang et al. (2018) Federrath – Korea 2018
Jet Feedback in Binary Star Formation Movies available: https://www.mso.anu.edu.au/~chfeder/pubs/binary_jets/binary_jets.html Wide Binary Single Star Tight Binary Jet structure and power depend on binary separation → different star masses → Challenge for understanding the formation of solar mass stars Kuruwita et al. (2017) Federrath – Korea 2018
Built-up of discs No Turbulence Low Turbulence Normal Turbulence Movies available: http://www.mso.anu.edu.au/~chfeder/pubs/binary_discs/binary_discs_xy.mp4 Turbulence makes bigger discs → relevant for planet formation Magnetic field structure is key for outflow/jet launching Kuruwita & Federrath (2018, submitted) Federrath – Korea 2018
Implications for the stellar initial mass function (IMF) Efficiency ~ 1/3 1/3 Alves et al. (2007); Andre et al (2010) Outflow feedback reduces average star mass by factor ~ 3 → IMF! (Federrath et al. 2014) Federrath – Korea 2018
The role of magnetic field structure Gerrard et al. (2018, submitted) Federrath – Korea 2018
The role of magnetic field structure Density (g cm -3 ) 2x10 -17 2x10 -16 2x10 -15 2x10 -14 2x10 -13 2x10 -12 z (AU) 1 star 1 star 3 stars x (AU) Gerrard et al. (2018, submitted) See also Hodapp & Chini (2018) on dual jet/outflow components launched in Serpens South → Need ordered magnetic field component for jet launching (Blandford & Payne 1982) Federrath – Korea 2018
The role of magnetic field structure → Key role of magnetic field structure for star mass and fragmentation Gerrard et al. (2018, submitted) Federrath – Korea 2018
Turbulence ▪ Reynolds numbers > 1000 ▪ Kinetic energy cascade Leonardo da Vinci E(k) ~ k -5/3 ~ k -1.67 incompressible V ~ L 1/3 Mach < 1 Kolmogorov (1941) Federrath – Korea 2018
Interstellar Turbulence – scaling BUT: Larson (1981) relation: E(k)~k -1.8–2.0 (see also Heyer & Brunt 2004; Roman-Duval et al. 2011) Observation Simulation (Larson 1981; Heyer & Brunt 2004) V ~ L 0.5 → E(k) ~ k -2 V [km/s] k 2 E(k) c s ~0.2 km/s L [pc] k Supersonic, compressible turbulence has steeper E(k)~k -1.9 than Kolmogorov (E~k -5/3 ) Federrath et al. (2010); see also Kritsuk et al. (2007) Federrath – Korea 2018
Interstellar Turbulence ▪ Reynolds numbers > 1000 ▪ Kinetic energy cascade E(k) ~ k -2 E(k) ~ k -5/3 shock-dominated subsonic Mach > 1 Mach < 1 Kolmogorov (1941) Federrath – Korea 2018
Interstellar Turbulence ▪ Reynolds numbers > 1000 ▪ Kinetic energy cascade E(k) ~ k -2 E(k) ~ k -5/3 protostars, discs molecular protostellar and planets clouds cores,filaments (AU scales) (100 pc) (0.1pc) Federrath – Korea 2018
Towards resolving the sonic scale: Turbulence @ 10048 3 Federrath – Korea 2018
Structure function è sonic scale (Federrath et al., submitted) Federrath – Korea 2018
Structure function è sonic scale (Federrath et al., submitted) Federrath – Korea 2018
Structure function è sonic scale (Federrath et al., submitted) Federrath – Korea 2018
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