The Role of Turbulence and Magnetic Fields for Star Formation - - PowerPoint PPT Presentation

Optical 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)

M51: The Whirlpool Galaxy

The Role of Turbulence and Magnetic Fields for Star Formation

Christoph Federrath

Cosmic Dust and Magnetism – Daejeon – 01 November 2018

Star Formation is inefficient

Federrath – Korea 2018

Turb+ Mag+ Jet/Outflow Feedback Turbulence

Movies available: http://www.mso.anu.edu.au/~chfeder/pubs/ineff_sf/ineff_sf.html

Star Formation is Inefficient

(Federrath 2015 MNRAS; 2018 Physics Today)

Turb+ Magnetic Fields Gravity

• nly

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Carina Nebula, NASA, ESA, N. Smith (University of California, Berkeley), and The Hubble Heritage Team (STScI/AURA), and NOAO/AURA/NSF

Turbulence Stars Feedback

Elmegreen & Scalo (2004) Mac Low & Klessen (2004) McKee & Ostriker (2007) Padoan et al. (2014)

Magnetic Fields

Turbulence driven by

• Shear
• Jets / Outflows
• Cloud-cloud collisions
• Winds / Ionization fronts
• Spiral-arm compression
• Supernova explosions
• Gravity / Accretion

Solenoidal Compressive

Dynamics (shear)

(Federrath & Klessen 2012; Federrath et al. 2017)

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Turbulence driving – solenoidal versus compressive

Solenoidal forcing Compressive forcing

Ñ×f = 0 Ñxf = 0

Ornstein-Uhlenbeck process (stochastic process with autocorrelation time) → forcing varies smoothly in space and time, following a well-defined random process

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Turbulence driving – solenoidal versus compressive

Compressive forcing produces stronger density enhancements Column Density

(Federrath 2013, MNRAS 436, 1245: Supersonic turbulence @ 40963 grid cells)

Df ~ 2.6 Df ~ 2.3

(see Federrath et al. 2009; Roman-Duval et al. 2010; Donovan-Meyer et al. 2013)

solenoidal forcing compressive forcing

Movies available: http://www.mso.anu.edu.au/~chfeder/pubs/supersonic/supersonic.html

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The density PDF → Star Formation

Density PDF

comp sol

Federrath et al. (2008, 2010); Price et al. (2011); Konstandin et al. (2012); Molina et al. (2012); Federrath & Banerjee (2015); Nolan et al. (2015)

b = 1/3 (sol) b = 1 (comp) log-normal:

Vazquez-Semadeni (1994); Padoan et al. (1997); Ostriker et al. (2001); Hopkins (2013)

(Federrath et al. 2010)

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The density PDF → Star Formation

Kainulainen, Federrath, Henning (2014, Science)

Active star formation No star formation

(Brunt, Federrath, Price 2010a,b)

2D → 3D conversion

A B A B No star forma*on Ac*ve star forma*on

• Log. density contrast s=ln(n/<n>)
• Log. density contrast s=ln(n/<n>)

log PDF(s) log PDF(s) Gas density n [par=cles/cm3] Gas density n [par=cles/cm3] Small dense-gas frac=on

low density medium density low density medium density

Large dense-gas frac=on

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Statistical Theory for the Star Formation Rate:

Hennebelle & Chabrier (2011) : “multi-freefall model”

mass fraction freefall time scrit SFR ~ Mass/time

The Star Formation Rate

Federrath & Klessen (2012)

Federrath – Korea 2018

Statistical Theory for the Star Formation Rate:

Hennebelle & Chabrier (2011) : “multi-freefall model”

mass fraction freefall time SFR ~ Mass/time

The Star Formation Rate

Federrath & Klessen (2012)

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Statistical Theory for the Star Formation Rate:

Hennebelle & Chabrier (2011) : “multi-freefall model”

mass fraction freefall time

(Krumholz & McKee 2005, Padoan & Nordlund 2011) (e.g., Federrath et al. 2008)

2 Ekin/Egrav forcing Mach number SFR ~ Mass/time

From sonic and Jeans scales:

The Star Formation Rate

Federrath & Klessen (2012)

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2 Ekin/Egrav forcing Mach number (solenoidal forcing)

Federrath & Klessen (2012)

Density PDF → Star Formation Rate

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2 Ekin/Egrav forcing Mach number (compressive forcing)

Federrath & Klessen (2012)

Density PDF → Star Formation Rate

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Solenoidal Driving (b=1/3) Compressive Driving (b=1)

Numerical experiment for Mach 10 and αvir ~ 1

SFRff (simulation) = 0.14 SFRff (theory) = 0.15 SFRff (simulation) = 2.8 SFRff (theory) = 2.3 x20 x15 Theory and Simulation agree well.

Federrath & Klessen (2012)

Density PDF → Star Formation Rate

Movies available: http://www.mso.anu.edu.au/~chfeder/pubs/sfr/sfr.html

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Statistical Theory for the Star Formation Rate:

2 Ekin/Egrav forcing Mach number

The Star Formation Rate – Magnetic fields

mass fraction freefall time MAGNETIC FIELD: SFR ~ Mass/time plasma β=Pth/Pmag

(Padoan & Nordlund 2011; Molina et al. 2012) Federrath & Klessen (2012)

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The Star Formation Rate – Magnetic fields

SFRff (simulation) = 0.46 SFRff (theory) = 0.45 SFRff (simulation) = 0.29 SFRff (theory) = 0.18 x0.63 x0.40 Magnetic field reduces SFR and fragmentation (by factor 2) → IMF B=0 (MA=∞, β = ∞) B=3μG (MA=2.7, β = 0.2)

Federrath & Klessen (2012)

Numerical experiment for Mach 10 and αvir ~ 1

Movies available: http://www.mso.anu.edu.au/~chfeder/pubs/sfr/sfr.html

Federrath – Korea 2018

The Star Formation Rate – Magnetic fields

SFRff (simulation) = 0.46 SFRff (theory) = 0.45 SFRff (simulation) = 0.29 SFRff (theory) = 0.18 x0.63 x0.40 Magnetic field reduces SFR and fragmentation (by factor 2) → IMF B=0 (MA=∞, β = ∞) B=3μG (MA=2.7, β = 0.2)

Federrath & Klessen (2012)

Numerical experiment for Mach 10 and αvir ~ 1

Movies available: http://www.mso.anu.edu.au/~chfeder/pubs/sfr/sfr.html

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Hull et al. (2017)

Serpens SMM1

The role of magnetic field structure

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The role of magnetic field structure

Cox et al. (2018)

ALMA cores and dust polarization in Perseus

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Lee et al. (2018)

Jet/Outflow Feedback

SO shows outflow in HH211-mms core in Perseus → ALMA to zoom in on details of accretion disk and outflow launching

See also Zhang et al. (2018)

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Jet Feedback in Binary Star Formation

Kuruwita et al. (2017)

Jet structure and power depend on binary separation → different star masses → Challenge for understanding the formation of solar mass stars

Movies available: https://www.mso.anu.edu.au/~chfeder/pubs/binary_jets/binary_jets.html

Single Star Tight Binary Wide Binary

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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

Kuruwita & Federrath (2018, submitted)

Turbulence makes bigger discs → relevant for planet formation Magnetic field structure is key for outflow/jet launching

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Alves et al. (2007); Andre et al (2010)

Implications for the stellar initial mass function (IMF)

Efficiency ~ 1/3

Outflow feedback reduces average star mass by factor ~ 3 → IMF!

(Federrath et al. 2014)

1/3

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The role of magnetic field structure

Gerrard et al. (2018, submitted)

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The role of magnetic field structure

Gerrard et al. (2018, submitted)

→ Need ordered magnetic field component for jet launching (Blandford & Payne 1982)

x (AU) z (AU)

2x10-17 2x10-16 2x10-15 2x10-14 2x10-13 2x10-12

Density (g cm-3)

1 star 1 star 3 stars

See also Hodapp & Chini (2018) on dual jet/outflow components launched in Serpens South

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The role of magnetic field structure

Gerrard et al. (2018, submitted)

→ Key role of magnetic field structure for star mass and fragmentation

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Turbulence

Leonardo da Vinci

▪ Reynolds numbers > 1000 ▪ Kinetic energy cascade E(k) ~ k-5/3 ~ k-1.67

incompressible

Mach < 1

Kolmogorov (1941)

V ~ L1/3

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Interstellar Turbulence – scaling

BUT: Larson (1981) relation: E(k)~k-1.8–2.0

(see also Heyer & Brunt 2004; Roman-Duval et al. 2011)

Federrath et al. (2010); see also Kritsuk et al. (2007)

Supersonic, compressible turbulence has steeper E(k)~k-1.9 than Kolmogorov (E~k-5/3)

(Larson 1981; Heyer & Brunt 2004)

cs~0.2 km/s

V ~ L0.5

→ E(k) ~ k-2

V [km/s] L [pc]

Observation Simulation

k2 E(k) k

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▪ Reynolds numbers > 1000 ▪ Kinetic energy cascade

Interstellar Turbulence

E(k) ~ k -2

shock-dominated

Mach > 1 E(k) ~ k -5/3

subsonic

Mach < 1

Kolmogorov (1941)

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▪ Reynolds numbers > 1000 ▪ Kinetic energy cascade

Interstellar Turbulence

E(k) ~ k -2 E(k) ~ k -5/3

molecular clouds (100 pc) protostellar cores,filaments (0.1pc) protostars, discs and planets (AU scales)

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Towards resolving the sonic scale: Turbulence @ 100483

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Structure function è sonic scale

(Federrath et al., submitted)

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Structure function è sonic scale

(Federrath et al., submitted)

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Structure function è sonic scale

(Federrath et al., submitted)

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Sonic scale: implications

Sonic scale → Filament width distribution:

(Arzoumanian et al. 2011)

(Federrath et al., submitted)

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Sonic scale: implications

Sonic scale → Critical density for star formation:

→ Critical density for star formation

• n 26 times larger scales than previously thought

(Krumholz & McKee 2005; Federrath & Klessen 2012)

→ By measuring the sonic scale directly, we find:

(Turbulence = Gravity)

(Federrath et al., submitted)

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Conclusions and next challenges

3) Filaments and cores may form by turbulent MHD shocks at the sonic scale 2) Observations and simulations are beginning to reveal the complex magnetic field structures in dense star-forming cores → Jets 1) Star Formation is inefficient →

Only the combination of Turbulence + Magnetic Fields + Feedback gives realistic (observed) SFRs

The End.

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