Gravitational Stability of Fluids in a Phase Transition. Andreas Füglistaler. July 17, 2017

Transcription

1 Gravitational Stability of Fluids in a Phase Transition July 17, 2017 Füglistaler & Pfenniger 2015, 2016 and 2017 (in preparation)

2 Motivation Physics Simulations Conclusions Solid H2 in the ISM Gravitational Stability of Fluids in a Phase Transition Gravitational Instability Phase Transition Credit: TrekEarth Credit: ESA, HERSCHEL Solid H2 in the ISM

3 Visualization

4 Motivation Physics Simulations Conclusions Solid H2 in the ISM Gravitational Stability of Fluids in a Phase Transition Gravitational Instability Jeans instability (1902) Solid H2 in the ISM Phase Transition van der Waals (1910)

5 Formation of Why is it interesting? How does it happen? What happens?

6 Formation of Why is it interesting? How does it happen? What happens?

7 Dark Baryons Missing Baryons in Galaxies Baryons in the Universe: 0.16 in galaxies: Type Gas/Plasma Gas + Solid Substellar bodies Massive compact halo object (MACHOS) Name Warm-hot IGM (WHIM) Molecular hydrogen H 2 + substellar bodies Snowballs Comets Planetoids Brown dwarfs Black holes

8 Motivation Physics Simulations Conclusions Star Formation Star Formation (In)Efficiency Milky Way SFRmax 200 M /yr SFRobs = 1 2 M /yr 2 Orders of magnitude lower Quasistatic model Angular momentum transport Feedback effects Formation of substellar bodies? Credit: APOD: Hubble, NASA, ESA Solid H2 in the ISM

9 Formation of Why is it interesting? How does it happen? Physical property of H 2 Missing baryons in galaxies Star formation inefficiency What happens?

10 Formation of Why is it interesting? How does it happen? Physical property of H 2 Missing baryons in galaxies Star formation inefficiency What happens?

11 van der Waals Fluid van der Waals P r = 8T r 3 n r 1 3n2 r Lennard-Jones Potential Φ LJ (r) = 4 ε ( ) rσ 12 rσ 6 m T c = ε k, n c = 0.316σ 3, P c = ε B k B σ 3 Virial Theorem ( P/ ρ) s = γ ( P/ ρ) T 0 = 2E kin + 12E }{{} r +6E a + E }{{ G } >0 <0

12 Gravitational Stability Jeans Criterion δρ exp[i(kx ωt)] ( ) P ω 2 = k 2 4πGρ ρ 0 s ω 2 < 0 Exponential growth Gaseous Fluid (Ideal Gas) 4πGρ 0 > 0 ( ) P ρ > 0 s Stability depends on k Phase Transition 4πGρ 0 > 0 ( P/ ρ) s = γ ( P/ ρ) T 0 ω < 0 k Fluid unstable at any scale

13 Collapsing Geometry Sheetlike Collapse Fastest collapsing geometry Remains optically thin Temperature increase 2.1 T < T c T 0 < T c /2.1 15K

14 Formation of Why is it interesting? Physical property of H 2 Missing baryons in galaxies Star formation inefficiency How does it happen? Plane-parallel collapse Phase transition Gravity What happens?

15 Formation of Why is it interesting? Physical property of H 2 Missing baryons in galaxies Star formation inefficiency How does it happen? Plane-parallel collapse Phase transition Gravity What happens?

16 Super-Molecules H 2 Number of Particles Today s limit: N max UniGeneva: 10 9 m H2 2u = kg N max m H kg = 1 picogram Astronomical Bodies M Dust grain kg ( 1 µm) M 67P/C G kg (Rosetta) M kg Virial Invariance η Number of molecules per super-molecule Invariance of E kin and E pot Constraint m S = η m M v 2 S = v 2 M ε S = η ε M σ S = 3 ησ M F G (r) F LJ (r) for r 5σ S m S,max = M Today s limit: M max M

17 Motivation Physics Simulations Conclusions Formation of Substellar Bodies in Cold Conditions Gravitational Stability of Fluids in a Phase Transition Phase Transition Gravitational Instability + Formation of gaseous bodies Solid H2 in the ISM Formation of small solid grains

18 Formation of Substellar Bodies in Cold Conditions Gravitational Stability of Fluids in a Phase Transition Gravity+Phase Transition Formation of solid substellar bodies

19 Planetoid Densities Rocky H 2 planetoid Gaseous He planetoid Laboratory condensed matter

20 Solid Mass Fraction Phase transition is faster than gravitational collapse M solid /M tot remains constant when adding gravity Mass Fraction Conversion Phase Diagram

21 Formation of Why is it interesting? Physical property of H 2 Missing baryons in galaxies Star formation inefficiency How does it happen? Plane-parallel collapse Phase transition Gravity What happens? Fluid phase transition gravity grains solid body

22 Gravitational Stability of Fluids in a Phase Transition T 15K + Plane-Parallel Collapse H 2 Phase Transition H 2 Phase Transition + Gravity Solid Substellar H 2 Bodies