# Gravitational collapse of gas

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1 Gravitational collapse of gas Assume a gas cloud of mass M and diameter D Sound speed for ideal gas is c s = γ P ρ = γ nkt ρ = γ kt m Time for sound wave to cross the cloud t sound = D == D m c s γ kt 1 2 Time for free-fall collapse is t ff = 1 Gρ Gravity beats pressure support when t ff < t sound

2 Gravitational collapse of gas Critical cloud size is then t ff = t sound 1 Gρ = D m γ kt 1 2 This is the Jeans length λ J = γ kt mgρ 1 2 Associated Jeans mass is M J = 4 3 π λ J 2 3 ρ M J = π γ kt 6 mg 3 2 ρ 1 2

3 Gravitational collapse of gas For a typical H 2 molecular cloud: T = K n = cm 3 m = g γ 1 Associated Jeans mass is M J = 70M n 10 3 cm T 10K 3 2

4 Stars are born in giant gas clouds. If the cloud is too hot and not dense enough, it will never collapse. Pressure wins! The Orion Nebula If the cloud is cool and dense enough, it will collapse. Gravity wins!

5 The Stellar Womb Stars are born deep in dark molecular clouds: cold (10 30 K), dense nebulae so cold that molecules (H 2 instead of atomic H) can exist dark because visible light cannot penetrate

6 Thackeray s Globules

7 something happens to perturb part of a molecular cloud and make it begin to fragment Stellar Gestation as a core of gas collapses, it wants to heat up radiates away the excess heat and thus remains cool Eagle Nebula Pillars

8 Giant Molecular Gas Cloud more dense Gravity wins less dense Pressure wins

9 Collapse of cold, unstable region

10 Collapse of cold, unstable region Gravity grows stronger

11 Collapse of cold, unstable region Gas starts to heat up

12 Collapse of cold, unstable region Heat is radiated away à Gas cools back down

13 Collapse of cold, unstable region Denser à Gravity grows stronger

14 gets smaller, denser, but not much hotter Stellar Gestation eventually, gas becomes opaque and light escapes less quickly à heats up and collapse slows down As it heats up, the emitted light moves toward the visible

15 Stellar Gestation bursts into view as a visible protostar hotter, denser, higher pressure but still contracting because gravity is stronger too McNeil s nebula

16 Collapse of cold, unstable region Denser à Gravity grows stronger Hotter à Pressure grows stronger

17 Collapse of cold, unstable region Denser à Gravity grows stronger Hotter à Pressure grows stronger

18 Stellar Gestation The protostar keeps on shrinking until internal pressure can resist gravity The protostar collapses until its core reaches 10 7 K in temperature and fusion starts. Fusion restores hydrostatic equilibrium. Hubble s nebula

19 The Role of Mass O stars are most massive ( M sun ) Enormous self-gravity, enormous compressive force need enormous pressure to resist gravity 10 7 K core temperature is not enough Continue to compress due to gravity, despite fusion Compression à higher temperature Higher temperature à faster rate of fusion (larger number of protons have enough energy to fuse) Higher fusion rate à more pressure Equilibrium is reached at very high fusion rate

20 The Role of Mass M stars are least massive ( M sun ) Weakest self-gravity, weakest compressive force need less pressure to resist gravity Pressure can balance gravity at lower temperature Lower temperature à lower rate of fusion Lower fusion rate à lower luminosity This is the origin of the Mass-Luminosity relation for Main Sequence stars. L = M 3.5 (in solar units)

21 Stages of Star Formation on the H-R Diagram

22 Arrival on the Main Sequence The mass of the protostar determines: how long the protostellar phase will last where the new-born star will land on the MS i.e., what spectral type the star will have while on the main sequence

23 Missing the Main Sequence: Brown Dwarfs If the protostar has a mass < 0.08 M : It does not contain enough gravitational strength to reach a core temperature of 10 7 K No proton-proton chain fusion reactions occur The object never becomes a star at 10 6 K, deuterium fusion begins (but there is not much deuterium) hydrostatic equilibrium reached this phase is short-lived

24 The First Brown Dwarf Discovery

25 Star Formation

26 Star Formation Starting Inputs: Mass: 50 Msun Diameter: pc Temperature: 10 K Mean mol. Weight: 2.46 (Jeans mass = 1 Msun) Time evolved = 266K years Initial density and turbulence spectra. Computing: SPH code, 3.5 M particles 100K CPU-hours on 64 CPUs (65 days) Resolution: 1-5 AU Bate, M. R., et al. (2002)

27 Star Formation Original cloud Denser cloud

28 Star Formation

29 These simulations show: Star Formation Star formation is a very chaotic and dynamic process Stars form so close together that they often interact before growing to full size Young stars compete for remaining gas with more massive stars About half the objects are kicked out of the cluster before they can grow enough to start fusion : brown dwarfs Many of the encounters btw. young stars and brown dwarfs strip the dusty disks off the stars suggesting planetary systems could be rare

30 Star Formation

31 Star Formation

32 Evolution of the Sun Stages in Evolution: Hayashi track Deuterium burning Main Sequence H à He in core Red Giant Branch He core, H à He in shell Tip of the Red Giant Branch Degenerate He core à He flash Horizontal Branch He à C,O in core, H à He in shell Asymptotic Giant Branch C,O core, He à C,O and H à He in shells Planetary Nebula Not massive enough to burn C,O Sheds outer layers. White Dwarf Degenerate C,O

33 Planetary Nebulae Cat s Eye nebula

34

35 Post - Main Sequence Evolution

36 Main Sequence Turn-off

37

38 MASS FUSION REMNANT M < 0.08M 0.08M < M < 0.5M 0.5M < M < 2M 2M < M < 8M 8M < M < 20M 20M < M < 50M M > 50M No fusion Central H burning Formation of degenerate core No He burning Central H burning Helium flash Central H burning He ignites in non-degenerate core Numerous burning phases Type II supernova Numerous burning phases Type II supernova Numerous burning phases Hypernova/Collapsar Brown Dwarf He White Dwarf CO White Dwarf CO White Dwarf Neutron Star Black Hole Black Hole

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