Molecular Cloud Fragmentation:

Discussion in 'Astronomy, Exobiology, & Cosmology' started by paddoboy, Oct 7, 2020.

  1. paddoboy Valued Senior Member

    27,543 the simulation, gravity,form a dense "core".

    The following animation conveys more clearly than a set of static pictures ever could, what happens to form stars. It starts with an almost quiescent molecular cloud, which is rotated in front of us to give a better view of its chaotic, filamentary structure. Then we zoom in toward the center and watch the action around a mass concentration that is spinning under the pull of its own gravitational field and pulling sub-condensations of the cloud toward it. Most of them, however, are deflected and bounce back into the molecular cloud. It is through this complex process that a molecular cloud breaks itself up into the full range of stellar masses. These fragments then cool and collapse under their own gravity to form individual stars.Finally,we zoom back out to see the whole cloud and the retinue of stellar-mass fragments it has produced.

    Stills from the movies show the stages of collapse and fragmentation:

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    Clouds of interstellar gas are very turbulent with rapid internal motions. We begin with such a gas cloud, 1.2 light-years across, and containing 50 times the mass of the Sun.

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    As the calculation proceeds, the turbulent motions in the cloud form shock waves that slowly damp the motions.

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    When enough energy has been lost in some
    regions of the simulation, gravity can pull the gas together to form a dense "core".

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    The formation of stars and brown dwarfs begins in this dense core.

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    As the stars and brown dwarfs interact with each other, many are ejected from the cloud.

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    The cloud and star cluster at the end of simulation (which covers 266,000 years). Some stars and brown dwarfs have been ejected to large distances from the regions of dense gas in which the star formation occurs.

    more at link.....
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  3. paddoboy Valued Senior Member

    Here's a paper:
    Fragmentation of Molecular Clouds: The Initial Phase of a Stellar Cluster:
    The isothermal gravitational collapse and fragmentation of a region within a molecular cloud and the subsequent formation of a protostellar cluster are investigated numerically. The clump mass spectrum that forms during the fragmentation phase can be well approximated by a power-law distribution dN/dM

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    . In contrast, the mass spectrum of protostellar cores that form in the centers of Jeans-unstable clumps and that evolve through accretion and N-body interactions is described by a lognormal distribution with a width that is in excellent agreement with observations of multiple stellar systems.

    Since collapse and fragmentation in molecular clouds is an extremely complex and dynamical process, many authors have sought to understand the stellar initial mass function as resulting from a sequence of statistical events that may naturally lead to a lognormal IMF (see, e.g., Zinnecker 1984 and Adams & Fatuzzo 1996; also Price & Podsiadlowski 1995, Murray & Lin 1996, and Elmegreen 1997).

    However, using numerical simulations, it is possible to identify underlying processes that may contribute to the form of the stellar initial mass function. In the calculations presented here, we find several trends. The "protostellar" cores that form first are generally formed in the clumps with the highest initial density, and they tend to have the highest final masses. Cores that form later originate from gas that was initially in low-density clumps or from distributed gas that converged to form a higher density clump before quickly collapsing. Overlaid on these general trends, dynamical interactions between individual cores can act to terminate accretion onto a core by ejecting it from a clump, thus setting its final mass. The excellent agreement between the numerically calculated mass function and the observed IMF for multiple stellar systems (Kroupa et al. 1990) strongly suggests that these gravitational fragmentation and accretion processes dominate the origin of stellar masses. In a subsequent paper, the results from calculations spanning a larger range of the parameter space relevant for molecular clouds shall be discussed in detail.

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  5. paddoboy Valued Senior Member

    Gravitational Collapse
    So we have lots of gas in the interstellar medium. What are the properties of these clouds?
    Diffuse HI CloudMolecular Cloud Core
    Temperature50 K150 K
    Density500 cm-3108 cm-3
    Mass1-100 Msun10-1000 Msun
    And the Jeans mass is given by:

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    So plugging in numbers, we find that

    • Diffuse HI cloud: MJ ~ 1500 Msun - stable.
    • Molecular cloud core: MJ ~ 15 Msun - unstable!
    So deep inside molecular clouds (the molecular clouds themselves may be 106 - 107 Msun), the cores are collapsing to form stars. How does this collapse proceed?

    Gravitational Free Fall
    Early on in the collapse, the cloud is optically thin (it has a low density, so energy can escape easily without being absorbed). Since the energy of collapse is immediately radiated away, the cloud won't heat up -- we call this an isothermal collapse.
    How fast does this collapse happen? Let's do a "back of the envelope" calculation.

    Consider a particle somewhere inside the cloud. What is the gravitational acceleration it feels pulling it inwards?

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    If it starts initially at rest, then (if acceleration is constant) it will reach the center when

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    So, solving for t,

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    Now, since this is just a crude calculation, we can say that sqrt(3/2pi) = 0.7 = 1, so that we have an expression for the free fall time:

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    which is good to within a factor of two or so.
    Note that the free-fall time depends only on density, not radius.

    So how fast does the molecular cloud core collapse? Since it is mostly hydrogen,

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    Fast! (by astronomical standards, anyway...)

    Of course this is a simplification -- a single cloud does not collapse down to r=0. What happens to complicate the collapse?
    As the cloud collapse, density rises. Since the collapse is isothermal, a rising density means the Jeans mass of the cloud is falling, so small pieces of the cloud start to collapse on their own. A rising density also means a declining free fall time, so these small dense clumps collapse faster than the overall cloud.

    Instead of one giant cloud undergoing a monolithic collapse, the cloud fragments into small collapsing pieces.

    So what stops this fragmentation?

    The transition to adiabatic collapse
    As the density rises, the opacity rises. At some point during the collapse and fragmentation process, the opacity rises high enough that the energy created during the collapse is absorbed within the star itself -- it begins to heat up. Since the energy is not lost from the cloud, we call this an adiabatic collapse.
    Higher temperature means higher pressures (the ideal gas law), which halt the free collapse of the star. Since the cloud absorbs all the gravitational energy of collapse, it heats up, and it starts to act like a blackbody.

    At what mass does this happen? We can balance the rate of energy loss through gravitational collapse to the rate at which the cloud radiates blackbody energy, and, solving for the mass (see pp 454-455), we find M ~ Msun. In other words, collapse halts when the fragment masses reach star-like masses. Protostars!
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