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Meeting update
Last week I finished reading Toro ch.'s 1-4 and met with Adam on the first program I will be writing. Basically it will be setting up a so-called Exact Riemann solver, which will take 2 initial data states (left and right) and solve for the pressure of an intermediate state in the "star region". This pressure will be found using an iterative approach from an initial approximation to the actual pressure. Once this is found, the remaining fluid variables can be solved for once the types of waves on either side of the star region have been identified as either shock or rarefaction. This is because each type of non linear wave has a set of conditions that apply for the density and velocity across them (only pressure is necessarily constant across the middle wave - the contact discontinuity). With this in mind, once P is found, the program will follow a flow chart to determine which conditions must be met, and hence which equation or set of equations should be solved to find the remaining fluid variables of the problem.
I also began working on writing the introduction and thinking about redoing the plots for the paper so that the curves show the actual resolution (which increases over time of simulation). I am thinking that for the plots, I can adjust my program to use just a constant line out in the center region of the sphere (where I think the angular distribution of data was symmetric), and an averaging scheme over the outer shells. In this way, the data sampled from Visit should automatically adjust for smaller radii as more refinement is added later on in the simulation.
Here is what I have for the Intro so far:
- Various properties of the “Bonnor-Ebert” (BE) sphere, a hydrostatic sphere in pressure equilibrium with its ambient environment, make it a good candidate for numerical modeling of protostellar collapse. First, as a candidate star forming structure is envisaged as gravitationally bound and unstable, it is easy to imagine a protostar evolving from an initially hydrostatic configuration. Indeed, spherical clumps have been observed in or near hydrostatic equilibrium, such as the Bok Globule, B68 (Myers). Second, the stability criterion against gravitational collapse has been worked out analytically. Third, pushing the sphere out of the stability regime with various physical perturbations illuminate collapse characteristics. Such features of the collapse may help advance single star formation theory as well as provide clues to observational astronomers in identifying potential star forming sites.
- While the collapse of a BE sphere has been studied extensively over the years, the literature reveals studies of the BE sphere in precarious and unphysical conditions. The BE sphere has largely been modeled as residing in low density ambient mediums, so to seemingly isolate the collapse of the sphere from the environment. Examples of previous works - in response to Shu’s claim that all collapse would be inside out - the BE sphere does not collapse in this way…
- Although modeling the collapse in this way does illuminate unique features of the BE collapse, it inadvertently constrains the model. If the BE sphere might be considered as an early basic model of star formation, it should be examined in a more physically plausible setting. That is, the BE sphere should be tied to its parent cloud as it would be in nature, by being modeled with no discontinuous boundary between BE sphere and parent clump. The collapse properties of such a simulation would be more physically accurate to any actual situation involving the collapse of a protostellar BE sphere. Discuss those papers that began to address this - Myers and Hannebelle.
- How this paper is different from previous similar work.
Self Gravity papers to read? https://clover.pas.rochester.edu/trac/astrobear/wiki/ExternalLinks#Self-GravityCoreCollapsePapers https://clover.pas.rochester.edu/trac/astrobear/wiki/SelfGravity
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