Editing ProjectsUnderway/CoreCollapseSupernovae (section)

==Introduction==

[[Image:Ott2009Review_Fig2B.png|300px|right|Ott (2009, Classical and Quantum Gravity, 26, 063001)]]Our principal objective is to help the gravitational-wave community more fully understand the underlying physics that is fundamentally responsible for the characteristic features that are expected to arise in the signals that are detected from core-collapse supernovae.  Building on early, simplified models of nonspherical core collapse presented by [http://adsabs.harvard.edu/abs/1974ApJ...191L.105T Thuan &amp; Ostriker (1974)] and by [http://adsabs.harvard.edu/abs/1984ApJ...285..721T Tohilne (1984)], our discussion is intended to supplement and complement published works from the past couple of decades that have focused on analyzing results from large-scale, multidimensional hydrodynamic (or magneto-hydrodynamic and fully relativistic) models, such as the the seminal work of [http://adsabs.harvard.edu/abs/1997A&A...320..209Z Zwerger and Mueller (1997)] and reviews by [http://iopscience.iop.org/0264-9381/26/6/063001/pdf/0264-9381_26_6_063001.pdf Ott (2009)], [http://relativity.livingreviews.org/open?pubNo=lrr-2011-1&amp;page=articlese4.html Fryer and New (2011)] and [http://arxiv.org/pdf/1202.3256v2.pdf Logue et al. (2012)].  

As an example, Figure 2 from [http://iopscience.iop.org/0264-9381/26/6/063001/pdf/0264-9381_26_6_063001.pdf Ott (2009)] is reprinted here, on the right.  Its published caption reads, in part:  "Note the generic shape of the waveforms, exhibiting one pronounced spike at core bounce and a subsequent ring down.  Very Rapid precollapse rotation &hellip; results in a significant slowdown of core bounce, leading to a lower-amplitude and lower-frequency GW burst."  As early as 1991, [http://adsabs.harvard.edu/abs/1991A%26A...246..417M M&ouml;nchmeyer et al. (1991)] identified four phases of a collapse evolution:
* Phase I:  ''Contraction and core flattening''.  "This phase &hellip; is characterized by a growing overall flattening of the density stratification inside and outside [of an] inner core (IC)."
* Phase II:  ''Rapid contraction of the IC''.  "Both the IC and the outer core get strongly deformed during this phase.  &hellip; The collapse of the IC is finally decelerated and stopped &hellip; by either the action of centrifugal forces &hellip; or the rise of [the effective adiabatic index] <math>~\Gamma</math> &hellip;"
* Phase III:  ''Core bounce''.  "Depending on the stiffness of the [equation of state] and the amount of rotational and kinetic energy the IC overshoots its (rotational) equilibrium position" then bounces back.
* Phase IV:  ''Shock propagation and post-bounce oscillations''.  "&hellip; the &hellip; IC oscillates [about its equilibrium configuration] with various volume and surface modes.  The amplitudes and frequencies of these modes strongly depend on the kinetic energy of the IC at bounce, the stiffness of the [equation of state], and the central and averaged density of the IC &hellip;.  The IC-oscillations are damped &hellip; [on a] time scale [that] strongly depends on the conditions of the shock heated material just outside the IC.  After a model dependent number of oscillations, the IC approaches rotational equilibrium &hellip;."

Here, we will develop analytic and semi-analytic models that encapsulate the physical phenomena that give rise to and that define the relevant scales of each of these evolutionary phases, then sew the models together to demonstrate how all of the principal features in the core-collapse gravitational-wave signal can be fairly readily understood.  We begin with a discussion of the free-fall collapse of rotationally flattened spheroids.