Spatial Distribution of Nucleosynthesis Products in Cassiopeia A: Comparison Between Observations and 3D Explosion Models

To model collapse and explosion, we use a 1-dimensional Lagrangian code developed by Herant et al. (1994). This code includes 3-flavor neutrino transport using a flux-limited diffusion calculation and a coupled set of equations of state to model the wide range of densities in the collapse phase [Herant et al. 1994, Fryer et al. 1999a]. It includes a 14-element nuclear network [Benz, Thielemann, & Hills 1989] to follow energy generation.

Our 3-dimensional simulations use the output of the 1-D explosion (23 M_⊙ star, 23m-run5) when the shock has reached 10⁹ cm. We map the structure of this explosion into our 3D Smooth Particle Hydrodynamics code SNSPH [Fryer et al. 2006a]. To simulate an asymmetric explosion, we modify the velocities within each shell based on angular position. The velocities of particles within 30^∘ of the z-axis were increased by a factor of 6 and the remaining particles were decreased by a factor of 1.2, roughly conserving the explosion energy. We will refer to these as high velocity structures (HVS). At these early times in the explosion, much of the energy remains in thermal energy, so the total asymmetry in the explosion is not as extreme as our velocity modifications suggest. The large velocity asymmetry results in roughly a factor of two spatial asymmetry between the axes. In this calculation, we model the explosion using 1 million SPH particles.

Nucleosynthesis post-processing was performed with the Burn code [Young & Fryer 2007], using a 524 element network terminating at ⁹⁹Tc. Reverse rates are calculated from detailed balance and allow a smooth transition to a nuclear statistical equilibrium (NSE) solver at $T>10^{10}$K.

Can actually detect the characteristic enhancement or ratios of nucleosynthetic products that can reliably indicate the presence of ²⁶Al in supernova ejecta?

Si and S abundances turn out to be highly diagnostic (Figure 1) because of the production channel. The burning raises the Si abundance from log(X) $\sim-3$ to $\sim-1.5$, primarily in ²⁸Si . This is the typical abundance in the high ²⁶Al   regions. Temperatures are not high enough to produce significant amounts of S, so S/Si drops by a factor of about 10. Oxygen burning produces S efficiently at low entropies (¹⁶O (¹⁶O ,$\gamma$)³²S ) and at high T transitioning to QSE, where S is thermodynamically favored over Si. As a result there is only a narrow range of mass in the star where S/Si drops much below 0.5. This coincides with the peak mass fraction of ²⁶Al .

We find a similar pattern in the 3D explosion to the 1D results (Figure 2. In this case, in the spherically symmetric region no material is processed at high enough temperatures to produce ²⁶Al . The HVS have a large region that consists of material that underwent carbon burning in the progenitor star at temperatures of $\sim 8\times 10^{8}$K and reached peak shock temperatures of between 1 and 2$\times 10^{9}$K. This is the ²⁶Al  bubble. The ring consists of material that undergoes Ne burning in the progenitor ($1-1.5\times 10^{9}$K) and explosive Ne and/or C burning ($2.2-2.8\times 10^{9}$K). As in the 1D explosions, S/Si is very low and P production is high. The 3D explosion, with its more complicated thermodynamic history, reminds us that 1D does not tell the whole story. The yield is increased by higher temperatures and higher densities, but ²⁶Al  is rapidly destroyed by succeeding reactions. if there is a freezeout after the shock in which density drops rapidly, the high production can be achieved without subsequent destruction. This is the reason for the higher ²⁶Al  production in the sub-explosive C burning bubble than the explosive ring, the opposite of the pattern found in 1D. Large amounts of ¹⁸F are produced under the same conditions. If this excess flourine is not destroyed by subsequent burning it preferentially decays by ¹⁸F ($\gamma,\alpha$)¹⁴N at temperatures above T$\sim 1\times 10^{9}$K. Thus we have materialwith high levels of both N and O, Si, and S. These are potentially analogous to the Mixed Emission Knots (MEKs) identified by [Fesen 2001] in Cas A.

Detection of ²⁶Al -rich material in core-collapse supernova remnants is a favorable situation. The characteristically low S/Si will be undiluted by mixing with ISM material in young remnants, so we should be able to predict which ejecta knots have high ²⁶Al  in well-resolved cases like Cas A. O-rich knots with high Mg or Na or moderately enhanced Si are good candidates for a combined optical/IR survey. The S/Si ratio of these knots would then provide a strong test of whether they would contain ²⁶Al at high abundance. The Mixed Emission Knots in Cas A may also be excellent candidates. These knots are unique due to the simultaneous presence of significant emission from N and from O and S. The burning stages in a star that produce O and S destroy N very efficiently. It has therefore been assumed that these knots are most likely material from different locations in the progenitor star that are superimposed on line of sight or somehow mixed during the explosion. If these clumps are produced by a nucleosynthetic process they are most likely produced in the same conditions favorable for ²⁶Al production.