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3.3. The destruction of SN condensates by the reverse shock

To these destruction processes we add the destruction of SN-condensed dust grains by the reverse shock propagating through the SN ejecta. The reverse shock is caused by the interaction of the ejecta with the ambient medium. Figure 4 is a schematic reproduction of a similar figure in [62], depicting the interaction of the SN ejecta during the free expansion phase of its evolution with its surrounding medium. This medium could consist of either circumstellar material that was ejected by the progenitor star during the red giant phase of its evolution, or interstellar material. The SN ejecta acts like a piston driving a blast wave into the ambient medium. Immediately behind the blast wave is a region of shocked swept-up gas. When the pressure of this shocked gas exceeds that of the cooling piston, a reverse shock will be driven into the ejecta [52].

Figure 4

Figure 4. A schematic diagram (after Truelove & McKee [62]) depicting the interaction of the SN ejecta with its ambient surrounding.

Dust formed in the ejecta will be subject to thermal sputtering by the reverse shock. The fraction of dust destroyed is roughly given by the ratio of the sputtering lifetime, tausput, to the expansion time (age), t, of the ejecta. The grain lifetime is initially a strongly rising function of gas temperature, reaching a plateau at about 106 K [16]. Figure 5 depicts the velocity history of the reverseshock as it traverses different layers of the ejecta, as a function of alpha ident Rr / Rej, where Rr is the radius of the reverse shock, and Rej is the outer radius of the ejecta. The calculations were performed using the analytical expressions of Truelove & McKee [62] for a SN explosion in a uniform medium. The initial velocity of the reverse shock at alpha = 1 is zero, reaching a maximum at alpha = 0, when it reaches the origin of the explosion. No dust will be destroyed at alpha = 1, since the gas temperature so low that most gas molecules have kinetic energies well below the sputtering threshold. Very little grain destruction is also expected to take place at alpha = 0 since in spite of the high gas temperature, the gas density is very low and the sputtering lifetime is longer than the expansion time of the ejecta. There is therefore an optimal location 0 < alpha < 1, where the shock velocity (gas temperature) and ejecta density are such that tausput / t < 1, and grain destruction can take place.

Figure 5

Figure 5. The velocity profile of the reverse shock traversing the SN ejecta. The reverse shock originates at alpha = 1, and over time propagates back into the ejecta, until it reaches the origin at alpha = 0.

The alpha-interval in which grains are completely destroyed will depend on the size of the newly-nucleated dust particles. Figure 6 depicts the location in the ejecta in which dust is completely destroyed by the reverse shock. The calculations were performed for dust particles with radii of 0.1 and 0.01 µm embedded in a smooth, O-rich ejecta. As expected, the smaller dust particles are destroyed over a wider range of ejecta layers compared to the larger size particles. In reality, SN ejecta are clumpy, and the SN dust is expected to reside predominantly in the clumpy phases of the ejecta, as is suggested by the detection of dust in the fast moving knots of the remnant of Cas A [45, 3]. The reverse shock slows down below the threshold for complete grain destruction as it traverses these density enhancements in the ejecta. Consequently, dust in the clumpy ejecta may only be shattered instead of being completely destroyed by sputtering. The total amount of grain processing in the SN ejecta is however still highly uncertain. An independent investigation into the effect of reverse shocks from the H-envelope, the presupernova wind, and the ISM on the formation of dust, the amount of grain processing, and the implantation of isotopic anomalies in SN ejecta was carried out by Deneault, Clayton, & Heger [9].

Figure 6

Figure 6. The survival of SN condensates in different layers of the ejecta. The survival of the dust is measured by the ratio of the sputtering timescale, tausput to that of the expansion time, t, of the ejecta. Grains are destroyed in layers for which tausput / t < 1.

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