The Astrophysical Journal, 597:362-373, 2003 November 1
© 2003. The American Astronomical Society. All rights reserved. Printed in U.S.A.
Where Was the Iron Synthesized in Cassiopeia A?
Una Hwang 1 and J. Martin Laming 2
Received 2003 April 4; accepted 2003 July 4
ABSTRACT
We investigate the properties of Fe-rich knots on the east limb of the Cassiopeia A supernova remnant using observations with Chandra/ACIS and analysis methods developed in a companion paper. We use the fitted ionization age and electron temperature of the knots to constrain the ejecta density profile and the Lagrangian mass coordinates of the knots. Fe-rich knots that also have strong emission from Si, S, Ar, and Ca are clustered around mass coordinates q 
0.35
0.4 in the shocked ejecta; for ejecta mass 2 M
, this places the knots 0.70.8 M out from the center (or 22.1 M, allowing for a 1.3 M compact object). We also find an Fe clump that is evidently devoid of line emission from lower mass elements, as would be expected if it were the product of 
-rich freezeout; the mass coordinate of this clump is similar to those of the other Fe knots.
1. INTRODUCTION
Cassiopeia A is the only supernova remnant for which decays of the important radioactive nucleus 44Ti have been confirmed by observation of 
-ray line emission from both of its decay products, 44Sc and 44Ca (Iyudin et al. 1994, 1997; Vink et al. 2001; Vink & Laming 2003). The 44Ti is almost uniquely produced in the explosive Si-burning condition known as -rich freezeout, wherein Si burns at high temperature and relatively low density. It takes place in the innermost ejecta and is highly sensitive to the explosion details and the position of the mass cut for the formation of a neutron star or black hole. The location of -rich freezeout is thus of great interest and importance to theoretical progress on the mechanisms by which core-collapse supernovae explode, but it is technically very difficult to directly image the hard X-rays or -rays from the 44Ti decay at the necessary spatial resolution (e.g., Chen et al. 2003). An attractive alternative approach, recently proposed by Silver et al. (2001), is to search for Doppler structure in the 44Sc emission lines at 67.9 and 78.4 keV using a very high spectral resolution calorimeter, but this also must await development of the required instrumentation.
A different approach explored in this paper depends on the nucleosynthesis signature of -rich freezeout. The usual explosive Si burning produces mainly 56Fe (originally as 56Ni, which decays radioactively), along with Si, S, Ar, and Ca. Because -rich freezeout takes place very fast at low density and high temperature, the burning products are almost exclusively 56Fe, apart from 44Ti and a small amount of 4He. The principal reason for this difference is that the low density suppresses the 3 
12C reaction, shifting the nuclear statistical equilibrium (or quasi-equilibrium) to heavier nuclei around the iron peak (Woosley & Hoffman 1991; Arnett 1996; The et al. 1998). Lighter nuclei, including 44Ti, are formed in small amounts toward the end of the freezeout by -captures. The X-ray spectrum of a freezeout region should thus show emission lines only from Fe. It is our purpose in this paper to locate such Fe-rich region(s) in the extant Chandra observations of Cas A and to characterize them in terms of their temperatures and ionization ages. By using a model for the supernova remnant hydrodynamics, we then place limits on the Lagrangian mass coordinates where such burning products were placed by the explosion.
2. THE STRUCTURE OF CASSIOPEIA A
Early Chandra X-ray observations showed that the Fe emission in Cas A is associated with ejecta and is dominant to the east, in the faint region outside the bright ejecta shell. Since the Fe originates in the innermost ejecta, this suggests a large-scale turbulent overturn of the ejecta layers, either during or since the explosion (Hughes et al. 2000). In the northwest, the Fe emission coexists with emission from Si and other intermediate-mass elements, at least in projection, but Doppler measurements made with XMM-Newton (Willingale et al. 2002) indicate larger line-of-sight velocities for Fe that imply that the Fe-emitting region is actually kinematically and spatially distinct from that of other elements such as Si. Overturn of the X-rayemitting Fe layers thus appears to have occurred in the northwest as well as in the southeast, except that it is not viewed in a favorable orientation. Turbulent overturns are also inferred for the optically emitting S and Ar ejecta relative to the N- and He-rich layers (Fesen 2001).
Typical X-ray surface brightness enhancements for the Fe features are only a factor of a few above their immediate surroundings. The Fe-rich knots are shown here (also see Laming & Hwang 2003, hereafter Paper I) to have higher characteristic ionization ages3 than the O/Si knots by factors of a few to 10, implying either a correspondingly higher density or an earlier shock time. Simulations and laboratory experiments show that knots and clouds with large density enhancements (or deficits) are subject to a number of hydrodynamic instabilities that act to destroy the knots within a few shock crossing timescales (Klein, McKee, & Colella 1994; Klein et al. 2003; Wang & Chevalier 2001; Poludnenko, Frank, & Blackman 2002; Poludnenko et al. 2003; McKee & Cowie 1975),4 so such knots are not expected to survive longer than several tens of years after passage of the reverse shock. We believe that early shock times and very modest (or no) density enhancements are the most consistent explanation for the Fe knots that have survived to be observed today, and we make this assumption in what follows in this paper. We can thereby account for the observed spectral characteristics of the knots while allowing for their low surface brightness enhancements and making it plausible for these shocked knots to exist at the present day. The low surface brightness enhancement that is observed for the Fe knots could be effected, not by increased density, but by the high emissivity of a Fe-rich plasma compared to a solar-abundance plasma at the same temperature and ionization age.
Mixing of the ejecta by Rayleigh-Taylor instabilities takes place not only during the remnant evolution but even earlier, during the explosion itself. In Cas A, the survival of knotty ejecta during the explosion is supported by the hydrodynamic simulations of Kifonidis et al. (2000, 2003). They have modeled core-collapse explosions in two dimensions with the aim of following the propagation of metal clumps within the ejecta. For a Type II explosion of a 15 M progenitor, they find that Rayleigh-Taylor instabilities at the interfaces between the Ni+Si and O layers and the O+C and He layers produce clumps of widely varying element compositions. As the explosion proceeds, however, the blast wave decelerates in the dense helium layer and generates a reverse shock that shreds and mixes the clumps so that by a time 20,000 s after bounce, almost all the metals are completely mixed throughout the inner 3.4 M. Only species such as 44Ti that are synthesized in the innermost layers remain correspondingly more localized. By contrast, a much weaker reverse shock develops in a 15 M progenitor that loses its outer envelope to a stellar wind before exploding as a Type Ib supernova. This reduces the effect of the mixing instabilities so that the metal clumps that are formed by the Rayleigh-Taylor instabilities may survive and propagate further out into the ejecta. At time 3,000 s after bounce, 28Si, 44Ti, and 56Ni exist in clumps throughout the inner 2 M (of an explosion progenitor of 5.1 M). The extent of the mixing during the explosion is thus directly related to the strength of the reverse shock and the pre-supernova mass loss of the progenitor.
There is little doubt that the progenitor of Cas A underwent substantial mass loss so that, based on the above, ejecta knots should have initially survived the mixing instabilities that operated during the explosion. For example, Paper I gives various arguments to suggest that the progenitor's main-sequence mass was 2025 M (at the lower end of the range of Wolf-Rayet masses) and that the progenitor possibly underwent a short phase as a WN star before exploding at 34 M. Chevalier & Oishi (2003) similarly consider the dynamical properties of Cas A to infer a Type IIb or IIn designation for the explosion. The inference of a WN progenitor was first made based on studies of the optically emitting fast-moving knots (Fesen, Becker, & Goodrich 1988; Fesen 2001 and references therein). Indeed, there is substantial evidence to support a circumstellar environment for Cas A. Slow-moving N-rich optically emitting knots are generally accepted to be relics of the progenitor's mass loss, and a wind circumstellar density profile is far more viable than a constant-density environment in light of such observations as the relative radii of the reverse and forward shocks (Gotthelf et al. 2001) and the X-ray expansion rate (DeLaney & Rudnick 2003) and also in terms of the implied ejecta mass and the production of nonthermal X-ray bremsstrahlung emission by electrons accelerated by lower hybrid waves (Laming 2001a, 2001b; Vink & Laming 2003).
In Paper I we use a new approach to make a quantitative analysis of the X-rayemitting ejecta of Cas A, specifically with regard to asymmetries in the ejecta and explosion. The method of Paper I makes the assumptions that Cas A is propagating into a circumstellar environment (i.e., the dependence of the density 
on the radius r is 
r-2) and that the spectra of individual knots can be modeled with a single temperature and ionization age. Arguments have just been presented for a circumstellar environment for Cas A. A single temperature and ionization age may plausibly be used to model the spectra of the knots because the knots have angular scales of 
1
in the Chandra images, corresponding to 5 × 1016 cm (at a distance of 3.4 kpc). A 1000 km s-1 reverse shock can traverse such a knot in just 20 yr, a time period much shorter than the timescale for the dynamical evolution of the remnant.
The model of Paper I extends the analytical hydrodynamic description of remnant evolution of Truelove & McKee (1999) to a r-2 circumstellar environment and includes the basic relevant atomic and plasma physical processes: the time-dependent ionization balance in shock-heated gas, Coulomb heating of the electrons by the ions (i.e., no additional collective plasma heating is assumed), and cooling due to radiation and adiabatic expansion. The ejecta themselves are assumed to have a power-law density distribution ( r-n) with a uniform-density core. The shocked ejecta mass is taken to be 2 M (following the discussion in Paper I), whereas the explosion energy and ambient density are adjusted. These models are used to predict the time-dependent behavior of the temperature and ionization age of the knots, which are then compared to the temperatures and ionization ages inferred for the ejecta knots from their Chandra X-ray spectra. This approach allows us to deduce the slope n of the ejecta envelope in each of the azimuthal directions we examine; by forcing the models to share a common core ejecta density and fixing the forward shock radius in the models to match the observed average X-ray radius, we may interpret the inferred variations in the ejecta envelope slope as due to variations in the locally deposited explosion energy. The variations we deduce are modest, at about a factor of 2 in energy, with shallower slopes (and higher inferred explosion energy) at the base of the ejecta jet in the northeast than in the east or northwest. A factor of 2 asymmetry is at the low end predicted by models, but at present, it is not possible on the basis of ejecta density and energy asymmetries alone to distinguish between the two basic mechanisms modeled to date to produce explosion asymmetries, namely, rotation of the progenitor or a jet-induced explosion (Bodenheimer & Woosley 1983; Fryer & Heger 2000; Fryer & Warren 2003; Khokhlov et al. 1999; Akiyama et al. 2003). Asymmetries of a comparable magnitude may also be produced by the instability that can arise in the standing accreting shocks of core-collapse supernovae as the injection of vorticity drives the rapid growth of turbulence behind the shock (Blondin, Mezzacappa, & DeMarino 2003).
3. DATA REDUCTION AND ANALYSIS
For the imaging analysis and most of the spectral analysis, we use the same 2000 January Chandra observation of Cas A with the Advanced CCD Imaging Spectrometer (ACIS) that is used and described in Paper I. For one interesting and faint region, however, we also use data from a second-epoch observation of Cas A taken 2 years after the first, in 2002 January. Both observations were of 50 ks duration and were taken with the same instrument in the same configuration. The spectra from the two epochs are fitted jointly, rather than being added into a single spectrum, because of the time-varying response of the ACIS detector. These effects include time-dependent changes in the gain and resolution caused by charge transfer inefficiency and, in particular, the temporally increasing absorption of soft X-rays (with energies below about 1 keV) by contaminants that build up on the detector surface. This detector absorption is modeled by ACISABS in the XSPEC X-ray spectral fitting package, with the number of days elapsed from launch to the observation date specified (198 days for the 2000 observation and 929 days for the 2002 observation).
3.1. Identification of Fe-rich Regions
In searching for regions dominated by Fe ejecta, we are aided by the combined spectral and imaging capabilities of the Chandra X-Ray Observatory. X-ray images of Cas A in its prominent Fe K blend (energy 6.7 keV) show that this emission is distributed in three primary regions: to the southeast, northwest, and west (Hwang, Holt, & Petre 2000; Willingale et al. 2002). The western region suffers from a higher interstellar column density that attenuates the low-energy X-ray emission, so that the Fe L emission (energies near 1 keV) is prominent only in the southeast and northwest. The southeast region is of particular interest in that the Fe emission there is located exterior to that of Si.
The left panel of Figure 1 shows the southeast region of Cas A. The blast-shocked material may be seen in places as faint, thin arcs at the outer boundary of the remnant, while the ejecta make up the bright irregular ring of emission. The faint, linear filaments of the ejecta "jet," which have optical counterparts, can be seen toward the top of the image. East of the bright ejecta ridge running southward from the jet, the fainter ejecta emission is largely Fe-rich. The Fe features have various morphologies ranging from compact knots to elongated knots to relatively diffuse features.
  | Fig. 1. |
Regions of the remnant that have strong line emission relative to the underlying continuum may be selected independently of surface brightness by forming an estimate of the line-to-continuum ratio at each position. For the Fe L blends, it is difficult to reliably subtract the true continuum, but in order to identify the Fe-richest regions, we have used spectral regions on either side of the L blend to make a rough estimate of the underlying continuum. The right panel of Figure 1 shows the Chandra image in the Fe L blends overlaid with smoothed contours showing the regions with prominent Fe L line-to-continuum ratios. It is evident that some of the strongest Fe line emission comes from a line of compact knots running due east at declination 58°46
30 as well as from diffuse regions of relatively low surface brightness about 1 to the south. These are thus our primary target regions to search for sites of -rich freezeout. The spectral extraction regions (generally a few arcseconds in extent) are shown in the left panel of Figure 1.
The surface brightness contrasts of the Fe and Si features are illustrated in Figure 2. Figure 2a shows a vertical cut through two representative Fe knots (numbered 13 and 14, starting with 10 closest to the center),5 which sit on a shelf of emission that rises above the general background. Figure 2b shows a vertical cut through the larger diffuse Fe-rich cloud, which also sits on a shelf of even fainter emission but with surface brightness contrasts that are significantly lower than for the other Fe-rich knots. In comparison, typical Si-rich emission features are very bright compared to the background or the Fe-rich emission, as shown in Figures 2c and 2d.
 Fig. 2a  Fig. 2b  Fig. 2c  Fig. 2d | Fig. 2. |
3.2. X-Ray Spectral Analysis
We carried out spectral fits for the regions indicated in Figure 1 with a model characterized by a single temperature and single ionization age net, wherein the lightest element included is O, and O provides the bulk of the continuum. This is consistent with the expectation that O is the primary constituent of the ejecta in Cas A and follows the approach first adopted by Vink, Kaastra, & Bleeker (1996) for modeling the X-ray ejecta spectra with an O-rich plasma. We also consider models where Si rather than O is the lightest element. The most prominent features in the spectra we consider are, however, from Fe. The background spectrum is generally taken from positions well off the source. For the Si/Fe ejecta models, we also take a more localized background from low surface brightness regions in the eastern part of the remnant near the Fe knots. The results of all these fits are summarized in Table 1, and the fits for a typical knot are shown in Figure 3.
 | Table 1 Fits to Fe-rich Knots |
   | Fig. 3. |
For the Fe knots (A series), the fits using the standard off-source background are generally better with O ejecta than with Si ejecta. In both cases, the fitted ionization ages are net 1011 cm-3 s or higher, while the O-continuum fits give temperatures that are higher by a few tens of percent. The use of a local background for the Si/Fe continuum fits naturally lowers the fit statistic per degree of freedom because the local background is less precisely determined than the standard background, but the actual fitted parameters are not much changed.
The spectra of the local background and of the regions surrounding the compact Fe-rich knots also show enhanced emission from Fe, with fitted Fe/Si abundance ratios of roughly 11.5 times solar. These Fe/Si ratios are significantly higher than in the Si-rich knots studied in Paper I, which are nearly devoid of Fe, but not as high as in the compact Fe knots in Table 1: the fitted Fe/Si ratio increases for regions closer to the compact knots. The fitted ionization ages of several times 10101011 cm-3 s are within a factor of 23 of most of the ionization ages given in Table 1 for the compact knots.
The faint c6a region lying southward of the knots in the A series is the most interesting of the Fe-rich features. For this faint feature we show the fits using the local background only, since the off-source background gives statistically unacceptable fits. The spectrum is well fitted with a model including only the elements Si and Fe (plus Ni), provided that the two elements can have different values of the ionization age. The temperature and ionization age for Fe are similar to those obtained for the Fe-rich knots in Table 1, while the Si ionization age is similar to that obtained in Paper I for the O/Si knots. We also performed a simultaneous fit of epoch 2000 and 2002 ACIS observations for this feature, allowing the two spectra to have different amounts of detector absorption according to their observation date. The parameters obtained are all very close to those obtained with the epoch 2000 observation alone, although with slightly smaller error ranges. From the error contours shown in Figure 4 for the joint fit, equality of the Si and Fe ionization ages can be excluded at higher than 99% confidence. Both sets of fits for the c6a region are shown in Figure 4, and the results summarized in Table 2.
   | Fig. 4. |
 | Table 2 Fits to Diffuse Regions |
The line-to-continuum ratio images in Figure 1 show that the regions near c6a having very slight surface brightness enhancements over the background should have high Fe line strengths. We therefore extracted source and background spectra for this entire region by specifying appropriate surface brightness cuts on the slightly smoothed image. The resulting background-subtracted spectrum can be fitted with a single-component model including only Si and Fe (and Ni) but does not necessarily require Si and Fe to have separate ionization ages. An enhancement of the Fe/Si abundance ratio at a level comparable to that found for the Fe knots is indicated. Thus, while this entire region is significantly Fe-enriched, on the whole it is not as pristine in Fe as is c6a. We have examined a number of other features in this region, and while many of them show Fe enrichments of the order of the Fe knots, we have so far identified no others where the Fe is a pure as in c6a.
The Fe-rich knots considered here have Fe/Si abundance ratios that are higher, generally by an order of magnitude or more, than the typical 0.25 ratio that is obtained through incomplete explosive Si burning in a 20 M progenitor (see Table 2 in Thielemann, Nomoto, & Hashimoto 1996). It is clearly indicated that some of the Fe is produced with complete Si exhaustion, as is already established, both by earlier X-ray spectral observations (Hughes et al. 2000) and by the confirmed detection of the decay products of 44Ti, which is formed by -rich freezeout (complete Si burning that occurs at lower densities). The explicit identification of a possible pure cloud of Fe ejecta in region c6a suggests strongly that this may be one of the sites where -rich freezeout occurred in Cas A.
The fitted ionization ages for the regions surrounding the A series of knots in the east are lower than but of the same order of magnitude as that in the knots themselves. A density contrast of a similar amount (a factor of 23) may be accommodated without triggering the hydrodynamic instabilities in a manner that destroys the knots. Paper I demonstrates that the curves of Te against net are essentially unchanged for such small degrees of clumping. The approximately solar Fe/Si abundances for this region are also at least a factor of 2 lower than the average Fe/Si abundance in the compact knots. A reasonable inference is that the Fe in the gas surrounding the compact knots was mixed with other gas less rich in Fe after being stripped from Fe-rich knots that initially had higher density contrasts compared to their surroundings and thus did not survive the action of instabilities. Another possible interpretation would be that the abundances surrounding the knots are the result of incomplete explosive Si burning, compared with complete explosive Si burning in the compact knots themselves (see, e.g., Thielemann et al. 1996).
4. Fe EJECTA MODELS AND DISCUSSION
In connection with Fe ejecta knots, it is also necessary to consider that 56Fe is originally formed as 56Ni, which decays radioactively. If the initially formed Ni clumps are sufficiently large, they will be opaque to the -ray radiation produced by the decays and thereby expand to form a hot, low-density Fe bubble. As the reverse shock traverses these bubbles, the resulting turbulence plays an important role in mixing the Fe ejecta into overlying ejecta layers (Li, McCray, & Sunyaev 1993), as well as causing filamentation in the overlying (Si-rich) ejecta (Blondin, Borkowski, & Reynolds 2001). The Fe associated with the bubble effect should be characterized by diffuse morphologies and low ionization ages. The relative compactness of an Fe ejecta knot seen in the Type Ia (thermonuclear runaway) remnant of Tycho's supernova caused Wang & Chevalier (2001) to suggest that the Fe in question there is not 56Fe but rather 54Fe, which is not formed by radioactive decays and is therefore not subject to the bubble effect. For core-collapse supernovae, and for Cas A in particular, this is a less satisfactory explanation because it is difficult to produce a sufficient mass of 54Fe, particularly if -rich freezeout occurred during the explosion. The bubble mechanism has also been suggested to be connected with the ringlike filamentation seen in the optically emitting ejecta (Fesen 2001) and indeed may have contributed to the highly filamentary X-ray emission from Si as well. Presumably, any Fe associated with the bubble effect is now too faint and underionized to be readily identifiable. On the other hand, if some of the 56Ni clumps were sufficiently small at the outset, these could become optically thin to the -ray radiation sufficiently early on that the bubble effect would be minimized for these clumps. These are the Fe clumps that we see today.
We can demonstrate that these Fe clumps were indeed small enough to minimize the bubble effect. The observed clump diameters of about 3
give present-day radii of 7.5 × 1016 cm at the 3.4 kpc distance of Cas A. Assuming that the radius increased proportionally to time, we get r = 6 × 1011tdays cm for the radius of a 56Ni/56Co clump at time tdays days after the explosion. The clump electron density varies as t-3 until interaction with the reverse shock, so extrapolating our n = 7 model back in time gives an electron density in the range ne = 
× 1014/t
cm-3. The optical depth to the center of the clump is then (Li et al. 1993)
where 
= 0.31T for -rays of energy about 1 MeV, and T is the Thomson cross section. Hence, we estimate that these clumps became optically thin (
1) to their own - rays about 5 days after explosion. This is significantly shorter than the 56Ni and 56Co lifetimes of 8.8 and 111.3 days, respectively, so most of the radioactive energy is deposited outside the clump. We therefore do not expect that the Fe knots we observe today have undergone any type of bubble expansion.
We pursue a more quantitative interpretation of the Fe knots in Cas A than has been previously attempted, by calculating the variation of the electron temperature Te with ionization age net for a variety of ejecta density profiles, as described in Paper I. We concentrate on models with an explosion energy of 2 × 1051 ergs, shocked ejecta mass 2 M, and circumstellar density r
= 14 pc2 cm-3, with rb the radius of the blast wave in parsecs. Paper I treated the case of pure O ejecta only; here we take compositions by mass of O : Si : Fe = 0.83 : 0.06 : 0.11 and Fe : Si = 0.9 : 0.1, which are approximately consistent with the spectral fits to the observed knots assuming an O-rich and Fe-dominated composition for the continuum, respectively. These models are shown in Figures 5 and 6 as solid lines; the fit results are superposed as crosses for the A series of knots and, in Figure 6 only, as boxes for the diffuse Fe clouds, with the symbol size indicating the fit uncertainties in Te and net. Table 3 gives the ejecta mass coordinates inferred for each knot by matching the fitted value of net to the corresponding location in the ejecta for the hydrodynamic model. In this, we assume that the clumps have the same density as their surroundings and infer electron densities of 1050 cm-3 for the clumps. If the knots are actually overdense, the net we fit would correspond to a later reverse shock passage and hence place the knots further in in the ejecta. We estimate that a factor of 3 overdensity would lead to an overestimate of q by around 0.06; a similar underdensity would place the knots further out in the ejecta, by a similar amount. Following reverse shock passage, our Lagrangian plasma parcel likely undergoes interactions with secondary shocks while the reverse shock is relatively nearby, leading in any case to uncertainties in q of a similar magnitude.
 | Fig. 5. |
 | Fig. 6. |
 | Table 3 Ejecta Knot Abundances and Mass Coordinates |
The mass of 56Fe contributed by the various knots is computed from the fitted emission measure and element abundances of the knots in Table 3. Spherical geometries were assumed for the knots, and boxes for the diffuse features. The corresponding electron densities are also given in the table, and for comparison, the electron densities that are inferred from the models. The agreement between the observationally and theoretically inferred densities is generally within a factor of 2, although it is somewhat worse for the larger east region. In any case, the observationally determined electron densities are systematically lower than the theoretically determined ones, which would seem to reinforce our assumption that the knots are not overdense.
According to the hydrodynamic model in Paper I, the reverse shock is currently at an ejecta mass coordinate q = 0.10.14 for n = 97 models, respectively. Hence, the inner 10% of ejecta, i.e., the inner 0.2 M, has yet to encounter the reverse shock. Cas A is highly unlikely to have ejected more than 0.050.1 M of 56Ni (which 
-decays to 56Fe), so the reverse-shocked 56Fe that we do see must have been mixed out into the envelope by Rayleigh-Taylor instabilities shortly after explosion. The estimated knot masses in Table 3 probably amount to a few percent of the total mass ejected, which is similar in magnitude to the mass of 56Ni inferred to have been mixed out into the envelope of SN 1987A (Pinto & Woosley 1988).
According to the mass coordinates we infer, the Fe clumps exist out to about 0.4 of the 2 M ejecta, or 0.8 M. Adding 1.3 M for the mass of the compact object, we arrive at 0.8 + 1.3 = 2.1 M for the observed outer extent of Ni mixing. This places the knots at a mass coordinate corresponding to the (Ni+Si)/O interface in a star that is initially of about 20 M (Woosley & Weaver 1995). Although this is an appealing inference, it is necessary to account for possible selection effects that determine the visibility of the knots. In the case of an O-rich composition for the knots, this apparent outer extent appears to be a real outer extent (see Fig. 5). We expect that if higher net knots exist now, we would be able to see them. For Fe-dominated composition, however, knots that encounter the reverse shock earlier than about 35 yr after explosion (at ejecta mass coordinates qFeSi 
0.45) will have by now cooled by radiative losses to temperatures below detectability as X-ray knots. In this case, the observed outer extent could be limited by this selection effect. We also fail to detect Fe knots with net 
1011 cm-3 s, i.e., in the inner 0.3 of the ejecta (or interior to 1.9 M, if the mass of the compact object is included). This might also be a selection effect caused by the rapid decrease in density as one move inward into the ejecta. Fe that is deep in the ejecta may also be more likely to have created bubbles because of the radioactivity of its parent 56Co nucleus and so to have become even less dense than the O-rich ejecta that is assumed to surround it. The inferred mixing of the c6a and east regions out into regions that were originally O and are burned to Si during the explosion is also consistent with the inference that 44Ca found in SiC X grains is a decay product of 44Ti formed in core-collapse supernovae (e.g., Clayton et al. 2002).
It appears that the O : Si : Fe composition required can be achieved only by mixing products of complete Si burning with the products of O burning (to get Fe : Si right), and it is unlikely that a knot would survive such mixing as a distinct object. More plausible is the pure Fe : Si composition, which requires no further mixing after Si burning. Consequently, the selection effect due to the radiative cooling of Fe-rich knots discussed above is probably operative, and more Fe may exist at lower temperatures further out in the ejecta of Cas A.
5. CONCLUSIONS
Using Chandra observations combined with new modeling techniques, we have constrained the ejecta density profiles and Lagrangian mass coordinates of some of the Fe-rich knots in the southeastern region of Cas A. This makes it possible for the first time to compare observations in a quantitative manner with explosion models and allows tests of nucleosynthesis and Rayleigh-Taylor instability in core-collapse supernova explosions. The inference is that Fe and Si in knots are relatively uncontaminated by lower Z elements and that their inferred ejecta mass coordinates appear to be entirely consistent with the expected Rayleigh-Taylor turbulence in a Type Ib supernova. We have further identified a region of nearly pure Fe ejecta that is a promising candidate for a site of -rich freezeout. Again it is mixed out by Rayleigh-Taylor turbulence, but as a site of -rich freezeout associated with 44Ti production, its origin should have been closer to the center and the mass cut than those of the other Fe-rich knots.
It is clearly desirable to make a complete census of the X-rayemitting Fe ejecta regions in Cas A and identify more regions that are highly enriched in Fe. For example, the ejected 44Ti mass is estimated at 1.8 × 10-4 M (Vink et al. 2001; Vink & Laming 2003), and 5001000 times more 56Ni by number is predicted globally from -rich freezeout (Woosley & Hoffman 1991; Arnett 1996; Thielemann et al. 1996; The et al. 1998). Hence, considerably more -rich freezeout ashes should be present in Cas A to account for the 44Ti emission than are inferred to be in regions "east" and "c6a." One might then be able to further speculate on issues concerning asymmetrical core-collapse explosions, such as pulsar kicks and gravitational radiation signatures (Burrows, Hayes, & Fryxell 1995; Burrows & Hayes 1996). In this work we have principally been limited by the statistical quality of the current Chandra data sets when extracting spectra from the smallest possible spatial regions. A considerably deeper observation is required to take full advantage of the unprecedented spatial resolution available with Chandra, which appears to be crucial in studying the Fe emission and making progress on important issues in supernova physics such as asymmetries, nucleosynthesis, and the location of the mass cut.
We wish to thank Larry Rudnick and Tracey DeLaney for communication of their results prior to publication and for allowing us access to their second-epoch Chandra/ACIS data of Cas A prior to their becoming public. J. M. L. was supported by basic research funds of the Office of Naval Research.
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2 = 2.3, 4.6, and 9.2 for the joint fit shown above.