# Harvard Astronomy 201b

## ARTICLE: The Three-Dimensional Structure of Cassiopeia A

### Read the Paper by T. DeLaney et al. (2010)

Summary by Ian Czekala and Nathan Sanders

### Abstract

We used the Spitzer Space Telescope’s Infrared Spectrograph to map nearly the entire extent of Cassiopeia A between 5-40 micron. Using infrared and Chandra X-ray Doppler velocity measurements, along with the locations of optical ejecta beyond the forward shock, we constructed a 3-D model of the remnant. The structure of Cas A can be characterized into a spherical component, a tilted thick disk, and multiple ejecta jets/pistons and optical fast-moving knots all populating the thick disk plane. The Bright Ring in Cas A identifies the intersection between the thick plane/pistons and a roughly spherical reverse shock. The ejecta pistons indicate a radial velocity gradient in the explosion. Some ejecta pistons are bipolar with oppositely-directed flows about the expansion center while some ejecta pistons show no such symmetry. Some ejecta pistons appear to maintain the integrity of the nuclear burning layers while others appear to have punched through the outer layers. The ejecta pistons indicate a radial velocity gradient in the explosion. In 3-D, the Fe jet in the southeast occupies a “hole” in the Si-group emission and does not represent “overturning”, as previously thought. Although interaction with the circumstellar medium affects the detailed appearance of the remnant and may affect the visibility of the southeast Fe jet, the bulk of the symmetries and asymmetries in Cas A are intrinsic to the explosion.

### Materials

• Handout given in class on 3/24/2011: Cas A Handout
• In order to follow along with this journal article, it will help a great deal to download the 3D PDF of the Cas A supernova remnant. Having this figure open throughout the paper will help guide one’s understanding of what structures are being referenced. Note that the 3D figure only works with Adobe PDF viewers (including the free Acrobat Reader).
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### Executive Summary

Supernova remnants (SNR) like Cassiopeia A (Cas A) are extremely interesting environments which can be studied to yield answers to many fundamental physical processes, such as enrichment of the interstellar medium with heavier metals synthesized in the supernova (SN) explosion, the structure of the SN explosion itself, and the accompanying astrophysical shocks. Cassiopeia A is the youngest known supernova remnant in our galaxy (determined to have exploded in the mid 1600’s), and because of its proximity to us, it is one of the best astrophysical objects to study to find answers to these questions.

In their 2010 paper, Delaney et al. utilize multi-wavelength observations of Cas A, including infrared (from Spitzer), optical (from Hubble), and x-ray (from Chandra) (Figure 1), and spectral line observations in order to decompose the complex structure of Cas A as we see it on the sky into a consistent 3D representation of the SNR as it actually exists in space. Most of the emission that the authors look at in this paper is from material that has been heated as it has passed through the reverse shock (see Figure 3), and therefore requires a suite of observations in multiple wavelengths in order to determine the source of the ejecta. By assuming a spherical fiducial reverse shock of the SNR, the authors are able to convert projected distance on the sky and Doppler shift information into 3D coordinates (see Figure 5).

Most importantly, the authors advance their “piston/jet” model (see Figure 2, or Figure 17 in the paper) in order to explain Cas A’s various ring-like structures.  If a column of ejecta was at a higher velocity than its surrounding ejecta, then it would push through the reverse shock sooner, and we would observe the piston/jet structure detailed in Figure 2. If we were to view this structure from above, then we would see a series of concentric rings of each element. From the shock structures, the authors conclude that the southeast Fe jet is not actually an overturning of the onion-shell structure of the ejecta, as previously thought, but instead represents a piston/jet structure. Delaney et al.’s The Three-Dimensional Structure of Cassiopeia A represents the first comprehensive 3D map of the structure of the Casseiopeia A supernova remnant compiled from an extensive set of multiwavelenth observations.

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Figure 1: Hubble and Chandra observations of Cas A, demonstrating it's two primary structures - the 200" Bright Ring (red, orange, green) and 300" thin X-ray filaments (blue). The remnant structures are labeled to help follow the structures talked about in Delaney et al. 2010

Figure 2: Piston-jet model proposed by Delaney et al. to explain much of the structure of Cas A.

### Introduction

A complete 3D map of a supernova explosion is vital to answering many important questions:

• Explosion mechanisms: does a magnetorotational instability form that actually helps to power the explosion? (Akiyama et al. 2003) What was the structure of the star during the explosion? (Wang et al. 2007)
• The role of rotation: again, what role does the MRI play in powering the explosion? (Moiseenko et al. 2007)
• Pulsar natal kicks: can gravitational and hydrodynamic forces associated with supernova asymmetries explain the observed proper motions of pulsars (Scheck et al. 2004)
• Interaction with circumstellar medium: how does the material ejected by the progenitor before it exploded effect the dynamics of the ejecta (Schure et al. 2008)?
• Supernova nucleosynthesis: can mixing in the explosion ejecta change the nucleosynthetic yields of supernovae? (Joggerst et al. 2009)
• Jets: could a jet geometry explain some of the peculiar optical properties of supernova remnants? (Wheeler et al. 2008)
• Gamma-ray bursts (GRBs): If jets can form in SNe explosions, are they responsible for GRBs? (Zhang et al. 2005) How is the association of GRBs with SNe related to explosion asymmetry and viewing angle? (Mazzali et al. 2005)

Why study Cas A? Because it’s perhaps the best nearby (at 3.4 kpc, it’s ~200″ in diameter!) example of a young (~330 year old) core-collapse supernova remnant. Cas A is bright at all wavelengths–in fact it is the brightest extrasolar radio source. It shows signs of high-velocity, clumpy ejecta that can be studied as distinct components of the ejecta through both Doppler shifts and proper motions.

What does Cas A look like? The primary feature of Cas A is the 200″ (3.3 pc)-diameter “Bright Ring.” This ring marks the location of the reverse shock (Figure 3), at which the ejecta gets compressed and heated. The location of the ring is expanding at thousands of km/s and has a measurable proper motion. Next is the 300″-diameter (5 pc) thin X-ray filaments, which mark the forward shock. These features are all apparent in the multi-wavelength image of Cas A below. Additionally, jets of Si and S-rich ejecta can be seen in the optical as far out as ~500″, rapidly expanding with proper motions reflecting velocities of up to 14,000 km/s. Some Fe-rich ejecta is found even farther out, perhaps due to an “overturning” of the outer ejecta layers during the explosion.

The three-dimensional structure of Cas A can be decomposed by simultaneous Doppler and proper-motion mapping of emission lines, primarily of S and O. These mappings indicate that the Bright Ring is actually made of two distinct rings and that there is a jet oriented approximately in the plane of the sky with an opening angle of 25 deg. Strangely, no knots of fast-moving material are observed in projection near the center of the remnant. Does this mean that the rings are truly two-dimensional, and that we are so fortunate as to see them face-on? It seems more likely that the ejecta is roughly spherical and the Bright Ring is simply a limb-brightened shell. High velocity ejecta is not observed near the center because it is too Doppler shifted to be detected in broadband imaging for proper motion studies and too faint to be observed in spectra.

In this paper, the authors assemble previous optical and X-Ray observations and structural modeling of Cas A and add new Spitzer infrared and Chandra X-Ray observations to compile the most complete three-dimensional reconstruction of Cas A.

Figure 3: A schematic explaining the forward shock, reverse shock, and ejecta structure of a supernova remnant. Velocity is plotted against radius from the center of the SNR. One can see that as the ejecta passes through the reverse shock it is decelerated. Figure from Truelove and McKee, 1999.

### Observations

In this paper, the authors primarily analyze:

• infrared data from Spitzer
• x-ray data from Chandra

Spitzer observations consisted of low-resolution spectra (R~60-128) from 5-15 $\mu$m and 15-38 $\mu$m and yielded three dimensional (RA, DEC, wavelength) data cubes. This encompasses nebular ionic emission lines for Ar, Ne, Si, S, Fe, O (blended with Fe), etc. In their first look at the data, the authors simply describe the spatial composition of the remnant by noting where they see these various emission feature. For example, they bought out a bright 26 micron emission line in the interior of the remnant and suggest that it is due to [O IV] and does not have a significant contribution from a nearby Fe line because there is little Fe emission at other wavelengths in this region.

How is the ejecta velocity determined from the spectra? First the authors binned the data cubes spatially by 2 pixels, so the effective resolution ranges from 3″.7 to 10″.2 depending on the feature. Next they do constrained Gaussian fitting and deblending (joint fitting) to extract the velocities (centroids) and brightnesses (fluxes) of the features. The automated fitting was then reviewed and adjusted manually (!!). In many cases, a second Gaussian component is used to account for additional projected features. The express a typical velocity error of 200 km/s, and as high as 700 km/s for weaker lines.

The authors note that the high resolution structure (knots on scales of 0″.2) seen in the optical will be obscured by their infrared observations.

The authors analyze more than a million seconds worth of archival Chandra data. The model that they fit to the X-ray spectra consists of background, interstellar absorption, bremsstrahlung continuum, and Gaussian lines from fifteen (!!) different emission features. The authors focus their analysis on the 6.6 keV Fe-K line because it is not contaminated by nearby lines and is located in a region with good energy calibration.

One caveat of the X-ray observations is that many emission features are blended such that the line centroid depends on both Doppler shift and ionization state. The authors are only able to correct for this ionization effect in one region of the remnant. This introduces a potential systematic error of thousands of km/s.

emission, where color represents velocity. The double ring structure (one redshifted, one blueshifted) is visible in the North.”]

### Results

The authors’ 3D reconstruction relies on the assumption of spherical free expansion, at least prior to encountering the reverse shock at the Bright Ring, such that distance from the center is proportional to velocity. The authors justify this because the higher resolution optical data from previous studies does not suggest that a more complicated model provides a better fit to the data.

The authors fit this spherical expansion model to the [Ar II] emission features, as illustrated in Figure 5. They determine that the center velocity of the shell is 860 km/s, the maximum (blueshifted) velocity is ~4000 km/s, and the scale factor for converting velocity to distance is 0″.022 per km/s. This second value is ~500 km/s slower than was determined from observations by Reed et al. 1995 and is potentially reflective of the reverse shock encountering slower ejecta over time.

Figure 5: Illustrating how deprojected distance is estimated from projected position and velocity assuming spherical free expansion. From Figure 9.

The authors investigate the suggestion that there could be a spatial progression from IR to X-ray emission as ejecta are increasingly ionized, but find that this is not visible at their resolution because the ejecta ionize so quickly; essentially, the inner edge of the bright ring is at the same location in infrared and X-ray emission. However, a different scale factor is required to convert X-ray Doppler velocity to distance than for infrared/optical velocities because the X-ray emission results from deceleration and heating following encounter of the reverse shock.

The authors claim that the [Ar II], [Ne II], and Si XIII emission forms rings on the surface of a sphere, and is not simply limb-brightened emission. When projected to our line of sight, these rings form the Bright Ring of Cassiopeia A. The Jet and the Counterjet of Cas A are associated with shock-heated Si/Ar/Ne rings. Additionally, thousands of “optical knots” composed of O, S, and N are seen outside of the reverse shock.

Pistons and Rings

As previously stated, the authors find that in many locations the Fe-K emission is encircled by the [Ar II] emission. On of the hallmarks of this paper is the conjuring of a piston/jet geometry in order to explain the many observed ringed structures (Figure 2, Figure 17 in the paper). If the explosion preserved the onion-shell structure of the massive progenitor star, then the ring-like structure could be explained by a piston/jet of faster moving material pushing through the reverse shock before the surrounding ejecta. This means that the faster ejecta are heated first and will then cool. Thus, the most intense emission will come from the regions that are just now crossing by the reverse shock. The piston head is “sliced” by the reverse shock, and these slices result in different concentric rings when viewed in a face-on projection. Fe-K emission is localized to three locations in the Cas A SNR, the west, north, and southeast, all of which represent piston/jet structures.

### The Thick-tilted disk

The authors find that most of the [Si II] emission is found interior (via Doppler correction) to the [Ar II] emission. They reject the idea that the [Si II] material has simply been decellerated via the shock, but is spatially coincident, because they do not find any evidence for shocked [Si II].  Thus, this emission must be interior to the shock. The authors conclude that there must be two populations of [Si II], the unshocked material interior to the shock, and then the shocked material that comprises the Bright Ring. The authors admit that their model reconstruction is very dependent upon this conclusion being true.

The rings of the [Ar II] match the holes of the [Si II], which according to the authors supports their idea that the Bright Ring is formed from the intersection of the spherical reverse shock and the flattened ejecta distribution, or “thick tilted-disk.” (Figure 6). This disk acts like a piston when it interacts with the reverse shock.

Figure 6: The 3D projections of Cas A showing the authors model of a "tilted thick disk."

In the southeast, both the Fe-K and the Ar II emission turn on at the reverse shock. The authors use the fact that the Fe-K emission correlates well with the rings of Ar II emission to confirm via a separate line of evidence that they have done a correct job of calculating the Doppler velocities. These fits are sensitive to the rest wavelength that was used. If this “rest wavelength” was off, then the entire Fe-K emission structure would be shifted into or out of the sky and thus loose alignment with the [Ar II] emission.

### Discussion and Conclusions

The piston/jet model (Figure 2) is essential to the authors’ discussion of the physical processes that are unfolding in the  Casseopia A supernova remnant. The ejecta from the explosion were expelled in a broad plane (thick tilted disk, Figure 6) that interacts with the (spherical) reverse shock to create the ring-like structures. For example, they map the Bright Ring onto a roughly spherical surface.

Hearteningly, the authors claim that separate light echo observations of Cas A are consistent with the calculated asymmetries of the supernova explosion. The thick tilted disk could explain why the supernova was not detected in the 1600s, which was projected explosion date given the current kinematics of the remnant. Most of the light would escape along the jet directions, which are in the plane of the sky, and the line of sight towards the observer would be obscured. For more information on light echos, please visit this astrobite post.

Many leading theories predict some asphericity intrinsic to core-collapse supernovae explosions (like Cas A). The authors use this fact to speculate that the oblate explosion geometry could be neutrino-driven as the progenitor star undergoes a core-collapse supernova. Indeed, the jet/toroidal structure evidenced by the bright-ring/jet could be caused by a jet-induced, thick disk model.  However, the authors concede that the models predict a perpendicular jet/toroidal structure while they observe that the toroidal structure and the jets are all in the same broad plane.

Speculations on the heating and cooling of ejecta during and after reverse shock passage seem to remain one of the undetermined areas upon which this paper relies. If radiative cooling of the x-ray ejecta were dominant, then the x-ray regions would be much thicker (spatially), since typical cooling scales for ejecta at these densities is $10^7$ to $10^8$ years. Therefore, the authors conclude that the x-ray shell is thin because of dynamical disruption and rapid disruption, which would give a timescale of ~200 years. However, the authors state that “the dominant physical processes are not clear,” and the authors point to the inconsistencies of dealing with the cooling times of the Fe ejecta. For example, the southeast Fe are more long-lived compared to the Bright Ring and other bright Fe regions, and these particular regions are consistent with the ~200 yr life times that are typical.  The proper motion measurements (more on this later) actually show that these optical knots are decellerated (probably from passing through the reverse shock).

### Forward shock vs. reverse shock asphericities

The authors find that the projected front shock (see Figure 3) does not show large asymmetries, and speculate that any early asymmetries may have been smoothed out through interaction with the circumstellar material. In fact, the question of whether the forward and reverse shocks are truly spherical is an important question in supernova remnant research. Bisnovatyi-Kogan and Blinnikov (1982) found that propagating shocks tend to isotropize with time, regardless of whether the initial shock was spherical or not.

Previously, the southeast region of the Cas A SNR was thought to be a region where there was overturning of the Si and Fe ejecta because the Fe ejecta were at a larger radius than the Si ejecta (again, think of the onion-shell structure of a massive star before explosion, where Si would be at a farther radius from Fe). However, this scenario could also be explained by the piston/jet model, in that the entire column of the ejecta has simply been displaced to a further radius, and the leading Si ejecta of the piston/jet has already passed through the reverse shock and cooled/dissipated significantly. The authors point to the fact that there is no Si emission immediately (radially) interior to the Fe emission, either shocked or unshocked, as evidence that their interpretation is correct.

Additionally, it remains a mystery why there are no ejecta knots at the reverse shock location on either the front or back sides of the SNR (as viewed by us from earth). The authors argue that this might be because the He and C layers (the outer layers of the onion-shell model of the progenitor star between us and the interior ejecta) would be at very low  densities. However, the low densities mean that the reverse shock structure would propagate faster and create a flattened reverse shock, which is not observed. From the shock structures, the authors conclude that the structure of the Cas A SNR was primarily shaped by the kinematics of the supernova explosion itself.

If one takes the time to play around with the 3D pdf of the Cas A remnant, one will likely notice a deficit of material at the interior of Cas A (projected view), which the authors admit is a puzzle and state that longer wavelength infrared observations are needed to to search for emission from unshocked Fe. Presumably, the trajectories of the unshocked ejecta have not been modified by the shock, and they retain the best information about the structure of the supernova event itself.

### Ways to observe the asymmetry of supernova explosions:

• Measure Doppler shifts of emission lines, assume a spherical reverse shock, and reconstruct the 3D structure using geometry, ala Delaney et al.
• Observe light echoes, the reflection/scattering of light from dust filaments that are hundreds of parsecs distant from the explosion (Figure 7).
• If the supernova remnant is particularly nearby, such as Cas A, it is possible to detect the proper motion of the ejecta over year-to-decade timescales.

Figure 7: Animated Light Echoes from the SN 1987A supernova remnant. Image courtesy EROS experiment.

### Remaining Questions

Ultimately, translating astrophysical data into 3D is hard. With all the sphericity/asphericity previously discussed, it can be difficult to match structures correctly in spatial coordinates. After reading Delaney et al. 2010, two questions remain concerning the previously mentioned “Doppler fingers” and the timescales of ejecta cooling. The authors claim that the “Doppler fingers” are not velocity structures, but rather where the ionization state is shifted, which skews their fit because this would show up as a blueshifted or redshifted line. However, how do they know which Doppler fingers to correct? Again, we have seen a discrepancy between the relatively short-lived ejecta to the north and west, and the longer-lived structures in the southeast. Why should these cooling scales be different? The authors venture that this might be due to interaction with circumstellar material that was ejected during the death-throes of the massive progenitor star.