Kinematics

17.2.4.1 Expansion Measurements

The availability of X-ray images of SNRs with angular resolution approaching those in the radio and optical made possible the first X-ray measurements of remnant expansion. For a remnant with an average forward shock velocity of 5000 km s^1 at a distance of 3 kpc, the average angular expansion rate is 0.35 arcsec per year. Thus even with the few arc second angular resolution of the early high resolution

-Cygnus Loop (NE)

Tycho, Knot g

imagers (Einstein and ROSAT) it became possible to measure global expansion rates of young, nearby remnants over the combined 10-15 yrs baseline spanned by these missions.

The first such measurement was facilitated by a deep ROSAT HRI image of Cas A taken in 1996, that could be used as a template. Koralesky et al. and Vink et al. independently used this observation together with archival ROSAT and Einstein HRI images to perform the first X-ray expansion rate measurements [87,167]. They both found an average expansion rate of (0.20± 0.01)% per year. The two studies differed on the presence of an azimuthal variation. The expansion rate corresponds to an expansion timescale of —500 yrs, which can be compared with the —340 yrs age of Cas A (in 1998). This difference is incompatible with the prediction of a model in which the remnant emission is dominated by ejecta interacting with a circumstellar shell created by a presupernova wind.

Early measurements of global expansion revealed a curious conundrum. In Cas A, Kepler and Tycho, the expansion rate measured in X-rays was roughly twice that measured in the radio [54,55]. For example, the expansion rate of Kepler from the X-ray measurement of 0.239% per year is to be compared with the radio measurement of 0.125% per year. In all three remnants, representing different explosion types and ages, the radio and X-ray features are interspersed, and so a common explanation entailing coincidental surperposition of X-ray filaments passing through the radio filaments is highly unlikely. For Cas A, the problem was compounded by the fact that the cospatial, fast-moving optical knots have an expansion rate 50% still higher than the X-ray. The difference was ascribed to different bands measuring distinct hydrodynamical structures (e.g., [87]), but begged the question of what band measures the true expansion rate.

Detailed kinematic studies using Chandra have helped resolve the issue. DeLaney et al. compared ACIS images of Cas A taken just 2 yrs apart [29]. Their difference map reveals a wide variety of proper motion speeds and directions. They were able to measure the proper motion of hundreds of individual features in addition to measuring the overall expansion of the remnant. They found that the motions throughout the remnant are complex, and cannot be modeled with a homologous expansion (e.g., [159]). The continuum-dominated filaments at the forward shock show a range of expansion rates from 0.02 to 0.33% per year. The median expansion rate of 0.2% per year can be compared with the expected free expansion rate of 0.3% per year to demonstrate that most of the forward shock has undergone significant deceleration. While X-ray ejecta are moving twice as fast as the cospatial radio knots, matched individual X-ray/radio features have the same velocity. Their interpretation of this complex situation is that the small-scale X-ray and radio features in the bright ring (which dominates the emission and thus the global proper motion studies) represent ejecta at various stages of deceleration after passage through the reverse shock. This establishes a velocity gradient from the densest knots, which emit primarily in the optical band, to the radio features which are the most decelerated. Features in all three bands show brightness evolution, however, potentially complicating this straightforward interpretation [30].

In contrast, a similar, preliminary analysis of the X-ray proper motions in Kepler from a pair of Chandra images reveals a mean expansion rate of 0.15% per year, consistent with the radio proper motion [134].

The proper motion study of Cas A also revealed three different classes of X-ray features, separable by their spectral and/or kinematic properties [30]. The Si and Fe dominated ejecta and continuum dominated forward shock filaments have roughly the same proper motion (a mean expansion rate of 0.2% per year), but distinct spatial distributions. This suggests the two components are somehow dynamically coupled. The ejecta knots are associated spatially with the optical fast moving knots, but have been significantly decelerated relative to them, probably as a consequence of lower density. A slow-moving component (0.05% per year) with enhanced low energy emission is apparently associated with the optical quasi-stationary flocculi, and thus might represent a clumpy circumstellar component. Thus, the power of Chandra is beginning to allow us to reconstruct the details of the presupernova environment of Cas A.

Chandra observations have also made possible the first expansion measurement of an extragalactic SNR. By comparing Chandra and ROSAT HRI observations taken 15yrs previously, Hughes et al. measured the expansion rate of 1E 0102.27219 in the SMC of 0.100 ± 0.025 percent per year, corresponding to a shock velocity of 6000 km s_1 [58].

17.2.4.2 Doppler Measurements

Measurements of radial velocities via Doppler shifts of X-ray lines in SNRs are challenging for even the current generation of instrumentation. While dispersive spectrometers such as crystals and gratings have adequate resolution to resolve velocity broadening produced by motion of a few thousand kilometers per second expected in young SNRs, the motion gets blurred by the finite angular size of the remnants. Nondispersive imaging spectrometers generally lack the spectral resolution to detect the broadening or line centroid shift resulting from radial motion. In only three instances have Doppler shifts been detected: Cas A, as a result of its asymmetric ejecta distribution; 1E 0102.2-7219, because of small size and its well-defined ring shape; and SN 1987A, because of its very small angular size. SN 1987A is discussed in Sect. 17.5.1.

The first measurement of Doppler motions in Cas A was performed using the Einstein FPCS. Markert et al. detected broadening and asymmetry in the Si and S lines [97]. They detected a systematic redshift of the northwest half of the remnant with respect to the southeast, with a mean velocity difference of 1820 ± 290 km s~1. Additionally, within each region a Doppler broadening of 5 000 km s^1 was detected. They suggested that the X-ray emission is concentrated in a ring inclined to the plane of the sky, with an expansion velocity greater than 2000 km s_1.

Subsequent results have largely substantiated these conclusions. Holt et al. constructed the first X-ray Doppler image of Cas A, using the ASCA SIS to measure spatially dependent shifts in the peak of the 1.85 keV Si Hea line [53]. Their map

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