Engineering topics

Reynolds, Stephen P.

Publications and source records attributed to Reynolds, Stephen P..

At least 19 records

DOE OSTI2022

The Eel Pulsar Wind Nebula: A PeVatron-candidate Origin for HAWC J1826-128 and HESS J182-130

HAWC J1826–128 is one of the brightest Galactic TeV γ-ray sources detected by the High Altitude Water Cherenkov (HAWC) observatory, with photon energies extending up to nearly ~100 TeV. This HAWC source spatially coincides with the H.E.S.S. TeV source HESS J1826–130 and the "Eel" pulsar wind nebula (PWN), which is associated with the GeV pulsar PSR J1826–1256. In the X-ray band, Chandra and XMM-Newton revealed that the Eel PWN is composed of both a compact nebula (~15'') and diffuse X-ray emission (~6' × 2') extending away from the pulsar. Our NuSTAR observation detected hard X-ray emission from the compact PWN up to ~20 keV and evidence of the synchrotron burn-off effect. In addition to the spatial coincidence between HESS J1826–130 and the diffuse X-ray PWN, our multiwavelength spectral energy distribution (SED) analysis using X-ray and γ-ray data establishes a leptonic origin of the TeV emission associated with the Eel PWN. Furthermore, our evolutionary PWN SED model suggests (1) a low PWN B-field of ~1 μG, (2) a significantly younger pulsar age (t ~ 5.7 kyr) than the characteristic age (τ = 14.4 kyr), and (3) a maximum electron energy of ${E}_{\max }=2$ PeV. The low B-field, as well as the putative supersonic motion of the pulsar, may account for the asymmetric morphology of the diffuse X-ray emission. Our results suggest that the Eel PWN may be a leptonic PeVatron particle accelerator powered by the ~6 kyr old pulsar PSR J1826–1256 with a spin-down power of 3.6 × 10 36 erg s –1 .

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS2018

Expansion and Age of the X-Ray Synchrotron-Dominated Supernova Remnant G330.2+1.0

We report new Chandra observations of one of the few Galactic supernova remnants whose X-ray spectrum is dominated by nonthermal synchrotron radiation, G330.2+1.0. We find that between 2006 and 2017, some parts of the shell have expanded by about 1%, giving a free-expansion (undecelerated) age of about 1000 yr, and implying shock velocities there of 9000 km/s for a distance of 5 kpc. Somewhat slower expansion is seen elsewhere around the remnant periphery, in particular in compact knots. Because some deceleration must have taken place, we infer that G330.2+1.0 is less than about 1000 yr old. Thus, G330.2+1.0 is one of only four Galactic core-collapse remnants of the last millennium. The large size, low brightness, and young age require a very low ambient density, suggesting expansion in a stellar-wind bubble. We suggest that in the east, where some thermal emission is seen and expansion velocities are much slower, the shock has reached the edge of the cavity. The high shock velocities can easily accelerate relativistic electrons to X-ray-emitting energies. A few small regions show highly significant brightness changes by 10%–20%, both brightening and fading, a phenomenon previously observed in only two supernova remnants, indicating strong and/or turbulent magnetic fields.

Borkowski, Kazimierz J.↗

NASA NTRS2018

The Expansion of the Young Supernova Remnant 0509-68.7 (N103B)

We present a second epoch of Chandra observations of the Type Ia Large Magellanic Cloud supernova remnant(SNR) 0509-68.7 (N103B) obtained in 2017. When combined with the earlier observations from 1999, we have a17.4 year baseline with which we can search for evidence of the remnant's expansion. Although the lack of strongpoint source detections makes absolute image alignment at the necessary accuracy impossible, we can measure thechange in the diameter and the area of the remnant, and find that it has expanded by an average velocity of 4170(2860, 5450) km s1. This supports the picture of this being a young remnant; this expansion velocity correspondsto an undecelerated age of 850 years, making the real age somewhat younger, consistent with results from lightecho studies. Previous infrared observations have revealed high densities in the western half of the remnant, likelyfrom circumstellar material, so it is probable that the real expansion velocity is lower on that side of the remnantand higher on the eastern side. A similar scenario is seen in Kepler's SNR. N103B joins the rare class ofMagellanic Cloud SNRs with measured proper motions.

Williams, Brian J.↗

NASA NTRS2017

The Three-Dimensional Expansion of the Ejecta from Tycho's Supernova Remnant

We present the first 3D measurements of the velocity of various ejecta knots in Tycho's supernova remnant, known to result from a Type Ia explosion. Chandra X-ray observations over a 12 yr baseline from 2003 to 2015 allow us to measure the proper motion of nearly 60 tufts of Si-rich ejecta, giving us the velocity in the plane of the sky. For the line-of-sight velocity, we use two different methods: a nonequilibrium ionization model fit to the strong Si and S lines in the 1.22.8 keV regime, and a fit consisting of a series of Gaussian lines. These methods give consistent results, allowing us to determine the redshift or blueshift of each of the knots. Assuming a distance of 3.5 kpc, we find total velocities that range from 2400 to 6600 km/s, with a mean of 4430 km/s. We find several regions where the ejecta knots have overtaken the forward shock. These regions have proper motions in excess of 6000 km/s. Some SN Ia explosion models predict a velocity asymmetry in the ejecta. We find no such velocity asymmetries in Tycho, and we discuss our findings in light of various explosion models, favoring those delayed-detonation models with relatively vigorous and symmetrical deflagrations. Finally, we compare measurements with models of the remnant's evolution that include both smooth and clumpy ejecta profiles, finding that both ejecta profiles can be accommodated by the observations.

ISM: individual objects (Tychoâ€™s SNR) â€“ ISM: s↗

NASA NTRS2017

Asymmetric Expansion of the Youngest Galactic Supernova Remnant G1.9+0.3

The youngest Galactic supernova remnant (SNR) G1.9+0.3, produced by a (probable) SN Ia that exploded approximately 1900 CE, is strongly asymmetric at radio wavelengths, much brighter in the north, but bilaterally symmetric in X-rays. We present the results of X-ray expansion measurements that illuminate the origin of the radio asymmetry. We confirm the mean expansion rate (2011-2015) of 0.58% per yr, but large spatial variations are present. Using the nonparametric 'Demons' method, we measure the velocity field throughout the entire SNR, finding that motions vary by a factor of 5, from 0.''09 to 0.''44 per yr. The slowest shocks are at the outer boundary of the bright northern radio rim, with velocities v(sub s) as low as 3600 km per sec (for an assumed distance of 8.5 kpc), much less than v(sub s) = 12,000-13,000 km per sec along the X-ray-bright major axis. Such strong deceleration of the northern blast wave most likely arises from the collision of SN ejecta with a much denser than average ambient medium there. This asymmetric ambient medium naturally explains the radio asymmetry. In several locations, significant morphological changes and strongly nonradial motions are apparent. The spatially integrated X-ray flux continues to increase with time. Based on Chandra observations spanning 8.3 yr, we measure its increase at 1.3% +/- 0.8% per yr. The SN ejecta are likely colliding with the asymmetric circumstellar medium ejected by the SN progenitor prior to its explosion.

ISM: individual objects (G1.9+0.3) ISM: individual↗

NASA NTRS2017

A Massive Shell of Supernova-Formed Dust in SNR G54.1+0.3

While theoretical models of dust condensation predict that most refractory elements produced in core-collapsesupernovae (SNe) efficiently condense into dust, a large quantity of dust has so far only been observed inSN1987A. We present an analysis of observations from the Spitzer Space Telescope, Herschel SpaceObservatory, Stratospheric Observatory for Infrared Astronomy, and AKARI of the infrared shell surrounding thepulsar wind nebula in the supernova remnant G54.1+0.3. We attribute a distinctive spectral feature at 21 m to amagnesium silicate grain species that has been invoked in modeling the ejecta-condensed dust in Cas A, whichexhibits the same spectral signature. If this species is responsible for producing the observed spectral feature andaccounts for a significant fraction of the observed infrared continuum, we find that it would be the dominantconstituent of the dust in G54.1+0.3, with possible secondary contributions from other compositions, such ascarbon, silicate, or alumina grains. The total mass of SN-formed dust required by this model is at least 0.3Me. Wediscuss how these results may be affected by varying dust grain properties and self-consistent grain heating models.The spatial distribution of the dust mass and temperature in G54.1+0.3 confirms the scenario in which the SNformeddust has not yet been processed by the SN reverse shock and is being heated by stars belonging to a clusterin which the SN progenitor exploded. The dust mass and composition suggest a progenitor mass of 1627Me andimply a high dust condensation efficiency, similar to that found for Cas A and SN1987A. The study providesanother example of significant dust formation in a Type IIP SN explosion and sheds light on the properties ofpristine SN-condensed dust.

Temim, Tea↗

NASA NTRS2016

The Distribution of Radioactive Ti-44 in Cassiopeia A

The distribution of elements produced in the innermost layers of a supernova explosion is a key diagnostic for studying the collapse of massive stars. Here we present the results of a 2.4 Ms NuSTAR observing campaign aimed at studying the supernova remnant Cassiopeia A (Cas A). We perform spatially resolved spectroscopic analysis of the Ti-44 ejecta, which we use to determine the Doppler shift and thus the three-dimensional (3D) velocities of the Ti-44 ejecta. We find an initial Ti-44 mass of (1.54 +/- 0.21) x 10(exp. -4) Solar Mass, which has a present-day average momentum direction of 340 degrees +/- 15 degrees projected onto the plane of the sky (measured clockwise from celestial North) and is tilted by 58 degrees +/- 20 degrees into the plane of the sky away from the observer, roughly opposite to the inferred direction of motion of the central compact object. We find some Ti-44 ejecta that are clearly interior to the reverse shock and some that are clearly exterior to it. Where we observe Ti-44 ejecta exterior to the reverse shock we also see shock-heated iron; however, there are regions where we see iron but do not observe Ti-44. This suggests that the local conditions of the supernova shock during explosive nucleosynthesis varied enough to suppress the production of Ti-44 by at least a factor of two in some regions, even in regions that are assumed to be the result of processes like Alpha-rich freezeout that should produce both iron and titanium.

rays: general â€“ ISM: supernova remnants â€“ nucl↗

NASA NTRS2016

An X-Ray and Radio Study of the Varying Expansion Velocities in Tycho's Supernova Remnant

We present newly obtained X-ray and radio observations of Tycho's supernova remnant using Chandra and the Karl G. Jansky Very Large Array in 2015 and 2013/14, respectively. When combined with earlier epoch observations by these instruments, we now have time baselines for expansion measurements of the remnant of 12-15 years in the X-rays and 30 years in the radio. The remnant's large angular size allows for proper motion measurements at many locations around the periphery of the blast wave. Consistent with earlier measurements, we find a clear gradient in the expansion velocity of the remnant, despite its round shape. The proper motions on the western and southwestern sides of the remnant are about a factor of two higher than those in the east and northeast. We showed in an earlier work that this is related to an offset of the explosion site from the geometric center of the remnant due to a density gradient in the ISM, and using our refined measurements reported here, we find that this offset is approximately 23″ toward the northeast. An explosion center offset in such a circular remnant has implications for searches for progenitor companions in other remnants.

dust↗

NASA NTRS2014

High-Energy X-Ray Imaging of the Pulsar Wind Nebula MSH 15-52: Constraints on Particle Acceleration and Transport

We present the first images of the pulsar wind nebula (PWN) MSH 15−52 in the hard X-ray band (8 keV), as measured with the Nuclear Spectroscopic Telescope Array (NuSTAR). Overall, the morphology of the PWN as measured by NuSTAR in the 3-7 keV band is similar to that seen in Chandra high-resolution imaging. However, the spatial extent decreases with energy, which we attribute to synchrotron energy losses as the particles move away from the shock. The hard-band maps show a relative deficit of counts in the northern region toward the RCW 89 thermal remnant, with significant asymmetry. We find that the integrated PWN spectra measured with NuSTAR and Chandra suggest that there is a spectral break at 6 keV, which may be explained by a break in the synchrotron emitting electron distribution at approximately 200 TeV and/or imperfect cross calibration. We also measure spatially resolved spectra, showing that the spectrum of the PWN softens away from the central pulsar B1509−58, and that there exists a roughly sinusoidal variation of spectral hardness in the azimuthal direction. We discuss the results using particle flow models. We find non-monotonic structure in the variation with distance of spectral hardness within 50 of the pulsar moving in the jet direction, which may imply particle and magnetic-field compression by magnetic hoop stress as previously suggested for this source. We also present two-dimensional maps of spectral parameters and find an interesting shell-like structure in the N(sub H) map. We discuss possible origins of the shell-like structure and their implications.

individual objects: G320.4-1.2↗

NASA NTRS2014

Nonuniform Expansion of the Youngest Galactic Supernova Remnant G1.9+0.3

We report measurements of the X-ray expansion of the youngest Galactic supernova remnant, G1.9+0.3, using Chandra observations in 2007, 2009, and 2011. The measured rates strongly deviate from uniform expansion, decreasing radially by about 60 along the X-ray bright SE-NW axis from 0.84 plus or minus 0.06% yr(exp -1) to 0.52% plus or minus 0.03 yr(exp -1). This corresponds to undecelerated ages of 120-190 yr, confirming the young age of G1.9+0.3 and implying a significant deceleration of the blast wave. The synchrotron-dominated X-ray emission brightens at a rate of 1.9% plus or minus 0.4% yr(exp -1). We identify bright outer and inner rims with the blast wave and reverse shock, respectively. Sharp density gradients in either the ejecta or ambient medium are required to produce the sudden deceleration of the reverse shock or the blast wave implied by the large spread in expansion ages. The blast wave could have been decelerated recently by an encounter with a modest density discontinuity in the ambient medium, such as may be found at a wind termination shock, requiring strong mass loss in the progenitor.

NONUNIFORM EXPANSION↗

NASA NTRS2014

Magnetic Field Amplification in the Thin X-Ray Rims of SN 1006

Several young supernova remnants, including SN 1006, emit synchrotron X-rays in narrow filaments, hereafter thin rims, along their periphery. The widths of these rims imply 50–100 μG fields in the region immediately behind the shock, far larger than expected for the interstellar medium compressed by unmodified shocks, assuming electron radiative losses limit rim widths. However, magnetic field damping could also produce thin rims. Here we review the literature on rim width calculations, summarizing the case for magnetic field amplification. We extend these calculations to include an arbitrary power-law dependence of the diffusion coefficient on energy, D ∝ Eμ. Loss-limited rim widths should shrink with increasing photon energy, while magnetic-damping models predict widths almost independent of photon energy. We use these results to analyze Chandra observations of SN 1006, in particular the southwest limb. We parameterize the FWHM in terms of energy as FWHM ∝ EmE γ. Filament widths in SN 1006 decrease with energy; mE ∼ −0.3 to −0.8, implying magnetic field amplification by factors of 10–50, above the factor of four expected in strong unmodified shocks. For SN 1006, the rapid shrinkage rules out magnetic damping models. It also favors short mean free paths (small diffusion coefficients) and strong dependence of D on energy (μ ≥ 1).

MAGNETIC FIELD AMPLIFICATION IN THE THIN X-RAY RIM↗

NASA NTRS2014

NuSTAR Study of Hard X-ray Morphology and Spectroscopy G21.5-0.9

We present NuSTAR high-energy X-ray observations of the pulsar wind nebula (PWN)/supernova remnant G21.5−0.9. We detect integrated emission from the nebula up to approx. 40 keV, and resolve individual spatial features over a broad X-ray band for the first time. The morphology seen by NuSTAR agrees well with that seen by XMM-Newton and Chandra below 10 keV. At high energies, NuSTAR clearly detects non-thermal emission up to approx. 20 keV that extends along the eastern and northern rim of the supernova shell. The broadband images clearly demonstrate that X-ray emission from the North Spur and Eastern Limb results predominantly from non-thermal processes. We detect a break in the spatially integrated X-ray spectrum at approx. 9 keV that cannot be reproduced by current spectral energy distribution models, implying either a more complex electron injection spectrum or an additional process such as diffusion compared to what has been considered in previous work. We use spatially resolved maps to derive an energy-dependent cooling length scale, E(sup m) is directly proportional to L(E) with m = −0.21 plus or minus 0.01. We find this to be inconsistent with the model for the morphological evolution with energy described by Kennel & Coroniti. This value, along with the observed steepening in power-law index between radio and X-ray, can be quantitatively explained as an energy-loss spectral break in the simple scaling model of Reynolds, assuming particle advection dominates over diffusion. This interpretation requires a substantial departure from spherical magnetohydrodynamic, magnetic-flux-conserving outflow, most plausibly in the form of turbulent magnetic-field amplification.

radiation mechanisms↗

NASA NTRS2014

A High-Resolution X-Ray and Optical Study of SN1006: Asymmetric Expansion and Small-Scale Structure in a Type Ia Supernova Remnant

We introduce a deep (670 ks) X-ray survey of the entire SN 1006 remnant from the Chandra X-Ray Observatory, together with a deep Hα image of SN 1006 from the 4 m Blanco telescope at CTIO. Comparison with Chandra images from 2003 gives the first measurement of the X-ray proper motions around the entire periphery, carried out over a 9 yr baseline. We find that the expansion velocity varies significantly with azimuth. The highest velocity of approx.7400 km/s (almost 2.5 times that in the northwest (NW)) is found along the southeast (SE) periphery, where both the kinematics and the spectra indicate that most of the X-ray emission stems from ejecta that have been decelerated little, if at all. Asymmetries in the distribution of ejecta are seen on a variety of spatial scales. Si-rich ejecta are especially prominent in the SE quadrant, while O and Mg are more uniformly distributed, indicating large-scale asymmetries arising from the explosion itself. Neon emission is strongest in a sharp filament just behind the primary shock along the NWrim, where the pre-shock density is highest. Here the Ne is likely interstellar, while Ne within the shell may include a contribution from ejecta. Within the interior of the projected shell we find a few isolated "bullets" of what appear to be supernova ejecta that are immediately preceded by bowshocks seen in Hα, features that we interpret as ejecta knots that have reached relatively dense regions of the surrounding interstellar medium, but that appear in the interior in projection. Recent three-dimensional hydrodynamic models for Type Ia supernovae display small-scale features that strongly resemble the ones seen in X-rays in SN 1006; an origin in the explosion itself or from subsequent hydrodynamic instabilities both remain viable options. We have expanded the search for precursor X-ray emission ahead of a synchrotron-dominated shock front, as expected from diffusive shock acceleration theory, to numerous regions along both the northeast and southwest rims of the shell. Our data require that a precursor be thinner than about 3, and fainter than about 5% of the post-shock peak. These limits suggest that the magnetic field is amplified by a factor of seven or more in a narrow precursor region, promoting diffusive particle acceleration.

galaxies: active↗

NASA NTRS2014

SN 2010j1: Optical to Hard X-Ray Observations Reveal an Explosion Embedded in a Ten Solar Mass Cocoon

Some supernovae (SNe) may be powered by the interaction of the SN ejecta with a large amount of circumstellar matter (CSM). However, quantitative estimates of the CSM mass around such SNe are missing when the CSM material is optically thick. Specifically, current estimators are sensitive to uncertainties regarding the CSM density profile and the ejecta velocity. Here we outline a method to measure the mass of the optically thick CSM around such SNe. We present new visible-light and X-ray observations of SN 2010jl (PTF 10aaxf), including the first detection of an SN in the hard X-ray band using NuSTAR. The total radiated luminosity of SN 2010jl is extreme atleast 9 1050 erg. By modeling the visible-light data, we robustly show that the mass of the circumstellar material within 1016 cm of the progenitor of SN 2010jl was in excess of 10M_. This mass was likely ejected tens of years prior to the SN explosion. Our modeling suggests that the shock velocity during shock breakout was 6000 km s1, decelerating to 2600 km s1 about 2 yr after maximum light. Furthermore, our late-time NuSTAR and XMM spectra of the SN presumably provide the first direct measurement of SN shock velocity 2 yr after the SN maximum light measured to be in the range of 2000-4500 km s1 if the ions and electrons are in equilibrium, and_2000 km s1 if they are not in equilibrium. This measurement is in agreement with the shock velocity predicted by our modeling of the visible-light data. Our observations also show that the average radial density distribution of the CSM roughly follows an r2 law. A possible explanation for the _10M_ of CSM and the wind-like profile is that they are the result of multiple pulsational pair instability events prior to the SN explosion, separated from each other by years.

circumstellar matter (CSM)↗

NASA NTRS2012

X-ray Proper Motions and Shock Speeds along the Northwest Rim of SN1006

We report the results of an X-ray proper motion measurement for the NW rim of SN 1006, carried out by comparing Chandra observations from 2001 and 2012. The NW limb has predominantly thermal X-ray emission, and it is the only location in SN 1006 with signi cant optical emission: a thin, Balmer-dominated lament. For most of the NW rim, the proper motion is approximately equal to 0.30"yr(exp -1), essentially the same as has been measured from the H alpha lament. Isolated regions of the NW limb are dominated by nonthermal emission, and here the proper motion is much higher, 0:49"yr(exp -1), close to the value measured in X-rays along the much brighter NE limb, where the X-rays are overwhelmingly nonthermal. At the 2.2 kpc distance to SN 1006, the proper motions imply shock velocities of approximately 3000 kms(exp -1) and approximately 5000 kms(exp -1) in the thermal and nonthermal regions, respectively. A lower velocity behind the H alpha filament is consistent with the picture that SN 1006 is encountering denser gas in the NW, as is also suggested by its overall morphology. In the thermally-dominated portion of the X-ray shell, we also see an o set in the radial profiles at different energies; the 0.5-0.6 keV peak dominated by O VII is closer to the shock front than that of the 0.8-3 keV emission|due to the longer times for heavier elements to reach ionization states where they produce strong X-ray emission.

Katsuda, Satoru↗

NASA NTRS2012

Dust in a Type Ia Supernova Progenitor: Spitzer Spectroscopy of Kepler's Supernova Remnant

Characterization of the relatively poorly-understood progenitor systems of Type Ia supernovae is of great importance in astrophysics, particularly given the important cosmological role that these supernovae play. Kepler's Supernova Remnant, the result of a Type Ia supernova, shows evidence for an interaction with a dense circumstellar medium (CSM), suggesting a single-degenerate progenitor system. We present 7.5-38 micron IR spectra of the remnant, obtained with the Spitzer Space Telescope, dominated by emission from warm dust. Broad spectral features at 10 and 18 micron, consistent with various silicate particles, are seen throughout. These silicates were likely formed in the stellar outflow from the progenitor system during the AGB stage of evolution, and imply an oxygen-rich chemistry. In addition to silicate dust, a second component, possibly carbonaceous dust, is necessary to account for the short-wavelength IRS and IRAC data. This could imply a mixed chemistry in the atmosphere of the progenitor system. However, non-spherical metallic iron inclusions within silicate grains provide an alternative solution. Models of collisionally-heated dust emission from fast shocks (> 1000 km/s) propagating into the CSM can reproduce the majority of the emission associated with non-radiative filaments, where dust temperatures are approx 80-100 K, but fail to account for the highest temperatures detected, in excess of 150 K. We find that slower shocks (a few hundred km/s) into moderate density material (n(sub o) approx 50-100 / cubic cm) are the only viable source of heating for this hottest dust. We confirm the finding of an overall density gradient, with densities in the north being an order of magnitude greater than those in the south.

Williams, Brian J.↗

NASA NTRS2012

The First Reported Infrared Emission from the SN1006 Remnant

We report results of infrared imaging and spectroscopic observations of the SN 1006 remnant, carried out with the Spitzer Space Telescope. The 24 m image from MIPS clearly shows faint filamentary emission along the northwest rim of the remnant shell, nearly coincident with the Balmer filaments that delineate the present position of the expanding shock. The 24 m emission traces the Balmer filaments almost perfectly, but lies a few arcsec within, indicating an origin in interstellar dust heated by the shock. Subsequent decline in the IR behind the shock is presumably due largely to grain destruction through sputtering. The emission drops far more rapidly than current models predict, however, even for a higher proportion of small grains than would be found closer to the Galactic plane. The rapid drop may result in part from a grain density that has always been lowera relic effect from an earlier epoch when the shock was encountering a lower densitybut higher grain destruction rates still seem to be required. Spectra from three positions along the NW filament from the IRS instrument all show only a featureless continuum, consistent with thermal emission from warm dust. The dust-to-gas mass ratio in the pre-shock interstellar medium is lower than that expected for the Galactic ISM-as has also been observed in the analysis of IR emission from other SNRs but whose cause remains unclear. As with other SNIa remnants, SN1006 shows no evidence for dust grain formation in the supernova ejecta.

Winkler, P. Frank↗

NASA NTRS2009

The First X-Ray Proper-Motion Measurements of the Forward Shock in the Northeastern Limb of Sn 1006

We report on the first X-ray proper-motion measurements of the nonthermally-dominated forward shock in the northeastern limb of SN 1006, based on two Chandra observations taken in 2000 and 2008. We find that the proper motion of the forward shock is about 0.48"/yr and does not vary around the rim within the approx.10% measurement uncertainties. The proper motion measured is consistent with that determined by the previous radio observations. The mean expansion index of the forward shock is calculated to be approx..0.54 which matches the value expected based on an evolutionary model of a Type Ia supernova with either a power-law or an exponential ejecta density profile. Assuming pressure equilibrium around the periphery from the thermally-dominated northwestern rim to the nonthermally-dominated northeastern rim, we estimate the ambient density to the northeast of SN 1006 to be approx..0.085/cu cm.

Katsuda, Satoru↗