Supernova remnants SNRs offer the means to study SN explosions dynamics and shocks at subparsec scales. In this white paper we discuss the major advances possible with Xray spectroimaging at arcsecond scales with a few eV spectral resolution and a large effective area.
['Astrophysics - High Energy Astrophysical Phenomena']
Supernova Remnants in High Definition
{'Supernova Remnants in High Definition': 'Thematic Areas:  \nGLYPH<3> Planetary Systems  \nGLYPH<3> Star and Planet Formation  \nGLYPH<3> 3 Formation and Evolution of Compact Objects  \nGLYPH<3> Cosmology and Fundamental Physics  \nGLYPH<3> 3 Stars and Stellar Evolution  \nGLYPH<3> Resolved Stellar Populations and their Environments  \nGLYPH<3> Galaxy Evolution  \nGLYPH<3> Multi-Messenger Astronomy and Astrophysics', 'Principal Author:': 'Name: Laura A. Lopez  \nInstitution: The Ohio State University  \nEmail: lopez.513@osu.edu  \nPhone: 814-404-1810', 'Co-authors:': 'Brian J. Williams (NASA Goddard Space Flight Center), Samar Safi-Harb (University of Manitoba), Sangwook Park (University of Texas Arlington), Paul P. Plucinsky (Harvard-Smithsonian Center for Astrophysics), David Pooley (Trinity University), Tea Temim (Space Telescope Science Institute), Katie Auchettl (DARK Cosmology Centre, Niels Bohr Institute), Aya Bamba (University of Tokyo), Carles Badenes (University of Pittsburgh), Daniel Castro (Harvard-Smithsonian Center for Astrophysics), Kristen Garofali (University of Arkansas), Denis Leahy (University of Calgary), Patrick Slane (Harvard-Smithsonian Center for Astrophysics), Jacco Vink (University of Amsterdam), Benjamin F. Williams (University of Washington), J. Craig Wheeler (University of Texas Austin)  \nAbstract : Supernova remnants (SNRs) offer the means to study SN explosions, dynamics, and shocks at sub-parsec scales. X-ray observations probe the hot metals synthesized in the explosion and the TeV electrons accelerated by the shocks, and thus they are key to test recent, high-fidelity three-dimensional SN simulations. In this white paper, we discuss the major advances possible with X-ray spectro-imaging at arcsecond scales, with a few eV spectral resolution and a large effective area. These capabilities would revolutionize SN science, offering a three-dimensional view of metals synthesized in explosions and enabling population studies of SNRs in Local Group galaxies. Moreover, this future X-ray mission could detect faint, narrow synchrotron filaments and shock precursors that will constrain the diffusive shock acceleration process.', 'I. The X-Ray View of Supernova Remnants': "Supernovae (SNe) play an essential role in the Universe. Metals synthesized during the explosion chemically enrich galaxies, supplying fodder for dust and the next generation of stars. Their shock waves plow through the interstellar medium (ISM) for thousands of years, accelerating particles to extreme energies ( GLYPH<24> 10 15 eV) and amplifying magnetic fields up to a thousand times that of the ISM. The shocks also heat surrounding gas and impart momentum, altering the phase structure of the ISM, shaping galaxies, and driving kpc-scale galactic winds.  \nAlthough hundreds of supernovae (SNe) are found each year at optical wavelengths by dedicated surveys, they are often too distant to resolve the SN ejecta and the immediate surroundings of the exploded stars. Studies of the closest SNe, such as SN 1987A (McCray & Fransson 2016), have advanced the field tremendously, but our understanding of SN progenitors and explosion mechanisms is hampered by the infrequency of nearby events.  \nSupernova remnants (SNRs) offer the means to study SN explosions, dynamics, and shocks at sub-pc scales, and they are an important tool to explore the relationship between compact objects and their explosive origins. Observations of SNR morphologies, kinematics, and chemical abundances are crucial to test and constrain recent, high-fidelity 3D SN simulations. Metals synthesized in the explosions are shock-heated to GLYPH<24> 10 7 K temperatures (see Fig. 1), and TeV electrons accelerated by the forward shock emit synchrotron radiation at X-ray energies. Thus, X-ray observations are a crucial means to probe the bulk of SNR ejecta material and the particle acceleration process. Magellanic Cloud SNRs N103B X-ray Surveyor C )  \nFuture X-ray facilities offer exciting prospects for major advancements in SN science. Increased effective area relative to Chandra and XMM-Newton will enable detailed investigation of faint and distant SNRs, including the > 600 SNRs in the Milky Way and Local Group galaxies (e.g., Badenes et al. 2010; Ferrand & Safi-Harb 2012; Sasaki et al. 2012; Maggi et al. 2016; Garofali et al. 2017; Green 2017). Sub-arcsecond spatial resolution will enable proper motion studies over a baseline of several decades, and it will facilitate a resolved view of the thin synchrotron filaments around the periphery of young SNRs. X-ray microcalorimeters will resolve He-like and H-like line complexes of many elements, facilitating 3D mapping of metals synthesized in the explosions. With these capabilities, the sample size of young SNRs with morphological, kinematic, and nucleosynthetic measurements dramatically increases, and these observations are crucial to inform SN models and probe SN feedback and chemical enrichment in different Galactic environments. 40 ks B. W i l l i a ms (G SF  \nAthena+  \n40 ks  \nExample: N103B in LMC ¥ Type Ia SNR similar to Kepler - strong evidence for CSM inte ¥ Chandra studies show eviden spectral variations on multiple ¥ Arcsecond resolution required t spectrum on physically importa Figure 1: Simulated Athena (left) and Lynx (middle) images of the Type Ia SNR N103B in the LMC. The right panel shows simulated microcalorimeter spectra from two locations in N103B. A 1 00 -pixel microcalorimeter is vital to obtain distinct spectra from the ejecta and the CSM components.  \n7  October 2015  \n<!-- image -->  \nPatrick Slane                                               X-ray Vision Workshop  \n<!-- image -->  \n<!-- image -->  \nFigure 2: Images of Cas A, with 5 00 resolution (left) and 1 00 resolution (middle), corresponding to the spatial resolution of the proposed microcalorimeters on Athena and Lynx . Right : 3D view of Cas A, with Fe (X-rays) in green, Ar and Si (optical) in purple and blue, and cold ejecta (IR) in red. An X-ray microcalorimeter with 1 00 -pixels would yield a resolved 3D view of Cas A's hot ejecta, the vast majority of the metals synthesized in the SN explosion.  \n<!-- image -->  \nIn this white paper, we focus on the SNR science enabled by a future X-ray facility with sub-arcsecond spatial resolution capabilities (0.5 00 imaging), superb spectral resolution with spectroimaging capabilities (a few eV at 1 00 scales), and a large effective area (2 m 2 ). In additional white papers, B. Williams et al. describes the major advances X-ray microcalorimeters will enable in understanding SN explosions, and S. Safi-Harb et al. summarizes the significant progress that spatial resolution and increased effective area provides regarding neutron stars (NSs) and pulsar wind nebulae (PWNe).", 'II. Resolving Galactic and Extragalactic SNRs': 'Since Chandra \'s first-light image of Cassiopeia A (Cas A) showing narrow, non-thermal filaments, small ejecta knots, and a neutron star at its center, the scientific benefit and beauty of high spatial resolution at X-ray energies became evident. However, a prime limitation of current facilities is that CCD energy resolution is insufficient to resolve He-like and H-like line complexes, and gratings spectrometers are only useful if SNRs have minimal angular extents (e.g., Dewey et al. 2008) or to study isolated ejecta knots (e.g., Bhalerao et al. 2015).  \nX-ray microcalorimeters (which are non-dispersive) will revolutionize SNR studies, and the few eV spectral resolution across these objects will yield the kinematics and a three-dimensional mapping of hot ejecta metals. The Hitomi spectra of the young SNR N132D, which showed bulk redshifted iron indicative of a highly asymmetric explosion (Hitomi Collaboration et al. 2018), gave a tantalizing glimpse of the power of high-resolution spectro-imaging capabilities. Within the Milky Way, the Athena microcalorimeter (with 5 00 pixels) will obtain superb spectra that will enable characterization of the individual components, e.g. the Si-rich jet, the Fe ahead of the forward shock, and the synchrotron filaments around the periphery (see Figure 2).  \nWith a 1 00 -pixel microcalorimeter, these features are resolved in even more detail, reducing confusion and enabling precise measures of the kinematics, shock heating, ejecta mixing, chemistry, and the non-thermal radiation. In particular, with a few eV spectral resolution on 1 00 scales, it is possible to obtain accurate radial velocities of ejecta knots in young, ejecta-dominated SNRs. Given the limitations associated with dispersed spectra from extended objects, current studies have only measured radial velocities for the brightest knots in a handful of SNRs (e.g., Bhalero et al. 2015). Thus, the combination of a few eV spectral resolution and 1 00 spatial resolution in the un-dispersed spectrum would truly revolutionize SNR studies, expanding the view of SNRs from two dimensions into 3D. For example, Figure 2 shows the 3D view of Cas A, obtained using  \nN  \nN  \n50  \n50  \n40  \n40  \n30  \nN  \n30  \n20  \n20  \n10  \n10  \nN  \n0  \n0  \n20  \n0  \n0  \n20  \n50  \n40  \n50  \nN  \n30  \n40  \n20  \n30  \n10  \n20  \n0  \n0  \n10  \n50  \n40  \n30  \n20  \n10  \n0  \n0  \nFig. 11. Cumulative X-ray luminosity function of SNRs in Local Group galaxies. See text for details and references on how L X was measured for each sample. The brightest SNR in each galaxy is marked by a dot. The thin dotted lines are nonlinear least-square fits of a power law ( N ( > L X) ∝ L X α ). Slopes α are given in the legend. These fits are only used to characterise the slopes and illustrate the di ff erences between galaxies; they do not represent a physical fit of the population. the median temperatures are kT = 0 . 31 keV for luminosities less than 10 35 erg s -1 , 0.55 keV between 10 35 erg s -1 and 10 36 erg s -1 , and 0.8 keV above 10 36 erg s -1 . The luminosities of M31 SNRs were given assuming kT = 0 . 2keV;wescaledthe the higher (recent) SFR in M33 compared to M31 (0.45 M /circledot yr -vs. 0.27 M /circledot yr -1 , Verley et al. 2009; Tabatabaei & Berkhuijsen 2010) leading to a larger production of CC SNRs in M33. In the same luminosity range, the number of LMC SNRs is comparable to that in M33. This is expected because the LMC is only slightly less massive than M33. Furthermore, the recent SFR of the LMC is high, 0.3-0.4 M /circledot yr -1 in the last 40 Myr (Harris & Zaritsky 2009). This conspires with the high current type Ia SN rate (Sect. 6.4) to build up the large population of SNRs in the LMC. Finally, the \'feather-weight\' SMC (about ten times less massive than the LMC, (Stanimirovi«cetal.2004; Harris & Zaritsky 2006) has a smaller, yet decent population of remnants, likely owing to its recent star formation activity Figure 3. Distribution of the SNR sizes listed in Table 1 for the LMC (red solid plots) and SMC (blue dashed plots), represented as cumulative (left) and differential (right) histograms. For illustrative purposes, linear size distributions normalized to give the correct number of SNRs at a diameter of 40 pc have been overplotted as dotted lines on the cumulative histograms. Both galaxies have SNR size distributions that are close to linear in the cumulative, orflatinthe differential, up to a cut-off at r ∼ 30 pc. Because the data points in a cumulative histogram are not independent of one another, these curves cannot be fitted in the usual way (using the χ 2 statistic). A robust, quantitative estimate for the smaller number of SNRs, it is consistent with both slopes. From Fig. 3, it appears that the steeper slope in the SMC is driven by the small-radius side of the distribution. Indeed, if we fit separately ps: / / academic. oup. com/ Figure 3. Distribution of the SNR sizes listed in Table 1 for the LMC (red solid plots) and SMC (blue dashed plots), represented as cumulative (left) and differential (right) histograms. For illustrative purposes, linear size distributions normalized to give the correct number of SNRs at a diameter of 40 pc have been overplotted as dotted lines on the cumulative histograms. Both galaxies have SNR size distributions that are close to linear in the cumulative, orflatinthe differential, up to a cut-off at r ∼ 30 pc. Because the data points in a cumulative histogram are not independent of one another, these curves cannot be fitted in the usual way (using the χ 2 statistic). A robust, quantitative estimate for the smaller number of SNRs, it is consistent with both slopes. From Fig. 3, it appears that the steeper slope in the SMC is driven by the small-radius side of the distribution. Indeed, if we fit separately ps: / / academic. oup. com/ Figure 3. Distribution of the SNR sizes listed in Table 1 for the LMC (red solid plots) and SMC (blue dashed plots), represented as cumulative (left) and differential (right) histograms. For illustrative purposes, linear size distributions normalized to give the correct number of SNRs at a diameter of 40 pc have been overplotted as dotted lines on the cumulative histograms. Both galaxies have SNR size distributions that are close to linear in the cumulative, orflatinthe differential, up to a cut-off at r ∼ 30 pc. Because the data points in a cumulative histogram are not independent of one another, these curves cannot be fitted in the usual way (using the χ 2 statistic). A robust, quantitative estimate for the smaller number of SNRs, it is consistent with both slopes. From Fig. 3, it appears that the steeper slope in the SMC is driven by the small-radius side of the distribution. Indeed, if we fit separately ps: / / academic. oup. com/ Figure 3. Distribution of the SNR sizes listed in Table 1 for the LMC (red solid plots) and SMC (blue dashed plots), represented as cumulati differential (right) histograms. For illustrative purposes, linear size distributions normalized to give the correct number of SNRs at a diameter o been overplotted as dotted lines on the cumulative histograms. Both galaxies have SNR size distributions that are close to linear in the cumulative, differential, up to a cut-off at r ∼ 30 pc. Because the data points in a cumulative histogram are not independent of one another, these curves cannot be fitted in the usual way (using the χ 2 statistic). A robust, quantitative estimate for the smaller number of SNRs, it is consistent with both s Fig. 3, it appears that the steeper slope in the SMC is the small-radius side of the distribution. Indeed, if we fit 0 20 40 60 Diameter [pc] Diameter [pc] Figure 3. Distribution of the SNR sizes listed in Table 1 for the LMC (red solid plots) and SMC (blue dashed plots), represented as cumulative (left) and differential (right) histograms. For illustrative purposes, linear size distributions normalized to give the correct number of SNRs at a diameter of 40 pc have been overplotted as dotted lines on the cumulative histograms. Both galaxies have SNR size distributions that are close to linear in the cumulative, orflatinthe differential, up to a cut-off at r ∼ 30 pc. Because the data points in a cumulative histogram are not independent of one another, these curves cannot be fitted in the usual way (using the χ 2 statistic). A robust, quantitative estimate for the slope of the distributions can be obtained by performing instead a maximum-likelihood fit, as follows (see Maoz & Rix 1993, for a smaller number of SNRs, it is consistent with both slopes. From Fig. 3, it appears that the steeper slope in the SMC is driven by the small-radius side of the distribution. Indeed, if we fit separately the first eight points and the following 14 points, the maximumlikelihood solution is 1.7 1.0 at small radii, and 0.17 rom ht t ps: / / academic. oup. com/ mnras/ Figure 3. Distribution of the SNR sizes listed in Table 1 for the LMC (red solid plots) and SMC (blue dashed plots), represented as cumulative (left) and differential (right) histograms. For illustrative purposes, linear size distributions normalized to give the correct number of SNRs at a diameter of 40 pc have been overplotted as dotted lines on the cumulative histograms. Both galaxies have SNR size distributions that are close to linear in the cumulative, orflatinthe differential, up to a cut-off at r ∼ 30 pc. Because the data points in a cumulative histogram are not independent of one another, these curves cannot be fitted in the usual way (using the χ 2 statistic). A robust, quantitative estimate for the smaller number of SNRs, it is consistent with both slopes. From Fig. 3, it appears that the steeper slope in the SMC is driven by the small-radius side of the distribution. Indeed, if we fit separately ps: / / academic. oup. com/ 0 20 40 60 80 100 120 Diameter [pc] 0 0 20 40 60 80 100 120 Diameter [pc] 0 Figure 3. Distribution of the SNR sizes listed in Table 1 for the LMC (red solid plots) and SMC (blue dashed plots), represented as cumulative (left) and differential (right) histograms. For illustrative purposes, linear size distributions normalized to give the correct number of SNRs at a diameter of 40 pc have been overplotted as dotted lines on the cumulative histograms. Both galaxies have SNR size distributions that are close to linear in the cumulative, orflatinthe differential, up to a cut-off at r ∼ 30 pc. f rom ht t ps: / / academic. Figure 3: Left : Luminosity function of known SNRs in nearby galaxies LMC, SMC, M31, and M33 (from Maggi et al. 2016). The anticipated number of counts in a 100 ks Lynx exposure from SNRs are shown along the top for a distance of 1 Mpc. Right : Histogram of the size distribution of SNRs in the LMC and SMC (Badenes et al. 2010). The dark grey line represents the physical size of 25 00 at a distance of 1 Mpc. Thus, arcsecond pixels would be sufficient to measure extension of the SNRs across many resolution elements, whereas 5 00 pixels would only resolve the largest SNRs.  \n<!-- image -->  \nSizes of SNRs in the Magellanic Clouds  \n1307  \nSizes of SNRs in the Magellanic Clouds  \n1307  \nCorbelli 2003; Peñarrubia et al. 2014). This shows the e  \nff  \nect of  \n80  \n100  \n120  \n0  \n20  \n40  \n60  \n80  \n100  \n120  \nα  \nSizes of SNRs in the Magellanic Clouds  \n1307  \nSizes of SNRs in the Magellanic Clouds  \n1307  \nLMC  \nSMC  \n120  \n120  \n60  \n80  \n100  \n120  \nDiameter [pc]  \nSizes of SNRs in the Magellanic Clouds  \nLMC  \nSMC  \nDownloaded  \nf  \nrom  \nDownloaded  \nf  \nht  \nt  \n1  \n1307  \n1307  \nDownloaded  \nDownloaded  \nf  \nf  \nrom  \nrom  \nht  \nht  \nt  \nDownloaded  \nf  \nrom  \nht  \nt  \nt  \n2  \nDownloaded  \n0.3 keV -8keVluminosityupby1.05,1.20,and1.35forsources with L X < 10 35 , 10 35 < L X < 10 36 , and L X > 10 36 erg s -1 , respectively. M33 SNRs were assumed to have a higher temperature (0.6 keV), which means that the luminosity of objects below ∼ 10 35 erg s -1 was overestimated by about 15%, while for those above 10 36 erg s -1 it was underestimated by ∼ 8%. Correcting for this e ff ect ensures a meaningful comparison between M31, M33, and the LMC. The SMC SNR population is comparatively smaller. van der Heyden et al. (2004) presented an X-ray spectral analysis of all SNRs in the SMC known at that time. We used their (0.08 -0.3 M /circledot yr -1 , Harris & Zaritsky 2004). In terms of shape, the XLF of M31 SNRs is the most uniform, following a power law ( N ( > L X) ∝ L X α )with α = -0 . 86 ± 0 . 04 down to ∼ 2 × 10 35 erg s -1 . This holds with or without including the candidates, which means that most are indeed bonafide SNRs. The M33 remnants follow mostly the same distribution, with α = -0 . 76 ± 0 . 05. Towards the faint end, the M33 XLF flattens and diverges from the power law below 10 35 erg s -1 , indicating incompleteness. Long et al. (2010) concluded that no SNR brighter than 4 10 35 erg s -1 was missed across the slope of the distributions can be obtained by performing instead a maximum-likelihood fit, as follows (see Maoz & Rix 1993, for a similar treatment applied to a different problem). Suppose that a particular model predicts a size distribution d N / d r = n ( r ), which integrates to ∫ r cut 0 n ( r )d r = N ,where N is the total number of remnants up to r cut. If we bin our data into many small bins between r = 0and r cut,eachofwidth δ r , most bins will have zero SNRs, and the first eight points and the following 14 points, the maximumlikelihood solution is α = 1.7 ± 1.0 at small radii, and α = 0.17 ± 0.23 thereafter. This result confirms the visual impression, but formally it is still consistent with a slope close to zero at all radii at the 1.7 σ level. We conclude that the SNR size distribution in both Clouds is consistent with being roughly uniform, although there are hints for a deviation at small radii in the SMC. It is possible that mnras/ art icle-abst ract slope of the distributions can be obtained by performing instead a maximum-likelihood fit, as follows (see Maoz & Rix 1993, for a similar treatment applied to a different problem). Suppose that a particular model predicts a size distribution d N / d r = n ( r ), which integrates to ∫ r cut 0 n ( r )d r = N ,where N is the total number of remnants up to r cut. If we bin our data into many small bins between r = 0and r cut,eachofwidth δ r , most bins will have zero SNRs, and the first eight points and the following 14 points, the maximumlikelihood solution is α = 1.7 ± 1.0 at small radii, and α = 0.17 ± 0.23 thereafter. This result confirms the visual impression, but formally it is still consistent with a slope close to zero at all radii at the 1.7 σ level. We conclude that the SNR size distribution in both Clouds is consistent with being roughly uniform, although there are hints for a deviation at small radii in the SMC. It is possible that mnras/ art icle-abst ract slope of the distributions can be obtained by performing instead a maximum-likelihood fit, as follows (see Maoz & Rix 1993, for a similar treatment applied to a different problem). Suppose that a particular model predicts a size distribution d N / d r = n ( r ), which integrates to ∫ r cut 0 n ( r )d r = N ,where N is the total number of remnants up to r cut. If we bin our data into many small bins between r = 0and r cut,eachofwidth δ r , most bins will have zero SNRs, and the first eight points and the following 14 points, the maximumlikelihood solution is α = 1.7 ± 1.0 at small radii, and α = 0.17 ± 0.23 thereafter. This result confirms the visual impression, but formally it is still consistent with a slope close to zero at all radii at the 1.7 σ level. We conclude that the SNR size distribution in both Clouds is consistent with being roughly uniform, although there are hints for a deviation at small radii in the SMC. It is possible that mnras/ art icle-abst ract slope of the distributions can be obtained by performing instead a maximum-likelihood fit, as follows (see Maoz & Rix 1993, for a similar treatment applied to a different problem). Suppose that a particular model predicts a size distribution d N / d r = n ( r ), which integrates to ∫ r cut 0 n ( r )d r = N ,where N is the total number of remnants up to r cut. If we bin our data into many small bins between r = 0and r cut,eachofwidth δ r , most bins will have zero SNRs, and the first eight points and the following 14 points, the likelihood solution is α = 1.7 ± 1.0 at small radii, and 0.23 thereafter. This result confirms the visual impressi mally it is still consistent with a slope close to zero at the 1.7 σ level. We conclude that the SNR size distribut Clouds is consistent with being roughly uniform, a hints for a deviation at small radii in the SMC. It is similar treatment applied to a different problem). Suppose that a particular model predicts a size distribution d N / d r = n ( r ), which integrates to ∫ r cut 0 n ( r )d r = N ,where N is the total number of remnants up to r cut. If we bin our data into many small bins between r = 0and r cut,eachofwidth δ r , most bins will have zero SNRs, and some will have one SNR. Given the model, the Poisson probability of finding j remnants in the i th bin, for which the model predicts n ( ri ) remnants, is P ( j | n ( ri )) = e -n ( ri ) n ( ri ) j /j ! . (1) 0.23 thereafter. This result confirms the visual impression, but formally it is still consistent with a slope close to zero at all radii at the 1.7 σ level. We conclude that the SNR size distribution in both Clouds is consistent with being roughly uniform, although there are hints for a deviation at small radii in the SMC. It is possible that a deficit at small radii is also present in the LMC distribution (see Fig. 3), but the Poisson errors are too large to claim that the data require it. The linear cumulative distribution of SNR sizes in the MCs (and also the Milky Way) has been previously noted and discussed art icle-abst ract / 407/ 2/ 1301/ slope of the distributions can be obtained by performing instead a maximum-likelihood fit, as follows (see Maoz & Rix 1993, for a similar treatment applied to a different problem). Suppose that a particular model predicts a size distribution d N / d r = n ( r ), which integrates to ∫ r cut 0 n ( r )d r = N ,where N is the total number of remnants up to r cut. If we bin our data into many small bins between r = 0and r cut,eachofwidth δ r , most bins will have zero SNRs, and the first eight points and the following 14 points, the maximumlikelihood solution is α = 1.7 ± 1.0 at small radii, and α = 0.17 ± 0.23 thereafter. This result confirms the visual impression, but formally it is still consistent with a slope close to zero at all radii at the 1.7 σ level. We conclude that the SNR size distribution in both Clouds is consistent with being roughly uniform, although there are hints for a deviation at small radii in the SMC. It is possible that mnras/ art icle-abst ract Because the data points in a cumulative histogram are not independent of one another, these curves cannot be fitted in the usual way (using the χ 2 statistic). A robust, quantitative estimate for the slope of the distributions can be obtained by performing instead a maximum-likelihood fit, as follows (see Maoz & Rix 1993, for a similar treatment applied to a different problem). Suppose that a smaller number of SNRs, it is consistent with both slopes. From Fig. 3, it appears that the steeper slope in the SMC is driven by the small-radius side of the distribution. Indeed, if we fit separately the first eight points and the following 14 points, the maximumlikelihood solution is α = 1.7 ± 1.0 at small radii, and α = 0.17 ± 0.23 thereafter. This result confirms the visual impression, but foroup. com/ mnras/ art optical, infrared, and X-ray facilities. A microcalorimeter with 1 00 -pixels would yield a similar 3D map of young SNRs\' hot ejecta, the majority of the metals synthesized in the SN explosion. In addition, improved effective area at hard X-ray energies ( GLYPH<24> 6-8 keV, where current X-ray telescopes have low sensitivity) would facilitate constraints on Fe-K and the Fe-group elements, which are especially crucial to explore Type Ia progenitor scenarios.  \n=  \n±  \nα  \n=  \n±  \nbest-fit models to measure the observed (i.e. absorbed) X-ray luminosity in the same 0.3 keV -8keVband 19 ,exceptforIKT16. For this SNR we used results from Owen et al. (2011), which included more data from subsequent XMM-Newton observations. Three additional SNRs were covered with XMM-Newton ; the results were published in Filipovi«c et al. (2008), from which we borrowed the best-fit spectral models. The latter study also reported a new SNR, HFPK 334. For this one, we used the best-fit model from Crawford et al. (2014), which combined XMM-Newton and Chandra observations. Also included is the SNR XMMU J0056.5 -7208 identified during the SMC survey (Haberl et al. 2012b; Sturm 2012). Finally, the Be / X-ray binary pulsar SXP 1062 was found to be associated to an SNR, of which it is most likely the progenitor (Hénault-Brunet et al. 2012). The thermal emission from the SNR was studied by Haberl et al. (2012c). This sample of 19 SMC SNRs is the most up to date. 19 The luminosity given in van der Heyden et al. (2004), Table 3, for IKT 22 (1E0102 -7219, the brightest SMC SNR) was mistyped. Instead of the 150 × 10 27 W, it should read 1500 × 10 27 W(1 . 5 × 10 37 erg s -1 ). × surveyed field. It is likely that they were over-conservative and that missing SNRs are only those which have luminosity below 10 35 erg s -1 . The combined ChASeM33 and XMM-Newton surveys cover the total extent of the galaxy (Plucinsky et al. 2008; Williams et al. 2015), so the missing SNRs are either too X-rayfaint (below the surveys\' detection limits), or absent / undetected at radio and optical wavelengths, precluding their identifications as SNRs. We performed Kolmogorov-Smirnov (KS) tests to compare the di ff erent populations. Using a bootstrapping method, we produced 1000 luminosity functions from the original data. We checked that similar results were obtained when increasing that number to 10 6 . Restricting the analysis to SNRs brighter than 3 × 10 35 erg s -1 to ensure completeness of the samples, we found that the XLFs of M31 and M33 SNRs follow the same distribution at the 3 σ confidence level. There was a marginal indication that the M33 distribution was steeper than that of M31 (Sasaki et al. 2012), but this di ff erence essentially disappears once the kT -L X trend is taken into account. A162, page 22 of 52 some will have one SNR. Given the model, the Poisson probability of finding j remnants in the i th bin, for which the model predicts n ( ri ) remnants, is P ( j | n ( ri )) = e -n ( ri ) n ( ri ) j /j ! . (1) We will define the likelihood of a given model as the product of these probabilities. The logarithm of the likelihood, considering that j always equals either 0 or 1, simplifies to ln L = [ ∑ i ( j> 0) ln n ( ri ) ] -N, (2) where the summation is only over the specific data values of the SNRradii. A power law of index α , having the proper normalization, will have the form n ( r ) = N ( α + 1) r α + 1 cut r α . (3) Inserting in equation (2), differentiating ln L with respect to α and a deficit at small radii is also present in the LMC distribution (see Fig. 3), but the Poisson errors are too large to claim that the data require it. The linear cumulative distribution of SNR sizes in the MCs (and also the Milky Way) has been previously noted and discussed by Mathewson et al. (1984), Mills et al. (1984), Green (1984), Hughes et al. (1984), Fusco-Femiano & Preite-Martinez (1984), Berkhuijsen (1987), Chu & Kennicutt (1988) and, most recently, Bandiera & Petruk (2010). Several of these papers also pointed out cut-offs in the distribution. All of these papers considered smaller SNR samples, often based on much shallower radio data and, with few exceptions, did not include multi-wavelength observations. Some of these authors interpreted the observed size distribution as evidence that most MC SNRs are in their \'free expansion\' phase, during which the shock velocity is constant, and inferred that these SNRs expand into an extremely low density medium. Alternatively, Green (1984) and Hughes et al. (1984) warned that the observed distribution was the result of selection effects; most objects they discussed had been selected in X-rays, and the X-ray flux limits / 407/ 2/ 1301/ 1127347 by O hio S t at e Universit y Library user some will have one SNR. Given the model, the Poisson probability of finding j remnants in the i th bin, for which the model predicts n ( ri ) remnants, is P ( j | n ( ri )) = e -n ( ri ) n ( ri ) j /j ! . (1) We will define the likelihood of a given model as the product of these probabilities. The logarithm of the likelihood, considering that j always equals either 0 or 1, simplifies to ln L = [ ∑ i ( j> 0) ln n ( ri ) ] -N, (2) where the summation is only over the specific data values of the SNRradii. A power law of index α , having the proper normalization, will have the form n ( r ) = N ( α + 1) r α + 1 cut r α . (3) Inserting in equation (2), differentiating ln L with respect to α and equating to zero to find the maximum gives the maximum likelihood a deficit at small radii is also present in the LMC distribution (see Fig. 3), but the Poisson errors are too large to claim that the data require it. The linear cumulative distribution of SNR sizes in the MCs (and also the Milky Way) has been previously noted and discussed by Mathewson et al. (1984), Mills et al. (1984), Green (1984), Hughes et al. (1984), Fusco-Femiano & Preite-Martinez (1984), Berkhuijsen (1987), Chu & Kennicutt (1988) and, most recently, Bandiera & Petruk (2010). Several of these papers also pointed out cut-offs in the distribution. All of these papers considered smaller SNR samples, often based on much shallower radio data and, with few exceptions, did not include multi-wavelength observations. Some of these authors interpreted the observed size distribution as evidence that most MC SNRs are in their \'free expansion\' phase, during which the shock velocity is constant, and inferred that these SNRs expand into an extremely low density medium. Alternatively, Green (1984) and Hughes et al. (1984) warned that the observed distribution was the result of selection effects; most objects they discussed had been selected in X-rays, and the X-ray flux limits / 407/ 2/ 1301/ 1127347 by O hio S t at e Universit y Library user some will have one SNR. Given the model, the Poisson probability of finding j remnants in the i th bin, for which the model predicts n ( ri ) remnants, is P ( j | n ( ri )) = e -n ( ri ) n ( ri ) j /j ! . (1) We will define the likelihood of a given model as the product of these probabilities. The logarithm of the likelihood, considering that j always equals either 0 or 1, simplifies to ln L = [ ∑ i ( j> 0) ln n ( ri ) ] -N, (2) where the summation is only over the specific data values of the SNRradii. A power law of index α , having the proper normalization, will have the form n ( r ) = N ( α + 1) r α + 1 cut r α . (3) Inserting in equation (2), differentiating ln L with respect to α and equating to zero to find the maximum gives the maximum likelihood a deficit at small radii is also present in the LMC distribution (see Fig. 3), but the Poisson errors are too large to claim that the data require it. The linear cumulative distribution of SNR sizes in the MCs (and also the Milky Way) has been previously noted and discussed by Mathewson et al. (1984), Mills et al. (1984), Green (1984), Hughes et al. (1984), Fusco-Femiano & Preite-Martinez (1984), Berkhuijsen (1987), Chu & Kennicutt (1988) and, most recently, Bandiera & Petruk (2010). Several of these papers also pointed out cut-offs in the distribution. All of these papers considered smaller SNR samples, often based on much shallower radio data and, with few exceptions, did not include multi-wavelength observations. Some of these authors interpreted the observed size distribution as evidence that most MC SNRs are in their \'free expansion\' phase, during which the shock velocity is constant, and inferred that these SNRs expand into an extremely low density medium. Alternatively, Green (1984) and Hughes et al. (1984) warned that the observed distribution was the result of selection effects; most objects they discussed had been selected in X-rays, and the X-ray flux limits / 407/ 2/ 1301/ 1127347 by O hio S t at e Universit y Library user some will have one SNR. Given the model, the Poisson probability of finding j remnants in the i th bin, for which the model predicts n ( ri ) remnants, is P ( j | n ( ri )) = e -n ( ri ) n ( ri ) j /j ! . (1) We will define the likelihood of a given model as the product of these probabilities. The logarithm of the likelihood, considering that j always equals either 0 or 1, simplifies to ln L = [ ∑ i ( j> 0) ln n ( ri ) ] -N, (2) where the summation is only over the specific data values of the SNRradii. A power law of index α , having the proper normalization, will have the form n ( r ) = N ( α + 1) r α + 1 cut r α . (3) Inserting in equation (2), differentiating ln L with respect to α and a deficit at small radii is also present in the LMC Fig. 3), but the Poisson errors are too large to claim require it. The linear cumulative distribution of SNR sizes (and also the Milky Way) has been previously noted by Mathewson et al. (1984), Mills et al. (1984), Hughes et al. (1984), Fusco-Femiano & Berkhuijsen (1987), Chu & Kennicutt (1988) and, Bandiera & Petruk (2010). Several of these papers also cut-offs in the distribution. All of these papers SNR samples, often based on much shallower radio few exceptions, did not include multi-wavelength Some of these authors interpreted the observed size as evidence that most MC SNRs are in their \'free e during which the shock velocity is constant, and inferre SNRs expand into an extremely low density medium. Al Green (1984) and Hughes et al. (1984) warned that distribution was the result of selection effects; most discussed had been selected in X-rays, and the X-ray We will define the likelihood of a given model as the product of these probabilities. The logarithm of the likelihood, considering that j always equals either 0 or 1, simplifies to ln L = [ ∑ i ( j> 0) ln n ( ri ) ] -N, (2) where the summation is only over the specific data values of the SNRradii. A power law of index α , having the proper normalization, will have the form n ( r ) = N ( α + 1) r α + 1 cut r α . (3) Inserting in equation (2), differentiating ln L with respect to α and equating to zero to find the maximum gives the maximum likelihood solution ( α + 1)ml = N N ln r cut -∑ j> 0 ln ri , (4) with an uncertainty on α of /Delta1α = ( -d 2 (ln L ) d α 2 ) -1 / 2 = α + 1 √ N . (5) This procedure yields a maximum-likelihood index of α = 0.14 ± 0.18 for the LMC, and α = 0.32 ± 0.28 for the SMC. Thus, the LMC appears to indeed have an SNR size distribution that is close to uniform. In the SMC, the best fit is intermediate between a flat by Mathewson et al. (1984), Mills et al. (1984), Green (1984), Hughes et al. (1984), Fusco-Femiano & Preite-Martinez (1984), Berkhuijsen (1987), Chu & Kennicutt (1988) and, most recently, Bandiera & Petruk (2010). Several of these papers also pointed out cut-offs in the distribution. All of these papers considered smaller SNR samples, often based on much shallower radio data and, with few exceptions, did not include multi-wavelength observations. Some of these authors interpreted the observed size distribution as evidence that most MC SNRs are in their \'free expansion\' phase, during which the shock velocity is constant, and inferred that these SNRs expand into an extremely low density medium. Alternatively, Green (1984) and Hughes et al. (1984) warned that the observed distribution was the result of selection effects; most objects they discussed had been selected in X-rays, and the X-ray flux limits then led to the exclusion of larger and fainter remnants, and their faint radio counterparts. Our present compilation is bigger; it incorporates the most recent multi-wavelength data; it extends to larger sizes; and, most importantly, it is sensitive to radio flux densities two orders of magnitude below the observed luminosity floor. With these data we now confirm the luminosity floor, the uniform size distribution and the cut-off at r cut ∼ 30 pc in the MC SNRs. These features of the SNR size distribution are also present in other galaxies. Due to its proximity and face-on orientation, M33 has probably the best SNR sample outside of the MCs. The most recent catalogue of M33 SNRs has been published by Long et al. (2010), and it includes data in the radio, optical and X-rays (from the ChASeM33 survey by Chandra ; Plucinsky et al. 2008). The 1127347 by O hio S t at e Universit y Library user on 05 March 2019 some will have one SNR. Given the model, the Poisson probability of finding j remnants in the i th bin, for which the model predicts n ( ri ) remnants, is P ( j | n ( ri )) = e -n ( ri ) n ( ri ) j /j ! . (1) We will define the likelihood of a given model as the product of these probabilities. The logarithm of the likelihood, considering that j always equals either 0 or 1, simplifies to ln L = [ ∑ i ( j> 0) ln n ( ri ) ] -N, (2) where the summation is only over the specific data values of the SNRradii. A power law of index α , having the proper normalization, will have the form n ( r ) = N ( α + 1) r α + 1 cut r α . (3) Inserting in equation (2), differentiating ln L with respect to α and equating to zero to find the maximum gives the maximum likelihood a deficit at small radii is also present in the LMC distribution (see Fig. 3), but the Poisson errors are too large to claim that the data require it. The linear cumulative distribution of SNR sizes in the MCs (and also the Milky Way) has been previously noted and discussed by Mathewson et al. (1984), Mills et al. (1984), Green (1984), Hughes et al. (1984), Fusco-Femiano & Preite-Martinez (1984), Berkhuijsen (1987), Chu & Kennicutt (1988) and, most recently, Bandiera & Petruk (2010). Several of these papers also pointed out cut-offs in the distribution. All of these papers considered smaller SNR samples, often based on much shallower radio data and, with few exceptions, did not include multi-wavelength observations. Some of these authors interpreted the observed size distribution as evidence that most MC SNRs are in their \'free expansion\' phase, during which the shock velocity is constant, and inferred that these SNRs expand into an extremely low density medium. Alternatively, Green (1984) and Hughes et al. (1984) warned that the observed distribution was the result of selection effects; most objects they discussed had been selected in X-rays, and the X-ray flux limits / 407/ 2/ 1301/ 1127347 by O hio S t at e Universit y Library user particular model predicts a size distribution d N / d r = n ( r ), which integrates to ∫ r cut 0 n ( r )d r = N ,where N is the total number of remnants up to r cut. If we bin our data into many small bins between r = 0and r cut,eachofwidth δ r , most bins will have zero SNRs, and some will have one SNR. Given the model, the Poisson probability of finding j remnants in the i th bin, for which the model predicts n ( ri ) remnants, is P ( j | n ( ri )) = e -n ( ri ) n ( ri ) j /j ! . (1) We will define the likelihood of a given model as the product of these probabilities. The logarithm of the likelihood, considering that j always equals either 0 or 1, simplifies to ln L = [ ∑ i ( j> 0) ln n ( ri ) ] -N, (2) where the summation is only over the specific data values of the SNRradii. A power law of index α , having the proper normalization, will have the form mally it is still consistent with a slope close to zero at all radii at the 1.7 σ level. We conclude that the SNR size distribution in both Clouds is consistent with being roughly uniform, although there are hints for a deviation at small radii in the SMC. It is possible that a deficit at small radii is also present in the LMC distribution (see Fig. 3), but the Poisson errors are too large to claim that the data require it. The linear cumulative distribution of SNR sizes in the MCs (and also the Milky Way) has been previously noted and discussed by Mathewson et al. (1984), Mills et al. (1984), Green (1984), Hughes et al. (1984), Fusco-Femiano & Preite-Martinez (1984), Berkhuijsen (1987), Chu & Kennicutt (1988) and, most recently, Bandiera & Petruk (2010). Several of these papers also pointed out cut-offs in the distribution. All of these papers considered smaller SNR samples, often based on much shallower radio data and, with few exceptions, did not include multi-wavelength observations. Some of these authors interpreted the observed size distribution as evidence that most MC SNRs are in their \'free expansion\' phase, during which the shock velocity is constant, and inferred that these icle-abst ract / 407/ 2/ 1301/ 1127347 by O hio S t at e Universit y Spatial resolution is especially important to probe the morphologies and distinct spectral components in extragalactic SNRs. For example, Figure 1 shows simulated Athena and Lynx images of the young SNR N103B in the Large Magellanic Cloud (LMC). In this case, 1 00 pixels are crucial to disentangle the ejecta and circumstellar medium (CSM) spectra. At the distance of the LMC, 1 00 GLYPH<25> 0.3 pc; thus with that resolution, maps of the youngest parsec-scale sources could be obtained, such as for SN 1987A (which will be 3 00 GLYPH<25> 1 pc across in the 2030s: Orlando et al. 2015). Improvements in effective area would enable detailed studies of large extragalactic populations (see Figure 3; left). For example, a 100-ks observation with a 2 m 2 effective area would detect > 10 3 counts from the dozens of SNRs in M31 and M33. In the LMC and Small Magellanic Cloud (SMC), X-ray imaging and microcalorimeter observations could achieve similar signal-to-noise to what current facilities achieve for Milky Way sources. Furthermore, spatial resolution is crucial to resolve SNRs in the Local Group. For example, the known SNRs in M31 and M33 have angular sizes of GLYPH<24> 3-30 00 . Assuming Local Group SNRs have the same size distribution as observed in the LMC and SMC (Badenes et al. 2010), arcsecond spatial resolution is crucial to resolve SNRs across tens of pixels at a distance of 1 Mpc (see Figure 3, right).  \nother galaxies. Due to its proximity and face-on orientation, M33  \nother galaxies. Due to its proximity and face-on orient  \nhas probably the best SNR sample outside of the MCs. The most  \nequating to zero to find the maximum gives the maximum likelihood solution ( α + 1)ml = N N ln r cut -∑ j> 0 ln ri , (4) with an uncertainty on α of /Delta1α = ( -d 2 (ln L ) d α 2 ) -1 / 2 = α + 1 √ N . (5) then led to the exclusion of larger and fainter remnants, and their faint radio counterparts. Our present compilation is bigger; it incorporates the most recent multi-wavelength data; it extends to larger sizes; and, most importantly, it is sensitive to radio flux densities two orders of magnitude below the observed luminosity floor. With these data we now confirm the luminosity floor, the uniform size distribution and the cut-off at r cut ∼ 30 pc in the MC SNRs. These features of the SNR size distribution are also present in other galaxies. Due to its proximity and face-on orientation, M33 on 05 March 2019 solution ( α + 1)ml = N N ln r cut -∑ j> 0 ln ri , (4) with an uncertainty on α of /Delta1α = ( -d 2 (ln L ) d α 2 ) -1 / 2 = α + 1 √ N . (5) then led to the exclusion of larger and fainter remnants, and their faint radio counterparts. Our present compilation is bigger; it incorporates the most recent multi-wavelength data; it extends to larger sizes; and, most importantly, it is sensitive to radio flux densities two orders of magnitude below the observed luminosity floor. With these data we now confirm the luminosity floor, the uniform size distribution and the cut-off at r cut ∼ 30 pc in the MC SNRs. These features of the SNR size distribution are also present in other galaxies. Due to its proximity and face-on orientation, M33 on 05 March 2019 solution ( α + 1)ml = N N ln r cut -∑ j> 0 ln ri , (4) with an uncertainty on α of /Delta1α = ( -d 2 (ln L ) d α 2 ) -1 / 2 = α + 1 √ N . (5) then led to the exclusion of larger and fainter remnants, and their faint radio counterparts. Our present compilation is bigger; it incorporates the most recent multi-wavelength data; it extends to larger sizes; and, most importantly, it is sensitive to radio flux densities two orders of magnitude below the observed luminosity floor. With these data we now confirm the luminosity floor, the uniform size distribution and the cut-off at r cut ∼ 30 pc in the MC SNRs. These features of the SNR size distribution are also present in on 05 March 2019 equating to zero to find the maximum gives the maximum likelihood solution ( α + 1)ml = N N ln r cut -∑ j> 0 ln ri , (4) with an uncertainty on α of /Delta1α = ( -d 2 (ln L ) d α 2 ) -1 / 2 = α + 1 √ N . (5) then led to the exclusion of larger and fainter remnant faint radio counterparts. Our present compilation is bigg porates the most recent multi-wavelength data; it e sizes; and, most importantly, it is sensitive to radio fl two orders of magnitude below the observed luminosity these data we now confirm the luminosity floor, the distribution and the cut-off at r cut ∼ 30 pc in the MC These features of the SNR size distribution are also distribution and one that rises linearly with radius, but given the distribution of SNR sizes given in table 3 of Long et al. (2010), C © 2010 The Authors. Journal compilation C © 2010 RAS, MNRAS 407, 1301-1313 solution ( α + 1)ml = N N ln r cut -∑ j> 0 ln ri , (4) with an uncertainty on α of /Delta1α = ( -d 2 (ln L ) d α 2 ) -1 / 2 = α + 1 √ N . (5) then led to the exclusion of larger and fainter remnants, and their faint radio counterparts. Our present compilation is bigger; it incorporates the most recent multi-wavelength data; it extends to larger sizes; and, most importantly, it is sensitive to radio flux densities two orders of magnitude below the observed luminosity floor. With these data we now confirm the luminosity floor, the uniform size distribution and the cut-off at r cut ∼ 30 pc in the MC SNRs. These features of the SNR size distribution are also present in other galaxies. Due to its proximity and face-on orientation, M33 on 05 March 2019 n ( r ) = N ( α + 1) r α + 1 cut r α . (3) Inserting in equation (2), differentiating ln L with respect to α and equating to zero to find the maximum gives the maximum likelihood solution ( α + 1)ml = N N ln r cut -∑ j> 0 ln ri , (4) with an uncertainty on α of SNRs expand into an extremely low density medium. Alternatively, Green (1984) and Hughes et al. (1984) warned that the observed distribution was the result of selection effects; most objects they discussed had been selected in X-rays, and the X-ray flux limits then led to the exclusion of larger and fainter remnants, and their faint radio counterparts. Our present compilation is bigger; it incorporates the most recent multi-wavelength data; it extends to larger sizes; and, most importantly, it is sensitive to radio flux densities two orders of magnitude below the observed luminosity floor. With Library user on 05 March As the morphologies and Fe-line centroid can be used to \'type" SNRs (Lopez et al. 2011; Yamaguchi et al. 2014), a sensitive X-ray telescope with arcsecond spatial resolution would foster constraints on the explosive origin of hundreds of SNRs in the Local Group. This sample would be large enough to do statistical comparisons of populations, in addition to studies of individual sources. These results would be useful to explore SN explosions in different Galactic environments and to probe SN feedback and enrichment in the Local Group.  \nThis procedure yields a maximum-likelihood index of  \nα  \nThis procedure yields a maximum-likelihood index of  \nα  \nThis procedure yields a maximum-likelihood index of  \nα  \nThis procedure yields a maximum-likelihood index of  \nα  \n2  \n=  \n=  \n±  \n0.18 for the LMC, and  \nα  \n0.18 for the LMC, and  \nα  \n0.18 for the LMC, and  \nα  \n0.18 for the LMC, and  \nα  \n(ln  \nL  \n)  \n2  \n=  \nhas probably the best SNR sample outside of the MCs. The most This procedure yields a maximum-likelihood index of 4  \n0.18 for the LMC, and  \nα  \n0.32  \n0.14  \n0.14  \n0.28 for the SMC. Thus, the  \n=  \n0.32  \n0.14  \nhas probably the best SNR sample outside of the MCs. The most  \nhas probably the best SNR sample outside of the MCs. The most  \nhas probably the best SNR sample outside of the M  \nthese data we now confirm the luminosity floor, the uniform size  \nrecent catalogue of M33 SNRs has been published by Long et al.  \n±  \n0.28 for the SMC. Thus, the  \n0.14  \n0.32  \n=  \n±  \n0.32  \n0.28 for the SMC. Thus, the  \nd  \n-  \nα  \n1  \nLMC appears to indeed have an SNR size distribution that is close  \n±  \n=  \n±  \n=  \n±  \n±  \nα  \n0.14  \nrecent catalogue of M33 SNRs has been published by Long et al.  \n0.32  \n0.28 for the SMC. Thus, the  \nrecent catalogue of M33 SNRs has been published by Long et al.  \n=  \n±  \n2019  \nrecent catalogue of M33 SNRs has been published by  \nrecent catalogue of M33 SNRs has been published by Long et al.  \ndistribution and the cut-off at  \nr  \ncut  \n30 pc in the MC SNRs.  \n(2010), and it includes data in the radio, optical and X-rays (from  \n0.28 for the SMC. Thus, the  \nLMC appears to indeed have an SNR size distribution that is close  \n=  \nLMC appears to indeed have an SNR size distribution that is close  \n=  \n±  \nLMC appears to indeed have an SNR size distribution that is close  \n/Delta1α  \n=  \n-  \nd  \nα  \n=  \n+  \n√  \n.  \n(5)  \nto uniform. In the SMC, the best fit is intermediate between a flat  \n±  \n(2010), and it includes data in the radio, optical and X-rays (from  \n(2010), and it includes data in the radio, optical and X-rays (from  \nThese features of the SNR size distribution are also present in  \nthe ChASeM33 survey by  \nChandra  \n; Plucinsky et al. 2008). The  \n(2010), and it includes data in the radio, optical and X-  \nthe ChASeM33 survey by  \nChandra  \n; Plucinsky et al. 2008). The  \n∼  \nother galaxies. Due to its proximity and face-on orientation, M33  \n(2010), and it includes data in the radio, optical and X-rays (from  \nLMC appears to indeed have an SNR size distribution that is close  \nN  \nto uniform. In the SMC, the best fit is intermediate between a flat  \nto uniform. In the SMC, the best fit is intermediate between a flat  \nto uniform. In the SMC, the best fit is intermediate between a flat  \nthe ChASeM33 survey by  \nChandra  \n; Plucinsky et al. 2008). The  \nthe ChASeM33 survey by  \nChandra  \n; Plucinsky et al.  \nthe ChASeM33 survey by  \nChandra  \n; Plucinsky et al. 2008). The  \nto uniform. In the SMC, the best fit is intermediate between a flat  \n(  \n)  \n1  \n/  \n2', 'III. Proper Motions Over Baselines of Several Decades': 'While a microcalorimeter will allow measurems of velocities along the line-of-sight, comparable spatial resolution to Chandra in a future X-ray facility would enable proper motion studies of many Galactic sources and SNR shocks over 30- to 40-year baselines. For example, Table 1 shows the proper motions in a 30-year baseline for different distances ( D = 1, 5, 10, or 50 kpc) and velocities ( v = 100, 500, 1000, 5000 km s GLYPH<0> 1 ). Depending on the object, proper motions can, in some cases, be measured better than the on-axis point spread function (PSF): e.g. Xi et al. (2019) used Chandra and measured an expansion of 0.1 00 over 17 years for the SNR 1E 0102.2 GLYPH<0> 7219 (corresponding to a v = 1600 km s GLYPH<0> 1 for a distance of D = 60 kpc). Thus, velocities of 500 km s GLYPH<0> 1 may be measurable out to D = 10 kpc, and velocities of 1000 km s GLYPH<0> 1 may be observable out to the Magellanic Clouds. For high-velocity shocks of 5000 km s GLYPH<0> 1 , sub-arcsecond angular resolution is sufficient to measure proper motions at the distance of the LMC, D = 50 kpc.  \nGiven that the mean velocity of neutron stars (NSs) is 380 km s GLYPH<0> 1 (Faucher-Giguère & Kaspi 2006), sub-arcsecond resolution over a 30- to 40-year baseline is sufficient to observe NS proper motions. As described in a separate white paper by S. Safi-Harb et al., these measurements set important constraints on the origin of NS kicks and on SN explosion models.  \nCombined with radial velocities from the microcalorimeter, proper motions will reveal the true 3D structure of the ejecta. Though Chandra has enabled proper motion measurements for a few SNRs (e.g., Yamaguchi et al. 2016), the off-axis PSF and sensitivity has limited the sample and the statistical significance of the results. Thus, an improved effective area and an arcsecond off-axis PSF would facilitate precise measurements of SNR dynamics across a much larger population.', 'IV. Non-Thermal Emission from Fast Shock Waves': "Several young SNRs (e.g., SN 1006, Tycho, and RCW 86), emit synchrotron emission in narrow filaments around their periphery. This synchrotron emission results from a non-thermal population of electrons, accelerated to relativistic energies behind the shock, spiraling around an amplified post-shock magnetic field. There are many open questions in this process: under what conditions do shocks efficiently accelerate particles? How are magnetic fields amplified, and how high can this amplification go? Shocks are ubiquitous in astrophysics, and these questions are relevant in all sorts of environments, from colliding galaxy clusters to AGN jets to the Earth's bow shock created by the interaction with the solar wind. Of these, only SNRs offer the chance to study shock physics on length scales comparable to those on which these processes operate.  \nThe width of the thin synchrotron rims ( < GLYPH<24> 5 00 ) in SNR shocks (e.g., Bamba et al. 2005) offers a diagnostic of acceleration properties. In SN 1006, the width of these rims varies with energy, implying that the relativistic electrons rapidly age in a field as strong as 100 GLYPH<22> G, inconsistent with the field damping quickly behind the shock (Ressler et al. 2014). However, in the well-studied Tycho SNR (shown in Figure 4), the thin synchrotron rims suggest strong amplification at the shock followed by quick damping (Tran et al. 2015). Thus, it is possible that two different mechanisms by which magnetic fields are amplified and subsequently damped in shock waves.  \nThe Astrophysical Journal Letters  \n,728:L28(5pp),2011February20  \nEriksen et al.  \nThe Astrophysical Journal Letters  \n,728:L28(5pp),2011February20  \nEriksen et al.  \n(d)  \n(c)  \nThe Astrophysical Journal Letters  \n,728:L28(5pp),2011February20  \n(a)  \nFigure 2.  \nLeft: the projected intensity profile for two regions containing the western stripes. The bright stripe is the red peak around a  \nof prominent stripes are indicated by the horizontal lines with tick marks. The peaks in the northern profile are spaced by 9 . '' 9, 11 . '' 3, southern profile are spaced by 4 . '' 4, 9 . '' 4, 6 . '' 8, and 7 . '' 4. Right: gray-scale image of the Chandra data in a line-free region of the extraction regions for the profiles plotted in the left panel. The profiles run from the lower left to the upper right and the tick marks same tick marks as in the left panel. The scale bar in the lower right is 10 '' long. The green boxes denote the spectral regions region is the bright stripe; the co-addition of the fainter regions constitutes the faint stripes. relative to the limb regions. We examined two regions of different brightness on the western rim with minimal ejecta contamination, and assumed a spherical shell model with a radius of 214 '' , chosen to match the curvature of the western ( Γ = 2 . 72 ± 0 . 02; this fit includes Tamagawa et al. 2009), and a surface brightness stripes ( Γ = 2 . 52 Fe K line). Figure 1. Chandra X-ray 4.0-6.0 keV image of the Tycho supernova remnant, smoothed with a ∼ 0 . '' 75 Gaussian and displayed with an arcsinh scaling, showing various regions of striping in the nonthermal emission. Clockwise from the upper right: (a) the main western stripes discussed in this Letter; (b) a fainter ensemble of stripes; (c) a previously known bright arc of nonthermal emission, with our newly discovered streamers; and (d) filaments of 'rippled sheet' morphology common in optical observations of middle-aged SNRs. of plasma and field, enclosed by 'wandering filaments' of high density and frozen-in field. One goal of observations is to discover evidence for structure in SNR shocks on this spatial the stripes, ruling out any dramatic flux variability like that observed in the non-thermal X-ray filaments of the SNR RX J1713.7 -3946 (Uchiyama et al. 2007). Our preliminary proper Figure 1. Chandra X-ray 4.0-6.0 keV image of the Tycho supernova remnant, smoothed with a ∼ 0 . '' 75 Gaussian and displayed with an arcsinh scaling, showing various regions of striping in the nonthermal emission. Clockwise from the upper right: (a) the main western stripes discussed in this Letter; (b) a fainter ensemble of stripes; (c) a previously known bright arc of nonthermal emission, with our newly discovered streamers; and (d) filaments of 'rippled sheet' morphology common in optical observations of middle-aged SNRs. of plasma and field, enclosed by 'wandering filaments' of high density and frozen-in field. One goal of observations is the stripes, ruling out any dramatic flux variability like that observed in the non-thermal X-ray filaments of the SNR RX Figure 4: Left panels : Chandra 4-6 keV image of the Tycho SNR from Eriksen et al. (2011). The nonthermal continuum dominates in this bandpass, and stripes and filaments are evident around the periphery and in projection inside the SNR. Right : Surface brightness profiles from the blue and red rectangles in panel a. The spacing of the stripes is 5 00 , and the width of the filaments is < 3 00 . Thus, sub-arcsecond imaging is imperative to resolve these features, and a large effective area would enable the detection and characterization of the non-thermal filaments in SNRs.  \n<!-- image -->  \nscale.  \nare visible in earlier  \nChandra  \ndata (Warren et al. 2005) our  \n±  \nWhile photon indices are useful  \n.  \nlimb. The radial brightness profile of the brighter rim region is  \nmotion measurements for the stripes are consistent with the  \nany features in the R-T plumes of thermal emission tracing the  \ntoo narrow and peaked to be consistent with a simple projected shell geometry, meaning that its high surface brightness likely arises from a local enhancement in emissivity, perhaps similar to the stripes. In contrast, the profile of the fainter region is well fit by a shell with thickness 2% of its radius and is likely more typical of the blast wave as a whole. This simple model predicts that features at 80% of the shock radius (where the stripes are located) would have a surface brightness 20% that of the limb. The observed peak surface brightness of the stripes is, however, five times that of the faint limb region. Thus, the peak intrinsic emissivity of the synchrotron-emitting plasma in the stripes must be a factor of 25 higher than is typical for the blast wave. In principle, this brightening could be due to a local enhancement in the ambient density and / or magnetic field. While we cannot entirely exclude this possibility, we consider the existence of a pre-existing structure around Tycho with the right combination of increased density, magnetic field, and, as we show below, turbulence necessary to produce the observed correlations between the ordered structure and spectral variations improbable. In contrast, models of CR-driven magnetic field amplification produce structure in the precursor density and field, and we find it more likely that the stripes mark a region extensively modified by the acceleration process. This the non-thermal spectrum, the departs from a simple power law over s Detailed DSA models of s degree of curvature through the r in the X-rays, set (in young SNRs cooling time of TeV-scale electrons detailed spectral calculations for Tyc approximation and assume a power distribution with an exponential cutoff, spectrum that is nearly a power law the UV and is curved in X-rays (Re For this model, the low energy ind normalization are set by radio observ of the high energy cutoff is constrained For the spectrum of the entire remnant, index of α radio = 0 . 65, a flux density at et al. 2006), and again including the f from Tamagawa et al. (2009), the fit ν cut = 1 . 9 × 10 17 Hz ( h ν cut ∼ 0 a remarkably good fit ( χ 2 ν = 1 . measurements from Suzaku .(Thestati is so small as to be irrelevant; the it is far greater than the efficacy of 2. OBSERVATIONS We observed Tycho in 2009 April with the Chandra X-ray Observatory Advanced CCD Imaging Spectrometer imaging array, as part of a Cycle 10 Large Program (LP), using the four ACIS-I front-side illuminated CCDs, operated in faint mode. The total program was split into nine individual ObsIDs, which we reprocessed with CIAO version 4.1, using the gain tables and charge transfer inefficiency correction in CALDB 4.1.3. Examination of the light curves revealed no significant background flares. The registration of the individual pointings was improved using the measured relative positions of background point sources, though the necessary shifts were typically /lessmuch 1 '' . For imaging analyses, the registered event lists were merged using the standard CIAO tools and have a total average livetime of ∼ 734 . 1ks. For spectroscopy, counts were extracted and RMFs and ARFs were generated for each individual ObsID, which we fit jointly in XSPEC version 12.6.0. In Figure 1 we show the image from the 4 to 6 keV band, which is dominated by the synchrotron component of the X-ray spectrum. Apart from the well-known limb-brightened shell, a number of bright regions are seen toward the projected interior of the remnant. While the strongest of these features overall expansion of the blast wave and, in particular, show no evidence for non-radial flow. There are no obvious counterparts to these features in the radio (Reynoso et al. 1997) nor in the mid-IR. 3. ANALYSIS 3.1. Location of the Stripes Before investigating the nature of the stripes, we first must locate them within the three-dimensional volume of the remnant. The canonical picture of a young SNR consists of three distinct fluid discontinuities: the blast wave, which marks the shock propagating into the ambient medium, a Rayleigh-Taylor (R-T) unstable contact discontinuity (CD) at the ejecta-interstellar material boundary, and a reverse shock that propagates into the stellar remains. Warren et al. (2005) set an upper limit for the azimuthally dependent projected radius of the reverse shock in Tycho using the location of the Fe K α emission. Adopting their center of expansion, the western stripes peak at a radius of 220 '' ,welloutsidethe190 '' position of the reverse shock at that azimuth. While the position of the stripes does coincide with the Warren et al. estimate of the CD, the regularly spaced, linear morphology of the non-thermal stripes does not correspond to to discover evidence for structure in SNR shocks on this spatial scale. 2. OBSERVATIONS We observed Tycho in 2009 April with the Chandra X-ray Observatory Advanced CCD Imaging Spectrometer imaging array, as part of a Cycle 10 Large Program (LP), using the four ACIS-I front-side illuminated CCDs, operated in faint mode. The total program was split into nine individual ObsIDs, which we reprocessed with CIAO version 4.1, using the gain tables and charge transfer inefficiency correction in CALDB 4.1.3. Examination of the light curves revealed no significant background flares. The registration of the individual pointings was improved using the measured relative positions of background point sources, though the necessary shifts were typically /lessmuch 1 '' . For imaging analyses, the registered event lists were merged using the standard CIAO tools and have a total average livetime of ∼ 734 . 1ks. For spectroscopy, counts were extracted and RMFs and ARFs were generated for each individual ObsID, which we fit jointly in XSPEC version 12.6.0. In Figure 1 we show the image from the 4 to 6 keV band, which is dominated by the synchrotron component of the X-ray spectrum. Apart from the well-known limb-brightened shell, J1713.7 -3946 (Uchiyama et al. 2007). Our preliminary proper motion measurements for the stripes are consistent with the overall expansion of the blast wave and, in particular, show no evidence for non-radial flow. There are no obvious counterparts to these features in the radio (Reynoso et al. 1997) nor in the mid-IR. 3. ANALYSIS 3.1. Location of the Stripes Before investigating the nature of the stripes, we first must locate them within the three-dimensional volume of the remnant. The canonical picture of a young SNR consists of three distinct fluid discontinuities: the blast wave, which marks the shock propagating into the ambient medium, a Rayleigh-Taylor (R-T) unstable contact discontinuity (CD) at the ejecta-interstellar material boundary, and a reverse shock that propagates into the stellar remains. Warren et al. (2005) set an upper limit for the azimuthally dependent projected radius of the reverse shock in Tycho using the location of the Fe K α emission. Adopting their center of expansion, the western stripes peak at a radius of 220 '' ,welloutsidethe190 '' position of the reverse shock at that azimuth. While the position of the stripes does coincide with To obtain these results, the time investments from Chandra have been substantial (e.g., GLYPH<24> 1 Ms toward Tycho). An effective area of 2 m 2 and 1 00 resolution would ensure the detection of even faint non-thermal filaments and expand the sample of objects for which these measurements can be made. Combined with high-resolution radio data from the upgraded Very Large Array or the upcoming Square Kilometer Array, sensitive X-ray observations of the synchrotron continuum will yield crucial constraints on diffusive shock acceleration. Some accelerated particles must diffuse from behind the shock into the upstream medium. In SNR shocks dominated by non-thermal synchrotron emission from accelerated particles, faint X-ray emission should be present ahead of the shock, yet this emission has never been detected (Winkler et al. 2014; see Figure 5). Finding and characterizing this precursor will put tight constraints on the universal properties of fast shock waves, such as the degree of magnetic field amplification and the diffusion and scattering length of energetic particles. Arcsecond spatial resolution, a low background, and large effective area are critical to identifying these features in Galactic SNRs.  \na number of bright regions are seen toward the projected  \ninterior of the remnant. While the strongest of these features  \ndeeper observation reveals a striking pattern of nearly regularly  \nspaced stripes. The brightest group, centered  \nthe western limb (see Figure 2), has a peak surface brightness  \nare visible in earlier  \ndeeper observation reveals a striking pattern of nearly regularly  \nspaced stripes. The brightest group, centered  \ntwice that of the brightest sections of the rims and is the  \nprimary subject of this communication. A second, fainter pattern  \nextends east-west, 55  \n''  \nthe western limb (see Figure 2), has a peak surface brightness  \ntwice that of the brightest sections of the rims and is the  \nevidence for several other regions of striping near the detection  \nlimit. Comparison with a shallower 2004  \nprimary subject of this communication. A second, fainter pattern  \nreveals no statistically significant change in the brightness of  \nextends east-west, 55  \nevidence for several other regions of striping near the detection  \nlimit. Comparison with a shallower 2004  \nreveals no statistically significant change in the brightness of  \nassumption is implicit in the analysis in this Letter. 3.2. Spectroscopy The spatial position of the stripes, seen in projection against the bright thermal X-rays of the shocked ejecta, greatly complicates spectroscopy. This can be mitigated by restricting analysis to the 4.2-10 keV range, where the emission is dominated by the synchrotron continuum and the Fe K α line complex at ∼ 6.45 keV. Throughout this work we set the absorbing column to N H = 7 × 10 21 cm -2 , which has negligible effect at these energies. The spectrum of the brightest stripe is well fit with a power law of photon index of Γ = 2 . 11 +0 . 08 -0 . 10 , significantly harder than the spectrum of the entire SNR at these energies accuracy of the radio flux and If we instead assume α radio = 0 . 61 fit is slightly worse ( χ 2 ν = 1 . 10), lower energies ( ν cut = 0 . 9 × 10 17 For the stripes, we estimated the ra from a Very Large Array (VLA) shallower indices ( α radio ∼ 0 . 60) ν cut = 19 +13 -9 × 10 17 Hz (7 . 9 +5 . 4 -3 . 7 keV) ν cut = (2 . 8 ± 0 . 2) × 10 17 Hz (1 . 16 ± 0 of fainter stripes. We plot the these regions in Figure 3. Although it is clear that the bright spectra require different best-fit 3 ejecta boundary, nor is the CD a prominent feature elsewhere in the 4-6 keV band. Conversely, the blast wave is a bright source of 4-6 keV emission, and we identify the stripes as projected 's blast wave is traced by a very thin shell of X-ray emission, with a typical thickness only 1%-2% of its radius (Warren et al. 2005). Since the stripes are seen in projection away from the rim, their line-of-sight path length through the shell is small. Thus, their intrinsic emissivity must be high the Warren et al. estimate of the CD, the regularly spaced, linear morphology of the non-thermal stripes does not correspond to any features in the R-T plumes of thermal emission tracing the ejecta boundary, nor is the CD a prominent feature elsewhere in the 4-6 keV band. Conversely, the blast wave is a bright source of 4-6 keV emission, and we identify the stripes as projected features of this forward shock. Tycho 's blast wave is traced by a very thin shell of X-ray emission, with a typical thickness only 1%-2% of its radius (Warren et al. 2005). Since the stripes are seen in projection away from the rim, their line-of-sight path length through the shell is small. Thus, their intrinsic emissivity must be high Figure 5: Chandra image of SN 1006 (left), with a radial profile from the yellow box (right). The red curve shows the Chandra PSF; the blue dots show a potential shock precursor model (Morlino et al. 2010). Even with Chandra 's resolution, the background level is too high to detect whether a shock precursor (particles that have diffused upstream of the shock) is present.  \n<!-- image -->"}