---
abstract: 'We present a complete atlas of the Cygnus Loop supernova remnant in the light of ø3 ($\lambda 5007$), , and 2 ($\lambda\lambda 6717, 6731$). We include low-resolution ($25\arcsec$) global maps and smaller fields at $6\arcsec$ resolution from observations using the Prime Focus Corrector on the 0.8-m telescope at McDonald Observatory. Despite its shell-like appearance, the Cygnus Loop is not a current example of a Sedov-Taylor blast wave. Rather, the optical emission traces interactions of the supernova blast wave with clumps of gas. The surrounding interstellar medium forms the walls of a cavity through which the blast wave now propagates, including a nearly complete shell in which non-radiative filaments are detected. We identify non-radiative shocks around half the perimeter of the Cygnus Loop, and they trace a circle of radius $R = 1\fdg 4$ (19 pc) in the spherical cavity walls. The Cygnus Loop blast wave is not breaking out of a dense cloud, but is instead running into confining walls. Modification of the shock velocity and gas temperature due to interaction of the blast wave with the surrounding medium introduces errors in estimates of the age of this supernova remnant. The optical emission of radiative shocks arises only where the blast wave encounters inhomogeneities in the ambient medium; it is not a consequence of gradual evolution to a global radiative phase. Distance measurements that rely on this uniform blast wave evolution are uncertain, but the radiative shocks can be used as distance indicators because of the spherical symmetry of the surrounding medium. The interstellar medium dominates not only the appearance of the Cygnus Loop but also the continued evolution of the blast wave. If this is a typical example of a supernova remnant, then global models of the interstellar medium must account for such significant blast wave deceleration.'
author:
- 'N. A. Levenson and James R. Graham'
- 'Luke D. Keller and Matthew J. Richter'
nocite:
- '[@Oort46]'
- '[@Fes82]'
- '[@Min58]'
- '[@Kir76]'
- '[@Gre91]'
- '[@Shu91]'
- '[@Fes82]'
- '[@McC79]'
- '[@Cha85]'
- '[@McK75]'
- '[@Lev97]'
- '[@Hes83]'
- '[@Hes94]'
- '[@Fes92]'
- '[@Fes92]'
- '[@Hes94]'
- '[@Hes94]'
- '[@Bla91]'
- '[@Mor96e]'
- '[@Cha85]'
- '[@Lev97]'
- '[@McK84]'
- '[@Fal82]'
- '[@Shu91]'
- '[@Lev97]'
- '[@PShu85]'
- '[@Van92]'
- '[@Vin97]'
- '[@Lev97]'
- '[@Min58]'
- '[@Hub37]'
- '[@Hes86]'
- '[@Che80]'
- '[@McK77]'
- '[@Shu87]'
title: Panoramic Views of the Cygnus Loop
---

ø3[\[\]]{} 2[\[\]]{} \#1\#2 \#1\#2\#3[ ]{}

Introduction\[secintro\]
========================

Supernova remnants greatly determine the large-scale structure of the interstellar medium. The energy of supernova remnants heats and ionizes the interstellar medium (ISM), and their blast waves govern mass exchange between various phases of the ISM. In doing so, supernova remnants (SNRs) influence subsequent star formation and the recycling of heavy elements in galaxies. Global models of the interstellar medium that include a hot ionized component ([@Cox74]; [@McK77]) are sensitive to the supernova rate, the persistence of their remnants, and the sizes they attain. A simple calculation of the last of these assumes that the blast wave expands adiabatically in a uniform medium once the blast wave has swept up mass comparable to the mass of the ejecta. During this Sedov-Taylor phase, the radius of the SNR as a function of $E_{51}$, the initial energy in units of $10^{51}$ erg, $n_o$, the ambient number density in units of ${\rm cm^{-3}}$, and $t_4$, time in units of $10^4$ yr, is $R=13 (E_{51}/n_o)^{1/5} t_4^{2/5} {\rm \,pc}$ in a medium where the mean mass per particle is $2.0 \times 10^{-24} {\rm \, g}$. This phase will last until radiative losses become important. The beginning of this subsequent phase, marked by the initial loss of pressure behind the blast wave, occurs at $t=1.9\times 10^4 E_{51}^{3/14} n_o^{-4/7} {\rm \,yr}$, when the radius is $R=16.2 E_{51}^{2/7} n_o^{-3/7} {\rm \,pc}$ ([@Shu87]), although the radiating shell is not fully formed yet.

We approach these large-scale questions with analysis of complete images of a particular supernova remnant, the Cygnus Loop, in three optical emission lines. This supernova remnant appears to be a limb-brightened shell at radio ([@Keen73]), infrared ([@Bra86]), optical ([@Fes82]), and X-ray ([@Ku84]; [@Lev97]) energies, which at first glance suggests that it is presently in the transition to the radiative stage. The Cygnus Loop has the advantages of being nearby, bright, and relatively unobscured by dust. This allows us to examine in detail the evolution of various portions of the shock front and to determine physical parameters, such as shock velocity and local ambient density, as they vary throughout the remnant. Despite its appearance, the Cygnus Loop is not a current example of blast wave propagation in a uniform medium at any stage. Instead, its evolution is governed by the inhomogeneous interstellar medium, which we map using the shock as a probe.

Many of the features we discuss have been noted by others. Oort (1946) first suggested that the Cygnus Loop is an expanding supernova shell. Spectroscopy of radiative shocks in selected locations (e.g., [@Mil74], [@Ray80a], and Fesen et al. 1982) combined with theoretical models of these shocks (e.g., [@Cox72], [@Dop77], [@Ray79], and [@Shu79]) has been used to derive the physical conditions of the observed shocks. We utilize the radial velocity measures of Minkowski (1958), Kirshner & Taylor (1976), Greidanus & Strom (1991), and Shull & Hippelein (1991) to discern some of the three-dimensional structure that is ambiguous from the data we present. Many non-radiative or Balmer-dominated shocks in the Cygnus Loop have been identified (e.g., [@Kir76], [@Ray80b], [@Tref81], Fesen et al. 1982, [@Fes92], and [@Han92]). Our observations qualitatively match these, and we rely on these works and others ([@Ray83]; [@Long92]; [@Hes94]) for quantitative measures of parameters such as shock velocity and preshock density. McCray & Snow (1979) and Charles, Kahn, & McKee (1985) have suggested that the Cygnus Loop is the result of a cavity explosion, and we adapt this global model to interpret the surrounding interstellar medium, as well.

This paper is a companion to the soft X-ray survey presently in progress with the [*ROSAT*]{} High Resolution Imager ([@Gra96]; [@Lev97]). With these two surveys, we examine the Cygnus Loop as a whole, not restricting our investigation only to those regions that are exceptionally bright or that appear to be particularly interesting. We hope to understand both the global processes and the specific variations that are responsible for the emission we detect. The X-rays probe hot (temperature $T\sim 10^6$ K) gas that shocks with velocities $v_s \sim 400 \kms$ heat. The optical emission is expected from slower shocks ($v_s \lesssim 200 \kms$) in which the post-shock region cools to temperatures $T\sim 10^4$ K, yet the most prominent regions at optical wavelengths are also bright in X-rays. McKee & Cowie (1975) suggested that the broad correlation of X-ray and optical emission is the result of a blast wave propagating in an inhomogeneous medium. In this scenario, the shock is significantly decelerated in dense clumps of gas, while portions of it proceed unimpeded through the lower-density intercloud medium. We apply the principles of this basic cloud–blast-wave interaction to a range of locations in the Cygnus Loop. In particular, we refine the cavity model introduced in Levenson et al. (1997), using these optical data to constrain the current ISM in the vicinity of the Cygnus Loop and to determine how the stellar progenitor modified it in the past.

We present the observations in §2. We describe them in detail, noting individual regions of interest, and we use these data to measure the physical conditions of the blast wave and the ambient medium in particular locations in §3. The purpose of the detailed examination is to combine the results in a complete map of the surrounding ISM. We present this three-dimensional model while providing a coherent explanation of the history that accounts for it in §4. We predict the future of this SNR and relate its fate to more general theories of supernova modification of the interstellar medium in §5 and summarize our conclusions in §6.

Observations
============

We obtained narrow-band images of the Cygnus Loop in 1995 August and September and 1995 September on the 0.8-m telescope at McDonald Observatory with the Prime Focus Corrector (PFC; [@Cla92]). The PFC system is a 5-element catadioptric corrector located at the F/3 prime focus of the telescope and projects a flat focal plane onto a Loral-Fairchild $2048 \times 2048$, $15\micron$-pixel charge-coupled device. The camera and corrector system has a $0\farcs3$ spot size in the V-band and projects each pixel to $1\farcs35$ on the sky, producing a $46\arcmin \times 46\arcmin$ field of view. The interference filters each have a rectangular transmission profile and full width at half maximum $FWHM = 40$Å  in the converging beam of the PFC. The filter centers in the F/3 beam are 5007Å, 6723Å, and 6563Å  to detect line emission from ø3 ($\lambda5007$), 2 ($\lambda\lambda6717, 6731$), and +\[\], which we refer to throughout as . Each individual integration of approximately $600$ s duration was bias-subtracted, flat-fielded, and scaled by its median sky value before being combined with other images. Every region of the Cygnus Loop was observed at least twice through each filter in order to remove cosmic rays and exclude bad regions of the detector, and most regions were observed three times in . We obtained a total of 62 observations in ø3, 89 in , and 54 and 2.

Over the large spatial scale of the Cygnus Loop ($3^\circ \times 3\fdg 5$), each observation is a distinct projection of the sky onto the plane of the detector, so images must be remapped to a common projection before being co-added. An astrometric solution for each integration was calculated based on the [*Hubble Space Telescope*]{} Guide Star Catalog. Alignment does not rely on overlapping observations of a particular region but depends instead on the astrometry of individual integrations. The final images are the result of pixel-by-pixel averaging in the combined image plane using nearest-neighbor matching and rejecting bad regions of the detector. The global maps of the Cygnus Loop with $25\arcsec$ pixels are shown with linear scaling in , ø3, and 2, and in a false-color combination with logarithmic scaling (Figure \[figwhole\]). While the observations at different wavelengths resemble each other broadly, their variation is apparent in the combined image. In this display, blends of  and 2 alone are yellow, ø3 and 2  together appear as magenta, and  and ø3  combine to make cyan. Only the regions that are displayed as white exhibit strong emission at all three wavelengths. In addition to the global maps, we present 5 smaller fields, each $95\arcmin$ across, at $6\arcsec$ resolution (Figs. \[figsubv\]–\[figsubz\]). Although we first describe the current physical conditions in specific regions of interest, our ultimate goal is to combine the understanding of the particular sites into a complete account of the surrounding ISM, its modification by the progenitor star, and the passage of the blast wave through it.

Emission Morphology and Structure of the ISM
============================================

Observed Morphologies
---------------------

The radiative shocks that are responsible for most of the optical emission from the Cygnus Loop result in two characteristic morphologies: filaments and diffuse emission. Figure \[figann\] identifies examples of these features and other structures to which we will refer by name. The morphological distinction is the result of different viewing geometry. As the “wavy sheet” model (Hester et al. 1983; [@Hes87]) describes, bright, sharp filaments are the result of long lines of sight through tangencies of the shock front. When the shock front is viewed face-on, the emission appears more diffuse.

Combined with the X-ray data, these observations provide more specific information on the evolutionary state of the Cygnus Loop and the distribution of inhomogeneities of the ISM around it. The widespread X-ray emission indicates that the global shock velocity is several hundred , so the optical emission comes from regions of denser gas that have decelerated the blast wave. The correlation of the X-rays with optically-bright regions make clear that this SNR is not globally in the gradual transition to the radiative phase that is the result of blast wave propagation in a uniform medium. The blast wave has recently and suddenly decelerated where radiative shocks are detected. This rapid, environmentally-imposed evolution is distinct from the simple model prediction for incremental change in a homogeneous medium.

These complete data sets demonstrate that many characteristics that have been investigated in small regions of the Cygnus Loop are widespread, and we adapt the physical explanations of these limited regions in previous work to understand the Cygnus Loop globally. For example, the bright emission from radiative shocks is found to be stratified at select observed locations ([@Fes82]), and we show this stratification to be typical of all prominent radiative shocks. The ø3 extends toward the projected exterior, and the  and 2 are located toward the projected interior. The 2 is farthest to the interior and is particularly diffuse. The stratification is a function of the column density that the shock has swept up. The incomplete ø3 emission is concentrated behind shocks that have encountered relatively little gas, while where the shock lags because it has swept up a greater column of gas,  and then 2 are prominent. The strong ø3 emission requires that the shock has progressed through a column density $N \approx 3\times 10^{17} {\rm \ cm^{-2}}$, while the complete recombination zone develops after the swept-up column $N \gtrsim 10^{18} {\rm \ cm^{-2}}$ for $v_s < 150 \kms$ ([@Ray88]). The apparent thickness of these zones and the extensive regions of bright emission in a combination of all the observed lines is a consequence of projection effects. The curved surface of the blast wave encounters the cloud at different projected radii, so some lines of sight intersect multiple stages of shock evolution.

Around most of the perimeter of the Cygnus Loop, filaments are detected in  alone. These Balmer-dominated filaments are the result of non-radiative shocks ([@Che78]; [@Che80]). Unlike the more common radiative shocks, the  emission here does not come from the extended cooling zone behind the shock. Instead, it is the result of collisional ionization before excitation in the immediate post-shock region, or the downward cascade toward the ground state following charge exchange. In either case, neutral atoms are required in the post-shock region. Because these do not survive long, the emission originates at the shock front. Thus, we use the Balmer filaments to trace the shock front directly. This  emission is intrinsically weak, so it is most obvious when the line of sight through the shock front is long. This is the case at the projected edge of the SNR, where the line of sight is tangent to the spherical blast wave.

Projected Edges\[subsecedge\]
-----------------------------

The projected edges of the Cygnus Loop are the simplest regions to understand because the geometric complications are minimized there. The observed structures may be slightly—but not significantly—in the foreground or background and still appear near the projected edge. The prominent regions, NGC 6992 at the northeast ($\alpha=\hms{20}{56}{24},\delta=31^\circ 43\arcmin$; Fig. \[figsubv\]) and NGC 6960 at the west ($\alpha=\hms{20}{45}{42},\delta=30^\circ 43\arcmin$; Fig. \[figsubw\]), are examples of interactions of the blast wave with large clouds ([@HesCox]; Hester et al. 1994; [@Gra95]; [@Lev96]), and the corresponding X-ray enhancement arises from reflected shocks that propagate through the hot, shocked SNR interior.

The observed length scales of optical and X-ray emission from NGC 6992 and NGC 6960 reveal the sizes of these large clouds. At the 770 pc distance of the Cygnus Loop, the coherent networks of filaments over $20\arcmin$ imply that the clouds have lengths of about $10^{19}$ cm. Balmer filaments, high-resolution X-ray observations or both constrain the location of clouds along the line of sight. X-ray emission extends beyond both of these bright optical edges, where some portion of the three-dimensional blast wave is not yet impeded by the clouds. Thus, the clouds do not extend over the complete edge of the blast wave along the line of sight.

In contrast, the southeast knot at $\alpha=\hms{20}{56}{20},\delta=30^\circ 25\arcmin$ (Fesen et al. 1992; [@Gra95]) is an example of a cloud that is clearly extended along the line of sight but is not necessarily large across the plane of the sky. The nearly-circular edge of the X-ray SNR and the Balmer filaments are distinctly concave at the southeast knot (Fig. \[figsubx\]a), and there is no X-ray emission to the exterior. Thus, this cloud must be at least 11 pc long along the line of sight in order to impede the entire projected edge of the blast wave at this location. Again, the presence of the complete optical cooling structure indicates that the shock has progressed through a column $N \gtrsim 10^{18} {\rm cm^{-2}}$ here.

The breakout to the south, centered on $\alpha=\hm{20}{50},\delta=29^\circ 10\arcmin$ and extending approximately $1^\circ$ across (Fig. \[figsubz\]), is the most significant departure from circularity in the remnant. The greater advance of the blast wave in the breakout compared with the circular loop north of $\delta=29^\circ40\arcmin$ indicates that the ambient density is lower in this southern region. Balmer-dominated filaments surround much of the breakout, where the blast wave has now encountered atomic gas. There are sections of incomplete shocks to the east and west (e.g., $\alpha=\hm{20}{53},\delta=29^\circ 20\arcmin$ and $\alpha=\hm{20}{48},\delta=29^\circ 15\arcmin$) and fully radiative shocks at the east ($\alpha=\hm{20}{52},\delta=29^\circ 15\arcmin$). Emission is absent across the face of this area. In the plane of the sky, the breakout is not very extended. Either the blast wave has only recently entered this low-density region, so it has not had enough time to advance significantly, or the extent of the low-density material is limited, so the blast wave no longer continues to progress rapidly. The stratification of emission around the edge of the breakout is apparent on smaller scales than those observed elsewhere in the Cygnus Loop, and the breakout exhibits smaller regions of common overlap. In the northeast, for comparison, the distinct regions of  and ø3 are typically $3\arcmin$ wide, and they are observed together over $10\arcmin$ scales, whereas in the breakout, the exclusive and common zones are both typically $1\arcmin$ wide. These characteristics are consequences of the more limited scale of interactions with clouds in the breakout. There is no evidence for indentation or blast wave progress beyond the optical-emitting regions, which could be due to either intrinsically small clouds or early stages of encounter. In either case, at least some dense material surrounds the SNR at its southern extremity.

The exterior of the southwest quadrant exhibits many filaments that are nearly aligned with one another (Fig. \[figsuby\]). Some of these are part of the radiative shock structure related to the southern end of NGC 6960, while farther away from the center, these are non-radiative and incomplete shocks (Fesen et al. 1992). Along some of the filaments, the transition from non-radiative to incomplete shock structure is clear where ø3 emission arises. The multiple filaments are easily understood as tangencies of a wavy sheet. These filaments are shorter than those at the north and east of the Cygnus Loop. This indicates that the ISM is clumpier here, which would distort the blast wave in many places and account for the number of filaments that we observe. Shock diffraction through low-density ($\delta \rho/ \rho \gtrsim 1$) regions may be responsible for the large curvature of some of these filaments, as Fesen et al. (1992) suggest, although multiple interfering shock fronts are not necessary to produce the different filaments. They arise from multiple projections of the same shock front.

### Balmer Filaments and X-ray Emission

The Balmer-dominated filaments around the periphery of the Cygnus Loop indicate that the fraction of atomic gas surrounding the SNR is high. The extreme circularity of these filaments requires that the blast wave remain nearly spherical with little deformation at the projected edge. With the exclusion of the breakout region, we fit them with a circle of radius $R=1\fdg 4$, which is equivalent to 19 pc at a distance of 770 pc. In Figure \[figcirc\], the model circle is drawn on the soft X-ray image obtained with the [*ROSAT*]{} High Resolution Imager ([@Lev97]). We calculate the correlation of radial variation as a function of angular separation and the corresponding Fourier coefficients for the Balmer filaments. Excluding the breakout, the amplitude of the $m = 2$ mode is less than 0.02, which implies that the surroundings of the Cygnus Loop are homogeneous on large scales.

The individual filaments tend to be very long, typically extending over more than $40\arcmin$. The continuity and smoothness of the Balmer filaments indicate the uniformity of the medium in which these shocks propagate. For constant ram pressure $\rho v_s^2$ behind the shock, variations in density and velocity are related $\delta \rho / \rho = -2 \delta v_s / v_s$. In terms of the radius, $R$, and time, $t$, $v=\eta R/t$, where $\eta$ is of order unity; for free expansion $\eta =1$, and for an adiabatic supernova remnant in a uniform medium, $\eta = 2/5$. Thus, $\delta \rho / \rho = (-2/\eta) (\delta R/ R)(t/\delta t)$. The observed radial variations of a particular filament are $\delta R/ R \sim 0.01$. An approximate timescale of these shocks is 1000 yr, and the age of the Cygnus Loop is about 14,000 yr (cf. §\[secage\]), so the overall density variations in the present medium of the Balmer-dominated filaments are of order $\delta \rho / \rho \sim 0.3  \eta$. We expect $ 2/5 < \eta < 1 $, so $0.1 \lesssim \delta \rho / \rho \lesssim 0.3$.

The Balmer-dominated filaments define the current location of the blast wave and mark the presence of neutral material. Detailed studies of particular locations at the northeast have used these non-radiative shocks as density probes ([@Ray83]; [@Long92]; Hester et al. 1994) and derive densities $n \sim 1 {\rm \ cm^{-3}}$. The total observed Balmer line intensity is sensitive to density, shock velocity, and geometric perspective. All of the filaments around the periphery share the same edge-on geometry. Because of the remnant’s circularity, it is reasonable to assume that the shock velocity is nearly constant around the extreme projected edge except at the breakout. The filaments that have been studied in detail to determine shock velocity and ambient density are the brightest ones, however, so these regions are most likely in the transition to incomplete radiative emission, and these densities are expected to be higher than elsewhere. Thus, we conclude that where typical non-radiative filaments are observed around the periphery, the density is constrained $n \lesssim 1 {\rm \, cm^{-3}}$, and most likely $n \sim 0.1 {\rm \ cm^{-3}}$.

We roughly calculate the  surface brightness of a non-radiative shock in the Cygnus Loop. We examine a portion of the blast wave in the southeast, near $\alpha=\hm{20}{56},
\delta=30^\circ 00\arcmin$. This is not an exceptionally bright filament, and there is no obvious interaction with a large cloud here. The whole filament extends over more than $20\arcmin$, so the blast wave edge is smooth here. We estimate a surface brightness of $4.2\times 10^{-6} {\rm \,erg\,s^{-1}\,cm^{-2}\,sr^{-1}}$ from this filament. Assuming that this line of sight passes through two folds of the spherical blast wave and the ISM does not distort it, the intensity of a single shock surface is $2.1\times 10^{-6} {\rm \,erg\,s^{-1}\,cm^{-2}\,sr^{-1}}$. The line intensity, $I$, depends on the energy of the transition, $h\nu$, and is given by $$I = {{h \nu}\over{4\pi}}n_H v_s{q_{ex}\over{q_i}} {\rm \,erg\,s^{-1}\,cm^{-2}\,sr^{-1}},$$ where $n_H$ is the preshock neutral density and the ratio of excitation and ionization rates $q_{ex}/q_i \approx 0.2$ for  ([@Ray91]). If we reasonably constrain the shock velocity $200 < v_s < 400 \kms$, these observations limit the density $0.3 > n_H > 0.15 {\rm \,cm^{-3}}$ at the location of the non-radiative shock. The lower velocity limit is based on observations of Balmer filaments ([@Ray83]; [@Long92]; Hester et al. 1994), which are likely to represent the slowest non-radiative shocks, as noted above, and the upper bound assumes that the forward shock does not heat the X-ray-emitting medium to temperatures greater than $2 \times 10^6 {\rm \, K}$.

The Balmer filaments are related to adjacent X-ray emission: the optical filaments form the exterior boundary of low surface brightness, limb-brightened X-rays ([@Lev97]). This characteristic morphology reveals where the blast wave is decelerated in the cavity walls. We combine the density determined from the Balmer observations with X-ray temperature measurements to calculate the unperturbed blast wave velocity and the original density of the cavity, and we compare this with the cavity density based on the observed X-ray surface brightness of the interior of the SNR. A bimodal temperature distribution has been detected in the Cygnus Loop, with peaks at $1.5 \times 10^6$ and $5 \times 10^6$ K in EXOSAT observations with the channel multiplier array (sensitive over 0.05–2 keV) and the medium energy experiment (sensitive over 1–50 keV; [@Bal89]). We suggest that the higher temperature component is due to the reflected shock and that previous low single-temperature measures are contaminated by the slow, forward shock in the cavity walls. We model these simply as a reflected shock and ignore non-equilibrium effects, which are probably important. The physical parameters temperature, pressure, and density, are related by the equations of conservation of mass, momentum, and energy flux across shock fronts. Assuming the temperature of $1.5 \times 10^6 {\rm \,K}$ corresponds to the decelerated shock in the cavity wall and $T=5 \times 10^6 {\rm \,K}$ corresponds to the reflected shock, the current blast wave velocity is around $300 \kms$, and the original, unperturbed blast wave velocity was around $500 \kms$.

The reflected shock model also predicts that the original cavity density, $n_c$, is related to the shell density $n_s/n_c = 5$. Combined with the surface brightness measurement of the Balmer filaments, this yields an atomic shell density $n_s = 0.2 {\rm \,cm^{-3}}$ and a cavity density $n_c = 0.04{\rm \,cm^{-3}}$ if the shell is entirely neutral. As described below (§\[subsecmodel\]), the shell is partially ionized, so the original cavity density was $n_c = 0.08 {\rm \,cm^{-3}}$. In addition to neglect of non-equilibrium effects, other sources of error include confusion of the reflected shock and the unperturbed shock in the cavity, uncertainty of the derived X-ray temperature, and uncertainty of the Balmer intensity of a single shock surface derived from observation through the spherical edge of the blast wave.

The predicted density is consistent with that derived from X-ray observations of the projected interior. In a featureless region of the southeast near $\alpha=\hm{20}{55},\delta=30^\circ 12\arcmin$, the median HRI surface brightness is $0.01 {\rm \, counts \, s^{-1} \, arcmin^{-2}}$. We compare this with a model of a Raymond-Smith plasma at $T_e = 3.5 \times 10^6$, correcting for absorbing column of $N_H = 6\times 10^{20} {\rm \, cm^{-2}}$. Assuming the emitting region is 22 pc deep (the predicted line of sight through the SNR at this radius), the observed count rate corresponds to a density $n_e = 0.2 {\rm \, cm^{-3}}$. This is the density of the shocked material; the original cavity density would have been $n_c = 0.05 {\rm \, cm^{-3}}$.

### Photoionization

One unusual feature at the east is a region of very smooth emission adjacent to the bright structure of NGC 6995 at $\alpha=\hms{20}{57}{30},\delta=31^\circ 00\arcmin$. This area is obvious in  and detectable in 2 but absent in ø3. There are no X-rays here ([@Lev97]), so a fast shock wave has not passed through. The X-ray map shows a clear indentation in this region, where dense gas has significantly impeded the blast wave over large scales, similar to the southeast cloud. There is no other direct evidence, such as a Balmer filament, that the blast wave is presently located toward the exterior of this region. We propose that this gas is photoionized by a shock precursor, and it has not been shocked.

Radiation from the shock-heated gas of the interior of the Cygnus Loop serves as the ionization source. Typically, when the shock velocity $v_s \gtrsim 100 {\rm \ km \ s^{-1}}$, much of the subsequent radiation is at UV wavelengths ([@Ray79]; [@Shu79]; [@Dop84]), which can ionize the surrounding gas, both ahead of and behind the shock front. The hardness of the ionizing spectrum increases with shock velocity, and the resulting emission from photoionized gas is a function of shock velocity and preshock density ([@Sut93]; [@Dop96]; [@Mor96]). The absence of ø3  in the ionized precursor indicates that the shock has intermediate velocity ($v_s \lesssim 200 {\rm \ km \ s^{-1}}$), which is consistent with UV spectroscopy of Blair et al. (1991) who find $v_s \sim 170 \kms$ is typical in this region. The bright emission ahead of the shock front is probably a consequence of relatively high density; the Balmer luminosity of the precursor scales linearly with density in the steady case ([@Ray79]; [@Shu79]; [@Dop96]). A second important factor is that the shock is fully radiative, having been decelerated in the dense cloud, so the shock front does not move through the ionized region before the ions have time to radiate (cf. [@Ray88]). Finally, the column density ahead of the shock must be great for the precursor emission to be observable.

The images do allow us to estimate crudely the density of the photoionized material. We assume that the length of the photoionized region along the line of sight is equal to its extent north-south in the plane of the sky and use the observed surface brightness to predict a density $n\sim 60 {\rm \, cm^{-3}}$. Spectral data would allow a more exact determination of the characteristics of the emitting region and quantitative measurements of the photoionizing source.

The blast wave history causes the ambient medium to be photoionized here and not elsewhere. The penetrating X-rays of very fast shocks ($v_s \gtrsim 400 \kms$) do not efficiently ionize the surrounding medium; the optical depth to 200 eV photons $\tau_{\rm 200 eV} = N/(1.1 \times 10^{20}{\rm \, cm^{-2}})$. Only the softer UV-dominated spectra of slower shocks are effective ionizing sources. In other regions of the Cygnus Loop, the recent shock velocity has been too great to produce much photoionization, and there has not been enough time for the ionizing field of the post-shock cooling and recombination zone to develop. Thus, most of the surrounding medium has remained sufficiently neutral to exhibit Balmer-dominated filaments. The exceptional photoionization at the eastern edge is consistent with the cavity model of this SNR. The blast wave has not slowed sufficiently elsewhere for most of the shocked gas to be a useful source of ionizing photons. Over nearly all of the Cygnus Loop, the deceleration has been recent, as the blast wave has run into the walls of the cavity. Only in this region has the softer spectrum of a slower shock existed long enough to ionize the preshock medium so that its radiative transitions can be detected.

Photoionized regions have been observed around other SNRs, including N132D ([@Mor95]) and N49 ([@Van92]) in the Large Magellanic Cloud, for example. One difference between the Cygnus Loop and the former SNR, however, is that while in the Cygnus Loop the photoionized precursor is the exception, detected only in a limited region, in N132D it is the rule, occurring over the majority of the younger remnant’s perimeter. Another difference is that the exceptional photoionization ahead of the Cygnus Loop blast wave is adjacent to the region that contains its brightest soft X-ray knots ([@Lev97]), while the photoionization and X-ray surface brightness variations are not correlated in N132D ([@Mor96e]). These differences are likely to be a consequence of the different sources of ionizing photons and the density of the surrounding medium. First, in N132D, the X-ray–emitting shock can account for only half of the ionization ([@Mor96e]), so another significant source must also contribute to the ionization in this case. The ubiquitous radiative shocks in clouds and O-rich filaments that Morse et al. (1996) propose as this additional source are not preferentially associated with the X-ray emission. Second, a large molecular cloud extends over the entire southern hemisphere of this SNR ([@Ban97]). While the present blast wave is not in the dense core that is observed in CO, the outer regions of the cloud are expected to be over-dense with respect to the typical ambient ISM. The higher densities that make the ionizing precursor visible are therefore characteristic of the majority of the perimeter of N132D. In contrast, we suggest that it is the unusual conditions of extreme blast wave deceleration and related high density that result in both the bright X-ray emission and the photoionized precursor in this small area at the eastern edge of the Cygnus Loop. These conditions make the Cygnus Loop precursor similar to that of N49. This middle-aged SNR is associated with a small molecular cloud on its eastern limb ([@Ban97]). The blast wave interaction with the cloud results in local optical emission and X-ray enhancement, blast wave deceleration observed in a range of shock velocities ([@Van92]), and a prominent photoionized precursor on the eastern limb of N49.

Projected Interior
------------------

The interior of the Cygnus Loop contains diffuse emission and filaments. Both morphologies share some characteristics, such as exclusive ø3 emission (e.g., $\alpha =\hm{20}{48}, \delta=30^\circ 30\arcmin$ in diffuse regions and $\alpha =\hm{20}{52}, \delta=30^\circ 30\arcmin$ in filaments), and blends of  and 2 (e.g., $\alpha =\hm{20}{50}, \delta=29^\circ 45\arcmin$ and $\alpha =\hm{20}{50}, \delta=29^\circ 45\arcmin$). A combination of emission in all three lines is observed only in diffuse emission (e.g., $\alpha =\hm{20}{52}, \delta=31^\circ 10\arcmin$), and  alone is observed only in filaments (e.g., $\alpha =\hm{20}{50}, \delta=30^\circ 30\arcmin$).

Projection effects are more severe in the interior, but these optical images and high-resolution spectroscopy ([@Kir76]; [@Gre91]; [@Shu91]) together help unravel the tangled Cygnus Loop. In all cases, the optical emission is the result of the interaction of the three-dimensional blast wave surface with dense structures in the ISM. The emitting regions are truly at the outside of the SNR, but some appear projected to the interior. The brighter filaments tend to have lower absolute radial velocities and narrower velocity dispersions than the fainter diffuse emission ([@Kir76]; [@Shu91]). This is consistent with the model in which filaments are long lines of sight through the edge of a wavy shock front, and diffuse emission results when the blast wave is observed nearly face-on. The shock velocity is primarily perpendicular to the line of sight in the former case and along the line of sight in the latter case. In some instances, adjacent filamentary and diffuse emission are related, being tangential and normal views of the same portion of the blast wave. Elsewhere, spatially separated shock regions are projected onto the same location in the observer’s view, causing significant confusion.

The extensive diffuse emission at the western interior near $\alpha=\hm{20}{47}$—$49^{\rm m}$ and $\delta=30^\circ 40\arcmin$—$31^\circ 20\arcmin$ suggests that a large wall of dense gas is present across the entire face of the SNR (Figs. \[figsubw\] and \[figsuby\]). The irregularity of the diffuse emission is due to the clumpiness of the cloud. This emission is blueshifted with respect to nearby gas ([@Gre91]; [@Shu91]) so it is on the front face. The bright filaments of the “carrot” (at $\alpha =\hm{20}{49}, \delta=31^\circ 40\arcmin$), having positive radial velocities, are on the rear face.

The filaments at $\alpha =\hm{20}{49}, \delta=31^\circ 00\arcmin$ (Fig. \[figsubw\]) are distinct on small scales, similar to the edges of the breakout, although here the region of common overlap is absent. The origin of the stratification is the same: the limited physical scale of the interaction with the intervening cloud, either because the cloud is intrinsically small or because the encounter is recent and the blast wave has not progressed far into the cloud. Along a particular line of sight, only a single coherent section of the blast wave is detected. Unlike the areas where strong emission is observed at all wavelengths, here there are not many projected overlapping regions of various stages of shock evolution. The filaments that are bright in  and 2 illustrate an earlier section of the cloud shock than do the ø3 filaments. In this area on the western half of the Cygnus Loop, there is no planar blast wave that actually moves to the east, however. Rather, the [*interaction*]{} with a cloud is progressing from west to east as the blast wave surface expands radially. The intervening cloud must be oriented along the line of sight to some degree, as shown in Figure \[figcartc\].

Another region of diffuse emission and fainter filaments runs north-south across the center of the remnant, around $\alpha=\hm{20}{50}$—$52^{{\rm m}}, 
\delta=30^\circ 20\arcmin$—$50\arcmin$ (Figs. \[figsubx\] and \[figsuby\]). The high-resolution spectra in the vicinity are of the diffuse component alone, which includes very bright central knots. These clumps are blueshifted, so these clouds are on the near face. The westernmost of these filaments, at $\alpha=20^{{\rm h}} 50^{{\rm m}} 20^{{\rm s}}$, is detected only in . The blast wave has run into an extended wall of gas, enabling us to look through a long edge of the shock front. These filaments are broader than most of the other pure Balmer filaments, which is expected in this scenario. The broad filaments appear where the blast wave is viewed through a point of inflection, whereas the sharper, narrow ones are viewed at a tangency. For these non-radiative filaments to be observable, the wall of gas must be extremely smooth at the present projected location of the shock front. The wall of gas is likely to be related to the source of the rest of the optical emission at the center of the SNR, not the clouds that are illuminated as the “carrot,” although this is uncertain.

History of the Cygnus Loop
==========================

Modelling the ISM\[subsecmodel\]
--------------------------------

Except in the single photoionized section, the optical emission traces dense shocked regions. Using some knowledge of shock evolution and geometry, we map the surrounding ISM. The basic principles applicable to these observations are: (1) optical emission due to radiative shocks requires that the blast wave has swept up a significant column density ($N \gtrsim 10^{18} {\rm \, cm^{-2}}$), which is likely in regions of increased density ($n\gtrsim 1 {\rm \, cm^{-3}}$); (2) sharp filaments are edge-on views of the blast wave surface, and diffuse emission is the result of face-on views of this surface; (3) the optical line emission from a radiative shock is progressively dominated by ø3, , then 2; and (4) filaments of  alone are the result of non-radiative shocks in material that has a significant neutral fraction.

With these data, we construct a three-dimensional model of the interstellar medium around the Cygnus Loop . Over much of its surface, the blast wave is propagating through large clouds. Long filaments, detected in  around the perimeter and in other lines across the interior, indicate that a spherical shell of atomic gas surrounds the SNR. The dense clumps of gas and the atomic shell together form the walls of a cavity in which the supernova occurred. Slices through the Cygnus Loop parallel to the plane of the sky from the near side to the far side (Fig. \[figcartmap\]) show some of the three-dimensional structure of the ISM before the supernova event. The center of the Cygnus Loop is at latitude $b = -8^\circ$. At the rear of the cavity, toward the Galactic plane, is a large wall of gas that is detected in neutral hydrogen ([@DeN75]) and in the IRAS sky survey ([@Bra86]). The cloud that causes the bright northeastern emission is also on the far side. Clumps at the edge of the breakout and at the northwest are on the near side. Some clouds, including the southeast knot and the molecular gas at the west, extend along the line of sight and appear in all slices.

The Cygnus Loop is not the result of a supernova explosion in an arbitrary region of the interstellar medium. Rather, the blast wave propagates through a medium that the progenitor star has processed. Several characteristics imply a massive progenitor, the sort most capable of modifying the surrounding ISM, which Charles et al. (1985) and Levenson et al. (1997) discuss. One strong piece of evidence is the paradoxical morphology of the Cygnus Loop. At optical and X-ray wavelengths, it appears to be nearly circular, yet it exhibits tremendous structure on smaller scales. The optical data alone could be interpreted as a SNR in transition from the adiabatic to the radiative phase, but the presence and correlation of X-rays require that overall the blast wave still has (or until very recently had) a high velocity, $v_s \gtrsim 400 {\rm \ km \ s^{-1}}$. A model of blast wave interaction with large clouds accounts for this correlation ([@HesCox]; [@Gra95]; [@Lev96]), but such large clouds cannot be typical of the pre-supernova interstellar medium. If they were, the SNR would not appear so circular, and X-ray emission due to clouds evaporating in the interior would be observed. Thus, although large clouds are found around the periphery of the Cygnus Loop, they were not located within the current blast wave prior to the supernova event. This structure is expected in the vicinity of an O or B star. During its main-sequence lifetime, such a massive star homogenizes the surrounding ISM, creating a uniform region at constant density, temperature, and pressure. The star’s UV emission removes clumps of denser gas within the H II region, either destroying the clouds through photoevaporation or relocating them to the exterior by the rocket effect ([@McK84]). The result is a homogeneous spherical region surrounded by dense clouds. A star of type earlier than B0 will clear a cavity with a radius of about 50 pc (McKee et al. 1984 ). The Cygnus Loop cavity is smaller, so its progenitor must be a later-type star ([@Cha85]), yet one still able to create the photoionized cavity. Thus, we suggest that a B0, $M\approx 15M_{\sun}$ star was the progenitor of the Cygnus Loop.

The observer’s line of sight through shocked clouds at the projected edge is preferentially longer than through those that appear at the projected center. Photoevaporation of clouds progresses radially outward from the central star, so lines of sight tangent to the cavity are biased to be through the longer dimensions of surviving clumps. Thus, optical emission on the projected interior is not as bright as on the projected edge of the SNR, despite their common cause. The same effect is even more pronounced in the X-ray data.

The atomic shell in which the non-radiative filaments appear is also a consequence of the progenitor’s evolution. While material is eroded from clouds during the star’s main sequence lifetime, increasing the density of the H II region, the radius of the ionized region decreases as the outer portions recombine, creating the shell ([@Elm76]). The atomic gas of this recombined region together with the cloud remnants on the periphery form the walls of the cavity (Fig. \[figcartmap\]). The Cygnus Loop blast wave has expanded through the uniform cavity and is now hitting the surrounding walls ([@Lev97]).

The atomic shell is not actually a sharp density discontinuity. It is more likely a gradual transition from the cavity interior to the maximum shell density. At the end of the progenitor’s main sequence lifetime, the pressure in the former H II region declines as the gas cools and recombines. (See [@PShu85] for a discussion of this phenomenon applied to N49.) In the extreme case of a sudden loss of pressure at the boundary, a rarefaction wave would move back through the dense shell resulting in a density profile of the form $n \propto (1 + {3r \over {at_{RG}}})^3$ ([@Zel66]), where the distance, $r$, from the original shell edge is constrained $-3at_{RG} \le r \le 0$ in terms of sound speed, $a$, and red giant lifetime, $t_{RG}$. The drop in pressure is not so sudden, however. Over $t_{RG} \sim 10^6$ for $M\approx 15M_{\sun}$ ([@Mae89]), about half the atoms in the former H II region have recombined. Thus, the density profile of the shell edge is likely to be intermediate between a sharp discontinuity and the offset power law above.

The Cygnus Loop has been suggested previously to be the result of an explosion in an incomplete cavity. Both Falle & Garlick (1982) and Shull & Hippelein (1991), for example, argue for a partial cavity at a density discontinuity, such as the edge of a molecular cloud. In these models, only half of the blast wave runs into the cavity boundary. Consequently, the bright radiative emission of NGC 6992 and NGC 6960 and the corresponding X-ray emission are physically separated by great distances along the line of sight: the former are the result of radiative shocks in the cavity wall, and the opposite hemisphere of the blast wave propagates through the low-density medium outside the cloud to cause the latter. In contrast, the model presented here and in Levenson et al. (1997) has a completely defined cavity, the atomic shell and dense clouds together forming its spherical boundary. The blast wave does not break [*out*]{} of the edge of the molecular cloud into lower-density material; instead, it slows down when it hits a wall of [*denser*]{} gas. Although NGC 6992 and NGC 6960 and the X-rays that appear to the exterior of these radiative regions are two slightly different portions of the blast wave, they are not significantly separated. Furthermore, some of the large clouds are obviously extended along the line of sight, not restricted to the rear boundary (Fig. \[figcartmap\]). These optical and previous X-ray data ([@Lev97]) demonstrate that the cavity wall is complete. All around the projected edges of the Cygnus Loop, the Balmer filaments and X-ray enhancements mark the smooth component of the cavity wall. [*Even the region called the breakout illustrates where the blast wave runs into a boundary of dense gas, not continued expansion in a low-density medium.*]{} Only the eastern third of the projected interior of the Cygnus Loop lacks direct evidence for a cavity wall, although the smooth atomic shell that is apparent in Balmer-dominated filaments elsewhere would not be detected across the face of the SNR. Only clumps of gas could be observed, and their distribution depends on the arrangement that existed before the ISM was processed by the progenitor. The southeast of the Cygnus Loop is farthest from the galactic plane, so we expect the original filling factor of clouds to have been lowest there.

Other SNRs, including RCW 86 ([@Vin97]) and N132D ([@Mor96e]), have been identified as cavity explosions. \[Shull (1985) identifies N49 as a cavity supernova, but Vancura et al. (1992) argue that the dense ambient material associated with the single observed CO cloud accounts for the data better.\] In these cases, interaction of the blast wave with the cavity wall enhances the observable properties of the SNRs. RCW 86 shares many features of the Cygnus Loop, including similar size, a limb-brightened (though very incomplete) X-ray shell (Vink et al. 1997), and Balmer-dominated filaments to the exterior of the X-ray emission ([@Smi97]). N132D is a younger remnant, and the apparent cavity is smaller. The progenitor’s wind during its main sequence lifetime may form the cavity boundary, or the scale of photoevaporation may have been limited in this dense environment adjacent to a molecular cloud ([@Ban97]). The bright interior X-ray emission ([@Mor96e]) does imply that the cavity interior was not uniform.

Age and Distance\[secage\]
--------------------------

Although the shell-like visual morphology of the Cygnus Loop and its X-ray limb-brightening broadly suggest that this is an example of a supernova remnant in the Sedov-Taylor or adiabatic expansion phase, in detail this model is inconsistent with the data presented here and in Levenson et al. (1997). The observed X-ray and optical limb-brightening are a consequence of interaction with the inhomogeneous interstellar medium, not the result of evolution of the blast wave in a uniform medium. Assuming that the blast wave has slowed sufficiently during its progress through a uniform medium to produce optical line emission (i.e. to $v_s \lesssim 200 \kms$) yields an age estimate of about 50,000 yr ([@Min58]; [@Fal82]). This is much too great because the age is inversely proportional to the blast wave velocity, and only in propagating through dense clouds has the shock been decelerated to $v_s \lesssim 200 \kms$. The Balmer filaments mark the location of the unimpeded, spherical blast wave, and the X-ray emission immediately behind these filaments demonstrates that the typical shock velocity is $v_s \gtrsim 400 \kms$, which is still to great for radiative cooling of the Sedov-Taylor shell to be significant. This SNR has not made the global transition to the radiative evolutionary phase. The X-ray emission alone has been used to determine an age of around 18,000 yr ([@Rap74]; [@Ku84]), assuming that this is presently an adiabatic blast wave expanding in a uniform medium; $t = 2R/5v_s$, where $R=19{\rm \ pc}$ and $v_s = 400 \kms$.

The X-ray data provide a more accurate measurement of the age, but it is still likely to be an upper limit because these calculations contain uncertainties in the shock temperature and the velocity that is derived from it. Only the current unperturbed shock velocity is relevant to the age in this model, but any observation of the SNR includes contributions from a variety of temperatures, heated by different stages of the blast wave’s history. Observing the projected edge of the SNR minimizes confusion due to overlapping projections of different temperature components, but the interaction of the blast wave with the inhomogeneous ISM greatly alters the shock velocity and the corresponding postshock gas temperature.

When the blast wave hits a density discontinuity, as it does over most of the surface of the Cygnus Loop, the continuing shock is suddenly decelerated and a reflected shock propagates back toward the interior, further heating the dense, hot, shocked material. At a density contrast of 10, for example, the twice-shocked matter will have a temperature approximately 1.5 times the singly-shocked material at the same radius, which leads to an overestimate of the unperturbed shock velocity by about $20\%$. Both the reflected shock and the forward shock through the dense cloud enhance the X-ray surface brightness and thus bias the mean measured temperature to favor blast-wave–cloud interactions rather than the undisturbed blast wave.

If the X-ray measurement of two temperature components ([@Bal89]) due to the decelerated cloud shock and the reflected shock is correct and the original velocity of the unperturbed blast wave was closer to $500 \kms$ (§\[subsecedge\]), the corresponding age $t = 14,000$ yr. A reliable determination of the age of the Cygnus Loop is required to determine the initial energy, $E_o$, accurately (§\[secintro\]). Adopting the parameters $n_o = 0.08 {\rm \, cm^{-3}}$, $R = 19$ pc, and $t = 14,000$ yr, and a partially-ionized cavity interior, we find $E_o=2\times10^{50} {\rm\, erg}$.

Because the radiative emission shows where the blast wave has run into clumpy material and decelerated, care is required to use it to measure the distance to the Cygnus Loop. Minkowski (1958) determined the expansion velocity to be $116 \kms$, fitting an ellipse to radial velocity measurements as a function of radius. This, combined with Hubble’s (1937) observed proper motion of filaments of $0.03\arcsec {\rm \ year^{-1}}$ yields the frequently-cited distance of 770 pc. This calculation assumes that all the optical filaments are part of a common expanding surface. In fact, the optical emission reveals different regions of inhomogeneity in the ISM. A second complication is the distinct geometry of the diffuse and filamentary emission on the face of the SNR. One is the result of a face-on shock, and the other is an example of a shock viewed edge-on. The latter does not have the radial velocity structure as a function of projected radius that is assumed in the model calculation. A third source of confusion arises because the observed filaments are the cooling zone behind the shock front, so their apparent motion may be the result of further development of the postshock region, not motion of the same clump of gas. The cooling zone may be propagating, without any physical motion of a parcel of gas in the ISM.

Despite these difficulties, however, the radiative shocked gas can be used to measure distance to the Cygnus Loop or other supernova remnants when the distribution of clumps in the surrounding medium is spherically symmetric. In this case, although the emission comes from distinct regions of the ISM, not a single expanding blast wave surface, the different clouds acquire the same velocity when the blast wave passes through them. This approach is not appropriate where the surrounding medium is asymmetric, however. IC 443, for example, is asymmetrical, and its corresponding distance determinations are highly uncertain ([@Gre84]).

The non-radiative filaments can also be used to determine distance, as Hester, Danielson, & Raymond (1986) have done, finding a distance of about 700 pc. These structures are advantageous because proper motion and spatial velocity can be calculated from the same filament. There is some uncertainty in the shock velocity because the derived value depends on the amount of ion-electron temperature equilibration (Chevalier et al. 1980). Measuring proper motion of filaments also introduces some uncertainty. All filaments are detected where the observer’s line of sight through the shock front is long, which may be the tangent surface of a spherical bubble. If it is instead the deformed surface of the blast wave that appears as a filament, however, the apparent filament will not necessarily persist or be detectable over the timescales required to obtain proper motion measurements. Long baselines over which to measure proper motion are desirable, but the oldest observations are sensitive to the brightest filaments. These bright filaments are exactly the locations where the shock is likely slowed in denser gas, so the present velocity differs from the spatial velocity that corresponds to the proper motion. With these caveats in mind, we adopt a distance of 770 pc to the Cygnus Loop.

Consequences
============

The Cygnus Loop blast wave is now in the walls of the cavity, the boundary between the low-density former H II region and the ambient ISM. Blast wave propagation in the atomic shell will be a long-lived phenomenon. The smooth material of the shell recombined as clumps were photoevaporated in the interior. We crudely calculate the thickness of the shell assuming a constant number of ions in the H II region in both the initial Stromgren sphere, in which only the less-dense intercloud material was ionized, and in the final Stromgren sphere of radius $R_f$, in which all material, having mean density $n_m$, is ionized. The typical, unprocessed ISM determines the initial conditions; we assume the intercloud density $n_{ic}=0.1 {\rm \, cm^{-3}}$, and a volume filling factor of 0.03 of clouds of density $n_{cl}=1 {\rm \, cm^{-3}}$, so $n_{m}=0.13 {\rm \, cm^{-3}}$. Conserving ion number and neglecting increased recombination as clouds are evaporated, we obtain for the shell thickness $$R_{sh}=R_f ((n_m/n_{ic})^{1/3} - 1),$$ so using the observed radius $R_f = 19{\rm \,pc}$ yields $R_{sh}=1.5 {\rm \, pc}$. A blast wave of velocity $v_s= 300\kms$ will propagate through the shell for 5000 years.

Eventually the blast wave will propagate through the denser medium of the cavity walls and clouds everywhere. It will rapidly decelerate, not only in the select locations where it has already encountered dense clumps that protrude into the cavity. Some of the surrounding material consists of large dense clumps like the ones observed presently in the very extended regions of radiative shocks. These, too, will light up and will be detectable at optical wavelengths. The southeast cloud may be an example of the earliest stages of interaction with a large cloud, and it may later resemble the northeast region ([@Gra95]). We also expect the entire northern limb, which in the optical regime is now detected primarily in bright Balmer filaments, to turn into an extended radiative region. The incomplete shocks along the northern limb are the early stages of interaction with a larger structure that is perhaps directly associated with the bright northeastern region. The entire western face of the Cygnus Loop will soon be bright when the blast wave has fully encountered the wall of gas that we have noted there. If the long filaments across the center of the SNR are the result of another wall of gas, the middle will also light up with optical emission in several hundred years.

Large clouds of gas will significantly affect blast wave evolution. The shock will no longer be adiabatic when the cooling timescale becomes comparable with the dynamical timescale. In large clouds, where density $n_{cl}=1 {\rm \, cm^{-3}}$, radius $R_{cl}= 5 {\rm \, pc}$, and in which the shock velocity $v_{cl}=200\kms$, the dynamical time $R_{cl}/v_{cl} \approx 2\times 10^4 {\rm \, yr}$. In these clouds, the cooling time $3kT/n_{cl}\Lambda(T)\approx 4 \times 10^4 {\rm \, yr}$, in terms of the cooling function, $\Lambda$, having units ${\rm erg\, cm^3\, s^{-1}}$. If the covering fraction of clumps in the surrounding medium is sufficiently great, they will force the Cygnus Loop into the radiative phase, and energy losses will further decelerate the blast wave. The time and radius at which this occurs are distinct from self-similar calculations, such as those of McKee & Ostriker (1977) and Shull & Draine (1987) in which the gradual transition to the radiative phase happens as the blast wave propagates through a uniform medium.

We use the pressure-driven snowplow model ([@McK77]) to set an upper limit on the final size of the SNR. In this model, work of the blast wave pushing into the ambient material and radiative losses of the hot interior are taken into account. In the Cygnus Loop, the radiative losses of the outer shell also will be significant, slowing the blast wave and making the final radius smaller. During this phase, $PV^\gamma$ is constant, where $P$ is the pressure inside the SNR, $V$ is its volume, and $\gamma$ is the ratio of specific heats. For $\gamma = 5/3$, this phase ends when $R = R_{PDS}(P_{PDS}/P_{ISM})^{1/5}$, in terms of the external pressure of the interstellar medium, $P_{ISM}$, and the radius and pressure inside the supernova remnant at the onset of the pressure-driven snowplow stage, $R_{PDS}$ and $P_{PDS}$, respectively. At this final time, the pressure inside the supernova remnant is equal to the ambient pressure. For the Cygnus Loop, we take $P_{ISM} = 10^{-12} {\rm \, dyne\, cm^{-2}}$, $R_{PDS}=20 {\rm \, pc}$, and $P_{PDS} = 4\times 10^{-9} {\rm \, dyne\, cm^{-2}}$, which places an upper limit on the final radius $R < 105 {\rm \, pc}$.

Assuming that blast waves propagate through uniform media over great distances yields misleading conclusions about the size of SNRs and how they distribute energy through the ISM. Global models of the interstellar medium that include the hot contribution of SNRs ([@Cox74]; [@McK77]) are sensitive to the supernova rate, the final sizes of supernova remnants, and their persistence as hot bubbles. These factors determine whether the dominant component of the ISM is hot and in which smaller regions of warm and cold gas are embedded, or whether the warm and cold components form the substrate in which the distinct hot bubbles of SNRs are located. For the former to occur, the onset of the radiative phase of the SNR must be postponed until $R > 100 {\rm \, pc}$, independent of its prior evolution ([@Cox86]). (This calculation assumes that the supernova rate is 1 per 30 yr in a disk of radius 15 kpc, yet the conclusion holds for a range of reasonable supernova rates.) Although the cavity of the Cygnus Loop is small because its progenitor is one of the least massive stars to undergo core collapse, the initial mass function favors these lower mass (and smaller cavity) progenitors. Furthermore, even more massive stars, where cavities of 50 pc radius are expected, will be forced into the radiative phase and not expand to overlap if the density of the cavity walls is sufficient. The cavity walls are indeed likely to be denser on average than the typical ISM because the walls contain much of the material that was cleared out of the cavity interior. The conditions of the ISM in general, however, constrain the mass that will be commonly available to form clouds and cavity walls around pre-supernova stars. If the hot, low-density medium is pervasive, cavity walls typically would not be sufficiently massive to induce the radiative phase early, and SNRs would then normally attain larger radii before their blast waves decelerate. In any case, the typical environments of supernova progenitors must be considered. If dense, molecular material normally surrounds these stars, the radiative phase will be induced early, even if globally the ISM has low density.

The cavity structure is significant also in determination of the mass of gas that a supernova remnant heats. The onset of shell formation for a supernova blast wave expanding in a uniform medium occurs at $R \propto n^{-3/7}$, so the shocked mass is then $M \propto n^{-2/7}$. If the ambient density varies by three orders of magnitude, the heated mass changes by only a factor of 7, for example. In contrast, when the supernova environment is a cavity with dense walls, the initial size of the cavity constrains the mass of the hot interior. The cavity interior is rarefied, so the heated cavity mass is significantly lower. In the Cygnus Loop, assuming a cavity density $n_c = 0.08 {\rm \, cm^{-3}}$, the heated mass is $20 M_{\sun}$, whereas in a uniform medium of this density, the heated mass would be greater than $400 M_{\sun}$.

Conclusions
===========

This optical emission line atlas of the Cygnus Loop supernova remnant provides the information to render a portrait of the surrounding ISM. The ambient medium, which the massive stellar progenitor shaped as it evolved, consists of many large, dense regions. These will significantly affect the subsequent development of the blast wave. The blast wave will decelerate, and it will no longer have sufficient velocity to excite the material through which it propagates to X-ray-emitting temperatures.

Although this is a study of a particular object, it has far-reaching consequences for the ISM as a whole. Supernova remnants provide the energy to heat the ISM, affect the velocity dispersion of interstellar clouds, and set the stage for future generations of star formation. Thus, any global model of the gas in the Galaxy critically depends on the evolution of SNR blast waves in their inhomogeneous environments, of which this example is typical. While optical emission-line characteristics identify supernova remnants, they may preferentially select those whose evolution the extant ISM determines. Other SNRs need to be examined over a broad range of energies in the same careful way to draw more certain conclusions about their net effect on the interstellar medium.

This research was supported in part by the Packard Foundation.

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