Abstract
The Chandra X-ray Observatory observed the Crab Nebula and Pulsar during orbital calibration. Zeroth-order images with the High-Energy Transmission Grating (HETG) read-out by the Advanced CCD Imaging Spectrometer spectroscopy array (ACIS-S) show a striking richness of x-ray structure, at a resolution comparable to that of the best ground-based visible-light observations. The HETG-ACIS-S images reveal, for the first time, an x-ray inner ring within the x-ray torus, the suggestion of a hollow-tube structure for the torus, and x-ray knots along the inner ring and (perhaps) along the inward extension of the x-ray jet. Although complicated by instrumental effects and the brightness of the Crab Nebula, the spectrometric analysis shows systematic variations of the x-ray spectrum throughout the Nebula.
INTRODUCTION
Remnants of the supernova of 1054, the Crab Nebula and Pulsar comprise an astrophysical system that is wellstudied throughout the electromagnetic spectrum. As evidenced by its broad power-law spectrum and high linear polarization observed in the radio (e.g., Mayer, McCullough, & Sloanaker 1957; Mayer & Hollinger 1968) , visible (e.g., Dombrovsky 1954; Oort & Walraven 1956; Hiltner 1957; Schmidt, Angel, & Beaver 1979) , and x radiation (Weisskopf et al. 1976; , the continuum emission (up to 100 MeV) of the Nebula results from synchrotron losses by relativistic electrons, as first proposed nearly a half century ago (Shklovsky 1953) .
The Crab Nebula is the archetypal filled-center supernova remnant, or plerion (Weiler & Panagia 1978) . Unlike shell-like supernova remnants, a central pulsar presumably powers each filled-center supernova remnant. Thus the inner nebula of a plerion is particularly interesting, because it is the site of conversion of pulsar-supplied energy into synchrotron-emitting electrons. Although this general picture seems valid, details of the coupling mechanism (e.g., Rees & Gunn 1974; Dobrowolny 1976; Kennel & Coroniti 1984; Michel 1985; Emmering & Chevalier 1987; Coroniti 1990; Begelman & Li 1992; Michel 1994) remain uncertain.
Detailed studies (Hester et al. 1995) of the Crab Nebula with the Hubble Space Telescope (HST) demonstrate the richness of structure of the Crab Nebula's synchrotron emission, on scales down to 0.2 ′′ . Especially intriguing are the structures of the inner Nebula near the Pulsarwisps (Scargle 1969) , knots, and fibrous texture (Hester et al. 1995 ) -which exhibit an overall, approximately cylindrical symmetry. Hubble observations (Hester et al. 1998 ) also show that wisps form and dissipate over a few weeks, while moving outward at about 0.5c, thus clarifying the dynamical nature of these features (Scargle 1969) .
Even more dramatic are the x-ray images of the Crab Nebula, which clearly show this cylindrical morphology. In a remarkable synthesis from lunar-occultation, modulation-collimator, and low-resolution-imaging x-ray observations, Aschenbach and Brinkmann (1975) had interpreted the ensemble of extant data in terms of an xray torus. Subsequent, higher-resolution x-ray datafrom Einstein (Brinkmann, Aschenbach, & Langmeier 1985) , RoSat (Hester et al. 1995; Greiveldinger & Aschenbach 1999) , and Chandra (reported here) -confirm this toroidal morphology and detect an apparent jet and counter jet nearly along the axis of symmetry of the torus.
On 1999 July 23, NASA's shuttle Columbia launched the Chandra X-Ray Observatory. The angular resolution of Chandra is less than 1 ′′ , an order of magnitude better than that of any other x-ray observatory and comparable to that of the best visible-light ground observations. Thus, Chandra provides an excellent tool for probing the rich structure of the inner Crab Nebula in x rays. Here, we report the first high-spatial-resolution observation ( §2) and describe the observed morphology ( §3) and spectrum ( §4) of the Crab Nebula, as obtained with Chandra.
OBSERVATION AND ANALYSIS
On 1999 August 29, during the orbital activation and calibration, Chandra obtained a 2667-s observation of the Crab Nebula, using the High-Energy Transmission Grating (HETG, Canizares et al. 2000) and the Advanced CCD Imaging Spectrometer spectroscopy array (ACIS-S, Garmire et al. 2000) of 6 CCDs. The data include events in both zero and higher spectral order, the latter being dispersed along two crossed tracks, owing to the slightly different orientation of the High-Energy Grating (HEG) facets from the Medium-Energy Grating (MEG) facets. In this paper, we examine only the zeroth-order image of the Nebula. Figure 1 shows the HETG-ACIS-S image of the Crab Nebula, for the centermost ACIS-S CCD -designated "S3" -which is one of two back-illuminated CCDs in the 10-CCD ACIS focal plane. The Chandra X-ray Center's standard processing software has applied aspect corrections and compensated for the effects of dither (which smooths pixel-to-pixel variations of the detector) over a 16
′′


×16
′′ area. Acquired in the timed-exposure graded garciaadam@example.org s/frame, the data comprise an event list, with each event recorded in a 3×3-pixel "island". In this mode, the on-board software detects events and grades them according to which pixels (including the central pixel) have enough charge to exceed pre-defined thresholds. Because charged-particle events dominate the ACIS background and are mainly in flight grades 255, 66, 24, 107, and 214, the on-board software removes these events before telemetering the data.
Owing to the x-ray brilliance of the Crab Nebula and Pulsar, Chandra observations of this source are particularly challenging. First, the total count rate is so high that the ACIS data saturates telemetry, resulting in dropped ACIS frames. Although this results in lost events, it does so in an unbiased manner and is not a substantive problem.
More problematic is "pile-up", in which multiple photons contribute charge to the same or adjacent pixels, thus appearing as a single detected event. First, pile-up effects "grade migration", changing the grade of a valid event (in the 3 × 3-pixel event island) to a grade which might normally be excluded from further analysis. To mitigate this, we retained all telemetered grades in the imaging analysis ( §3), but not in the spectral analysis ( §4). Second, in regions of high surface brightness, the detected event rate is no longer proportional to the photon rate; thus, reducing the contrast. In regions of very high surface brightness, the pile-up is so extreme that the charge deposited in a 3×3-pixel island exceeds a pre-determined threshold (corresponding to about 15 keV), causing on-board rejection of the event. This "saturation" results in no detected events in the very brightest areas of the image -namely, at the position of the Pulsar (Figures 1 and 2) .
Pile-up severely complicates spectral analysis ( §4), by allowing two or more photons to masquerade as a single, higher-energy photon. To assess the impact of pile-up on the spectral distribution, we analyzed the "trailed" image ( Figure 1 ). The trailed image results from x-ray photons which strike the CCD during the time the frame-transfer electronics moves the exposed frame into the frame-store region of the CCD. As each of the 1024 rows transfers toward the frame-store region, it spends about 40 µs at each physical row. Compared to the 3.20-s integration time per frame, the 41-ms transfer time is quite small, so the effects of pile up are negligible for the trailed image. Of course, the trailed image is only one-dimensional, having no spatial information in the transfer (trail) direction.
The region from which we extracted the trailed image also contains photons from the timed exposure of the xray halo surrounding the Nebula. To subtract this component from the trailed image, we extracted a "background" from regions B (Figure 1) . Further complicating this process is the presence in region B, of a component due to the trailed image of the first-order dispersed spectrum of the Nebula. Because this contribution is small, we simply scaled the flux in region D of the dispersed image by 300 × 4(10 −5 )/3.20 = 0.0038 -number of rows occupied by the first-order image of the Nebula, times transfer time per row, divided by integration time per frame -and subtracted its spectrum from that of regions B. This results in a 5% decrease in the total rate of regions B, with most of the change occurring above 4 keV. We then used this modified spectrum as the "background" in the trailed-image regions T.
RESULTS -MORPHOLOGY

Figure 2 shows a 200
′′ ×200 ′′ image of the Crab Nebula, extracted from the S3 full-frame image (Figure 1) . The Chandra image clearly shows the x-ray torus (Aschenbach & Brinkmann 1975 ) and jet and counterjet previously observed (Brinkmann, Aschenbach, & Langmeier 1985; Hester et al. 1995; Greiveldinger & Aschenbach 1999) , which define the SE-to-NW axis of the inner Nebula. On somewhat larger scales, the image shows a sharply bounded notch (WSW of the Pulsar) into the x-ray nebular emission, earlier associated with the "west bay" of the Nebula (Hester et al. 1995) . Visible-light polarization maps of the Crab Nebula (Schmidt, Angel, & Beaver 1979; Hickson & van den Bergh 1990) demonstrate that the magnetic field is parallel to the boundary of this notch, thus excluding the x-ray-emitting relativistic electrons from the west bay.
Of course, it is for scales from 1 ′′ to 10 ′′ , that Chandra provides unique information on x-ray structure. To call attention to specific features, we processed the image (Figure 2) using the flux-conserving adaptive-smoothing algorithm CSMOOTH (Ebeling, White, & Rangarajan 2000) from the Chandra Interactive Analysis of Observations (CIAO) package. Figure 3 thus emphasizes small-scale structure, sometimes artificially. To avoid misinterpretation, we use it only in conjunction with the raw image.
The most striking feature of the x-ray image is the inner ring, lying between the Pulsar and the torus, which may correspond to a shock in the Pulsar wind (Rees & Gunn 1974; Kennel & Coroniti 1984) . Comparing the Hubble image (Hester et al. 1995) with the Chandra image, we find that the positions of the visible-light "wisp 1" and the "counter wisp" correspond -at least in projectionapproximately to the NW and SE quadrants, respectively, of the x-ray inner ring. On the ring, reside a few compact (approximately 3 ′′ ) knots. One of these lies to the SE of the Pulsar, along the projected inward extension of the jet. This knot seems to be real rather than a simple superposition, in that its surface brightness exceeds the sum of the surface brightness of the inner ring, the jet, and the more diffuse emission.
Having a semi-major axis of about 14 ′′ (0.14 pc) and a semi-minor axis of about 7 ′′ (0.07 pc), the projected rotational-symmetry axis of the inner ring lies about 58
• W of N. Under the assumption that the ring is circular, the rotational-symmetry axis lies about 30
• out of the celestial plane. Hence, the out-of-plane tilt of the inner ring is consistent with tilts estimated for the x-ray torus (Aschenbach & Brinkmann 1975 ) and for various visible-light structures (Hester et al. 1995) .
The potentially most provocative feature of the Crab Nebula's x-ray torus is the apparent circular structure at each extremity. These features resemble the limbbrightened cross-section of a hollow-tube ring torus, with a tube radius of about 8 ′′ (0.08 pc). Such structures, if indeed present, significantly constrain models for the inner Nebula. Among other explanations, the apparent tube geometry may indicate a role for relativistic ions with Larmor radii on this scale (Gallant & Arons 1994) or a toroidal current which generates a meridional magnetic field wrapping the torus.
Elsewhere, the torus exhibits circumferential fibrous texture but no knots. As noted previously (Aschenbach & Brinkmann 1975) , the surface brightness varies significantly with toroidal azimuth, resulting from moderate relativistic beaming (Pelling et al. 1987; Greiveldinger & Aschenbach 1999) . In contrast, the surface brightness of the inner ring is more uniform in azimuth (except for the knots), indicating that relativistic beaming is less significant for it than for the torus. Measured from the center of the torus to the center of its tube, the semi-major and semi-minor axes are approximately 38 ′′ (0.37 pc) and 18 ′′ (0.17 pc), respectively. The rotational-symmetry axis of the toroid lies about 48
• W of N and about 28
• out of the celestial plane. Because the boundary of the torus is rather diffuse and dependent upon azimuth, these values are less certain than those for the inner ring. Nevertheless, the in-plane orientation of the torus differs noticeably from that of the inner ring, suggesting that the torus is warped.
The Chandra image probes the jet (to the SE) and counterjet (to the NW) at higher resolution than previous images with Einstein (Brinkmann, Aschenbach, & Langmeier 1985) or with RoSat (Hester et al. 1995; Greiveldinger & Aschenbach 1999) . Although the Chandra image shows little additional structure or fibrous texture in the jet or counterjet (or "channel" -or, more descriptively, "cocoon" -encasing it), it traces them inward closer to the Pulsar than previously possible -at least to its projection onto the inner ring. In addition to the knot at the projected intersection of the jet with the inner ring, there may be another knot, between the inner ring and the Pulsar, on the extension of the jet to inside the inner ring. Due to pile-up around the image of the Pulsar, we cannot exclude that this feature is an artifact. However, Hubble images (Hester et al. 1995) do exhibit similar structure ("knot 2" and "anvil") in this same region (a few arseconds SE of the Pulsar). On the other hand, we need not expect features in the inner Nebula to be static (e.g., Scargle 1969; Hester et al. 1995; Greiveldinger & Aschenbach 1999) . Indeed, those regions showing the brightest x-ray emission tend to correspond to especially dynamic structure (Hester et al. 1998) , supporting the interpretation of these features as shocks in the polar jet (Hester et al. 1995) .
RESULTS -SPECTRAL VARIATIONS
In examining the spectral distribution, we use standard flight grades (ASCA grades 02346), for which response matrices currently exist. Before fitting spectra, we first define an x-ray spectral hardness h 2.7 as the ratio of flux above 2.7 keV to that below. We establish from the trailed image ( §2), which is free of pile-up effects, that h 2.7 = 0.57 ± 0.06 for the Nebula as a whole. To search for spectral variations within the Nebula, we determine h 2.7 for each 5 ′′ ×5 ′′ bin of a 22×22 array (region Z of Figure 1) . Figure 4 shows the distribution of hardness h 2.7 within the Nebula. For counting rates below about 0.7 s −1 , there are numerous 5
×5
′′ bins with hardness ratio less than the nebular average. This cannot result from pile-up, which can only harden the spectrum. Obviously, because there are many bins with hardness ratios below the average, some of the remaining bins must be above average. Thus, the majority of the high-count-rate data, although artificially harder due to pile-up, is nonetheless truly harder than the average -i.e., there are real variations of x-ray hardness within the Nebula. The outer Nebula is significantly softer than the average, as expected for synchrotron losses and previously observed for the visible (Scargle 1969; VeronCetty & Woltjer 1993) and ultraviolet (Hennessy et al. 1992) continua. The jet and counter-jet (and its cocoon) have hardness comparable to the average; whereas, the inner ring appears to be harder. However, the highercontrast structure in the inner ring means that the peak surface brightness in each bin may significantly exceed the average in the bin, leading to more pile up than suggested by the mean surface brightness.
Unfortunately, the surface brightness of the torus and inner ring is so high that pile-up precludes accurate determination of the spectrum of these regions. However, we did analyze the spectral distribution, using XSPEC (Arnaud 1996) , of the trailed image and of the timed-exposure image of the outer Nebula. For the trailed image, we fit the spectrum obtained from region T of Figure 1 , which is matched to the same range of columns covered by region Z (used in the hardness analysis), but excludes the Pulsar.
Current uncertainties in the detector's response below 1 keV and in the zeroth-order effective area result in systematic errors in the spectral analysis. Consequently, we are skeptical of the absolute values of the best-fit spectral parameters. However, because these systematic effects comparably influence the fits for the trailed image and for the outer Nebula, we believe that the relative values are significant. For a column density N H = 3.45 × 10 21 cm −2 (Schattenburg & Canizares 1986) , we find that the spectral index of the outer Crab Nebula is steeper than that of the average Nebula by 0.62; for 2.35×10 21 cm −2 (formal best-fit value), by 0.50. The scatter diagram, color-coded by location in the Nebula, shows hardness h 2.7 ( §4) against count rate in 5 ′′ ×5 ′′ spatial bins. The horizontal red line denotes average hardness (solid line) and associated error (dashed line) of the trailed image; the horizontal violet line, average hardness of the timed-exposure image, which is biased by pile-up effects ( §2). The outer Nebula is softer than the trailed-image average; the jet and counter jet (and its cocoon) have about average hardness.

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