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The Astronomical Journal, 137:2956–2967, 2009 February c 2009. The American Astronomical Society. All rights reserved. Printed in the U.S.A. 

doi:10.1088/0004-6256/137/2/2956

1.4 GHz HIGH-RESOLUTION FLUX-ACCURATE IMAGES OF SN 1006 K. K. Dyer1,4 , T. J. Cornwell2,5 , and R. J. Maddalena3 1

Naval Research Lab, Remote Sensing, Code 7213, 4555 Overlook Road, Washington DC 20375, USA; [email protected] 2 National Radio Astronomy Observatory, 1003 Lopezville Road, Socorro, NM-87801, USA; [email protected] 3 National Radio Astronomy Observatory, P.O. Box 2, Green Bank, WV, USA; [email protected] Received 2005 July 3; accepted 2008 October 7; published 2009 January 13

ABSTRACT We present interferometric+single-dish images, constructed from the Green Bank Telescope (GBT) and VLA observations, of the supernova remnant SN 1006. The image was created using a Multiscale CLEAN algorithm in conjunction with a novel approach for correcting the effect of the non-coplanar baselines. We demonstrate that integrating with a single dish to the confusion limit of the highest resolution interferometric element is not required. Instead, the noise in the map is limited by the signal-to-noise ratio in each observation. The noise in the combined map at the full resolution is dominated by uncertainties in the VLA data, not by uncertainties in our short GBT observation. The resulting image is a significant improvement over images missing short spacing information, and paves the way for future joint GBT+VLA proposals that need to accurately image objects ranging from galaxies to H ii regions. Key words: ISM: individual (SN1006) – radio continuum: ISM – supernova remnants Online-only material: color figures

measurement can never be restored by mosaics.7 While at the VLA these numbers are confusingly similar (35 m versus 25 m) for instruments such as Merlin and the Very Long Baseline Array they are quite different. The 1.4 GHz VLA images of SN 1006 contain only about 20% (Reynolds & Gilmore 1986) and 40% (Moffett et al. 1993) of the flux density measured by single dishes, illustrating how poorly interferometric images represent SN 1006. Historically for large sources, scientists have had to choose between accurate measurements of total flux density available from single-dish instruments, and interferometric images with high resolution but without accurate flux density information. The combination of accurate flux density with high resolution, which we present here, changes the study of supernova remnants (and large objects in general) in two ways. First, radio interferometric observations are often compared to optical and X-ray observations. While morphological comparisons (limited to the location of small bright features) are less affected by large scale flux density deficites, quantitative comparisons, in the case of SN 1006 fitting shock acceleration models to radio, X-ray, and γ -ray observations (i.e., Allen et al. 2005), are severely hampered by the flux-accuracy of radio images. Second, comparison within the radio, in particular spectral index studies, depend on having sensitivity to similar scales at multiple frequencies. There have been a host of methods designed to overcome disparate UV coverage, including T–T plots, regression methods, and simulated re-observation. These methods are poorly tested and can produce inconsistent results (see, for instance, conflicting results on 3C397 in Dyer & Reynolds 1999; Anderson & Rudnick 1993). Having high-resolution images which accurately detect flux density at all relevant8 scales is obviously preferable to any correction scheme. Imaging the SNR correctly at 1.4 GHz requires all VLA configurations (from A, where the telescopes are furthest apart, to D, where the telescopes are closest together), supplemented

1. INTRODUCTION While the Galaxy contains approximately 230 known supernova remnants (SNRs), a few select objects define what we know about the supernova process and the shock acceleration that produces emission from radio to X-ray wavelengths. SN 1006 is such an object. Many parameters which have to be assumed in other SNRs are known for SN 1006. The supernova was observed in China, Korea, Japan, Arab dominions, and Europe, giving it a precise age (Stephenson et al. 1977). The expansion of the remnant has been measured at optical and radio wavelengths (Moffett et al. 1993, 2004; Winkler et al. 2003). The distance is less well known, but is most likely ∼2.2 kpc (Winkler et al. 2003). SN 1006 has a deceptively simple structure. The classic symmetric shell remnant is located 15◦ off the Galactic plane, in a region of low-density interstellar medium (ISM). Therefore the morphology is thought to be dominated by the initial explosion, rather than inhomogeneities in the ISM. The frequently published radio image from the VLA6 of SN 1006 is, in fact, a poor representation of the radio structure. SN 1006 is too large: ∼30 in diameter and thus is at the limit of the size scale the VLA can measure. Here we define large as having spacial information on the size scales corresponding to (or larger than) the shortest spacing of the interferometer, angular size[rad] = λ/Dshortest . Despite the similarity of the equation, short spacing issues are not related to the size of the primary beam. One can imagine an example where one wanted to image a field of sources, smaller than the short spacing limit, in a field larger than the primary beam. This example can be taken care of by mosaicking whereas information on scales larger than the short spacing 4

National Research Council Postdoctoral Fellow. Currently at the Australia Telescope National Facility. 6 The Very Large Array is operated by the National Radio Astronomy Observatory which is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. 5

7

Despite the statement to the contrary in the Observational Status Summary, http://www.vla.nrao.edu/astro/guides/vlas/current/node8.html. Note that our map is still insensitive to emisson scales larger than the area mapped by the Green Bank Telescope.

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Table 1 Selected Data for SN 1006 Observation ID AGBT03B_042_03 AM0353

Date

Telescope

Freq. (MHz)

Bandwidth (MHz)

Time (m)

2004 Jul 31 1991 Oct 12 1992 Feb 2 1992 Jul 4

GBT:DCR VLA:BnA VLA:CnB VLA:DnC

1370 1370 1370 1376

20 6.25 12.5 6.25

132 177 176 177

Table 2 GBT Mapping Parameters Parameter

Value

Map Center Front End Back End Map Type Integration Time Scan Rate (DEC) Sample spacing (DEC) Sample spacing (RA) (Nyquist Frequency Bandwidth Beam (FWHM) Pointing calibrators Theoretical noise Confusion limit

15h 02m 51s , −40◦ 59 57 Gregorian L Band 1.15–1.73 GHz DCR On-the-Fly 0.1 s 10 s−1 1 sample per 3 1 sample per 1  1 sample per 3.7) 1370 MHz 20 MHz  9.2 3C386, 1501–3918 5 mJy 21.4 mJy

by Green Bank Telescope (GBT) continuum observations, to sample the large-scale structure. Adding single-dish and interferometric observations was first done for SN 1006 by Roger et al. (1988) using Parkes and Molonglo observations, resulting in a flux-accurate image with 44 × 66 resolution. In this paper we present new GBT observations of SN 1006 at 1.4 GHz, added to archival VLA observations, producing a final image with both the full flux density and full resolution. In addition to addressing our scientific goals, we hope to demonstrate that obtaining flux-accurate radio images is both possible and straightforward, improving the study of large radio sources in many other fields. In Section 2 we describe the single-dish and interferometric observations. In Section 3 we briefly describe the method used to reduce the data. We present the final image in Section 4 and in Section 5 we delve more fully into the technical obstacles which must be addressed in the creation of the final image. We summarize our results in Section 6. 2. OBSERVATIONS 2.1. Interferometric Observations Observations of SN 1006 were made with NRAO’s VLA under Obsid AM0353 between 1991 October and 1992 July (see Table 1) in hybrid configurations BnA, CnB and DnC, to optimize UV coverage for the low elevation of SN 1006. These observations were previously used to make the first radio expansion measurements (Moffett et al. 1993).

data are collected while the telescope slews within a rectangular area of the sky.9 Details of the GBT observation are given in Tables 1 & 2. 3. DATA REDUCTION Here we outline the data reduction. All data reduction and imaging took place in AIPS++. We calibrate our single-dish data, make an inital image, and use it to remove short timescale background effects (Section 3.1). Since we use the single-dish image as a starting model (discussed at length in Section 5.3) we grid the single-dish data and deconvolve to obtain a preliminary sky model (Section 3.2). This image has the correct total flux density, but not yet the VLA resolution. We calibrate and combine data from the VLA configurations. Next we cross calibrate the GBT and VLA flux density measurements and use the result to correct the flux density of the GBT starting model (Section 3.4). We then create and compare flux-accurate high-resolution images using maximum entropy and multiscale clean (Section 3.5). For investigative purposes we also create a multiscale clean image without any single-dish information. We have documented our work, including the Glish scripts used at each stage, at the NRAO Green Bank wiki.10 3.1. Removing the Atmosphere From the Single-Dish Data Standard methods were used for calibrating single-dish continuum observations (O’Neil 2002). The pointing was checked with observations of 3C286 and 1501–3918. SN 1006 is at declination −42◦ and so does not reach an elevation greater than about 10◦ (7◦ above the hills) at the latitude of the GBT. Even at our observing frequency of 1.37 GHz, continuum imaging at low elevations is affected by the elevation-dependent background emission, due to both ground pickup and atmospheric emission. These variations can been seen in images made from four consecutive scans, shown in Figure 1. As a diagnostic of the background effects, we found it useful to image all the data in Azimuth-Elevation coordinates (Figure 2). The trend of increasing background with decreasing elevation is clear. This allows us to perform an “on-source tipping calibration” as the source goes through a range of elevations. We model the background purely as a function of air mass. We take the minimum value of this Azimuth-Elevation image at any air mass as the estimate of the background for that air mass. The resulting curve, along with a linear fit is shown in Figure 3. As can be seen, the air mass is well fit by a straight line. The air mass for a spherical Earth (Rohlfs & Wilson 2004) is given by

2.2. Single-Dish Observations 1.4 GHz radio continuum observations were made at the Robert C. Byrd GBT in Green Bank, West Virginia in 2004 July under Obsid ABGT03B_042. Observations were carried out with the L-Band receiver and the digital continuum receiver (DCR). We used the “On-The-Fly” observing technique where

ma = −0.0045 + 9

1.00672 0.002234 0.0006247 − . − sin(el) (sin(el))2 (sin(el))3

http://www.nrao.edu//GBT/proposals/proposers_guide/ GBTPROPOSERSGUIDE.pdf 10 http://wiki.gb.nrao.edu/bin/view/Main/KristyDyer

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Figure 1. Successive 1.4 GHz observations of SN1006 taken with the GBT. In constructing these images, the measured data were convolved onto the grid using a model of the primary beam. All images are in the J2000 frame.

Figure 2. Same as Figure 1 but shown in Azimuth, Elevation coordinates.

Using this model, we correct the original data sample by sample, and remake the images. Figure 4 shows SN 1006 after correction for the background. Repeating this process two times converges to a model for the background B = 8.861 + 1.364ma , where the units are Jy. Since the gain of the GBT at this frequency and at all elevations is 2 K Jy−1 (O’Neil 2002, page 308), our background model implies a system temperature of 20 K

at the zenith. The model includes a contribution from spillover or ground radiation which, due to the offset optics of the GBT, is 2–3 K higher at low elevations than at high elevations. Once we take into consideration spillover, the model agrees very well with the expected zenith system temperature of 18 K.11 In 11

http://www.gb.nrao.edu/∼rmaddale/GBT/Commissioning/ Surface_Efficiency_2-3GHz/gaineffmemo.pdf; http://www.gb.nrao.edu/gbt/GBTMANUAL; http://www.gb.nrao.edu/GBT/memos/memo16.ps

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Figure 3. Background plotted as a function of air mass. The data points come from the minimum value of the emission detected at a given air mass. The line is a linear fit to air mass. This plot shows the result of the first iteration only. The second iteration improved the fit by about 1.5%. (A color version of this figure is available in the online journal.)

Figure 5 we show the best (average) image and standard deviation. 3.2. Gridding and Deconvolving the Single-Dish Image Before creating our inital GBT image we must make several decisions about our final goal. First, we choose to combine the single-dish and interferometer data by using the single dish as a starting model for the interferometric deconvolution. We discuss other methods of using short spacing information to inform the final high-resolution image in Section 5.3. Choosing this method leads us to two further decisions: (1) to maximize signal-to-noise (S/N) ratio, we grid the single-dish data using primary beam gridding (gridding choices are discussed further in Section 5.2), and (2) to use the GBT image as a starting model for the deconvolution of the synthesis data, we will need to deconvolve the GBT image to remove the smoothing caused by the gridding. Although the primary beam for the off-axis GBT is known to have very low sidelobes, there are as yet few measurements. We have therefore used an analytical beam corresponding to Gaussian taper of the unblocked aperture with a 15 dB taper at the edge of the aperture. This model predicts the observations of the main lobe on 3C286 quite well. We created an image from the gridded GBT data using both Multiscale CLEAN and a maximum entropy algorithm (ME). We prefer the ME image since ME provides particularly good results with faint extended emission (Cornwell & Evans 1985; Stanimirovic 2002) and was less effected by the limited size of the map. The deconvolution converged quickly, which is important since the deconvolution must converge to within the expected noise level if the GBT data are to be consistent with the short spacing VLA data.

The resulting deconvolved image (Figure 6) has finer resolution, the primary beam having been removed, although there are three defects: the detail at resolution finer than the telescope resolution is determined largely by the deconvolution algorithm; there is a low-level trough around the remnant; and emission piles up at the edge of the image (where the implicit boundary condition is zero emission outside the sampled region). The fine detail and the low-level trough both correspond to spacings not measured by the GBT and so both will be remedied by information from the VLA D configuration. The edge effects will be tapered by VLA primary beam, and will therefore not effect the final image; however, they illustrate the need for sampling a wider region than that directly needed for imaging. 3.3. Calibrating the VLA Data The VLA data was calibrated in AIPS++ using the straightforward approach documented in the AIPS++ Cook Book (http://aips2.nrao.edu/ docs/cookbook/cbvol3/cbvol3.html). The data were flagged for a small fraction (< 1%) of obviously bad observations. The flux density scale was referred to 3C286 using the standard Perley–Taylor12 formulas. Phase calibration was performed using the nearby source 1451-400. No polarization calibration was performed. 3.4. Flux Calibrating the GBT to the VLA Before combining the data, we must ensure that the calibrations of the GBT and VLA data are consistent. Because (1) the GBT is a new instrument, (2) we did not make measurements of the GBT beam, and (3) because a great deal of work has gone 12

VLA Calibrator Manual 1999– http://www.vla.nrao.edu/astro/calib/manual/index.shtml

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Figure 4. Four images taken in successive sets of scans, shown in Right Ascension, Declination coordinates, after removal of the best fitting background from the original data. All images are in the J2000 frame.

into setting a flux scale for the VLA, we assume that the VLA flux scale is more accurate than what we could measure from the GBT data. We can use the overlap in Fourier components on projected spacings between the D-configuration (35–1030 m) and the GBT (0–100 m) to check the GBT flux scale with respect to the VLA flux scale (themselves set by observations of 3C286). We use the deconvolved GBT model (tapered by the VLA primary beam) to predict values for the visibilities of the short spacings (from a few meters up to 100 m). In Figure 7 we plot the ratio of the observed VLA visibilities to those predicted from the deconvolved GBT image. There are two regions of the UV ratio plot where we have enough S/N to calibrate the GBT data with the VLA data: 34–40 m and 60–70 m. Between these, the visibility function tends to be close to zero, magnifing the errors in the model. We want to pick a range where both the VLA and the GBT are well understood. Since we did not measure the GBT beam, our analytic model is most likely to be wrong on small scales, which would show up on the larger UV spacings (60–70 m). Therefore we use the 34–40 m overlap for calibration. An alternative would be to have truncated the data processed in the GBT deconvolution to about 40 m. However, the decon-

volution would then have provided different estimates beyond 40 m which would also have been overridden by the VLA data. 3.5. Creating the GBT+VLA Image At the low elevations at which SN 1006 must be observed with the VLA, the effect of non-coplanar baselines (Cornwell & Perley 1992) is particularly troublesome. This effect manifests as smearing of sources that increases with distance from the phase center. To correct for this effect, we used the new “W projection” algorithm (Cornwell et al. 2003, 2005). This performs a corrective Fresnel transform while griding the visibility data for the Fourier transform. With the use of W projection, the transform from visibility data to image plane now no longer dominates the processing time. We used two methods for deconvolving and restoring the single-dish+interferometric image, the maximum entropy method, and Multiscale CLEAN. The conventional CLEAN algorithm (H¨ogbom 1974; Clark 1980) represents the emission by a set of point sources found by an iterative algorithm that finds the brightest points first. Such an approach is clearly inefficient and suboptimum for extended emission and an alternative

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approach is necessary. Cornwell & Holdaway (2005) have developed a variant of the CLEAN algorithm, called Multiscale CLEAN, that represents the emission by not just point sources but compact blobs of emission of a range of scale sizes, typically from a few pixels up to tens or hundreds of pixels. The best representation by blobs is found using a CLEAN-like approach whereby in each of a sequence of iterations a search over all blob scales is performed to find that scale which reduces the maximum residual by the largest amount. For comparison, we also created a Multiscale CLEAN image with the interferometric data only, which we discuss in Section 4.2. The deconvolved GBT image13 is used as the starting model in CLEAN. Thus, the GBT image is convolved with the dirty beam and then subtracted from the dirty image, forming a residual image which is then passed to Multiscale CLEAN for further deconvolution. The results are shown in Figure 8. The broad-scale emission in the deconvolved GBT image is assumed to be basically correct. The fine-scale emission is undoubtedly less accurate since it requires accurate deconvolution of the GBT beam, which we have assumed to be a Gaussian. However, our approach ensures that the synthesis data, which does represent the finer scale emission more accurately, correct any errors on these scales (corresponding to baselines of 50 m and longer). The ME image uses the Cornwell–Evans algorithm (Cornwell & Evans 1985). For ME, the deconvolved GBT image is again used as the default image. ME is substantially faster than the Multiscale CLEAN on this data set but Multiscale CLEAN gives no noticeable positive bias and significantly more noise-like residuals. Thus, in general we prefer to use Multiscale CLEAN. At this level of sensitivity, the image is affected by sources of a few mJy beam−1 in the first sidelobe of the VLA primary beam (at ∼0.75 degree radius). We model these sources by performing a limited deconvolution of a field twice the size, and then fitting discrete components which are then removed as part of the deconvolution. By incorporating this step we can limit the required image size to 4096 by 4096 pixels with cell size 1. 13

Created with ME for reasons discussed in Section 3.1.

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Figure 5. Average and standard deviation of Figure 1 after removal of the best fitting background from the original data. Both images are in the J2000 frame.

Figure 6. The deconvolved GBT image.

4. RESULTS 4.1. Image Quality In the resulting GBT+VLA image (Figure 8), SN 1006 has an integrated flux density of 12.69 Jy, and the background rms noise is 77 μJy beam−1 . After correction for the VLA primary beam (Figure 9), the integrated flux density is 18.68 Jy. In Figure 10 we plot the flux density of our final image with other single-dish values. These single-dish values were collected from the literature and analyzed and corrected to the same flux scale as part of a study of single-dish observations of SNRs by Andrew Ford, published in Ellison et al. (2000), using techniques similar to that used by Laing & Peacock (1980) and Kuehr et al. (1981) for single-dish studies of 3C objects. Table 3 includes the corrected single-dish flux densities with errorbars. The full-resolution image (without convolution with a CLEAN beam) shows excellent estimation of the extended

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Figure 7. Ratio of observed VLA visibilities to model visibilities predicted from the deconvolved GBT image. Table 3 Single Dish Flux Density Measurements of SN1006 Frequency [MHz] 29.9 59.2 85.5 87.0 105.2 153.0 160.0 408.0 408.0 635.0 843.0 1410.0 2700.0 2700.0 5000.0 5000.0 5000.0

Flux [Jy]

Error [Jy]

Citation

150.0 76.0 77.0 60.9 40.7 32.9 46.0 30.8 32.3 25.5 17.5 15.2 10.4 9.9 7.7 7.0 8.1

12.0 9.1 16.0 12.2 6.9 4.1 13.8 0.0 3.2 3.8 1.5 2.3 1.2 1.5 1.1 1.2 0.0

Finlay and Jones (1973) Haynes et al. (1968) Mills et al. (1960) Haynes & Hamilton (1968) Haynes & Hamilton (1968) Hamilton & Haynes (1967) Milne (1971) Stephenson et al. (1977) Milne (1971) Milne (1971) Roger et al. (1988) Milne (1971) Milne (1971) Gardner & Milne (1965) Milne (1971) Kundu (1970) Milne & Dickel (1975)

emission with no noticeable breaking up of smooth regions into points, as occurs with the conventional CLEAN algorithm. The noise background is very well behaved on a fine scale. We see some evidence for very low contrast extended emission on the scale of about 5–10 arcmin, running northwest/southeast. This scale size is right at the transition between the GBT and VLA. Given the scale, the GBT should be sensitive to this emission; however, the emission is not apparent in the GBT image. That means that, if real, it must be visible mostly in the

VLA data. We have searched hard for any spurious data on the relevant spacings but have found none.

4.2. Comparison of Images with and without Short Spacing Information In Figure 11 we compare flux density cross sections from the single-dish+interferometric image to the best Multiscale CLEAN image without short spacing information. Two conclusions are obvious even from an intutive understanding of Fourier transforms: (1) the most significant difference is in the central region, where one expects the flux density to be distributed on large scales and (2) the location of the small-scale emission peaks does not change. However two deviations may catch the unwary observer: (1) even features which appear to be small scale have incorrect fluxes, sometimes off by 50% or more, and (2) the flux density ratios between small scale features would also be in error without the short spacing information. These issues fundamentaly limit our ability to analyze large objects and small regions within them without short spacing information.

5. DISCUSSION Here we will discuss at greater length issues related to adding single-dish and interferometric data, including the dominant source of error in the GBT data, gridding choices, methods of combining the data, how uncertainty in the GBT data limits the final image, and dealing with the expansion of SN 1006.

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Figure 8. Deconvolved GBT+VLA image. Top: GBT-derived starting model (tapered with VLA primary beam), and full-resolution multiscale model; brightness range 0 to 20 μJy (square arcsecond)−1 . Bottom: restored multiscale image and residuals; brightness range −150 to 1500 μJy beam−1 . All images are in the J2000 frame.

5.1. What was the Dominant Source of Error in the Single-Dish Data? The errors displayed in the standard deviation image (Figure 5) have components that are uniform across in right ascesion (here equilivent to elevation) and vary with declination. The average error is 0.05 Jy beam−1 , and the typical S/N on the source is about 50. For the typical air mass of SN 1006 (6.5–7), the expected GBT sensitivity in the time taken to traverse one beam width (200–300 ms) is about 12 mJy beam−1 . We believe that this increase in the overall level of errors is partly due to the increased system temperature at low elevations (about 36 K instead of the zenith value of about 18 K). Possible explanations for the systematic errors include transient weather, water pooling on the GBT feed, and radio frequency interference (RFI). The noise bands seen in Figure 5 correspond to 5–10 scans, each of which is 12 s long, so the noise is changing on a timescale of 1–2 minutes. The operator’s log notes the presence of heavy clouds and lightning so this is not unreasonable. During moderate to heavy rain showers, moisture can pool on the receiver’s feed, causing significant changes in the perceived brightness. Finally, differences in the images could be the result of Radio Frequency Interference. While the

GBT is in a National Radio Quiet Zone, the restrictions only apply to fixed ground-based transmitters. Global Positioning Satellites (GPS) use the 1381 MHz band eight times per day to communicate with ground stations. These frequencies are also allocated to fixed and mobile radio location. Nevertheless, we believe that the most likely explanation for the stripes is transient weather. There are various possible countermeasures possible at observing time: 1. Wait for better weather. 2. Use the Basketweaving technique (Emerson & Graeve 1988) which can mitigate such problems by combining multiple maps, pairs of which scan the source in orthogonal directions. However, for a source at the low declination of SN 1006, it is not possible to obtain constant elevation (required to minimize gradient effects) scans at significantly different position angles on the sky. 3. Use a dual beam system or a focal-plane array that would help significantly in subtracting out the contributions from transient weather. 4. Use robust estimation in the data reduction by taking the median of a number of images instead of the average.

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where P is the GBT primary beam and N is the additive noise. For the P B and SF images I P B = P ∗ P ∗ I + P ∗ N, I SF = G ∗ P ∗ I + G ∗ N, J2000 DECLINATION

where G is the spheroidal function. Choosing the wrong gridding method for the scientific purpose at hand can lead to problems such as unexpectedly poor resolution. For imaging with the best resolution, boxcar gridding is preferred if the telescope can observe on an right ascension, declination grid (as the GBT can). If the image is to be deconvolved, primary beam gridding is more suitable since the output image can be more finely sampled than the sampled data. In order to maximize the S/N in our deconvolved single-dish image we chose primary beam gridding. 5.3. Methods of Combining Single-Dish and Inteferometric Data

Figure 9. Final deconvolved GBT+VLA restored multiscale image, corrected for the VLA primary beam. The displayed brightness range is −300 to 3000 μJy beam−1 .

This may well be worthwhile if we had more than four independent measurements. Finally, we note that our GBT observations have a noise level, ∼30 mJy beam−1 , that is only 50% worse than the confusion limit, 21 mJy beam−1 , which we consider to be excellent performance for a source so low on the sky. 5.2. Gridding Choices for the Single-Dish Image It is possible to create a single-dish image using one of several functions to grid the samples. Nearest neighbor gridding (hereafter referred to as BOX)—a sample is moved to the nearest grid point. This works well if the data are actually sampled on a regular grid in right ascension, declination. This is analogous to the uniform weighting used in synthesis imaging—the noise is highest and the resolution finest. The disadvantage is that the output image must have the same sampling as the observed data. Primary beam gridding (PB)—the samples are convolved with a model of the primary beam and then resampled on the desired grid. This is an analog to synthesis natural weighting—it produces the image with the least variance √ but 2 worse resolution. The image and data sampling need not be the same in this case. Spheroidal function gridding (SF)—the samples are convolved with a spheroidal function and then resampled on the desired grid. In this option, one would choose a spheroidal function since it is limited in extent but also reasonably smooth (superior to, for example, a truncated Gaussian). If the data and sample grids are the same, then the relationship between the true sky I and the BOX image is the classic convolution equation, I Box = P ∗ I + N,

There is an excellent discussion of relative merits of different methods of combining single-dish and interferometric data in the paper by Stanimirovic (2002). Possibilities include: 1. Merge: add the images after deconvolution of the respective point-spread functions (GBT primary beam and VLA synthesized beam). 2. Fake synthesis: make fake synthesis data from the deconvolved single-dish image, add it to the real synthesis data, and deconvolve together. 3. Joint deconvolution: perform a joint deconvolution of the single-dish and synthesis data. 4. Single dish as starting model: use the deconvolved singledish image as the starting point in a deconvolution of the synthesis data. For the CLEAN algorithm (H¨ogbom 1974; Clark 1980), we would use it as an a priori image (Cornwell et al. 1999), and for ME (Cornwell & Evans 1985), we would use it as the default image. Since the deconvolution process is nonlinear, the merge technique does not take optimum advantage of the entire data set. While the fake synthesis approach is possible, and joint deconvolution is known to produce very good results on simulated data, we chose the last approach, single dish as the starting model. As discussed by Stanimirovic (2002), it is easily performed, requiring only that we start the deconvolution from a known image instead of developing special computational codes as needed for the other two approaches (in addition to our path in AIPS++, it is currently possible to carry out this method in classic AIPS and Miriad). In addition, choosing single-dish as a starting model allows the synthesis data to override the singledish image on small scales (corresponding to baselines of 50 m and longer), correcting deficits in the GBT starting model that result from not having measured the GBT beam. Note that combination methods that work in the Fourier plane (Fake Synthesis and Joint Deconvolution, discussed below) require a much larger area to be imaged to avoid ringing in the final image, created by edge effects in the Fourier transform. At higher frequencies this may be prohibitively time consuming, as discussed below. 5.4. How Does Uncertainty in the Single-Dish Image Limit the Final Image? The conventional wisdom in radio astronomy is that, in order to add single dish and interferometric observations, the single

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Record of Flux Density Measurements of SN1006 1000

Flux Density [mJy]

100

10

1

10

100

1000

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Frequency [GHz] Figure 10. Triangles: single-dish flux densities, collected by Andrew Ford and originally published in Ellison et al. (2000); Dimond: Parkes measurement by Roger et al. (1988); Circle: our work, this paper.

dish observations must be made to the same nominal pointsource sensitivity, rather than, for example, to the confusion limit in the single-dish beam. Since the total collecting area, antenna efficiency, system temperature, and bandwidth are similar for the GBT and the VLA, for a single pointing, the two telescopes have roughly comparable nominal point-source sensitivity. For example, during a 100 ms integration at 1.4 GHz at high elevations, the nominal sensitivities are 10 mJy beam−1 (GBT) and 4 mJy beam−1 (VLA). For continuum imaging, the GBT is much slower (×100) since it has to scan the area covered by the VLA primary beam. In the case of SN 1006 at 1.4 GHz, it would take two years for the GBT to map the VLA primary beam to the same point-source sensitivity. Unfortunately the assumption that this is required has prevented many researchers from pursuing the single-dish measurements required for accurate imaging of large structures. The analog of this conventional wisdom for interferometers is not widely followed since it would require equal observing time at all resolutions. Instead, for example, at the VLA there is a rule of thumb that each larger configuration gets a factor of four decrease in observing time. Applying this rule to the GBT (equivalent to two steps in the VLA configuration from the D configuration) implies that the GBT observing should be about 45 times less than the 6 hr spent in VLA B configuration— about 20 s per GBT beam, which is much more reasonable than 6 hr. Even this would make our GBT observations expensive, requiring 8 hr (further compounded by the fact that SN 1006 is only above the horizon 2 hr at a time). The relevant criterion is not uniform noise across the Fourier plane, but roughly uniform signal-to-noise across the Fourier plane (Cornwell et al. 1993). Since the signal for complex sources inevitably is stronger for shorter Fourier spacings, less observing time is needed. The role of the GBT in our observation

is to measure the extended emission on scales larger than the maximum scale for which the VLA has any significant sensitivity—about 15 . Thus, one should equalize the SNR at the size scale where GBT and VLA are complementary—about 15 —corresponding to a factor of about 42 less than the D configuration observing time. A simple rule of thumb, good to within a factor of a few, is therefore to spend about the same time observing with the GBT and the VLA D configuration. If desired, a more accurate answer could be derived by simulations. In this paper, we have demonstrated that relatively short observations with the GBT greatly improve interferometric deconvolution. In fact our GBT observations used one second per beam, a factor of 20 less than the VLA rule of thumb, and the noise in our final, combined image is correlated on a size scale of the GBT beam (8. 5) with strengths of about 10 mJy beam−1 . For the full-resolution image, the GBT noise will cause a random noise term (scaled by the ratio of the beam volumes) of about 4 μJy beam−1 and, so, is much less than the noise from the VLA, 300 μJy beam−1 (Moffett et al. 1993). 5.5. Expansion SN 1006 is expanding (Moffett et al. 1993, 2004; Winkler & Long 1997; Winkler et al. 2003). New VLA expansion measurements (D. Moffett, private communication; Moffett et al. 2004) show an expansion of 0.477 arcsec year−1 in radius with the fitted optical center R.A. 15h 03m 16.s 2, Decl. −42◦ 00 03 from Winkler & Long (1997). Here we examine the effect of expansion in two cases which do not turn out to be significant. First there is the differential expansion between the VLA configurations in 1991–1992. The effect the expansion will have on the image is proportional to the expansion distance divided

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by the beam width. If we choose to work in the epoch of the BnA observations, the SNR will have expanded by 0. 13 at the CnB and 0. 18 at the DnC observations. As a fraction of the beam in each configuration, the CnB introduces an error of 0. 13/12. 5 = 10% and DnC introduces an error of 0. 18/44 = 0.4%. This is less than the finest resolution we have (minor axis of 5 ). Thus we can ignore that effect. Second, SN 1006 has changed 6 in radius between the 1991 VLA and the GBT observations (2003). Since the resolution of

the GBT data are nominally 510 , this is a 1% effect and we ignore it as well. SN 1006 was observed with the GBT for the purpose of creating a radio image to compare to optical and X-ray images. While the epoch differences of the radio observations are not sufficient to cause problems, in fact expansion due to the time between the radio (1991) observations and X-ray (2003) and optical (1998) observations is significant (12 years, 5. 7, compared to a 5 beam). For scientific analysis in Paper II, we

No. 2, 2009

HIGH-RESOLUTION FLUX-ACCURATE IMAGES OF SN 1006

do adjust for the expansion, bringing the radio image to the scale of the 1998 optical observations (Winkler et al. 2003). 6. CONCLUSIONS In conclusion, we have shown that synthesis imaging of extended emission can be aided by relatively short duration observations with a single dish. Despite 1 s per beam exposure, the GBT image had a S/N of 50 and the GBT contribution to noise in the final image was not significant in comparison to VLA contributions. Observations should aim to equalize S/N across Fourier spacings, rather than obtaining identical pointsource sensitivity. This leads to a simple rule of thumb—spend about the same total time observing with VLA D configuration and GBT. The impact of flux-accurate images of large sources on science is greater than one first might expect. While these sources only make up a few of ∼200 Galactic SNRs, or two (Coma and Virgo) of thousands of clusters, the proximity that causes the short spacing problem also provides high resolution and flux high enough to permit observations at complementary wavelengths (IR, optical, UV, X-ray). We know more about these objects, and therefore our models and understanding of all objects in that class depend on having accurate images of these cannonical sources. We suggest that single dish observations should be made in brief repeated maps, in basketweaving mode, when possible, to remove transient noise on minute timescales. Combining the GBT and VLA data using single-dish information as a starting model has several advantages. It is simple from a computational perspective, possible in several current software packages, including AIPS++, and requires smaller single dish maps than Fourier plane methods. 6.1. The Future The lack of flux-accurate images affects astronomical subjects beyond supernova remnants. The list also includes nearby galaxies, the galaxy clusters Coma and Virgo, planetary nebulae, all structures in the Galactic plane, and Galactic H i emission. If it is an issue at centimeter wavelengths, it is and will be critical for millimeter instruments. CARMA’s 12 m dishes are insensitive to structures larger than 1 arcmin at 90 GHz. ALMA, with 15.4 m dishes, will be insensitive to structures larger than 10 arcsec at 490 GHz. To ensure the highest quality science, with both current and future instruments, two things need to happen. Software paths for adding single-dish and interferometric data need to be developed and tested (as we have done for AIPS++ in this paper), and observatories need to make acquiring the necessary short-spacing data a standard part of observing proposal.

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Our future work with this data includes analyzing radio images of SN 1006 with optical and X-ray images, work that was made difficult in Long et al. (2003) by poor S/N in the radio image. Lack of large-scale structure information created large negative bowls surrounding the SNR, which limited the effectiveness of the CLEAN algorithm, even on small scale structure. While working on this paper K.K.D. was supported by a National Science Foundation Astronomy and Astrophysics Postdoctoral Fellowship14 under award AST 01-03879 and by the National Academy of Sciences through a National Research Council Fellowship at the Naval Research Laboratory. Basic Research in Radio Interferometry at the Naval Research Laboratory is supported by the Office of Naval Research. REFERENCES Allen, G. E., Houck, J. C., & Sturner, S. J. 2005, X-Ray and Radio Connections ed. L. O. Sjouwerman & K. K Dyer (Santa Fe, NM: NRAO), 4.7, http://www.aoc.nrao.edu/events/xraydio Anderson, M. C., & Rudnick, L. 1993, ApJ, 408, 514 Clark, B. G. 1980, A&A, 89, 377 Cornwell, T. J., Braun, R., & Briggs, D. S. 1999, ASP Conf. Ser. 180, Synthesis Imaging in Radio Astronomy II (San Francisco, CA: ASP), 151 Cornwell, T. J., & Evans, K. F. 1985, A&A, 143, 77 Cornwell, T. J., Golap, K., & Bhatnagar, S. 2005, A&AS, 347, 86 Cornwell, T. J., Golap, K., & Bhatnagar, S. 2003, in Projection: A New Algorithm for Non-coplanar Baselines (EVLA memo 67; Socorro: NRAO), http://www.nrao.edu/evla/geninfo/memoseries/evlamemo67.pdf Cornwell, T. J., & Holdaway, M. A. 2005, A&AS, submitted Cornwell, T. J., Holdaway, M. A., & Uson, J. M. 1993, A&A, 271, 697 Cornwell, T. J., & Perley, R. A. 1992, A&A, 261, 353 Dyer, K. K., & Reynolds, S. P. 1999, ApJ, 526, 365 Ellison, D. C., Berezhko, E. G., & Baring, M. G. 2000, ApJ, 540, 292 Emerson, D. T., & Graeve, R. 1988, A&A, 190, 353 H¨ogbom, J. A. 1974, A&AS, 15, 417 Kuehr, H., Witzel, A., Pauliny-Toth, I. I. K., & Nauber, U. 1981, A&AS, 45, 367 Laing, R. A., & Peacock, J. A. 1980, MNRAS, 190, 903 Long, K. S., Reynolds, S. P., Raymond, J. C., Winkler, P. F., Dyer, K. K., & Petre, R. 2003, ApJ, 586, 1162 Moffett, D., Caldwell, C., Reynoso, E., & Hughes, J. 2004, in IAU Symp. 218, Young Neutron Stars and Their Environments, eds. F. Camilo & B. Gaensler (San Fransisco, CA: ASP), 69 Moffett, D. A., Goss, W. M., & Reynolds, S. P. 1993, AJ, 106, 1566 O’Neil, K. 2002, in ASP Conf. Ser. 278, Single-Dish Radio Astronomy: Techniques and Applications (San Francisco, CA: ASP), 293 Reynolds, S. P., & Gilmore, D. M. 1986, AJ, 92, 1138 Roger, R. S., Milne, D. K., Kesteven, M. J., Wellington, K. J., & Haynes, R. F. 1988, ApJ, 332, 940 Rohlfs, K., & Wilson, T. L. 2004, Tools of Radio Astronomy (4th ed.; Berlin: Springer) Stanimirovic, S. 2002, ASP Conf. Ser. 278, Single-Dish Radio Astronomy: Techniques and Applications (San Francisco, CA: ASP), 278, 375 Stephenson, F. R., Clark, D. H., & Crawford, D. F. 1977, MNRAS, 180, 567 Winkler, P. F., Gupta, G., & Long, K. S. 2003, ApJ, 585, 324 Winkler, P. F., & Long, K. S. 1997, ApJ, 491, 829

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