SN 1979C VLBI: 22 YEARS OF ALMOST FREE EXPANSION Norbert Bartel and Michael F. Bietenholz

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1 The Astrophysical Journal, 591: , 2003 July 1 # The American Astronomical Society. All rights reserved. Printed in U.S.A. SN 1979C VLBI: 22 YEARS OF ALMOST FREE EXPANSION Norbert Bartel and Michael F. Bietenholz Department of Physics and Astronomy, York University, Toronto, ON M3J 1P3, Canada Received 2002 December 31; accepted 2003 March 7 ABSTRACT VLBI measurements of the size of SN 1979C in M100 (NGC 4321) in the Virgo Cluster, from t ¼ 3:7 yr after the explosion, show an expansion /t m, which is, with m ¼ 0:95 0:03, almost consistent with being free for 22 years. The last size measurement, at t ¼ 22 yr, may indicate for the first time a change of the expansion of the supernova and suggests, as an alternative, free expansion /t m with m ¼ 1:00 0:05 up to t b 17 yr followed by marginally significant deceleration with m ¼ 0:74 0:17. The possible deceleration could be weaker within the errors for t b < 17 yr or stronger for t b > 17 yr. With the assumption for the density profile of the circumstellar medium (CSM) of CSM / r s, we derive a model-dependent value of s ¼ 1:95 þ0:10 0:05 up to a distance from the progenitor, r ¼ r b, that corresponds to t b 17 yr, which changes to sd1:5 for r > r b. For a kinetic energy of the shocked ejecta and CSM shells of E kin ¼ ergs, our results require a mass loss to wind velocity ratio for the progenitor of _M w =w M yr 1 per w ¼ 10 km s 1, an order of magnitude smaller than estimated from radio light-curve fitting. The swept-up mass at t ¼ 22 yr is then M sw ¼ 0:3 M and the inferred mass of the shocked ejecta M shock ej ¼ 2 þ4 1 M. Our last observations give an image of a barely resolved source with a first hint on the structure of the supernova, consistent with being circular within 9% and possibly center filled. The expanding shock front method (ESM) of combining the transverse radio expansion velocities with the radial optical velocities gives direct distance estimates to M100, with standard errors of D ¼ 16:5 2:5to19:8 3:0 Mpc, depending on whether the supernova has a bright center or is a shell without such a center. These estimates are comparable with those from Cepheid observations (e.g., 16.1 and 15.2 Mpc). Subject headings: distance scale galaxies: distances and redshifts galaxies: individual (M100) radio continuum: stars supernovae: individual (SN 1979C) 1. INTRODUCTION SN 1979C was discovered in the Virgo Cluster galaxy M100 (NGC 4321) in a spiral arm south-southeast of the galaxy s center on 1979 April 19 by G. E. Johnson (Mattei et al. 1979) and is believed to have exploded a couple of weeks earlier. Here we assume the date 1979 April 4 for the explosion (see Weiler et al. 1986), hereafter t ¼ 0 yr. The supernova was subsequently classified as of Type II-L. At a distance of 15.2 Mpc (Freedman et al. 2001) it reached M B 20 (Young & Branch 1989; with an assumed distance of 18 Mpc) and became one of the most optically luminous Type II supernovae ever found. After a short featureless period its spectrum developed strong emission lines with P Cygni absorption troughs, with indicated maximum expansion velocities of 11,700 km s 1 (Branch et al. 1981). The H emission lines indicated expansion velocities between 10,800 (Barbon et al. 1982) and 9000 km s 1 (Penston & Blades 1980) at early times. At late times of t 14 yr, the expansion velocity indicated by the H emission line is smaller, only 6200 km s 1, and the line is asymmetric, possibly as a result of clumpiness in the ejecta (Fesen et al. 1999). At radio frequencies the supernova peaked at a flux density, S 8 mjy, at, e.g., a frequency of ¼ 5 GHz (Weiler et al. 1986), and is therefore also one of the most radioluminous supernovae ever detected. The radio emission is synchrotron radiation that, for the minishell model, which exhibits self-similar evolution, emanates in the region around the contact discontinuity where the supernova ejecta hit the circumstellar medium (CSM) left over from the wind of the progenitor star (Chevalier 1982a, 1982b). This is also the region where the recently detected X-ray emission 301 (Immler, Pietsch, & Aschenbach 1998; Ray, Petre, & Schlegel 2001; Kaaret 2001) is likely to be emitted. At early times after the explosion, most of the radio radiation from the interaction region in this model is free-free absorbed by the photoionized CSM with the optical depth,, being a function of the mass loss to wind velocity ratio, _M w =w, of the progenitor and the size of the supernova. During the expansion, the shock front sweeps up the obscuring layers of the CSM and decelerates with the radius /t m and m < 1. After the supernova expanded to a size where 5 1, the radio light curves in this model decline with a power law with S / t, where is the spectral index of the optically thin synchrotron radio shell and is the flux density decay index. Weiler et al. (1992) found indications of an oscillating behavior in the declining radio light curves, which caused them to speculate that the shock front is running into a spiral-shaped stellar wind, modeled as having been left over from a detached eccentric binary system instead of a single progenitor. On the basis of model fits to the radio light curves, _M w =w 1: M yr 1 per w ¼ 10 km s 1 (Montes et al. 2000). Based on studies of the environment of SN 1979C, Van Dyk et al. (1999) believe that the progenitor of SN 1979C had a main-sequence mass of 18 3 M. For the time after 1990, Montes et al. (2000) found that the radio light curves changed, being flat or increasing modestly for the next 8 yr, and speculated that the density of the CSM in the outer regions is enhanced. If indeed true, the expansion of the supernova should be slowed. A determination of the deceleration parameter, m, up to the present is therefore of particular interest.

2 302 BARTEL & BIETENHOLZ Very long baseline interferometry (VLBI) observations were made from 1982 to 1984 (t ¼ 3:7 5:2 yr), the first ones of any supernova, 1 and succeeded in partly resolving the radio supernova and in measuring the angular expansion (Bartel 1985; Bartel et al. 1985). With more observations, up to 1986 (t ¼ 7:2 yr), Bartel (1991) allowed for deceleration in the fit and estimated m ¼ 1:03 0:15. Recently, Marcaide et al. (2002) reported on a measurement of the radius of the supernova in 1999 (t ¼ 20 yr) and found strongly decelerated expansion with m ¼ 0:62 0:17 þ0:22, which they claimed started at t b ¼ 6 2 yr, approximately at the start of the oscillations in the light curve, but clearly before the onset of its flattening or slight increase. We, however, disagree with some of their analyses and conclusions and discuss possible causes for differences in the Appendix. Here we report on new VLBI observations at three epochs, 1990, 1996, and 2001 (t ¼ 11, 17, and 22 yr), on further observations at two earlier epochs, 1985 and 1986 (t ¼ 5:9, and 7.2 yr), of which the results were already reported in proceedings papers (Bartel 1988, 1991), and on a comprehensive analysis of all these VLBI observations of SN 1979C. We show that the data are consistent with SN 1979C having expanded almost freely for 22 yr. We first describe our observations and data reduction in xx 2 and 3. In x 4 we present results on the brightness distribution and show an image of SN 1979C from our last observations that gives first indications of the barely resolved structure. We give our radio light-curve measurements in x 5. Then we give our determinations of the size of the supernova in x 6 and combine them with earlier measurements to derive the angular expansion of the supernova and its deceleration in x 7. In x 8 we discuss our results, and in x 9 we give our conclusions. 2. OBSERVATIONS The observations were made with a global array of between three and 12 antennas at 5 and 1.7 GHz with a total time of 5 10 hr for each run. The low declination of SN 1979C (R:A: ¼ 12 h 22 m 58966, decl: ¼ >9, epoch J2000.0) caused the u-v coverage in general to be rather elliptical, resulting in an angular resolution at least twofold higher in the east-west direction than in the north-south direction. As usual, a hydrogen maser was used as a time and frequency standard at each telescope. The data were recorded with the Very Long Baseline Array (VLBA) and either the MK III or the MK IV VLBI systems with sampling rates of 112 or 256 Mbit s 1. The characteristics of the observations are given in Table 1. In all observations we observed besides SN 1979C one or more of the sources, OQ 208 (J ), OJ 287 (J ), and 3C 274 (J ), and used them as fringe finders and in most cases also as amplitude calibrators. For the first observations, at t ¼ 5:9 yr, the brightness of the supernova was still sufficiently high for obtaining detections on each of the interferometer baselines of the array during a scan time of a few minutes at 5.0 GHz. For 1 The earliest VLBI observations of any source resembling a supernova or supernova remnant were made of the source in the central region of M82 (NGC 3034; Geldzahler et al. 1977; Wilkinson & de Bruyn 1984). The source was originally thought to more likely be an active galactic nucleus. Later it was thought to be likely a several decade old supernova remnant (Bartel et al. 1987; Wilkinson & de Bruyn 1990). The most recent observations put this interpretation into question (McDonald et al. 2001). the second observations, at t ¼ 7:2 yr, detections were obtained only on one of the three baselines at 5.0 GHz. The third observations, at t ¼ 11 yr, were made on 4 consecutive days at 5.0 GHz and 3 consecutive days at 1.7 GHz. For this campaign an MK III data acquisition system was carried to Arecibo to include that antenna for superior sensitivity and improved north-south u-v coverage. While the observations at Arecibo were successful at both frequencies, a human error prevented useful observations from being obtained at the VLA at 5.0 GHz. As a consequence, the observations at 5.0 GHz were largely useless, but those at 1.7 GHz proved successful. For the fourth observations, at t ¼ 17 yr, an extended array was used at a frequency of 1.7 GHz only, resulting in detections on most of the baselines. Our most sensitive observations were made at t ¼ 22 yr, by phasereferencing to the nearby source, J We used a cycle time of 3 minutes in which SN 1979C was observed for 120 s and J for 80 s. From these observations we made an image that shows the first signs of the supernova s structure. Simultaneously with the VLBI observations, we obtained interferometry data with the VLA alone for most of the observations. 3. DATA REDUCTION 3.1. Correlation, Calibration, and Imaging of the VLBI Data The data from the first three sessions, at t ¼ 5:9, 7.2, and 11 yr, were correlated with the MK III VLBI processor of MIT s Haystack Observatory at Westford, Massachusetts, and the data from the last two sessions, at t ¼ 17 and 22 yr, with NRAO s VLBA processor at Socorro, New Mexico. For the first two observations, at 5.0 GHz, fringe-fitting and coherent averaging of the data over the time of the scan of 13 minutes and the bandwidth of 56 MHz were carried out with software from Haystack Observatory. We limited the ranges for the search for fringes in delay and delay rate to be as narrow as possible to maximize the number of reliable detections. However, even with these additional efforts for the 5.0 GHz observations, the supernova was already so weak and relatively extended that detections were obtained only on a limited number of interferometer baselines. Subsequent incoherent averaging of the data over several scans ensured the reliability of the detections. The amplitudes of the complex correlation coefficients were corrected for any apparent coherence losses. In addition, in several cases the signal-to-noise ratio was so low that the amplitudes were significantly biased toward larger values because the noise fluctuations were always positive. We corrected these amplitudes for the noise bias. The amplitudes were then calibrated on the basis of the system temperatures and gains of the antennas to yield correlated flux densities. The calibration was improved somewhat by modeling the compact calibrator source, OQ 208, in the u-v plane as a Gaussian and using this source for corrections. For the third observations, at t ¼ 11 yr at 1.7 GHz, only fringe-fitting was carried out at Haystack Observatory. For further analysis of the data, we used NRAO s Astronomical Image Processing System (AIPS). At the frequency of 1.7 GHz, the supernova was sufficiently strong that detections were obtained on most baselines. Again, the calibrator source, OQ 208, was used to improve the a priori system temperatures and gains of the antennas for the calibration of the amplitudes.

3 TABLE 1 VLBI Observations of SN 1979C Date Age b (yr) Antenna a Frequency (GHz) Eb Hh Jb Mc Nt Wb On Go Ro Ar Gb Hs Y Br Fd Hn Kp La Mk Nl Ov Pt Sc Total Time c (hr) On-Source Time d (baseline hr) Recording Circular Mode e Polarization f 1985 Feb X X X X* III-A L 1986 Jun X g X X X* III-A L 1990 Mar 18 h X X X X X X* III-A L 1996 Mar X X X X X X X X X X X X R+L 2001 Feb X X X X X X X X X X X X X X X X X X X R+L Earlier Observations i 1982 Dec X X X X* III-A L 1983 May X X j X X X X j X* X* III-A R 1983 Dec X X X j X X* III-A L 1984 May X X X X* III-A L a Eb = 100 m, MPIfR, Effelsberg, Germany; Hh = 26 m, Hartbeesthoek Radio Astronomy Observatory, Johannesburg, South Africa; Jb = 76 m, Jodrell Bank Observatory, Lower Withington, UK; Mc = 32 m, IRA-CNR, Medicina, Italy; Nt = 32 m, IRA-CNR, Noto, Italy; On = 20 m, Onsala Space Observatory, Ansala, Sweden; Go = 70 m, NASA-JPL, Goldstone, California; Ro = 70 m, NASA-JPL, Robledo, Spain; Ar = 305 m, Arecibo Observatory, Arecibo, Puerto Rico; Hs = 36 m, Haystack Observatory, Westford, Massachusetts; Gb = 43 m, NRAO, Green Bank, West Virginia; Y = equivalent diameter 130 m, NRAO, near Socorro, New Mexico; Br = 25 m, NRAO, Brewster, Washington; Fd = 25 m, NRAO, Fort Davis, Texas (asterisk denotes use of the 40 m antenna at this location); Hn = 25 m, NRAO, Hancock, New Hampshire; Kp = 25 m, NRAO, Kitt Peak, Arizona; La = 25 m, NRAO, Los Alamos, New Mexico; Mk = 25 m, NRAO, Mauna Kea, Hawaii; Nl = 25 m, NRAO, North Liberty, Iowa; Ov = 25 m, NRAO, Owens Valley, California (asterisk denotes use of the 40 m antenna at this location); Pt = 25 m, NRAO, Pie Town, New Mexico; Sc = 25 m, NRAO, St. Croix, Virgin Islands. b Time since assumed explosion data of 1979 April 4 ( ). c Maximum span in hour angle at any one antenna. d Number of baseline hours spent on SN 1979C, after data calibration and editing. e Recording mode: III-A = Mk III mode A, 56 MHz recorded (effectively only 48 MHz at the VLA); = VLBA format, 256 Mbit s 1 recorded in eight baseband channels with 2 bit sampling. f The sense of circular polarization recorded: R = right and L = left circular polarization (IEEE convention). g No useful data were recorded. h Observations were made on 1990 March 18 and 19. i Observations reported earlier by Bartel et al j No fringes were found for this antenna on any of its baselines at this epoch.

4 304 BARTEL & BIETENHOLZ Vol. 591 The data from the last two observations, at t ¼ 17 and 22 yr, both at 1.7 GHz, were all processed and analyzed exclusively with AIPS. At t ¼ 17 yr the data were fringed by using 3C 274 as the reference source. Since the supernova was still sufficiently strong, detections were again obtained on most baselines. The calibration was done as for the observations at t ¼ 11 yr, but now by imaging 3C 274 and using this source instead of OQ 208. For the last observations, at t ¼ 22 yr, the processing and analysis of the data were different because of the phasereferencing. We first fringe-fitted, self-calibrated, and imaged the calibrator source, J , and then in an iterative procedure determined the complex antenna gains as a function of time. Antenna phases were derived first, with a timescale of 4 minutes, and then amplitudes, with a final timescale of 30 minutes. Then we derived the phases for the supernova through phase-referencing. More specifically, the antenna phases for J were interpolated to the times of the alternating supernova scans and taken as the antenna phases for the supernova, thus avoiding the need for self-calibration of the latter phases with an arbitrary starting model. We then produced a phase-referenced image of the supernova. We improved this image somewhat by self-calibrating the antenna phases for the supernova with a timescale of 20 minutes using the phase-referenced image of the supernova as a model. The image was deconvolved using the CLEAN algorithm. The CLEAN components were convolved with an elliptical Gaussian beam and the residuals from the deconvolution process were added. Its FWHM size along the major and minor axes and its orientation were chosen to be approximately equal to the equivalent size and orientation of the elliptical Gaussian fit to the inner portion of the dirty beam from the u-v data weighted according to the robust weighting scheme of Briggs (1995; see also Briggs, Schwab, & Sramek 1998). We also produced a superresolved image by deconvolving the image using the maximum entropy method (task VTESS), which gives the smoothest image that is still consistent with the u-v data. We reviewed the observations at t ¼ 3:7 and4.7yrat5.0 GHz and at t ¼ 4:1 and 5.2 yr at 2.3 and 1.7 GHz, respectively. We confirmed the previous analysis of the 5.0 GHz observations (see Bartel et al. 1985). For the 2.3 GHz observations the information on possible coherence losses was not fully available to us. However, information on the 1.7 GHz observations was still available. In particular, we reinspected the fringed data from the Haystack correlator for all individual scans for almost every baseline. We found correlation losses over time for a few correlation coefficients, mostly on the crucial Eb-Y baseline, that had not been previously accounted for. We therefore reanalyzed these observations along the lines of the analysis of the observations at t ¼ 17 yr described above Reduction of the VLA Data We determined the total flux densities of SN 1979C from the observations with the VLA. They were obtained from the CLEAN images made from the fully phase selfcalibrated interferometric data. In the case of observations with a relatively low angular resolution, the emission from the galaxy was detected. In Figure 1 we show the radio image of M100 with SN 1979C located prominently at the M DECLINATION (J2000) SN 1979C RIGHT ASCENSION (J2000) Fig. 1. Radio image of the spiral galaxy M100 (NGC 4321) in the Virgo Cluster prominently showing SN 1979C at the southern edge of a spiral arm southeast of the center of the galaxy. The observations were made with the VLA in the C configuration on 1996 March 15. The gray scale is given in mjy beam 1 on the right margin. The contour levels are at 1.3%, 2.5%, 4%, 8%, 16%, 32%, and 64% of the peak brightness of 15.8 mjy beam 1. The background noise level is 56 ljy beam 1. The FWHM of the beam is 11>2 10>5, oriented at a p.a. of 54 and plotted in the lower left corner.

5 No. 1, 2003 SN 1979C VLBI 305 southern edge of a spiral arm. The total flux density of the supernova was corrected for emission from the galaxy. The flux densities were referred to the flux density of 3C 48 on the scale of Baars et al. (1977). For the standard error of a measurement, we take the sum in quadrature of the statistical error and a 5% systematic uncertainty in the VLA data calibration. 4. THE BRIGHTNESS DISTRIBUTION OF SN 1979C 4.1. An Image of SN 1979C In Figure 2 (left-hand panel) we show an image of SN 1979C obtained from the latest and most extensive VLBI observations at t ¼ 22 yr. The source is resolved, although only barely so. No separate emission components are found outside the main emission region. More revealing perhaps is the superresolved version of the image shown in the right-hand panel. A strong component is visible approximately in the center of the image. If confirmed with higher resolution, such a component would be intriguing. Neither SN 1986J (Bartel et al. 1991; Bietenholz, Bartel, & Rupen 2002) 2 nor SN 1993J (Bartel et al. 2000; Marcaide et al. 1997) shows such a strong central component. Instead they show hot spots on the ridge of the projected shell that are clearly displaced from the center of the radio source. 2 See also Perez-Torres et al. (2002) for an image of the supernova independently reduced from the same data. The outer contours are clearly not as elliptical as the beam, as they would be expected to be if the supernova were unresolved. In particular, the source is extended toward the northeast and southwest approximately along the minor axis of the beam where the angular resolution is highest. The source may also be extended approximately along the major axis of the beam. However, it is not clear whether the latter extension is significant. A higher relative angular resolution is needed to reveal details of the structure of the supernova A Limit on Ellipticity of the Structure In order to investigate further whether any significant asymmetry in the structure of SN 1979C can be found, we focused on our last observations of SN 1979C at t ¼ 22 yr, which have the highest relative angular resolution and promised to give the most reliable results. We fitted, by weighted least squares, a model consisting of the projection of an ellipsoid with uniform emissivity to the u-v data and simultaneously self-calibrated the phases. Our best-fit model has a radius along the major axis of 3.12 mas and a ratio of the minor to major radius of 0:96 0:05 with the major axis oriented at a p.a. of The errors are statistical only. We think that this result is evidence against the supernova having a simple elongated structure. The apparent northwest-southeast extension seen in Figure 2 may therefore be a real feature of the supernova, balancing the extension in the almost perpendicular direction and limiting any ellipticity of the structure to the small value determined MilliARC SEC 0 MilliARC SEC MilliARC SEC MilliARC SEC Fig. 2. Image of SN 1979C made from the VLBI observations of 2001 February 24 at 1.7 GHz. The left-hand panel shows a CLEAN version with a convolving beam with 6:8 mas 2:4 mas FWHM at a p.a. of 14 plotted in the lower left corner. The beam parameters are those estimated from the fit of an elliptical Gaussian to the inner portion of the dirty beam obtained with natural weighting. The contour levels are drawn at 6.8%, 6.8%, 8%, 16%, 32%, 50% (emphasized), 70%, and 90% of the peak brightness of 2.0 mjy beam 1. The brightness rms of the background is 43 ljy beam 1. The right-hand panel shows a maximum-entropy superresolved version with a convolving beam with 3:5 mas 1:5 mas FWHM at a p.a. of 10 also plotted in the lower left corner. The contour levels are at 11.8%, 11.8%, 16%, 32%, 50% (emphasized), 70%, and 90% of the peak brightness of 1.09 mjy beam 1. The rms of the background brightness is also 43 ljy beam 1. The gray scale gives the brightness in mjy beam 1 as indicated at the top of each panel. North is up and east to the left in each panel.

6 306 BARTEL & BIETENHOLZ Vol. 591 The ratio of the minor to major axis of the fit elliptical model is similarly close to unity as the ratio 0.95 found for SN 1993J as early as at t 90 days, when that supernova was also only barely resolved (Bartel et al. 1994). However, beyond the limit on ellipticity no further information on structural symmetry or lack thereof can be obtained for SN 1979C because of our limited relative resolution. A higher relative resolution is needed to see whether the rms of the deviations from circularity of the outer contours is as small as 3% as recently determined for SN 1993J (Bietenholz, Bartel, & Rupen 2001) The Visibility Curve at t ¼ 22 yr The angular resolution and/or the sensitivity of the array on the longest baselines is not quite large enough to reveal clearly the general structural type of the supernova: plerion, composite, or shell (see Fig. 2). To investigate the general structure in more detail, we plot the real part of the visibility curve as a function of the u-v radius in Figure 3. For comparison we also plot the corresponding real parts of the visibility curves for the projections on the sky of three models that approximately describe the range of different possible structures in their simplest forms. We chose the models of a sphere with uniform emissivity, a disk, and a spherical shell also with uniform emissivity. For the last we chose a ratio of the outer to the inner angular radius of o = i ¼ 1:25, which is close to the best-fit ratio for SN 1993J of 1.29 in the absence of absorption in the shell center (Bartel et al. 2002). The uniform sphere model has a brightness distribution peaking in the central region. The model may be appropriate to describe a plerion, i.e., a pulsar nebula. It may also be appropriate to describe a composite, i.e., a shell with a pulsar nebula in its center (e.g., Chevalier & Fransson 1992), where in this case the pulsar nebula outshines the surrounding shell. As a perhaps more unusual example, it could also describe a shell with a hot spot in the front or rear. The disk Fig. 3. Real parts of the vector-averaged visibilities of SN 1979C on 2001 February 24 at 1.7 GHz as a function of u-v radius. The visibilities are plotted as correlated flux densities as a function of u-v radius. The individual (complex) visibility measurements were first phase-shifted, so that the brightness peak of the image was at the phase center, and then binned. The uncertainties of the data points are the rms of the scatter of the correlated flux densities within each bin. For comparison we plot the equivalent visibility curves for a uniform sphere, a disk, and a spherical shell with uniform emissivity and a ratio of the outer to inner angular radius of model is the physically correct model for any circularly symmetric supernova regardless of its three-dimensional emissivity distribution, if the supernova is optically thick at the observation radio frequency. Only once has such a model been inferred for a supernova, namely, for SN 1993J at very early times (Bartel et al. 2002). SN 1979C is not optically thick at our frequency at t ¼ 22 yr and is therefore expected to have a brightness distribution that is modulated over the surface of the projected source. However, to first approximation more moderate examples of brightness distributions than those described above for the uniform sphere, namely, a plerion with a flat emission profile, a composite with a relatively weak pulsar nebula, or a shell with an only moderately strong hot spot, could also be approximated by a disk. As to our last model, the shell model has in projection a circular brightness distribution with the ridge at h i and a brightness minimum in the center. In general the emissivity may be different in different parts of the shell and the brightness modulated along the ridge, but, if SN 1993J is any guide, even such a more complex shell would be well represented by our shell model. It can be seen that most parts of our observed visibility curve are fitted very well by any of the three models. In fact, the three models are virtually indistinguishable apart from a scaling factor for size, except at the longest u-v distances at which the supernova was observed. In particular, our observed visibility curve falls slightly above the visibility curve for a shell model. It is better fitted, by 1, byadisk model. It is best fitted by a uniform sphere model but only very marginally so, by 0.1, in comparison to the disk model. No matter whether a disk or uniform sphere model is favored, perhaps this is an early indication that the supernova has indeed a filled center. However, a relative resolution at least 30% higher or an array sensitivity for the longest u-v distances at least 4 times better is needed to more definitively determine the structure of the supernova. 5. THE RADIO LIGHT CURVES From the interferometric observations with the VLA during the time of our VLBI observations we determined the total flux density, S, of SN 1979C. We list these flux densities at frequencies,, of 8.4, 5.0, and 1.7 GHz in Table 2. Then we plot them in Figure 4 together with the much larger set of flux density determinations of Weiler et al. (1986, 1991) and Montes et al. (2000), after conversion to their frequencies of 4.85 and 1.47 GHz using a spectral index ¼ 0:63 (Montes et al. 2000), with S /. Our determinations are consistent with theirs. At 5 GHz we have enough measurements to confirm the wavy behavior of the radio light curve. We also confirm at both frequencies the flattening of the radio light curve for te12 yr. Such relative increase of the flux density could perhaps be caused by a flattening of the density profile of the CSM (e.g., Montes et al. 2000). If that is indeed the case, then it is probable that the expansion slows. In the following two sections we will first report on measurements of the size of SN 1979C and then investigate the expansion of SN 1979C in detail. 6. SIZE MEASUREMENTS To measure the size of SN 1979C, we fitted, by weighted least squares, models to the u-v data. Since the structure of the supernova was best fitted by a uniform sphere, we used

7 No. 1, 2003 SN 1979C VLBI 307 Date TABLE 2 Total Flux Densities of SN 1979C Flux Densities b (mjy) Age a (yr) 8.46 GHz 4.99 GHz 1.67 GHz 1985 Feb Oct Jun Sep Nov Mar Mar Feb Earlier Observations c 1982 Dec Dec May a Time since assumed explosion date of 1979 April 4 ( ). b Total flux density, S, measured with the VLA. The uncertainties are approximately standard errors and were computed by adding in quadrature the statistical standard error and a 5% systematic calibration error. c Values determined with the VLA, from Bartel et al Date TABLE 3 Angular Radii of SN 1979C Age a (yr) Frequency (GHz) Radius b (mas) 1985 Feb Jun Mar 18 c Mar Feb Earlier Observations d 1982 Dec May e 1983 Dec May f a Time since assumed explosion date of 1979 April 4 ( ). b The angular radius, h, of the projection of a uniform sphere model, fitted to the u-v data. The uncertainties are (approximately) standard errors with the statistical and systematic contributions added in quadrature. c Observations were made on 1990 March 18 and 19. d Reported earlier by Bartel et al e The errors were reestimated; see text. f The data were reanalyzed; see text. Fig. 4. Radio light curves at 4.85 and 1.47 GHz covering the time of our VLBI observations. Values with open symbols are taken from Weiler et al. (1986, 1991) and Montes et al. (2000). Those with filled symbols are from this paper. Our values were measured at slightly different frequencies and converted to the above frequencies with ¼ 0:63 (Montes et al. 2000). Only for our last values at t ¼ 22 yr did we use ¼ 0:38 0:15 þ0:10 from our simultaneous observations at 8.46 and 1.67 GHz. this model as our primary one to display the expansion of the supernova. We list the angular radius determinations, h, for the five epochs of our new VLBI observations in Table 3. At t ¼ 5:9 yr the supernova was already so weak and extended that it could only be detected with certainty on the Gb-Ov baseline, but not on the longest baselines. More observations were made in the 1980s at 5.0 GHz; however, no convincing detections were obtained. For the next observations we included the antenna at Arecibo for superior sensitivity and u-v coverage. However, only the 1.7 GHz observations were successful. The supernova was detected on all baselines. From then on observations were made only at 1.7 GHz and resulted in relatively precise radius determinations. For completeness reasons we also list in Table 3 the angular radius determinations for a uniform sphere, h, for the earliest epochs taken from Bartel et al. (1985). The radius at t ¼ 5:2 yr was reestimated (see x 3.1) and found to be at the lower end of the error of the previously estimated radius of 1:08 0:25 þ0:22 mas. The uncertainties of our radius determinations are (approximately) standard errors with statistical and systematic contributions added in quadrature. The systematic contributions were determined as follows. For the observations at t ¼ 5:9 and 7.2 yr, we varied the gains of the individual antennas by 15% one at a time by leaving the gains of all other antennas unchanged and took the largest radius change as the systematic contribution. This method was also used for the earlier radius determinations at t ¼ 3:7 and 4.7 yr at 5.0 GHz and originally also for the observations at t ¼ 4:1 and 5.2 yr at 2.3 and 1.7 GHz, respectively (Bartel et al. 1985). However, we realized that this method provided unrealistically small error estimates for the latter two observations at t ¼ 4:1 and 5.2 yr. In comparison to the observations at 5.0 GHz, detections were made on more baselines. For instance, the array for the observations at t ¼ 4:1 yr had two antennas in Europe and in the western US that provided detections on long baselines. The determinations of the antenna gains could have been correlated by the amplitude calibration rendering the independent variation of the gains for the error determination as not sufficient. We therefore reestimated the errors of the radius determinations of these two observations by changing the procedure to one more appropriate for these observations. We simultaneously varied the gain of each antenna randomly by up to 10% using a uniform distribution and took the rms of the variations of the values of the radius of a large number of realizations as the systematic contribution. The above error study revealed that the size of a source, only barely resolved, could not be determined with an accuracy better than 15% 20%. In particular, we reinspected the analysis of the 2.3 GHz observations at t ¼ 4:1 yr. We

8 308 BARTEL & BIETENHOLZ Vol. 591 confirmed the previous analysis by Bartel et al. (1985). However, we were not able to reinvestigate whether any possibly subtle coherence losses occurred as for the 1.7 GHz observations mentioned in x 3.1. Since the supernova was only barely resolved, we increased the original relative errors of the radius determination to 18%. For the observations at t ¼ 11 yr, the number of baselines for which detections were obtained was larger than for the observations at 5.0 GHz at the earliest times. For the determination of the systematic error, we therefore also simultaneously varied all the antenna gains randomly as described above. For the last two observations, at t ¼ 17 and 22 yr, we assumed the same systematic errors of 0.08 mas as estimated for the parallel observations of SN 1993J at 1.7 GHz, which were analyzed in the same way (Bartel et al. 2002). 7. THE EXPANSION 7.1. Angular Expansion Velocity and Deceleration We plot the values of h from Table 3 in Figure 5. A weighted least-squares power-law fit to the values of h of the form fit ¼ Aðt=1 yrþ m gives mð3:6 yr t 22 yrþ ¼0:95 0:03 ; with A ¼ 0:164 0:011 mas and a reduced 2 of 2 ¼ 0:74. This fit indicates that the expansion of SN 1979C is consistent with being almost free for 22 yr. We plot the fit line in Figure 5. The errors are statistical. 3 In particular, from our nine observations from t ¼ 3:6 to 22 yr, we find deceleration only at the 1.7 significance level. As an alternative, a slightly better fit can be obtained if we exclude the last radius determination from the fit, in which case we get mð3:6 yr t 17 yrþ ¼1:00 0:05 ; with A ¼ 0:152 0:015 mas and 2 ¼ 0:55. This fit 3 Here and elsewhere, they are adjusted to reflect 2 ¼ C in the cases in which the measured 2 > C, where C is the most probable value of 2 that approaches unity as the number of degrees of freedom becomes large. indicates exact free expansion for that interval. The last radius determination is 0.27 mas, or 2.7 lower than the corresponding h fit value. From only the last two radius determinations we get mð17 yr t 22 yrþ ¼0:74 0:17, indicating marginally significant deceleration for this interval. The possible deceleration could be weaker within the errors, i.e., m > 0:74, if its onset, t b, is less than 17 yr or stronger if t b is greater than 17 yr. Excluding even earlier radius determinations until the first three epochs gives estimates of m always consistent with unity within 0.7. In this scenario the supernova expanded essentially freely up to t b 17 yr and experienced marginally significant deceleration from there on. These results are in conflict with the claim by others of strongly decelerated expansion from t b ¼ 6 2 yr onward (Marcaide et al. 2002). For a discussion, see the Appendix Time of Explosion We also solved for the time of explosion, t 0, by fitting the expression fit /½ðt t 0 Þ=1 yrš m to all the h data. We obtained t 0 ¼ 1:2 0:8 yr. This value is consistent within 1.5 with a zero offset from our assumed date of explosion. It is, however, far less accurate than the date of explosion computed from optical observations and the fitting of the radio light curves. The most precise estimate of the explosion time can be obtained by assuming exact free expansion and fitting the above expression, with m ¼ 1, to the h data for t 17 yr. With this fit we get t 0 ¼ 0:08 0:39 yr. This estimate is close to the assumed explosion date Frequency-dependent Expansion? In view of the early 1.7 and 2.3 GHz size determinations being consistent with larger values than those at 5.0 GHz, Bartel et al. (1985) considered already a possible frequency dependence of the size of SN 1979C. They speculated that interstellar scattering could have increased the apparent size of the supernova, despite the high Galactic latitude of SN 1979C of b II ¼ 77 and the expected broadening from largescale scattering models of the Galaxy of no more than 4% and 2%, respectively. We investigated whether perhaps small-scale anomalies in the scattering properties of the Galaxy could account for the possibly larger sizes at low frequencies by determining the size of the phase-reference source J for the last observations at t ¼ 22 yr at 1.7 GHz. A fit of an elliptical Gaussian to the main component of the source in the image plane gave a 1 upper limit of the FWHM along the minor axis, which is also approximately in the direction of the minor axis of the beam, of 0.25 mas. This value is indeed consistent with the expectations from the large-scale scattering model of the Galaxy. Any broadening of SN 1979C at 1.7 and 2.3 GHz at the early epochs is therefore indeed limited to 4% and 2%, respectively. 4 We also considered the possibility that the size of SN 1979C is intrinsically frequency dependent. A fit to all 1.7 and 2.3 GHz observations gives m ¼ 0:78 0:08, A ¼ 0:273 0:060 mas, and 2 ¼ 0:1. This fit is almost completely determined by the late size measurements but is very consistent with the early 2.3 GHz radius value, which is 1.5 higher than the fit value. One could be tempted to Fig. 5. Angular radius, h, of the uniform sphere model from Table 3, plotted against time since the explosion. The solid line gives the weighted least-squares fit. 4 The limits are computed after conversion to a uniform sphere model and by assuming the same scattering properties for SN 1979C for the early times as for J at the late times.

9 No. 1, 2003 SN 1979C VLBI 309 speculate that at early times the source appeared as a shell at the low frequencies and as a more compact source, e.g., a pulsar nebula, at 5.0 GHz. However, it is unlikely that the 5.0 GHz measurements refer to a pulsar nebula. First, the ejecta are likely opaque to radio waves, and a nebula is not expected to become visible at 5.0 GHz for more than 50 yr unless the debris were fractured and radiation leaked out through the inner ejecta. Second, the pulsar nebula is not expected to have an expansion velocity similar to that of the shell, but rather a more modest one fivefold to 10-fold lower. Third, even if we assume that in our case a pulsar nebula expands with a velocity close to that of the shell, the pulsar nebula would be expected to have continued to expand without deceleration, and rather with acceleration instead, and therefore would have overtaken the shell at t 17 yr and enlarged the radio source to a size greater than measured at t ¼ 22 yr. Fourth, there is no indication from the early spectral measurements of a pulsar nebula component. Fifth, observations of SN 1986J and SN 1993J, the only other supernovae with accurate size measurements at different frequencies, show consistent sizes at different frequencies. Sixth, and most importantly, there is no need from the size measurements to conclude that the size of SN 1979C is frequency dependent, since the early 1.7 and 2.3 GHz size measurements are also consistent with the predictions from the 5.0 GHz expansion curve within a very small fraction of 1 and within 1.5, respectively. All in all, we think that it is unlikely that the intrinsic size of SN 1979C is frequency dependent on the scale discussed here. Future observations could perhaps shed more light on this issue. 8. DISCUSSION Observations at three more epochs have tripled the time range over which the size of SN 1979C was monitored and, with previous results, provide information on the expansion over 22 yr, the longest time range for any (certain) supernova measured with VLBI. The expansion, with m ¼ 0:95 0:03, is consistent with being almost free for the total time range. In fact, only our last measurement gives any indication of the possibility that the expansion has begun to decelerate. These results are important for discussions concerning (1) the radio structure and its implications, (2) the density profiles of the supernova ejecta and the CSM, (3) the mass loss of the progenitor, (4) the relation between the radio and optical expansion velocity determinations, and (5) the determination of the dynamical distance to the host galaxy M100 in the Virgo Cluster. We will discuss each of these aspects in turn The Radio Structure and Its Implications The image made from the observations of the last epoch and, in particular, the associated visibility curve indicate that the supernova radio structure may have a filled center. Such a structure would be different from the shell structure observed for SN 1987A (Manchester et al. 2002; Gaensler et al. 1997), SN 1993J (Bartel et al. 2000; Marcaide et al. 1997), the source in the galaxy M82, which could be a young supernova remnant (McDonald et al. 2001; Bartel et al. 1987), and two supernova remnants in that same galaxy (McDonald et al. 2001). The structure of SN 1979C could be more similar to that of SN 1986J with some emission from the geometric center, but even this supernova has shell morphology albeit with a highly brightness-modulated ridge (Bietenholz et al. 2002). If the uniform sphere structure is confirmed, it would point to either an extraordinarily strongly modulated shell with a hot spot in the front part of the shell or more likely, in view of the measured high degree of overall circularity, emission arising from the inner part of the supernova. Such emission could perhaps be due to a young pulsar nebula. Bandiera, Pacini, & Salvati (1984) computed that young pulsar nebulae would have spectral luminosities times that of the Crab Nebula, depending on the period of the pulsar. A flux density of 1.1 mjy as measured for the peak in our high-resolution image, at 15.2 Mpc, corresponds to a spectral luminosity 250 times that of the Crab Nebula and would therefore be within the above expected range for a pulsar nebula. However, two points qualify this interpretation. First, while SN 1979C was optically thin, its spectral index has in general been relatively steep with between 1 and 0.5. A pulsar nebula is expected to have a flatter spectrum similar to that of the Crab Nebula with ¼ 0:3 (Kovalenko, Pynzar, & Udal Tsov 1994). Second, perhaps the structure of SN 1979C is a composite with a shell and a young pulsar nebula in its center. In that case one might expect a spectrum that consists of two spectral components. One component, originating in the shell, would be steep, and the other, originating in the purported pulsar nebula, would be flat. However, the interior of the supernova is expected to be optically thick to radio waves for about 100 yr at 1.7 GHz (Mioduszewski, Dwarkadas, & Ball 2001). The only possibility of detecting a pulsar nebula at this relatively early time and low frequency appears to be that the ejecta are considerably fractured. The fluctuation of the flux densities, seen to be much stronger at the high frequency than at the low frequency for the late radio light curve, could perhaps be an indication of the sporadic transparency of the shell to such a pulsar nebula. In addition, the latest spectrum at t ¼ 22 yr is, with ¼ 0:38 0:15 þ0:10, rather flat and consistent with the emission at least partly coming from a young pulsar nebula. Further monitoring of the radio light curves of SN 1979C at different frequencies and a high-resolution image could help to shed more light on the nature of the supernova The Density Profiles of the Supernova Ejecta and the CSM Chevalier s (1982a, 1982b) minishell model of radio supernovae analytically describes physical parameters in a region on both sides of the contact surface where the supernova ejecta hit the CSM generated through the wind from the progenitor star in the tens of thousands of years before the star exploded. In particular, the model involves a forward shock that moves out from the contact surface into the CSM, which is assumed to have a density profile CSM / r s, and a reverse shock that moves inward from the contact surface into the supernova ejecta, which are assumed to have a density profile SN / r n. For n > 5, self-similar solutions are possible, and the two profiles determine the deceleration of the contact surface, the outward shock, and the reverse shock, all of whose radii

10 310 BARTEL & BIETENHOLZ Vol. 591 evolve /t m with m ¼ðn 3Þ=ðn sþ. Further, s ¼ ð2=mþ f ½ þ mð 6ÞŠ= ð 3Þ 1g, where is the decay exponent of the radio light curve in the optically thin limit, with S / t (Chevalier 1982a, 1982b; Fransson, Lundqvist, & Chevalier 1996). Montes et al. (2000) report results from least-squares fits of the radio light curves of ¼ 0:75 0:01 þ0:12 and ¼ 0:80 þ0:02 0:03 for td12 yr. Combining these values with our value of m ¼ 0:95 0:03, we obtain s ¼ 1:94 0:05 þ0:09, where the errors are determined by varying each parameter individually within its uncertainty and computing the rootsum-square of the derivations of all parameter variations. These values suggest a very steep ejecta density profile with n ¼ 23 þ30 8. The value of s is consistent with s ¼ 2 or equivalently with _M w =w being constant in time. In fact, for the earlier interval up to t ¼ 17 yr, for which we obtained m ¼ 1:0, we obtain s ¼ 2:03. From then on, with m ¼ 0:74, ¼ 0, and ¼ 0:65, the latter two parameter values reflecting the flattening of the radio light curve and the spectrum, the density profile is inferred to flatten to s ¼ 1:1. A softer transition to, say, s ¼ 1:4, as suggested by Montes et al. (2000) on the basis of the flattening of the radio light curve alone without reference to direct deceleration measurements, is given by a softer change of m to 0.9. In any case, based on the model there is good evidence that, apart from a possibly oscillating component, the CSM density profile is standard with s ¼ 2 within the errors up to t yr and may flatten significantly to sd1:5 from there on The Mass Loss of the Progenitor With the expansion curve determined and _M w =w implied from the fits of the radio light curves, the swept-up mass, M sw, can be computed and the mass of the shocked ejecta, M shock ej, estimated. Taking the radii from our uniform sphere fits, _M w =w ¼ 1: M yr 1 per 10 km s 1 (Montes et al. 2000), and s ¼ 2, we find M sw ¼ 2:8 M at t ¼ 17 yr and 3.6 M at t ¼ 22 yr. If we assume a flattening density profile of the CSM from s ¼ 2 to 1.4, starting at the time of the flattening of the radio light curve at t ¼ 12 yr, then M sw ¼ 5:0 M at t ¼ 22 yr. These values are relatively high and would imply an unreasonably high value for M shock ej (see also Chevalier & Fransson 1994 and Montes et al. 2000, who earlier alluded to this problem). For instance, for undecelerated expansion, without any power source like a pulsar inside the supernova, momentum conservation would dictate M shock ej =M sw! 1. The deceleration parameter, m, is therefore expected to be less than 1. Chevalier (1982a) and Chevalier & Fransson (1994) have computed the ratio M shock ej =M sw for different values of n on the basis of the assumption of mass and energy conservation. If we take for the expansion up to t ¼ 17 yr the 1 lower limit of the deceleration parameter, namely, m ¼ 0:95, then n ¼ 15 and M shock ej =M sw ¼ 7. Consequently, at t ¼ 17 yr, M shock ej > 20 M. This lower limit of M shock ej becomes even larger if s changes to 1.4. For our solution of m ¼ 0:95 0:03 for 3 t 22 yr, M shock ej =M sw ¼ 7 þ13 3 for s ¼ 2 and only slightly smaller if s changes to 1.4. We therefore get M shock ej ¼ 25 þ50 10 M at t ¼ 22 yr for s ¼ 2 and 30 þ60 15 M if s changes to 1.4 starting at t ¼ 12 yr as discussed above. The velocity of the contact discontinuity at t ¼ 22 yr can be estimated from the expansion curve to be 7400 þ km s 1 if o = i ¼ 1:29 is assumed, as estimated for SN 1993J 5 (Bartel et al. 2002). We then get for the kinetic energy of the shells of the shocked ejecta and the shocked CSM E kin;shock ¼ 1:5 þ3 0: and 2 þ ergs for the two cases of s ¼ 2 throughout and s changing to 1.4 at t ¼ 12 yr. The total kinetic energy of the ejecta, including the kinetic energy of the unshocked ejecta, is even larger. With this energy for a Type II supernova of ergs, we can assume a typical value for E kin;shock of ergs. These energies require a much lower value of _M w =w M yr 1 per 10 km s 1. With this new value, M sw ¼ 0:23 M at t ¼ 22 yr for s ¼ 2 and 0.31 M for s changing to 1.4 as discussed above. Further, M shock ej ¼ 1:5 þ3 0:5 M for s ¼ 2 and 2 þ4 1 M for s changing to 1.4. These values are still larger than the mass of the hydrogen-rich envelope of 0.6 (Branch et al. 1981) or 1 M (Chugai 1985) although only by 1 2. Perhaps at this relatively late time, the reverse shock has penetrated into the more massive ejecta, therefore encompassing more mass than that of the hydrogen-rich envelope. It is also possible that _M w =w is even smaller than computed above. However, the values are not larger than the estimated mass of all the ejecta of 6 M given by Branch et al. (1981) and Blinnikov & Bartunov (1993). Our value of _M w =w M yr 1 per 10 km s 1 is an order of magnitude smaller than those reported from radio light-curve fitting with the assumption of free-free absorption in the CSM (Montes et al. 2000; Weiler et al. 1991). Those values would be biased toward larger values if the effect of free-free absorption in the external CSM is overestimated. Synchrotron self-absorption (e.g., Chevalier 1982b; Shklovsky 1985; Slysh 1990) could in general be considered as the cause for such bias. The importance of synchrotron self-absorption as a competing mechanism for the early rise of the radio light curves can be estimated by comparing the directly measured size with that computed on the basis of synchrotron theory for the time of the peak flux density. Our size determinations are clearly larger than those computed under the assumption of synchrotron selfabsorption (Chevalier 1998); therefore, this mechanism can probably not be considered to be the main cause of the bias. Another possible source of the bias is clumping of the CSM. However, a bias of an order of magnitude appears to be rather large and puts into question whether the parameter _M w =w can be determined from radio light-curve fitting with an accuracy better than a factor of 10. In view of this result, model fits to the radio light curves (see, e.g., Weiler et al. 2002) may have to be interpreted with caution The Relation between the Radio and Optical Expansion Velocity Determinations The emission and absorption of the broad optical lines are expected to arise in the gas of the ejecta, i.e., behind the contact surface. In particular, emission was discussed as to come from (1) the freely expanding ejecta and be caused by the heating and ionizing radiation from the interaction region, as well as from (2) the shocked ejecta and be linked to radiative cooling (Chevalier & Fransson 1994 and references therein). The conceivably highest expansion velocity in emission and absorption lines is therefore expected from the shocked gas of the envelope of the progenitor star, 5 This is for the case without central absorption.