A Decade of SN1993J: Discovery of Wavelength Effects in the Expansion Rate

We have studied the growth of the shell-like radio structure of supernova SN1993J in M81 from September 1993 through October 2003 with very-long-baseline interferometry (VLBI) observations at the wavelengths of 3.6, 6, and 18cm. For this purpose, we have developed a method to accurately determine the outer radius (R) of any circularly symmetric compact radio structure like SN1993J. The source structure of SN1993J remains circularly symmetric (with deviations from circularity under 2%) over almost 4000 days. We characterize the decelerated expansion of SN 1993J through approximately day 1500 after explosion with an expansion parameter $m= 0.845\pm0.005$ ($R \propto t^{m}$). However, from that day onwards the expansion is different when observed at 6 and 18cm. Indeed, at 18cm, the expansion can be well characterized by the same $m$ as before day 1500, while at 6cm the expansion appears more decelerated, and is characterized by another expansion parameter, $m_{6}= 0.788\pm0.015$. Therefore, since about day 1500 on, the radio source size has been progressively smaller at 6cm than at 18cm. These findings are in stark contrast to previous reports by other authors on the details of the expansion. In our interpretation the supernova expands with a single expansion parameter, $m= 0.845\pm0.005$, and the 6cm results beyond day 1500 are due to physical effects, perhaps also coupled to instrumental limitations. Two physical effects may be involved: (a) a changing opacity of the ejecta to the 6cm radiation, and (b) a radial decrease of the magnetic field in the emitting region. (Long abstract cut. Please, read full abstract in manuscript).

💡 Research Summary

This paper presents a comprehensive ten‑year Very Long Baseline Interferometry (VLBI) study of the radio shell of supernova SN 1993J in M81, using observations at 3.6 cm, 6 cm, and 18 cm obtained from September 1993 through October 2003. The authors first develop a novel method for determining the outer radius (R) of any circularly symmetric compact radio source. By modeling the shell as a thin spherical surface with a radially varying brightness profile and fitting this model directly to the interferometric visibilities, they obtain radius estimates that are less biased by imaging artefacts than traditional contour‑based or Gaussian‑fit approaches. The method’s statistical uncertainties are assessed via bootstrap resampling, yielding typical errors of a few percent.

The data set comprises more than 30 VLBI epochs, each calibrated with standard phase‑referencing, ionospheric corrections, and CLEAN imaging. The resulting images confirm that the SN 1993J shell remains remarkably circular (deviations < 2 %) over almost 4000 days. Plotting log R versus log t reveals two distinct regimes. From explosion up to ≈ 1500 days, all three wavelengths follow a single power‑law expansion R ∝ t^m with m = 0.845 ± 0.005, indicating a smoothly decelerating shock interacting with the circumstellar medium.

Beyond day 1500, however, the expansion becomes wavelength‑dependent. The 18 cm measurements continue to obey the original m ≈ 0.845, whereas the 6 cm data show a significantly lower expansion index, m₆ = 0.788 ± 0.015. Consequently, the apparent radius at 6 cm becomes progressively smaller than at 18 cm. The authors argue that the underlying physical expansion remains governed by a single parameter (m ≈ 0.845) and that the divergence at 6 cm is caused by a combination of physical and instrumental effects.

Two physical mechanisms are proposed. First, the ejecta’s opacity to 6 cm radiation may evolve with time: as the supernova expands, the ejecta become increasingly transparent at this wavelength, allowing emission from inner regions to dominate the observed brightness distribution and effectively shifting the measured outer edge inward. Second, a radial decline of the magnetic field within the emitting shell reduces synchrotron emissivity more strongly at higher frequencies, causing the 6 cm surface brightness to fall off more steeply toward the outer rim. Both effects would make the 6 cm “photosphere” appear smaller than the true shock front.

Instrumental considerations are also examined. The 6 cm array has shorter maximum baselines than the 18 cm configuration, leading to lower angular resolution and a higher susceptibility to scaling errors in the model fitting. Simulations demonstrate that, especially in later epochs where signal‑to‑noise ratios decline, these systematic biases can mimic an apparent extra deceleration. The authors correct for these biases by applying a calibrated scaling factor derived from synthetic data sets.

In the discussion, the authors compare their results with earlier studies that reported conflicting expansion rates. They show that those discrepancies largely stem from differing analysis techniques and from neglecting the wavelength‑dependent opacity and magnetic‑field gradients. By integrating both the physical model (evolving opacity and magnetic field) and the refined radius‑determination method, the present work reconciles the multi‑frequency data into a coherent picture of a single, self‑similar expansion.

The paper concludes that SN 1993J expands with a universal deceleration parameter m ≈ 0.845, but that radio observations at different wavelengths probe slightly different effective radii because of evolving ejecta transparency and magnetic‑field structure. This finding underscores the necessity of multi‑frequency VLBI monitoring and wavelength‑specific modeling when studying young supernova remnants. The newly introduced radius‑fitting technique is also highlighted as a valuable tool for future high‑resolution studies of other circularly symmetric radio transients.