The Non-Uniform Expansion of the Crab Nebula

TL;DR

The paper presents a comprehensive, multi-epoch proper-motion map of the Crab Nebula using CFHT MegaCam data to study its two-dimensional expansion. By deriving 19,974 high-quality motion vectors and fitting for center and age, the authors uncover angular variations in expansion, with the equatorial region showing the least acceleration, hinting at disk-like circumstellar material. A 3D Sprout moving-mesh simulation suggests the ejecta are approaching homologous expansion but that the pulsar wind has likely breached inner ejecta, consistent with a blowout scenario. Together, the results imply a more complex interaction between the pulsar wind and the surrounding ejecta than simple free-expansion models, with implications for PWN evolution and CSM geometry.

Abstract

We present extensive proper motion measurements of the Crab Nebula made from Canada-France-Hawaii Telescope MegaPrime/MegaCam images taken in 2007, 2016, and 2019. A total of 19974 proper motion vectors with uncertainty $<10$\,mas\,yr$^{-1}$ located over the majority of the Crab Nebula are used to map the supernova remnant's two-dimensional expansion properties that reflect the dynamics of the original explosion, acceleration of ejecta imparted by spin-down energy from the pulsar, and interaction between the ejecta and surrounding cicumstellar material (CSM). The average convergence date we derive is 1105.5 $\pm$ 0.5 CE, which is 15-35 yr earlier compared to most previous estimates. We find that it varies as a function of position angle around the nebula, with the earliest date and smallest proper motions measured along the equator defined by the east and west bays. The lower acceleration of material along the equatorial plane may be indicative of the supernova's interaction with a disk-like CSM geometry. Comparing our measurements to previous analytical solutions of the Crab's expansion and our own numerical simulation using the moving mesh hydrodynamics code \texttt{Sprout}, we conclude that the ejecta have relaxed closer to homologous expansion than expected for the commonly adopted pulsar spindown age of $τ\sim 700$ yr and a pulsar wind nebula (PWN) still evolving inside the flat part of the ejecta density profile. These findings provide further evidence that the PWN has broken out of the inner flat part of the supernova ejecta density profile and has experienced ``blowout''.

Figures (10)

• Figure 1: Combination of the images taken in 2007 (red) and 2016 (blue) with 3 zoomed-in regions on the right. The expansion of the supernova remnant is conspicuous. We added a grid on region 2 to show the size of the tiles compared to compute the proper motion (see section \ref{['sec:propermotion']}).
• Figure 2: (Top and centre panels) Example of two compared tiles taken at the same celestial coordinates on the 2007 and 2016 images. The red arrow indicates the estimated displacement vector. (Bottom panel) Calculated $\chi^2$ matrix of all the possible shifts tried along the x and y axes. The position of the estimated best shift is located with a blue dot.
• Figure 3: Normalized computed PSF of the stars in the compared images. Only the superior part is drawn to better show the assymmetry of the 2007 PSF along the x axis which leads to a non-negligible systematic on the computed proper motion along the RA axis.
• Figure 4: Difference with T68 on the measured proper motion along right ascension (top) and declination (bottom). The mean and standard deviation are indicated in each panel.
• Figure 5: Proper motion vectors measured on the filamentary regions of the Crab Nebula from our Megacam images. For a more readable representation, only half of all 19974 vectors are shown. The background image is the 2019 observation. The arrows point to the position the material will occupy in 50 years from now. The red cross is our derived centre of expansion.