We report on very long baseline interferometry ( VLBI ) observations of the radio emission from the inner region of the Crab Nebula , made at 1.6 GHz and 5 GHz after a recent high-energy flare in this object .
The 5 GHz data have provided only upper limits of 0.4 milli-Jansky ( mJy ) on the flux density of the pulsar and 0.4 mJy/beam on the brightness of the putative flaring region .
The 1.6 GHz data have enabled imaging the inner regions of the nebula on scales of up to \approx 40 \hbox { $ { } ^ { \prime \prime } $ } .
The emission from the inner “ wisps ” is detected for the first time with VLBI observations .
A likely radio counterpart ( designated “ C1 ” ) of the putative flaring region observed with Chandra and HST is detected in the radio image , with an estimated flux density of 0.5 \pm 0.3 mJy and a size of 0 ^ { \prime \prime } . 2–0 ^ { \prime \prime } . 6 .
Another compact feature ( “ C2 ” ) is also detected in the VLBI image closer to the pulsar , with an estimated flux density of 0.4 \pm 0.2 mJy and a size smaller than 0 ^ { \prime \prime } . 2 .
Combined with the broad-band SED of the flare , the radio properties of C1 yield a lower limit of \approx 0.5 mG for the magnetic field and a total minimum energy of 1.2 \times 10 ^ { 41 } ergs vested in the flare ( corresponding to using about 0.2 % of the pulsar spin-down power ) .
The 1.6 GHz observations provide upper limits for the brightness ( 0.2 mJy/beam ) and total flux density ( 0.4 mJy ) of the optical Knot 1 located at 0 ^ { \prime \prime } . 6 from the pulsar .
The absolute position of the Crab pulsar is determined , and an estimate of the pulsar proper motion ( \mu _ { \alpha } = -13.0 \pm 0.2 mas/yr , \mu _ { \delta } = +2.9 \pm 0.1 mas/yr ) is obtained .