Properties of the inner penumbral boundary and temporal evolution of a decaying sunspot

Context. It has been empirically determined that the umbra-penumbra boundaries of stable sunspots are characterized by a constant value of the vertical magnetic field.
Aims: We analyzed the evolution of the photospheric magnetic field properties of a decaying sunspot belonging to NOAA 11277 between August 28-September 3, 2011. The observations were acquired with the spectropolarimeter on-board of the Hinode satellite. We aim to prove the validity of the constant vertical magnetic-field boundary between the umbra and penumbra in decaying sunspots.
Methods: A spectral-line inversion technique was used to infer the magnetic field vector from the full-Stokes profiles. In total, eight maps were inverted and the variation of the magnetic properties in time were quantified using linear or quadratic fits.
Results: We find a linear decay of the umbral vertical magnetic field, magnetic flux, and area. The penumbra showed a linear increase of the vertical magnetic field and a sharp decay of the magnetic flux. In addition, the penumbral area quadratically decayed. The vertical component of the magnetic field is weaker on the umbra-penumbra boundary of the studied decaying sunspot compared to stable sunspots. Its value seem to be steadily decreasing during the decay phase. Moreover, at any time of the sunspot decay shown, the inner penumbra boundary does not match with a constant value of the vertical magnetic field, contrary to what is seen in stable sunspots.
Conclusions: During the decaying phase of the studied sunspot, the umbra does not have a sufficiently strong vertical component of the magnetic field and is thus unstable and prone to be disintegrated by convection or magnetic diffusion. No constant value of the vertical magnetic field is found for the inner penumbral boundary.