Hinode SOT/SP and SoHO/MDI quiet Sun magnetic field. Implications of their differences on the extrapolated chromospheric field and the height of the magnetic canopy

Aims. We explore the differences in the measurement of the magnetic field of the quiet solar photosphere provided by the Michelson Doppler Imager (MDI) onboard SoHO and the SpectroPolarimeter (SOT/SP) onboard Hinode and the ensuing implications for the extrapolated chromospheric magnetic field and the determination of the location of the magnetic canopy. Methods. We employ potential field extrapolation to reconstruct the chromospheric magnetic field using the magnetic field of the photosphere provided by the two instruments. We also calculate the plasma-beta parameter using the VAL C model atmosphere of the quiet Sun to determine the height of the magnetic canopy. Results. MDI underestimates the magnetic field of the quiet Sun sometimes by a factor of five, which leads to an overestimation of the height of the magnetic canopy by up to similar to 550 km. Although the overall magnetic field configuration does not differ significantly when calculated with either MDI or SOT/SP, the data of the latter lead to lower and more extended canopies. The difference in the resolution of the two instruments does not seem to affect the chromospheric magnetic field higher than 1000 km. Conclusions. The height of the magnetic canopy is an important parameter to consider when investigating wave propagation and the oscillatory properties of the quiet Sun regions in the network and internetwork. The canopy height's derivation depends very much on the sensitivity of the instruments used to measure the photospheric magnetic field. Consequently precise measurements of the photospheric magnetic field are crucial to accurately reconstruct the chromospheric magnetic field and to distinguish between the various wave modes.