Assessing the impact of two independent direction-dependent calibration algorithms on the LOFAR 21 cm signal power spectrum And applications to an observation of a field flanking the north celestial pole

Context. Detecting the 21 cm signal from the epoch of reionisation (EoR) has been highly challenging due to the strong astrophysical foregrounds, ionospheric effects, radio frequency interference (RFI), and instrumental effects. Better characterisation of their effects and precise calibration are, therefore, crucial for the 21 cm EoR signal detection. Aims. In this work we introduce a newly developed direction-dependent calibration algorithm called DDECAL, and compare its performance with an existing direction-dependent calibration algorithm called SAGECAL, in the context of the LOFAR-EoR 21 cm power spectrum experiment. Methods. We process one night of data from LOFAR observed by the HBA system. The observing frequency ranges between 114 and 127 MHz, corresponding to the redshift from 11.5 and 10.2. The north celestial pole (NCP) and its flanking fields were observed simultaneously in this data set. We analyse the NCP and one of the flanking fields. While the NCP field is calibrated by the standard LOFAR-EoR processing pipeline, using SAGECAL for the direction-dependent calibration with an extensive sky model and 122 directions, for the RA 18h flanking field, DDECAL and SAGECAL are used with a relatively simple sky model and 22 directions. Additionally, two different strategies are used for the subtraction of the very bright and far sources Cassiopeia A and Cygnus A. Results. The resulting estimated 21 cm power spectra show that DDECAL performs better at subtracting sources in the primary beam region, due to the application of a beam model, while SAGECAL performs better at subtracting Cassiopeia A and Cygnus A. The analysis shows that including a beam model during the direction-dependent calibration process significantly improves its overall performance. The benefit is obvious in the primary beam region. We also compare the 21 cm power spectra results on two different fields. The results show that the RA 18h flanking field produces better upper limits compared to the NCP for this particular observation. Conclusions. Despite the minor differences between DDECAL and SAGECAL, due to the beam application, we find that the two algorithms yield comparable 21 cm power spectra on the LOFAR-EoR data after foreground removal. Hence, the current LOFAR-EoR 21 cm power spectrum limits are not likely to depend on the direction-dependent calibration method. For this particular observation, the RA 18h flanking field seems to produce improved upper limits (similar to 30%) compared to the NCP.