Emission line stacking of 21cm intensity maps with MeerKLASS: Inference pipeline and application to the L-band deep-field data

We present a novel analysis of observational systematics through the emission line stacking of the MeerKLASS L-band deep-field intensity maps, following the detection reported in arXiv:2407.21626. A stacking signal is obtained by stacking the 21cm intensity map cubelets around the galaxy positions from the GAMA survey at $0.39\lesssim z \lesssim 0.46$. An extensive simulation framework is built to study the viability of the stacking detection, the covariance estimation, and the model inference, which are then applied to the data. The statistical significance of the detection is $8.66\sigma$ when averaged into an angular map, and $7.45\sigma$ when averaged into a spectrum. The stacked spectrum exhibits an oscillating component of systematics, and we provide evidence that the systematics is a convolutional effect on the map data. The frequency of the oscillation matches the diffraction from the secondary reflector into the primary beam of the MeerKAT telescope. Bayesian inference can be used to constrain the systematics and the average HI emission of the galaxies. The fitting of the parameters gives a constraint on the systematics frequency $\nu_{\rm sys}\,[{\rm MHz}] = 17.90^{+6.53}_{-4.27}$. The amplitude of the systematics is $>6.71\%$ at the 95\% confidence level. A tentative measurement of the average HI mass of the sources is achieved at ${\rm log}_{10}[\langle M_{\rm HI}\rangle/M_\odot ]=9.84^{+0.48}_{-0.59}$, limited by the narrow redshift bin of the data, the existence of the systematics, and the low-density galaxy sample. These shortfalls will be resolved for future MeerKLASS data to enable accurate measurements of the HI density through stacking of 21cm intensity maps.