Deep search for gamma-ray emission from the accreting X-ray pulsar 1A 0535+262

Binary systems are a well-established subclass of gamma-ray sources. The high mass X-ray binary pulsar 1A~0535+262 has been considered to be a possible gamma-ray emitter for a long time, although former gamma-ray searches using \textit{Fermi}-LAT and VERITAS data resulted in upper limits only. We aim at a deep search for gamma-ray emission and pulsations from 1A~0535+262 using more than 13 years of \textit{Fermi}-LAT data. The analysis was performed for both the whole \textit{Fermi}-LAT data set, as well as for the X-ray outbursts that 1A~0535+262 has experienced since the launch of \textit{Fermi}. Various X-ray observations have been used to generate the ephemeris for the pulsation search. We also investigate the long-term gamma-ray flux variability and perform orbital phase-resolved analysis for the outbursts. We did not detect any steady or pulsed gamma-ray emission from 1A~0535+262 during the whole \textit{Fermi}-LAT mission span or its X-ray outbursts. We thus derived the deepest gamma-ray luminosity upper limits to date at the 95\% confidence level to be around (2.3$-$4.7)$\times 10^{32}\, \rm erg \, s^{-1}$ depending on different spectral indices assumed, which results in a ratio of $L_{\rm \gamma}$ to $L_{\rm X}$ (2$-$150 keV) being (1.9$-$3.9)$\times10^{-6}$.