First detection of X-ray polarization in Galactic ULX pulsar Swift J0243.6$+$6124 with { IXPE}

We report the results of first ever spectro-polarimetric analyses of the Galactic ultra-luminous X-ray pulsar Swift J0243.6$+6124$ during the 2023 outburst using quasi-simultaneous { IXPE}, { NICER} and { NuSTAR} observations. A pulsation of period ~ 9.79 s is detected in { IXPE} and { NuSTAR} observations with pulse fractions (PFs) ~ 18% ($2-8$ keV) and ~ 28% ($3-78$ keV), respectively. Energy-dependent study of the pulse profiles with { NuSTAR} indicates an increase in PF from ~ 27% ($3-10$ keV) to ~ 50% ($40-78$ keV). Further, epoch-dependent polarimetric measurements during decay phase of the outburst confirm the detection of significant polarization degree (PD) varying as ~ 2-3.1% with polarization angle ~ 8.6∘-10.8∘ in $2-8$ keV energy range. We also observe that PD increases up to ~ 4.8% at higher energies (5 keV) with dominating bbodyrad flux contribution (1.5 FBB/FPL 3.4) in { IXPE} spectra. The phase-resolved polarimetric study yields PD as ~ 1.7-3.1% suggesting a marginal correlation with the pulse profiles. Moreover, the broad-band ($0.6-70$ keV) energy spectrum of combined { NICER} and { NuSTAR} observations is well described by the combination of bbodyrad and cutoffpl components with seed photon temperature (kTbb) ~ 0.86 ± 0.03 keV and photon index (Γ) ~ 0.98 ± 0.01. With the above findings, we infer that the observed `low' PD in Swift J0243.6$+6124$ is resulted possibly due to `vacuum resonance' effect occurred between the overheated and relatively cooler regions of the neutron star boundary layer.