First detection of X-ray polarization in Galactic ULX pulsar Swift J0243.6$+$6124 with {\it 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 {\it IXPE}, {\it NICER} and {\it NuSTAR} observations. A pulsation of period $\sim 9.79$ s is detected in {\it IXPE} and {\it NuSTAR} observations with pulse fractions (PFs) $\sim 18\mathrm{\%}$ ($2-8$ keV) and $\sim 28\mathrm{\%}$ ($3-78$ keV), respectively. Energy dependent study of the pulse profiles with {\it NuSTAR} indicates an increase in PF from $\sim 27\mathrm{\%}$ ($3-10$ keV) to $\sim 50\mathrm{\%}$ ($40-78$ keV). Further, epoch-dependent polarimetric measurements during the decay phase of the outburst confirm the detection of significant polarization, with the polarization degree (PD) and polarization angle (PA) ranging between $\sim 2-3.1\mathrm{\%}$ and $\sim {8.6}^{\circ }-{10.8}^{\circ }$, respectively, in the $2-8$ keV energy range. We also observe that the PD increases up to $\sim 4.8\mathrm{\%}$ at higher energies ($\gtrsim 5$ keV) with dominating $\mathtt{\text{bbodyrad}}$ flux contribution ($1.5\lesssim F_{\mathrm{B}\mathrm{B}}\mathrm{/}{F}_{\mathrm{P}\mathrm{L}}\lesssim 3.4$) in the {\it IXPE} spectra. The phase-resolved polarimetric study yields PD as $\sim 1.7-3.1\mathrm{\%}$ suggesting a marginal correlation with the pulse profiles. Moreover, the broad-band ($0.6-70$ keV) energy spectrum of combined {\it NICER} and {\it NuSTAR} observations is well described by the combination of $\mathtt{\text{bbodyrad}}$ and $\mathtt{\text{cutoffpl}}$ components with seed photon temperature ($k{T}_{\mathrm{b}\mathrm{b}}$) $\sim 0.86\pm 0.03$ keV and photon index ($\mathrm{\Gamma }$) $\sim 0.98\pm 0.01$. With the above findings, we infer that the observed low' PD in Swift J0243.6$+6124$ is attributed possibly due to vacuum resonance’ effect between the overheated and relatively cooler regions of the neutron star boundary layer.