Multi-messenger signatures of a deformed magnetar in gamma-ray bursts

We study the evolution of a newly formed magnetized neutron-star (NS) as a power source of gamma-ray bursts (GRBs) in the light of both gravitational wave (GW) and electromagnetic (EM) radiations. The compressible and incompressible fluids are employed in order to model the secular evolution of Maclaurian spheroids. It is shown that the GW and EM light curves evolve as a function of eccentricity and rotational frequency with time. We find that the light curve characteristics crucially depend on NS parameters such as magnitude and structure of magnetic field, ellipticity and the equation of state (EOS) of the fluid. The presence of X-ray flares, whose origins are not yet well understood, can be captured in our model regarding some specific nuclear EOSs. Our model allowing us to explain flares that occur within the wide range of $ 10$ to $10^4$ seconds and the peak luminosity in the order of $10^{46}$ - $10^{51}$ $\rm \text{erg}/s$ by using a reasonable set of parameters such as magnetic field strength around $10^{14}-10^{16}$ Gauss, the quadrupole to dipole ratio of magnetic field up to 500. By applying our model to a sample of GRB X-ray flares observed by Swift/XRT, we try to constraint the crucial parameters of a deformed magnetar via MCMC fitting method. Our analysis shows that ongoing and upcoming joint multi-messenger detections can be used to understand the nature of GRB's central engine and its evolution at the early times of the burst formation.