Multimessenger 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 stable Maclaurian spheroids. It is shown that the GW and EM emissions evolve as a function of eccentricity and rotational frequency with time. We find that the luminosity 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 $10^4$ s and the peak EM luminosity in the order of $10^{46}$ - $10^{51}$ $\rm \text{erg} s^{-1}$ by using a reasonable set of parameters, such as magnetic field strength around $10^{14}-10^{16}$ G, 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 the Swift/X-ray Telescope, we try to constraint the crucial parameters of a deformed magnetar via a Marcov Chain Monte Carlo fitting method. Our analysis shows that ongoing and upcoming joint multimessenger detections can be used to understand the nature of a GRB's central engine and its evolution at the early times of the burst formation.