The Effect of Anisotropic Energy Injection on the Ejecta Emission

A rapidly rotating magnetar has long been assumed to inject energy into the ejecta through isotropic output energy in previous works. However, the output energy of a magnetar is anisotropic and a jet is generally presented in the rotational direction of a magnetar. In this paper, we present a consistent model of the energy injection from a magnetar, considering both the anisotropic magnetic dipole radiation and the jet’s ingredient (i.e., the late jet mentioned refers to the beamed magnetars wind). In the situation that the energy injection into the ejecta presents a significant effect on the ejecta’s emission, two facts are obtained. (1) For an observer in the equatorial direction, there is no significant difference between the light curves of the ejecta’s emission based on the consistent model and those obtained in previous works (i.e., based on the isotropic energy injection). (2) For an on jet-axis observer, however, the difference is significant, especially in the optical/U-band. If the jet is not present in the system, the rise of the optical/U-band light-curve is actually steeper than that in previous works because the output energy of the anisotropic magnetic dipole radiation is mainly in the equatorial direction. If the jet is present in the system, a bump from the cocoon (i.e., the late jet launch is expected to shock and heat-up the ejecta) may only appear in the optical/U-band light curve for a quasi-isotropic ejecta. Our results reveal that the anisotropic energy output of the magnetic dipole radiation and the jet’s ingredient should be well considered in modeling the ejecta emission by considering the energy injection from a magnetar. In addition, the optical/U-band light-curve may disclose the central engine of the burst.