The shallow-decay phase in both the optical and X-ray afterglows of Swift GRB 090529A: Energy injection into a wind-type medium?

The energy injection model is the usual choice for interpreting the shallow-decay phase in Swift gamma-ray burst (GRB) X-ray afterglows. However, very few GRBs have simultaneous signatures of energy injection in their optical and X-ray afterglows. Here, we report on the optical observations of GRB 090529A from 2000s to ~10⁶s after the burst, in which an achromatic decay is seen at both wavelengths. The optical light curve shows a decay from 0.37 to 0.99, with a break at ~10⁵ s. In the same time interval, the decay indices of the X-ray light curve changed from 0.04 to 1.2. Comparing these values with the closure relations, the segment after 3 × 10⁴s is consistent with the prediction of the forward shock in an interstellar medium without any energy injection. The shallow-decay phase between 2000 and 3 × 10⁴s could be a result of the external shock in a wind-type medium with an energy injection under the condition of ν_o < ν_c < ν_x. However, the constraint of the spectral region is not consistent with the multiband observations. For this shallow-decay phase, other models are also possible, such as energy injection with evolving microphysical parameters, a jet viewed off-axis, etc.