Plotting curved peaks on PSD graph
Different methods exist for estimating PSDs. They can be broadly classified as parametric or non-parametric methods. Indeed you should learn which method they used to obtain the associated PSD.

An FFT based PSD estimation is a non-parametric method such as Periodogram and its variants. This method will produce random looking non-smooth output result which can be smoothed, but this has limits and has side effects too.

On the other hand, parametric estimators can produce very smooth and high resolution looking PSD estimates. There are many parametric PSD estimators. The authors probably used a model based parametric estimator to obtain the plotted PSD, that's why they are smooth looking and that's what I understand from your word curved ?