Context. Observations of young stars hosting transition disks show that several of them have high accretion rates, despite their disks presenting extended cavities in their dust component. This represents a challenge for theoretical models, which struggle to reproduce both features simultaneously. Aims. We aim to explore if a disk evolution model, including a dead zone and disk dispersal by X-ray photoevaporation, can explain the high accretion rates and large gaps (or cavities) measured in transition disks. Methods. We implemented a dead zone turbulence profile and a photoevaporative mass-loss profile into numerical simulations of gas and dust. We performed a population synthesis study of the gas component and obtained synthetic images and SEDs of the dust component through radiative transfer calculations. Results. This model results in long-lived inner disks and fast dispersing outer disks that can reproduce both the accretion rates and gap sizes observed in transition disks. For a dead zone of turbulence αdz = 10 −4 and an extent rdz = 10 AU, our population synthesis study shows that 63% of our transition disks are still accreting with Ṁg ≥ 10 −11M⊙ yr −1 after opening a gap. Among those accreting transition disks, half display accretion rates higher than 5.0 × 10 −10M⊙ yr −1. The dust component in these disks is distributed in two regions: in a compact inner disk inside the dead zone, and in a ring at the outer edge of the photoevaporative gap, which can be located between 20 and 100 AU. Our radiative transfer calculations show that the disk displays an inner disk and an outer ring in the millimeter continuum, a feature that resembles some of the observed transition disks. Conclusions. A disk model considering X-ray photoevaporative dispersal in combination with dead zones can explain several of the observed properties in transition disks, including the high accretion rates, the large gaps, and a long-lived inner disk at millimeter emission.
