  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. We 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. We implement a dead zone turbulence
profile and a photoevaporative mass loss profile into numerical simulations of
gas and dust. We perform a population synthesis study of the gas component, and
obtain synthetic images and SED of the dust component through radiative
transfer calculations. 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 $\alpha_{dz}
= 10^{-4}$ and extent $r_{dz}$ = 10 AU, our population synthesis study shows
that $63\%$ of our transition disks are accreting with $\dot{M}_g > 10^{-11}
M_\odot/yr$ after opening a gap. Among those accreting transition disks, half
display accretion rates higher than $5\times10^{-10} M_\odot/yr$ . 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 AU 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 observed in some transition disks. 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 long-lived inner disks at
mm-emission.
