Magneto-rotational instability ( MRI ) and gravitational instability ( GI ) are the two principle routes to turbulent angular momentum transport in accretion disks .
Protoplanetary disks may develop both .
This paper aims to reinvigorate interest in the study of magnetized massive protoplanetary disks , starting from the basic issue of stability .
The local linear stability of a self-gravitating , uniformly magnetized , differentially rotating , three-dimensional stratified disk subject to axisymmetric perturbations is calculated numerically .
The formulation includes resistivity .
It is found that the reduction in the disk thickness by self-gravity can decrease MRI growth rates ; the MRI becomes global in the vertical direction , and MRI modes with small radial length scales are stabilized .
The maximum vertical field strength that permits the MRI in a strongly self-gravitating polytropic disk with polytropic index \Gamma = 1 is estimated to be B _ { z, \mathrm { max } } \simeq c _ { s 0 } \Omega \sqrt { \mu _ { 0 } / 16 \pi G } , where c _ { s 0 } is the midplane sound speed and \Omega is the angular velocity .
In massive disks with layered resistivity , the MRI is not well-localized to regions where the Elsasser number exceeds unity .
For MRI modes with radial length scales on the order of the disk thickness , self-gravity can enhance density perturbations , an effect that becomes significant in the presence of a strong toroidal field , and which depends on the symmetry of the underlying MRI mode .
In gravitationally unstable disks where GI and MRI growth rates are comparable , the character of unstable modes can transition smoothly between MRI and GI .
Implications for non-linear simulations are discussed briefly .