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Toomre Q parameter

(Q, Q parameter)
(stability criterion for differentially rotating disks)

The Toomre Q parameter (Q parameter) is a criterion for the stability of differentially rotating disks, devised by Alar Toomre, and constructed so that Q<1 implies instability.

Q = ———

The condition of Q > 1 is known as Toomre's stability criteria, analogous to the Jeans criterion but including the effects of the disk's rotation. It specifically includes the effects of self-gravity of the disk material.

For a gaseous disk, it is often labeled Qgas, and for molecular clouds, the assumption is that >1 means no star formation, i.e., a stable disk, and <1 means star formation.

It has also been applied to stars in a disk galaxy, and to disks such as protoplanetary disks.

The parameter and criteria are based upon the assumption that the disk is of a homogeneous substance. Stability criteria can be more complex given more than one substance, e.g., a disk of both a gas an dust. Some instability may be present given higher thresholds (e.g., 3).

(fluid dynamics,mathematics,measure,limit)